mean - A statistical measurement also known as the average

$1.40 pays for 30 minutes of parking. How long can you park for with $2.80?

$1.40 pays for 30 minutes of parking. How long can you park for with $2.80?
Immediately, I see that $2.80 is $1.40 * 2
Which means, if $1.40 pays for 30 minutes of parking
$1.40 * 2 = $2.80 means $2.80 pays for 30 minutes * 2 = [B]60 minutes or 1 hour
[/B]
[I]Double the rate means double the time you can park[/I]

$13 in the bank. You write a check for $17. What is your balance?

$13 in the bank. You write a check for $17. What is your balance?
When you write a check, it's a debit against your account, which means we subtract.
So we start with $13.
We subtract $17
Our balance is $13 - $17 = [B]-$4[/B]

$96 less x dollars

$96 less x dollars
The word [I]less[/I] means we subtract, so we have:
[B]$96 - $x or $(96 - x)[/B]

-2 times the quantity t plus 7

-2 times the quantity t plus 7
The key word here is quantity. In this case, the quantity is t plus 7
t + 7
-2 times the quantity means we multiply -2 times the quantity t + 7
[B]-2(t + 7)
[MEDIA=youtube]nUWLUPfX52k[/MEDIA][/B]

-28 is the solution to the sum of a number p and 21

-28 is the solution to the sum of a number p and 21
The sum of a number p and 21:
p + 21
The phrase [I]is the solution to[/I] means an equation, so we set p + 21 equal to -28:
[B]p + 21 = -28
[/B]
If the problem asks you to solve for p, then we [URL='https://www.mathcelebrity.com/1unk.php?num=p%2B21%3D-28&pl=Solve']type this into our search engine[/URL] and we get:
p = [B]-49[/B]

-3x to the negative one power

-3x to the negative one power
Raising to a negative power means taking 1 over the same expression to the positive power"
(-3x)^-1 = 1/-3x = [B]-1/3x[/B]

-65 times the difference between a number and 79 is equal to the number plus 98

-65 times the difference between a number and 79 is equal to the number plus 98
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
The first expression, [I]the difference between a number and 79[/I] means we subtract 79 from our arbitrary variable of x:
x - 79
Next, -65 times the difference between a number and 79 means we multiply our result above by -65:
-65(x - 79)
The phrase [I]the number[/I] refers to the arbitrary variable x earlier. The number plus 98 means we add 98 to x:
x + 98
Now, let's bring it all together. The phrase [I]is equal to[/I] means an equation. So we set -65(x - 79) equal to x + [B]98:
-65(x - 79) = x + 98[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=-65%28x-79%29%3Dx%2B98&pl=Solve']type this equation into our search engine[/URL], and you get:
x = [B]76.31818[/B]

1 multiplied by b squared multiplied by c squared

1 multiplied by b squared multiplied by c squared
b squared means we raise b to the power of 2:
b^2
c squared means we raise c to the power of 2:
c^2
b squared multiplied by c squared
b^2c^2
1 multiplied by b squared multiplied by c squared means we multiply 1 by b^2c^2
1b^2c^2
Multiplying by 1 can be written by [U][I]removing[/I][/U] the 1 since it's an identity multiplication:
[B]b^2c^2[/B]

1 over 14 cubed

1 over 14 cubed
14 cubed means we raise 14 to the power of 3:
14^3
1 over 14 cubed is written as:
1/14^3
To simplify this, we [URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=14%5E3&pl=Calculate']evaluate 14^3[/URL] = 2744
So we have:
[B]1/2744[/B]

1 year from now Paul will be 49 years old. The current sum of the ages of Paul and Sharon is 85. How

1 year from now Paul will be 49 years old. The current sum of the ages of Paul and Sharon is 85. How old is Sharon right now?
If Paul will be 49 years old 1 year from now, this means today, he is 49 - 1 = 48 years old.
Let Sharon's age be s. Then from the current sum of Paul and Sharon's ages, we get:
s + 49 = 85
[URL='https://www.mathcelebrity.com/1unk.php?num=s%2B49%3D85&pl=Solve']Type this equation into our search engine[/URL], and get:
s = [B]36[/B]

1, 4, 9, 16, 25 What is the next number? What is the 50th term?

1, 4, 9, 16, 25
What is the next number?
What is the 50th term?
We see that 1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25
We build a formula for the nth term:
f(n) = n^2
The next number means n = 6th term:
f(6) = 6^2 = [B]36
[/B]
The 50th term means n = 50:
f(50) = 50^2 = [B]2500[/B]

1/2 of a number decreased by twice a number

1/2 of a number decreased by twice a number
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]1/2 of a number: x/2
[*]Twice a number means we multiply x by 2: 2x
[*]The phrase [I]decreased by[/I] means we subtract
[/LIST]
[B]x/2 - 2x[/B]

1/2 of x and 10 is 30. Find the x.

1/2 of x and 10 is 30. Find the x.
x and 10 means we add:
x + 10
1/2 of this:
1/2(x + 10)
The phrase is means equal to, so we set 1/2(x + 10) equal to 30 for our algebraic expression
[B]1/2(x + 10) = 30[/B]

1/2 the difference of x and 4

1/2 the difference of x and 4
The difference of x and 4:
x - 4
1/2 of the difference means we divide x -4 by 2:
[B](x - 4)/2[/B]

1/2 the quantity of x plus y

1/2 the quantity of x plus y
The quantity of x plus y
x + y
1/2 the quantity means we multiply x + y by 1/2:
[B](x + y)/2[/B]

1/3 a number increased by 10 times by that same number

1/3 a number increased by 10 times by that same number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
1/3 a number
1/3 * x = x/3
That same number means the same arbitrary variable as above:
x
10 times that same number:
10x
The phrase [I]increased by[/I] means we add:
[B]x/3 + 10x
[MEDIA=youtube]29TGt3i28jw[/MEDIA][/B]

1/3 of the sum of a number and 2 plus 5 is -20

1/3 of the sum of a number and 2 plus 5 is -20
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
the sum of a number and 2:
x + 2
1/3 of the sum of a number and 2
1/3(x + 2)
1/3 of the sum of a number and 2 plus 5
1/3(x + 2) + 5
The phrase [I]is[/I] means equal to, so we set 1/3(x + 2) + 5 equal to -20:
[B]1/3(x + 2) + 5 = -20[/B]

1/3 times q plus 5 equal q minus 4

1/3 times q plus 5 equal q minus 4
1/3 times q plus 5:
(q + 5)/3
q minus 4:
q - 4
The word [I]equal[/I] means we set (q + 5)/3 equal to q - 4:
[B](q + 5)/3 = q - 4[/B]

1/3x plus twice y

1/3x plus twice y
Twice y means we multiply y by 2:
2y
1/3x plus twice y
[B]1/3x + 2y[/B]

1/4 of the difference of 6 and a number is 200

1/4 of the difference of 6 and a number is 200
Take this [B]algebraic expression[/B] in 4 parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The difference of 6 and a number means we subtract x from 6: 6 - x
[*]1/4 of the difference means we divide 6 - x by 4: (6 - x)/4
[*]Finally, the phrase [I]is[/I] means an equation, so we set (6 - x)/4 equal to 200
[/LIST]
[B](6 - x)/4 = 200[/B]

1/5 of the sum of the number u and 2

1/5 of the sum of the number u and 2
The sum of the number u and 2 means we add 2 to u:
u + 2
1/5 of the sum:
[B](u + 2)/5[/B]

1/6 of n subtracted from 3

1/6 of n subtracted from 3
1/6 of n:
n/6
Subtracted from 3 means we subtract this expression from 3:
[B]3 - n/6[/B]

10 divided by the sum of 4 and u

10 divided by the sum of 4 and u
Take this algebraic expression in parts:
The sum of 4 and u means we add 4 to u:
4 + u
Next, we divide 10 by this sum:
[B]10/(4 + u)[/B]

10 is twice the sum of x and 5

10 is twice the sum of x and 5
The sum of x and 5 means we add:
x + 5
Twice the sum means we multiply by 2:
2(x + 5)
The word [I]is[/I] means an equation, so we set 2(x + 5) equal to 10
[B]2(x + 5) = 10[/B]

10 more than a number z, divided by k

10 more than a number z, divided by k
The phrase [I]a number[/I] means an arbitrary variable, lets call it x.
10 more than a number means we add 10 to x:
x + 10
We divide this quantity by k:
[B](x + 10)/k[/B]

10 times a number is 420

10 times a number is 420
A number denotes an arbitrary variable, let's call it x.
10 times a number:
10x
The phrase is means equal to, so we set 10x equal to 420
[B]10x = 420 <-- This is our algebraic expression
[/B]
If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=10x%3D420&pl=Solve']equation calculator[/URL]
We get x = 42

10 times the first of 2 consecutive even integers is 8 times the second. Find the integers

10 times the first of 2 consecutive even integers is 8 times the second. Find the integers.
Let the first integer be x. Let the second integer be y. We're given:
[LIST=1]
[*]10x = 8y
[*]We also know a consecutive even integer means we add 2 to x to get y. y = x + 2
[/LIST]
Substitute (1) into (2):
10x = 8(x + 2)
Multiply through:
10x = 8x + 16
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=10x%3D8x%2B16&pl=Solve']we type this equation into our search engine[/URL] and we get:
[B]x = 8[/B]
Since y = x + 2, we plug in x = 8 to get:
y = 8 + 2
[B]y = 10
[/B]
Now, let's check our work. Does x = 8 and y = 10 make equation 1 hold?
10(8) ? 8(10)
80 = 80 <-- Yes!

104 subtracted from the quantity 6 times r is the same as r

104 subtracted from the quantity 6 times r is the same as r
The quantity 6 times r means we multiply 6 by r:
6r
104 subtracted from 6r is written as:
6r - 104
[B]The phrase [I]is the same as[/I] means we have an equation. So we set 6r - 104 equal to r
6r - 104 = r[/B]

108 times a, reduced by 147 is k subtracted from 56

108 times a, reduced by 147 is k subtracted from 56
Take this algebraic expression in pieces:
Step 1: 108 times a:
108a
Step 2: Reduced by means subtract, so we subtract 47 from 108a:
108a - 47
Step 3: ksubtracted from 56:
56 - k
Step 4: The phrase [I]is[/I] means equal to, so we set 108a - 47 equal to 56 - k
[B]108a - 47 = 56 - k
[MEDIA=youtube]KrY6uzKeeB0[/MEDIA][/B]

11 more then n

The Phrase more then means add, so we have:
n + 11

11 to the power of 6 multiply 11 to the power of 3

11 to the power of 6 multiply 11 to the power of 3
Take this in parts.
[U]Step 1: 11 to the power of 6 means we raise 11 to the 6th power using exponents:[/U]
11^6
[U]Step 2: 11 to the power of 3 means we raise 11 to the 3rd power using exponents:[/U]
11^3
[U]Step 3: Multiply each term together:[/U]
11^6 * 11^3
[U]Step 4: Simplify[/U]
Because we have 2 numbers that are the same, in this case, 11, we can add the exponents together when multiplying:
11^(6 + 3)
[B]11^9
[MEDIA=youtube]gCxVq7LqyHk[/MEDIA][/B]

110 subtracted from the product of 244 and w is the product of r and 177 increased by 266

110 subtracted from the product of 244 and w is the product of r and 177 increased by 266
The product of 244 and w:
244w
110 subtracted from the product of 244 and w
244w - 110
the product of r and 177
177r
the product of r and 177 increased by 266
177r + 266
The word [I]is[/I] means equal to, so we set 244w - 110 equal to 177r + 266
[B]244w - 110 = 177r + 266[/B]

12 is multiplied by some number, that product is reduced by 9, and the total is equal to 37

12 is multiplied by some number, that product is reduced by 9, and the total is equal to 37
The phrase [I]some number[/I] means an arbitrary variable, let's call it x.
12 multiplied by this number:
12x
The product of 12x is reduced by 9
12x - 9
The phrase [I]the total is equal to[/I] means an equation, so we set 12x - 9 equal to 37:
[B]12x - 9 = 37[/B]

12 is subtracted from d and the result is tripled

12 is subtracted from d and the result is tripled
12 is subtracted from d:
d - 12
the result is tripled means we multiply d - 12 by 3
[B]3(d - 12)[/B]

12 is subtracted from d and the result is tripled.

12 is subtracted from d and the result is tripled.
12 is subtracted from d:
d - 12
The result is tripled means we multiply d - 12 by 3
[B]3(d - 12)
[MEDIA=youtube]1xqWstiIDP0[/MEDIA][/B]

12 plus 6 times a number is 9 times the number

12 plus 6 times a number is 9 times the number
The phrase [I]a number [/I]means an arbitrary variable. Let's call it x.
6 times a number is written as:
6x
12 plus 6 times the number means we add 6x to 12:
12 + 6x
9 times a number is written as:
9x
The phrase [I]is[/I] means an equation, so we set 12 + 6x equal to 9x
[B]12 + 6x = 9x <-- This is our algebraic expression[/B]
[B][/B]
If the problem asks you to solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B6x%3D9x&pl=Solve']type this expression into our search engine[/URL] and you get:
x = [B]4[/B]

12 plus the product of 4 and a number is greater than 72

A number means an arbitrary variable, let's call it x.
The product of 4 and a number is 4x.
12 plus that product is 4x + 12
Is greater than means an inequality, so we set the entire expression greater than 72
4x + 12 > 72

13 is the product of 5p and 5

13 is the product of 5p and 5
the product of 5p and 5 means we multiply 5p by 5:
5p * 5
25p
The word [I]is[/I] means equal to, so we set 25p equal to 13
[B]13 = 25p
25p = 13[/B]

13 more than x is greater than 14

13 more than x means we add:
x + 13
This expression is greater than 14, so we write an inequality:
x + 13 > 14

13 times the sum of x and 9y

13 times the sum of x and 9y
The sum of x and 9y means we add 9y to x:
x + 9y
Now multiply this sum by 13:
[B]13(x + 9y)[/B]

132 is 393 multiplied by y

132 is 393 multiplied by y
393 multiplied by y
393y
The word [I]is[/I] means equal to, so we set 393y equal to 132 as our algebraic expression
[B]393y = 132
[/B]
If you need to solve for y, use our [URL='http://www.mathcelebrity.com/1unk.php?num=393y%3D132&pl=Solve']equation calculator[/URL]

14 increased by twice Carlos’s age. Use the variable c to represent Carlos age

14 increased by twice Carlos’s age. Use the variable c to represent Carlos age
Twice means me multiply a by 2:
2a
14 increased by twice Carlos's age means we add 2a to 14:
[B]14 + 2a[/B]

15 added to a number is 16 times the number

15 added to a number is 16 times the number
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]15 added to a number: 15 + x
[*]16 times the number: 16x
[*]The phrase [I]is[/I] means equal to. So we set 15 + x equal to 16x
[/LIST]
[B]15 + x = 16x[/B]

15 added to the quotient of 8 and a number is 7.

15 added to the quotient of 8 and a number is 7.
Take this algebraic expression in pieces:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[*]The quotient of 8 and a number: 8/x
[*]15 added to this quotient: 8/x + 15
[*]The word [I]is[/I] means an equation, so we set 8/x + 15 equal to 7
[/LIST]
[B]8/x + 15 = 7[/B]

15 less than a number squared

15 less than a number squared
A number is denoted by an arbitrary variable, let's call it x.
x
Squared means we raise that number to a power of 2
x^2
15 less means we subtract
[B]x^2 -15[/B]

15 minus twice a equals b

15 minus twice a equals b
Twice a means we multiply a by 2:
2a
15 minus 2a:
15 - 2a
Set this equalto b:
[B]15 - 2a = b[/B]

16 decreased by 3 times the sum of 3 and a number

16 decreased by 3 times the sum of 3 and a number
Take this algebraic expression in parts:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[*]The sum of 3 and a number: 3 + x
[*]3 times the sum: 3(3 + x)
[*]16 decreased by... means we subtract 3(3 + x) from 16
[/LIST]
[B]3(3 + x) from 16[/B]

17 decreased by three times d equals c

17 decreased by three times d equals c
three times d means we multiply d by 3:
3d
17 decreased by three times d means we subtract 3d from 17
17 - 3d
The word [I]equals[/I] means an equation, so we set 17 - 3d equal to c:
[B]17 - 3d = c[/B]

17 multiplied by the quantity 9 minus 5

17 multiplied by the quantity 9 minus 5
The quantity 9 minus 5:
9 - 5
17 multiplied by the quantity means we wrap 9 - 5 in parentheses:
[B]17(9 - 5)[/B]

175 students separated into n classes is 25

175 students separated into n classes is 25
[U]Divide 175 by n[/U]
175/n
[U]The word [I]is[/I] means equal to, so set this expression equal to 25[/U]
175/n = 25
[U]Cross multiply[/U]
25n = 175
[U]Divide each side by 25[/U]
[B]n = 7[/B]

18 multiplied by the quantity of 11 plus r

18 multiplied by the quantity of 11 plus r
The quantity of 11 plus r is written as:
11 + r
18 multiplied by the [I]quantity[/I] means we take 18 and multiply it by the term 11 + r
[B]18(11 + r)
[MEDIA=youtube]2GYjQTjt8qM[/MEDIA][/B]

18 seconds faster than Tina’s time

18 seconds faster than Tina’s time
Let Tina's time be t. Speaking in terms of time, faster means less. So we have an algebraic expression of:
[B]t - 18[/B]

19 increased by twice Greg’s score use the variable g to represent Greg’s score

19 increased by twice Greg’s score use the variable g to represent Greg’s score
Use g for Greg's score
g
Twice g means we multiply g by 2:
2g
19 increased by means we add 2g to 19
[B]2g + 19
[MEDIA=youtube]E9a_U7z-fHE[/MEDIA][/B]

19 increased by twice Vanessa's age

19 increased by twice Vanessa's age
Let Vanessa's age be a.
Twice means we multiply a by 2:
2a
The phrase [I]increased by[/I] means we add 2a to 19:
[B]19 + 2a[/B]

2 Asset Portfolio

Given a portfolio with 2 assets, this determines the expected return (mean), variance, and volatility (standard deviation) of the portfolio.

2 consecutive even integers that equal 118

Let x be the first even integer. That means the next consecutive even integer must be x + 2.
Set up our equation:
x + (x + 2) = 118
Group x terms
2x + 2 = 118
Subtract 2 from each side
2x = 116
Divide each side by 2
x = 58
Which means the next consecutive even integer is 58 + 2 = 60
So our two consecutive even integers are [B]58, 60[/B]
Check our work:
58 + 60 = 118

2 less than 3 times n is 4 more than n

2 less than 3 times n is 4 more than n
3 times n:
3n
2 less than 3 times n
3n - 2
4 more than n:
n + 4
The word [I]is[/I] means equal to, so we set 3n - 2 equal to n + 4:
[B]3n - 2 = n + 4[/B]

2 less than half a number

A number means we pick an arbitrary variable, let's call it "x".
Half a number is 1/2x.
2 less than that is [B]1/2x - 2[/B]

2 minus 7 times a number

A number is represented by an arbitrary variable, let's call it x.
7 times x means we multiply 7 times x.
7x
2 minus 7x is written:
2 - 7x

2 more than twice the sum of 10 and a number

2 more than twice the sum of 10 and a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of 10 and a number means we add x to 10:
10 + x
Twice the sum means we multiply 10 + x by 2:
2(10 + x)
2 more than twice the sum means we add 2 to 2(10 + x):
[B]2(10 + x) + 2[/B]

2 times a number equals that number plus 5

2 times a number equals that number plus 5
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
2 times a number means we multiply 2 by x:
2x
That number plus 5 means we add 5 to the number x
x + 5
The phrase [I]equals[/I] means we set both expressions equal to each other
[B]2x = x + 5[/B] <-- This is our algebraic expression
If you want to take this further and solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%3Dx%2B5&pl=Solve']type this expression in the search engine[/URL] and we get:
[B]x = 5[/B]

2 times a number subtracted by x

2 times a number subtracted by x
The phrase [I]a number[/I] means an arbitrary variable, let's call it n.
n
2 times a number means we multiply n by 2:
2n
The phrase [I]subtracted by[/I] means we subtract 2n from x:
[B]x - 2n[/B]

2 times b squared minus 6

2 times b squared minus 6
b squared means we raise b to the 2nd power:
b^2
2 times b squared
2b^2
Minus 6:
[B]2b^2 - 6[/B]

2 times half of a number

A number means an arbitrary variable, let's call it x.
Half of x means we divide x by 2, or multiply by 0.5
x/2
2 times half x is written:
[B]2(x/2)[/B]
If we simplify by cancelling the 2's, we just get x.

2 times itself

2 times itself
Itself means we multiply 2 by 2:
2 * 2
[B]4[/B]

2 times the quantity x minus 1 is 12

2 times the quantity x minus 1 is 12
The quantity x minus 1 is written as:
x - 1
2 times this quantity:
2(x - 1)
The word [I]is[/I] means an equation, so we set 2(x - 1) equal to 12:
[B]2(x - 1) = 12[/B]

2 times the sum of 1 and some number is 30. What is the number?

2 times the sum of 1 and some number is 30. What is the number?
We let the phrase "some number" equal the variable x.
The sum of 1 and some number is:
x + 1
2 times the sum:
2(x + 1)
The word "is" means equal to, so we set [B]2(x + 1) = 30[/B]

2 times the sum of 7 times a number and 4

2 times the sum of 7 times a number and 4
This is an algebraic expression. Let's take it in 4 parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]7 times a number means we multiply x by 7: 7x
[*]The sum of 7 times a number and 4 means we add 4 to 7x: 7x + 4
[*]Finally, we multiply the sum in #3 by 2
[/LIST]
Build our final algebraic expression:
[B]2(7x + 4)[/B]

2 times the sum of a number and 3 is equal to 3x plus 4

2 times the sum of a number and 3 is equal to 3x plus 4
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 3 means we add 3 to x:
x + 3
2 times this sum means we multiply the quantity x + 3 by 2
2(x + 3)
3x plus 4 means 3x + 4 since the word plus means we use a (+) sign
3x + 4
The phrase [I]is equal to[/I] means an equation, where we set 2(x + 3) equal to 3x + 4
[B]2(x + 3) = 3x + 4[/B]

2 times the sum of a number x and 5

2 times the sum of a number x and 5
The sum of a number x and 5 means we add 5 to x:
x + 5
2 times the sum:
[B]2(x + 5)[/B]

2 times the sum of x and 7 plus 10

2 times the sum of x and 7 plus 10
The sum of x and 7 means we add 7 to x
x + 7
2 times the sum means we multiply the quantity x + 7 by 2
2(x + 7)
Plus 10 means we add 10 to the 2(x + 7):
[B]2(x + 7) + 10[/B]

2-thirds of the sum of 5 and a plus the product of 3 and z

2-thirds of the sum of 5 and a plus the product of 3 and z
The sum of 5 and a
5 + a
2-thirds of this sum:
2(5 + a)/3
The product of 3 and z:
3z
The word [I]plus[/I] means we add the two terms together:
[B]2(5 + a)/3 + 3z[/B]

2/3 of a number 17 is at least 29

2/3 of a number 17 is at least 29
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
2/3 of a number means we multiply x by 2/3:
2x/3
The phrase [I]is at least[/I] also means greater than or equal to, so we set up the inequality:
[B]2x/3 >= 29[/B]

2/5 the cube of a number

2/5 the cube of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The cube of a number means we raise x to the power of 3:
x^3
2/5 of the cube means we multiply x^3 by 2/5:
[B](2x^3)/5[/B]

20 teachers made a bulk purchase of some textbooks. The teachers received a 24% discount for the bul

20 teachers made a bulk purchase of some textbooks. The teachers received a 24% discount for the bulk purchase, which originally cost $5230. Assuming the cost was divided equally among the teachers, how much did each teacher pay?
[U]Calculate Discount Percent:[/U]
If the teachers got a 24% discount, that means they paid:
100% - 24% = 76%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=76&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']76% as a decimal[/URL] = 0.76 (Discount Percent)
[U]Calculate discount price:[/U]
Discount Price = Full Price * (Discount Percent)
Discount Price = 5230 * 0.76
Discount Price = 3974.80
Price per teacher = Discount Price / Number of Teachers
Price per teacher = 3974.80 / 20
Price per teacher = [B]$198.74[/B]

20 yards longer than p

20 yards longer than p
We want to build an algebraic expression. Longer means we add 20 to p:
[B]p + 20[/B]

20% of Kay’s pencils in her pencil case are broken. What is the chance of taking a pencil that is no

20% of Kay’s pencils in her pencil case are broken. What is the chance of taking a pencil that is not broken from the case if she picks one at random?
This means 100% - 20% = 80% of pencils are not broken
So the probability of drawing a pencil which is [I]not broken[/I] is 80%

200 feet shorter than the height of a light house

200 feet shorter than the height of a light house
Let the height of a light house be h:
h
200 fee shorter mean we subtract 200 from h:
[B]h - 200[/B]

21 apples and 49 pears. What is the largest number of baskets to make and still use up all the fruit

21 apples and 49 pears. What is the largest number of baskets to make and still use up all the fruit
We use our [URL='https://www.mathcelebrity.com/gcflcm.php?num1=21&num2=49&num3=&pl=GCF+and+LCM']greatest common factor calculator for GCF(21, 49)[/URL] to get:
GCF(21, 49) = 7
This means with [B]7 baskets[/B]:
[LIST]
[*]We divide 21 apples by 7 to get 3 apples per basket
[*]We divide 49 pears by 7 to get 7 pears per basket
[/LIST]

217 times u, reduced by 180 is the same as q

217 times u, reduced by 180 is the same as q.
Take this algebraic expression pieces:
Step 1: 217 times u
We multiply the variable u by 217
217u
Step 2: reduced by 180
Subtract 180 from 217u
217u - 180
The phrase [I]is the same as[/I] means an equation, so we set 217u - 180 equal to q
[B]217u - 180 = q[/B]

223 subtracted from the quantity 350 times a is equal to b

223 subtracted from the quantity 350 times a is equal to b
Take this algebraic expression in parts:
[LIST]
[*]the quantity 350 times a: 350a
[*]223 subtracted from the quantity: 350a - 223
[*]The phrase [I]is equal to[/I] means an equation, so we set 350a - 223 equal to b
[/LIST]
[B]350a - 223 = b[/B]

23 decreased by thrice of y is not equal to 15

Thrice of y means multiply y by 3
3y
23 decreased by 3y means we subtract
23 - 3y
Is not equal to means we set up an equation with not equal sign
23 - 3y <> 15

231 is 248 subtracted from the quantity h times 128

231 is 248 subtracted from the quantity h times 128
Let's take this algebraic expression in parts:
[LIST=1]
[*]h times 128: 128h
[*]24 subtracted from this: 128h - 248
[*]The word [I]is[/I] means an equation, so we set 128h - 248 equal to 231
[/LIST]
[B]128h - 248 = 231[/B] <-- This is our algebraic expression
If the problem asks you to solve for h, then you [URL='https://www.mathcelebrity.com/1unk.php?num=128h-248%3D231&pl=Solve']type in this equation into our search engine[/URL] and get:
h = [B]3.742[/B]

249 equals 191 times c, decreased by 199

249 equals 191 times c, decreased by 199
[U]Take this in pieces:[/U]
191 times c: 191c
The phrase [I]decreased by[/I] means we subtract 199 from 191c: 191c - 199
We set this expression equal to 249:
[B]191c - 199 = 249[/B] <-- This is our algebraic expression
If you want to solve for c, type this equation into the search engine and we get:
[B]c = 2.346[/B]

26 diminished by twice m

26 diminished by twice m
Twice m means multiply m by 2
2m
26 diminished by twice m means subtract 2m from 26
[B]26 - 2m[/B]

26 increased by 12 times a number

26 increased by 12 times a number
A number is represented by an arbitrary variable, let's call it x
12 times a number is written as 12x
26 increased by 12 times a number means we add:
[B]26 + 12x[/B]

28 less than twice a number

[U]A number means an arbitrary variable, let's call it x.[/U]
[LIST]
[*]x
[/LIST]
[U]Twice a number means multiply by 2[/U]
[LIST]
[*]2x
[/LIST]
[U]28 less than twice a number means we subtract 28[/U]
[LIST]
[*][B]2x - 28[/B]
[/LIST]

298 is the same as c and 230 more

[I]Is the same as[/I] means equal to. 230 more means we add 230.
Set up this equation:
c + 230 = 298
To solve for c if needed, visit our [URL='http://www.mathcelebrity.com/1unk.php?num=c%2B230%3D298&pl=Solve']calculator[/URL].
c = 68

2x decreased by 15 is equal to -27

2x decreased by 15 is equal to -27
The phrase [I]decreased by[/I] 15 means we subtract 15 from 2x:
2x - 15
The phrase [I]is equal to[/I] means an equation, so we set 2x - 15 equal to -27
[B]2x - 15 = -27 [/B] <-- This is our algebraic expression
To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D-27&pl=Solve']type 2x - 15 = -27 into the search engine[/URL].

2x increased by 3 times a number

2x increased by 3 times a number
The phrase [I]a number[/I] means an arbitary variable, let's call it x.
3 times a number means we multiply x by 3:
3x
The phrase [I]increased by[/I] means we add 3x to 2x:
2x + 3x
Simplifying, we get:
[B]5x[/B]

2x plus 4 increased by 15 is 57

2x plus 4 increased by 15 is 57
Take this algebraic expression in parts:
[LIST]
[*]2x plus 4: 2x + 4
[*][I]Increased by[/I] means we add 15 to 2x + 4: 2x + 4 + 15 = 2x + 19
[*]The word [I]is[/I] means an equation, so we set 2x + 19 equal to 57:
[/LIST]
Our final algebraic expression is:
[B]2x + 19 = 57
[/B]
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B19%3D57&pl=Solve']type this equation into our search engine [/URL]and we get
x = [B]19[/B]

2x plus 8, quantity squared

2x plus 8, quantity squared
2x plus 8 means we add 8 to 2x:
2x + 8
Squaring the quantity means we raise it to the power of 2:
[B](2x + 8)^2[/B]

2y divided by the sum of 3x and 5

2y divided by the sum of 3x and 5
The sum of 3x and 5 means we add 5 to 3x:
3x + 5
2y divided by the sum of 3x and 5:
[B]2y/(3x + 5)[/B]

3 boys share 100 in the ratio 1:2:2. how much each boy will get?

3 boys share 100 in the ratio 1:2:2. how much each boy will get?
Given the ratio 1 : 2 : 2, calculate the expected number of items from a population of 100
A ratio of 1 : 2 : 2 means that for every of item A, we can expect 2 of item B and 2 of item c
Therefore, our total group is 1 + 2 + 2 = 5
[SIZE=5][B]Calculate Expected Number of Item A:[/B][/SIZE]
Expected Number of Item A = 1 x 100/5
Expected Number of Item A = 100/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=100&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item A = 20/1
Expected Number of Item A = [B]20[/B]
[SIZE=5][B]Calculate Expected Number of Item B:[/B][/SIZE]
Expected Number of Item B = 2 x 100/5
Expected Number of Item B = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item B = 40/1
Expected Number of Item B = [B]40[/B]
[SIZE=5][B]Calculate Expected Number of Item C:[/B][/SIZE]
Expected Number of Item C = 2 x 100/5
Expected Number of Item C = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item C = 40/1
Expected Number of Item C = [B]40[/B]
[B]Final Answer:[/B]
(A, B, C) =[B] (20, 40, 40)[/B] for 1:2:2 on 100 people

3 decreased by 7 times a number

3 decreased by 7 times a number
A number signifies an arbitrary variable, let's call it x.
7 times a number:
7x
3 decreased by this means we subtract 7x
[B]3 - 7x[/B]

3 is subtracted from 3/4 of g

3 is subtracted from 3/4 of g
3/4 of g means we multiply g by 3/4:
3g/4
Subtracted from means we subtract 3 from 3g/4
[B]3g/4 - 3[/B]

3 is subtracted from square of a number

3 is subtracted from square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Square of a number means we raise x to the 2nd power:
x^2
3 is subtracted from square of a number
[B]x^2 - 3[/B]

3 is subtracted from the square of x

3 is subtracted from the square of x
Let's take this algebraic expression in two parts:
Part 1: The square of x means we raise x to the power of 2:
x^2
Part 2: 3 is subtracted means we subtract 3 from x^2
[B]x^2 - 3[/B]

3 less than a number times itself

3 less than a number times itself
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Itself means the same variable as above. So we have:
x * x
x^2
3 less than this means we subtract 3 from x^2:
[B]x^2 - 3[/B]

3 times a number increased by 1 is between -8 and 13

3 times a number increased by 1 is between -8 and 13.
Let's take this algebraic expression in [U]4 parts[/U]:
Part 1 - The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Part 2 - 3 times this number means we multiply x by 3:
3x
Part 3 - Increased by 1 means we add 1 to 3x:
3x + 1
The phrase [I]between[/I] means we have an inequality:
[B]-8 <= 3x + 1 <=13[/B]

3 times a number is 3 more a number

3 times a number is 3 more a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
3 times a number:
3x
3 more than a number means we add 3 to x:
x + 3
The word [I]is[/I] means and equation, so we set 3x equal to x + 3
[B]3x = x + 3[/B]

3 times the difference of a and b is equal to 4 times c

3 times the difference of a and b is equal to 4 times c
[U]The difference of a and b:[/U]
a - b
[U]3 times the difference of a and b:[/U]
3(a - b)
[U]4 times c:[/U]
4c
The phrase [I]is equal to[/I] means an equation. So we set 3(a - b) equal to 4c:
[B]3(a - b) = 4c[/B]

3 times the difference of x and 5 is 15

The difference of x and 5 means we subtract:
x - 5
3 times the difference means we multiply (x - 5) by 3
3(x - 5)
Is, means equal to, so we set our expression equal to 15
[B]3(x - 5) = 15
[/B]
If you need to take it one step further to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3%28x-5%29%3D15&pl=Solve']equation calculator[/URL]

3 times the quantity 2 decreased by x is 9

3 times the quantity 2 decreased by x is 9
The quantity 2 decreased by x. The phrase [I]decreased by[/I] means we subtract:
2 - x
3 times the quantity:
3(2 - x)
The word [I]is[/I] means equal to, so we set 3(2 - x) equal to 9:
[B]3(2 - x) = 9
[MEDIA=youtube]Hzyt_GajZA4[/MEDIA][/B]

3 times the sum of 2 decreased by x is 9

3 times the sum of 2 decreased by x is 9
2 decreased by x:
2 - x
3 times the sum means we multiply 2 - x by 3:
3(2 - x)
The phrase [I]is 9[/I] means equal to, so we set 3(2 - x) equal to 9:
[B]3(2 - x) = 9[/B]

3 times the sum of twice k and 8

3 times the sum of twice k and 8
Twice k means we multiply k by 2:
2k
The sum of twice k and 8:
2k + 8
3 times the sum:
[B]3(2k + 8)[/B]

3 times the sum of x and 9y

3 times the sum of x and 9y
The sum of x and 9y means we add 9y to x:
x + 9y
Now we take this sum, and multiply by 3 to get our final algebraic expression:
3(x + 9y)

3 times x minus y is 5 times the sum of y and 2 times x

3 times x minus y is 5 times the sum of y and 2 times x
Take this algebraic expression in pieces:
3 times x:
3x
Minus y means we subtract y from 3x
3x - y
The sum of y and 2 times x mean we add y to 2 times x
y + 2x
5 times the sum of y and 2 times x:
5(y + 2x)
The word [I]is[/I] means an equation, so we set 3x - y equal to 5(y + 2x)
[B]3x - y = 5(y + 2x)[/B]

30 increased by 3 times the square of a number

Let "a number" equal the arbitrary variable x.
The square of that is x^2.
3 times the square of that is 3x^2.
Now, 30 increased by means we add 3x^2 to 30
30 + 3x^2

30 increased by 3 times the square of a number

30 increased by 3 times the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The square of a number means we raise x to the power of 2:
x^2
3 times the square:
3x^2
The phrase [I]increased by[/I] means we add 3x^2 to 30:
[B]30 + 3x^2[/B]

30 is equal to thrice y decreased by z

30 is equal to thrice y decreased by z
Thrice y means we multiply y by 3:
3y
Decreased by z means we subtract z from 3y
3y - z
The phrase [I]is[/I] means an equal to, so we set up an equation where 3y - z is equal to 30
[B]3y - z = 30[/B]

30 people are selected randomly from a certain town. If their mean age is 60.5 and ? = 4.6, find a 9

30 people are selected randomly from a certain town. If their mean age is 60.5 and ? = 4.6, find a
95% confidence interval for the true mean age, ?, of everyone in the town.

30% larger then 1/3 of twice q

30% larger then 1/3 of twice q
Take this algebraic expression in 3 parts:
[LIST=1]
[*]Twice q means multiply q by 2: 2q
[*]1/3 of twice q means we multiply 2q in Step 1 by 1/3: 2q/3
[*]30% larger means we multiply 2q/3 in step 2 by 1.3, since 30% = 0.3: 1.3(2q/3)
[/LIST]
[B]1.3(2q/3)[/B]

300 reduced by 5 times my age is 60

300 reduced by 5 times my age is 60
Let my age be a. We have:
5 times my age = 5a
300 reduced by 5 times my age means we subtract 5a from 300:
300 - 5a
The word [I]is[/I] means an equation, so we set 300 - 5a equal to 60 to get our final algebraic expression:
[B]300 - 5a = 60
[/B]
If you have to solve for a, you [URL='https://www.mathcelebrity.com/1unk.php?num=300-5a%3D60&pl=Solve']type this equation into our search engine[/URL] and you get:
a = [B]48[/B]

309 is the same as 93 subtracted from the quantity f times 123

309 is the same as 93 subtracted from the quantity f times 123.
The quantity f times 123:
123f
Subtract 93:
123f - 93
The phrase [I]is the same as[/I] means an equation, so we set 123f - 93 equal to 309
[B]123f - 93 = 309[/B] <-- This is our algebraic expression
If you wish to solve for f, [URL='https://www.mathcelebrity.com/1unk.php?num=123f-93%3D309&pl=Solve']type this equation into the search engine[/URL], and we get f = 3.2683.

324 times z, reduced by 12 is z

324 times z, reduced by 12 is z.
Take this algebraic expression in pieces:
324 [I]times[/I] z means we multiply 324 by the variable z.
324z
[I]Reduced by[/I] 12 means we subtract 12 from 324z
324z - 12
The word [I]is[/I] means we have an equation, so we set 324z - 12 equal to z
[B]324z - 12 = z [/B] <-- This is our algebraic expression

339 equals 303 times w, minus 293

339 equals 303 times w, minus 293
Take this algebraic expression in pieces:
303 times w:
303w
Minus 293:
303w - 293
The phrase [I]equals[/I] means we have an equation. We set 303w - 293 = 339
[B]303w - 293 = 339[/B] <-- This is our algebraic expression
To solve for w, [URL='https://www.mathcelebrity.com/1unk.php?num=303w-293%3D339&pl=Solve']we type this equation into our search engine[/URL] to get:
[B]w = 2.086[/B]

35 added to n is greater than or equal to the sum of k and 21

35 added to n is greater than or equal to the sum of k and 21
Take this algebraic expression in 3 parts:
[LIST=1]
[*]35 added to n means we have a sum: n + 35
[*]The sum of k and 21 means we add 21 to k: k +21
[*]The phrase [I]greater than or equal to[/I] means an inequality using this sign (>=), so we write this as follows:
[/LIST]
[B]n + 35 >= k + 21[/B]

36% of the pupils in class 2 are boys the remaining 16 are girls how many pupils are in class 2?

36% of the pupils in class 2 are boys the remaining 16 are girls how many pupils are in class 2?
This means 100% - 36% = 64% of the class are girls. And if the class size is s, then we have:
64% of s = 16
Or, written as a decimal:
0.64s = 16
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.64s%3D16&pl=Solve']type it into our search engine[/URL] and we get:
s = [B]25[/B]

365 subtracted from the quantity q times 146 is the same as w

[U]q times 146:[/U]
146q
[U]365 subtracted from that:[/U]
146q - 365
[U]Is the same as means equal to, so we have:[/U]
[B]146q - 365 = w[/B]

3f,subtract g from the result, then divide what you have by h

3f,subtract g from the result, then divide what you have by h
Take this algebraic expression in pieces:
3f subtract g means we subtract the variable g from the expression 3f:
3f - g
Divide what we have by h, means we take the result above, 3f - g, and divide it by h:
[B](3f - g)/h[/B]

3x less than 2 times the sum of 2x and 1 is equal to the sum of 2 and 5

3x less than 2 times the sum of 2x and 1 is equal to the sum of 2 and 5
This is an algebraic expression. Let's take this algebraic expression in 5 parts:
[LIST=1]
[*]The sum of 2x and 1 means we add 1 to 2x: 2x + 1
[*]2 times the sum of 2x and 1: 2(2x + 1)
[*]3x less than the sum of 2x and 1 means we subtract 3x from 2(2x + 1): 2(2x + 1) - 3x
[*]The sum of 2 and 5 means we add 5 to 2: 2 + 5
[*]Finally, the phrase [I]equal[/I] means an equation, so we set #3 equal to #4
[/LIST]
Our algebraic expression is:
[B]2(2x + 1) - 3x = 2 + 5[/B]
[B][/B]
Now, some problems may ask you to simplify. In this case, we multiply through and group like terms:
4x + 2 - 3x = 7
[B]x + 2 = 7 <-- This is our simplified algebraic expression
[/B]
Now, what if the problem asks you to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B2%3D7&pl=Solve']you type this into our search engine[/URL] and get:
x =[B] 5[/B]

4 added to twice a

[U]Twice a means we multiply a by 2[/U]
2a
[U]4 added to that means we add 4[/U]
[B]2a + 4[/B]

4 minus 3p equals 36

4 minus 3p equals 36
4 minus 3p:
4 - 3p
The phrase [I]equals[/I] means an equation, so we set 4 - 3p equal to 36:
[B]4 - 3p = 36[/B]

4 multiplied by the cube of p is reduced by 5

4 multiplied by the cube of p is reduced by 5
The cube of p means we raise p to the 3rd power:
p^3
4 multiplied by the cube of p
4p^3
reduced by 5:
[B]4p^3 - 5[/B]

4 people like ketchup, 1 person likes tomato. How many people like ketchup or tomato?

4 people like ketchup, 1 person likes tomato. How many people like ketchup or tomato?
[I]Or[/I] means we add. We want to add people that like both ketchup and tomatoes.
4 ketchup + 1 tomato = [B]5[/B] total people

4 times a number cubed decreased by 7

4 times a number cubed decreased by 7
A number is denoted as an arbitrary variable, let's call it x
x
Cubed means raise x to the third power
x^3
Decreased by 7 means subtract 7
x^3 - 7

4 times a number is the same as the number increased by 78

4 times a number is the same as the number increased by 78.
Let's take this algebraic expression in parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]4 times a number is written as 4x
[*]The number increased by 78 means we add 78 to x: x + 78
[*]The phrase [I]the same as[/I] mean an equation, so we set #2 equal to #3
[/LIST]
[B]4x = x + 78[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further, then [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3Dx%2B78&pl=Solve']we type this equation into our search engine [/URL]and get:
x = 26

4 times a number plus 9

A number means an arbitrary variable, let's call it "x".
4 times a number is 4x.
Plus 9 means we add:
4x + 9

4 times b increased by 9 minus twice y

4 times b increased by 9 minus twice y
Take this algebraic expression in parts:
Step 1: 4 times b means we multiply the variable b by 4:
4b
Step 2: Increased by 9 means we add 9 to 4b:
4b + 9
Step 3: Twice y means we multiply the variable y by 2:
2y
Step 4: The phrase [I]minus[/I] means we subtract 2y from 4b + 9
[B]4b + 9 - 2y[/B]

4 times of the sum of the cubes of x and y

4 times of the sum of the cubes of x and y
The cube of x means we raise x to the 3rd power:
x^3
The cube of y means we raise y to the 3rd power:
y^3
The sum of the cubes means we add:
x^3 + y^3
4 times the sum of the cubes:
[B]4(x^3 + y^3)[/B]

4 times the difference of 6 times a number and 7

4 times the difference of 6 times a number and 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
6 times a number
6x
The difference of 6x and 7 means we subtract 7 from 6x:
6x - 7
Now we multiply this difference by 4:
[B]4(6x - 7)[/B]

4 times the quantity of a number plus 6

4 times the quantity of a number plus 6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The word [I]plus[/I] means we addd 6 to x
x + 6
The phrase [I]4 times the quantity [/I]means we multiply x + 6 by 4
[B]4(x + 6)[/B]

4 times the sum of 10 and twice x

4 times the sum of 10 and twice x
Twice x means we multiply x by 2:
2x
The sum of 10 and twice x:
10 + 2x
Now multiply this sum by 4:
[B]4(10 + 2x)[/B]

4 times the sum of 3 plus x squared

4 times the sum of 3 plus x squared
x squared means we raise x to the power of 2:
x^2
3 plus x squared:
3 + x^2
4 times the sum of 3 plus x squared
3(3 + x^2)

4 times x plus 2 is at most 10

4 times x plus 2 is at most 10
4 times x
4x
Plus 2
4x + 2
At most means less than or equal to, so we have:
[B]4x + 2 <= 10[/B]

4/5 of the sum of k and 3

4/5 of the sum of k and 3
The sum of k and 3 means we add 3 to k:
k + 3
4/5 of the sum means we multiply 4/5 times the sum k + 3:
[B]4(k + 3)/5[/B]

400 reduced by 3 times my age is 214

400 reduced by 3 times my age is 214
Let my age be a. We have:
3 times my age:
3a
400 reduced by 3 times my age:
400 - 3a
The word [I]is[/I] means an equation. So we set 400 - 3a equal to 214
400 - 3a = 214
Now if you want to solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D214&pl=Solve']type it in the search engin[/URL]e and we get;
a = [B]62[/B]

41% of the passengers on the plane are men. 36% of them are women and 11% of them are boys. The rema

41% of the passengers on the plane are men. 36% of them are women and 11% of them are boys. The remaining 30 passengers are girls. How many passengers are on the plane?
Add up the percents:
41% + 36% + 11% = 88%
This means that (100% - 88% = 12%) are girls.
So if the total amount of passengers on the plane is p, we write 12% s 0.12, and we have:
0.12p = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=0.12p%3D30&pl=Solve']Type this equation into our search engine[/URL], and we get:
p = [B]250[/B]

4800$ salary spent 12% on clothes 20% on house rent how much money is she left with

4800$ salary spent 12% on clothes 20% on house rent how much money is she left with
12% on clothes plus 20% on house rent = 32% total spendings.
If she spent 32%, that means she's left with:
100% - 32% = 68%
So we want 68% of 4800.
We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=68&den1=4800&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type [I]68% of 4800 [/I]into our search engine[/URL] and we get:
[B]3,264[/B]

4subtractedfrom6timesanumberis32

4 subtracted from 6 times a number is 32.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
6 times this number means we multiply by x by 6
6x
4 subtracted from this expression means we subtract 4
6x - 4
The phrase [I]is[/I] means an equation, so we set 6x - 4 equal to 32
[B]6x - 4 = 32
[/B]
If you need to solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=6x-4%3D32&pl=Solve']type it in the search engine here[/URL].

5 added to xis 11

5 added to x means we use the plus sign for a sum.
x + 5
"is" means equals, so we set that equal to 11.
x + 5 = 11 <-- This is our algebraic expression.

5 diminished by twice the sum of a and b

5 diminished by twice the sum of a and b
Take this algebraic expression in parts:
[LIST]
[*]The sum of a and b: a + b
[*]Twice the sum means we multiply a + b by 2: 2(a + b)
[*]5 diminished by twice the sum means we subtract 2(a + b) from 5
[/LIST]
[B]5 - 2(a + b)[/B]

5 is one-fourth of a number c

5 is one-fourth of a number c
[LIST]
[*]A number c is just written as c
[*]one-fourth of c means we multiply c by 1/4: c/4
[*]The phrase [I]is[/I] means equal to, so we set c/4 equal to 5
[/LIST]
[B]c/4 = 5[/B]

5 less than x is y

5 less than x means we subtract 5 from x.
x - 5
Is, means equal to, so we set x - 5 equal to y
x - 5 = y

5 more than the reciprocal of a number

5 more than the reciprocal of a number
Take this algebraic expression in pieces:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The reciprocal of this number means we divide 1 over x:
1/x
5 more means we add 5 to 1/x
[B]1/x + 5[/B]

5 more than twice the cube of a number

5 more than twice the cube of a number.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The cube of a number means we raise it to a power of 3
x^3
Twice the cube of a number means we multiply x^3 by 2
2x^3
5 more than twice the cube of a number means we multiply 2x^3 by 5
5(2x^3)
Simplifying, we get:
10x^3

5 more than twice the cube of a number

5 more than twice the cube of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The cube of a number means we raise x to the power of 3:
x^3
Twice the cube means we multiply x^3 by 2
2x^3
Finally, 5 more than twice the cube means we add 5 to 2x^3:
[B]2x^3 + 5[/B]

5 squared minus a number x

5 squared minus a number x
5 squared is written as 5^2
Minus a number x means we subtract the variable x
[B]5^2 - x[/B]

5 subtracted from 3 times a number is 44

5 subtracted from 3 times a number is 44.
The problem asks for an algebraic expression.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
3 times this number is 3x.
5 subtracted from this is written as 3x - 5.
The phrase [I]is[/I] means an equation, so we set 3x - 5 equal to 44
[B]3x - 5 = 44[/B]

5 times a number increased by 13

5 times a number increased by 13
A number is denoted as an arbitrary variable, let's call it x
x
5 times that number
5x
Increased by 13 means we add
5x + 13

5 times a number increased by 4 is divided by 6 times the same number

5 times a number increased by 4 is divided by 6 times the same number
Take this algebraic expression in parts.
Part 1: 5 times a number increased by 4
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x
[*]5 times the number means multiply x by 5: 5x
[*][I]Increased by 4[/I] means we add 4 to 5x: 5x + 4
[/LIST]
Part 2: 6 times the same number
[LIST]
[*]From above, [I]a number[/I] is x: x
[*]6 times the number means we multiply x by 6: 6x
[/LIST]
The phrase [I]is divided by[/I] means we have a quotient, where 5x + 4 is the numerator, and 6x is the denominator.
[B](5x + 4)/6x[/B]

5 times a number is 4 more than twice a number

5 times a number is 4 more than twice a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
5 times a number:
5x
Twice a number means we multiply x by 2:
2x
4 more than twice a number
2x + 4
The word [I]is[/I] means equal to, so we set 5x equal to 2x + 4
[B]5x = 2x + 4[/B]

5 times a number is that number minus 3

5 times a number is that number minus 3
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[LIST]
[*]5 times a number: 5x
[*]That number means we use the same number from above which is x
[*]That number minus 3: x - 3
[*]The phrase [I]is[/I] means an equation, so we set 5x equal to x - 3
[/LIST]
[B]5x = x - 3[/B]

5 times g reduced by the square of h

5 times g reduced by the square of h
Take this algebraic expression in pieces:
[LIST=1]
[*]5 times g means we multiply g by 5: 5g
[*]The square of h means we raise h to the 2nd power: h^2
[*]5 times g reduced by the square of h means we subtract h^2 from 5g:
[/LIST]
[B]5g - h^2[/B]

5 times the product of 2 numbers a and b

5 times the product of 2 numbers a and b
The product of 2 numbers a and be means we multiply the variables together:
ab
5 times the product means we multiply ab by 5:
[B]5ab[/B]

5 times the sum of 3 times a number and -5

5 times the sum of 3 times a number and -5
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
3 times a number means we multiply x by 3:
3x
the sum of 3 times a number and -5 means we add -5 to 3x:
3x - 5
5 times the sum means we multiply 3x - 5 by 5:
[B]5(3x - 5)[/B]

5 times the total of 60 and x

5 times the total of 60 and x
The total of 60 and x means we add:
60 + x
5 times the total means we multiply the sum by 5
5(60 + x)

50 is more than the product of 4 and w

50 is more than the product of 4 and w
Take this algebraic expression in pieces:
The product of 4 and w mean we multiply the variable w by 4:
4w
The phrase [I]is more than[/I] means an inequality using the (>) sign, where 50 is greater than 4w:
[B]50 > 4w[/B]

51 decreased by twice a number

A number is denoted as an arbitrary variable, let's call it x.
Twice a number means we multiply by 2, so 2x.
51 decreased by twice a number means we subtract 2x from 51
[B]51 - 2x[/B]

54 is the sum of 15 and Vidyas score

54 is the sum of 15 and Vidyas score.
Let Vida's score be s.
The sum of 15 and s:
s + 15
When they say "is", they mean equal to, so we set s + 15 equal to 54. Our algebraic expression is below:
[B]s + 15 = 54
[/B]
To solve this equation for s, use our [URL='http://www.mathcelebrity.com/1unk.php?num=s%2B15%3D54&pl=Solve']equation calculator[/URL]

54 is the sum of 24 and Julies score. Use the variable J to represent Julies score.

54 is the sum of 24 and Julies score. Use the variable J to represent Julies score.
Sum of 24 and Julie's score:
24 + J
The phrase [I]is[/I] means an equation, so we set 24 + J equal to 54 to get an algebraic expression:
[B]24 + J = 54[/B]

56 is the sum of 20 and Donnie's savings. Use the variable d to represent Donnie's savings

56 is the sum of 20 and Donnie's savings. Use the variable d to represent Donnie's savings
The sum of 20 and Donnie's savings using [I]d[/I] to represent Donnie's savings:
20 + d
The word [I]is[/I] means equal to, so we set 20 + d equal to 56:
[B]20 + d = 56[/B]

59 is the difference of vanessas height and 20

59 is the difference of vanessas height and 20.
Let h be Vanessa's height. We have the difference of h and 20:
h - 20
The phrase [I]is[/I] means equal to, so we set h - 20 equal to 59
[B]h - 20 = 59[/B]

59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving.

59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving.
The phrase [I]the sum of[/I] means we add Donnie's savings of d to 16:
d + 16
The phrase [I]is[/I] means an equation, so we set d + 16 equal to 59
d + 16 = 59 <-- [B]This is our algebraic expression[/B]
Now, if the problem asks you to solve for d, then you[URL='https://www.mathcelebrity.com/1unk.php?num=d%2B16%3D59&pl=Solve'] type the algebraic expression into our search engine to get[/URL]:
d = [B]43[/B]

6 boys have a mean age of 10 years and 14 girls have a mean age of 5 work out the mean age of the 20

6 boys have a mean age of 10 years and 14 girls have a mean age of 5 work out the mean age of the 20 children
[U]Calculate Sum of boys ages:[/U]
Sum of boys ages/6 = 10
Cross multiply, and we get:
Sum of boys ages = 6 * 10
Sum of boys ages = 60
[U]Calculate Sum of girls ages:[/U]
Sum of girls ages/14 = 5
Cross multiply, and we get:
Sum of girls ages = 14 * 5
Sum of girls ages = 70
Average of 20 children is:
Average of 20 children = (Sum of boys ages + sum of girls ages)/20
Average of 20 children = (60 + 70)/20
Average of 20 children = 130/20
Average of 20 children = [B]6.5 years[/B]

6 diminished by twice x is at most 8

6 diminished by twice x is at most 8
Twice x means we multiply x by 2:
2x
6 diminished by twice x means we subtract 2x from 6:
6 - 2x
The phrase [I]is at most[/I] is an inequality using the sign <=, so we have:
[B]6 - 2x <= 8[/B]

6 is divided by square of a number

6 is divided by square of a number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
x
the square of this means we raise x to the power of 2:
x^2
Next, we divide 6 by x^2:
[B]6/x^2[/B]

6 is one third of a number s

6 is one third of a number s
A number s is written as s:
s
One third of a number s means we multiply s by 1/3
s/3
The word [I]is[/I] means equal to, so we set s/3 equal to 6
[B]s/3 = 6[/B]

6 numbers have a mean of 4. What is the total of the 6 numbers?

6 numbers have a mean of 4. What is the total of the 6 numbers?
Mean = Sum of numbers / Count of numbers
Plug our Mean of 4 and our count of 6 into this equation:
4 = Sum/Total of Numbers / 6
Cross multiply:
Sum/Total of Numbers = 6 * 4
Sum/Total of Numbers = [B]24[/B]

6 plus twice the sum of a number and 7.

6 plus twice the sum of a number and 7.
The phrase [I]a number[/I] mean an arbitrary variable, let's call it x.
The sum of a number and 7 means we add 7 to the variable x.
x + 7
Twice the sum means we multiply the sum by 2:
2(x + 7)
6 plus means we add 6 to 2(x + 7)
[B]6 + 2(x + 7)[/B]

6 sided die probability to roll a odd number or a number less than 6

6 sided die probability to roll a odd number or a number less than 6
First, we'll find the set of rolling an odd number. [URL='https://www.mathcelebrity.com/1dice.php?gl=1&opdice=1&pl=Odds&rolist=+2%2C3%2C4&dby=+2%2C3%2C5&montect=+100']From this dice calculator[/URL], we get:
Odd = {1, 3, 5}
Next, we'll find the set of rolling less than a 6. [URL='https://www.mathcelebrity.com/1dice.php?gl=4&pl=6&opdice=1&rolist=+2%2C3%2C4&dby=+2%2C3%2C5&montect=+100']From this dice calculator[/URL], we get:
Less than a 6 = {1, 2, 3, 4, 5}
The question asks for [B]or[/B]. Which means a Union:
{1, 3, 5} U {1, 2, 3, 4, 5} = {1, 2, 3, 4, 5}
This probability is [B]5/6[/B]

6 subtracted from the product of 5 and a number is 68

6 subtracted from the product of 5 and a number is 68
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The product of 5 and this number is:
5x
We subtract 6 from 5x:
5x - 6
The phrase [I]is[/I] means an equation, so we set 5x - 6 equal to 68
[B]5x - 6 = 68[/B]

6 times a number multiplied by 3 all divided by 4

6 times a number multiplied by 3 all divided by 4
Take this algebraic expression in parts:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]6 times a number: 6x
[*]Multiplied by 3: 3(6x) = 18x
[*]All divided by 4: 18x/4
[/LIST]
We can simplify this:
We type 18/4 into our search engine, simplify, and we get 9/2. So our answer is:
[B]9x/2[/B]

6 times a number, x, is at least 22.

6 times a number, x, is at least 22.
6 times a number x:
6x
The phrase [I]is at least[/I] means greater than or equal to. So we have an inequality:
[B]6x >= 22[/B] <-- This is our algebraic expression
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6x%3E%3D22&pl=Show+Interval+Notation']To solve this for x, paste this into the search engine[/URL] and we get:
[B]x >= 3.666667[/B]

6 times j squared minus twice j squared

6 times j squared minus twice j squared
j squared means we raise the variable j to the power of 2:
j^2
6 times j squared means we multiply j^2 by 6:
6j^2
Twice j squared means we multiply j^2 by 2:
2j^2
The word [I]minus[/I] means we subtract 2j^2 from 6j^2
6j^2 - 2j^2
So if you must simplify, we group like terms and get:
(6 - 2)j^2
[B]4j^2[/B]

6 times the reciprocal of a number equals 2 times the reciprocal of 7. What is the number

6 times the reciprocal of a number equals 2 times the reciprocal of 7. What is the number
We've got two algebraic expressions here. Let's take it in parts:
Term 1:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The reciprocal is 1/x
Multiply this by 6: 6/x
Term 2:
Reciprocal of 7: 1/7
2 times this: 2/7
We set these terms equal to each other:
6/x = 2/7
[URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=2&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get:
[B]x = 21[/B]

6 times the reciprocal of a number equals 3 times the reciprocal of 7 .

6 times the reciprocal of a number equals 3 times the reciprocal of 7 .
This is an algebraic expression. Let's take it in parts:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The reciprocal of a number x means we divide 1 over x:
1/x
6 times the reciprocal means we multiply 6 by 1/x:
6/x
The reciprocal of 7 means we divide 1/7
1/7
3 times the reciprocal means we multiply 1/7 by 3:
3/7
Now, the phrase [I]equals[/I] mean an equation, so we set 6/x = 3/7
[B]6/x = 3/7[/B] <-- This is our algebraic expression
If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=3&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']we type this proportion in our search engine[/URL] and get:
x = 14

6 times the sum of a number and 3 is equal to 42. What is this number?

6 times the sum of a number and 3 is equal to 42. What is this number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The sum of a number and 3 means we add 3 to x:
x + 3
6 times the sum:
6(x + 3)
The word [I]is[/I] means an equation, so we set 6(x + 3) equal to 42 to get our [I]algebraic expression[/I] of:
[B]6(x + 3) = 42[/B]
[B][/B]
If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/1unk.php?num=6%28x%2B3%29%3D42&pl=Solve']you type this equation into our search engine[/URL] and you get:
x = [B]4[/B]

6 times the sum of a number and 5 is 16

6 times the sum of a number and 5 is 16
A number represents an arbitrary variable, let's call it x
x
The sum of x and 5
x + 5
6 times the sum of x and 5
6(x + 5)
Is means equal to, so set 6(x + 5) equal to 16
[B]6(x + 5) = 16[/B]

6 times y divided by x squared

6 times y divided by x squared
6 times y:
6y
x squared means we raise x to the power of 2:
x^2
The phrase [I]divided by[/I] means we have a fraction:
[B]6y/x^2[/B]

6 times y divided by x squared

6 times y divided by x squared
6 times y:
6y
x squared means we raise x to the power of 2:
x^2
The phrase [I]divided by[/I] means we divide 6y by x^2:
[B]6y/x^2[/B]

6 years from now Cindy will be 25 years old. in 12 years, the sum of the ages of Cindy and Jose will

6 years from now Cindy will be 25 years old. in 12 years, the sum of the ages of Cindy and Jose will be 91. how old is Jose right now?
Let c be Cindy's age and j be Jose's age. We have:
c + 6 = 25
This means c = 19 using our [URL='https://www.mathcelebrity.com/1unk.php?num=c%2B6%3D25&pl=Solve']equation calculator[/URL].
We're told in 12 years, c + j = 91.
If Cindy's age (c) is 19 right now, then in 12 years, she'll be 19 + 12 = 31.
So we have 31 + j = 91.
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=31%2Bj%3D91&pl=Solve']equation calculator[/URL], we get [B]j = 60[/B].

60 percent of a number minus 17 is -65

60 percent of a number minus 17 is -65
Using our [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=60&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percent to decimal calculator[/URL], we see that 60% is 0.6, so we have:
0.6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So 60% of a number is:
0.6x
Minus 17:
0.6x - 17
The word [I]is[/I] means an equation, so we set 0.6x - 17 equal to -65 to get our algebraic expression of:
[B]0.6x - 17 = -65[/B]
[B][/B]
If you want to solve for x in this equation, you [URL='https://www.mathcelebrity.com/1unk.php?num=0.6x-17%3D-65&pl=Solve']type it in our search engine and you get[/URL]:
[B]x = -80[/B]

64 divided by the cube of y

64 divided by the cube of y
The cube of y means y raised to the 3rd power:
y^3
64 divided by this:
[B]64/y^3[/B]

64 is 4 times the difference between Sarah's age, a, and 44. Assume Sarah is older than 44.

64 is 4 times the difference between Sarah's age, a, and 44. Assume Sarah is older than 44.
The phrase [I]difference between[/I] means we subtract 44 from a:
a - 44
The phrase [I]64 is[/I] means an equation, so we set a - 44 equal to 64
[B]a - 44 = 64 <-- This is our algebraic expression
[/B]
If you want to solve for a, then we [URL='https://www.mathcelebrity.com/1unk.php?num=a-44%3D64&pl=Solve']type this expression into our search engine[/URL] and get:
[B]a = 108[/B]

64 is 4 times the difference between Sarah’s age a, and 44.Assume Sarah is older than 44

64 is 4 times the difference between Sarah’s age a, and 44.Assume Sarah is older than 44
Difference between Sarah's age (a) and 44 (Assuming Sarah is older than 44):
a - 44
4 times the difference:
4(a - 44)
The word [I]is[/I] means equal to, so we set 4(a - 44) equal to 64 to get our algebraic expression:
[B]4(a - 44) = 64[/B]
If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=4%28a-44%29%3D64&pl=Solve']type this equation into our search engine[/URL] and we get:
a = [B]60[/B]

66 decreased by Janelle's savings is 15

66 decreased by Janelle's savings is 15
Let Janelle's savings be s.
66 decreased by s is:
66 - s
The word [I]is[/I] means equal so we set 66 - s equal to 15
[B]66 - s = 15[/B]

67 less than twice tims age

Let Tim's age be a.
Twice that is 2a.
67 less than that means we subtract:
2a - 67

7 is 1/4 of some number

7 is 1/4 of some number
The phrase [I]some number[/I] means an arbitrary variable, let's call it x.
1/4 of this is written as:
x/4
The word [I]is[/I] means an equation, so we set x/4 equal to 7:
[B]x/4 = 7[/B]

7 less than -2 times a number x is greater than or equal to 41

-2 times a number x is written as -2x.
Less means subtract, so we have 7 less than this is -2x - 7.
Finally, greater than or equal to is >=, so our expression becomes:
-2x - 7 >= 41

7 less than -2 times a number x is greater than or equal to 41

-2 times a number x is denoted as -2x.
7 less than that means we subtract 7:
-2x - 7
Finally, that entire expression is greater than or equal to 41
-2x - 7 >= 41

7 less than -2 times a number x is greater than or equal to 41

-2 times a number x is denoted as -2x.
7 less means we subtract, so 7 less than that is -2x - 7.
Finally, that entire expression is greater than or equal to 41
-2x - 7 >= 41

7 minus a number all divided by 4

7 minus a number all divided by 4
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
7 minus a number
7 - x
All divided by 4:
[B](7 - x)/4[/B]

7 plus the quantity of 9 increased by a number

7 plus the quantity of 9 increased by a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
9 increased by a number means we add 9 to x
9 + x
7 plus this quantity means we add (9 + x) to 7
[B]7 + (9 + x)[/B]

7 plus the quotient of 12 and x is 2

7 plus the quotient of 12 and x is 2
The quotient of 12 and x:
12/x
7 plus the quotient of 12 and x:
7 + 12/x
The word [I]is[/I] means equal to, so we set 7 + 12/x equal to 2:
[B]7 + 12/x = 2[/B]

7 subtracted from x cubed

7 subtracted from x cubed
x cubed means x raised to the 3rd power
x^3
7 subtracted from this
[B]x^3 - 7[/B]

7 times a number and 2 is equal to 4 times a number decreased by 8

7 times a number and 2 is equal to 4 times a number decreased by 8
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
7 times a number:
7x
and 2 means we add 2:
7x + 2
4 times a number
4x
decreased by 8 means we subtract 8:
4x - 8
The phrase [I]is equal to[/I] means an equation, so we set 7x + 2 equal to 4x - 8:
[B]7x + 2 = 4x - 8[/B]

7 times a number increased by 4 times the number

7 times a number increased by 4 times the number
Let [I]a number[/I] and [I]the number[/I] be an arbitrary variable. Let's call it x. We have an algebraic expression. Let's take it in pieces:
[LIST]
[*]7 times a number: 7x
[*]4 times the number: 4x
[*]The phrase [I]increased by[/I] means we add 4x to 7x:
[*]7x + 4x
[*]Simplifying, we get: (7 + 4)x
[*][B]11x[/B]
[/LIST]

7 times a number is the same as 12 more than 3 times a number

7 times a number is the same as 12 more than 3 times a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[B][U]Algebraic Expression 1:[/U][/B]
7 times a number means we multiply 7 by x:
7x
[B][U]Algebraic Expression 2:[/U][/B]
3 times a number means we multiply 3 by x:
3x
12 more than 3 times a number means we add 12 to 3x:
3x + 12
The phrase [I]is the same as[/I] means an equation, so we set 7x equal to 3x + 12
[B]7x = 3x + 12[/B] <-- Algebraic Expression

7 times a positive number n is decreased by 3, it is less than 25

7 times a positive number n is decreased by 3, it is less than 25
7 times a positive number n:
7n
Decreased by 3:
7n - 3
The phrase [I]it is less than [/I]means an inequality. So we relate 7n - 3 less than 25 using the < sign to get our algebraic expression of:
[B]7n - 3 < 25[/B]

7 times the cube of the sum of x and 8

7 times the cube of the sum of x and 8
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The sum of x and 8 means we add 8 to x: x + 8
[*]The cube of this sum means we raise the sum to the 3rd power: (x + 8)^3
[*]7 times this cubed sum means we multiply (x + 8)^3 by 7:
[/LIST]
[B]7(x + 8)^3[/B]

7 times the quantity of 3 times a number reduced by 10

7 times the quantity of 3 times a number reduced by 10
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
3 times a number:
3x
Reduced by 10 means we subtract 10:
3x - 10
7 times this quantity:
[B]7(3x - 10)[/B]

70 decreased by twice Carlos's age

Let Carlos's age be a. Twice a means we multiply by 2
2a
70 decreased by that amount means we subtract:
[B]70 - 2a[/B]

76 decreased by twice a number. Use the variable n to represent the unknown number

76 decreased by twice a number. Use the variable n to represent the unknown number.
Twice a number (n) means we multiply the unknown number n by 2:
2n
76 decreased by twice a number means we subtract 2n from 76 using the (-) operator
[B]76 - 2n[/B]

76 subtracted from p is equal to the total of g and 227

76 subtracted from p is equal to the total of g and 227
We've got two algebraic expressions. Take them in pieces:
Part 1:
76 subtracted from p
We subtract 76 from the variable p
p - 76
Part 2:
The total of g and 227
The total means a sum, so we add 227 to g
g + 227
Now the last piece, the phrase [I]is equal to[/I] means an equation. So we set both algebraic expressions equal to each other:
[B]p - 76 = g + 227[/B]

8 increased by the product of a number and 7 is greater than or equal to -18

Take this in parts:
First, the phrase, "a number" means we pick an arbitrary variable, let's call it x.
The product of a number and 7 is 7x.
8 increased by the product of 7x means we add them together.
7x + 8
Finally that entire expression is greater than [U]or equal to[/U] -18
[B]7x + 8 >=-18[/B]

8 is subtracted from the square of x

8 is subtracted from the square of x
Take this algebraic expression in parts:
[LIST]
[*]The square of x means we raise x to the power of 2: x^2
[*]8 subtracted from the square of x is found by subtracting 8 from x^2
[/LIST]
[B]x^2 - 8[/B]

8 is subtracted from thrice a number

Thrice a number means we multiply by 3. A number means an arbitrary variable, let's call it x
3x
8 is subtracted from 3x
[B]3x - 8[/B]

8 is subtracted from twice a number

Twice a number:
[LIST]
[*]Choose an arbitrary variable, let's call it x
[*]Twice x means multiply by 2
[*]2x
[/LIST]
8 subtracted from 2x:
[B]2x - 8[/B]

8 less than x is 31

8 less than X means X - 8.
The word is means equal to. So we have:
X - 8 = 31

8 less thantriplethedifferenceof2xand6

8 less than triple the difference of 2x and 6
The [I]difference[/I] of 2x and 6 means we [B]subtract[/B] 6 from 2x
2x - 6
[I]Triple[/I] this difference means we [B]multiply by 3[/B]
3(2x - 6)
8 [I]less[/I] means we [B]subtract 8 from this expression
3(2x - 6) - 8[/B]

8 more than the product of x and 2 equals 4

8 more than the product of x and 2 equals 4
The product of x and 2:
2x
8 more than this, means we add 8:
2x + 8
Set this equal to 4:
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B8%3D4&pl=Solve']2x + 8 = 4[/URL] <-- Algebraic expression
to solve for x, type this into the search engine and we get [B]x = -2[/B].

8 more than twice a number is less than 6 more than the number

8 more than twice a number is less than 6 more than the number.
This is an algebraic expression, let's take it in pieces...
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
8 more than twice a number:
Twice a number means multiply x by 2: 2x
Then add 8: 2x + 8
6 more than the number, means we add 6 to x
x + 6
The phrase [I]is less than[/I] means an inequality, where we set 2x + 8 less than x + 6
[B]2x + 8 < x + 6[/B]

8 taken away from y

8 taken away from y
This is an algebraic expression. The phrase [I]taken away[/I] means we subtract 8 from y:
[B]y - 8[/B]

8 times 4 plus m squared

8 times 4 plus m squared
m squared means we raise m to the power of 2
m^2
4 plus m squared:
4 + m^2
8 times 4 plus m squared
[B]8(4 + m^2)[/B]

8 times the difference of 5y and 3

8 times the difference of 5y and 3
The difference of 5y and 3 means we subtract 3 from 5y:
5y - 3
8 times the difference means we multiply (5y - 3) by 8:
[B]8(5y - 3)[/B]

8 times the difference of a number and 2 is the same as 3 times the sum of the number and 3. What is

8 times the difference of a number and 2 is the same as 3 times the sum of the number and 3. What is the number?
Let the number be n. We're given two expressions:
[LIST=1]
[*]8(n - 2) [I]difference means we subtract[/I]
[*]3(n + 3) [I]sum means we add[/I]
[/LIST]
The phrase [I]is the same as[/I] mean an equation. So we set the first expression equal to the second expression:
8(n - 2) = 3(n + 3)
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=8%28n-2%29%3D3%28n%2B3%29&pl=Solve']type it in our search engine[/URL] and we see that:
n =[B] 5[/B]

8 times the sum of 5 times a number and 9

8 times the sum of 5 times a number and 9
Take this algebraic expression in parts:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
5 times a number means:
5x
The sum of this and 9 means we add 9 to 5x:
5x + 9
Now we multiply 8 times this sum:
[B]8(5x + 9)[/B]

8 to the power of x over 2 to the power of y

8 to the power of x over 2 to the power of y
Step 1: 8 to the power of x means we take 8 and raise it to an exponent of x:
8^x
Step 2: 2 to the power of y means we take 2 and raise it to an exponent of y:
2^y
Step 3: The word [I]over[/I] means a quotient, also known as divided by, so we have:
[B]8^x/2^y
[MEDIA=youtube]SPQKOt5EoqA[/MEDIA][/B]

80 people 40% were women 12 were children. How many men?

80 people 40% were women 12 were children. How many men?
Calculate the number of women:
40% of 80 is 32.
12 were children, so the women and children = 32 + 12 = 44.
Which means the men = 80 - 44 = [B]36[/B]

9 divided by the sum of x and 4 is equal to 6 divided by x minus 4

9 divided by the sum of x and 4 is equal to 6 divided by x minus 4.
Build our two algebraic expressions first:
9 divided by the sum of x and 4
9/(x + 4)
6 divided by x minus 4
6/(x - 4)
The phrase [I]is equal to[/I] means and equation, so we set the algebraic expressions equal to each other:
[B]9/(x + 4) = 6/(x - 4) <-- This is our algebraic expression[/B]
[B][/B]
If the problem asks you to solve for x, we cross multiply:
9(x - 4) = 6(x + 4)
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=9%28x-4%29%3D6%28x%2B4%29&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]20[/B]

9 is one-third of a number x

9 is one-third of a number x
A number x can be written as x
x
one-third of a number x means we multiply x by 1/3:
x/3
The phrase [I]is[/I] means an equation, so we set 9 equal to x/3 to get our final algebraic expression of:
[B]x/3 = 9[/B]
If the problem asks you to solve for x, you [URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=9&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type this algebraic expression into our search engine[/URL] and you get:
[B]x = 27[/B]

9 is the sum of 7 and twice a number

9 is the sum of 7 and twice a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Twice a number means we multiply x by 2:
2x
The sum of 7 and twice a number
7 + 2x
The word [I]is[/I] mean equal to, so we set 7 + 2x equal to 9:
[B]7 + 2x = 9[/B]

9 is the sum of thrice x and y

9 is the sum of thrice x and y
Thrice x means multiply x by 3:
3x
Sum of this and y:
3x + y
Now we set this expression equal to 9:
[B]3x + y = 9[/B]

9 less than 5 times a number is 3 more than 2x

9 less than 5 times a number is 3 more than 2x
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
5 times a number means we multiply x by 5:
5x
9 less than 5x means we subtract 9 from 5x:
5x - 9
3 more than 2x means we add 3 to 2x:
2x + 3
The word [I]is[/I] means an equation, so we set 5x - 9 equal to 2x + 3:
[B]5x - 9 = 2x + 3 <-- This is our algebraic expression[/B]
[B][/B]
If you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-9%3D2x%2B3&pl=Solve']type this equation into the search engine[/URL], and we get:
x = [B]4[/B]

9 less than thrice x

9 less than thrice x
Thrice x means multiply x by 3
3x
9 less than that means subtract 9
[B]3x - 9[/B]

9 less than twice x is twice y

9 less than twice x is twice y
Twice x means we multiply x by 2:
2x
9 less than Twice x means we subtract 9 from 2x
2x - 9
Twice y means we multiply y by 2:
2y
The word [I]is[/I] means equal to, so we set 2x - 9 equal to 2y:
[B]2x - 9 = 2y[/B]

9 subtracted from the product of 3 and a number is greater than or equal to 16

9 subtracted from the product of 3 and a number is greater than or equal to 16
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The product of 3 and a number means we multiply 3 times x: 3x
[*]9 subtracted from the product: 3x - 9
[*]The phrase is greater than or equal to means an inequality. So we set up an inequality with >= for the greater than or equal to sign in relation to 3x - 9 and 16
[/LIST]
Our algebraic expression (inequality) becomes:
[B]3x - 19 >= 16[/B]

9 times a number is that number minus 10

9 times a number is that number minus 10
The phrase [I]a number[/I] means we define a random/arbitrary variable, let's call it x:
x
9 times a number means we multiply x by 9:
9x
The phrase [I]that number[/I] refers back to the original arbitrary variable we defined above, which is x:
x
That number minus 10 means we subtract 10 from x:
x - 10
The word [I]is[/I] means equal to, so we set 9x equal to x - 10
[B]9x = x - 10[/B]

9 times a number is that number minus 3

9 times a number is that number minus 3
Let [I]a number[/I] be an arbitrary variable, let's call it x. We're given:
9 times a number is 9x
The number minus 3 is x - 3
The word [I]is[/I] means an equation, so we set 9x equal to x - 3 to get our [I]algebraic expression[/I]:
[B]9x = x - 3[/B]
To solve for x, we type this equation into our search engine and we get:
x = [B]-0.375 or -3/8[/B]

9 times x is twice the sum of x and 5

9 times x is twice the sum of x and 5
9 times x:
9x
the sum of x and 5
x + 5
twice the sum of x and 5
2(x + 5)
The phrase [I]is[/I] means equal to, so we set 9x equal to 2(x + 5)
[B]9x = 2(x + 5)[/B]

a 12 sided die is rolled find the probability of rolling a number greater than 7

a 12 sided die is rolled find the probability of rolling a number greater than 7
We assume this is a fair die, not loaded.
This means each side 1-12 has an equal probability of 1/12 of being rolled.
The problem asks, P(Roll > 7)
Greater than 7 means our sample space is {8, 9, 10, 11, 12}
If each of these 5 faces have an equal probability of being rolled, then we have:
P(Roll > 7) = P(Roll = 8) + P(Roll = 9) + P(Roll = 10) + P(Roll = 11) + P(Roll = 12)
P(Roll > 7) = 1/12 + 1/12 + 1/12 + 1/12 + 1/12
P(Roll > 7) =[B] 5/12[/B]

A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12}. Find t

A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12}. Find the probability of rolling a number less than 6.
We have 12 outcomes.
Less than 6 means 1, 2, 3, 4, 5.
Our probability P(x < 6) is:
P(x < 6) = [B]5/12[/B]

a 24 sheet of aluminum is to be cut into 2.5 strips. how wide is the remaining wasted piece of alumi

a 24 sheet of aluminum is to be cut into 2.5 strips. how wide is the remaining wasted piece of aluminum
Divide 24 by 2.5 to get number of sheets:
24/2.5 = 9.6
So we have 9 full sheets. Which means each strip is [B]0.6 wide[/B]

A = { 0 , 2 , 4 , 6 , 8 } B = { 0 , 1 , 2 , 3 , 4 , 5 , 6 } C = { 4 , 5 , 6 , 7 , 8 , 9 , 10 } Find

A = { 0 , 2 , 4 , 6 , 8 } B = { 0 , 1 , 2 , 3 , 4 , 5 , 6 } C = { 4 , 5 , 6 , 7 , 8 , 9 , 10 } Find ( A ? B ) ? C
A U B is everything in A and B
A U B = {0, 1, 2, 3, 4, 5, 6, 8}
( A ? B ) ? C means everything in both ( A ? B ) and C
[B]( A ? B ) ? C = {4, 5, 6, 8}[/B]

A bacteria population increases every hour. At 12pm there are 5 cells. At 1pm there are 10 cells. At

A bacteria population increases every hour. At 12pm there are 5 cells. At 1pm there are 10 cells. At 2pm there are 20 cells. At 3pm there are 40 cells. If this pattern continues, how many cells will there be at 7pm?
The bacteria cells double each hour in the example above.
From 3pm to 7pm, we have 4 hours, meaning 4 doubling periods. Which is 2 * 2 * 2 * 2 or 2^4.
So we have:
40 * 2^4
40 * 16 = [B]640 cells[/B]

A bag contains 3 black, 4 red, 3 yellow, and 2 green marbles. What is the probability of drawing a b

A bag contains 3 black, 4 red, 3 yellow, and 2 green marbles. What is the probability of drawing a black and then a red marble out of the bag without replacing the black marble before drawing the red marble?
The phrase [U][B]without replacement[/B][/U] is a huge clue on this problem.
Take each draw and calculate the probability.
Draw 1: P(Drawing a red)
P(Drawing a red) = Total Red marbles n the jar / Total marbles in the jar
P(Drawing a red) = 4/12
4/12 simplifies to 1/3 using a common factor of 4:
P(Drawing a red) = 1/3
Draw 2: P(Drawing a black)
P(Drawing a black) = Total Black marbles in the jar / Total marbles in the jar
[I]We drew one red marble already. Without replacement means we do not put it back. Therefore, we have 12 - 1 = 11 marbles left in the jar.[/I]
P(Drawing a black) = 3/11
The question asks, what is the the following probability:
P(Drawing a Red, Drawing a Black)
Because each draw is [I][U]independent[/U], [/I]we multiply each draw probability together:
P(Drawing a Red, Black) = P(Drawing a Red) * P(Drawing a Black)
P(Drawing a Red, Black) = 1/3 * 3/11
P(Drawing a Red, Black) = [B]1/11[/B]

A bag contains 3 red marbles and 4 blue marbles. a marble is taken at random and replaced. another m

A bag contains 3 red marbles and 4 blue marbles. a marble is taken at random and replaced. Another marble is taken from the bag. Work out the probability that the two marbles taken from the bag are the same color.
[LIST]
[*]Total number of marbles in the bag is 3 + 4 = 7.
[*]The problem asks for the probability of (RR) [I]or[/I] (BB).
[*]It's worthy to note we are replacing the balls after each draw, which means we always have 7 to draw from
[/LIST]
Since each draw is independent, we take the product of each event for the total event probability.
P(RR) = 3/7 * 3/7 = 9/49
P(BB) = 4/7 * 4/7 = 16/49
We want to know P(RR) + P(BB)
P(RR) + P(BB) = 9/49 + 16/49 = 25/49
[MEDIA=youtube]26F9vjsgNGs[/MEDIA]

A bag of marbles is said to contain 50 marbles to the nearest ten. What is the greatest number of ma

A bag of marbles is said to contain 50 marbles to the nearest ten. What is the greatest number of marbles that could be in the bag and what is the least number of marbles that could be in the bag
The key word in this problem is [I][B]nearest ten[/B][/I].
The nearest ten below 50 starts at 45. Why? Because the last digit is 5. At 5, we round up to the nearest ten.
Therefore, the least number of marbles in the bag is 45 since it rounds up to 50 for the nearest ten
The greatest number above 50 rounded to the nearest ten is 54, because less than 5 on the last digit means we round down.
Therefore, the greatest number of marbles in the bag is 54 since it rounds down to 50 when the last digit is less than 5
Answer:
{[B]45, 54}
[MEDIA=youtube]-cl_OHA8-yc[/MEDIA][/B]

A bakery has a fixed cost of $119.75 per a day plus $2.25 for each pastry. The bakery would like to

A bakery has a fixed cost of $119.75 per a day plus $2.25 for each pastry. The bakery would like to keep its daily costs at or below $500 per day. Which inequality shows the maximum number of pastries, p, that can be baked each day.
Set up the cost function C(p), where p is the number of pastries:
C(p) = Variable Cost + Fixed Cost
C(p) = 2.25p + 119.75
The problem asks for C(p) at or below $500 per day. The phrase [I]at or below[/I] means less than or equal to (<=).
[B]2.25p + 119.75 <= 500[/B]

A ball was dropped from a height of 6 feet and began bouncing. The height of each bounce was three-f

A ball was dropped from a height of 6 feet and began bouncing. The height of each bounce was three-fourths the height of the previous bounce. Find the total vertical distance travelled by the all in ten bounces.
The height of each number bounce (n) is shown as:
h(n) = 6(0.75)^n
We want to find h(10)
h(n) = 6(0.75)^n
Time Height
0 6
1 4.5
2 3.375
3 2.53125
4 1.8984375
5 1.423828125
6 1.067871094
7 0.8009033203
8 0.6006774902
9 0.4505081177
10 0.3378810883
Adding up each bounce from 1-10, we get:
16.98635674
Since vertical distance means both [B]up and down[/B], we multiply this number by 2 to get:
16.98635674 * 2 = 33.97271347
Then we add in the initial bounce of 6 to get:
33.97271347 + 6 = [B]39.97271347 feet[/B]

A band came on stage at 9:55 and preformed for 2hours and 27 minutes what time did there performance

A band came on stage at 9:55 and preformed for 2hours and 27 minutes what time did there performance end?
2 hours from 9:55 means we add 2 hours to the hour of 9: 9 + 2 = 11
11:55
Now we add 27 minutes to this time:
5 more minutes gets us to 12:00 PM
27 -5 = 22 minutes
So we add 22 more minutes to get [B]12:22 PM[/B]

a baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many m

a baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many more tickets would they need to sell to earn at least $441?
Let the number of tickets above 42 be t.
A few things to note on this question:
[LIST]
[*]The phrase [I]at least[/I] means greater than or equal to, so we have an inequality.
[*]Earnings = Price * Quantity
[/LIST]
We're given:
Earnings = 4.50 * 42 + 4.5t >= 441
Earnings = 189 + 4.5t >= 441
We want to solve this inequality for t:
Solve for [I]t[/I] in the inequality 189 + 4.5t ? 441
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 189 and 441. To do that, we subtract 189 from both sides
4.5t + 189 - 189 ? 441 - 189
[SIZE=5][B]Step 2: Cancel 189 on the left side:[/B][/SIZE]
4.5t ? 252
[SIZE=5][B]Step 3: Divide each side of the inequality by 4.5[/B][/SIZE]
4.5t/4.5 ? 252.4.5
[B]t ? 56[/B]

A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many dif

A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many different ways are there to arrange the batting order of 9 starting players if only one pitcher is used at a time and the pitcher always bats last.
(This means that 8 players are taken from the position players and one pitcher is then added at the end of the lineup.)
First 8 positions:
[URL='https://www.mathcelebrity.com/permutation.php?num=15&den=8&pl=Permutations']15P8[/URL] = 259,459,200
For the pitcher, we can have 10 different possibilities for the 9th player:
259,459,200 x 10 = [B]2,594,592,000 ways[/B]

A belongs to Both X and Y

A belongs to Both X and Y
What this means is Element A belongs to Set X and Set Y.
We write this as follows
A is an element of X is written as A ? X
A is an element of Y is written as A ? Y
[B]A ? X & A ? Y[/B]
[FONT=Droid Serif][COLOR=rgb(34, 34, 34)][SIZE=14px][/SIZE][/COLOR][/FONT]

A bicycle helmet is priced at $18.50. If it is on sale for 10% off and there is 7% sales tax, how mu

A bicycle helmet is priced at $18.50. If it is on sale for 10% off and there is 7% sales tax, how much will it cost after tax?
[U]Calculate percent off first:[/U]
10% off means 90% off the price
$18.50 * (1 - 0.1)
$18.50 * (0.9) = 16.65
[U]Now, add 7% sales tax to the discounted price[/U]
Price after sales tax = Discounted Price * 1.07
Price after sales tax = 16.65(1.07)
[B]Price after sales tax = 17.82[/B]

A bicycle store costs $1500 per month to operate. The store pays an average of $60 per bike. The ave

A bicycle store costs $1500 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicycle is $80. How many bicycles must the store sell each month to break even?
Profit = Revenue - Cost
Let the number of bikes be b.
Revenue = 80b
Cost = 60b + 1500
Break even is when profit equals 0, which means revenue equals cost. Set them equal to each other:
60b + 1500 = 80b
We [URL='https://www.mathcelebrity.com/1unk.php?num=60b%2B1500%3D80b&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]75[/B]

A bicycle store costs $2750 per month to operate. The store pays an average of $45 per bike. The a

A bicycle store costs $2750 per month to operate. The store pays an average of $45 per bike. The average selling price of each bicycle is $95. How many bicycles must the store sell each month to break even?
Let the number of bikes be b.
Set up our cost function, where it costs $45 per bike to produce
C(b) = 45b
Set up our revenue function, where we earn $95 per sale for each bike:
R(b) = 95b
Set up our profit function, which is how much we keep after a sale:
P(b) = R(b) - C(b)
P(b) = 95b - 45b
P(b) = 50b
The problem wants to know how many bikes we need to sell to break-even. Note: break-even means profit equals operating cost, which in this case, is $2,750. So we set our profit function of 50b equal to $2,750
50b = 2750
[URL='https://www.mathcelebrity.com/1unk.php?num=50b%3D2750&pl=Solve']We type this equation into our search engine[/URL], and we get:
b = [B]55[/B]

A board must be cut into three pieces that are the same length. If it takes five minutes for each cu

A board must be cut into three pieces that are the same length. If it takes five minutes for each cut, how long will it take to saw the board into three pieces that are the same size?
Three equal pieces means only 2 cuts on the board:
2 cuts * 5 minutes per cut = [B]10 minutes[/B]

A book is discounted 45%. If the original price is $40, what is the new price?

A book is discounted 45%. If the original price is $40, what is the new price?
45% discount means we pay 100% - 45% = 55%
40 * 55% = [B]22[/B]

A box contains 10 bells. There are 6 red bells and the rest are silver. What is the probability of p

A box contains 10 bells. There are 6 red bells and the rest are silver. What is the probability of picking two bells of the same color if the bell is replaced after each pick?
If there are 6 red bells, then we have 10 - 6 = 4 silver bells.
The problem asks for the probability of picking two bells of the same color. Which mean we have 2 scenarios:
[LIST=1]
[*]Silver, Silver
[*]Red, Red
[/LIST]
Find the probability of Silver, Silver:
Since each draw is independent, and we replace the bells, we have a 4/10 chance of picking silver. [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F10&frac2=3%2F8&pl=Simplify']Simplified, this is 2/5[/URL].
(2/5)(2/5) = 4/25
Find the probability of Red, Red:
Since each draw is independent, and we replace the bells, we have a 6/10 chance of picking silver. [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F10&frac2=3%2F8&pl=Simplify']Simplified, this is 3/5[/URL].
(3/5)(3/5) = 9/25
Because we want Silver, Silver [B][U]or[/U][/B] Red, Red, we add the two probabilities.
4/25 + 9/25 = [B]13/25[/B]

A box contains 4 red jellies, 6 blue jellies and 5 yellow jellies. What is the probability that a j

A box contains 4 red jellies, 6 blue jellies and 5 yellow jellies. What is the probability that a jelly chosen randomly from the box is not red?
Calculate Total Jellies:
Total Jellies = Red Jellies + Blue Jellies + Yellow Jellies
Total Jellies = 4 + 6 + 5
Total Jellies = 15
Not choosing a red jelly means choosing a blue [B]or[/B] yellow jelly
P(not red jelly) = P(blue) + P(Yellow)
P(not red jelly) = (Blue Jelly + Yellow Jelly) / Total Jellies
P(not red jelly) = (6 + 5)/15
P(not red jelly) = [B]11/15[/B]

A box contains 6 yellow, 3 red, 5 green, and 7 blue colored pencils. A pencil is chosen at random, i

A box contains 6 yellow, 3 red, 5 green, and 7 blue colored pencils. A pencil is chosen at random, it is not replaced, then another is chosen. What is the probability of choosing a red followed by a green?
We have 6 + 3 + 5 + 7 = 21 total pencils
P(Red on the first draw) = Total Red / Total pencils
P(Red on the first draw) = 3/21
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F21&frac2=3%2F8&pl=Simplify']P(Red on the first draw)[/URL] = 1/7
We're drawing without replacement, this means on the next draw, we have 21 - 1 = 20 pencils
P(Green on the second draw) = Total Green / Total pencils
P(Green on the second draw) = 5/20
[URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F20&frac2=3%2F8&pl=Simplify']P(Green on the second draw) [/URL]= 1/4
Since each event is independent, we have:
P(Red on first, green on second) = P(Red on First) * P(green on second)
P(Red on first, green on second) = 1/7 * 1/4
P(Red on first, green on second) = [B]1/28[/B]

A box had x pencils. Then 6 pencils were removed from the box. The box now has 54 pencils.

A box had x pencils. Then 6 pencils were removed from the box. The box now has 54 pencils.
Removed means we subtract from the total. So Our equation is:
x - 6 = 54
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-6%3D54&pl=Solve']type it in our search engine [/URL]and we get:
x = [B]60[/B]

A box has y oranges. 5 oranges are rotten and removed. The remaining oranges are placed equally into

A box has y oranges. 5 oranges are rotten and removed. The remaining oranges are placed equally into 2 containers . Each container has ______oranges
Remove 5 rotten oranges means we subtract 5 from y:
y - 5
If each of the two remaining boxes contains an equal amount of the remaining oranges, we have:
[B](y - 5)/2[/B] oranges in each box

A box is filled with 10 green cards, 4 blue cards, and 4 brown cards. A card is chosen at random fr

A box is filled with 10 green cards, 4 blue cards, and 4 brown cards. A card is chosen at random from the box. What is the probability that it is a green or a brown card?
Calculate Total Cards:
10 green cards + 4 blue cards + 4 brown cards = 18 cards
"Or", means either or, so we want P(Green) + P(Brown)
[U]Find P(Green)[/U]
P(Green) = Green Cards / Total Cards
P(Green) = 10/18 <-- Simplify by dividing top and bottom by 2
P(Green)= 5/9 <-- Simplify by dividing top and bottom by 2
Find P(Brown)
P(Brown) = Brown Cards / Total Cards
P(Brown) = 4/18 <-- Simplify by dividing top and bottom by 2
P(Brown)= 2/9 <-- Simplify by dividing top and bottom by 2
P(Green) + P(Brown) = 5/9 + 2/9
P(Green) + P(Brown) = [B]7/9[/B]

A boy has 6 toys he loses 3. How many does the boy have?

A boy has 6 toys he loses 3. How many does the boy have?
We subtract 3 from 6 since losing means less, and we have:
6 - 3 = [B]3[/B]

a boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that

a boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that the middle piece is 6inches longer than the shortest piece and the shortest piece is 9 inches shorter than the longest price. how long should the three pieces be?
Let the longest piece be l. The middle piece be m. And the short piece be s. We have 2 equations in terms of the shortest piece:
[LIST=1]
[*]l = s + 9 (Since the shortest piece is 9 inches shorter, this means the longest piece is 9 inches longer)
[*]m = s + 6
[*]s + m + l = 57
[/LIST]
We substitute equations (1) and (2) into equation (3):
s + (s + 6) + (s + 9) = 57
Group like terms:
(1 + 1 + 1)s + (6 + 9) = 57
3s + 15 = 57
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3s%2B15%3D57&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]14
[/B]
[U]Plug s = 14 into equation 2 to solve for m:[/U]
m = 14 + 6
m = [B]20
[/B]
[U]Plug s = 14 into equation 1 to solve for l:[/U]
l = 14 + 9
l = [B]23
[/B]
Check our work for equation 3:
14 + 20 + 23 ? 57
57 = 57 <-- checks out
[B][/B]

A bus usually takes 25 minutes. Because of traffic the trip took 7 minutes longer. How long did the

A bus usually takes 25 minutes. Because of traffic the trip took 7 minutes longer. How long did the trip take?
The word [I]longer[/I] means we add, so we have:
25 + 7 = [B]32 minutes[/B]

A car is traveling on a freeway at 50 mph with the cruise control set at 50 mph. Another car is trav

A car is traveling on a freeway at 50 mph with the cruise control set at 50 mph. Another car is traveling at 90 mph with the cruise control set at 90 mph. Which car has a higher acceleration?
Acceleration means a change in speed.
Neither car has a change in speed, [B]so both cars have the same acceleration which is 0[/B]

A car salesman earns $800 per month plus a 10% commission on the value of sales he makes for the mon

A car salesman earns $800 per month plus a 10% commission on the value of sales he makes for the month. If he is aiming to earn a minimum of $3200 a month, what is the possible value of sales that will enable this?
to start, we have:
[LIST]
[*]Let the salesman's monthly sales be s.
[*]With a 10% discount as a decimal of 0.1
[*]The phrase [I]a minimum[/I] also means [I]at least[/I] or [I]greater than or equal to[/I]. This tells us we want an inequality
[*]We want 10% times s + 800 per month is greater than or equal to 3200
[/LIST]
We want the inequality:
0.1s + 800 >= 3200
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.1s%2B800%3E%3D3200&pl=Solve']type this inequality into our search engine[/URL] and we get:
[B]s >= 24000[/B]

a car was bought for $24300 and sold at a loss of $2290. Find the selling price.

a car was bought for $24300 and sold at a loss of $2290. Find the selling price.
A loss means the car was sold for less than the buying price. Let the selling price be S. we have:
24300 - S = 2290
[URL='https://www.mathcelebrity.com/1unk.php?num=24300-s%3D2290&pl=Solve']Typing this equation into our search engine[/URL], we get:
s = [B]22,010[/B]

A car worth $43,000 brand new, depreciates at a rate of $2000 per year. What is the formula that des

A car worth $43,000 brand new, depreciates at a rate of $2000 per year. What is the formula that describes the relationship between the value of the car (C) and the time after it has been purchased (t)?
Let t be the number of years since purchase. Depreciation means the value decreases, so we have:
[B]C = 43000 - 2000t[/B]

A card is picked from a deck of 52 cards. Find the probability of getting a black ace or a red queen

A card is picked from a deck of 52 cards. Find the probability of getting a black ace or a red queen.
In a standard deck of 52 cards, we have:
[LIST]
[*]2 black Aces with probability 2/52 = 1/26 [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F52&frac2=3%2F8&pl=Simplify']using our fraction simplifier[/URL]
[*]2 red Queens with probability 2/52 = 1/26 [URL='http://using our fraction simplifier']using our fraction simplifier[/URL]
[/LIST]
The problems asks for P(Red Queen Or Black Ace). Or means we add, so we have:
P(Red Queen Or Black Ace) = P(Red Queen) + P(Black Ace)
P(Red Queen Or P Black Ace) = 1/26 + 1/26
P(Red Queen Or P Black Ace) = 2/26
P(Red Queen Or P Black Ace) = [B]1/13[/B] [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F26&frac2=3%2F8&pl=Simplify']using our fraction simplifier[/URL]

A carpenter wants to cut a 45 inch board into two pieces such that the longer piece will be 7 inches

A carpenter wants to cut a 45 inch board into two pieces such that the longer piece will be 7 inches longer than the shorter. How long should each piece be
Let the shorter piece of board length be s. Then the larger piece is:
[LIST]
[*]l = s + 7
[/LIST]
And we know that:
Shorter Piece + Longer Piece = 25
Substituting our values above, we have:
s + s + 7 = 45
to solve this equation for s, we type it in our search engine and we get:
s = [B]19[/B]
Plugging this into our equation for l above means that:
l = 19 + 7
l =[B] 26[/B]

A car’s purchase price is $24,000. At the end of each year, the value of the car is three-quarters o

A car’s purchase price is $24,000. At the end of each year, the value of the car is three-quarters of the value at the beginning of the year. Write the first four terms of the sequence of the car’s value at the end of each year.
three-quarters means 3/4 or 0.75. So we have the following function P(y) where y is the number of years since purchase price:
P(y) = 24000 * 0.75^y
First four terms:
P(1) = 24000 * 0.75 = [B]18000[/B]
P(2) = 18000 * 0.75 = [B]13500[/B]
P(3) = 13500 * 0.75 = [B]10125[/B]
P(4) = 10125 * 0.75 = [B]7593.75[/B]

A certain species of fish costs $3.19 each. You can spend at most $35. How many of this type of f

A certain species of fish costs $3.19 each. You can spend at most $35. How many of this type of fish can you buy for your aquarium?
Let the number of fish be f. We have the following inequality where "at most" means less than or equal to:
3.19f <= 35
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3.19f%3C%3D35&pl=Show+Interval+Notation']Typing this inequality into our search engine[/URL], we get:
f <= 10.917
Since we need a whole number of fish, we can buy a maximum of [B]10 fish[/B].

A class has 35 boys and girls. There are 7 more girls than boys. Find the number of girls and boys i

A class has 35 boys and girls. There are 7 more girls than boys. Find the number of girls and boys in the class
Let the number of boys be b and the number of girls be g. We're given two equations:
[LIST=1]
[*]b + g = 35
[*]g = b + 7 (7 more girls means we add 7 to the boys)
[/LIST]
To solve for b, we substitute equation (2) into equation (1) for g:
b + b + 7 = 35
To solve for b, we type this equation into our search engine and we get:
b = [B]14[/B]
Now, to solve for g, we plug b = 14 into equation (2) above:
g = 14 + 7
g = [B]21[/B]

A classroom fish tank contains x goldfish. The tank contains 4 times as many guppies as goldfish. En

A classroom fish tank contains x goldfish. The tank contains 4 times as many guppies as goldfish. Enter an equation that represents the total number of guppies, y, in the fish tank.
The phrase [I]4 times as many[/I] means we multiply the goldfish (x) by 4 to get the number of guppies (y):
[B]y = 4x[/B]

A classroom had x students. Then 9 of them went home. There are now 27 students in the classroom.

A classroom had x students. Then 9 of them went home. There are now 27 students in the classroom.
Take this one piece at a time:
[LIST]
[*]We start with x students
[*]9 of them went home. This means we have 9 less students. So we subtract 9 from x: x - 9
[*]The phrase [I]there are now[/I] means an equation, so we set x - 9 equal to 27
[/LIST]
x - 9 = 27
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-9%3D27&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]36[/B]

A coffee franchise is opening a new store. The company estimates that there is a 75% chance the sto

A coffee franchise is opening a new store. The company estimates that there is a 75% chance the store will have a profit of $45,000, a 10% chance the store will break even, and a 15% chance the store will lose $2,500. Determine the expected gain or loss for this store.
Calculate the expected value E(x). Expected value is the sum of each event probability times the payoff or loss:
E(x) = 0.75(45,000) + 0.1(0) + 0.15(-2,500) <-- Note, break even means no profit and no loss and a loss is denoted with a negative sign
E(x) = 33,750 + 0 - 375
E(x) = [B]33,375 gain[/B]

A compact disc is designed to last an average of 4 years with a standard deviation of 0.8 years. Wha

A compact disc is designed to last an average of 4 years with a standard deviation of 0.8 years. What is the probability that a CD will last less than 3 years?
Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=3&mean=4&stdev=0.8&n=1&pl=P%28X+%3C+Z%29']Z-score and Normal distribution calculator[/URL], we get:
[B]0.10565[/B]

A company has 81 employees of whom x are members of a union how many are not in the union

A company has 81 employees of whom x are members of a union how many are not in the union
You can either be a union member or a non-union member. This is our sample space.
If we have 81 employees and x are union members, this means that:
Non-Union membes = [B]81 - x[/B]

a confidence interval for a population mean has a margin of error of 0.081

a confidence interval for a population mean has a margin of error of 0.081

A culture of bacteria doubles every hour. If there are 500 bacteria at the beginning, how many bacte

A culture of bacteria doubles every hour. If there are 500 bacteria at the beginning, how many bacteria will there be after 9 hours?
Assumptions and givens;
[LIST]
[*]h is the number of hours.
[*]B(h) is the number of bacteria at time h
[*]B(0) is the starting bacteria amount
[*]Doubling means multiplying by 2, so we have:
[/LIST]
B(h) = B(0) * 2^h
We want h = 9, so we have:
B(9) = 500 * 2^9
B(9) = 500 * 512
B(9) = [B]256,000[/B]

A day after tomorrow is 3 days before Monday. What’d day is today

A day after tomorrow is 3 days before Monday. What’d day is today
Three days before Monday is:
Sunday, Saturday, Friday
A day after tomorrow is Friday.
Which means we rewind 2 days to get:
Friday, Thursday, [B]Wednesday[/B]

A Fahrenheit thermometer shows that the temperature is 15 degrees below zero. Enter the integer that

A Fahrenheit thermometer shows that the temperature is 15 degrees below zero. Enter the integer that represents the temperature in degrees Fahrenheit.
Below zero means negative in Fahrenheit, so we have:
[B]-15[/B]

A fair die is rolled. What is the probability of rolling a 3 or a 6?

A fair die is rolled. What is the probability of rolling a 3 or a 6?
P(3 or 6) can be written as:
P(3) + P(6)
A fair die means all faces have an equal probability of 1/6
P(3) = 1/6
P(6) = 1/6
P(3 or 6) = P(3) + P(6)
P(3 or 6) = 1/6 + 1/6
P(3 or 6) = 2/6
[URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F6&frac2=3%2F8&pl=Simplify']Using our fractions simplifier for 2/6[/URL], we get:
P(3 or 6) = [B]1/3[/B]

A farmer was 1/3 of his land to grow corn, a quarter of his land to grow lettuce, and 12.5% of his l

A farmer was 1/3 of his land to grow corn, a quarter of his land to grow lettuce, and 12.5% of his land to grow green beans. He uses the remaining 7 acres to grow wheat.How many total acres does the farmer own?
Convert all land portions to fractions or decimals. We will do fractions:
[LIST]
[*]1/3 for corn
[*][I]A quarter[/I] means 1/4 for lettuce
[*]12.5% is 12.5/100 or 1/8 for green beans
[/LIST]
Now add all these up:
1/3 + 1/4 + 1/8
We need a common factor for 3, 4, and 8. Using our [URL='https://www.mathcelebrity.com/gcflcm.php?num1=3&num2=4&num3=8&pl=LCM']LCM Calculator[/URL], we get 24.
1/3 = 8/24
1/4 = 6/24
18 = 3/24
Add them all up:
(8 + 6 + 3)/24
17/24
This means 17/24 of the land is used for everything but wheat. Wheat occupies (24-17)/24 = 7/24 of the land.
We'll use a for the number of acres on the farm.
7a/24 = 7
[B]a = 24[/B]

A financial analyst computed the ROI for all companies listed on the NYSE. She found that the mean o

A financial analyst computed the ROI for all companies listed on the NYSE. She found that the mean of this distribution was 10% with standard deviation of 5%. She is interested in examining further those companies whose ROI is between 14% and 16% of the approximately 1,500 companies listed on the exchange, how many are of interest of her?
First, use our [URL='http://www.mathcelebrity.com/zscore.php?z=p%280.14%3Cz%3C0.16%29&pl=Calculate+Probability']z-score calculator[/URL] to get P(0.14 < z < 0.16) = 0.007889
Divide that by 2 for two-tail test to get0.003944729
Use the NORMSINV(0.003944729) in Excel to get the Z value of 2.66
Therefore, the companies of interest are 2.66 * 1500 * 0.10 = [B]399[/B]

A firm wants to know with a 98% level of confidence if it can claim that the boxes of detergent it s

A firm wants to know with a 98% level of confidence if it can claim that the boxes of detergent it sells contain more than 500g of detergent. From past experience the firm knows that the amount of detergent in the boxes is normally distributed. The firm takes a random sample of n =25 and finds that X = 520 g and s = 75g. What's your final conclusion?
(Ho: u = 500; Ha: u > 500)
[URL='http://www.mathcelebrity.com/mean_hypothesis.php?xbar=520&n=25&stdev=75&ptype==&mean=500&alpha=0.02&pl=Mean+Hypothesis+Testing']Perform a hypothesis testing of the mean[/URL]
[B]Yes, accept null hypothesis[/B]

A first number plus twice a second number is 10. Twice the first number plus the second totals 35. F

A first number plus twice a second number is 10. Twice the first number plus the second totals 35. Find the numbers.
[U]The phrase [I]a number[/I] means an arbitrary variable[/U]
A first number is written as x
A second number is written as y
[U]Twice a second number means we multiply y by 2:[/U]
2y
[U]A first number plus twice a second number:[/U]
x + 2y
[U]A first number plus twice a second number is 10 means we set x + 2y equal to 10:[/U]
x + 2y = 10
[U]Twice the first number means we multiply x by 2:[/U]
2x
[U]Twice the first number plus the second:[/U]
2x + y
[U]Twice the first number plus the second totals 35 means we set 2x + y equal to 35:[/U]
2x + y = 35
Therefore, we have a system of two equations:
[LIST=1]
[*]x + 2y = 10
[*]2x + y = 35
[/LIST]
Since we have an easy multiple of 2 for the x variable, we can solve this by multiply the first equation by -2:
[LIST=1]
[*]-2x - 4y = -20
[*]2x + y = 35
[/LIST]
Because the x variables are opposites, we can add both equations together:
(-2 + 2)x + (-4 + 1)y = -20 + 35
The x terms cancel, so we have:
-3y = 15
To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D15&pl=Solve']type it in our search engine[/URL] and we get:
y = [B]-5
[/B]
Now we substitute this y = -5 into equation 2:
2x - 5 = 35
To solve this equation for x, we[URL='https://www.mathcelebrity.com/1unk.php?num=2x-5%3D35&pl=Solve'] type it in our search engine[/URL] and we get:
x = [B]20[/B]

A first number plus twice a second number is 14. Twice the first number plus the second totals 40. F

A first number plus twice a second number is 14. Twice the first number plus the second totals 40. Find the numbers.
[B][U]Givens and assumptions:[/U][/B]
[LIST]
[*]Let the first number be x.
[*]Let the second number be y.
[*]Twice means multiply by 2
[*]The phrases [I]is[/I] and [I]totals[/I] mean equal to
[/LIST]
We're given two equations:
[LIST=1]
[*]x + 2y = 14
[*]2x + y = 40
[/LIST]
To solve this system, we can take a shortcut, and multiply the top equation by -2 to get our new system:
[LIST=1]
[*]-2x - 4y = -28
[*]2x + y = 40
[/LIST]
Now add both equations together
(-2 _ 2)x (-4 + 1)y = -28 + 40
-3y = 12
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D12&pl=Solve']type it in our search engine[/URL] and we get:
y = [B]-4
[/B]
We substitute this back into equation 1 for y = -4:
x + 2(-4) = 14
x - 8 = 14
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-8%3D14&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]22[/B]

A first number plus twice a second number is 22. Twice the first number plus the second totals 28. F

A first number plus twice a second number is 22. Twice the first number plus the second totals 28. Find the numbers.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x + 2y = 22 <-- Since twice means multiply by 2
[*]2x + y = 28 <-- Since twice means multiply by 2
[/LIST]
We have a set of simultaneous equations. We can solve this three ways
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28+&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer:
[LIST]
[*][B]x = 11 & 1/3[/B]
[*][B]y = 5 & 1/3[/B]
[/LIST]

A first number plus twice a second number is 3. Twice the first number plus the second totals 24.

A first number plus twice a second number is 3. Twice the first number plus the second totals 24.
Let the first number be x. Let the second number be y. We're given:
[LIST=1]
[*]x + 2y = 3 <-- Because [I]twice[/I] means multiply by 2
[*]2x + y = 24 <-- Because [I]twice[/I] means multiply by 2
[/LIST]
We have a system of equations. We can solve it any one of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which way we choose, we get:
[LIST]
[*]x = [B]15[/B]
[*]y = [B]-6[/B]
[/LIST]

A first number plus twice a second number is 7

A first number plus twice a second number is 7
Let the first number be x. Let the second number be y. We're given:
[LIST]
[*]A first number is x
[*]A second number is y
[*]Twice the second number means we multiply y by 2: 2y
[*][I]Plus [/I]means we add x to 2y: x + 2y
[*]The phrase [I]is[/I] means an equation, so we set x + 2y equal to 7
[/LIST]
[B]x + 2y = 7[/B]

A football team loses 27 yards total during its first 3 plays. On average, what is the yards per pl

A football team loses 27 yards total during its first 3 plays. On average, what is the yards per play for these 3 plays?
A loss of yards means negative yardage.
Average Yards per play = Total Yards / Total plays
Average Yards per play = -27/3
Average Yards per play = -[B]9 or 9 yard loss[/B]

A fuel injection system is designed to last 18 years, with a standard deviation of 1.4 years. What i

A fuel injection system is designed to last 18 years, with a standard deviation of 1.4 years. What is the probability that a fuel injection system will last less than 15 years?
Using our [URL='https://www.mathcelebrity.com/probnormdist.php?xone=15&mean=18&stdev=14&n=1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that:
P(X < 15) = [B]0.416834[/B]

A garden table and a bench cost $977 combined. The garden

A garden table and a bench cost $977 combined. The garden table costs $77 more than the bench. What is the cost of the bench?
Let the garden table cost be g and the bench cost be b. We're given
[LIST=1]
[*]b + g = 977
[*]g = b + 77 <-- The phrase [I]more than[/I] means we add
[/LIST]
Substitute (2) into (1):
b + (b + 77) = 977
Combine like terms:
2b + 77 = 977
[URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B77%3D977&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]b = $450[/B]

A gardener plants flowers in the following order: carnations,daffodils, larkspurs, tiger lillies, an

A gardener plants flowers in the following order: carnations,daffodils, larkspurs, tiger lillies, and zinnias. if the gardener planted 47 plants, what kind of flower did he plant last?
Let c be carnations, d be daffodils, l be larkspurs, t be tiger lillies, and z be zinnias. The order goes as follows:
c, d, l, t, z.
So each cycle of plants counts as 5 plants. We know that 9 * 5 = 45. So the gardener plants 9 full cycles. Which means they have 47 - 45 = 2 plans left over.
In the order above, the second plant is the daffodil. So the gardener planted the [B]daffodil[/B] last.
Now, can we shortcut this problem? Yes, using modulus.
47 plants, with 5 plants per cycle, we do [URL='https://www.mathcelebrity.com/modulus.php?num=47mod5&pl=Calculate+Modulus']47 mod 5 through our calculator[/URL], and get 2. So we have 2 plants left over, and the daffodil is the second plant.

A gasoline tank is leaking at a rate of n gallons in t hours. If the gasoline cost $2 per gallon, wh

A gasoline tank is leaking at a rate of n gallons in t hours. If the gasoline cost $2 per gallon, what is the value of the gasoline that will be lost in m minutes?
n gallons / t hours = n/t gallons per hour are leaking
The value of the gas that leaks each hour is $2, so we have:
2n/t dollar per hour is leaking
Value per minute means we divide by 60:
2n/60t
Dividing top and bottom by 2 to simplify, we have:
n/30t
Given m minutes, we multiply to get:
[B]nm/30t[/B]

A girl is three years older than her brother. If their combined age is 35 years, how old is each

A girl is three years older than her brother. If their combined age is 35 years, how old is each
Let the girl's age be g. Let the boy's age be b. We're given two equations:
[LIST=1]
[*]g = b + 3 ([I]Older means we add)[/I]
[*]b + g = 35
[/LIST]
Now plug in equation (1) into equation (2) for g:
b + b + 3 = 35
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2Bb%2B3%3D35&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]16
[/B]
Now, to solve for g, we plug in b = 16 that we just solved for into equation (1):
g = 16 + 3
g = [B]19[/B]

A girl makes 12 foul shots for every eight that she misses how many shots did you make if she shot 1

A girl makes 12 foul shots for every eight that she misses how many shots did you make if she shot 125 foul shots
This means she makes 12/20
We want to know x shots, if 12/20 = x/125.
[URL='http://www.mathcelebrity.com/prop.php?num1=12&num2=x&den1=20&den2=125&propsign=%3D&pl=Calculate+missing+proportion+value']Enter this proportion into the search engine[/URL] to get [B]x = 75[/B]

A golf ball is selected at random from a golf bag. If the golf bag contains 5 type A balls, 4 type B

A golf ball is selected at random from a golf bag. If the golf bag contains 5 type A balls, 4 type B balls, and 9 type C balls, find the probability that the golf ball is not a type A ball
Not Type A means Type B or Type C.
Our total balls = 5 + 4 + 9 = 18
P(B or C) = P(B) + P(C)
P(B or C) = 4/18 + 9/18
P(B or C) = [B]13/18[/B]

A group of people was surveyed to determine what newspaper they read. 80% of those interviewed read

A group of people was surveyed to determine what newspaper they read. 80% of those interviewed read the New York Times, while 50% read U.S.A. Today. If 35% read both papers, what percent read neither paper?
New York Times:
80% - 35% for both = 45%
USA Today:
50% - 35% for both = 15%
45% + 15% + 35% = 95%
Which means 100% - 95% = [B]5% read neither[/B]

A group of students at a school takes a history test. The distribution is normal with a mean of 25,

A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4.
(a) Everyone who scores in the top 30% of the distribution gets a certificate.
(b) The top 5% of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state?
(a) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.70&pl=Calculate+Critical+Z+Value']Top 30% is 70% percentile[/URL]
Inverse of normal distribution(0.7) = -0.5244005
Plug into z-score formula, -0.5244005 = (x - 25)/4
[B]x = 22.9024[/B]
(b) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.95&pl=Calculate+Critical+Z+Value']Top 5% is 95% percentile[/URL]
Inverse of normal distribution(0.95) = 1.644853627
Plug into z-score formula, 1.644853627 = (x - 25)/4
[B]x = 31.57941451[/B]

A helicopter is flying at an altitude of 785 feet. It descends 570 feet, and then ascends 595 feet.

A helicopter is flying at an altitude of 785 feet. It descends 570 feet, and then ascends 595 feet. Write an expression to represent this situation. Then determine and interpret the sum.
[LIST]
[*]Start at +785 feet
[*]Descend 570 feet means using a minus sign -570
[*]Ascend 595 feet means using a plus sign +595
[/LIST]
[U]Calculate the sum:[/U]
+785 - 570 + 595
[B]+810[/B]

A hot air balloon at 1120 feet descends at a rate of 80 feet per minute. Let y represent the height

A hot air balloon at 1120 feet descends at a rate of 80 feet per minute. Let y represent the height and let x represent the number of minutes the balloon descends.
Descending means we subtract height, so we have:
[B]y = 1120 - 80x[/B]

a hypothesis test is to be performed.Determine the null and alternative hypotheses.

The mean credit card debt among households in one state is $8400. A hypothesis test is to be performed to decide whether the mean credit card debt for households in the formerly affluent town of Rich-No-More differs from the mean credit card debt for the state.

A hypothetical population consists of eight individuals ages 14,15,17,20,26,27,28, and 30 years. Wh

A hypothetical population consists of eight individuals ages 14,15,17,20,26,27,28, and 30 years. What is the probability of selecting a participant who is at least 20 years old?
At least 20 means 20 or older, so our selection of individuals is:
{20, 26, 27, 28, 30}
This is 5 out of a possible 8, so we have [URL='http://www.mathcelebrity.com/perc.php?num=5&den=8&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']5/8 of 0.625, which is 62.5%[/URL]

A is thrice as much as B

A is thrice as much as B
Thrice means multiply by 3, so we have
[B]A = 3B[/B]

A light flashes every 2 minutes a, second light flashes every 7 minutes, and a third light flashes e

A light flashes every 2 minutes a, second light flashes every 7 minutes, and a third light flashes every 8 minutes. If all lights flash together at 8 P.M., what is the next time of day they will all flash together
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=2&num2=7&num3=8&pl=LCM']We use our least common multiple calculator[/URL] to see when the 3 numbers have a common multiple:
LCM of (2, , 8) = 56 minutes
So this means we add 56 minutes to 8:00 P.M. and we get [B]8:56 P.M.[/B]

A line segment is 26 centimeters long. If a segment, x centimeters, is taken, how much of the line s

A line segment is 26 centimeters long. If a segment, x centimeters, is taken, how much of the line segment remains?
This means the leftover segment has a length of:
[B]26 - x[/B]

A local sports centre charges $8 per visit. For an annual membership fee of$45, the cost per visit i

A local sports centre charges $8 per visit. For an annual membership fee of$45, the cost per visit is only $5.50. What is the least number of visits needed in a year in order for the membership to be a better deal?
Set up the cost for the visitors plan C(v) where v is the number of visits:
C(v) = 8v
Set up the cost for the membership plan C(v) where v is the number of visits:
C(v) = 5v + 45
The problem asks for v where:
5v + 45 < 8v
[URL='https://www.mathcelebrity.com/1unk.php?num=5v%2B45%3C8v&pl=Solve']Type this inequality into our search engine[/URL] and get:
v > 15
This means, the least number of visits is 1 more which is [B]16[/B]

A magic box has pennies in it that double every minute. If the box takes a full hour to become compl

A magic box has pennies in it that double every minute. If the box takes a full hour to become completely full, how long does it take for the box to become half full?
At the hour mark, it's 100% full. Half full means 50%. Since it doubles every minute, then at the [B]59th minute[/B], it's half full.

A man's age (a) 10 years ago is 43

A man's age (a) 10 years ago is 43
[U]10 years ago means we subtract 10 from a:[/U]
a - 10
[U]The word [I]is[/I] means an equation. So we set a - 10 equal to 43 to get our algebraic expression[/U]
[B]a - 10 = 43[/B]
If the problem asks you to solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=a-10%3D43&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = 53

A man's age (a) 10 years ago is 43.

A man's age (a) 10 years ago is 43.
Years ago means we subtract
[B]a - 10 = 43
[/B]
If the problem asks you to solve for a, we type this equation into our math engine and we get:
Solve for [I]a[/I] in the equation a - 10 = 43
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants -10 and 43. To do that, we add 10 to both sides
a - 10 + 10 = 43 + 10
[SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE]
a = [B]53[/B]

a mans age (a) ten years ago

a mans age (a) ten years ago
The problem asks for an algebraic expression for age. The phrase [I]ago[/I] means before now, so they were younger. And younger means we [B]subtract[/B] from our current age:
[B]a - 10[/B]

A man’s age 10 years ago, if he is now n years old.

A man’s age 10 years ago, if he is now n years old.
10 years ago means we subtract from current age:
[B]n - 10[/B]

A Middleweight UFC fighter weighs between 170 lbs and 185 lbs.

A Middleweight UFC fighter weighs between 170 lbs and 185 lbs.
Let w be the UFC fighter's weight:
We have a compound inequality.
Right side includes 185 lbs. because between means includes 185lbs.
Left side includes 170 lbs. because between means includes 17lb0s
[B]170 <= w <= 185[/B]

a more than b is greater than 6

a more than b is greater than 6
a more than b:
b + a
Is greater than 6 means an inequality using the > sign:
[B]b + a > 6[/B]

A motorist pays $4.75 per day in tolls to travel to work. He also has the option to buy a monthly pa

A motorist pays $4.75 per day in tolls to travel to work. He also has the option to buy a monthly pass for $80. How many days must he work (i.e. pass through the toll) in order to break even?
Let the number of days be d. Break even means both costs are equal. We want to find when:
4.75d = 80
To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=4.75d%3D80&pl=Solve']type this equation into our search engine[/URL] and we get:
d = 16.84 days
We round up to an even [B]17 days[/B].

A new company president is said to have caused the company "to do a 180." Before the new president,

A new company president is said to have caused the company "to do a 180." Before the new president, the company was losing money. What is the company most likely doing under the new president?
A 180 is a completely different direction. Since 180 degrees means the other way, a half-circle, a switch in direction.
This means if the company was losing money, after doing a "180", they're making money.

a number added to 5 minus p

a number added to 5 minus p
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We add 5 minus p to this number x:
[B]x + 5 - p[/B]

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the pro

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 3 and the coin toss is heads? Write your answer as a fraction in simplest form
Let's review the vitals of this question:
[LIST]
[*]The probability of heads on a fair coin is 1/2.
[*]On a fair die, greater than 3 means either 4, 5, or 6. Any die roll face is a 1/6 probability.
[*]So we have a combination of outcomes below:
[/LIST]
Outcomes
[LIST=1]
[*]Heads and 4
[*]Heads and 5
[*]Heads and 6
[/LIST]
For each of the outcomes, we assign a probability. Since the coin flip and die roll are independent, we multiply the probabilities:
[LIST=1]
[*]P(Heads and 4) = 1/2 * 1/6 = 1/12
[*]P(Heads and 5) = 1/2 * 1/6 = 1/12
[*]P(Heads and 6) = 1/2 * 1/6 = 1/12
[/LIST]
Since we want any of those events, we add all three probabilities
1/12 + 1/12 + 1/12 = 3/12
This fraction is not simplified. S[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F12&frac2=3%2F8&pl=Simplify']o we type this fraction into our search engine, and choose Simplify[/URL].
We get a probability of [B]1/4[/B].
By the way, if you need a decimal answer or percentage answer instead of a fraction, we type in the following phrase into our search engine:
[URL='https://www.mathcelebrity.com/perc.php?num=1&den=4&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']1/4 to decimal[/URL]
Alternative Answers:
[LIST]
[*]For a decimal, we get [B]0.25[/B]
[*]For a percentage, we get [B]25%[/B]
[/LIST]

a number increased by 8 and then tripled

a number increased by 8 and then tripled
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Increased by 8 means we add 8 to x:
x + 8
Then tripled means we multiply the expression x + 8 by 3:
[B]3(x + 8)[/B]

a number is twice another number

a number is twice another number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
The phrase [I]another number [/I]means another arbitrary variable, let's call it y
Twice means we multiply y by 2:
2y
The phrase [I]is [/I]means an equation, so we set x equal to 2y:
[B]x = 2y[/B]

A number K is doubled and then increased by 3

A number K is doubled and then increased by 3
K is doubled means we multiply K by 2:
2K
Increased by 3 means we add:
[B]2K + 3[/B]

A number m is no less than -8 and fewer than 9.

A number m is no less than -8 and fewer than 9.
No less than means greater than or equal to:
m >= -8
Fewer than 9 means less than 9:
m < 9
Combine these two inequalities to get
[B]-8 <= m < 9[/B]

A number multiplied by 6 and divided by 5 give four more than a number?

A number multiplied by 6 and divided by 5 give four more than a number?
A number is represented by an arbitrary variable, let's call it x.
Multiply by 6:
6x
Divide by 5
6x/5
The word "gives" means equals, so we set this equal to 4 more than a number, which is x + 4.
6x/5 = x + 4
Now, multiply each side of the equation by 5, to eliminate the fraction on the left hand side:
6x(5)/5 = 5(x + 4)
The 5's cancel on the left side, giving us:
6x = 5x + 20
Subtract 5x from each side
[B]x = 20[/B]
Check our work from our original equation:
6x/5 = x + 4
6(20)/5 ? 20 + 4
120/5 ?24
24 = 24 <-- Yes, we verified our answer

A number n diminished by 8 gives 12

A number n diminished by 8 gives 12
A number n can be written as n:
n
Diminished by means we subtract, so we subtract 8 from n:
n - 8
The word [I]gives[/I] means an equation, so we set n - 8 equal to 12:
[B]n - 8 = 12[/B]

A number n is no less than 2 and no more than 49.

A number n is no less than 2 and no more than 49.
This is a compound inequality. Let's break it into parts.
Step 1: No more than 49 means 49 or less. Or, less than or equal to 49
<= 49
Step 2: no less than 2 means 2 or greater. Or, greater than or equal to 2
>=2
Writing this in terms of the number n, we have:
[B]2 <= n <= 49[/B]

a number of bacteria b tripled

a number of bacteria b tripled
The word [I]tripled[/I] means we multiply by 3, so we have:
[B]3b[/B]

a number of pennies splits into 4 equal groups

a number of pennies splits into 4 equal groups
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take x and divide it by 4 to get 4 equal groups:
[B]x/4[/B]

A number p subtracted by its double is 10

A number p subtracted by its double is 10
The double of a number means we multiply p by 2:
2p
A number p is subtracted by its double
p - 2p
The phrase [I]is[/I] means equal to, so we set p - 2p equal to 10:
[B]p - 2p = 10[/B]

A number t is no less than 30 and fewer than 40.

A number t is no less than 30 and fewer than 40.
This is a compound inequality. Take it in 3 parts:
Step 1: fewer than 40 means less than (does not include 40)
t < 40
Step 2: no less than 30 means greater than or equal to
t >= 30
Step 3: Combine these 2 statements into one compound inequality:
[B]30 <= t < 40[/B]

A number y increased by itself

A number y increased by itself
increased by itself means we add the variable y to itself to get our final algebraic expression of:
[B]y + y
[/B]
[I]If[/I] the problem asks you to simplify, we group like terms and get:
[B]2y[/B]

A pair of dice is rolled. Find the probability of rolling a sum of not less than 5

A pair of dice is rolled. Find the probability of rolling a sum of not less than 5.
The phrase [I]not less than[/I] also means greater than or equal to. So we [URL='https://www.mathcelebrity.com/2dice.php?gl=3&pl=5&opdice=1&rolist=+&dby=&ndby=&montect=+']use our 2 dice calculator for a sum roll of 5 or greater[/URL] and we get:
[B]5/6[/B]

A Pairs of fair dice is tossed. What is the probability of not getting a sum 7 or 8?

A Pairs of fair dice is tossed. What is the probability of not getting a sum 7 or 8?
Not a 7 or 8 means 2 - 6 or 9 - 12
[URL='https://www.mathcelebrity.com/2dice.php?gl=5&pl=6&opdice=1&rolist=+&dby=&ndby=&montect=+']Using our 2-dice calculator[/URL], P(2 - 6) = 5/12
[URL='https://www.mathcelebrity.com/2dice.php?gl=3&pl=9&opdice=1&rolist=+&dby=&ndby=&montect=+']Using our 2-dice calculator[/URL], P(9 - 12) = 5/18
Since the sum could be either of these, we add probabilities:
P(Not a 7 or 8) = P(2 - 6) + P(9 - 12)
P(Not a 7 or 8) = 5/12 + 5/18
[URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F12&frac2=5%2F18&pl=Add']P(Not a 7 or 8) [/URL]= [B]25/36[/B]

A parking lot has seventy-one parking spaces numbered from 1 to 71. There are no cars in the parking

A parking lot has seventy-one parking spaces numbered from 1 to 71. There are no cars in the parking lot when Jillian pulls in and randomly parks. What is the probability that the number on the parking space where she parks is greater than or equal to 31?
Greater than or equal to means including 31 all the way through 71
31-71 is 40 spaces
P(s>=31) = [B]40/71[/B]

A patient’s temperature was 103°. The temperature then fell by 4° and later rose by 2°. What was the

A patient’s temperature was 103°. The temperature then fell by 4° and later rose by 2°. What was the patient’s final temperature
Start with 103
Fell by 4 means we subtract 4: 103 - 4 = 99
Rose by 2 means we add 2L 99 + 2 = [B]101[/B]

A person has $13,000 invested in stock A and stock B. Stock A currently sells for $20 a share and

A person has $13,000 invested in stock A and stock B. Stock A currently sells for $20 a share and stock B sells for $90 a share. If stock B triples in value and stock A goes up 50%, his stock will be worth $33,000. How many shares of each stock does he own?
Set up the given equations, where A is the number of shares for Stock A, and B is the number of shares for Stock B
[LIST=1]
[*]90A + 20B = 13000
[*]3(90A) + 1.5(20B) = 33000 <-- [I]Triple means multiply by 3, and 50% gain means multiply by 1.5[/I]
[/LIST]
Rewrite (2) by multiplying through:
270A + 30B = 33000
Using our simultaneous equations calculator, we get [B]A = 100 and B = 200[/B]. Click the links below to solve using each method:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]
Check our work using equation (1)
90(100) + 20(200) ? 13,000
9000 + 4000 ? 13,000
13000 = 13000

A pet store has 10 rabbits. What’s the probability that they have at least 1 female rabbit.

A pet store has 10 rabbits. What’s the probability that they have at least 1 female rabbit.
At least 1 female rabbit means we [U]must[/U] have a female rabbit
First, we calculate the probability of 0 females
A rabbit can be either male or female with equal probabilities of 1/2 or 0.5.
Since each birth is independent, we can multiply to get the probability of all males:
P(MMMMMMMMMM) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2
P(MMMMMMMMMM) = 1/1024
Then, we subtract this probability from 1 to get the probability of [B]at least[/B] one female:
P(At least one F) = 1 - 1/1024
Since 1 = 1024/1024, we have:
P(At least one F) = (1024 - 1)/1024
P(At least one F) = [B]1023/1024[/B]

A Petri dish contains 2000. The number of bacteria triples every 6 hours. How many bacteria will exi

A Petri dish contains 2000. The number of bacteria triples every 6 hours. How many bacteria will exist after 3 days?
Determine the amount of tripling periods:
[LIST]
[*]There are 24 hours in a day.
[*]24 hours in a day * 3 days = 72 hours
[*]72 hours / 6 hours tripling period = 12 tripling periods
[/LIST]
Our bacteria population function B(t) where t is the amount of tripling periods. Tripling means we multiply by 3, so we have:
B(t) = 2000 * 3^t
with t = 12 tripling periods, we have:
B(12) = 2000 * 3^12
B(12) = 2000 * 531441
B(12) = [B]1,062,882,000[/B]

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the custome

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the customer pays 8 cents per minute of use. In Plan B, the customer pays a monthly fee of $1.50 and then an additional 7 cents per minute of use.
For what amounts of monthly phone use will Plan A cost more than Plan B?
Set up the cost equations for each plan. The cost equation for the phone plans is as follows:
Cost = Cost Per Minute * Minutes + Monthly Fee
Calculate the cost of Plan A:
Cost for A = 0.08m + 0. <-- Since there's no monthly fee
Calculate the cost of Plan B:
Cost for B = 0.07m + 1.50
The problem asks for what amounts of monthly phone use will Plan A be more than Plan B. So we set up an inequality:
0.08m > 0.07m + 1.50
[URL='https://www.mathcelebrity.com/1unk.php?num=0.08m%3E0.07m%2B1.50&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]m > 150
This means Plan A costs more when you use more than 150 minutes per month.[/B]

A population grows at 6% per year. How many years does it take to triple in size?

A population grows at 6% per year. How many years does it take to triple in size?
With a starting population of P, and triple in size means 3 times the original, we want to know t for:
P(1.06)^t = 3P
Divide each side by P, and we have:
1.06^t = 3
Typing this equation into our search engine to solve for t, we get:
t = [B]18.85 years[/B]
Note: if you need an integer answer, we round up to 19 years

A pound of popcorn is popped for a class party. The popped corn is put into small popcorn boxes that

A pound of popcorn is popped for a class party. The popped corn is put into small popcorn boxes that each hold 120 popped kernels. There are 1,600 kernels in a pound of unpopped popcorn. If all the boxes are filled except for the last box, how many boxes are needed and how many popped kernels are in the last partially filled box?
Using modulus calculator, we know [URL='https://www.mathcelebrity.com/modulus.php?num=1600mod120&pl=Calculate+Modulus']1600 mod 120[/URL] gives us [B]13 full boxes[/B] of unpopped popcorn.
We also know that 13*120 = 1,560. Which means we have 1,600 - 1,560 = [B]40[/B] popped kernels left in the last box.
FB Live:
[URL='https://www.facebook.com/plugins/video.php?href=https%3A%2F%2Fwww.facebook.com%2FMathCelebrity%2Fvideos%2F10156733590718291%2F&show_text=0&width=560']https://www.facebook.com/plugins/video.php?href=https://www.facebook.com/MathCelebrity/videos/10156733590718291/&show_text=0&width=560[/URL]

A professor wanted to test all possible pairwise comparisons among six means. How many comparisons d

A professor wanted to test all possible pairwise comparisons among six means. How many comparisons did he need to compare?
a. 5
b. 6
c. 10
d. 15
[B]d. 15[/B] using our [URL='http://www.mathcelebrity.com/permutation.php?num=6&den=2&pl=Combinations']combinations calculator[/URL]

A professor wants to test all possible pairwise comparisons among three means. If we need to maintai

A professor wants to test all possible pairwise comparisons among three means. If we need to maintain an experiment-wise alpha of 0.05, what is the error rate per comparison after applying Bonferroni correction?
We are given:
[LIST]
[*]? = 0.05
[*]n = 3
[/LIST]
Bonferroni Correction = ?/n
Bonferroni Correction = 0.05/3
Bonferroni Correction = [B]0.01666666667[/B]

A quantity x is at least 10 and at most 20

A quantity x is at least 10 and at most 20
The phrase [I]at most[/I] means less than or equal to
The phrase [I]at least[/I] means greater than or equal to.
So we have the following inequality
[B]10 <= x <= 20[/B]

A quarter of a number is greater than or equal to 38

A quarter of a number is greater than or equal to 38.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
A quarter of a number means 1/4, so we have:
x/4
The phrase [I]is greater than or equal to[/I] means an inequality, so we use the >= sign in relation to 38:
[B]x/4 >= 38 <-- This is our algebraic expression
[/B]
If you want to solve this inequality, [URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=38&propsign=%3E%3D&den1=4&den2=1&pl=Calculate+missing+proportion+value']we type it in the search engine[/URL] to get:
x >= [B]152[/B]

A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population sta

A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime.
[B]2902 < u < 3098[/B] using our [URL='http://www.mathcelebrity.com/normconf.php?n=100&xbar=3000&stdev=500&conf=95&rdig=4&pl=Large+Sample']confidence interval for the mean calculator[/URL]

A random sample of 144 with a mean of 100 and a standard deviation of 70 is known from a population

A random sample of 144 with a mean of 100 and a standard deviation of 70 is known from a population of 1,000. What is the 95% confidence interval for the unknown population?
[URL='http://www.mathcelebrity.com/normconf.php?n=144&xbar=100&stdev=70&conf=95&rdig=4&pl=Large+Sample']Large Sample Confidence Interval Mean Test[/URL]
[B]88.5667 < u < 111.4333[/B]

A random sample of 149 students has a test score average of 61 with a standard deviation of 10. Find

A random sample of 149 students has a test score average of 61 with a standard deviation of 10. Find the margin of error if the confidence level is 0.99. (Round answer to two decimal places)
Using our [URL='https://www.mathcelebrity.com/normconf.php?n=149&xbar=61&stdev=10&conf=99&rdig=4&pl=Large+Sample']confidence interval of the mean calculator[/URL], we get
[B]58.89 < u < 63.11[/B]

A random sample of 25 customers was chosen in CCP MiniMart between 3:00 and 4:00 PM on a Friday afte

A random sample of 25 customers was chosen in CCP MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes).
Checkout Time (in minutes) | Frequency | Relative Frequency
1.0 - 1.9 | 2 | ?
2.0 - 2.9 | 8 | ?
3.0 - 3.9 | ? | ?
4.0 - 5.9 | 5 | ?
Total | 25 | ?
(a) Complete the frequency table with frequency and relative frequency.
(b) What percentage of the checkout times was less than 3 minutes?
(c)In what class interval must the median lie? Explain your answer.
(d) Assume that the largest observation in this dataset is 5.8. Suppose this observation were incorrectly recorded as 8.5 instead of 5.8. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Why?
(a)
[B]Checkout Time (in minutes) | Frequency | Relative Frequency
1.0 - 1.9 | 2 | 2/25
2.0 - 2.9 | 8 | 8/25
3.0 - 3.9 | 10 (since 25 - 5 + 8 + 2) = 10 | 10/25
4.0 - 5.9 | 5 | 5/25
Total | 25 | ?[/B]
(b) (2 + 8)/25 = 10/25 = [B]40%[/B]
c) [B]3.0 - 3.9[/B] since 2 + 8 + 10 + 5 = 25 and 13 is the middle value which occurs in the 3.0 - 3.9 interval
(d) [B]Mean increases[/B] since it's a higher value than usual. Median would not change as the median is the most frequent distribution and assuming the 5.8 is only recorded once.

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leis

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.22 hours, with a standard deviation of 2.31 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.44 hours, with a standard deviation of 1.74 hours. Construct and interpret a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children left parenthesis mu 1 minus mu 2 right parenthesis (?1 - ?2).
Using our confidence interval for [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+40&xbar1=+5.22&stdev1=+2.31&n2=+40&xbar2=+4.44&stdev2=1.74&conf=+90&pl=Mean+Diff+Conf.+Interval+%28Large+Sample%29']difference of means calculator[/URL], we get:
[B]0.0278 < ?1 - ?2 < 1.5322[/B]

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leis

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.22 hours, with a standard deviation of 2.31 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.29 hours, with a standard deviation of 1.58 hours. Construct and interpret a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children (u1 - u2)
What is the interpretation of this confidence interval?
A. There is 90% confidence that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours
B. There is a 90% probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours
C. There is 90% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours
D. There is a 90% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours
0.2021 < u1 - u2 < 1.6579 using our [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+40&xbar1=+5.22&stdev1=2.31&n2=40&xbar2=4.29&stdev2=1.58&conf=+90&pl=Mean+Diff+Conf.+Interval+%28Large+Sample%29']difference of means confidence interval calculator[/URL]
[B]Choice D
There is a 90% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours[/B]

A random sample of n = 10 flash light batteries with a mean operating life X=5 hr. And a sample stan

A random sample of n = 10 flash light batteries with a mean operating life X=5 hr. And a sample standard deviation S = 1 hr. is picked from a production line known to produce batteries with normally distributed operating lives. What's the 98% confidence interval for the unknown mean of the working life of the entire population of batteries?
[URL='http://www.mathcelebrity.com/normconf.php?n=10&xbar=5&stdev=1&conf=98&rdig=4&pl=Small+Sample']Small Sample Confidence Interval for the Mean test[/URL]
[B]4.1078 < u < 5.8922[/B]

A random variable X follows the uniform distribution with a lower limit of 670 and an upper limit

A random variable X follows the uniform distribution with a lower limit of 670 and an upper limit
a. Calculate the mean and standard deviation of this distribution. (Round intermediate calculation for standard deviation to 4 decimal places and final answer to 2 decimal places.)
Using our [URL='http://www.mathcelebrity.com/uniform.php?a=+670&b=+770&x=+680&t=+3&pl=PDF']uniform distribution calculator[/URL], we get:
[B]Mean = 720
Standard deviation = 28.87
[/B]
b. What is the probability that X is less than 730? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Using our [URL='http://www.mathcelebrity.com/uniform.php?a=+670&b=+770&x=+730&t=+3&pl=CDF']uniform distribution calculator[/URL], we get:
[B]0.6[/B]

A rectangular field is twice as long as it is wide. If the perimeter is 360 what are the dimensions?

A rectangular field is twice as long as it is wide. If the perimeter is 360 what are the dimensions?
We are given or know the following about the rectangle
[LIST]
[*]l = 2w
[*]P = 2l + 2w
[*]Since P = 360, we have 2l + 2w = 360
[/LIST]
Since l = 2w, we have 2l + (l) = 360
3l = 360
Divide by 3, we get [B]l = 120[/B]
Which means w = 120/2
[B]w = 60[/B]

A rectangular garden is 5 ft longer than it is wide. Its area is 546 ft2. What are its dimensions?

A rectangular garden is 5 ft longer than it is wide. Its area is 546 ft2. What are its dimensions?
[LIST=1]
[*]Area of a rectangle is lw. lw = 546ft^2
[*]We know that l = w + 5.
[/LIST]
Substitute (2) into (1)
(w + 5)w = 546
w^2 + 5w = 546
Subtract 546 from each side
w^2 + 5w - 546 = 0
Using the positive root in our [URL='http://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B5w-546%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get [B]w = 21[/B].
This means l = 21 + 5.
[B]l = 26[/B]

A researcher believed that there was a difference in the amount of time boys and girls at 7th grade

A researcher believed that there was a difference in the amount of time boys and girls at 7th grade studied by using a two-tailed t test. Which of the following is the null hypothesis?
a. Mean of hours that boys studied per day was equal to mean of hours that girls studied per day
b. Mean of hours that boys studied per day was greater than mean of hours that girls studied per day
c. Mean of hours that boys studied per day was smaller than mean of hours that girls studied per day
d. Mean of hours that boys studied per day was smaller than or equal to mean of hours that girls studied per day
[B]a. Mean of hours that boys studied per day was equal to mean of hours that girls studied per day[/B]
Reason is that in hypothesis testing, you take a position other than what is assumed or what is being tested as the null hypothesis

A researcher posed a null hypothesis that there was no significant difference between boys and girls

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 120 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 6.0. What's the absolute value of the difference between means?
|70 -65| = |5| = 5

A researcher posed a null hypothesis that there was no significant difference between boys and girls

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 5.0. What is the standard error of the difference in means?
[B]0.707106781187[/B] using our [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+100&xbar1=70&stdev1=5&n2=+100&xbar2=65&stdev2=5&conf=+99&pl=Hypothesis+Test']difference of means calculator[/URL]

A researcher posed a null hypothesis that there was no significant difference between boys and girls

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 5.0. What's the t-value (two-tailed) for the null hypothesis that boys and girls have the same test scores?
t = 7.07106781187 using our [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+100&xbar1=70&stdev1=5&n2=+100&xbar2=65&stdev2=5&conf=+99&pl=Hypothesis+Test']difference of means calculator[/URL]

A restaurant is going to raise all their prices by 7%. If the current price of an item is p dollars

A restaurant is going to raise all their prices by 7%. If the current price of an item is p dollars, write an expression for the price after the increase.
A 7% increase on price means we multiply the current price of p by 1.07. So our algebraic expression is:
[B]1.07p[/B]

A river is rising at a rate of 3 inches per hour. If the river rises more than 2 feet, it will excee

A river is rising at a rate of 3 inches per hour. If the river rises more than 2 feet, it will exceed flood stage. How long can the river rise at this rate without exceeding flood stage?
Let the number of inches be i. Remember 12 inches to a foot, so we have 2 feet = 12*2 = 24 inches.
[LIST]
[*]Inequality: 3i <= 24. (since more than means the river can go [U]up to[/U] 2 feet or 24 inches
[/LIST]
To solve the inequality for I, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3i%3C%3D24&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]I <= 8
This means after 8 hours, the river will flood[/B]

A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of

A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of the coaster after the first descent.
90 feet above and then we descend 105 feet, meaning we subtract:
90 - 105 = -15.
We read this [B]15 feet below ground level[/B]

A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of

A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of the roller coaster after the first descent.
90 feet above ground level is written as +90
Descending 105 feet means we subtract 105 feet to get:
+90 - 105 = [B]-15 or 15 feet below ground level[/B]

A roller coaster car carriers 32 people every 10 minutes there are 572 people in line in front of Ru

A roller coaster car carriers 32 people every 10 minutes there are 572 people in line in front of Ruben how long will it take for Ruben to ride the roller coaster
527/32 = 17.875
Which means on the 18th ride, Ruben will get a seat.
18 rides * 10 minutes per ride = [B]180 minutes, or 3 hours.[/B]

A sample of 71 college students yields a mean annual income of $3595. Assuming that ? = $898, find t

A sample of 71 college students yields a mean annual income of $3595. Assuming that ? = $898, find the margin of error in estimating µ at the 99% level of confidence

A sample of 71 college students yields a mean annual income of $3595. Assuming that ? = $898, find t

A sample of 71 college students yields a mean annual income of $3595. Assuming that ? = $898, find the margin of error in estimating µ at the 99% level of confidence

A school theater group is selling candy to raise funds in order to put on their next performance. Th

A school theater group is selling candy to raise funds in order to put on their next performance. The candy cost the group $0.20 per piece. Plus, there was a $9 shipping and handling fee. The group is going to sell the candy for $0.50 per piece. How many pieces of candy must the group sell in order to break even?
[U]Set up the cost function C(p) where p is the number of pieces of candy.[/U]
C(p) = Cost per piece * p + shipping and handling fee
C(p) = 0.2p + 9
[U]Set up the Revenue function R(p) where p is the number of pieces of candy.[/U]
R(p) = Sale price * p
R(p) = 0.5p
Break-even means zero profit or loss, so we set the Cost Function equal to the Revenue Function
0.2p + 9 = 0.5p
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B9%3D0.5p&pl=Solve']type it in our math engine[/URL] and we get:
p = [B]30[/B]

A secret number is added to 6. The total is multiplied by 5 to get 50. What is the secret number?

A secret number is added to 6. The total is multiplied by 5 to get 50. What is the secret number?
Take this algebraic expression in pieces:
[LIST]
[*]Let the secret number be n.
[*]Added to means we add 6 to n: n + 6
[*]The total is multiplied by 5: 5(n + 6)
[*]The phrase [I]to get[/I] means equal to, so we set 5(n + 6) equal to 50
[/LIST]
5(n + 6) = 50
To solve this equation for n, we type it in our search engine and we get:
n = [B]4[/B]

A Septon said that he has 3 eyes. Does that mean he really has 3 eyes in base 10?

A Septon said that he has 3 eyes. Does that mean he really has 3 eyes in base 10?
3 in base 7 is:
3 * 7^0 = 3 * 1 = 3
So [B]Yes[/B]

A set of 19 scores has a mean of 6.3. A new score of 8 is then included in the data set. What is th

A set of 19 scores has a mean of 6.3. A new score of 8 is then included in the data set. What is the new mean?
We know the mean formula is:
Sum of scores / Number of Scores = Mean
We're given mean = 6.3 and number of scores = 19, so we have:
Sum of scores / 19 = 6.3
Cross multiply:
Sum of scores = 19 * 6.3
Sum of scores = 119.7
Now a new score is added of 8, so we have:
Sum of scores = 119.7 + 8 = 127.7
Number of scores = 19 + 1 = 20
So our new mean is:
Mean = Sum of scores / Number of Scores
Mean = 127.7/20
Mean = [B]6.385[/B]
[COLOR=rgb(0, 0, 0)][SIZE=5][FONT=arial][B][/B][/FONT][/SIZE][/COLOR]

A square of an integer is the integer. Find the integer.

A square of an integer is the integer. Find the integer.
Let the integer be n. The square means we raise n to the power of 2, so we have:
n^2 = n
Subtract n from each side:
n^2 - n = n - n
n^2 - n = 0
Factoring this, we get:
n(n - 1) = 0
So n is either [B]0 or 1[/B].

A store had 600 pounds of feed. After delivering equal amounts to 4 farmers, there are 60 pounds lef

A store had 600 pounds of feed. After delivering equal amounts to 4 farmers, there are 60 pounds left. How many pounds did each farmer receive?
If there were 60 pounds left, then the store had 600 - 60 = 540 pounds delivered.
540 pounds delivered in equal amounts to 4 farmers means each farmer got:
540/4 = [B]135 pounds of feed[/B]

A store is offering a 11% discount on all items. Write an equation relating the final price

A store is offering a 11% discount on all items. Write an equation relating the final price
11% discount means we pay 100% - 11% = 89% of the full price. Since 89% as a decimal is 0.89. With a final price f and an original price p, we have:
[B]F = 0.89p[/B]

A store is offering a 18% discount on all items. Write an equation relating the sale price S for an

A store is offering a 18% discount on all items. Write an equation relating the sale price S for an item to its list price L.
18% discount means we subtract 18% (0.18) as a decimal, from the 100% of the price:
S = L(1 - 0.18)
[B]S = 0.82L[/B]

A store sells books for 50% off on Sundays. The store advertises that on Easter Sunday the store tak

A store sells books for 50% off on Sundays. The store advertises that on Easter Sunday the store takes an additional 25% off. What would a pile of books cost on Easter Sunday that normally sell for $100 on a Thursday?
50% off means we'd pay 100% - 50% = 50%
An additional 25% off means we'd pay 100% - 25% = 75%
Build this percentage paid stack below
100 * 50% * 75% = [B]37.50[/B]

A student and the marine biologist are together at t = 0. The student ascends more slowly than the m

A student and the marine biologist are together at t = 0. The student ascends more slowly than the marine biologist. Write an equation of a function that could represent the student's ascent. Please keep in mind the slope for the marine biologist is 12.
Slope means rise over run.
In this case, rise is the ascent distance and run is the time.
12 = 12/1, so for each second of time, the marine biologist ascends 12 units of distance
If the student ascends slower, than the total distance gets reduced by an unknown factor, let's call it c. So we have the student's ascent function as:
[B]y(t) = 12t - c[/B]

A student posed a null hypothesis that during the month of September, the mean daily temperature of

A student posed a null hypothesis that during the month of September, the mean daily temperature of Boston was the same as the mean daily temperature of New York. His alternative hypothesis was that mean temperatures in these two cities were different. He found the P value of his null hypothesis was 0.56. Thus, he could conclude:
a. In September, Boston was colder than New York
b. In September, Boston was warmer than New York
c. He may reject the null hypothesis
d. He failed to reject the null hypothesis
[B]d. He failed to reject the null hypothesis[/B]
[I]Higher p value tells us we cannot reject the null hypothesis[/I]

A submarine at an elevation of -185 meters descends to 3 times that elevation. Then, it elevates 90

A submarine at an elevation of -185 meters descends to 3 times that elevation. Then, it elevates 90 meters. What is the submarines new elevation?
3 times the current elevation is:
3 * -185 = -555
Elevating 90 meters means we have a positive change:
-555 + 90 = [B]-465[/B]

A submarine dove 132.58 meters to reach a resting depth of 700 meter below sea level. What was it's

A submarine dove 132.58 meters to reach a resting depth of 700 meter below sea level. What was it's original depth
Below sea level is a negative amount. So they end up at -700.
To go back up toward sea level, we'd be at:
-700 + 132.58 = -567.42
Negative numbers mean below sea level, so the original depth was [B]567.42 meters below sea level[/B]

A submarine hovers at 240 meters below sea level. If it descends 160 meters and then ascends 390 met

A submarine hovers at 240 meters below sea level. If it descends 160 meters and then ascends 390 meters, what is its new position?
240 meters below sea level means a negative number, so we start with:
-240
Descending 160 meters means our depth decreases, so we subtract:
-240 - 160 = -400
Ascends means our depth increases, so we add:
-400 + 390 = [B]-10 or 10 feet below sea level[/B]

a submarine is 450 feet below sea level. It descends 300 feet. What is its new position?

a submarine is 450 feet below sea level. It descends 300 feet. What is its new position?
We start at 450 feet below sea level. We descend another 300 feet, so we're now at:
-450 - 300 = -750
Negative depth means below sea level, so the submarine is at [B]750 feet below sea level[/B]

A submarine sits at –300 meters in relation to sea level. Then it descends 115 meters. What is its n

A submarine sits at –300 meters in relation to sea level. Then it descends 115 meters. What is its new position in relation to sea level?
Descending means we go down in sea level, so we subtract:
-300 - 115 = [B]-415 or 415 meters below sea level[/B]

A survey was conducted that asked 1007 people how many books they had read in the past year. Results

A survey was conducted that asked 1007 people how many books they had read in the past year. Results indicated that x overbarequals11.3 books and sequals16.6 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval.
x bar = 11.3
s = 16.6
n = 1007
[URL='https://www.mathcelebrity.com/normconf.php?n=1007&xbar=11.3&stdev=16.6&conf=90&rdig=4&pl=Not+Sure']We use our confidence interval calculator[/URL] and get [B]10.4395 < u < 12.1605[/B].
[B][I]We interpret this as:
If we repeated experiments, the proportion of such intervals containing u would be 90%[/I][/B]

A sweater costs $40. That is 5 times as much as a shirt. What is the price of the shirt?

A sweater costs $40. That is 5 times as much as a shirt. What is the price of the shirt?
State this as an equation. Let the price of the shirt be s. 5 times as much means we multiply s by 5:
5s = 40
[URL='https://www.mathcelebrity.com/1unk.php?num=5s%3D40&pl=Solve']Type this equation into the search engine[/URL], we get:
s = [B]8[/B]

A tank has 800 liters of water. 12ml of water leaks from the tank every second.how long does it take

A tank has 800 liters of water. 12ml of water leaks from the tank every second.how long does it take for the tank to be empty
Assumptions and givens:
[LIST]
[*]Let the number of seconds be s.
[*]An empty tank means 0 liters of water.
[*]Leaks mean we subtract from the starting volume.
[/LIST]
We have the following relation:
800 - 12s = 0
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=800-12s%3D0&pl=Solve']type it in our search engine[/URL] and we get:
s = 66.67 seconds

A times r squared multiplied by h

A times r squared multiplied by h
r squared means we raise r to the power of 2:
r^2
a times r squared:
ar^2
Multiplied by h:
[B]ahr^2[/B]

a total of one and x is less than 5

a total of one and x is less than 5
A total of one and x means we add x to 1:
1 + x
We set up an inequality, where 1 + x is less than (<) 5
[B]1 + x < 5[/B]

A town has a population of 50,000. Its rate increases 8% every 6 months. Find the population after 4

A town has a population of 50,000. Its rate increases 8% every 6 months. Find the population after 4 years.
Every 6 months means twice a year. So we have 4 years * twice a year increase = 8 compounding periods.
Our formula for compounding an initial population P at time t is P(t) at a compounding percentage i:
P(t) = P * (1 + i)^t
Since 8% is 0.08 as a decimal and t = 4 *2 = 8, we have:
P(8) = 50000 * (1.08)^8
P(8) = 50000 * 1.85093
P(8) = 92,546.51
Since we can't have a partial person, we round down to [B]92,545[/B]

A toy factory makes 5,000 teddy bears per day. The supervisor randomly selects 10 teddy bears from a

A toy factory makes 5,000 teddy bears per day. The supervisor randomly selects 10 teddy bears from all 5,000 teddy bears and uses this sample to estimate the mean weight of teddy bears and the sample standard deviation. How many degrees of freedom are there in the estimate of the standard deviation?
DF = n - 1
DF = 10 - 1
[B]DF = 9[/B]

A train leaves San Diego at 1:00 PM. A second train leaves the same city in the same direction at 3

A train leaves San Diego at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels 30mph faster than the first. If the second train overtakes the first at 6:00 PM, what is the speed of each of the two trains?
Distance = Rate x Time
Train 1:
d = rt
t = 1:oo PM to 6:00 PM = 5 hours
So we have d = 5r
Train 2:
d = (r + 30)t
t = 3:oo PM to 6:00 PM = 3 hours
So we have d = 3(r + 30)
Set both distances equal to each other since overtake means Train 2 caught up with Train 1, meaning they both traveled the same distance:
5r = 3(r + 30)
Multiply through:
3r + 90 = 5r
[URL='https://www.mathcelebrity.com/1unk.php?num=3r%2B90%3D5r&pl=Solve']Run this equation through our search engine[/URL], and we get [B]r = 45[/B]. This is Train 1's Speed.
Train 2's speed = 3(r + 30).
Plugging r = 45 into this, we get 3(45 + 30).
3(75)
[B]225[/B]

A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selec

A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ test, what is the probability that the sample mean scores will be between 85 and 125 points?
For x = 125, our z-score and probability is seen [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+125&mean=+105&stdev=+20&n=+1&pl=P%28X+%3C+Z%29']here[/URL]
Z = 1
P(x < 1) = 0.841345
For x = 85, our z-score and probability is seen [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+85&mean=+105&stdev=+20&n=+1&pl=P%28X+%3C+Z%29']here[/URL]
Z = -1
P(x < -1) = 0.158655
So what we want is the probability between these values:

0.841345 - 0.158655 = [B]0.68269[/B]

0.841345 - 0.158655 = [B]0.68269[/B]

a variable tripled less 40

a variable tripled less 40
[I]A variable[/I] means we pick an arbitrary variable, let's call it x
x
Tripled means we multiply by 3
3x
Less 40 means we subtract 40:
[B]3x - 40[/B]

A varies directly as B and inversely as C.

A varies directly as B and inversely as C.
There exists a constant k such that:
[B]a = kb/c
[/B]
Inversely means we divide by and directly means we multiply by

a varies directly with b and inversely with c

a varies directly with b and inversely with c
Direct variation means we multiply.
Inverse variation means we divide.
There exists a constant k such that:
[B]a = kb/c[/B]

a varies inversely with b, c and d

a varies inversely with b, c and d
Varies inversely means we divide. Given a constant, k, we have:
[B]a = k/bcd[/B]

A vehicle purchased for $25,000 depreciates at a constant rate of 5%. Determine the approximate valu

A vehicle purchased for $25,000 depreciates at a constant rate of 5%. Determine the approximate value of the vehicle 11 years after purchase. Round to the nearest whole dollar.
Depreciation at 5% means it retains 95% of the value. Set up the depreciation equation to get Book Value B(t) at time t.
B(t) = $25,000 * (1 - 0.05)^t
Simplifying, this is:
B(t) = $25,000 * (0.95)^t
The problem asks for B(11)
B(11) = $25,000 * (0.95)^11
B(11) = $25,000 * 0.5688
B(11) = [B]$14,220[/B]

A woman dies at the age of 100 and her son is 35 years old how old was she when she gave birth to hi

A woman dies at the age of 100 and her son is 35 years old how old was she when she gave birth to him.
35 years ago meant she was 100 - 35 = [B]65 years[/B].

A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and

A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and walked back to the starting point along the same path. She walks 4mph on level ground, 3 mph uphill, and 6 mph downhill. Find the distance she walked.
Hint: Think about d = rt, which means that t = d/r. Think about each section of her walk, what is the distance and the rate. You know that the total time is 5 hours, so you know the sum of the times from each section must be 5.
Let Level distance = L and hill distance = H. Add the times it took for each section of the walk:
L/4 + H /3 + H/6 + L/4 = 5
The LCD of this is 12 from our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=3&num3=6&pl=LCM']LCD Calculator[/URL]
[U]Multiply each side through by our LCD of 12[/U]
3L + 4H + 2H + 3L = 60
[U]Combine like terms:[/U]
6L + 6H = 60
[U]Divide each side by 3:[/U]
2L + 2H = 20
The woman walked [B]20 miles[/B]

A young dad, who was a star football player in college, set up a miniature football field for his fi

A young dad, who was a star football player in college, set up a miniature football field for his five-year-old young daughter, who was already displaying an unusual talent for place-kicking. At each end of the mini-field, he set up goal posts so she could practice kicking extra points and field goals. He was very careful to ensure the goalposts were each straight up and down and that the crossbars were level. On each set, the crossbar was six feet long, and a string from the top of each goalpost to the midpoint between them on the ground measured five feet. How tall were the goalposts? How do you know this to be true?
The center of each crossbar is 3 feet from each goalpost. We get this by taking half of 6, since midpoint means halfway.
Imagine a third post midway between the two goal posts. It has the same height as the two goalposts.
From the center post, the string from the top of a goalpost to the base of the center post, and half the crossbar form and right triangle with hypotenuse 5 feet and one leg 3 feet.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=3&hypinput=5&pl=Solve+Missing+Side']Using the Pythagorean Theorem[/URL], the other leg -- the height of each post -- is 4 feet.

Adam has 20 sweets he eats a quarter of them how many does he have left?

Adam has 20 sweets he eats a quarter of them how many does he have left?
A quarter means 1/4. There's 2 ways you can approach this problem.
[B][U]Approach #1:[/U][/B]
Adam eats a quarter, or 1/4 of the sweets. So he eats:
20 * 1/4 = 5
Remaining sweets = Total Apples - Eaten Apples
Remaining sweets = 0 - 5
Remaining sweets= 15
[U][B]Approach #2:[/B][/U]
If Adam eats 1/4 of the sweets, this means he has:
1 - 1/4 sweets remaining.
Since 1 equals 4/4, we have:
4/4 - 1/4 = 3/4
Therefore, he has 20 * 3/4 sweets remaining.
This is 60/4, or [B]15[/B]

Add 3 to 6, subtract w from the result, then triple what you have

Add 3 to 6, subtract w from the result, then triple what you have
Add 3 to 6;
3 + 6
Subtract w from the result;
3 + 6 - w
Triple what you have (means multiply by 3):
[B]3(3 + 6 - w)[/B]

Add 5 to the sum of 2x and y

Add 5 to the sum of 2x and y
The sum of 2x and y means we add y to 2x:
2x + y
Add 5
[B]2x + y + 5[/B]

add c and b, multiply the result by a, then double what you have

add c and b, multiply the result by a, then double what you have
Take this algebraic expression in pieces:
[LIST]
[*]add c and b: c + b
[*]Multiply the result by a: a(c + b)
[*]Double what you have means take the last step result, and multiply it by 2:
[/LIST]
[B]2a(c + b)[/B]

add c to b, subtract d from the result, then double what you have

add c to b, subtract d from the result, then double what you have
Add c to b:
b + c
Subtract d from the result:
b + c - d
Double what you have means multiply the entire expression by 2:
[B]2(b + c - d)[/B]

add d to 5, raise the result to the 9th power, then subtract what you have from 2

add d to 5, raise the result to the 9th power, then subtract what you have from 2
Add d to 5:
d + 5
Raise the result to the 9th power means we raise (d + 5) to the 9th power using an exponent:
(d + 5)^9
the subtract what we have (the result) from 2:
[B]2 - (d + 5)^9[/B]

add f and g, then triple the result

add f and g, then triple the result
Add f and g
f + g
Triple the result means we multiply f + g by 3
[B]3(f + g)[/B]

Add q and t, subtract s from the result, then multiply by r

Add q and t, subtract s from the result, then multiply by r
Take this algebraic expression in parts:
[LIST]
[*]Add q and t: q + t
[*]Subtract s from the result: q + t - s
[*]Multiply by r means we multiply the entire expression by r:
[/LIST]
[B]r(q + t - s)[/B]

add r and q, divide the result by s, then triple what you have

add r and q, divide the result by s, then triple what you have
Add r and q:
r + q
Divide the result by s. The result above is r + q, so we have:
(r + q)/s
Triple what you have means we multiply the expression above by 3:
[B]3(r + q)/s[/B]

add r to 3, triple the result, then divide s by what you have

add r to 3, triple the result, then divide s by what you have
Take this algebraic expression in parts:
[LIST=1]
[*]Add r to 3: 3 + r
[*]Triple the result means multiply the result above by 3: 3(3 + r)
[*]Then divide s by what you have. [B]s/3(3 + r)[/B]
[/LIST]

add s and t, multiply the result by u, then add r to what you have

add s and t, multiply the result by u, then add r to what you have.
Take this algebraic expression in 3 parts:
[LIST=1]
[*]Add s and t: s + t
[*]Multiply the result by u means me multiply (s + t) times u: u(s + t)
[*]Then add r to what you have. [I]what you have means the result in #2.[/I]
[/LIST]
[B]u(s + t) + r[/B]

add s to r, double the result

add s to r, double the result
Add s to r:
r + s
Double the result means multiply r + s by 2:
[B]2(r + s)[/B]

add t and r and double the result

add t and r and double the result
Add t and r:
t + r
Double the result means multiply by 2:
[B]2(t + r)[/B]

add u and t divide s by the result then triple what you have

add u and t divide s by the result then triple what you have
Take this algebraic expression in parts:
[LIST]
[*]Add u and t: u + t
[*]Divide s by the result: s/(u + t)
[*]Triple what you have means we you multiply s/(u + t) by 3
[/LIST]
[B]3s/(u + t)[/B]

Add u and w, triple the result, then add what you have to v

Add u and w, triple the result, then add what you have to v
Add u and w
u + w
Triple the result means multiply the sum of u and w by 3:
3(u + w)
Then add what you have to v:
[B]v + 3(u + w)[/B]

add w to u, triple the result, then add v to what you have

add w to u, triple the result, then add v to what you have
Take this algebraic expression in parts:
[LIST]
[*]add w to u: w + u
[*]triple the result means we multiply w + u by 3: 3(w + u)
[*]Then add v to what you have
[/LIST]
[B]3(w + u) + v[/B]

add x and 3; then multiply by y

Add x and 3
x + 3
Then multiply by y (they mean the total)
[B]y(x + 3)[/B]

After 20 minutes, Juan had completed 12 questions, which is 0.7 of his assignment. What percent of t

After 20 minutes, Juan had completed 12 questions, which is 0.7 of his assignment. What percent of the assignment has Juan NOT completed?
We know that 0.7 as a percentage is:
0.7 * 100% = 70%
In this problem, we have either or. Juan either completed the question or DID NOT complete the question.
100% of questions has one of two classifications - Completed or not completed.
This means Juan did not complete the following amount of questions:
100% - 70% = [B]30%[/B]

After John worked at a job for 10 years, his salary doubled. If he started at $x, his salary after 1

After John worked at a job for 10 years, his salary doubled. If he started at $x, his salary after 10 years is _____.
Doubled means we multiply by 2, so we have a new salary in 10 years of:
[B]2x[/B]

Age now and then

Let j be Jacob's age and c be Clinton's age. We have:
[LIST=1]
[*]j = 4c
[*]j - 8 = 9(4c - 8)
[/LIST]
Substitute (1) into (2)
(4c) - 8 = 36c - 72
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=4c-8%3D36c-72&pl=Solve']equation solver,[/URL] we get c = 2
Which means j = 4(2) = 8
8 years ago, Jacob was just born. Which means Clinton wasn't even born yet.

Age now and then

I read it wrong before. Here you go:
Jacob is 4 times the age of Clinton. 8 years ago Jacob was 10 times the age of Clinton. How old are they now and how old were they 8 years ago?
[LIST=1]
[*]j = 4c
[*]j - 8 = 10(c - 8)
[/LIST]
Substitute (1) into (2)
(4c) - 8 = 10c - 80
[URL='http://www.mathcelebrity.com/1unk.php?num=4c-8%3D10c-80&pl=Solve']Equation solver[/URL] gives us [B]c = 12[/B] which means j = 4(12) = [B]48[/B].
8 years ago,[B] j = 40 and c = 4[/B] which holds the 10x rule.

Age now and then

[QUOTE="math_celebrity, post: 1163, member: 1"]I read it wrong before. Here you go:
Jacob is 4 times the age of Clinton. 8 years ago Jacob was 10 times the age of Clinton. How old are they now and how old were they 8 years ago?
[LIST=1]
[*]j = 4c
[*]j - 8 = 10(c - 8)
[/LIST]
Substitute (1) into (2)
(4c) - 8 = 10c - 80
[URL='http://www.mathcelebrity.com/1unk.php?num=4c-8%3D10c-80&pl=Solve']Equation solver[/URL] gives us [B]c = 12[/B] which means j = 4(12) = [B]48[/B].
8 years ago,[B] j = 40 and c = 4[/B] which holds the 10x rule.[/QUOTE]
Thank you, I see what I did wrong!

Alan is y years old. Beth is 3 years old than Alan.Write an expression for how old Beth is?

Alan is y years old. Beth is 3 years old than Alan.Write an expression for how old Beth is?
The word [I]older[/I] means we add 3 to Alan's age of y. So Beth's age is:
[B]y + 3[/B]

Alberto’s salary was $1500 greater than 5 times Nick’s salary. Write an equation stating Alberto’s a

Alberto’s salary was $1500 greater than 5 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y.
Let x be Alberto's salary. Let y be Nick's salary. We have:
Let's break this down:
[LIST=1]
[*]5 times Nick's salary (y), means we multiply the variable y by 5
[*]$1500 greater means we add $1500 to 5y
[/LIST]
[B]x = 5y - 1500[/B]

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s a

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y.
If Alberto's salary is x and Nick's is y, we have:
[B]x = 4y + 2000 [/B](since greater than means we add)

Alec had c caramels. Then, Alecs sister took 85 of the caramels. Choose the expression that shows th

Alec had c caramels. Then, Alecs sister took 85 of the caramels. Choose the expression that shows the number of caramels Alec has left.
Alec starts with c caramels. His sister took 85. The word [I]took[/I] means subtract, so we have:
[B]c - 85[/B]

Alfred carries a load of 12 kilograms. He finds it heavy so he removes a weight of 4 kilograms. What

Alfred carries a load of 12 kilograms. He finds it heavy so he removes a weight of 4 kilograms. What is the weight of the remaining load?
Removes means he subtract weight. So we have:
12 kilograms - 4 kilograms = [B]8 kilograms[/B]

algebraic expression for the sum of x and double the value of y

algebraic expression for the sum of x and double the value of y
Double the value of y means we multiply y by 2:
2y
The sum of x and 2y means we add 2y to x:
[B]x + 2y[/B]

algexpress: letthefirstnumberequalx.thesecondnumberis3morethantwicethefirstnumber.expressthesecondnu

Let the first number equal x. The second number is 3 more than twice the first number. Express the second number in terms of the first number x.
[LIST]
[*]Let the second number be y.
[*]Twice means multiply by 2
[*]3 more than means we add 3
[/LIST]
So we have the following algebraic expression:
[B]y = 2x + 3[/B]

Ali runs each lap in 6 minutes. He will run at least 11 laps today. What are the possible numbers of

Ali runs each lap in 6 minutes. He will run at least 11 laps today. What are the possible numbers of minutes he will run today?
Let m be the number of minutes. The phrase [I]at least[/I] means an inequality, also known as greater than or equal to. So we have:
m >= 11*6
[B]m >= 66
You can read this as Ali will run 66 or more minutes today. Or at least 66 minutes. Or greater than or equal to 66 minutes[/B]

Alicia deposited $41 into her checking account. She wrote checks for $31 and $13. Now her account ha

Alicia deposited $41 into her checking account. She wrote checks for $31 and $13. Now her account has a balance of $81. How much did she have in her account to start with?
We start with a balance of b.
Depositing 41 means we add to the account balance:
b + 41
Writing checks for 31 and 13 means we subtract from the account balance:
b + 41 - 31 - 13
The final balance is 81, so we set b + 41 - 31 - 13 equal to 81:
b + 41 - 31 - 13 = 81
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B41-31-13%3D81&pl=Solve']type this equation into our math engine[/URL] and we get:
b = [B]84[/B]

Alisha is 5 years younger than her brother. If the age of her brother is y years then age of Alisha

Alisha is 5 years younger than her brother. If the age of her brother is y years then age of Alisha in terms of her brother
Younger means we subtract. If her brother is y years of age, then Alisha is:
[B]y - 5[/B]

Aliyah has $24 to spend on 7 pencils. After buying them she had $10. How much did each pencil cost?

Aliyah has $24 to spend on 7 pencils. After buying them she had $10. How much did each pencil cost?
Let the cost of each pencil be p. The phrase [I]leftover[/I] means we add to the cost of the pencils after buying them. We're given the equation:
7p + 10 = 24
To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B10%3D24&pl=Solve']type this equation into our search engine[/URL] and we get:
p = [B]2[/B]

all real numbers y greater than or equal to 12

all real numbers y greater than or equal to 12
Greater than or equal to means we use the sign >=
[B]y >= 12[/B]

Alvin planted t fewer trees than Danielle. Danielle planted 56 trees. Write an expression that shows

Alvin planted t fewer trees than Danielle. Danielle planted 56 trees. Write an expression that shows how many trees Alvin planted.
The word [I]fewer[/I] means we subtract, so we have Alvin's tree planting of:
[B]56 - t[/B]

Amanda runs each lap in 4 minutes. She will run less than 44 minutes today. What are the possible nu

Amanda runs each lap in 4 minutes. She will run less than 44 minutes today. What are the possible number of laps she will run today?
Notes for this problem:
[LIST]
[*]Let laps be l.
[*]Lap time = Time per lap * number of laps (l)
[*]Less than means we have an inequality using the < sign
[/LIST]
We have the inequality:
4l < 44
To solve this inequality for l, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4l%3C44&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get:
[B]l < 11[/B]

Amanda spent 2/5 of her time after school doing homework and ¼ of her remaining time riding her bike

Amanda spent 2/5 of her time after school doing homework and ¼ of her remaining time riding her bike. If she rode her bike for 45 minutes in a week, how much time did she devote to homework in the same week
If Amanda spent 2/5 of her time after school doing homework, she has 1 - 2/5 time left over.
We convert 1 to a fraction using a denominator of 5, we get:
5/5 - 2/5 = 3/5
And Amanda spent 1/4 of 3/5 of her time bike riding, which means she spent:
1(3)/4(5) = 3/20 of her time.
If the total time after school is t, we have:
3t/20 = 45
[URL='https://www.mathcelebrity.com/prop.php?num1=3t&num2=45&den1=20&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Typing in 3t/20 = 45 to our search engine[/URL], we get t = 300.
So Amanda has 300 total minutes after school, which means she spent 2/5(300) = [B]120 minutes (2 hours)[/B] doing homework.

An 8 yard gain and a 3 yard loss results in what kind of gain or loss?

An 8 yard gain and a 3 yard loss results in what kind of gain or loss?
[LIST=1]
[*]Start with 0 yards
[*]Gains means we add, so we have 0 + 8 = 8
[*]Losses mean we subtract, so we have 8 - 3 = 5
[/LIST]
The overall result is a [B]5 yard gain[/B]

An analysis of the final test scores for Managerial Decision Making Tools reveals the scores follow

An analysis of the final test scores for Managerial Decision Making Tools reveals the scores follow the normal probability distribution. The mean of the distribution is 75 and the standard deviation is 8. The instructor wants to award an "A" to students whose score is in the highest 10 percent. What is the dividing point for those students who earn an "A"?
Top 10% is equivalent to the 90th percentile.
Using our [URL='http://www.mathcelebrity.com/percentile_normal.php?mean=+75&stdev=8&p=+90&pl=Calculate+Percentile']percentile calculator[/URL], the 90th percentile cutoff point is [B]85.256[/B]

An angle is 30 degrees less than 5 times it's complement. Find the angle.

An angle is 30 degrees less than 5 times it's complement. Find the angle.
Let the angle be a. The complement of a is 90 - a. We're given the following equation:
a = 5(90 - a) - 30 <-- Less means we subtract
Multiplying though, we get:
a = 450 - 5a - 30
a = 420 - 5a
[URL='https://www.mathcelebrity.com/1unk.php?num=a%3D420-5a&pl=Solve']Typing this equation into our search engine[/URL], we get:
a =[B] 70[/B]

An eccentric millionaire decided to give away $1,000,000 if Janelle took one die and rolled a "4". H

An eccentric millionaire decided to give away $1,000,000 if Janelle took one die and rolled a "4". He wanted Janelle to have a better than 1 in 6 chance of winning, so before she rolled the die he told her that she could roll the die 3 times. If any roll was a "4", she would win the million dollars. What are Janelle's chances of winning the million dollars?
Chance of winning each roll is 1/6. Which means the chances of losing each roll are 1 - 1/6 = 5/6
Calculate the probability of 3 straight losing rolls:
P(Lose) = P(Loser) * P(Loser) * P(Loser) = 5/6 * 5/6 * 5/6 = 125/216
P(Win) = 1 - P(Lose)
P(Win) = 1 - 125/216
P(Win) = 216/216 -125/216
P(Win) = [B]91/216[/B]

An elevator has a maximum weight of 3000 pounds. How many 150-pound people can safely ride the eleva

An elevator has a maximum weight of 3000 pounds. How many 150-pound people can safely ride the elevator? (Use "p" to represent the number of people)
Maximum means less than or equal to. We have the inequality:
150p <= 3000
To solve this inequality for p, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=150p%3C%3D3000&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]p <= 20[/B]

An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumpin

An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumping it on the people below. One bucket dumps water every 18 minutes. The other bucket dumps water every 21 minutes. It is currently 1:15 P.M. and both buckets dumped water 5 minutes ago. Find the next two times that both buckets dump water at the same time.
We want to find the Least Common Multiple between 18 minutes and 21 minutes. This shows us when both bucket dumping cycles happen simultaneously. So we[URL='https://www.mathcelebrity.com/gcflcm.php?num1=18&num2=21&num3=&pl=GCF+and+LCM'] type in LCM(18,21) into our search engine and we get[/URL]:
LCM(18, 21) = 126
This means, in 126 minutes, both buckets will dump water. Since 60 minutes is in an hour, we find out how many full hours we have. To find the full hours and remainder, we [URL='https://www.mathcelebrity.com/modulus.php?num=126mod60&pl=Calculate+Modulus']type in 126 mod 60[/URL] into our search engine and we get:
6. This means 126 minutes is 2 hours and 6 minutes.
Find the next bucket dumping time:
[LIST=1]
[*]We start at 1:15 PM
[*]Add 2 hours and we get 3:15 PM
[*]Add 6 minutes and we get [B]3:21 PM[/B]
[/LIST]

An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three tim

An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three times as long as the shortest side. The remaining two sides are each 8m longer than the shortest side. The perimeter of the Pentagon is 79m. Find the length of each side of the Pentagon.
Let long sides be l. Let short sides be s. Let medium sides be m. We have 3 equations:
[LIST=1]
[*]2l + 2m + s = 79
[*]m = s + 8
[*]l = 3s
[/LIST]
Substitute (2) and (3) into (1):
2(3s) + 2(s + 8) + s = 79
Multiply through and simplify:
6s + 2s + 16 + s = 79
9s + 16 = 79
[URL='https://www.mathcelebrity.com/1unk.php?num=9s%2B16%3D79&pl=Solve']Using our equation calculator[/URL], we get [B]s = 7[/B].
This means from Equation (2):
m = 7 + 8
[B]m = 15
[/B]
And from equation (3):
l = 3(7)
[B]l = 21[/B]

An isosceles triangles non-congruent angle is 16 more than twice the congruent ones. What is the mea

An isosceles triangles non-congruent angle is 16 more than twice the congruent ones. What is the measure of all 3 angles?
Let the congruent angles measurement be c. And the non-congruent angle measurement be n. We're given:
[LIST=1]
[*]n = 2c + 16 <-- Twice means we multiply by 2, and more than means we add 16
[*]2c + n = 180 <-- Since the sum of angles in an isosceles triangle is 180
[/LIST]
Substitute (1) into (2):
2c + (2c + 16) = 180
Group like terms:
4c + 16 = 180
[URL='https://www.mathcelebrity.com/1unk.php?num=4c%2B16%3D180&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]c = 41[/B]
Substituting this value into Equation 1, we get
n = 2(41) + 16
n = 82 + 16
[B]n = 98[/B]

An ordinary fair die is rolled twice. The face value of the rolls is added together. Compute the pro

An ordinary fair die is rolled twice. The face value of the rolls is added together. Compute the probability of the following events: Event A: The sum is greater than 6. Event B: The sum is divisible by 5 or 6 or both.
[URL='http://www.mathcelebrity.com/2dice.php?gl=2&pl=6&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum greater than 6[/URL] = [B]7/12[/B]
Sum is divisible by 5 or 6 or both
This means a sum of 5, a sum of 6, a sum of 10, or a sum of 12.
[URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=5&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 5[/URL] = 1/9 or 4/36
[URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=6&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 6[/URL] = 5/36
[URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=10&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 10[/URL] = 1/12 or 3/36
[URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=12&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 12[/URL] = 1/36
Adding all these up, we get:
(4 + 5 + 3 + 1)/36
[B]13/36[/B]

Ana was y years old 7 years ago. Represent her age twenty years from now

Ana was y years old 7 years ago. Represent her age twenty years from now
twenty years from now, means we add 7 years to get to now and another 20 years to get to twenty years from now:
y + 7 + 20
[B]y + 27[/B]

Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What

Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What was the original number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it n.
[LIST]
[*]Start with n
[*]Add 20 to it: n + 20
[*]Double it means we multiply the expression by 2: 2(n + 20)
[*]Get an answer of 53: means an equation, so we set 2(n + 20) equal to 53
[/LIST]
2(n + 20) = 53
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=2%28n%2B20%29%3D53&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]6.5[/B]

Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community col

Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community college charges a $35 registration fee plus $375 per course, what is the greatest number of courses for which Angelica can register?
We set up the Tuition function T(c), where c is the number of courses:
T(c) = Cost per course * c + Registration Fee
T(c) = 35c + 375
The problem asks for the number of courses (c) where her tuition [I]cannot exceed[/I] $1000. The phrase [I]cannot exceed[/I] means less than or equal to, or no more than. So we setup the inequality for T(c) <= 1000 below:
35c + 375 <= 1000
To solve this inequality for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=35c%2B375%3C%3D1000&pl=Solve']type it in our search engine and we get[/URL]:
c <= 17.85
Since we cannot have fractional courses, we round down and get:
c[B] <= 17[/B]

are all integers whole numbers true or false

are all integers whole numbers true or false
[B]False
[/B]
[LIST]
[*]All whole numbers are integers but not all integers are whole numbers.
[*]Whole numbers are positive integers. Which means negative integers are not whole numbers
[*]-1 for instance is an integer, but not a whole number
[/LIST]

As a salesperson you will earn $600 per month plus a commission of 20% of sales. Find the minimum am

As a salesperson you will earn $600 per month plus a commission of 20% of sales. Find the minimum amount of sales you need to make in order to receive a total income of at least $1500 per month.
Let the amount of sales be s. The phrase [I]at least[/I] means greater than or equal to. Since 20% is 0.2, We want to know when:
0.20s + 600 >= 1500
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.20s%2B600%3E%3D1500&pl=Solve']type this inequality into our search engine to solve for s[/URL] and we get:
s >= [B]4500[/B]

As a salesperson, you are paid $50 per week plus $2 per sale. This week you want your pay to be at l

As a salesperson, you are paid $50 per week plus $2 per sale. This week you want your pay to be at least $100. What is the minimum number of sales you must make to earn at least $100?
Set up the inequality where s is the amount of sales you make:
50 + 2s >= 100
We use >= because the phrase [I]at least[/I] 100 means 100 or more
Subtract 50 from each side:
2s >= 50
Divide each side by 2
[B]s >= 25[/B]

As the sample size increases, we assume:

As the sample size increases, we assume:
a. ? increases
b. ? increases
c. The probability of rejecting a hypothesis increases
d. Power increases
[B]d. Power increases[/B]
[LIST]
[*]Power increases if the standard deviation is smaller.
[*]If the difference between the means is bigger, the power is bigger.
[*]Sample size also increases power
[/LIST]

Ashley deposited $4000 into an account with 2.5% interest, compounded semiannually. Assuming that no

Ashley deposited $4000 into an account with 2.5% interest, compounded semiannually. Assuming that no withdrawals are made, how much will she have in the account after 10 years?
Semiannual means twice a year, so 10 years * 2 times per year = 20 periods. We use this and [URL='https://www.mathcelebrity.com/compoundint.php?bal=4000&nval=20&int=2.50&pl=Semi-Annually']plug the numbers into our compound interest calculator[/URL] to get:
[B]$5,128.15[/B]

Assume that in your Abnormal Psychology class you have earned test scores of 74%, 78%, and 63%, and

Assume that in your Abnormal Psychology class you have earned test scores of 74%, 78%, and 63%, and only one test remains. If you need a mean score of 80% to earn a B for you final grade, is it possible for you to accomplish this? Assume there is no extra credit. Show work and explain why or why not. Hint: you're taking 4 tests total.
Using our [URL='https://www.mathcelebrity.com/missingaverage.php?num=74%2C78%2C63&avg=80&pl=Calculate+Missing+Score']missing average calculator with our 3 given scores and target average[/URL], we get:
A 4th score needed of 105.
Since the most you can score on an exam is 100, [B][I]this is impossible[/I][/B].

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.
a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?
b. What proportion of the vehicles would be going less than 50 mph?
c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion?
d. In what way do you think the actual distribution of speeds differs from a normal distribution?
a. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=65&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<65) = [B]22.66%[/B]
b. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+50&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<50) = [B]0.4269%[/B]
c. [URL='http://www.mathcelebrity.com/zcritical.php?a=0.9&pl=Calculate+Critical+Z+Value']Inverse of normal for 90% percentile[/URL] = 1.281551566
Plug into z-score formula: (x - 71)/8 = 1.281551566
[B]x = 81.25241252[/B]
d. [B]The shape/ trail differ because the normal distribution is symmetric with relatively more values at the center. Where the actual has a flatter trail and could be expected to occur.[/B]

At midnight in Winnipeg, the temperature was ?23°C. During the next 24 hours, the temperature rose 1

At midnight in Winnipeg, the temperature was ?23°C. During the next 24 hours, the temperature rose 12°C, then dropped 8°C. What was the final temperature?
We start with ?23°C
Temperatures rising 12°C mean we add:
-23 + 12 = -11
Temperatures dropping 8°C mean we subtract:
-11 - 8 = [B]-19°C[/B]

At midnight, the temperature was -15 degrees Fahrenheit. By the next morning, the temperature had go

At midnight, the temperature was -15 degrees Fahrenheit. By the next morning, the temperature had gone up to 20 degrees. What was the temperature then?
The student meant to say gone up 20 degrees.
We start with -15.
We add 20
-15 + 20 = [B]5[/B]

At night, the average temperature on the surface of Saturn is -150 C. During the day, the temperatur

At night, the average temperature on the surface of Saturn is -150 C. During the day, the temperature rises 27 C. What is the average temperature on the planet's surface during the day?
Rising temperature means we add, so we have:
-150+ 27 = [B]-123C[/B]

At the beginning of Jack's diet, he was 257 pounds. If he lost 3 pounds per week, find his weight af

At the beginning of Jack's diet, he was 257 pounds. If he lost 3 pounds per week, find his weight after 12 weeks.
A loss of weight means we subtract from Jack's current weight.
New Weight = Current Weight - Weight Loss per week * number of weeks
New Weight =257 - 3*12
New Weight =257 - 36
New Weight =[B] 221[/B]

At the end of the day, the temperature is -16°C. During the day it dropped 12°C. What was the temper

At the end of the day, the temperature is -16°C. During the day it dropped 12°C. What was the temperature in the morning? Write an equation to represent, then solve and verify your answer
let the starting temperature be s. If the temperature dropped, that means we subtract, so we have the following equation:
s - 12 = -16
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=s-12%3D-16&pl=Solve']type it in our search engine[/URL] and we get:
s = [B]-4[/B]

At the end of the week, Francesca had a third of her babysitting money left after spending $14.65 on

At the end of the week, Francesca had a third of her babysitting money left after spending $14.65 on a movie and popcorn and another $1.35 on a pen. How much did she earn babysitting?
Let the original amount of money earned for babysitting be b. We're given:
[LIST=1]
[*]Start with b
[*]Spending 14.65 for a movie means we subtract 14.65 from b: b - 14.65
[*]Spending 1.35 on a pen means we subtract another 1.35 from step 2: b - 14.65 - 1.35
[*]Francesca has a third of her money left. So we set step 3 equal to 1/3 of b
[/LIST]
b - 14.65 - 1.35 = b/3
Multiply each side of the equation by 3 to remove the fraction
3(b - 14.65 - 1.35) = 3b/3
3b - 43.95 - 4.05 = b
To solve this equation for b, [URL='https://www.mathcelebrity.com/1unk.php?num=3b-43.95-4.05%3Db&pl=Solve']we type it in our search engine[/URL] and we get:
b =[B] 24[/B]

b bags of beans there are 7 beans in each bag

b bags of beans there are 7 beans in each bag
This means we have 7 beans x b bags = 7b beans total beans.

b is decreased by twice a

b is decreased by twice a
Twice a means we multiply a by 2:
2a
b decreased by twice a means we subtract 2a from b:
[B]b - 2a[/B]

B out of 6 is 12

B out of 6 is 12
b out of 6:
b/6
The phrase [I]is[/I] means an equation, so we set b/6 equal to 12:
[B]b/6 = 12[/B]

b to the fifth power decreased by 7

b to the fifth power decreased by 7
Take this algebraic expression in steps:
[LIST]
[*]b to the fifth power: b^5
[*]Decreased by 7 means we subtract 7 from b^5: [B]b^5 - 7[/B]
[/LIST]

b varies directly as the sum of x and y

b varies directly as the sum of x and y
This is a direct variation problem.
Direct variation means there exists a constant k such that:
[B]b = k(x + y)[/B]

B varies jointly as u, v, and w

B varies jointly as u, v, and w
Varies jointly means we have a constant k such that:
[B]B = kuvw[/B]

b/3d - h = 343 for b

b/3d - h = 343 for b
A literal equation means we solve for one variable in terms of another variable or variables
Add h to each side to isolate the b term:
b/3d - h + h = 343 + h
Cancel the h's on the left side, we get:
b/3d = 343 + h
Cross multiply:
b = [B]3d(343 + h)[/B]

Barbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants co

Barbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants cost $4 each. If she plans to spend at least $20 and purchase less than 15 plants in total, create a system of equations or inequalities that model the situation. Define the variables you use.
[U]Define variables[/U]
[LIST]
[*]Let c be the number of corn plants
[*]Let p be the number of potato plants
[/LIST]
Since cost = price * quantity, we're given two inequalities:
[LIST=1]
[*][B]3p + 4c >= 20 (the phrase [I]at least[/I] means greater than or equal to)[/B]
[*][B]c + p < 15[/B]
[/LIST]

Barney has $450 and spends $3 each week. Betty has $120 and saves $8 each week. How many weeks will

Barney has $450 and spends $3 each week. Betty has $120 and saves $8 each week. How many weeks will it take for them to have the same amount of money?
Let w be the number of weeks that go by for saving/spending.
Set up Barney's balance equation, B(w). Spending means we [U]subtract[/U]
B(w) = Initial Amount - spend per week * w weeks
B(w) = 450 - 3w
Set up Betty's balance equation, B(w). Saving means we [U]add[/U]
B(w) = Initial Amount + savings per week * w weeks
B(w) = 120 + 8w
The same amount of money means both of their balance equations B(w) are equal. So we set Barney's balance equal to Betty's balance and solve for w:
450 - 3w = 120 + 8w
Add 3w to each side to isolate w:
450 - 3w + 3w = 120 + 8w + 3w
Cancelling the 3w on the left side, we get:
450 = 120 + 11w
Rewrite to have constant on the right side:
11w + 120 = 450
Subtract 120 from each side:
11w + 120 - 120 = 450 - 120
Cancelling the 120's on the left side, we get:
11w = 330
To solve for w, we divide each side by 11
11w/11 = 330/11
Cancelling the 11's on the left side, we get:
w = [B]30
[MEDIA=youtube]ifG_q-utgJI[/MEDIA][/B]

based on a sample of size 41, a 95% confidence interval for the mean score of all students,µ, on an

based on a sample of size 41, a 95% confidence interval for the mean score of all students,µ, on an aptitude test is from 60 to 66. Find the margin of error

Basic Statistics

Given a number set, and an optional probability set, this calculates the following statistical items:

Expected Value

Mean = μ

Variance = σ^{2}

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Expected Value

Mean = μ

Variance = σ

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign

Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign, then divided by 3. What was the original equation
[LIST=1]
[*]If we added 7 to both sides, that means we had a minus 7 (-7) to start with as a constant. Since subtraction undoes addition.
[*]If we divided by 3, this means we multiplied x by 3 to begin with. Since division undoes multiplication
[/LIST]
So we have the start equation:
3x - 7
If the answer was x = -4, then we plug this in to get our number on the right side of the equation:
3(-4) - 7
-12 - 7
-19
This means our original equation was:
[B]3x - 7 = -19[/B]
And if we want to solve this to prove our answer, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D-19&pl=Solve']type the equation into our search engine [/URL]and we get:
x = -4

Below are data showing the results of six subjects on a memory test. The three scores per subject ar

Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials (a, b, and c) of a memory task. Are the subjects getting better each trial? Test the linear effect of trial for the data.
A score trial B score trial 2 C Score trial 3
4 6 7
3 7 8
2 8 5
1 4 7
4 6 9
2 4 2
(a) Compute L for each subject using the contrast weights -1, 0, and 1. That is, compute (-1)(a) + (0)(b) + (1)(c) for each subject.
(b) Compute a one-sample t-test on this column (with the L values for each subject) you created. Formula t = To computer a one-sample t-test first know the meaning of each letter
(a) Each L column value is just -1(Column 1) + 0(Column2) + 1(Column 3)
A score trial B score trial 2 C Score trial 3 L = (-1)(a) + (0)(b) + (1)(c)
4 6 7 3
3 7 8 5
2 8 5 3
1 4 7 6
4 6 9 5
2 4 2 0
(b) Mean = (3 + 5 + 3 + 6 + 5 + 0)/6 = 22/6 = 3.666666667
Standard Deviation = 2.160246899
Use 3 as our test mean
(3.666667 - 3)/(2.160246899/sqrt(6)) = 0.755928946

Big John weighs 300 pounds and is going on a diet where he'll lose 3 pounds per week. Write an equat

Big John weighs 300 pounds and is going on a diet where he'll lose 3 pounds per week. Write an equation in slope-intercept form to represent this situation.
[LIST]
[*]The slope intercept form is y = mx + b
[*]y is John's weight
[*]x is the number of weeks
[*]A 3 pound per week weight loss means -3 as the coefficient m
[*]b = 300, John's starting weight
[/LIST]
[B]y = -3x + 300[/B]

Bill is q years old. How old will he in 6 years ? How old was he 4 years ago ?

Bill is q years old. How old will he in 6 years ? How old was he 4 years ago ?
Start with q years old.
In 6 years means we add since it's the future:
[B]q + 6[/B]
4 years ago means we subtract since it's in the past:
[B]q - 4[/B]

Binomial Distribution

Calculates the probability of 3 separate events that follow a binomial distribution. It calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, standard deviation, skewness and kurtosis.

Also calculates the normal approximation to the binomial distribution with and without the continuity correction factor

Calculates moment number t using the moment generating function

Also calculates the normal approximation to the binomial distribution with and without the continuity correction factor

Calculates moment number t using the moment generating function

blair’s bank account was overdrawn by $40. she spent $30 at the grocery store. what is the balance i

blair’s bank account was overdrawn by $40. she spent $30 at the grocery store. what is the balance in her account now?
The word [I]overdrawn[/I] means a negative balance. So we start with:
-40
Spending 30 at the grocery store means we subtract 30 from our initial balance:
-40 - 30 = [B]-70 or $70 overdrawn[/B]

Bob has 4/5 of a pound of fudge. He wants to share it with Sue. How much of a pound of fudge will bo

Bob has 4/5 of a pound of fudge. He wants to share it with Sue. How much of a pound of fudge will both of them get?
If Bob shares the fudge with Sue, we assume they split equal parts. This means:
We take 4/5 total and divide into 2 for 2 people:
4/5/2
This is the same as 4/5 * 1/2
4/10
This fraction is not simplified.
Factor of 4 = {1, [U]2[/U], 4}
Factors of 10 = {1, [U]2[/U], 5, 10}
In both of these lists, we see the greatest common factor is 2.
So we divide top and bottom of 4/10 by 2:
4/2 / 10 / 2
[B]2/5
Bob gets 2/5 of a pound of fudge and Sue gets [B]2/5 of a pound of fudge[/B][/B]

Bob weighs between 125 and 135

Bob weighs between 125 and 135
Let w be Bob's weight. Between means includes, so we have a compound inequality:
[B]125 <= w <= 135[/B]

Boris baked 40 cookies. His family ate m of them

Boris baked 40 cookies. His family ate m of them
If his family ate m, that mean we [I]subtract[/I] m from 40. So Boris has the remaining cookies:
[B]40 - m[/B]

Brendan bought an aquarium originally priced at $50 but on sale for 50% off. After 12% sales tax, wh

Brendan bought an aquarium originally priced at $50 but on sale for 50% off. After 12% sales tax, what was the total cost?
50% off of 50 means they pay half, or 1/2(50) = 25.
Now, this gets taxed at 12%. So we multiply 25 * 1.12
Total Cost = 25(1.12)
Total Cost = [B]$28[/B]

Brighthouse charges $120 a month for their basic plan, plus $2.99 for each on demand movie you buy.

Brighthouse charges $120 a month for their basic plan, plus $2.99 for each on demand movie you buy. Write and solve and inequality to find how many on demand movies could you buy if you want your bill to be less than $150 for the month.
Let x equal to the number room movie rentals per month. Our inequality is:
120 + 2.99x < 150
To solve for the number of movies, Add 120 to each side
2.99x < 30
Divide each side by 2.99
x < 10.03, which means 10 since you cannot buy a fraction of a movie

Bruno is 3x years old and his son is x years old now. Their combined age is 40 years. How old is Bru

Bruno is 3x years old and his son is x years old now. Their combined age is 40 years. How old is Bruno
Combined age means we add, so we have:
3x + x = 40
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x%2Bx%3D40&pl=Solve']type it in our search engine[/URL] and we get:
x = 10
This means Bruno is:
3(10) = [B]30[/B]

By how much does 162 exceed 58

Exceed means above, or more than.
162 - 58 = [B]104[/B]

c increased by a factor of 20

c increased by a factor of 20
This means we multiply c by 20:
[B]20c[/B]

C varies directly as d use k as the constant of variation

C varies directly as d use k as the constant of variation
Direct variation means we multiply below:
[B]C = kd[/B]

C varies directly as the cube of a and inversely as the 4th power of B

C varies directly as the cube of a and inversely as the 4th power of B
The cube of a means we raise a to the 3rd power:
a^3
The 4th power of B means we raise b to the 4th power:
b^4
Varies directly means there exists a constant k such that:
C = ka^3
Also, varies inversely means we divide by the 4th power of B
C = [B]ka^3/b^4[/B]
Varies [I]directly [/I]as means we multiply by the constant k.
Varies [I]inversely [/I]means we divide k by the term which has inverse variation.
[MEDIA=youtube]fSsG1OB3qdk[/MEDIA]

c varies jointly as the square of q and cube of p

c varies jointly as the square of q and cube of p
The square of q means we raise q to the 2nd power:
q^2
The cube of p means we raise p to the rdd power:
p^3
The phrase [I]varies jointly[/I] means there exists a constant k such that:
[B]c = kp^3q^2[/B]

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appr

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appropriate pair of equations.
Let Cam's age be c. Let Lara's age be l. We're given two equations:
[LIST=1]
[*]c = l + 3 <-- older means we add
[*]c + l = 63 <-- combined ages mean we add
[/LIST]
Substitute equation (1) into equation (2):
l + 3 + l = 63
Combine like terms to simplify our equation:
2l + 3 = 63
To solve for l, [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B3%3D63&pl=Solve']we type this equation into our search engine[/URL] and we get:
l = [B]30[/B]
Now, we plug l = 30 into equation (1) to solve for c:
c = 30 + 3
c = [B]33[/B]

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appr

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appropriate pair of equations.
Let Cam's age be c.
Let Lara's age be l.
We're given two equations:
[LIST=1]
[*]c = l + 3 (Since older means we add)
[*]c + l = 63
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for c:
l + 3 + l = 63
To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l%2B3%2Bl%3D63&pl=Solve']type it in our search engine [/URL]and we get:
l = [B]30
[/B]
Now, we take l = 30 and substitute it in equation (1) to solve for c:
c = 30 + 3
c = [B]33[/B]

Cameron knows that 2 dogs are given 8 cups of food and 3 dogs are given 12 cups of food. How much fo

Cameron knows that 2 dogs are given 8 cups of food and 3 dogs are given 12 cups of food. How much food will be given to 5 dogs?
2:8 --> 3:12 --> 1:4
This means for every dog, 4 cups of food are given. With 5 dogs, we have:
5 * 4 = [B]20 cups of food[/B]

Carlos age increased by is 16 is 62

Carlos age increased by is 16 is 62.
Let a be Carlos's age.
Increased by 16 means we add 16
a + 16
Now the phrase [I]is[/I] means equal to, so we set [B]a + 16 = 62[/B]

Carmen has $30 in store bucks and a 25% discount coupon for a local department store. What maximum d

Carmen has $30 in store bucks and a 25% discount coupon for a local department store. What maximum dollar amount can Carmen purchase so that after her store bucks and discount are applied, her total is no more than $60 before sales tax
Let the original price be p.
p
Apply 25% discount first, which is the same as subtracting 0.25:
p(1 - 0.25)
Subtract 30 for in store buck
p(1 - 0.25) - 30
The phrase [I]no more than[/I] means an inequality using less than or equal to:
p(1 - 0.25) - 30 <= 60
To solve this inequality for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=p%281-0.25%29-30%3C%3D60&pl=Solve']type it in our math engine[/URL] and we get:
[B]p <= 120[/B]

Charmaine’s fish tank has 16 liters of water in it. she plans to add 6 liters per minute until the t

Charmaine’s fish tank has 16 liters of water in it. she plans to add 6 liters per minute until the tank has at least 58 liters. What are the possible numbers of minutes Charmaine could add water?
This is an algebraic inequality. The phrase [I]at least[/I] means greater than or equal to. So we have:
6m + 16 >= 58 <-- This is our algebraic expression/inequality.
To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=6m%2B16%3E%3D58&pl=Solve']we type this into our search engine [/URL]and we get:
[B]m >= 7[/B]

Charrie found a piece of 8 meters rope. She cuts it into equal length. She made three cuts. How long

Charrie found a piece of 8 meters rope. She cuts it into equal length. She made three cuts. How long is each piece of the rope?
Equal length means we divide the length of the rope by the number of equal cuts
[B]8/3 or 2 & 2/3 meters[/B]

Chebyshevs Theorem

Using Chebyshevs Theorem, this calculates the following:

Probability that random variable X is within k standard deviations of the mean.

How many k standard deviations within the mean given a P(X) value.

Probability that random variable X is within k standard deviations of the mean.

How many k standard deviations within the mean given a P(X) value.

Cindy is c years old. Cindy is 5 years younger than half Jennifer's age ( j )

Cindy is c years old. Cindy is 5 years younger than half Jennifer's age ( j )
Build an algebraic expression:
[B]c = j/2 - 5[/B] <-- Half means we divide by 2 and [I]younger[/I] means we subtract

Class A has 8 pupils and class B has 10 pupils. Both classes sit the same maths test. The mean sco

Class A has 8 pupils and class B has 10 pupils. Both classes sit the same maths test. The mean score for class A is 55. The mean score for both classes is 76. What is the mean score (rounded to 1 DP) in the maths test for class B
Mean of the sum equals the sum of the means.
U(A + B) = U(A) + U(B)
76 = 55 + U(B)
Subtract 55 from each side, we get:
[B]U(B) = 21[/B]

Colin was thinking of a number. Colin divides by 8, then adds 1 to get an answer of 2. What was the

Colin was thinking of a number. Colin divides by 8, then adds 1 to get an answer of 2. What was the original number?
Let the number be n.
Divide by 8:
n/8
Then add 1:
n/8 + 1
The phrase [I]get an answer[/I] of means an equation, so we set n/8 + 1 equal to 2:
n/8 + 1 = 2
To solve for n, we subtract 1 from each side to isolate the n term:
n/8 + 1 - 1 = 2 - 1
Cancel the 1's on the left side, we get:
n/8 = 1
Cross multiply:
n = 8*1
n = [B]8[/B]

Common Prefixes

Shows common prefixes, meanings, and example words

Common Suffixes

Shows common suffixes, meanings, and example words

Compute a 75% Chebyshev interval around the mean for x values and also for y values.

Compute a 75% Chebyshev interval around the mean for [I]x[/I] values and also for [I]y[/I] values.
[B][U]Grid E: [I]x[/I] variable[/U][/B]
11.92 34.86 26.72 24.50 38.93 8.59 29.31
23.39 24.13 30.05 21.54 35.97 7.48 35.97
[B][U]Grid H: [I]y[/I] variable[/U][/B]
27.86 13.29 33.03 44.31 16.58 42.43
39.61 25.51 39.14 16.58 47.13 14.70 57.47 34.44
According to Chebyshev's Theorem,
[1 - (1/k^2)] proportion of values will fall between Mean +/- (k*SD)
k in this case equal to z
z = (X-Mean)/SD
X = Mean + (z*SD)
1 - 1/k^2 = 0.75
- 1/k^2 = 0.75 - 1= - 0.25
1/k^2 = 0.25
k^2 = 1/0.25
k^2 = 4
k = 2
Therefore, z = k = 2
First, [URL='http://www.mathcelebrity.com/statbasic.php?num1=11.92%2C34.86%2C26.72%2C24.50%2C38.93%2C8.59%2C29.31%2C23.39%2C24.13%2C30.05%2C21.54%2C35.97%2C7.48%2C35.97&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']determine the mean and standard deviation of x[/URL]
Mean(x) = 25.24
SD(x) = 9.7873
Required Interval for x is:
Mean - (z * SD) < X < Mean + (z * SD)
25.24 - (2 * 9.7873) < X < 25.24 - (2 * 9.7873)
25.24 - 19.5746 < X < 25.24 + 19.5746
5.6654 < X < 44.8146
Next, [URL='http://www.mathcelebrity.com/statbasic.php?num1=27.86%2C13.29%2C33.03%2C44.31%2C16.58%2C42.43%2C39.61%2C25.51%2C39.14%2C16.58%2C47.13%2C14.70%2C57.47%2C34.44&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']determine the mean and standard deviation of y[/URL]
Mean(y) = 32.29
SD(y) = 9.7873
Required Interval for y is:
Mean - (z * SD) < Y < Mean + (z * SD)
32.29 - (2 * 13.1932) < Y < 32.29 - (2 * 13.1932)
32.29 - 26.3864 < Y < 32.29 + 26.3864
5.9036 < X < 58.6764

Confidence Interval for the Mean

Calculates a (90% - 99%) estimation of confidence interval for the mean given a small sample size using the student-t method with (n - 1) degrees of freedom or a large sample size using the normal distribution Z-score (z value) method including Standard Error of the Mean. confidence interval of the mean

Confidence Interval/Hypothesis Testing for the Difference of Means

Given two large or two small distriutions, this will determine a (90-99)% estimation of confidence interval for the difference of means for small or large sample populations.

Also performs hypothesis testing including standard error calculation.

Also performs hypothesis testing including standard error calculation.

Consider the following 15 numbers 1, 2, y - 4, 4, 5, x, 6, 7, 8, y, 9, 10, 12, 3x, 20 - The mean o

Consider the following 15 numbers
1, 2, y - 4, 4, 5, x, 6, 7, 8, y, 9, 10, 12, 3x, 20
- The mean of the last 10 numbers is TWICE the mean of the first 10 numbers
- The sum of the last 2 numbers is FIVE times the sum of the first 3 numbers
(i) Calculate the values of x and y
We're given two equations:
[LIST=1]
[*](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10 = 2(1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/10
[*]3x - 20 = 5(1 + 2 + y - 4)
[/LIST]
Let's evaluate and simplify:
[LIST=1]
[*](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10 = (1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/5
[*]3x - 20 = 5(y - 1)
[/LIST]
Simplify some more:
[URL='https://www.mathcelebrity.com/polynomial.php?num=x%2B6%2B7%2B8%2By%2B9%2B10%2B12%2B3x%2B20&pl=Evaluate'](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10[/URL] = (4x + y + 72)/10
[URL='https://www.mathcelebrity.com/polynomial.php?num=1%2B2%2By-4%2B4%2B5%2Bx%2B6%2B7%2B8%2By&pl=Evaluate'](1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/5[/URL] = (2y + x + 29)/5
5(y - 1) = 5y - 5
So we're left with:
[LIST=1]
[*](4x + y + 72)/10 = (2y + x + 29)/5
[*]3x - 20 = 5y - 5
[/LIST]
Cross multiply equations in 1, we have:
5(4x + y + 72) = 10(2y + x + 29)
20x + 5y + 360 = 20y + 10x + 290
We have:
[LIST=1]
[*]20x + 5y + 360 = 20y + 10x + 290
[*]3x - 20 = 5y - 5
[/LIST]
Combining like terms:
[LIST=1]
[*]10x - 15y = -70
[*]3x - 5y = 15
[/LIST]
Now we have a system of equations which we can solve any of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
(x, y) = [B](-115, -72)[/B]

Construct a data set of seven temperature readings where the mean is positive and the median is nega

Construct a data set of seven temperature readings where the mean is positive and the median is negative.
[B]{-20,-10.-5,-2,-1,20,40}[/B]
[URL='https://www.mathcelebrity.com/statbasic.php?num1=-20%2C-10%2C-5%2C-2%2C-1%2C20%2C40&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Using our mean and median calculator[/URL], we see that:
[B]Mean = 3.142857 (positive)
Median = -2[/B]

cube root of a number and 7

cube root of a number and 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Cube root of a number means we raise x to the 1/3 power:
x^1/3
And 7 means we add 7:
[B]x^1/3 + 7[/B]

Cube the difference of b and c

Cube the difference of b and c
the difference of b and c:
b - c
Cubing means raising to the power of 3:
[B](b - c)^3[/B]

d is h decreased by 301

d is h decreased by 301
h decreased by 301 means we subtract 301 from h
h - 301
The phrase [I]is[/I] means equal to, so we set d equal to this expression:
[B]d = h - 301[/B]

d squared is greater than or equal to 17

d squared is greater than or equal to 17
d squared means we raise the variable d to the power of 2:
d^2
The phrase [I]greater than or equal to[/I] means an inequality. So we set this up using the >= in relation to 17:
[B]d^2 >= 17[/B]

Dad is (y) years old. Mom is 5 years younger than Dad. What is the total of their ages

Dad is (y) years old. Mom is 5 years younger than Dad. What is the total of their ages
Dad's age:
y
Mom's age (younger means we subtract):
y - 5
The total of their ages is found by adding them together:
y + y - 5
Group like terms, and we get:
[B]2y - 5[/B]

Dan bought 7 new baseball trading cards to add to his collection. The next day his dog ate half of h

Dan bought 7 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 26 cards left. How many cards did Dan start with?
Let the starting amount of cards be s. We're given:
[LIST]
[*]Dan bought 7 new cards: s + 7
[*]The dog ate half of his collection. This means he's left with half, or (s + 7)/2
[*]Now, he's got 26 cards left. So we set up the following equation:
[/LIST]
(s + 7)/2 = 26
Cross multiply:
s + 7 = 26 * 2
s + 7 = 52
To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B7%3D52&pl=Solve']we plug this equation into our search engine[/URL] and we get:
s = [B]45[/B]

data below consists of the pulse rates (in beats per minute) of 32 students. Assuming ? = 10.66,

The data below consists of the pulse rates (in beats per minute) of 32 students. Assuming ? = 10.66, obtain a 95.44% confidence interval for the population mean.
80 74 61 93 69 74 80 64
51 60 66 87 72 77 84 96
60 67 71 79 89 75 66 70
57 76 71 92 73 72 68 74

David has b dollars in his bank account; Claire has three times as much money as David. The sum of t

David has b dollars in his bank account; Claire has three times as much money as David. The sum of their money is $240. How much money does Claire have?
David has b
Claire has 3b since three times as much means we multiply b by 3
The sum of their money is found by adding David's bank balance to Claire's bank balance to get the equation:
3b + b = 240
To solve for b, [URL='https://www.mathcelebrity.com/1unk.php?num=3b%2Bb%3D240&pl=Solve']we type this equation into our search engine[/URL] and we get:
b = 60
So David has 60 dollars in his bank account.
Therefore, Claire has:
3(60) = [B]180[/B]

Dawn has less than $60. She wants to buy 3 sweaters. What price of sweaters can she afford if all th

Dawn has less than $60. She wants to buy 3 sweaters. What price of sweaters can she afford if all the sweaters are the same price? Let s be the price of each sweater. Write this as an inequality.
The phrase [I]less than[/I] means an inequality, so we have the following inequality:
3s < 60
To solve this inequality, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3s%3C60&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get:
s < [B]20[/B]

Decrease 12 by a number

Decrease 12 by a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take 12 and decrease it by x, meaning we subtract x from 12:
[B]12 - x[/B]

decrease a number by 7 and multiply by 6.

decrease a number by 7 and multiply by 6.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Decrease a number by 7:
x - 7
Multiply by 6
[B]6(x - 7)[/B]

Del and his 5 friends eat 4 pizzas. If each has the same amount and there is 1/4 of a pizza left ove

Del and his 5 friends eat 4 pizzas. If each has the same amount and there is 1/4 of a pizza left over, how much did each person eat?
This means 4 full pizzas - 1/4 of a pizza = 3 & 3/4 pizzas eaten
Del and his 5 friends means 6 people total. Since they ate equal amounts, we divide pizzas eaten by total people:
3 & 3/4 / 6
Convert 3 & 3/4 to a mixed fraction:
(4*3 + 3)/4 = 15/4
15/4/6
Divide by a fraction is the same as multiply by a reciprocal:
15/4 * 1/6 = [B]15/24 pizzas per person[/B]

Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up

Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up her account with a starting amount of $850 and is going to take out $65 per month. When would the two accounts have the same amount of money?
We set up a balance equation B(m) where m is the number of months.
[U]Set up Deon's Balance equation:[/U]
Withdrawals mean we subtract from our current balance
B(m) = Starting Balance - Withdrawal Amount * m
B(m) = 650 - 40m
[U]Set up Mai's Balance equation:[/U]
Withdrawals mean we subtract from our current balance
B(m) = Starting Balance - Withdrawal Amount * m
B(m) = 850 - 65m
When the two accounts have the same amount of money, we can set both balance equations equal to each other and solve for m:
650 - 40m = 850 - 65m
Solve for [I]m[/I] in the equation 650 - 40m = 850 - 65m
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables -40m and -65m. To do that, we add 65m to both sides
-40m + 650 + 65m = -65m + 850 + 65m
[SIZE=5][B]Step 2: Cancel -65m on the right side:[/B][/SIZE]
25m + 650 = 850
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 650 and 850. To do that, we subtract 650 from both sides
25m + 650 - 650 = 850 - 650
[SIZE=5][B]Step 4: Cancel 650 on the left side:[/B][/SIZE]
25m = 200
[SIZE=5][B]Step 5: Divide each side of the equation by 25[/B][/SIZE]
25m/25 = 200/25
m = [B]8[/B]

Determine the formula of the given statement by following the procedures. Choose any number then add

Determine the formula of the given statement by following the procedures. Choose any number then add 2. Multiply your answer to 3 and minus 2
For the phrase [I]choose any number[/I] we can use an arbitrary variable, let's call it x.
Add 2:
x + 2
Multiply your answer to 3:
3(x + 2)
And minus 2 which means we subtract:
[B]3(x + 2) - 2[/B]

Deyante made a loss of $79.45 on shirt he sold for $240. What was the price of the shirt?

Deyante made a loss of $79.45 on shirt he sold for $240. What was the price of the shirt?
He sold for $240. If he took a loss, that means he bought the shirt for:
$240 + 79.45 = [B]$319.45[/B]

Dick invested $9538 in an account at 10% compounded annually. Calculate the total investment after

Dick invested $9538 in an account at 10% compounded annually. Calculate the total investment after 10 years. Round your answer to the nearest penny if necessary.
Annual compounding means we don't need to make adjustments to interest rate per compounding period.
[URL='https://www.mathcelebrity.com/compoundint.php?bal=9538&nval=10&int=10&pl=Annually']Using our compound interest calculator[/URL], we get our new balance after 10 years of:
[B]$24,739.12[/B]

Diegos savings increased by 9 is 68 . Use the variable to represent Diegos savings.

Diegos savings increased by 9 is 68 . Use the variable to represent Diegos savings.
Let Diego's savings be s.
The phrase [I]increased by[/I] means add, so we add 9 to s
s + 9
The phrase [I]is [/I]means equal to, so we set 2 + 9 = 68
[B]s + 9 = 68[/B]

Difference between 23 and y is 12

Difference between 23 and y
23 - y
Is, means equal to, so we set 23 - y equal to 12
[B]23 - y = 12
[/B]
If you need to solve this algebraic expression, use our [URL='http://www.mathcelebrity.com/1unk.php?num=23-y%3D12&pl=Solve']equation calculator[/URL]:
[B]y = 11[/B]

Dina is twice as old as Andrea. The sum of their age is 72. Find their present ages.

Dina is twice as old as Andrea. The sum of their age is 72. Find their present ages.
Let d be Dina's age. Let a be Andrea's age. We're given:
[LIST=1]
[*]d = 2a <-- Twice means multiply by 2
[*]a + d = 72
[/LIST]
Substitute equation (1) into equation (2):
a + 2a = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=a%2B2a%3D72&pl=Solve']Type this equation into our search engine[/URL] and we get:
[B]a = 24[/B]
Substitute a = 24 into equation (1):
d = 2(24)
[B]d = 48
So Andrea is 24 years old and Dina is 48 years old[/B]

Dina is twice the age of Anton. If Anton is 12, how will you represent the age of Dina?

Dina is twice the age of Anton. If Anton is 12, how will you represent the age of Dina?
Twice means multiply by 2, so we have:
Dina = 2 * Anton's age
Dina = 2 * 12
Dina = [B]24[/B]

Divide 10 by the difference of z and y

[U]The difference of z and y means we subtract y from z[/U]
z - y
[U]Now, we form a fraction, where 10 is the numerator and z - y is the denominator[/U]
10/(z - y)

divide 8 by t, raise the result to the 7th power

divide 8 by t, raise the result to the 7th power.
We take this algebraic expression in two parts:
1. Divide 8 by t
8/t
2. Raise the result to the 7th power. (This means we use an exponent of 7)
[B](8/t)^7[/B]

divide a by 8, triple the result, then add 7

divide a by 8, triple the result, then add 7
[LIST]
[*]Divide a by 8: a/8
[*]Triple the result means multiply by 3: 3a/8
[*]Then add 7
[/LIST]
[B]3a/8 + 7[/B]

Divide a by b, double the result, then multiply c by what you have

Divide a by b, double the result, then multiply c by what you have
Take this algebraic expression in parts:
[LIST]
[*]Divide a by b: a/b
[*]Double the result means multiply by 2: 2a/b
[*]Then multiply c by what you have:
[/LIST]
[B]2ac/b[/B]

divide a by c, triple the result, then subtract what you have from b

divide a by c, triple the result, then subtract what you have from b
Let's take this algebraic expression in parts:
[LIST=1]
[*]Divide a by c: a/c
[*]Triple the result. This means we multiply a/c by 3: 3a/c
[*]Then subtract what you have (the result) from b: b - 3a/c
[/LIST]
[B]b - 3a/c[/B]

Divide a number by 10. Then, add 10.

Divide a number by 10. Then, add 10.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Divide the number by 10 mean we have a quotient, of x over 10
x / 10
Then, add 10:
[B](x / 10) + 10[/B]

Divide the difference of 4 and r by 10

Divide the difference of 4 and r by 10
The difference of 4 and r, mean we subtract r from 4:
4 - r
Now we divide this expression by 10:
[B](4 - r)/10 [/B]

divide the difference of q and s by the sum of p and r

divide the difference of q and s by the sum of p and r
Take this algebraic expression in pieces:
[LIST]
[*]The difference of q and s: q - s
[*]The sum of p and r: p + r
[*]The word [I]divide[/I] means we divide q - s by p + r
[/LIST]
[B](q - s)/(p + r)[/B]

Divide the sum of a and b by the square of c

Divide the sum of a and b by the square of c
The sum of a and b:
a + b
The square of c means we raise c to the power of 2:
c^2
Divide means we have a quotient, with a + b on top, and c^2 on the bottom:
[B](a + b)/c^2[/B]

divide the sum of the square of a and b by thrice c

divide the sum of the square of a and b by thrice c
Sum of the squares of a and b is found as follows:
[LIST]
[*]a squared means we raise a to the power of 2: a^2
[*]b squared means we raise b to the power of 2: b^2
[*]Sum of the squares means we add both terms: a^2 + b^2
[*]Thrice c means we multiply c by 3: 3c
[/LIST]
Divide means we have a quotient:
[B](a^2 + b^2)/3c[/B]

Divide v by the sum of 4 and w

Divide v by the sum of 4 and w
The sum of 4 and w means we add w to 4:
4 + w
Next, we divide v by this sum to get our final algebraic expression:
[B]v/(4 + w)[/B]

Divide x cubed by the quantity x minus 7

Divide x cubed by the quantity x minus 7
x cubed means we raise x to the power of 3:
x^3
We divide this by x - 7:
[B]x^3/(x - 7)[/B]

Divya has 70 rocks. She donates half of the rocks to a science center. Then she collects 3 rocks on

Divya has 70 rocks. She donates half of the rocks to a science center. Then she collects 3 rocks on each of her nature hikes. Write an expression to represent the number of rocks Divya has after she collects rocks on n nature hikes.
For each hike, we have:
[LIST=1]
[*]Start with 70 rocks
[*]She donates half which is 35, which means she's left with 35
[/LIST]
Since each nature hike gives her 3 more rocks, and she goes on n nature hikes, we have the following algebraic expression:
[B]3n + 35[/B]

Do the phrases 7 less than a number and a number less than 7 mean the same thing explain

Do the phrases 7 less than a number and a number less than 7 mean the same thing explain
No, they are different, here's how:
First, the phrase [I]a number[/I] means an arbitrary variable, let's call it x.
7 less than a number means we subtract 7 from x:
x - 7
A number less than 7 means we subtract x from 7:
7 - x
As you can see:
x - 7 <> 7 - x so [B]they are different[/B]

double 10, add the result to 9, then add y

double 10, add the result to 9, then add y
Double 10 means multiply 10 by 2:
10 * 2
20
Add the result to 9, means we add 20 to 9:
20 + 9
29
Then we add y:
[B]29 + y[/B]

double 6 , divide the result by y ,then raise what you have to the 10th power

double 6 , divide the result by y ,then raise what you have to the 10th power
Take this in pieces:
Double 6 means multiply 6 by 2 --> 6(2) = 12
Divide the result by y:
12/y
Then raise what you have to the 10th power:
[B](12/y)^10[/B]

double n, multiply answer by 3

double n, multiply answer by 3
Double n means multiply n by 2
2n
Multiply the answer by 3:
3(2n) = [B]6n[/B]

double the quotient of 4 and 7

double the quotient of 4 and 7
The quotient fo 4 and 7:
4/7
Double means multiply by this expression by 2:
[B]2(4/7)[/B]
If you need to evaluate and simplify this, it's:
[B]8/7[/B]

double v, add u, then divide t by what you have

double v, add u, then divide t by what you have
Double v means we multiply the variable v by 2:
2v
Add u:
2v + u
We build a fraction, with t as the numerator, and 2v + u as the denominator
[B]t/(2v + u)[/B]

double v, raise the result to the 6th power, then multiply what you have by w

double v, raise the result to the 6th power, then multiply what you have by w
Double v means multiply v by 2:
2v
Raise the result to the 6th power, means we use an exponent of 6 on 2v:
(2v)^6
Then multiply what you have by w, means take the result above, and multiply by w:
[B]w(2v)^6[/B]

Dunder Mifflin will print business cards for $0.10 each plus setup charge of $15. Werham Hogg offers

Dunder Mifflin will print business cards for $0.10 each plus setup charge of $15. Werham Hogg offers business cards for $0.15 each with a setup charge of $10. What numbers of business cards cost the same from either company
Declare variables:
[LIST]
[*]Let b be the number of business cards.
[/LIST]
[U]Set up the cost function C(b) for Dunder Mifflin:[/U]
C(b) = Cost to print each business card * b + Setup Charge
C(b) = 0.1b + 15
[U]Set up the cost function C(b) for Werham Hogg:[/U]
C(b) = Cost to print each business card * b + Setup Charge
C(b) = 0.15b + 10
The phrase [I]cost the same[/I] means we set both C(b)'s equal to each other and solve for b:
0.1b + 15 = 0.15b + 10
Solve for [I]b[/I] in the equation 0.1b + 15 = 0.15b + 10
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 0.1b and 0.15b. To do that, we subtract 0.15b from both sides
0.1b + 15 - 0.15b = 0.15b + 10 - 0.15b
[SIZE=5][B]Step 2: Cancel 0.15b on the right side:[/B][/SIZE]
-0.05b + 15 = 10
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 15 and 10. To do that, we subtract 15 from both sides
-0.05b + 15 - 15 = 10 - 15
[SIZE=5][B]Step 4: Cancel 15 on the left side:[/B][/SIZE]
-0.05b = -5
[SIZE=5][B]Step 5: Divide each side of the equation by -0.05[/B][/SIZE]
-0.05b/-0.05 = -5/-0.05
b = [B]100[/B]

During the 2016 christmas season,UPS had 14 employees retire, 122 employees were hired and 31 left d

During the 2016 christmas season,UPS had 14 employees retire, 122 employees were hired and 31 left due to illness. If UPS ended the year with 410 employees, how many did they have at the start of the season?
Let x be the number of employees at the start of the season. We have:
[LIST]
[*]-14 since retiring is an employee loss
[*]+122 hired since hiring is an employee gain
[*]-31 since illness means a leave
[/LIST]
x - 14 + 122 - 31 = 410
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=x-14%2B122-31%3D410&pl=Solve']equation solver[/URL], we get:
[B]x = 333[/B]

Dwayne has 9 peppermints. Mary has p fewer peppermints than Dwayne. Choose the expression that shows

Dwayne has 9 peppermints. Mary has p fewer peppermints than Dwayne. Choose the expression that shows how many peppermints Mary has.
The phrase [I]fewer than[/I] means we subtract:
[B]9 - p[/B]

Each of 6 students reported the number of movies they saw in the past year. Here is what they repor

Each of 6 students reported the number of movies they saw in the past year. Here is what they reported. 19, 9, 14, 10, 16, 17. Find the mean number of movies that the students saw. If necessary, round your answer to the nearest tenth.
The mean is the average, so we add up the 6 movie scores, and divide by 6.
[URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = Sum of 6 Movie Scores / 6
[URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = 84 / 6
[URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = 14.16666667
The problem asks us to round to the nearest tenth, which is the first decimal place.
Since the 2nd decimal place, 6 is more than 5, we round the first decimal place up one and remove the rest.
[B]14.2[/B]

Explain the relationship between "squaring" a number and finding the "square root" of a number. Use

Explain the relationship between "squaring" a number and finding the "square root" of a number. Use an example to further explain your answer.
Squaring a number means raising it to the power of 2
The square root of a number [I]undoes[/I] a square of a number.
So square root of x^2 is x
x squared is x^2
Let x = 5.
x squared = 5^2 = 25
Square root of 25 = square root of 5^2 = 5

Exponential Distribution

Calculates the Probability Density Function (PDF) and Cumulative Density Function (CDF) of the exponential distribution as well as the mean, variance, standard deviation, and entropy.

Express the fact that x differs from 3 by less than 2/7 as an inequality involving absolute value. S

Express the fact that x differs from 3 by less than 2/7 as an inequality involving absolute value. Solve for x.
Let's build this algebraic expression in pieces:
The phrase [I]differs from[/I] means a difference.
x - 3
By less than 2/7 means we use the < sign compared to 2/7
x - 3 < 2/7
Finally, the problem says we involve absolute value. So we write this as:
[B]|x - 3| < 2/7[/B]

F varies directly as g and inversely as r^2

F varies directly as g and inversely as r^2
[U]Givens and assumptions[/U]
[LIST]
[*]We take a constant of variation called k.
[*][I]Varies directly means we multiply our variable term by k[/I]
[*][I]Varies inversely means we divide k by our variable term[/I]
[/LIST]
The phrase varies directly or varies inversely means we have a constant k such that:
[B]F = kg/r^2[/B]

f varies jointly with u and h and inversely with the square of y.

f varies jointly with u and h and inversely with the square of y.
Variation means we have a constant k.
Varies jointly with u and h means we multiply k by hu
Varies inversely with the square of y means we divide by y^2
[B]f = khu/y^2[/B]

Facebook provides a variety of statistics on its Web site that detail the growth and popularity of t

Facebook provides a variety of statistics on its Web site that detail the growth and popularity of the site.
On average, 28 percent of 18 to 34 year olds check their Facebook profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a standard deviation of five percent.
a. Find the probability that the percent of 18 to 34-year-olds who check Facebook before getting out of bed in the morning is at least 30.
b. Find the 95th percentile, and express it in a sentence.
a. P(X >=0.30), calculate the [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+0.30&mean=+0.28&stdev=+0.05&n=+1&pl=P%28X+%3E+Z%29']z-score[/URL] which is:
Z = 0.4
P(x>0.4) = [B]0.344578 or 34.46%[/B]
b. Inverse Normal (0.95) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.95&pl=Calculate+Critical+Z+Value']calculator[/URL] = 1.644853627
Use NORMSINV(0.95) on Excel
0.28 + 0.05(1.644853627) = [B]0.362242681 or 36.22%[/B]

Factors of 36 between 2 and 12

Factors of 36 between 2 and 12
We type in [I][URL='https://www.mathcelebrity.com/factoriz.php?num=36&pl=Show+Factorization']factors of 36[/URL][/I] into our search engine and we get:
{1, 2, 3, 4, 6, 9, 12, 18, 36}
The problem asks for factors of 36 between 2 and 12:
Between does not mean inclusive, so we have anything greater than 2 and less than 12:
[B]{3, 4, 6, 9}[/B]

Fifteen less than 3

Convert to numbers:
Fifteen = 15.
Less than means subtract.
3 - 15.
Evaluating, that is 12.

fifty feet less than 2n feet

fifty feet less means we subtract 50 from 2n.
2n - 50

Fifty-two less than 75% of a number

Fifty-two less than 75% of a number
A number means an arbitrary variable, let's call it x.
75% of this is 0.75x
Fifty-two less is:
[B]0.75x - 52[/B]

Find 3 consecutive integers such that the sum of twice the smallest and 3 times the largest is 126

Find 3 consecutive integers such that the sum of twice the smallest and 3 times the largest is 126.
Let the first integer be n, the second integer be n + 1, and the third integer be n + 2. We have:
Sum of the smallest and 3 times the largest is 126:
n + 3(n + 2) = 126
Multiply through:
n + 3n + 6 = 126
Group like terms:
4n + 6 = 126
[URL='https://www.mathcelebrity.com/1unk.php?num=4n%2B6%3D126&pl=Solve']Type 4n + 6 = 126 into our calculator[/URL], we get n = 30. Which means the next two integers are 31 and 32.
[B]{30, 31, 32}[/B]

Find Mean 106 and standard deviation 10 of the sample mean which is 25

mean of 106 inches and a standard deviation of 10 inches and for sample of size is 25. Determine the mean and the standard deviation of /x

Find Mean 106 and standard deviation 10 of the sample mean which is 25

Do you mean x bar?
mean of 106 inches and a standard deviation of 10 inches and for sample of size is 25. Determine the mean and the standard deviation of /x
If so, x bar equals the population mean. So it's [B]106[/B].
Sample standard deviation = Population standard deviation / square root of n
10/Sqrt(25)
10/5
[B]2[/B]

Find Mean and standard deviation

one trunk can carry 5068.8 lb. weight of boxes that it carries have a mean of 75lb and a standard deviation of 16 Ib. For Sample size of 64 ,find the mean and standard deviation of /x

Find Mean and standard deviation

one trunk can carry 5068.8 lb. weight of boxes that it carries have a mean of 75lb and a standard deviation of 16 Ib. For Sample size of 64 ,find the mean and standard deviation of /x

Find Mean and standard deviation

Sample Mean = Population Mean
Sample Mean = [B]75[/B]
Sample Standard Deviation = Population Standard Deviation / Sqrt(n)
Sample Standard Deviation = 16/sqrt(64)
Sample Standard Deviation = 16 / 8
Sample Standard Deviation = [B]2[/B]

Find Necessary Sample Size

The monthly earnings of a group of business students are are normally distributed with a standard deviation of 545 dollars. A researcher wants to estimate the mean monthly earnings of all business students. Find the sample size needed to have a confidence level of 95% and a margin of error of 128 dollars.

Find Requested Confidence Value

The data below consists of the pulse rates (in beats per minute) of 32 students. Assuming ? = 10.66, obtain a 95.44% confidence interval for the population mean.
80 74 61 93 69 74 80 64
51 60 66 87 72 77 84 96
60 67 71 79 89 75 66 70
57 76 71 92 73 72 68 74

Find Requested Value

Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, in liters.
5.2 4.9 2.9 5.3 3.0
4.0 5.2 5.2 3.2 4.7
3.2 3.5 4.8 4.0 5.1
Use the data to obtain a point estimate of the mean forced vital capacity for all asthmatics

Find Requested Value

Using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=5.2%2C4.9%2C2.9%2C5.3%2C3.0%2C4.0%2C5.2%2C5.2%2C3.2%2C4.7%2C3.2%2C3.5%2C4.8%2C4.0%2C5.1&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']statistics number set calculator[/URL], we get a mean of [B]4.28[/B]

Find the confidence interval specified.

Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, in liters.
5.1 4.9 4.7 3.1 4.3
3.7 3.7 4.3 3.5 5.2
3.2 3.5 4.8 4.0 5.1
Use the data to obtain a 95.44% confidence interval for the mean forced vital capacity for all asthmatics. Assume that ? = 0.7.

Find two consecutive odd integers such that the sum of their squares is 290

Find two consecutive odd integers such that the sum of their squares is 290.
Let the first odd integer be n.
The next odd integer is n + 2
Square them both:
n^2
(n + 2)^2 = n^2 + 4n + 4 from our [URL='https://www.mathcelebrity.com/expand.php?term1=%28n%2B2%29%5E2&pl=Expand']expansion calculator[/URL]
The sum of the squares equals 290
n^2 + n^2 + 4n + 4 = 290
Group like terms:
2n^2 + 4n + 4 = 290
[URL='https://www.mathcelebrity.com/quadratic.php?num=2n%5E2%2B4n%2B4%3D290&pl=Solve+Quadratic+Equation&hintnum=+0']Enter this quadratic into our search engine[/URL], and we get:
n = 11, n = -13
Which means the two consecutive odd integer are:
11 and 11 + 2 = 13. [B](11, 13)[/B]
-13 and -13 + 2 = -11 [B](-13, -11)[/B]

Find two consecutive positive integers such that the difference of their square is 25

Find two consecutive positive integers such that the difference of their square is 25.
Let the first integer be n. This means the next integer is (n + 1).
Square n: n^2
Square the next consecutive integer: (n + 1)^2 = n^2 + 2n + 1
Now, we take the difference of their squares and set it equal to 25:
(n^2 + 2n + 1) - n^2 = 25
Cancelling the n^2, we get:
2n + 1 = 25
[URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B1%3D25&pl=Solve']Typing this equation into our search engine[/URL], we get:
n = [B]12[/B]

Find two consecutive positive integers such that the sum of their squares is 25

Find two consecutive positive integers such that the sum of their squares is 25.
Let the first integer be x. The next consecutive positive integer is x + 1.
The sum of their squares equals 25. We write this as::
x^2 + (x + 1)^2
Expanding, we get:
x^2 + x^2 + 2x + 1 = 25
Group like terms:
2x^2 + 2x + 1 = 25
Subtract 25 from each side:
2x^2 + 2x - 24 = 0
Simplify by dividing each side by 2:
x^2 + x - 12 = 0
Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-12%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get x = 3 or x = -4. The problem asks for positive integers, so we discard -4, and use 3.
This means, our next positive integer is 3 + 1 = 4. So we have [B](3, 4) [/B]as our answers.
Let's check our work:
3^2 + 4^2 = 9 + 16 = 25

Finn has 8 toy cars. Dirk has t times as many toy cars as Finn

Finn has 8 toy cars. Dirk has t times as many toy cars as Finn
The phrase [I]times as many [/I]means we multiply:
[B]8t[/B]

Fiona thinks of a number. fiona halves the number and gets an answer of 72.8. Form an equation with

Fiona thinks of a number. fiona halves the number and gets an answer of 72.8. Form an equation with x from the information
Halving means dividing by 2, so our equation is:
[B]x/2 = 72.8[/B]

Five less than a number is at least -7 and at most 7.

Five less than a number is at least -7 and at most 7.
A number signifies an arbitrary variable, let's call it x.
Five less than a number: x - 5
Is at least -7 means greater than or equal to and at most 7 means less than or equal to, so we have a joint inequality:
[B]-7 <= x - 5 <= 7[/B]

Five times Kim's age plus 13 equals 58. How old is Kim?

Five times Kim's age plus 13 equals 58. How old is Kim?
Let Kim's age be a. We have:
Five times Kim's age:
5a
Plus 13 means we add 13
5a + 13
Equals 58 means we set the expression 5a + 13 equal to 58
5a + 13 = 58 <-- This is our algebraic expression
To solve this equation for a, [URL='https://www.mathcelebrity.com/1unk.php?num=5a%2B13%3D58&pl=Solve']we type it into our search engine[/URL] and get:
a = [B]9[/B]

For a population with ? = 60 and ? = 12, what is the z-score that corresponds to a score of 66?

For a population with ? = 60 and ? = 12, what is the z-score that corresponds to a score of 66?
[URL='https://www.mathcelebrity.com/probnormdist.php?xone=66&mean=60&stdev=12&n=1&pl=P%28X+%3C+Z%29']Using our z-score calculator[/URL], we get a probability:
[B]0.691462[/B]

for every 10 white cars a dealer sells he sells 7 silver, 6 blue, 5 red, 4 yellow, 3 green, 2 black,

for every 10 white cars a dealer sells he sells 7 silver, 6 blue, 5 red, 4 yellow, 3 green, 2 black, 2 purple and 1 brown car. If he sells 120 cars how many blue cars?
[U]Take this in blocks, so each block has:[/U]
10 white + 7 silver + 6 blue + 5 red + 4 yellow + 3 green + 2 black + 2 purple + 1 brown = 40 cars
[U]Calculate the number of blocks:[/U]
120 cars / 40 cars = 3 blocks.
[U]For 120 cars sold, it takes 3 blocks, which means we multiply:[/U]
6 blue cars per block * 3 blocks = [B]18 blue cars[/B]

For the normal distribution with parameters ? = 4, ? = 3 ; calculate P(x > 1)

For the normal distribution with parameters ? = 4, ? = 3 ; calculate P(x > 1)
[URL='https://www.mathcelebrity.com/probnormdist.php?xone=1&mean=4&stdev=3&n=1&pl=P%28X+%3E+Z%29']Using our calculator[/URL], we get P(x > 1) = [B]0.841345[/B]

Four consecutive integers beginning with n

Four consecutive integers beginning with n
consecutive meaning one after another. So we have:
[LIST]
[*][B]n[/B]
[*][B]n + 1[/B]
[*][B]n + 2[/B]
[*][B]n + 3[/B]
[/LIST]

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?
So the last cousin is n years old. this means consecutive cousins are n + 2 years older than the next.
whether their ages are even or odd, we have the sum of 4 consecutive (odd|even) integers equal to 36. We [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof4consecutiveevenintegersis36&pl=Calculate']type this into our search engine[/URL] and we get the ages of:
[B]6, 8, 10, 12[/B]

Four more then double a number is greater than 2

Four more then double a number is greater than 2
Double a number:
A number implies an arbitrary variable, let's call it "x". Double means multiply this by 2
2x
Four more than this:
2x + 4
Now, we set this expression as an inequality greater than 2
[B]2x + 4 > 2[/B]

Fred earns $420 a month. If his monthly car payment is one quarter of his pay, how much is his car p

Fred earns $420 a month. If his monthly car payment is one quarter of his pay, how much is his car payment?
1/4 means divided by 4, so we have:
Monthly Payment = Earnings/4
Monthly Payment =420/4
Monthly Payment = [B]$105[/B]

From 199 meters above sea level, Linda took off in her helicopter and descended 296 meters. What is

From 199 meters above sea level, Linda took off in her helicopter and descended 296 meters. What is Lindas elevation now?
[I]Descended[/I] means we subtract 296 meters from 199 meters.
Elevation Now = 199 - 296
Elevation Now = -97
Negative elevation means [I]below sea level[/I]. So our answer is:
[B]97 meters [I]below sea level[/I][/B]

From a regular deck of 52 playing cards, you turn over a 6 and then a 7. What is the probability tha

From a regular deck of 52 playing cards, you turn over a 6 and then a 7. What is the probability that the next card you turn over will be a face card?
Key phrases: 52 card standard deck so you know there's no tricks or missing cards.
[U]Calculate the number of face cards in a standard 52 card deck[/U]
First, we know that face cards = (J, K, Q)
We also know that there are 4 suits (Hearts, Diamonds, Spades, Clubs)
Total Face Cards = 3 face card types * 4 possible suits = 12 face cards
[U]Calculate total face down cards[/U]
First card, you turn over a 6
Next card, you turn over a 7
This means, we have 52 cards - 2 cards from the draws = 50 cards left in the deck which are face down.
P(Face Card) = Total Face Cards / Total Cards in the Deck Face Down
P(Face Card) = 12/50
Simplifying this fraction [URL='https://www.mathcelebrity.com/fraction.php?frac1=12%2F50&frac2=3%2F8&pl=Simplify']using our math engine[/URL], we get:
P(Face Card) = [B]6/25[/B]

g less than 143 is equal to 39 reduced by w

g less than 143 is equal to 39 reduced by w
g less than 143 means we subtract g from 143
143 - g
39 reduced by w means we subtract w from 39
39 - w
We set these 2 expressions equal to each other:
[B]143 - g = 39 - w[/B]

g times by 5 then add 3

g times by 5 then add 3
The phrase [I]times by [/I]means times or multiplied by:
5g
Then add 3 means we add 3 to 5g:
[B]5g + 3
[MEDIA=youtube]7KeEWSY1WMg[/MEDIA][/B]

Geometric Distribution

Using a geometric distribution, it calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, standard deviation, skewness, and kurtosis.

Calculates moment number t using the moment generating function

Calculates moment number t using the moment generating function

geometric mean of 6 and 24

Use the [URL='http://www.mathcelebrity.com/statbasic.php?num1=6%2C24&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Central+Tendency']geometric mean calculator[/URL]:
We get [B]12[/B]

Geometric Mean of a Triangle

Given certain segments of a special right triangle, this will calculate other segments using the geometric mean

Giovanni is thinking of a number. If he adds 2 to it, then divides that sum by 3, he gets 7. What is

Giovanni is thinking of a number. If he adds 2 to it, then divides that sum by 3, he gets 7. What is the number?
Let the number be n:
[LIST]
[*]n
[*]Add 2: n + 2
[*]Divide the sum by 3: (n + 2)/3
[*]The word "gets" means an equation, so we set (n + 2)/3 equal to 7
[/LIST]
(n + 2)/3 = 7
Cross multiply:
n + 2 = 21
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B2%3D21&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]19[/B]

Given y= 4/3x what is the constant of proportionality

Given y= 4/3x what is the constant of proportionality
Direct variation means the constant of proportionality is y/x.
Cross multiplying, we get:
y/x = [B]4/3[/B]

Golden Ratio

Solves for 2 out of the 3 variables for a segment broken in 2 pieces that satisfies the Golden Ratio (Golden Mean).

(a) Large Segment

(b) Small Segment

(a + b) Total Segment

(a) Large Segment

(b) Small Segment

(a + b) Total Segment

Grand Mean

Calculates the grand mean of a set of number sets.

Grandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older tha

Grandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older than her daughter, but 31 years younger than her mother (the grandmother). How old are the three
Let grandmother's age be g. Let mother's age be m. Let daughter's age be d. We're given 3 equations:
[LIST=1]
[*]m = d + 25
[*]m = g - 31
[*]d + g + m = 150
[/LIST]
This means the daughter is:
d = 25 + 31 = 56 years younger than her grandmother. So we have:
4. d = g - 56
Plugging in equation (2) and equation(4) into equation (3) we get:
g - 56 + g + g - 31
Combine like terms:
3g - 87 = 150
[URL='https://www.mathcelebrity.com/1unk.php?num=3g-87%3D150&pl=Solve']Typing this equation into the search engine[/URL], we get:
[B]g = 79[/B]
Plug this into equation (2):
m = 79 - 31
[B]m = 48[/B]
Plug this into equation (4):
d = 79 - 56
[B]d = 23[/B]

Gregg has 8 cards.Half red,half black. He picks 2 cards from the deck.What is the probability both o

Gregg has 8 cards.Half red,half black. He picks 2 cards from the deck.What is the probability both of them are red?
Half means 4 cards are red and 4 cards are black.
The first draw probability of red is:
4 total red cards out of 8 total cards = 4/8.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F8&frac2=3%2F8&pl=Simplify']Simplified, this is[/URL] 1/2
The second draw is 3 total red cards out of 7 remaining cards. Since 1 red was drawn (4 - 1) = 3 reds left and 1 card was drawn (8 -1) = left
3/7
Since each draw is independent, we multiply the probabilities:
1/2 * 3/7 = [B]3/14[/B]

H minus 6 all cubed

H minus 6 all cubed
H minus 6
h - 6
All cubed means raise the entire expression to the 3rd power
(h - 6)^3

Half of ab

Half of ab
Half means we divide by 2:
[B]ab/2[/B]

half of c subtracted from the sum of a and b

half of c subtracted from the sum of a and b
The sum of a and b:
a + b
half of c means we divide c by 2:
c/2
half of c subtracted from the sum of a and b:
[B]a + b - c/2[/B]

Half of g multiplied by t squared is equal to d.

Half of g multiplied by t squared is equal to d.
Half of g:
g/2
t squared:
t^2
Half of g multiplied by t squared:
gt^2/2
The phrase [I]is equal to[/I] mean we set gt^2/2 equal to d:
[B]gt^2/2 = d[/B]

Half of the difference of a and b

Half of the difference of a and b
The difference of a and b is written as:
a - b
Half of the difference means we divide (a - b) by 2:
[B](a - b)/2[/B]

half of the sum of 2p and q

half of the sum of 2p and q
The sum of 2p and q means we add q to 2p:
2p + q
Half of this means we divide the sum by 2:
[B](2p + q)/2[/B]

half of z increased by 10

half of z increased by 10
Half of z (means we divide z by 2)
z/2
Increased by 10 means we add 10
[B]z/2 + 10[/B]

half the difference of x and 3

half the difference of x and 3
The difference of x and 3 means we subtract 3 from x:
x - 3
half of the difference means we divide the difference by 2:
[B](x - 3)/2[/B]

half the sum of the numbers s, t, and u

half the sum of the numbers s, t, and u
The [I]sum [/I]of s, t, and u means we add all 3:
s + t + u
[I]Half[/I] the sum means we divide the sum by 2:
[B](s + t + u)/2[/B]

Hari planted 324 plants in such a way that there were as many rows of plants as there were number of

Hari planted 324 plants in such a way that there were as many rows of plants as there were number of columns. Find the number of rows and columns.
Let r be the number of rows and c be the number of columns. We have the area:
rc = 324
Since rows equal columns, we have a square, and we can set r = c.
c^2 = 324
Take the square root of each side:
[B]c = 18[/B]
Which means [B]r = 18[/B] as well.
What we have is a garden of 18 x 18.

Height and weight are two measurements used to track a child's development. TheWorld Health Organiza

Height and weight are two measurements used to track a child's development. The World Health Organization measures child development by comparing the weights of children who are the same height and the same gender.
In 2009, weights for all 80 cm girls in the reference population had a mean μ = 10.2 kg and standard deviation σ = 0.8 kg. Weights are normally distributed. X ~ N(10.2, 0.8).
Calculate the z-scores that correspond to the following weights and interpret them.
a. 11 kg

b. 7.9 kg

c. 12.2 kg a. [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+11&mean=10.2&stdev=8&n=+1&pl=1" target="_blank']Answer A[/URL] - Z = 0.1 b. [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+7.9&mean=+10.2&stdev=+8&n=+1&pl=1']Answer B[/URL] - Z = -0.288 c. [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+12.2&mean=+10.2&stdev=+8&n=+1&pl=1']Answer C[/URL] - Z = 0.25

b. 7.9 kg

c. 12.2 kg a. [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+11&mean=10.2&stdev=8&n=+1&pl=1" target="_blank']Answer A[/URL] - Z = 0.1 b. [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+7.9&mean=+10.2&stdev=+8&n=+1&pl=1']Answer B[/URL] - Z = -0.288 c. [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+12.2&mean=+10.2&stdev=+8&n=+1&pl=1']Answer C[/URL] - Z = 0.25

HELP SOLVE

Perform a one-sample z-test for a population mean. Be sure to state the hypotheses and the significance level, to compute the value of the test statistic, to obtain the P-value, and to state your conclusion.
Five years ago, the average math SAT score for students at one school was 475. A teacher wants to perform a hypothesis test to determine whether the mean math SAT score of students at the school has changed. The mean math SAT score for a random sample of 40 students from this school is 469. Do the data provide sufficient evidence to conclude that the mean math SAT score for students at the school has changed from the previous mean of 475? Perform the appropriate hypothesis test using a significance level of 10%. Assume that ? = 73.

HELP SOLVE

A sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level.
x = 20.5, n = 11, ? = 7, H0: µ = 18.7 , Ha: µ ? 18.7 , ? = 0.01

HELP SOLVE

sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level.
x = 3.7, n = 32, ? = 1.8, H0: µ = 4.2 , Ha: µ ? 4.2 , ? = 0.05

HELP SOLVE

A sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test about the mean, µ, of the population from which the sample was drawn
x = 3.26 , S = 0.55, ?N= 9, H0: µ = 2.85, Ha: µ > 2.85 , ? = 0.01

HELP SOLVE

[URL]http://www.mathcelebrity.com/mean_hypothesis.php?xbar=469&n=40&stdev=73&ptype=%3D&mean=475&alpha=0.10&pl=Mean+Hypothesis+Testing[/URL]

HELP SOLVE

[URL]http://www.mathcelebrity.com/mean_hypothesis.php?xbar=3.7&n=3.2&stdev=1.8&ptype=%3D&mean=4.2&alpha=0.05&pl=Mean+Hypothesis+Testing[/URL]

HELP SOLVE

[URL]http://www.mathcelebrity.com/mean_hypothesis.php?xbar=20.5&n=11&stdev=7&ptype=%3D&mean=18.7&alpha=0.01&pl=Mean+Hypothesis+Testing[/URL]

Henrietta hired a tutor to help her improve her math scores. While working with the tutor, she took

Henrietta hired a tutor to help her improve her math scores. While working with the tutor, she took four tests. She scored 10 points better on the second test than she did on the first, 20 points better on the third test than on the first, and 30 points better on the fourth test than on the first. If the mean of these four tests was 70, what was her score on the third test?
Givens:
[LIST]
[*]Let the first test score be s:
[*]The second test score is: s + 10
[*]The third test score is: s + 20
[*]The fourth test score is: s + 30
[/LIST]
The mean of the four tests is 70, found below:
Sum of test scores / Number of Tests = Mean
Plugging in our number, we get:
(s + s + 10 + s + 20 + s + 30) / 4 = 70
Cross multiply and simplify:
4s + 60 = 70 * 4
4s + 60 = 280
To [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B60%3D280&pl=Solve']solve this equation for s, we type it in our search engine[/URL] and we get:
s = 55
So the third test score:
s + 20 = 55 + 20
[B]75[/B]

HomeWork Help Please Respond ASAP!!!

The phrase a number means an arbitrary variable, let's call it x.
Three times a number:
3x
And 18 means we add 18
3x + 18
The word is means equal to, so we set 3x + 18 equal to -39
3x + 18 = -39
This is your algebraic expression. If you want to solve for x, plug it into the [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']search engine[/URL] and you get x = -19

How many 8$, tickets can I get for 100$

How many 8$, tickets can I get for 100$
Tickets = Total Money / price per ticket
Tickets = 100/8
Tickets = [B]12.5
[/B]
If the problem asks for a whole number, this means you cannot have a partial ticket. Therefore, we round down to [B]12 tickets[/B]

How old am I if 400 reduced by 3 times my age is 124?

How old am I if 400 reduced by 3 times my age is 124?
Let my age be a. We're given an algebraic expression:
[LIST]
[*]3 times my age means we multiply a by 3: 3a
[*]400 reduced by 3 times my age means we subtract 3a from 400:
[*]400 - 3a
[*]The word [I]is[/I] mean an equation, so we set 400 - 3a equal to 124
[/LIST]
400 - 3a = 124
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D124&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]92[/B]

How old am I if: 210 reduced by 3 times my current age is 4 times my current age?

How old am I if: 210 reduced by 3 times my current age is 4 times my current age?
Let your current age be a. We're given:
[LIST]
[*]210 reduced by 3 times current age = 210 - 3a
[*]4 times current age = 4a
[*]The word [I]is[/I] means equal to. So we set 210 - 3a equal to 4a
[/LIST]
210 - 3a = 4a
To solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=210-3a%3D4a&pl=Solve']type this equation into our search engine [/URL]and we get:
a = [B]30[/B]

How old am I of 400 reduced by 2 times my age is 224

How old am I of 400 reduced by 2 times my age is 224
[LIST=1]
[*]Let my age be a.
[*]2 times my age: 2a
[*]400 reduced by 2 times my age: 400 - 2a
[*]The phrase [I]is [/I]means an equation. So we set 400 - 2a equal to 224 for our algebraic expression
[/LIST]
[B]400 - 2a = 224
[/B]
If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D224&pl=Solve']type this equation into our search engine[/URL] and we get:
a = [B]88[/B]

Hypothesis testing for the mean

Performs hypothesis testing on the mean both one-tailed and two-tailed and derives a rejection region and conclusion

I am 12 years old. My brother is 5 years older than me. How old is my brother?

I am 12 years old. My brother is 5 years older than me. How old is my brother?
Older means we add, so we have:
Brother's age = 12 + 5
Brother's age = [B]17[/B]

I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5

I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5 and add 283. What is my number?
Let the number be n. We're given two expressions:
[LIST=1]
[*]Multiply it by 14 and add 13: 14n + 13
[*]Multiply by 5 and add 283: 5n + 283
[/LIST]
The phrase [I]I get the same answer[/I] means an equation. So we set expression 1 equal to expression 2:
14n + 13 = 5n + 283
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=14n%2B13%3D5n%2B283&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]30[/B]

I am thinking of a number. I multiply it by 14 and add 21. I get the same answer if I multiply by 4

I am thinking of a number. I multiply it by 14 and add 21. I get the same answer if I multiply by 4 and add 141.
Let the number be n.
We have two expressions:
[LIST=1]
[*]Multiply by 14 and add 21 is written as: 14n + 21
[*]Multiply by 4 and add 141 is written as: 4n + 141
[/LIST]
The phrase [I]get the same expression[/I] means they are equal. So we set (1) and (2) equal to each other and solve for n:
14n + 21 = 4n + 141
[URL='https://www.mathcelebrity.com/1unk.php?num=14n%2B21%3D4n%2B141&pl=Solve']Type this equation into our search engine [/URL]to solve for n and we get:
n = [B]12[/B]

I am thinking of a number. I multiply it by 7 and add 25. I get the same answer if I multiply by 3 a

I am thinking of a number. I multiply it by 7 and add 25. I get the same answer if I multiply by 3 and add 93. What is my number?
Let the number be n. We're given two expressions:
[LIST]
[*]Multiply the number by 7: 7n
[*]add 25: 7n + 25. <-- Expression 1
[*]Multiply by 3: 3n
[*]Add 93: 3n + 93 <-- Expression 2
[*]The phrase [I]get the same answer[/I] means both expression 1 and expression 2 are equal. So we set them equal to each other:
[/LIST]
7n + 25 = 3n + 93
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=7n%2B25%3D3n%2B93&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]17[/B]

I had $21 to spend on two notebooks after buying them I had $13 how much did each notebook cost

I had $21 to spend on two notebooks after buying them I had $13 how much did each notebook cost?
If you had $13, leftover, this means you spent the following on notebooks:
$21 - $13 = $7
Cost per notebook = Total Notebook spend / Total Notebooks
Cost per notebook = $7/2
Cost per notebook = [B]$3.50[/B]

If 10% of 400 is decreased by 25, the result is

If 10% of 400 is decreased by 25, the result is?
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=10&den1=400&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']10% of 400 using our search engine[/URL] is 40.
The phrase [I]decreased by[/I] means we subtract 25 from 40:
40 - 25 = [B]15[/B]

If 11 times a number is added to twice the number, the result is 104

If 11 times a number is added to twice the number, the result is 104
Let [I]the number[/I] be an arbitrary variable we call x.
11 times a number:
11x
Twice the number (means we multiply x by 2):
2x
The phrase [I]is added to[/I] means we add 2x to 11x:
11x + 2x
Simplify by grouping like terms:
(11 + 2)x = 13x
The phrase [I]the result is[/I] means an equation, so we set 13x equal to 104:
13x = 104 <-- This is our algebraic expression
To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=13x%3D104&pl=Solve']we type it in our search engine[/URL] and we get:
x = [B]8[/B]

If 2 times an integer x is increased by 5

If 2 times an integer x is increased by 5
2 times an integer x:
2x
The phrase [I]increased by[/I] means we add, so we add 5 to 2x:
[B]2x + 5[/B]

If 3 times a number added to 2 is divided by the number plus 4 the result is 4/3

If 3 times a number added to 2 is divided by the number plus 4 the result is 4/3
Take this in pieces, where "a number" means an arbitrary variable, let's call it "x".
[LIST=1]
[*]3 times a number --> 3x
[*]3 times a number added to 2 --> 3x + 2
[*]The number plus 4 --> x + 4
[*]is divided by --> (3x + 2)/(x + 4)
[*]the result is 4/3 --> (3x + 2)/(x + 4) = 4/3
[/LIST]

If 4 times a number is added to 9, the result is 49

If 4 times a number is added to 9, the result is 49.
[I]A number[/I] means an arbitrary variable, let's call it x.
4 [I]times a number[/I] means we multiply x by 4
4x
[I]Added to[/I] 9 means we add 9 to 4x
4x + 9
[I]The result is[/I] means we have an equation, so we set 4x + 9 equal to 49
[B]4x + 9 = 49[/B] <-- This is our algebraic expression
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%2B9%3D49&pl=Solve']we type it in the search engine[/URL] and get x = 10

If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integ

If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integer.
[LIST]
[*]Let the integer be "x".
[*]Square the integer: x^2
[*]7 times the square: 7x^2
[*]5 times the integer: 5x
[*]Add them together: 7x^2 + 5x
[*][I]The result is[/I] means an equation, so we set 7x^2 + 5x equal to 2
[/LIST]
7x^2 + 5x = 2
[U]This is a quadratic equation. To get it into standard form, we subtract 2 from each side:[/U]
7x^2 + 5x - 2 = 2 - 2
7x^2 + 5x - 2 = 0
[URL='https://www.mathcelebrity.com/quadratic.php?num=7x%5E2%2B5x-2%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get two solutions:
[LIST=1]
[*]x = 2/7
[*]x= -1
[/LIST]
The problem asks for an integer, so our answer is x[B] = -1[/B].
[U]Let's check our work by plugging x = -1 into the quadratic:[/U]
7x^2 + 5x - 2 = 0
7(-1)^2 + 5(-1) - 2 ? 0
7(1) - 5 - 2 ? 0
0 = 0
So we verified our answer, [B]x = -1[/B].

If 72 is added to a number it will be 4 times as large as it was originally

If 72 is added to a number it will be 4 times as large as it was originally
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
72 added to a number:
x + 72
4 times as large as it was originally means we take the original number x and multiply it by 4:
4x
Now, the phrase [I]it will be[/I] means an equation, so we set x + 72 equal to 4x to get our final algebraic expression:
[B]x + 72 = 4x[/B]
[B][/B]
If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B72%3D4x&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]24[/B]

If 9 is added to 1/3 of a number, the result is 15. What is the number?

If 9 is added to 1/3 of a number, the result is 15. What is the number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
1/3 of a number means we multiply x by 1/3:
x/3
9 is added to 1/3 of a number:
x/3 + 9
The phrase [I]the result is[/I] means an equation. so we set x/3 + 9 equal to 15
x/3 + 9 = 15
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2F3%2B9%3D15&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]18[/B]

if 9 times a number is decreased by 6, the result is 111

if 9 times a number is decreased by 6, the result is 111
A number means an arbitrary variable, let's call it x.
9 times a number:
9x
Decreased by 6
9x - 6
The result is 11, this means we set 9x - 6 equal to 11
[B]9x - 6 = 11
[/B]
To solve this equation for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=9x-6%3D11&pl=Solve']equation calculator[/URL]

If a die is rolled, what is the probability that the number rolled will not be a "5"?

If a die is rolled, what is the probability that the number rolled will not be a "5"?
Possible rolls:
{1, 2, 3, 4, 5, 6}
Probability of not a 5 means:
{1, 2, 3, 4, 6}
P(Not 6) = 1 - P(6)
P(Not 6) = 1 - 1/6
P(Not 6) = [B]5/6[/B]

if a number is added to its square, it equals 20

if a number is added to its square, it equals 20.
Let the number be an arbitrary variable, let's call it n.
The square of the number means we raise n to the power of 2:
n^2
We add n^2 to n:
n^2 + n
It equals 20 so we set n^2 + n equal to 20
n^2 + n = 20
This is a quadratic equation. So [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn%3D20&pl=Solve+Quadratic+Equation&hintnum=+0']we type this equation into our search engine[/URL] to solve for n and we get two solutions:
[B]n = (-5, 4)[/B]

if a number is decreased by 5, and then the result is multiplied by 2, the result is 26

If a number is decreased by 5, and then the result is multiplied by 2, the result is 26
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
[I]Decreased by[/I] means we subtract 5 from x:
x - 5
Multiply the result by 2:
2(x - 5)
The result is 26 means we set 2(x - 5) equal to 26:
[B]2(x - 5) = 26[/B]

if a number is tripled the result is 60

if a number is tripled the result is 60
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Triple the number means we multiply by 3:
3x
The phrase [I]the result is[/I] means an equation, so we set 3x equal to 60:
[B]3x = 60 <-- This is our algebraic expression
[/B]
If you want to solve this equation, then [URL='https://www.mathcelebrity.com/1unk.php?num=3x%3D60&pl=Solve']you type in 3x = 60 into the search engine[/URL] and get:
x = 20

If approximately 68% of the scores lie between 40.7 and 59.9 , then the approximate value of the sta

If approximately 68% of the scores lie between 40.7 and 59.9 , then the approximate value of the standard deviation for the distribution, according to the empirical rule, is
The empirical rule states 68% of the values lie within 1 standard deviation of the mean. The mean is the midpoint of the interval above:
(59.9 + 40.7)/2 = 50.3
Standard deviation is the absolute value of the mean - endpoint
|59.9 - 50.3| = [B]9.6[/B]

If Frank’s age is double of Willis’ age and the sum of their ages is 42. What are their ages?

If Frank’s age is double of Willis’ age and the sum of their ages is 42. What are their ages?
Let Frank's age be f. Let Willis's age be w. We're given two equations:
[LIST=1]
[*]f = 2w <-- Double means multiply by 2
[*]f + w = 42
[/LIST]
Substitute equation (1) into equation (2):
2w + w = 42
To solve for w, [URL='https://www.mathcelebrity.com/1unk.php?num=2w%2Bw%3D42&pl=Solve']type this equation into our search engine[/URL]. We get:
w = [B]14
[/B]
Now, take w = 14, and substitute it back into equation (1) to solve for f:
f = 2(14)
f = [B]28[/B]

If Hailey makes $300 every two weeks, how much will Hailey have at the end of the year?

If Hailey makes $300 every two weeks, how much will Hailey have at the end of the year?
52 weeks in a year, which means we have:
52/2 = 26 two week periods
300 * 26 two week periods = [B]7,800[/B]

If i triple the number then subtract 7 the answer is 2. What is the number

If i triple the number then subtract 7 the answer is 2. What is the number
Let the number be x.
Triple the number:
3x
Subtract 7
3x - 7
The answer is 2 means we set:
[B]3x - 7 = 2[/B]
This is our algebraic expression. To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D2&pl=Solve']we type this problem into the search engine[/URL] and get [B]x = 3[/B].

If p is inversely proportional to the square of q, and p is 2 when q is 4, determine p when q is equ

If p is inversely proportional to the square of q, and p is 2 when q is 4, determine p when q is equal to 2.
We set up the variation equation with a constant k such that:
p = k/q^2 [I](inversely proportional means we divide)
[/I]
When q is 4 and p is 2, we have:
2 = k/4^2
2 = k/16
Cross multiply:
k = 2 * 16
k = 32
Now, the problem asks for p when q = 2:
p = 32/2^2
p = 32/4
p = [B]8[/B]

If power is big, you can assume:

If power is big, you can assume:
a. The difference between the means is more likely to be detected
b. The significance level set by the researcher must be high
c. We increase the probability of type I error
d. Your study result will be more likely to be inconclusive
[B]b. The significance level set by the researcher must be high[/B]

If Susie is 14, what was her age x years ago?

If Susie is 14, what was her age x years ago?
x years ago means we subtract x from 14:
[B]14 - x[/B]

If the difference of a number and 4 is multiplied by 3 the result is 19

If the difference of a number and 4 is multiplied by 3 the result is 19
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The difference of a number and 4:
x - 4
The phrase [I]is multiplied by[/I] means we multiply x - 4 by 3:
3(x - 4)
The phrase [I]the result is[/I] means equals, so we set 3(x - 4) equal to 19
[B]3(x - 4) = 19
[MEDIA=youtube]Q8bnVJuWeVk[/MEDIA][/B]

If the distribution of IQ scores is bell-shaped, with a mean of 100 and a standard deviation of 15,

If the distribution of IQ scores is bell-shaped, with a mean of 100 and a standard deviation of 15, then approximately ____% of IQ scores are less than 55?
A bell-shaped curved implies a normal distribution. By using our [URL='https://www.mathcelebrity.com/probnormdist.php?xone=55&mean=100&stdev=15&n=1&pl=Empirical+Rule']empirical rule calculator[/URL], we see that:
99.7% of all normal distribution values lie within 3 standard deviations of the mean.
This means the percent of scores less than 55 which is 3 standard deviations away from the mean is:
100% - 99.7% = [B]0.3%[/B]

If the number of professors in a college is P and the number is students S, and there are 14 times a

If the number of professors in a college is P and the number is students S, and there are 14 times as many students as professors
14 times as many means we multiply:
[B]S = 14P[/B]

If the probability of winning is X, what is the probability of losing? (Assume there are no ties.)

If the probability of winning is X, what is the probability of losing? (Assume there are no ties.)
This means you can either win or lose. Since all probabilities in the sample space must add up to 1, then we have:
P(Winning) + P(Losing) = 1
P(Losing) = 1 - P(Winning)
Since P(Winning) = X, we have:
P(Losing) = [B]1 - X[/B]

If the ratio of private school students to public school students in a city is 4 to 15 and there is

If the ratio of private school students to public school students in a city is 4 to 15 and there is a total of 18,601 students, how many students are in public schools?
Since 4 out of 15 are public school students, this means (15 - 4)/15 = 11/15 are public school students.
The total public school students are (11/15) * 18601 = 13,640.73. Rounded up, it is [B]13,641[/B].

If the temperature during the day is 6° and the temperature drops 15° after sunset, what is the temp

If the temperature during the day is 6° and the temperature drops 15° after sunset, what is the temperature at night?
A drop in temperature means we subtract, so we have:
6 - 15 = [B]-9 or 9 below zero[/B]

If thrice a number is increased by 11,the result is 35. What is the number

If thrice a number is increased by 11,the result is 35. What is the number?
[LIST]
[*]The phrase [I]a number [/I]means an arbitrary variable. Let's call it x.
[*]Thrice means multiply by 3, so we have 3x
[*]Increased by 11 means we add 11, so we have 3x + 11
[*]The [I]result is[/I] means an equation, so we set 3x + 11 equal to 35
[/LIST]
3x + 11 = 35 <-- This is our algebraic expression
The problem ask us to solve the algebraic expression.
[URL='https://www.mathcelebrity.com/1unk.php?num=3x%2B11%3D35&pl=Solve']Typing this problem into our search engine[/URL], we get [B]x = 8[/B].

If twice a number is divided by 7, the result is -28

If twice a number is divided by 7, the result is -28.
The phrase [I]a number[/I] means an arbitrary variable, let's call it "x".
Twice x means we multiply x by 2: 2x
Divide this by 7: 2x/7
We set this equal to -28, and we have our algebraic expression:
[B]2x/7 = -28 [/B]

if two angles are supplementary and congruent then they are right angles

if two angles are supplementary and congruent then they are right angles
Let the first angle be x. Let the second angle be y.
Supplementary angles means their sum is 180:
x + y = 180
We're given both angles are congruent, meaning equal. So we set x = y:
y + y = 180
To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=y%2By%3D180&pl=Solve']type this equation into our search engine[/URL] and we get:
y = [B]90. <-- 90 degrees is a right angle, so this is TRUE[/B]

If two coins are flipped, what is the probability that there will not be two heads?

If two coins are flipped, what is the probability that there will not be two heads?
There's only one way to flip 2 coins and get 2 heads:
P(HH) = 1/2 * 1/2 = 1/4
Which means the probability of NOT getting 2 heads is:
1 - 1/4 = [B]3/4[/B]

If y varies directly as x and inversely as z, then which equation describes the relation?

If y varies directly as x and inversely as z, then which equation describes the relation?
Directly means we multiply, inversely means we divide, so we have a constant k such that:
[B]y = kx/z[/B]

if you add 35 to twice a number, the result is 17. What is the number?

if you add 35 to twice a number, the result is 17. What is the number?
A number is represented by a variable, let's call it "x".
Twice a number means we multiply by 2 --> 2x
Add 35
2x + 35
Now set that entire expression equal to 17
2x + 35 = 17
[URL='http://www.mathcelebrity.com/1unk.php?num=2x%2B35%3D17&pl=Solve']Plug that into the search engine to solve for x[/URL]
[B]x = -9[/B]

if you add 7 to 2x, the result is 17

if you add 7 to 2x, the result is 17
Add 7 to 2x:
2x + 7
The phrase [I]the result is[/I] means an equation, so we set 2x + 7 = 17
[B]2x + 7 = 17 [/B] <-- This is our algebraic expression
Now, if you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B7%3D17&pl=Solve']type in 2x + 7 = 17 into the search engine[/URL], and we get [B]x = 5[/B].

If you multiply me by 33 and subtract 20, the result is 46. Who am I?

If you multiply me by 33 and subtract 20, the result is 46. Who am I?
[LIST]
[*]Start with the variable x
[*]Multiply me by 33 = 33x
[*]Subtract 20: 33x - 20
[*]The result is 46, means we set this expression equal to 46: 33x - 20 = 46
[/LIST]
Run this through our [URL='http://www.mathcelebrity.com/1unk.php?num=33x-20%3D46&pl=Solve']equation calculator[/URL], and we get:
[B]x = 2[/B]

Imagine a researcher wanted to test the effect of the new drug on reducing blood pressure. In this s

Imagine a researcher wanted to test the effect of the new drug on reducing blood pressure. In this study, there were 50 participants. The researcher measured the participants' blood pressure before and after the drug intake. If we want to compare the mean blood pressure from the two time periods with a two-tailed t test, how many degrees of freedom are there?
a. 49
b. 50
c. 99
d. 100
[B]a. 49[/B]
Degrees of Freedom = n - 1
Degrees of Freedom = 50 - 1
Degrees of Freedom = 49

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He r

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. What's the [B][U]standard error of the mean[/U][/B]?
9.29839 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics#standard_error_of_the_mean']statistics calculator[/URL]

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He r

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. The researcher posed a null hypothesis that the average weight for boys in that high school should be 100 lbs. What is the [B][U]absolute value[/U][/B] of calculated t that we use for testing the null hypothesis?
Mean is 109.4 and Standard Deviation = 20.79182532 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']statistics calculator[/URL]
Now use those values and calculate the t-value
Abs(t value) = (100 - 109.4)/ 20.79182532/sqrt(5)
Abs(tvalue) = [B]1.010928029[/B]

In 2000 a company increased its workforce by 50%. In 2001 it decreased its workforce by 50%. How doe

In 2000 a company increased its workforce by 50%. In 2001 it decreased its workforce by 50%. How does the size of its workforce at the end of 2001 compare with the size of the workforce at the beginning of 2000?
Let w be the size of the workforce before any changes. We have:
[LIST]
[*]w(2000) = w(1999) * 1.5 [I](50% increase is the same as multiplying by 1.5)[/I]
[*]w(2001) = w(2000)/1.5 [I](50% decrease is the same as dividing by 1.5)[/I]
[/LIST]
Substitute the first equation back into the second equation
w(2001) = w(1999) * 1.5/1.5
Cancel the 1.5 on top and bottom
w(2001) = w(1999)
This means the workforce had [B]zero net change[/B] from the beginning of 2000 to the end of 2001.

In 32, what is the value of 2

In 32, what is the value of 2
For place value, starting from the right decimal with no decimals, we have:
tens, ones
3 is the tens digit
2 is the ones digit
32 = 3 * 10 + 2 * 1
Which means 2 is the [B]ones digit[/B]

In 8 years kelly's age will be twice what it is now. How old is kelly?

In 8 years kelly's age will be twice what it is now. How old is kelly?
Let Kelly's age be a.
In 8 years means we add 8 to a:
a + 8
Twice means we multiply a by 2:
2a
The phrase [I]will be[/I] means equal to, so we set a + 8 equal to 2a
a + 8 = 2a
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B8%3D2a&pl=Solve']type it in our math engine[/URL] and we get:
a = [B]8
[/B]
[U]Evaluate a = 8 and check our work[/U]
8 + 8 ? 2(8)
16 = 16
[MEDIA=youtube]y4jaQpkaJEw[/MEDIA]

In a theatre audience of 500 people, 80 percent were adults. How many children were in the audience

In a theatre audience of 500 people, 80 percent were adults. How many children were in the audience?
If 80% were adults, this means 100% - 80% = 20% were children.
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=20&den1=500&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']We type the expression 20% of 500 into our search engine[/URL] and get [B]100 children[/B]

In base 10 the number 25.12 actually means 20 + 5 + 1/10 + 2/100. What does the base 7 number 25.12

In base 10 the number 25.12 actually means 20 + 5 + 1/10 + 2/100. What does the base 7 number 25.12 mean?
2 groups of 7
5 groups of 1
1 group of 1/7
2 groups of 1/49 (1/7)^2
14 + 5 + 1/7 + 2/49

In base 10, the number .1111... approaches 1/9. What does .111111 base 2 approach in base 10?

In base 10, the number .1111... approaches 1/9. What does .111111 base 2 approach in base 10?
Base 2 .11111 means:
(1/2)^1 + (1/2)^2 + + (1/2)^3 + (1/2)^4
1/2 + 1/4 + 1/8 + 1/16
[B]This approaches 1[/B]

In order to test if there is a difference between means from two populations, which of following ass

In order to test if there is a difference between means from two populations, which of following assumptions are NOT required?
a. The dependent variable scores must be a continuous quantitative variable.
b. The scores in the populations are normally distributed.
c. Each value is sampled independently from each other value.
d. The two populations have similar means
[B]a and d
[/B]
[I]because b and c [U]are[/U] required[/I]

In the last year a library bought 237 new books and removed 67 books. There were 5745 books in the l

In the last year a library bought 237 new books and removed 67 books. There were 5745 books in the library at the end of the year. How many books were in the library at the start of the year
Let the starting book count be b. We have:
[LIST]
[*]We start with b books
[*]Buying 237 books means we add (+237)
[*]Removing 67 books means we subtract (-67)
[*]We end up with 5745 books
[/LIST]
Our change during the year is found by the equation:
b + 237 - 67 = 5745
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B237-67%3D5745&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]5575[/B]

In the wild, monkeys eat an average of 28 bananas a day with a standard deviation of 2 bananas. One

In the wild, monkeys eat an average of 28 bananas a day with a standard deviation of 2 bananas. One monkey eats only 21 bananas. What is the z-score for this monkey? Is the number of bananas the monkey eats unusually low?
Using [URL='https://www.mathcelebrity.com/probnormdist.php?xone=21&mean=28&stdev=2&n=1&pl=P%28X+%3C+Z%29']our z-score calculator[/URL], we get:
Z < -3.5
P(Z < -3.5) = 0.499767
Also, this [B]is unusually low as it's more than 3 deviations away from the mean[/B]

In x years time, Peter will be 23 years old. How old is he now?

In x years time, Peter will be 23 years old. How old is he now?
Let Peter's current age be a. In x years time means we add x to a, so we're given:
a + x = 23
We want to find a, s we subtract x from each side to get:
a + x - x = 23 - x
Cancel the x terms on the left side and we get:
a = [B]23 - x[/B]

Increase 6 by d

Increase 6 by d
Increase means add:
[B]6 + d[/B]

Is 3 standard deviations above the means considered an outlier?

Is 3 standard deviations above the means considered an outlier?
[B]Yes.[/B]
Using the empirical rule, we know that:
[LIST]
[*]68% of the values lie within one standard deviation of the mean
[*]95% of the values lie within two standard deviations of the mean
[/LIST]
Anything out side of two standard deviations is considered an outlier.

Is it correct to word "10% * 50 + 50" as "10% upper 50"?

Upper meaning upper bound? Upper percentile? Upper quartile?
I need a bit more background on what lesson or concept you are working on right now.

is parallel to the x-axis and has an y-intercept of 3

is parallel to the x-axis and has an y-intercept of 3
Parallel to the x axis means it runs through the y-axis
y-intercept of 3 means our equation is [B]y = 3[/B]

Isabel earns $7.50 per hour on the weekends. Write and solve an inequality to find how many hours sh

Isabel earns $7.50 per hour on the weekends. Write and solve an inequality to find how many hours she needs to work to earn at least $120.
A few things to note:
[LIST]
[*]Earnings = Rate * time
[*]Let h be the number of hours worked
[*]The phrase [I]at least[/I] means greater than or equal to, so we have the following inequality.
[/LIST]
We represent this with the following inequality:
7.5h < 120
To solve this inequality for h, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=7.5h%3C120&pl=Show+Interval+Notation']type it into our math engine[/URL] and we get:
[B]h < 16[/B]

It is estimated that weekly demand for gasoline at new station is normally distributed, with an aver

It is estimated that weekly demand for gasoline at new station is normally distributed, with an average of 1,000 and standard deviation of 50 gallons. The station will be supplied with gasoline once a week. What must the capacity of its tank be if the probability that its supply will be exhausted in a week is to be no more than 0.01?
0.01 is the 99th percentile
Using our [URL='http://www.mathcelebrity.com/percentile_normal.php?mean=+1000&stdev=50&p=99&pl=Calculate+Percentile']percentile calculator[/URL], we get [B]x = 1116.3[/B]

It is known that 45% of men snore an 25% of women snore. A doctor looked at these numbers and made t

It is known that 45% of men snore an 25% of women snore. A doctor looked at these numbers and made the following statement:
"If you put a man and a woman together, there is a 70% chance that someone is snoring."
Explain why the doctor's math is wrong.
The doctor added the percents together: 45% + 25% = 70%.
Here's why this is incorrect:
[LIST]
[*]45% of men snore means 100% - 45% = 55% of men do not snore
[*]25% of women snore means 100% - 25% = 75% of women do not snore
[*]Both men and women not snoring is: 55% * 75% = 41.25% neither of them snore
[*]100% - 41.25% = [B]58.75%[/B] somebody is snoring
[/LIST]

It takes 3/4 of an hour to complete a puzzle. How many puzzles can Cindy finish in 3 hours?

It takes 3/4 of an hour to complete a puzzle. How many puzzles can Cindy finish in 3 hours?
We setup a proportion of time to puzzles where p is the number of puzzles Cindy can complete in 3 hours:
3/4/1 = 3/p
Dividing by 1 means the same as the original fraction, so we have:
3/4 = 3/p
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=3&den1=4&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into the search engine[/URL], we get:
p = [B]4[/B]

It takes Spot 2 hours to paint a fence and Steven 4 hours to paint the same fence. If they work toge

It takes Spot 2 hours to paint a fence and Steven 4 hours to paint the same fence. If they work together, how long will it take them to paint the fence?
Spot paints 1/2 of a fence in an hour
Steven paints 1/4 of a fence in an hour
Together, in an hour, they paint 1/2 + 1/4 of a fence in an hour
1/2 = 2/4, so we have 2/4 + 1/4 = 3/4 of a fence in an hour
Meaning they take another 20 minutes to pain the last 1/4 of the fence
[B]1 hour + 20 minutes[/B] is the total time it takes

Jack scored a mean of 15 points per game in his first 3 basketball games. In his 4th grade, he score

Jack scored a mean of 15 points per game in his first 3 basketball games. In his 4th grade, he scored 27 points. What was Jack's mean score for the four games?
The mean is the average:
Mean = (15 + 15 + 15 + 27)/4
Mean = 72/4
[B]Mean = 18[/B]

Jada scored 15 points in one basketball game and p points in another. Her two-game total is 34 point

Jada scored 15 points in one basketball game and p points in another. Her two-game total is 34 points
The phrase [I]total[/I] means a sum, so we have the following equation:
15 + p = 34
To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=15%2Bp%3D34&pl=Solve']type this equation into our search engine [/URL]and we get:
p = [B]19[/B]

James Bond has a secret code. The code is 3 digits long and less than 160. The digits add to 10. Wha

James Bond has a secret code. The code is 3 digits long and less than 160. The digits add to 10. What is his secret code?
less than 160 means 0 to 159
Working backwards with 1 in the hundreds place and 5 in the 10's place, we see that 1 + 5 + 4 = 10
[B]154[/B]

jane has 55$ to spend at cedar point. the admission price is 42$ and each soda is 4.25. write an ine

jane has 55$ to spend at cedar point. the admission price is 42$ and each soda is 4.25. write an inequality to show how many sodas he can buy.
Let s be the number of sodas.
Cost for the day is:
Price per soda * s + Admission Price
4.25s + 42
We're told that Jane has 55, which means Jane cannot spend more than 55. Jane can spend up to or less than 55. We write this as an inequality using <= 55
[B]4.25s + 42 <= 55[/B]
[B][/B]
If the problems asks you to solve for s, we type it in our math engine and we get:
Solve for [I]s[/I] in the inequality 4.25s + 42 ? 55
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 42 and 55. To do that, we subtract 42 from both sides
4.25s + 42 - 42 ? 55 - 42
[SIZE=5][B]Step 2: Cancel 42 on the left side:[/B][/SIZE]
4.25s ? 13
[SIZE=5][B]Step 3: Divide each side of the inequality by 4.25[/B][/SIZE]
4.25s/4.25 ? 13/4.25
[B]s ? 3.06[/B]

jared bakes 2 apple pies. he cuts two pies into pieces. Each piece is 1/8 of a pie. Enter the number

jared bakes 2 apple pies. he cuts two pies into pieces. Each piece is 1/8 of a pie. Enter the number of pieces of pie jared cuts
1/8 of a pie per slice means there are 8 slices per pie
2 pies * 8 pieces per pie = [B]16 pieces[/B]

Jennifer spent $11.25 on ingredients for cookies shes making for the school bake sale. How many cook

Jennifer spent $11.25 on ingredients for cookies shes making for the school bake sale. How many cookies must she sale at $0.35 apiece to make profit?
Let x be the number of cookies she makes. To break even, she must sell:
0.35x = 11.25
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=0.35x%3D11.25&pl=Solve']equation calculator[/URL], and we get:
x = 32.14
This means she must sell [B]33[/B] cookies to make a profit.

Jenny added $150 to her savings account in July. At the end if the month she had $500. How much did

Jenny added $150 to her savings account in July. At the end if the month she had $500. How much did she start with?
Let the starting balance be s. A deposit means we added 150 to s to get 500. We set up this equation below:
s + 150 = 500
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B150%3D500&pl=Solve']type this equation into our search engine[/URL] and we get:
s = 3[B]50[/B]

Jenny has $1200 and is spending $40 per week. Kelsey has $120 and is saving $50 a week. In how many

Jenny has $1200 and is spending $40 per week. Kelsey has $120 and is saving $50 a week. In how many weeks will Jenny and Kelsey have the same amount of money?
Jenny: Let w be the number of weeks. Spending means we subtract, so we set up a balance equation B(w):
B(w) = 1200 - 40w
Kelsey: Let w be the number of weeks. Saving means we add, so we set up a balance equation B(w):
B(w) = 120 + 50w
When they have the same amount of money, we set the balance equations equal to each other:
1200 - 40w = 120 + 50w
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=1200-40w%3D120%2B50w&pl=Solve']type this equation into our search engine[/URL] and we get:
w = [B]12[/B]

Jenny has $40 in her checking account. If she writes a check for $19 find her new account balance

Jenny has $40 in her checking account. If she writes a check for $19 find her new account balance
Writing a check means we take out of the account, so we subtract:
Balance = $40 - $19
Balance = [B]$21[/B]

Jeremy can plant 10 trees in 4 hours. How many trees can he plant in 10 hours?

Jeremy can plant 10 trees in 4 hours. How many trees can he plant in 10 hours?
Set up a proportion of trees planted to hours where t is the number of trees planted in 10 hours.
10/4 = t/10
[URL='https://www.mathcelebrity.com/prop.php?num1=10&num2=t&den1=4&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']Type this expression into the search engine[/URL] and we get [B]t = 25[/B].
This means Jeremy can plant 25 trees in 10 hours.

Jerry, an electrician, worked 7 months out the year. What percent of the year did he work?

Jerry, an electrician, worked 7 months out the year. What percent of the year did he work?
We know that there are 12 months in a year.
Percentage worked = Months worked in a year / months in a year * 100%
Percentage worked = 7/12 * 100%
Percentage worked = 0.5833333 * 100%
Multiplying by 100 means we shift the decimal place 2 spaces to the right:
Percentage worked = [B]58.33%[/B]

Jessie had 8 apples. Katie had 3 more. How many apples does Katie have

Jessie had 8 apples. Katie had 3 more. How many apples does Katie have
3 more means we add to Jessie's total:
Katie = Jessie + 3
Katie = 8 + 3
Katie = [B]11[/B]

jimmy has 5 apples and beth has 8 apples how many apples do they have together

jimmy has 5 apples and beth has 8 apples how many apples do they have together
[U]The word [I]together[/I] means we add:[/U]
Total Apples = Jimmy's apples + Beth's apples
Total Apples = 5 + 8
Total Apples = [B]13[/B]

Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth

Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs at least 76 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this.
At least means greater than or equal to, so we have:
[B]3x + 4y >= 76[/B]

Joe opens a bank account that starts with $20 and deposits $10 each week. Bria has a different accou

Joe opens a bank account that starts with $20 and deposits $10 each week. Bria has a different account that starts with $1000 but withdraws $15 each week. When will Joe and Bria have the same amount of money?
Let w be the number of weeks. Deposits mean we add money and withdrawals mean we subtract money.
[U]Joe's Balance function B(w) where w is the number of weeks:[/U]
20 + 10w
[U]Bria's Balance function B(w) where w is the number of weeks:[/U]
1000 - 15w
[U]The problem asks for when both balances will be the same. So we set them equal to each other and solve for w:[/U]
20 + 10w = 1000 - 15w
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=20%2B10w%3D1000-15w&pl=Solve']type this equation into our search engine[/URL] and we get:
w = 39.2
We round up to full week and get:
w = [B]40[/B]

joe plans to watch 3 movies each month. white an equation to represent the total number of movies n

joe plans to watch 3 movies each month. white an equation to represent the total number of movies n that he will watch in m months
Build movie equation. 3 movies per month at m months means we multiply:
[B]n = 3m[/B]

Joey withdrew $125 from his savings account. After the withdrawal, his balance was $785. How much wa

Joey withdrew $125 from his savings account. After the withdrawal, his balance was $785. How much was in his account initially?
[U]Withdrawal means he took money out, which means his initial balance is found by adding back the withdrawal:[/U]
Initial Balance = Current Balance + Withdrawal
Initial Balance = 785 + 125
Initial Balance = [B]910[/B]

John has x number of marbles. His friend gave him 6 marbles more. Write an expression for the total

John has x number of marbles. His friend gave him 6 marbles more. Write an expression for the total number of marbles John now has.
More means we add:
[B]x + 6[/B]

John is n years old now. How old was he 10 years ago? What will be his age in 20 years time?

John is n years old now. How old was he 10 years ago? What will be his age in 20 years time?
10 years ago means we [I]subtract[/I] 10 from n:
[B]n - 10[/B]
20 years time or 20 years from now means we [I]add[/I] 20 to n:
[B]n + 20[/B]

John is y years old. Sarah is 9 years older than John. How old is Sarah

John is y years old. Sarah is 9 years older than John. How old is Sarah
Older means we add, so we have Sarah's age s as:
s = [B]y + 9[/B]

John took 20,000 out of his retirement and reinvested it. He earned 4% for one investment and 5% on

John took 20,000 out of his retirement and reinvested it. He earned 4% for one investment and 5% on the other. How much did he invest in each if the total amount earned was 880?
The first principal portion is x. Which means the second principal portion is 20,000 - x. We have:
0.04x + 0.05(20,000 - x) = 880
0.04x + 1,000 - 0.05x = 880
Group like terms:
-0.01x + 1000 = 880
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=-0.01x%2B1000%3D880&pl=Solve']equation solver[/URL], we get x = [B]12,000[/B]. Which means the other fund has 20,000 - 12,000 = [B]8,000[/B].

Jon earned money baby-sitting. He spent 1/4 of the money on a guitar and then he gave 1/4 of what wa

Jon earned money baby-sitting. He spent 1/4 of the money on a guitar and then he gave 1/4 of what was left to charity. If he has $108 left, how much money did he start with?
Calculate initial spend:
Charity = 1/4 * 3/4 left = 3/16
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=3%2F16&pl=Add']1/4 + 3/16[/URL] = 7/16
This means he has 1 = 7/16 left
16/16 - 7/16 = 9/16
Let the starting amount be s:
If he has 108 left, then we have [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=9s&num2=108&den1=16&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']9s/16 = 108[/URL]
s =$[B]192[/B]

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15%

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathan and Raymond have to sell in order to earn the same amount each month?
[U]Step 1: Set up Jonathan's sales equation S(m) where m is the amount of sales made each month:[/U]
S(m) = Commission percentage * m + Base Salary
10% written as a decimal is 0.1. We want decimals to solve equations easier.
S(m) = 0.1m + 1500
[U]Step 2: Set up Raymond's sales equation S(m) where m is the amount of sales made each month:[/U]
S(m) = Commission percentage * m + Base Salary
15% written as a decimal is 0.15. We want decimals to solve equations easier.
S(m) = 0.15m + 1200
[U]The question asks what is m when both S(m)'s equal each other[/U]:
The phrase [I]earn the same amount [/I]means we set Jonathan's and Raymond's sales equations equal to each other
0.1m + 1500 = 0.15m + 1200
We want to isolate m terms on one side of the equation.
Subtract 1200 from each side:
0.1m + 1500 - 1200 = 0.15m + 1200 - 1200
Cancel the 1200's on the right side and we get:
0.1m - 300 = 0.15m
Next, we subtract 0.1m from each side of the equation to isolate m
0.1m - 0.1m + 300 = 0.15m - 0.1m
Cancel the 0.1m terms on the left side and we get:
300 = 0.05m
Flip the statement since it's an equal sign to get the variable on the left side:
0.05m = 300
To solve for m, we divide each side of the equation by 0.05:
0.05m/0.05 = 300/0.05
Cancelling the 0.05 on the left side, we get:
m = [B]6000[/B]

Jordan has already scored 153 points this basketball season. If he scores 17 points per game, which

Jordan has already scored 153 points this basketball season. If he scores 17 points per game, which inequality represents the number of addional games he needs to play in order to score at least 255 points for the season?
Let g be the number of games Jordan plays. Total points per game is 17g. And he’s already scored 153. So we need 17g + 153 to be [I]at least [/I]255. The phrase at least means greater than or equal to, so we use the >= operator for our inequality:
[B]17g + 153 >= 255[/B]

Jose earned 60 points on a game show. In the next round he lost 64 points then gained 12 points and

Jose earned 60 points on a game show. In the next round he lost 64 points then gained 12 points and at last lost 28 points. What was his score at the end of the show?
Start with 60 points:
60
lose 64 means we subtract 64 from our points
60 - 64 = -4
Gained 12 means we add 12 to our points:
-4 + 12 = 8
Lost 28 means we subtract 28 from our points:
8 - 28 = [B]-20 points[/B]

Jose has scored 556 points on his math tests so far this semester. To get an A for the semester, he

Jose has scored 556 points on his math tests so far this semester. To get an A for the semester, he must score at least 660 points. Write and solve an inequality to find the minimum number of points he must score on the remaining tests, n, in order to get an A.
We want to know n, such that 556 + n >= 660. <-- We use >= symbol since at least means greater than or equal to.
556 + n >= 660
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=556%2Bn%3E%3D660&pl=Solve']equation/inequality calculator[/URL], we get [B]n >= 104[/B]

JP's age is twice the age of Reyna. The sum of their ages does not exceed 51

JP's age is twice the age of Reyna. The sum of their ages does not exceed 51
Let JP's age be j. Let Reyna's age be r. We're given two expressions:
[LIST=1]
[*]w = 2r
[*]r + w <= 51. ([I]Does not exceed means less than or equal to)[/I]
[/LIST]
We substitute (1) into (2) for w to get the inequality:
r + 2r <= 51
To solve this inequality, we type it in our search engine and we get:
[B]r <= 17[/B]

Juan spent at most $2.50 on apples and oranges. He bought 5 apples at $0.36 each. What is the most h

Juan spent at most $2.50 on apples and oranges. He bought 5 apples at $0.36 each. What is the most he spent on oranges?
Let a be spending apples and o be spending on oranges, we have:
[LIST=1]
[*]a + o <= 2.36 <-- At most means less than or equal to
[*]a = 5 * 0.36 = 1.8
[/LIST]
Substitute (2) into (1)
1.8 + o <= 2.36
Subtract 1.8 from each side
[B]o <= 0.56[/B]

Julius Caesar was born and 100 BC and was 66 years old when he died in which year did he die?

Julius Caesar was born and 100 BC and was 66 years old when he died in which year did he die?
BC means "Before Christ". On a timeline, it represents a negative number, where year 0 is the birth of Christ. So we have -100 + 66 = -34
-34 means [B]34 BC[/B].

k equals the sum of h and 23

The sum of h and 23 means we add:
h + 23
k equals means we set our expression above equal to k
h + 23 = k

K varies inversely with square root of m and directly with the cube of n.

K varies inversely with square root of m and directly with the cube of n.
[LIST]
[*]We take a constant c as our constant of proportionality.
[*]The word inversely means we divide
[*]The word directly means we multiply
[/LIST]
[B]k = cn^3/sqrt(m)[/B]

k varies jointly with m,n, p

k varies jointly with m,n, p
The phrase [I]varies jointly[/I] means we have a constant c such that:
[B]k= cmnp[/B]

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft squared. What are the dimensions of the kennel? How many feet of fencing did she use? Explain.
Area of a square with side length (s) is:
A = s^2
Given A = 64, we have:
s^2 = 64
[URL='https://www.mathcelebrity.com/radex.php?num=sqrt(64%2F1)&pl=Simplify+Radical+Expression']Typing this equation into our math engine[/URL], we get:
s = 8
Which means the dimensions of the kennel are [B]8 x 8[/B].
How much fencing she used means perimeter. The perimeter P of a square with side length s is:
P = 4s
[URL='https://www.mathcelebrity.com/square.php?num=8&pl=Side&type=side&show_All=1']Given s = 8, we have[/URL]:
P = 4 * 8
P = [B]32[/B]

Karleys bank account was negative $12.14. she then deposited $21.63. What was her account balance

Karleys bank account was negative $12.14. she then deposited $21.63. What was her account balance
negative 12.14 can be written as
-12.14
She then deposited 21.63 which means we add 21.63 to her bank account balance:
+21.63
Final account balance is:
-12.14 + 21.63 = [B]$9.49[/B]

kate is twice as old as her sister mars. the sum of their ages is 24. find their ages.

kate is twice as old as her sister mars. the sum of their ages is 24. find their ages.
Let k be Kate's age
Let m be Mars's age
We're given two equations:
[LIST=1]
[*]k = 2m. (Because twice means multiply by 2)
[*]k + m = 24
[/LIST]
Substitute equation (1) for k into equation (2):
2m + m = 24
T o solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=2m%2Bm%3D24&pl=Solve']type this equation into our math engine[/URL]:
m = [B]8
[/B]
We want to solve for k using m= 8. Substitute this into equation 1
k = 2(8)
k = [B]16
[/B]
Check our work for equation 1
16 = 2 * 8
16 = 16
Check our work for equation 2
16 + 8 ? 24
24 = 24
[MEDIA=youtube]TJMTRYP-Ct8[/MEDIA]

Kate spent at most $2.50 on apples and oranges. She bought 5 apples at $0.36 each. What is the most

Kate spent at most $2.50 on apples and oranges. She bought 5 apples at $0.36 each. What is the most She spent on oranges
[U]Assumptions and givens:[/U]
[LIST]
[*]Let a be the total cost of apples
[*]Let o be the total cost of oranges
[/LIST]
The phrase [I]at most[/I] means less than or equal to, so we have:
a + o <= 2.50
[U]Find the cost of apples (a)[/U]
a = price per apple * quantity of apples
a = 0.36 * 5
a = 1.8
Our new inequality with a = 1.8 is:
1.8 + o <= 2.50
[URL='https://www.mathcelebrity.com/1unk.php?num=1.8%2Bo%3C%3D2.50&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]o <= 0.7[/B]

keisha is babysitting at 8$ per hour to earn money for a car. So far she has saved $1300. The car th

keisha is babysitting at 8$ per hour to earn money for a car. So far she has saved $1300. The car that keisha wants to buy costs at least $5440. How many hours does Keisha need to babysit to earn enough to buy the car
Set up the Earning function E(h) where h is the number of hours Keisha needs to babysit:
E(h) = 8h + 1300
The question asks for h when E(h) is at least 5440. The phrase [I]at least[/I] means an inequality, which is greater than or equal to. So we have:
8h + 1300 >= 5440
To solve this inequality, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h%2B1300%3E%3D5440&pl=Solve']type it in our search engine[/URL] and we get:
h >= [B]517.5[/B]

kelly's test score is 6 points higher than Mike's

kelly's test score is 6 points higher than Mike's
Assumptions:
[LIST]
[*]Let Kelly's test score be k
[*]Let Mike's test score be m
[/LIST]
Higher means we add, so we have
[B]k = m + 6[/B]

Kelsi has 10 pens , she gave 2 away , how many does she have now

Giving away 2 means subtracting, so we have 10 - 2 = 8 pens left over.

kim and jason just had business cards made. kim’s printing company charged a one time setup fee of $

kim and jason just had business cards made. kim’s printing company charged a one time setup fee of $8 and then $20 per box of cards. jason,meanwhile ordered his online. they cost $8 per box. there was no setup fee, but he had to pay $20 to have his order shipped to his house. by coincidence, kim and jason ended up spending the same amount on their business cards. how many boxes did each buy? how much did each spend?
Set up Kim's cost function C(b) where b is the number of boxes:
C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee
C(b) = 20c + 8 + 0
Set up Jason's cost function C(b) where b is the number of boxes:
C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee
C(b) = 8c + 0 + 20
Since Kim and Jason spent the same amount, set both cost equations equal to each other:
20c + 8 = 8c + 20
[URL='https://www.mathcelebrity.com/1unk.php?num=20c%2B8%3D8c%2B20&pl=Solve']Type this equation into our search engine[/URL] to solve for c, and we get:
c = 1
How much did they spend? We pick either Kim's or Jason's cost equation since they spent the same, and plug in c = 1:
Kim:
C(1) = 20(1) + 8
C(1) = 20 + 8
C(1) = [B]28
[/B]
Jason:
C(1) = 8(1) + 20
C(1) = 8 + 20
C(1) = [B]28[/B]

Kim, Jenny, and Wendy are basketball players. Each plays a different position (guard, forward, and c

Kim, Jenny, and Wendy are basketball players. Each plays a different position (guard, forward, and center) and wears a different number (30, 32, and 35).Kim and number 30 are too small to play center. Number 35 is the center. Neither Kim nor Wendy is the forward. Who plays guard, and what uniform number does she wear?
[LIST]
[*]Kim does not play center
[*]Kim does not play forward
[*]Which means [B]Kim is the guard[/B]
[*]Since Kim is not number 30, and she cannot be number 35 since Number 35 is the center, the only number left is [B]Number 32[/B]
[/LIST]
[B]Kim is the guard with number 32[/B]

Krutika was thinking of a number. Krutika doubles it and adds 8.7 to get an answer of 64.9. Form an

Krutika was thinking of a number. Krutika doubles it and adds 8.7 to get an answer of 64.9. Form an equation with x from the information.
[LIST=1]
[*]The number we start with is x.
[*]Double it means we multiply by 2: 2x
[*]Add 8.7: 2x + 8.7
[*][I]Get an answer[/I] means we have an equation, so we set (3) above equal to 64.9
[*][B]2x + 8.7 = 64.9[/B]
[/LIST]
If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=2x%2B8.7%3D64.9&pl=Solve']equation calculator[/URL].

Kyle got 3 shirts on his birthday. He had already 5 shirts.how many shirts does he have?

Kyle got 3 shirts on his birthday. He had already 5 shirts.how many shirts does he have?
He started with 5 shirts:
5
He got 3 more shirts, which means we add:
5 + 3 = [B]8 shirts[/B]

Larry Mitchell invested part of his $31,000 advance at 6% annual simple interest and the rest at 7%

Larry Mitchell invested part of his $31,000 advance at 6% annual simple interest and the rest at 7% annual simple interest. If the total yearly interest from both accounts was $2,090, find the amount invested at each rate.
Let x be the amount invested at 6%. Then 31000 - x is invested at 7%.
We have the following equation:
0.06x + (31000 - x)0.07 = 2090
Simplify:
0.06x + 2170 - 0.07x = 2090
Combine like Terms
-0.01x + 2170 = 2090
Subtract 2170 from each side
-0.01x = -80
Divide each side by -0.01
x = [B]8000 [/B]at 6%
Which means at 7%, we have:
31000 - 8000 = [B]23,000[/B]

Last December at Dubai International Airport 1,309,738 passengers travelled through terminal 1 and 2

Last December at Dubai International Airport 1,309,738 passengers travelled through terminal 1 and 2,516,989 passengers through terminal 2. How many passengers travelled through terminal 1 and terminal 2 altogether?
The word [I]altogether[/I] means we add Terminal 1 to Terminal 2:
1,309,738 + 2,516,989 = [B]3,826,727[/B]

Last month, my saving account was balance was $1,000. since then, i spent x dollars from my saving

Last month, my saving account was balance was $1,000. since then, i spent x dollars from my saving
Spending means reducing our balance, so we have a new balance of:
[B]1000 - x[/B]

Lauren's savings increased by 12 and is now 31

Lauren's savings increased by 12 and is now 31
[LIST]
[*]Let Lauren's savings be s.
[*]The phrase increased by means we add.
[*]The phrase [I]is now[/I] means an equation.
[*]We have an algebraic expression of:
[/LIST]
[B]s + 12 = 31
[/B]
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B12%3D31&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]19[/B]

Leah is 12 years older than Anna. if the age of Anna is x, what is the age of Leah?

Leah is 12 years older than Anna. if the age of Anna is x, what is the age of Leah?
Older means we add 12 to Anna's age. So if Anna's age is x, then Leah's age (l) is:
l = [B]x + 12[/B]

Lei is 15 years old, represent her age m years ago

Lei is 15 years old, represent her age m years ago
years ago means we subtract:
[B]15 - m[/B]

Let A={a,b,c} and B={1,2,3} Compute A?B

Let A={a,b,c} and B={1,2,3} Compute A?B
Union means all elements in either A or B, so we have:
A?B = [B]{a,b,c,1,2,3}[/B]

Let n be the middle number of three consecutive integers

Let n be the middle number of three consecutive integers
This means:
[LIST]
[*]n is the second of three consecutive integers
[*]The first consecutive integer is n - 1
[*]The third consecutive integer is n + 1
[/LIST]
The sum is found by:
n - 1 + n + n + 1
Simplifying, we get:
(n + n + n) + 1 - 1
[B]3n[/B]

Let x be an integer. If x is odd, then x^2 is odd

Let x be an integer. If x is odd, then x^2 is odd
Proof: Let x be an odd number. This means that x = 2n + 1 where n is an integer.
[U]Squaring x, we get:[/U]
x^2 = (2n + 1)^2 = (2n + 1)(2n + 1)
x^2 = 4n^2 + 4n + 1
x^2 = 2(2n^2 + 2n) + 1
2(2n^2 + 2n) is an even number since 2 multiplied by any integer is even
So adding 1 is an odd number
[MEDIA=youtube]GlzV80M33x0[/MEDIA]

Let x be the dog’s age in years. What is the dog’s age when he is thrice as old?

Let x be the dog’s age in years. What is the dog’s age when he is thrice as old?
Thrice means triple, or multiply by 3. So we have the future age as:
[B]3x[/B]

let x be the variable, an age that is at least 57 years old

let x be the variable, an age that is at least 57 years old
At least means greater than or equal to
x >= 57

Lindsey took a total of 8 quizzes over the course of 2 weeks. After attending 5 weeks of school this

Lindsey took a total of 8 quizzes over the course of 2 weeks. After attending 5 weeks of school this quarter, how many quizzes will Lindsey have taken in total? Assume the relationship is directly proportional.
Since the relationship is directly proportional, set up a proportion of quizzes to weeks, where q is the number of quizzes Lindsey will take in 5 weeks:
8/2 = q/5
[URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=q&den1=2&den2=5&propsign=%3D&pl=Calculate+missing+proportion+value']We type this proportion into our search engine[/URL], and we get:
[B]q = 20
[/B]
Another way to look at this is, Lindsey takes 8 quizzes over 2 weeks. This means she takes 4 per week since 8/2 = 4.
So if she takes 4 quizzes per week, then in 5 weeks, she takes 4*5 = 20 quizzes.

Logan is 8 years older than 4 times the age of his nephew. Logan is 32 years old. How old is his nep

Logan is 8 years older than 4 times the age of his nephew. Logan is 32 years old. How old is his nephew?
Let the age of Logan's nephew be n. We're given:
4n + 8 = 32 (Since [I]older[/I] means we add)
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=4n%2B8%3D32&pl=Solve']type it into our search engine[/URL] and we get:
[B]n = 6[/B]

Louis kept money through a hole inn his pocket. He started with 35 cents, lost 20 cents , put in 75

Louis kept money through a hole inn his pocket. He started with 35 cents, lost 20 cents , put in 75 cents , spent 43 cents, lost 16 cents again, and then put in 14 cents. How much change should there be in his pocket?
The phrase [I]put in[/I] mean we add money to the total
The phrases s[I]pent or lost[/I] mean we subtract
35 - 20 + 75 - 43 - 16 + 14 = [B]45 cents[/B]

Luke and 5 friends packed enough food for a 2-week canoe trip. If one extra person decided to go on

Luke and 5 friends packed enough food for a 2-week canoe trip. If one extra person decided to go on the trip at the last minute, how long will the food last?
Luke and 5 friends = 6 people.
2 weeks = 14 days, so the food lasts 6 people * 14 days = 84 days
One extra person on the trip means 6 + 1 = 7 people.
84 days of food / 7 people = [B]12 days[/B]

Luna had $50 when she got to the carnival. After riding 12 rides she had $26. What was the price aft

Luna had $50 when she got to the carnival. After riding 12 rides she had $26. What was the price after each ride?
After riding 12 rides, Lucy had $26. Which means she spent $50 - $26 = $24.
$24 / 12 rides = [B]$2 per ride[/B].

M decreased by the sum of 13 and the number P is less than 12

M decreased by the sum of 13 and the number P is less than 12
The sum of 13 and the number P
13 + P
M decreased by the sum of 13 and the number P
M - (13 + P)
Less than 12 means we set this entire expression less than 12 as an inequality
[B]M - (13 + P) < 12[/B]

M is halved, then 7 is added

M is halved, then 7 is added
Take this algebraic expression in parts:
[LIST]
[*]M is halved. This means we divide M by 2: M/2
[*]Then 7 is added. We add 7 to M/2
[/LIST]
[B]M/2 + 7[/B]

m is inversely proportional to the square of p-1 when p=4 m=5 find m when p=6

m is inversely proportional to the square of p-1 when p=4 and m=5. find m when p=6
Inversely proportional means there is a constant k such that:
m = k/(p - 1)^2
When p = 4 and m = 5, we have:
5 = k/(4 - 1)^2
5 = k/3^2
5 = k/9
[U]Cross multiply:[/U]
k = 45
[U]The problems asks for m when p = 6. And we also now know that k = 45. So plug in the numbers:[/U]
m = k/(p - 1)^2
m = 45/(6 - 1)^2
m = 45/5^2
m = 45/25
m = [B]1.8[/B]

M is the sum of a and its reciprocal

M is the sum of a and its reciprocal
The reciprocal of a variable is 1 divided by the variable
1/a
The sum of a and its reciprocal means we add:
a + 1/a
The phrase [I]is[/I] means an equation, so we set M equal to the sum of a + 1/a:
[B]M = 1 + 1/a[/B]

MAPE - MPE - MAPD

Given a time series of actual and forecasted values, this determines the following:

* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)

* Symmetric Mean Absolute Percentage Error (sMAPE)

* Mean Absolute Percentage Error (MPE)

* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)

* Symmetric Mean Absolute Percentage Error (sMAPE)

* Mean Absolute Percentage Error (MPE)

Margaret earns 15 an hour at her job. Each week she earns at least 450 and no more than 600. How man

Margaret earns 15 an hour at her job. Each week she earns at least 450 and no more than 600. How many hours does Margaret work each week?
Let h be the hours worked
We know that hourly rate * h equals total earnings.
The phrases at least and no more than signify inequalities, so we have:
450 <= 15h <= 600
Divide each entry by 15:
[B]30 <= h <= 40[/B]
This means Margaret works at least 30 hours a week and no more than 40

Margin of Error from Confidence Interval

Given a confidence interval, this determines the margin of error and sample mean.

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. How many did she start with?
Take this in parts
[LIST=1]
[*]Maria starts with b boxes.
[*]She buys seven more. So she has b + 7 boxes
[*]A week later, half of all her boxes are destroyed in a fire. Which means she's left with 1/2. (b + 7)/2
[*]Now she has 22 boxes. So we set (b + 7)/2 = 22
[/LIST]
(b + 7)/2 = 22
Cross multiply:
b + 7 = 22 * 2
b + 7 = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B7%3D44&pl=Solve']Typing this equation into our search engine and solving for b[/URL], we get:
[B]b = 37[/B]

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. With how many did she start?
Let the number of boxes Maria started with be b. We're given the following pieces:
[LIST]
[*]She starts with b
[*]She bought 7 boxes. So we add 7 to b: b + 7
[*]If half the boxes were destroyed, she's left with 1/2. So we divide (b + 7)/2
[*]Only 22 boxes left means we set (b + 7)/2 equal to 22
[/LIST]
(b + 7)/2 = 22
Cross multiply:
b + 7 = 22 * 2
b + 7 = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B7%3D44&pl=Solve']Type this equation into our search engine[/URL] to solve for b and we get:
b = [B]37[/B]

Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find t

Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find the ages of Martha and Harry.
Let m be Martha's age. Let h be Harry's age. We're given two equations:
[LIST=1]
[*]m = h + 18 [I](older means we add)[/I]
[*]h + m = 106
[/LIST]
Substitute equation (1) into equation (2) for m:
h + h + 18 = 106
To solve for h, [URL='https://www.mathcelebrity.com/1unk.php?num=h%2Bh%2B18%3D106&pl=Solve']we type this equation into our search engine[/URL] and we get:
h = [B]44[/B]

Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than

Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than 11. What is the youngest age Warren can be?
Let m be Marty's age and w be Warren's age. We have two equations:
(1) m = 6w - 3
(2) m + w > 11
Plug (1) into (2)
6w - 3 + w > 11
Combine w terms
7w - 3 > 11
Add 3 to each side
7w > 14
Divide each side by 7
w > 2 which means [B]w = 3[/B] as the youngest age.

Max is 23 years younger than his father.Together their ages add up to 81.

Max is 23 years younger than his father.Together their ages add up to 81.
Let Max's age be m, and his fathers' age be f. We're given:
[LIST=1]
[*]m = f - 23 <-- younger means less
[*]m + f = 81
[/LIST]
Substitute Equation (1) into (2):
(f - 23) + f = 81
Combine like terms to form the equation below:
2f - 23 = 81
[URL='https://www.mathcelebrity.com/1unk.php?num=2f-23%3D81&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]f = 52[/B]
Substitute this into Equation (1):
m = 52 - 23
[B]m = 29[/B]

Max sneezes every 5 minutes, Lina coughs every 6 minutes, and their dog barks every 3 minutes. If th

Max sneezes every 5 minutes, Lina coughs every 6 minutes, and their dog barks every 3 minutes. If there was sneezing, barking, and coughing at 3:15 PM, when is the next time that these three sounds will happen simultaneously?
To find the next time the sounds happen simultaneously, we want to find the Least Common Multiple (LCM).
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=3&num2=5&num3=6&pl=LCM']Using our LCM Calculator[/URL], we find the least common multiple of 3, 5, and 6 is 30. The least common multiple gives us a common time where each sound reaches a "cycle".
[LIST]
[*]Dog: A bark every e minutes means the dog has 10 barks, with the 10th bark at 30 minutes after 3:15
[*]Max: A sneeze every 5 minutes means he has 6 sneezes, with the 6th sneeze at 30 minutes after 3:15
[*]Lisa: A cough every 6 minutes means she has 5 coughs, with the 5th cough at 30 minutes after 3:15
[/LIST]
30 minutes after 3:15 means we have: 3:15 + 30 = [B]3:45 PM[/B]

mcubemultipliedbyntothefourthpower

mcubemultipliedbyntothefourthpower
m cubed means we raise m to the 3rd power:
m^3
n to the fourth power:
n^4
Multiply both expressions together:
[B]m^3n^4[/B]

Men's heights are normally distributed with mean 69.0 inches and standard deviation 2.8 inches. Mimi

Men's heights are normally distributed with mean 69.0 inches and standard deviation 2.8 inches. Mimi is designing a plane with a height that allows 95% of the men to stand straight without bending in the plane. What is the minimum height of the plane?
Using the [URL='http://www.mathcelebrity.com/probnormdist.php?xone=50&mean=69&stdev=2.8&n=1&pl=Empirical+Rule']empirical rule calculator[/URL], we have a [B]63.4[/B] minimum height.

Molly is making strawberry infused water. For each ounce of strawberry juice, she uses two times as

Molly is making strawberry infused water. For each ounce of strawberry juice, she uses three times as many ounces of water as juice. How many ounces of strawberry juice and how many ounces of water does she need to make 40 ounces of strawberry infused water?
Let j be the ounces of strawberry juice and w be the ounces of water. We're given:
[LIST=1]
[*]j + w = 40
[*]w = 3j
[/LIST]
Substitute (2) into (1):
j + 3j = 40
Combine like terms:
4j = 40
[URL='https://www.mathcelebrity.com/1unk.php?num=4j%3D40&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]j = 10[/B]
From equation (2), we substitute j = 2:
w = 3(10)
[B]w = 30
[/B]
This means we have [B]10 ounces of juice[/B] and [B]30 ounces of water[/B] for a 40 ounce mix.

Mr.coulter has n calculators and mr Riley has 4 more calculators then him

Mr.coulter has n calculators and mr Riley has 4 more calculators then him
More means add, so Riley's calculators are:
[B]n + 4[/B]

Mrs diaz works 40 hours per week regularly at a rate of $15.15 per hour.When she works overtime , he

Mrs diaz works 40 hours per week regularly at a rate of $15.15 per hour.When she works overtime , her rate is time and a half of her regular rate. What is Mrs. Diaz overtime rate?
Time and a half means your hourly rate plus 50% or 1/2 of your hourly rate:
15.15 * 1.5 = $[B]22.73[/B]

multiply 3 by the difference of u and t

multiply 3 by the difference of u and t
Take this algebraic expression in parts:
The difference of u and t means we subtract t from u
u - t
Multiply this difference by 3:
[B]3(u - t)[/B]

multiply 5 and sum of twice of d and 10

multiply 5 and sum of twice of d and 10
Twice d means we multiply d by 2:
2d
The sum of twice d and 10 means we add 2d to 10
2d + 10
We multiply this quantity by 5:
[B]5(2d + 10)[/B]

multiply a number by 4 and then subtract the answer from 30

multiply a number by 4 and then subtract the answer from 30
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Multiply this number by 4:
4x
Subtract the answer from 30:
[B]30 - 4x[/B]

Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and su

Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and subtracting 4. Find the number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
multiply a number by 6 and subtract 6:
6x - 6
Multiply a number by 3 and subtract 4:
3x - 4
The phrase [I]gives the same result[/I] means an equation. So we set 6x - 6 equal to 3x - 4
6x - 6 = 3x - 4
To solve this equation for x, we type it in our search engine and we get:
x = [B]2/3[/B]

Multiply c by five and square the answer

Multiply c by five and square the answer
Multiply c by five:
5c
Square the answer means we raise 5c to the power of 2:
[B](5c)^2 [/B]
This can also be written as [B]25c^2[/B]

multiply m by 5, double the result, then multiply 10 by what you have

multiply m by 5, double the result, then multiply 10 by what you have
Take this algebraic expression in parts:
[LIST]
[*]Multiply m by 5: 5m
[*]double the result means multiply 5m by 2: 2(5m) = 10m
[*]Multiply 10 by what you have means multiply 10 by the result of 10m above:
[/LIST]
10(10m) = [B]100m[/B]

multiply r by t, add the result to u, then multiply what you have by s

multiply r by t, add the result to u, then multiply what you have by s
Take this algebraic expression in parts:
[LIST=1]
[*]Multiply r by t: rt
[*]Add the result to u means we add rt to u: u + r
[*]Multiply what you have by s. This means we take the result in #2, u + r, and multiply it by s:
[/LIST]
[B]s(u + r)[/B]

multiply t by u, add the to v, then triple what you have

multiply t by u, add the to v, then triple what you have
Multiply t by u:
tu
Add this to v:
v + tu
Then triple what you have - This means we multiply the expression above by 3:
[B]3(v + tu)[/B]

Multiply the difference of 3 and q by p

Multiply the difference of 3 and q by p.
Take this algebraic expression in pieces:
[B][U]Step 1: The difference of 3 and q[/U][/B]
The word [I]difference[/I] means we subtract the variable q from 3
3 - q
[B][U]Step 2: Multiply the expression 3 - q by p:[/U]
p(3 - q)[/B]

Multiplying a number by 6 is equal to the number increased by 9

Multiplying a number by 6 is equal to the number increased by 9.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Multiply it by 6 --> 6x
We set this equal to the same number increased by 9. Increased by means we add:
[B]6x = x + 9 <-- This is our algebraic expression
[/B]
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x%3Dx%2B9&pl=Solve']type it into the search engine [/URL]and get x = 1.8.

My brother is x years old. I am 5 years older than him. Our combined age is 30 years old. How old is

My brother is x years old. I am 5 years older than him. Our combined age is 30 years old. How old is my brother
Brother's age is x:
I am 5 years older, meaning I'm x + 5:
The combined age is found by adding:
x + (x + 5) = 30
Group like terms:
2x + 5 = 30
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B5%3D30&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]12.5[/B]

n and m are congruent and supplementary. prove n and m are right angles

n and m are congruent and supplementary. prove n and m are right angles
Given:
[LIST]
[*]n and m are congruent
[*]n and m are supplementary
[/LIST]
If n and m are supplementary, that means we have the equation:
m + n = 180
We're also given n and m are congruent, meaning they are equal. So we can substitute n = m into the supplementary equation:
m + m = 180
To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%3D180&pl=Solve']we type it in our search engine[/URL] and we get:
m = 90
This means m = 90, n = 90, which means they are both right angles since by definition, a right angle is 90 degrees.

n is the sum of twenty-five and fifteen

n is the sum of twenty-five and fifteen
The sum of twenty-five and fifteen:
25 + 15
The word [I]is[/I] means an equal to, so we set 25 + 15 equal to n:
[B]n = 25 + 15
n = 40[/B]

n is tripled then decreased by 5

n is tripled then decreased by 5
n is tripled means we multiply n by 3:
3n
Decreased by 5 means we subtract 5 from 3n:
[B]3n - 5[/B]

N reduced by 2 is the same as Z increased by 7

N reduced by 2 is the same as Z increased by 7
[LIST]
[*]N reduced by 2 means subtract --> n - 2
[*]z increased by 7 means add --> z + 7
[*][I]Is the same as[/I] means equal to, so we set these expressions equal to each other
[*][B]n - 2 = z + 7[/B]
[/LIST]

N squared multiplied by the difference of n and 3

N squared multiplied by the difference of n and 3
n squared means we raise n to the power of 2:
n^2
The difference of n and 3 means we subtract 3 from n:
n - 3
Now we multiply both terms together:
[B]n^2(n - 3)[/B]

n times 146, reduced by 94 is the same as h

n times 146, reduced by 94 is the same as h
n time 146
146n
Reduced by 94
146n - 94
Is the same as h means an equation:
[B]146n - 94 = h[/B]

Nancy started the year with $435 in the bank and is saving $25 a week. Shane started with $875 and i

Nancy started the year with $435 in the bank and is saving $25 a week. Shane started with $875 and is spending $15 a week. [I]When will they both have the same amount of money in the bank?[/I]
[I][/I]
Set up the Account equation A(w) where w is the number of weeks that pass.
Nancy (we add since savings means she accumulates [B]more[/B]):
A(w) = 25w + 435
Shane (we subtract since spending means he loses [B]more[/B]):
A(w) = 875 - 15w
Set both A(w) equations equal to each other to since we want to see what w is when the account are equal:
25w + 435 = 875 - 15w
[URL='https://www.mathcelebrity.com/1unk.php?num=25w%2B435%3D875-15w&pl=Solve']Type this equation into our search engine to solve for w[/URL] and we get:
w =[B] 11[/B]

Negative Binomial Distribution

Calculates the probability of the k^{th} success on the x^{th} try for a negative binomial distribution also known as the Pascal distribution.? ? It calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, and standard deviation.

Nick is given $50 to spend on a vacation . He decides to spend $5 a day. Write an equation that show

Nick is given $50 to spend on a vacation . He decides to spend $5 a day. Write an equation that shows how much money Nick has after x amount of days.
Set up the function M(x) where M(x) is the amount of money after x days. Since spending means a decrease, we subtract to get:
[B]M(x) = 50 - 5x[/B]

Nine less than a number is no more than 8 and no less than 3

Nine less than a number is no more than 8 and no less than 3
A number is denoted as an arbitrary variable, let's call it x.
We have a double inequality:
[LIST=1]
[*]No more than 8 means less than or equal to 8
[*]No less than 3 means greater than or equal to 3
[/LIST]
[B]3 <= x <= 8[/B]

Nine less than the product of 2 and y is not less than 15

The product of 2 and y means we multiply
2y
Nine less than that product means we subtract 9
2y - 9
Finally, the entire expression is not less than 15, which means 15 or more. We use greater than or equal to
[B]2y - 9 >= 15
[/B]
If you want to solve this inequality and write the interval notation, use [URL='http://www.mathcelebrity.com/1unk.php?num=2y-9%3E%3D15&pl=Solve']our calculator[/URL].

Nine times the sum of a number and 6

Nine times the sum of a number and 6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 6 means we add 6 to x:
x + 6
9 times the sum:
[B]9(x + 6)[/B]

nine times x is twice the sum of x and five

nine times x is twice the sum of x and five
Take this algebraic expression in 4 pieces:
[U]Step 1: nine time x:[/U]
9x
[U]Step 2: The sum of x and five means we add 5 to x:[/U]
x + 5
[U]Step 3: The word [I]twice[/I] means we multiply the sum x + 5 by 2:[/U]
2(x + 5)
[U]Step 4: The word [I]is[/I] means equal to, so we set 9x equal to 2(x + 5) to get our final algebraic expression of:[/U]
[B]9x = 2(x + 5)[/B]

Noah scores 20 points. Mai’s score was 30 points. The mean for Noah’s, Mia’s, and Clare’s was 40 poi

Noah scores 20 points. Mai’s score was 30 points. The mean for Noah’s, Mia’s, and Clare’s was 40 points. What was Clare’s score?
[URL='https://www.mathcelebrity.com/missingaverage.php?num=20%2C30&avg=40&pl=Calculate+Missing+Score']Using our missing average calculator[/URL], Claire's score was [B]70[/B].

Normal body temperature is 98.6 ? F. Write an inequality that describes the temperature

Normal body temperature is 98.6 ? F. Write an inequality that describes the temperature, T, of people with above normal temperatures.
Above means greater than, so we set up the inequality:
[B]T > 98.6 ?[/B]

Norwood High Schools jazz band includes 33 trombone players and 27 trumpet players. Meanwhile, Lakew

Norwood High Schools jazz band includes 33 trombone players and 27 trumpet players. Meanwhile, Lakewood High Schools jazz band has 37 trombone players and 28 trumpet players. Which jazz band has a lower ratio of trombone to trumpet players?
Norwood: 33 : 27, is 33 out of 60 = 55%
Lakewood: 37 : 28 = 37/65 = 57%
Since [B]Norwood[/B] is lower than Lakewood, they have the lower ratio or trombone to trumpet players

On Melissa 6 birthday she gets a $2000 cd that earns 4% interest, compounded semiannual. If the cd m

On Melissa 6 birthday she gets a $2000 cd that earns 4% interest, compounded semiannual. If the cd matures on her 16th birthday, how much money will be available?
Semiannual compounding means twice a year. With 16 - 6 = 10 years of compounding, we have:
10 x 2 = 20 semiannual periods.
[URL='https://www.mathcelebrity.com/compoundint.php?bal=2000&nval=20&int=4&pl=Semi-Annually']Using our interest on balance calculator[/URL], we get:
[B]$2,971.89[/B]

One and one third less x

One and one-third can be written as 4/3.
Less x means minus x, or subtract x.
4/3 - x
Or in mixed number notation:
1 & 1/3 - x

One day a quarter of the class is absent and 21 children are present. How many children are there on

One day a quarter of the class is absent and 21 children are present. How many children are there on the class when no one is away?
If 1/4 of the class is absent, this means that 1 - 1/4 is present.
Since 1 = 4/4, we have 4/4 - 1/4 = 3/4 of the class is present.
If the full size of the class is c, then we have
3/4c = 21
[URL='https://www.mathcelebrity.com/1unk.php?num=3%2F4c%3D21&pl=Solve']Typing 3/4c = 21 into the search engine[/URL], we get:
[B]c = 28[/B]

One fifth of the square of a number

One fifth of the square of a number
We have an algebraic expression. Let's break this into parts.
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The square of a number means we raise it to the power of 2. So we have x^2
[*]One-fifth means we have a fraction, where we divide our x^2 in Step 2 by 5. So we get our final answer below:
[/LIST]
[B]x^2/5[/B]

One number is 1/5 of another number. The sum of the two numbers is 18. Find the two numbers.

One number is 1/5 of another number. The sum of the two numbers is 18. Find the two numbers.
Let the two numbers be x and y. We're given:
[LIST=1]
[*]x = 1/5y
[*]x + y = 18
[/LIST]
Substitute (1) into (2):
1/5y + y = 18
1/5 = 0.2, so we have:
1.2y = 18
[URL='https://www.mathcelebrity.com/1unk.php?num=1.2y%3D18&pl=Solve']Type 1.2y = 18 into the search engine[/URL], and we get [B]y = 15[/B].
Which means from equation (1) that:
x = 15/5
[B]x = 3
[/B]
Our final answer is [B](x, y) = (3, 15)[/B]

one-fifth of forty-five

one-fifth of forty-five
one-fifth is 1/4
forty-five is 45
When you see a fraction then the word of and then a number, it means you multiply:
1/5 * 45
45/5
[B]9[/B]

One-fourth the sum of m and p

One-fourth the sum of m and p
Take this algebraic expression in parts:
[LIST]
[*]The sum of m and p means we add p to m: m + p
[*]1/4 of the sum mean we divide m + p by 4
[/LIST]
[B](m + p)/4[/B]

One-half the sum of 5 and t

One-half the sum of 5 and t
The sum of 5 and t:
5 + t
One-half of this means we multiply 5 + t by 1/2
[B](5 + t)/2[/B]

opposite of twice the quotient of a and a

opposite of twice the quotient of a and a
the quotient of a and a:
a/a
1
Twice the quotient of a and a
2(1)
2
Opposite means multiply 2 by -1:
-1 * 2
[B]-2[/B]

p decreased by 65 is the same as the total of f and 194

p decreased by 65 is the same as the total of f and 194
p decreased by 65
p - 65
The total of f and 194
f + 194
The phrase [I]is the same as[/I] means equal to, so we set the expressions above equal to each other
[B]p - 65 = f + 194[/B]

p is equal to r plus 2 times q

p is equal to r plus 2 times q
2 times q:
2q
r plus 2 times q:
r + 2q
is equal to means we set p equal to r + 2q
[B]p = r + 2q[/B]

p is halved and 4 is added

p is halved and 4 is added
[U]p is halved means we divide p by 2:[/U]
p/2
[U]4 is added:[/U]
[B]p/2 + 4[/B]

P is twice the length plus twice the width

P is twice the length plus twice the width
Let the length be l. Let the width be w. The phrase [I]twice[/I] means we multiply by 2. We have:
[B]2l + 2w = P[/B]

p more than the square of q

p more than the square of q
Take this algebraic expression in parts:
Step 1: Square of q means raise q to the 2nd power:
q^2
Step 2: The phrase [I]more[/I] means we add p to q^2
[B]q^2 + p[/B]

p varies directly as the square of r and inversely as q and s and p = 40 when q = 5, r = 4 and s = 6

p varies directly as the square of r and inversely as q and s and p = 40 when q = 5, r = 4 and s = 6, what is the equation of variation?
Two rules of variation:
[LIST=1]
[*]Varies directly means we multiply
[*]Varies inversely means we divide
[/LIST]
There exists a constant k such that our initial equation of variation is:
p = kr^2/qs
[B][/B]
With p = 40 when q = 5, r = 4 and s = 6, we have:
4^2k / 5 * 6 = 40
16k/30 = 40
Cross multiply:
16k = 40 * 30
16k = 1200
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=16k%3D1200&pl=Solve']equation calculator[/URL], we get:
k = [B]75[/B]
So our final equation of variation is:
[B]p = 75r^2/qs[/B]

Paired Means Difference

Calculates an estimation of confidence interval for a small or large sample difference of data. Confidence interval for paired means

Patricia has $425.82 in her checking account. How much does she have in her account after she makes

Patricia has $425.82 in her checking account. How much does she have in her account after she makes a deposit of $120.75 and a withdrawal of $185.90?
Start with $425.82
Deposits mean we [B]add[/B] money to the bank account:
425.82 + 120.75 = 546.57
Our new balance is 546.57.
Withdrawals mean we [B]subtract[/B] money from the bank account:
546.57 - 185.90 = [B]360.67[/B]

People with a drivers license are at least 16 years old and no older than 85 years old

People with a drivers license are at least 16 years old and no older than 85 years old.
Set up the inequality, where p represents the people:
[LIST=1]
[*]The phrase [I]at least[/I] means greater than or equal to. So we use the >= sign. 16 <= p
[*]The phrase [I]no older than[/I] means less than or equal to. So we use the <= sign. p <= 85
[/LIST]
Combine these inequalities, and we get:
[B]16 <= p <= 85[/B]
To see the interval notation for this inequality and all possible values, visit the [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=16%3C%3Dp%3C%3D85&pl=Show+Interval+Notation']interval notation calculator[/URL].

Percentile for Normal Distribution

Given a mean, standard deviation, and a percentile range, this will calculate the percentile value.

Peter was thinking of a number. Peter doubles it and adds 0.8 to get an answer of 31. Form an equati

Peter was thinking of a number. Peter doubles it and adds 0.8 to get an answer of 31. Form an equation with x from the information.
Take this algebraic expression in parts, starting with the unknown number x:
[LIST]
[*]x
[*][I]Double it [/I]means we multiply x by 2: 2x
[*]Add 0.8: 2x + 0.8
[*]The phrase [I]to get an answer of[/I] means an equation. So we set 2x + 0.8 equal to 31
[/LIST]
Build our final algebraic expression:
[B]2x + 0.8 = 31[/B]
[B][/B]
If you have to solve for x, then we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B0.8%3D31&pl=Solve']type this equation into our search engine[/URL] and we get:
x = 15.1

Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Sup

Pleasantburg has a population growth model of P(t)=at^2+bt+P0 where P0 is the initial population. Suppose that the future population of Pleasantburg t years after January 1, 2012, is described by the quadratic model P(t)=0.7t^2+6t+15,000. In what month and year will the population reach 19,200?
Set P(t) = 19,200
0.7t^2+6t+15,000 = 19,200
Subtract 19,200 from each side:
0.7t^2+6t+4200 = 0
The Quadratic has irrational roots. So I set up a table below to run through the values. At t = 74, we pass 19,200. Which means we add 74 years to 2012: 2012 + 74 = [B]2086[/B]
t 0.7t^2 6t Add 15000 Total
1 0.7 6 15000 15006.7
2 2.8 12 15000 15014.8
3 6.3 18 15000 15024.3
4 11.2 24 15000 15035.2
5 17.5 30 15000 15047.5
6 25.2 36 15000 15061.2
7 34.3 42 15000 15076.3
8 44.8 48 15000 15092.8
9 56.7 54 15000 15110.7
10 70 60 15000 15130
11 84.7 66 15000 15150.7
12 100.8 72 15000 15172.8
13 118.3 78 15000 15196.3
14 137.2 84 15000 15221.2
15 157.5 90 15000 15247.5
16 179.2 96 15000 15275.2
17 202.3 102 15000 15304.3
18 226.8 108 15000 15334.8
19 252.7 114 15000 15366.7
20 280 120 15000 15400
21 308.7 126 15000 15434.7
22 338.8 132 15000 15470.8
23 370.3 138 15000 15508.3
24 403.2 144 15000 15547.2
25 437.5 150 15000 15587.5
26 473.2 156 15000 15629.2
27 510.3 162 15000 15672.3
28 548.8 168 15000 15716.8
29 588.7 174 15000 15762.7
30 630 180 15000 15810
31 672.7 186 15000 15858.7
32 716.8 192 15000 15908.8
33 762.3 198 15000 15960.3
34 809.2 204 15000 16013.2
35 857.5 210 15000 16067.5
36 907.2 216 15000 16123.2
37 958.3 222 15000 16180.3
38 1010.8 228 15000 16238.8
39 1064.7 234 15000 16298.7
40 1120 240 15000 16360
41 1176.7 246 15000 16422.7
42 1234.8 252 15000 16486.8
43 1294.3 258 15000 16552.3
44 1355.2 264 15000 16619.2
45 1417.5 270 15000 16687.5
46 1481.2 276 15000 16757.2
47 1546.3 282 15000 16828.3
48 1612.8 288 15000 16900.8
49 1680.7 294 15000 16974.7
50 1750 300 15000 17050
51 1820.7 306 15000 17126.7
52 1892.8 312 15000 17204.8
53 1966.3 318 15000 17284.3
54 2041.2 324 15000 17365.2
55 2117.5 330 15000 17447.5
56 2195.2 336 15000 17531.2
57 2274.3 342 15000 17616.3
58 2354.8 348 15000 17702.8
59 2436.7 354 15000 17790.7
60 2520 360 15000 17880
61 2604.7 366 15000 17970.7
62 2690.8 372 15000 18062.8
63 2778.3 378 15000 18156.3
64 2867.2 384 15000 18251.2
65 2957.5 390 15000 18347.5
66 3049.2 396 15000 18445.2
67 3142.3 402 15000 18544.3
68 3236.8 408 15000 18644.8
69 3332.7 414 15000 18746.7
70 3430 420 15000 18850
71 3528.7 426 15000 18954.7
72 3628.8 432 15000 19060.8
73 3730.3 438 15000 19168.3
74 3833.2 444 15000 19277.2

Please help!!

(1) |P(A)| = 4 <-- Cardinality of the power set is 4, which means we have 2^n = 4.[B] |A| = 2
[/B]
(2) |B| = |A|+ 1 and |A×B| = 30
|B| = 6 if [B]|A| = 5[/B] and |A x B| = 30
(3) |B| = |A|+ 2 and |P(B)|?|P(A)| = 24
Since |B| = |A|+ 2, we have: 2^(a + 2) - 2^a = 24
2^a(2^2 - 1) = 24
2^a(3) = 24
2^a = 8
[B]|A |= 3[/B]
To check, we have |B| = |A| + 2 --> 3 + 2 = 5
So |P(B)| = 2^5 = 32
|P(A)| = 2^3 = 8
And 32 - 8 = 24

Points A, B, and C are collinear. Point B is between A and C. Find AB if AC=15 and BC=7.

Points A, B, and C are collinear. Point B is between A and C. Find AB if AC=15 and BC=7.
Collinear means on the same line.
By segment subtraction, we have:
AB = AC - BC
AB = 15 - 7
AB = [B]8[/B]

Poisson Distribution

Calculates the probability of 3 separate events that follow a poisson distribution.

It calculates the probability of exactly k successes P(x = k)

No more than k successes P (x <= k)

Greater than k successes P(x >= k)

Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis.

Calculates moment number t using the moment generating function

It calculates the probability of exactly k successes P(x = k)

No more than k successes P (x <= k)

Greater than k successes P(x >= k)

Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis.

Calculates moment number t using the moment generating function

population MEAN OF ENVIRONMENTAL SPECIALIST SALARY IS $62000.A RANDOM SAMPLE OF 45 SPECIALIST IS DRA

population MEAN OF ENVIRONMENTAL SPECIALIST SALARY IS $62000.A RANDOM SAMPLE OF 45 SPECIALIST IS DRAWN FROM THE POPULATION. WHAT IS THE LIKELIHOOD THAT THE MEAN SALARY SAMPLE IS $59000. ASSUME SIGMA IS $6000.
Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=59000&mean=62000&stdev=6000&n=45&pl=P%28X+%3C+Z%29']Z-Score calculator[/URL], we get the probability as [B]0.0004[/B].

positive even numbers less than 10

positive even numbers less than 10
First, list out all positive even numbers less than 10.
Less than 10 means we do [U]not[/U] include 10.
[B]{2, 4, 6, 8}
[MEDIA=youtube]5YsPQo_2dpI[/MEDIA][/B]

Positive numbers less than 4

Less than means we do not include 4.
But positive means greater than 0, so we have:
{1, 2, 3}

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the pho

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test, [U][B]the Type I error is[/B][/U]:
a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher

b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same

c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher [B]b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same [/B] [I]A Type I error is when you reject the null hypothesis when it is in fact true[/I]

b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same

c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher [B]b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same [/B] [I]A Type I error is when you reject the null hypothesis when it is in fact true[/I]

Probability of getting either a sum of 8 or at least one 4 in the roll of a pair dice

Sum of 8 equal to 5/36 shown [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=8&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']here[/URL].
At least one 4 means one of three scenarios:
[LIST=1]
[*](4, not 4) = 1/6 * 5/6 = 5/36
[*](not 4, 4) = 5/6 * 1/6 = 5/36
[*](4, 4) = 1/6 * 1/6 = 1/36
[/LIST]
The phrase "or", means we add both probabilities (sum of 8) and (at least one 4):
5/36 + (5/36 + 5/36 + 1/36)
16/36
Simplify by dividing each part of the fraction by 4
[B]4/9[/B]

product of a number and its reciprocal is increased by 7

product of a number and its reciprocal is increased by 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Its reciprocal means we take the reciprocal of x:
1/x
product of a number and its reciprocal:
x * 1/x
x/x
The x's cancel giving us:
1
is increased by 7 means we add 7:
1 + 7
[B]8[/B]

product of r plus 7 and 4

product of r plus 7 and 4
r plus 7 means we add 7 to r:
r + 7
The product means we multiply the expression r + a 7 by 4:
[B]4(r + 7)[/B]

Prove sqrt(2) is irrational

Use proof by contradiction. Assume sqrt(2) is rational.
This means that sqrt(2) = p/q for some integers p and q, with q <>0.
We assume p and q are in lowest terms.
Square both side and we get:
2 = p^2/q^2
p^2 = 2q^2
This means p^2 must be an even number which means p is also even since the square of an odd number is odd.
So we have p = 2k for some integer k. From this, it follows that:
2q^2 = p^2 = (2k)^2 = 4k^2
2q^2 = 4k^2
q^2 = 2k^2
q^2 is also even, therefore q must be even.
So both p and q are even.
This contradicts are assumption that p and q were in lowest terms.
So sqrt(2) [B]cannot be rational.
[MEDIA=youtube]tXoo9-8Ewq8[/MEDIA][/B]

q increased by the difference between 18 times q and 5

q increased by the difference between 18 times q and 5
Take this algebraic expression in parts.
18 times q:
18q
The difference between 18 times q and 5 means we subtract 5 from 18q:
18q - 5
q increased by the difference between 18 times q and 5 means we add 18q - 5 to q:
q + (18q - 5)
[B]q + 18q - 5[/B]
IF we want to simplify, we group like terms:
[B]19q - 5[/B]

Q is 5% less than P

The phrase is means equal to, so we have:
Q = P - 5%
5% is written as 0.05, so we have:
Q = P - 0.05

quotient of the sum of 17 and x and y

quotient of the sum of 17 and x and y
The sum of 17 and x means we add x to 17:
17 + x
quotient of the sum of 17 and x and y means we divide 17 + x by y
[B](17 + x)/y[/B]

quotient of the sum of 2 numbers and 6

quotient of the sum of 2 numbers and 6
The phrase [I]two numbers[/I] means we choose 2 arbitrary variables, let's call them x and y
x, y
The sum of 2 numbers:
x + y
quotient of the sum of 2 numbers and 6
[B](x + y)/6[/B]

r decreased by the quotient of r and 3

r decreased by the quotient of r and 3
The quotient of r and 3 is:
r/3
The phrase [I]decreased by[/I] means we subtract r/3 from r
[B]r - r/3[/B]

r less than 164 is 248 more than the product of 216 and r

r less than 164 is 248 more than the product of 216 and r
[U]r less than 164:[/U]
164 - r
[U]The product of 216 and r:[/U]
216r
[U]248 more than the product of 216 and r[/U]
216r + 248
[I]The word is means an equation, so we set 164 - r equal to 216r + 248[/I]
[B]164 - r = 216r + 248[/B]

r squared plus the product of 3 and s plus 5

r squared plus the product of 3 and s plus 5
r squared means we raise r to the power of 2
r^2
The product of 3 and s means we multiply s by 3:
3s
plus 5 means we add
3s + 5
R squared plus means we add r^2:
[B]r^2 + 3s + 5[/B]

r varies directly with s and inversely with the square root of t

r varies directly with s and inversely with the square root of t
Varies directly means we multiply
Varies inversely means we divide
There exists a constant k such that:
[B]r = ks/sqrt(t)[/B]

Raise 9 to the 3rd power, subtract d from the result, then divide what you have by c

Raise 9 to the 3rd power, subtract d from the result, then divide what you have by c.
This is an algebraic expression, let's take in parts (or chunks).
Raise 9 to the 3rd power. This means we take 9, and raise it to an exponent of 3
9^3
Subtract d from the result, means we subtract d from 9^3
9^3 - d
Now we divide 9^3 - d by c
[B](9^3 - d) / c[/B]

Raise c to the 7th power, divide the result by 4, then triple what you have

Raise c to the 7th power, divide the result by 4, then triple what you have.
Take this algebraic expression in pieces.
Raise c to the 7th power:
c^7
Divide the result by 4, means we divide c^7 by 4
c^7 / 4
Triple what you have means multiply c^7 / 4 by 3
[B]3(c^7 / 4)[/B]

raise f to the 3rd power, then find the quotient of the result and g

raise f to the 3rd power, then find the quotient of the result and g
Take this algebraic expression in two parts:
[LIST=1]
[*]Raise f to the 3rd power means we take f, and write it with an exponent of 3: f^3
[*]Find the quotient of the result and g. We take f^3, and divide it by g
[/LIST]
[B]f^3/g[/B]

Raise f to the 8th power, divide the result by 5, then multiply 10

Raise f to the 8th power, divide the result by 5, then multiply 10
f to the 8th power means we raise f to the power of 8 using an exponent:
f^8
Divide f^8 by 5
(f^8)/5
Now multiply this by 10:
10(f^8)/5
We can simplify this algebraic expression by dividing 10/5 to get 2 on top:
2[B](f^8)[/B]

raise q to the 5th power add the result to p then divide what you have by r

raise q to the 5th power add the result to p then divide what you have by r
Take this algebraic expression in parts:
[LIST]
[*]Raise q to the 5th power: q^5
[*]Add the result to p: p + q^5
[*]Divide what you have by r. This means we take our result above and divide it by r:
[/LIST]
[B](p + q^5)/r[/B]

raise r to the 8th power then find the product of the result and 3

raise r to the 8th power then find the product of the result and 3
Raise r to the 8th power means we raise r with an exponent of 8:
r^8
The product of the result and 3 means we muliply r^8 by 3
[B]3r^8[/B]

raise t to the 10th power, then find the quotient of the result and s

raise t to the 10th power, then find the quotient of the result and s
Raise t to the 10th power means we use t as our variable and 10 as our exponent:
t^10
The quotient means a fraction, where the numerator is t^10 and the denominator is s:
[B]t^10/s[/B]

raise v to the 9th power, then dividethe result by u

V to the 9th power means we use an exponent:
v^9
Divide that result by u
[B]v^9/u[/B]

raise y to the 10th power, then find the quotient of the result and 2

y to the 10th power means we give y an exponent of 10
y^10
The quotient of y^10 and 2 is:
y^10
-----
2

Random Sampling from the Normal Distribution

This performs hypothesis testing on a sample mean with critical value on a sample mean or calculates a probability that Z <= z or Z >= z using a random sample from a normal distribution.

ratio of the squares of t and u

ratio of the squares of t and u
Ratio is also known as quotient in algebraic expression problems.
The square of t means we raise t to the power of 2:
t^2
The square of u means we raise u to the power of 2:
u^2
ratio of the squares of t and u means we divide t^2 by u^2:
[B]t^2/u^2[/B]

ratio of x cubed and the sum of y and 5

ratio of x cubed and the sum of y and 5
x cubed means we raise x to the power of 3:
x^3
The sum of y and 5:
y + 5
ratio of x cubed and the sum of y and 5
[B]x^3/(y + 5)[/B]

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a ball at random.
a. What is the probability that you choose a red or even numbered ball?
b. What is the probability you choose a green ball or a ball numbered less than 5?
a. The phrase [I]or[/I] in probability means add. But we need to subtract even reds so we don't double count:
We have 18 total balls, so this is our denonminator for our fractions.
Red and Even balls are {2, 4, 6, 8, 10, 12}
Our probability is:
P(Red or Even) = P(Red) + P(Even) - P(Red and Even)
P(Red or Even) = 13/18 + 9/18 - 6/18
P(Red or Even) = 16/18
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=16%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have:
P(Red or Even) = [B]16/18[/B]
[B][/B]
b. The phrase [I]or[/I] in probability means add. But we need to subtract greens less than 5 so we don't double count:
We have 18 total balls, so this is our denonminator for our fractions.
Green and less than 5 does not exist, so we have no intersection
Our probability is:
P(Green or Less Than 5) = P(Green) + P(Less Than 5) - P(Green And Less Than 5)
P(Green or Less Than 5) = 5/18 + 4/18 - 0
P(Green or Less Than 5) = 9/18
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have:
P(Red or Even) = [B]1/2[/B]

Researchers in Antarctica discovered a warm sea current under the glacier that is causing the glacie

Researchers in Antarctica discovered a warm sea current under the glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate if 0.06 m per day.
Which function can be used to find the thickness of the ice shelf in meters x days since the discovery?
We want to build an function I(x) where x is the number of days since the ice shelf discovery.
We start with 450 meters, and each day (x), the ice shelf loses 0.06m, which means we subtract this from 450.
[B]I(x) = 450 - 0.06x[/B]

Richard earns $2700 a month. He received a 3% raise. What is Richard's new annual salary? Remember 1

Richard earns $2700 a month. He received a 3% raise. What is Richard's new annual salary? Remember 12 months in 1 year
$2,700 per month * 12 months = 32,400 per year.
A 3% raise means the new salary is:
32,400 * 1.03 = [B]$33,372[/B]

Richard is thrice as old as Alvin. The sum of their ages is 52 years. Find their ages

Richard is thrice as old as Alvin. The sum of their ages is 52 years. Find their ages.
Let r be Richard's age. And a be Alvin's age. We have:
[LIST=1]
[*]r = 3a
[*]a + r = 52
[/LIST]
Substitute (1) into (2)
a + 3a = 52
Group like terms:
4a = 52
[URL='https://www.mathcelebrity.com/1unk.php?num=4a%3D52&pl=Solve']Typing this into the search engine[/URL], we get [B]a = 13[/B].
This means Richard is 3(13) = [B]39[/B]

Ronnie, liza, vivien, and vina are classmates. They send each other a Valentines card. Find the numb

Ronnie, liza, vivien, and vina are classmates. They send each other a Valentines card. Find the number of Valentines cards they send altogether
We've got 4 classmates. Which means each person sends 3 Valentine's cards (to everybody else in the class but themselves):
3 * 3 * 3 * 3 or 4 * 3 = 12 Valentine's cards.

Ryan buys candy that costs $4 per pound. He will buy at least 12 pounds of candy. What are the possi

Ryan buys candy that costs $4 per pound. He will buy at least 12 pounds of candy. What are the possible amounts he will spend on candy?
Clue for you: the phrase [I]at least[/I] means an inequality.
Let s be the spend on candy.
Cost = Price * quantity
Cost = 4 * 12
Cost = 48
The phrase [I]at least[/I] means greater than or equal to:
[B]s >= 48[/B]

S equals the quotient of r and the sum of r and 8.

S equals the quotient of r and the sum of r and 8.
A quotient means a fraction, so we have:
[B]S = r/(r + 8)[/B]

S varies jointly with t cubed and v

S varies jointly with t cubed and v
Varied jointly means there exists a constant k such that:
[B]s = kt^3v[/B]

Sally is 4 years older than Mark. Twice Sally's age plus 5 times Mark's age is equal to 64.

Sally is 4 years older than Mark. Twice Sally's age plus 5 times Mark's age is equal to 64.
Let Sally's age be s. Let Mark's age be m. We're given two equations:
[LIST=1]
[*]s = m + 4
[*]2s + 5m = 64 <-- [I]Since Twice means we multiply by 2[/I]
[/LIST]
Substitute equation (1) into equation (2):
2(m + 4) + 5m = 64
Multiply through:
2m + 8 + 5m = 64
Group like terms:
(2 + 5)m + 8 = 64
7m + 8 = 64
[URL='https://www.mathcelebrity.com/1unk.php?num=7m%2B8%3D64&pl=Solve']Type this equation into the search engine[/URL] and we get:
m = [B]8[/B]

Sam has x model planes. Anton has 8 more planes than Sam does. How many model planes Does Anton have

Sam has x model planes. Anton has 8 more planes than Sam does. How many model planes Does Anton have? how many planes do they have together?
Sam has x
Anton has [B]x + 8[/B] since the word [I]more[/I] means we add
The word [I]together[/I] means we add, so we have:
Sam + Anton = x + x + 8
Grouping like terms, we have:
Sam + Anton = [B]2x + 8[/B]

Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is John

Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is John
Let John's age be j. We're given the following equation:
3j - 20 = 52 ([I]Less than[/I] means we subtract)
To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=3j-20%3D52&pl=Solve']type this equation into our search engine[/URL] and we get:
j = [B]24[/B]

Sara earns $6000 more than 1/3 of Claudia's yearly salary. If Claudia's salary is n, what is Sara's

Sara earns $6000 more than 1/3 of Claudia's yearly salary. If Claudia's salary is n, what is Sara's salary?
1/3 Claudia's salary:
n/3
6000 more means we add:
[B]n/3 + 6000[/B]

Sarah has $250 in her account. She withdraws $25 per week. How many weeks can she withdraw money fro

Sarah has $250 in her account. She withdraws $25 per week. How many weeks can she withdraw money from her account and still have money left?
Let w be the number of weeks. We have the following equation for the Balance after w weeks:
B(w) = 250 - 25w [I]we subtract for withdrawals[/I]
The ability to withdrawal money means have a positive or zero balance after withdrawal. So we set up the inequality below:
250 - 25w >= 0
To solve this inequality for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=250-25w%3E%3D0&pl=Solve']type it in our search engine[/URL] and we get:
w <= [B]10
So Sarah can withdrawal for up to 10 weeks[/B]

Sarah makes $9 per hour working at a daycare center and $12 per hour working at a restaurant. Next

Sarah makes $9 per hour working at a daycare center and $12 per hour working at a restaurant. Next week, Sarah is scheduled to work 8 hours at the daycare center. Which of the following inequalities represents the number of hours (h) that Sandra needs to work at the restaurant next week to earn at least $156 from these two jobs?
Set up Sarah's earnings function E(h) where h is the hours Sarah must work at the restaurant:
12h + 9(8) >= 156 <-- The phrase [I]at least[/I] means greater than or equal to, so we set this up as an inequality. Also, the daycare earnings are $9 per hour * 8 hours
Multiplying through and simplifying, we get:
12h + 72 >= 156
We [URL='https://www.mathcelebrity.com/1unk.php?num=12h%2B72%3E%3D156&pl=Solve']type this inequality into the search engine[/URL], and we get:
[B]h>=7[/B]

Sean is helping his dad build a tiled walkway in their backyard. The walkway will be 606060 feet lon

I assume you want to know how many tiles or how many boxes of tile they need? I'll do both:
Since each tile covers the full 2 foot width of the walkway, we need to see how many tiles length wise we need.
60/2 = [B]30 tiles[/B] needed to cover the full walkway.
Now, each box contains 6 tiles, which means we need 30 tiles/6 tiles per box = [B]5 boxes of tiles[/B]

Set C is the set of two-digit even numbers greater than 72 that do not contain the digit 8.

Set C is the set of two-digit even numbers greater than 72 that do not contain the digit 8.
First, two-digit numbers mean anything less than 100. Let's, list out our two-digit even numbers greater than 72 but less than 100.
C = {74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98}
The problem asks for numbers that do not contain the digit 8. Let's remove those numbers from the list.
C = {74, 76, [S]78[/S], [S]80, 82, 84, 86, 88[/S], 90, 92, 94, 96, [S]98[/S]}
[B]C = {74, 76, 90, 92, 94, 96}[/B]

Set C is the set of two-digit even numbers less than 56 that are divisible by 5

[U]Two digit Numbers less than 56:[/U]
{10, 11, 12, ..., 55}
[U]Two Digit Even Numbers of that Set:[/U]
{10, 12, 14, ..., 54}
[U]Two Digit Even numbers Divisible by 5[/U]
[B]C = {10, 20, 30, 40, 50}[/B]
[I]Note: Even means you can divide it by 2 with no remainder. Divisible by 5 means the number ends in 5 or 0. Since it is even numbers only, end in 0.[/I]

Set D is the set of two-digit even numbers less than 67 that are divisible by 5

Set D is the set of two-digit even numbers less than 67 that are divisible by 5
two-digit numbers start at 10. Divisible by 5 means the last digit is either 0 or 5. But even numbers don't end in 5, so we take the two-digit numbers ending in 0:
D = {[B]10, 20, 30, 40, 50, 60}[/B]

Set of 2 digit even numbers less than 40

Set of 2 digit even numbers less than 40
Knowns and givens:
[LIST]
[*]2 digit numbers start at 10
[*]Less than 40 means we do not include 40
[*]Even numbers are divisible by 2
[/LIST]
[B]{10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38}[/B]

Seven less than 1/4 of a number is 9.

Seven less than 1/4 of a number is 9.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
1/4 of a number means we multiply x by 1/4:
x/4
Seven less than this means we subtract 7 from x/4:
x/4 - 7
The word [I]is[/I] means an equation, so we set x/4 - 7 equal to 9:
[B]x/4 - 7 = 9[/B]

Seven subtracted from the product of 3 and a number is greater than or equal to -26

Seven subtracted from the product of 3 and a number is greater than or equal to -26
[LIST=1]
[*]A number means an arbitrary variable, let's call it x.
[*]The product of 3 and a number is written as 3x
[*]Seven subtracted from 3x is written as 3x - 7
[*]Finally, that entire expression is greater than or equal to -26: [B]3x - 7 >= - 26[/B]
[/LIST]

Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself how many

Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself how many plums did she have at first?
Let p be the number of plums Shalini started with. We have:
[LIST]
[*]0.4 given to her brother
[*]20% which is 0.2 given away to her sister
[*]What this means is she kept 1 - (0.4 + 0.2) = 1 - 0.6 = 0.4 for herself
[/LIST]
0.4p = 16
Divide each side by 0.4
[B]p = 40[/B]

Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself. How man

Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself. How many plums did she have first?
Let's convert everything to decimals. 20% = 0.2
So Shalini gave 0.4 + 0.2 = 0.6 of the plums away. Which means she has 1 = 0.6 = 0.4 or 40% left over.
40% represents 16 plums
So our equation is 0.4p = 16 where p is the number of plums to start with
Divide each side by 0.4
[B]p = 40[/B]

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants i

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants it to be 5 times as long as it is wide. What dimensions should the play area be?
Sheila wants:
[LIST=1]
[*]l =5w
[*]2l + 2w = 100 <-- Perimeter
[/LIST]
Substitute (1) into (2)
2(5w) + 2w = 100
10w + 2w = 100
12w = 100
Divide each side by 12
[B]w = 8.3333[/B]
Which means l = 5(8.3333) -->[B] l = 41.6667[/B]

Sign Test

This will determine whether to accept or reject a null hypothesis based on a number set, mean value, alternative hypothesis, and a significance level using the Sign Test.

Six Less than the total of three times a number and negative eight

Six Less than the total of three times a number and negative eight.
Let's take this in pieces:
Three times a number = 3x
The total of this and negative eight means we subtract eight
3x - 8
Six Less than this total means we subtract 6
3x - 8 - 6
Simplify by combining like terms:
[B]3x - 14[/B]

Six less than twice a number is at least -1 and at most 1

First, the phrase [I]a number[/I] means we choose an arbitrary variable, let's call it x.
Twice a number means we multiply it by 2.
2x
Six less than that means we subtract 6
2x - 6
Now, the last piece, we set up an inequality. At least -1 means greater than or equal to 1. At most 1 means less than or equal to 1. Notice, for both points, we include the number.
-1 <= 2x - 6 <= 1

Solve for x

[IMG]https://mathcelebrity.com/community/data/attachments/0/supp-angles.jpg[/IMG]
The angle with measurements of 148 degrees lies on a straight line, which means it's supplementanry angle is:
180 - 148 = 32
Since the angle of 2x - 16 and 32 lie on a straight line, their angle sum equals 180:
2x + 16 + 32 = 180
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B16%2B32%3D180&pl=Solve']type it in our math engine [/URL]and we get:
x = [B]66[/B]

Solve Problem

based on a sample of size 41, a 95% confidence interval for the mean score of all students,µ, on an aptitude test is from 60 to 66. Find the margin of error

Solve Problem

A sample of 71 college students yields a mean annual income of $3595. Assuming that ? = $898, find the margin of error in estimating µ at the 99% level of confidence

Solve Problem

[URL]http://www.mathcelebrity.com/marginoferror.php?num=60%2C66&pl=Calculate+Margin+of+Error+and+Sample+Mean[/URL]

Solve the problem

a confidence interval for a population mean has a margin of error of 0.081. Determine the length of the confidence interval

square root of the sum of 2 variables

square root of the sum of 2 variables
The phrase [I]2 variables[/I] means we choose 2 arbitrary variables, let's call them x and y:
x, y
The sum of 2 variables means we add:
x + y
Square root of the sum of 2 variables is written as:
[B]sqrt(x + y)[/B]

Squaring a number equals 5 times that number

Squaring a number equals 5 times that number.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Squaring this number:
x^2
5 times this number means we multiply by 5:
5x
The phrase [I]equals[/I] means we set both expressions equal to each other:
[B]x^2 = 5x [/B] <-- This is our algebraic expression
If you want to solve for x, then we subtract 5x from each side:
x^2 - 5x = 5x - 5x
Cancel the 5x on the right side, leaving us with 0:
x^2 - 5x = 0
Factor out x:
x(x - 5)
So we get x = 0 or [B]x = 5[/B]

Start with q. Multiply by p. Add 3. Divide A

Start with q. Multiply by p. Add 3. Divide A
Start with q:
q
Multiply by p:
pq
Add 3:
pq + 3
Divide A means divide by A. We wrap pq + 3 in parentheses to divide by the sum
(pq + 3)/A

Start with t and cube it.

Start with t and cube it.
Cubing a variable means raising it to the power of 3:
[B]t^3[/B]

Start with x , subtract 6, then times by 3.

Start with x , subtract 6, then times by 3.
We start with x:
x
Subtract 6:
x - 6
The phrase [I]times by[/I] means we multiply (x - 6) by 3
[B]3(x - 6) [/B] <-- This is our algebraic expression
If the problem asks you to multiply through, then you'd have:
3x - 18

Steve Has Overdrawn His Checking Account By $27. His Bank Charged Him $15 For An Overdraft Fee Then

Steve Has Overdrawn His Checking Account By $27. His Bank Charged Him $15 For An Overdraft Fee Then He Quickly Deposited $100. What Is His Current Balance?
[LIST=1]
[*]Overdrawn means money he doesn't have, so we go into the negative. Start with -27.
[*]A bank charge of $15 means he goes in the negative another $15, so -27 - 15 = -42
[*]Then he deposits $100, so his balance is: $100 - 42 = [B]$58[/B]
[/LIST]

Steve woke up and it was -12 Fahrenheit outside the weatherman said it was supposed to warm up to 20

Steve woke up and it was -12 Fahrenheit outside the weatherman said it was supposed to warm up to 20 degrees. how many degrees will the temperature increase
We start with a temperature of -12F
Warming up means we [U][B]add[/B][/U] degrees to the original temperature.
-12 + 20 = [B]+8F[/B]

Storm Center 7 was tracking a cold front approaching Cedarburg. Before it rolled in, the temperature

Storm Center 7 was tracking a cold front approaching Cedarburg. Before it rolled in, the temperature was – 7°F. Then, the temperature decreased by 9°F. What was the temperature after the cold front rolled in?
Using signed integers, we start with 7 below or -7
-7
The temperature decreased by 9 which means we subtract:
-7 - 9 or -7 + (-9)
[B]-16°F or 16 below 0
[MEDIA=youtube]oJjEhkdnTxA[/MEDIA][/B]

Subtract 4 from the sum of 2x and 5y

Subtract 4 from the sum of 2x and 5y.
The sum of 2x and 5y means we add both terms:
2x + 5y
Subtract 4 from this sum to get our algebraic expression:
[B](2x + 5y) - 4[/B]

subtract 5 from the sum of 3x and 8y

subtract 5 from the sum of 3x and 8y
Take this algebraic expression in parts:
[U]The sum of 3x and 8y means we add 8y to 3x:[/U]
3x + 8y
[U]Subtract 5 from this sum above:[/U]
[B]3x + 8y - 5[/B]

subtract half of a number from 10

subtract half of a number from 10
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
half of a number means we divide x by 2:
x/2
subtract half of a number from 10
[B]10 - x/2[/B]

subtract the product of 5 and x from 7

subtract the product of 5 and x from 7
The product of 5 and x means we multiply 5 by x:
5x
We subtract this product, 5x, from 7
[B]7 - 5x[/B]

Subtract the quotient of m and 7 from 4

Subtract the quotient of m and 7 from 4
The quotient of m and 7 means we add divide m by 7
m/7
Subtract this quotient from 4
[B]4 - m/7[/B]

subtract w from u, triple the result, then multiply v by what you have

subtract w from u, triple the result, then multiply v by what you have
Take this algebraic expression in 3 parts:
[U]1) subtract w from u:[/U]
u - w
[U]2) Triple the result means we multiply u - w by 3:[/U]
3(u - w)
[U]3) Multiply v by what you have. [I]What you have[/I] means the result from step 2:[/U]
[B]3v(u - w)[/B]

subtract w from v, add the result to u, then triple what you have

subtract w from v, add the result to u, then triple what you have
Take this algebraic expression in parts:
[LIST=1]
[*]Subtract w from v: v - w
[*]Add the result to u (the result is #1): u + v - w
[*]Triple what you have. This means multiply the result in #2 by 3:
[/LIST]
[B]3(u + v - w)[/B]

sum of 5 times h and twice g is equal to 23

sum of 5 times h and twice g is equal to 23
Take this [U]algebraic expressions[/U] problem in pieces.
Step 1: 5 times h:
5h
Step 2: Twice g means we multiply g by 2:
2g
Step 3: sum of 5 times h and twice g means we add 2g to 5h
5h + 2g
Step 4: The phrase [I]is equal to[/I] means an equation, so we set 5h + 2g equal to 23:
[B]5h + 2g = 23[/B]

sum of a number and 7 is subtracted from 15 the result is 6.

Sum of a number and 7 is subtracted from 15 the result is 6.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take this expression in pieces. Sum of a number and 7
x + 7
Subtracted from 15
15 - (x + 7)
The result is means an equation, so we set this expression above equal to 6
[B]15 - (x + 7) = 6 <-- This is our algebraic expression[/B]
If the problem asks you to solve for x, we Group like terms
15 - x - 7 = 6
8 - x = 6
[URL='https://www.mathcelebrity.com/1unk.php?num=8-x%3D6&pl=Solve']Type 8 - x = 6 into the search engine[/URL], and we get [B]x = 2[/B]

Sum of a number and it's reciprocal is 6. What is the number?

Sum of a number and it's reciprocal is 6. What is the number?
Let the number be n.
The reciprocal is 1/n.
The word [I]is[/I] means an equation, so we set n + 1/n equal to 6
n + 1/n = 6
Multiply each side by n to remove the fraction:
n^2 + 1 = 6n
Subtract 6n from each side:
[B]n^2 - 6n + 1 = 0 [/B]<-- This is our algebraic expression
If the problem asks you to solve for n, then you [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-6n%2B1%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type this quadratic equation into our search engine[/URL].

Sum of N and its next consecutive even integer is 65

Sum of N and its next consecutive even integer is 65
Next even consecutive integer is N + 2.
We have N + (N + 2) = 65.
Combine like terms, we have 2N + 2 = 65
[URL='http://www.mathcelebrity.com/1unk.php?num=2n%2B2%3D65&pl=Solve']Running this problem through the search engine[/URL], we get n = 31.5. Meaning this problem is impossible, it cannot be done. n is not an integer, and neither is the next consecutive even integer.

sum of the cube of x and half of y

sum of the cube of x and half of y
The cube of x means we raise x to the 3rd power:
x^3
half of y means we divide y by 2:
y/2
sum of the cube of x and half of y means we add y/2 to x^3
[B]x^3 + y/2[/B]

sum of the squares of u and v

sum of the squares of u and v
The square of u means we raise u to the power of 2
u^2
The square of v means we raise v to the power of 2
v^2
The sum means we add v^2 to u^2:
[B]u^2 + v^2[/B]

sum of twice f plus h

sum of twice f plus h
Twice f means we multiply f by 2:
2f
sum of twice f plus h
[B]2f + h[/B]

sum of twice w and 3 times l

sum of twice w and 3 times l
Twice w means we multiply w by 2:
2w
3 times l:
3l
When we see the phrase [I]sum of[/I], we add:
[B]2w + 3l[/B]

Suppose a firm producing light bulbs wants to know if it can claim that its light bulbs it produces

Suppose a firm producing light bulbs wants to know if it can claim that its light bulbs it produces last 1,000 burning hours (u). To do this, the firm takes a random sample of 100 bulbs and find its average life time (X=980 hrs) and the sample standard deviation s = 80 hrs. If the firm wants to conduct the test at the 1% of significance, what's you final suggestion?
(i..e, Should the producer accept the Ho that its light bulbs have a 1,000 burning hrs. at the 1% level of significance?)
Ho: u = 1,000 hours.
Ha: u <> 1,000 hours.
[URL='http://www.mathcelebrity.com/mean_hypothesis.php?xbar=+980&n=+100&stdev=+80&ptype==&mean=+1000&alpha=+0.01&pl=Mean+Hypothesis+Testing']Perform a hypothesis test of the mean[/URL]
[B]Yes, accept null hypothesis[/B]

Suppose that h(x) varies directly with x and h(x)=44 when x = 2. What is h(x) when x = 1.5?

Suppose that h(x) varies directly with x and h(x)=44 when x = 2. What is h(x) when x = 1.5?
Direct variation means we set up an equation:
h(x) = kx where k is the constant of variation.
For h(x) = 44 when x = 2, we have:
2k = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=2k%3D44&pl=Solve']Type this equation into our search engine[/URL], we get:
k = 22
The question asks for h(x) when x = 1.5. So we set up our variation equation, knowing that k = 22.
kx = h(x)
With k = 22 and x = 1.5, we get:
22(1.5) = h(x)
h(x) = [B]33[/B]

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls.
a. If X = average distance in feet for 49 fly balls, then X ~ _______(_______,_______)

b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.

c. Find the 80^{th} percentile of the distribution of the average of 49 fly balls
a. N(250, 50/sqrt(49)) = [B]0.42074[/B]
b. Calculate Z-score and probability = 0.08 shown [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+240&mean=+250&stdev=+7.14&n=+1&pl=P%28X+%3C+Z%29']here[/URL]
c. Inverse of normal distribution(0.8) = 0.8416. Use NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL]
Using the Z-score formula, we have
0.8416 = (x - 250)/50
x = [B]292.08[/B]

b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.

c. Find the 80

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and
a standard deviation of 50 feet.
a. If X = distance in feet for a fly ball, then X ~
b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability.
c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.
a. [B]N(250, 50/sqrt(1))[/B]
b. Calculate [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+220&mean=250&stdev=50&n=+1&pl=P%28X+%3C+Z%29']z-score[/URL]
Z = -0.6 and P(Z < -0.6) = [B]0.274253[/B]
c. Inverse of normal distribution(0.8) = 0.8416 using NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL]
Z-score formula: 0.8416 = (x - 250)/50

x = [B]292.08[/B]

x = [B]292.08[/B]

Suppose you write a book. The printer charges $4 per book to print it, and you spend 5500 on adverti

Suppose you write a book. The printer charges $4 per book to print it, and you spend 5500 on advertising. You sell the book for $15 a copy. How many copies must you sell to break even.
Profit per book is:
P = 15 - 4
P = 11
We want to know the number of books (b) such that:
11b = 5500 <-- Breakeven means cost equals revenue
[URL='https://www.mathcelebrity.com/1unk.php?num=11b%3D5500&pl=Solve']Typing this equation into the search engine[/URL], we get:
b = [B]500[/B]

t varies directly with the square of r and inversely with w

t varies directly with the square of r and inversely with w
There exists a constant k such that:
[B]t = kr^2/w[/B]
[I]Directly means multiply and inversely means divide[/I]

take away 1 from the cube of e

The cube of e is e^3.
Take away 1 means subtract 1
e^3 - 1

take away the product of 12 and p from 25

take away the product of 12 and p from 25
The product of 12 and p means we multiply 12 by p:
12p
Take away this product means we subtract 12p from 25:
[B]25 - 12p[/B]

Ten subtracted from the product of 9 and a number is less than ?24

Ten subtracted from the product of 9 and a number is less than ?24.
A number means an arbitrary variable, let's call it x
x
The product of 9 and a number:
9x
Ten subtracted from that
9x - 10
Finally, is less than means we set our entire expression less than -24
[B]9x - 10 < -24[/B]

the absolute value of the difference 6 and k

the absolute value of the difference 6 and k
The difference of 6 and k means we subtract k from 6:
6 - k
Take the absolute value:
[B]|6 - k|[/B]

The age of a woman 15 years ago

The age of a woman 15 years ago
Let the woman's current age be a.
15 years ago means we subtract 15 from a:
[B]a - 15[/B]

The age of denver 3 years ago if he is x years old now

The age of denver 3 years ago if he is x years old now
3 years ago means we subtract:
[B]x - 3[/B]

The age of woman 15 years ago

The age of woman 15 years ago
Let a be the woman's age today. 15 years ago means we subtract 15 from a:
[B]a - 15[/B]

The ages of three siblings are all consecutive integers. The sum of of their ages is 39.

The ages of three siblings are all consecutive integers. The sum of of their ages is 39.
Let the age of the youngest sibling be n. This means the second sibling is n + 1. This means the oldest/third sibling is n + 2.
So what we want is the[URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof3consecutiveintegersequalto39&pl=Calculate'] sum of 3 consecutive integers equal to 39[/URL]. We type this command into our search engine. We get:
n = 12. So the youngest sibling is [B]12[/B].
The next sibling is 12 + 1 = [B]13[/B]
The oldest/third sibling is 12 + 2 = [B]14[/B]

The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. Wha

The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. What is the value of N ?
Average of the first number set is [URL='https://www.mathcelebrity.com/statbasic.php?num1=17%2C26%2C42%2C59&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']using our average calculator[/URL] is:
36
Now, the mean (average) or 19 and N is found by adding them together an dividing by 2:
(19 + N)/2
Since both number sets have equal means, we set (19 + N)/2 equal to 36:
(19 + N)/2 = 36
Cross multiply:
19 + N = 36 * 2
19 + n = 72
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=19%2Bn%3D72&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]53[/B]

The auditorium can hold a maximum of 150 people

The auditorium can hold a maximum of 150 people
We want an inequality for the number of people (p) in the auditorium.
The word [I]maximum[/I] means [I]no more than[/I] or [I]less than or equal to[/I]. So we have:
[B]p <= 150[/B]

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height re

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height remained the same. What is the height of the mother?
[LIST]
[*]Let the height of the family without the mom be f. Let the height of the mother be m.
[*]Averages mean we add the heights and divide by the number of people who were measured.
[/LIST]
We're given two equations:
[LIST=1]
[*](f + m)/6 = 6
[*]f/5 = 6
[/LIST]
Cross multiplying equation (2), we get:
f = 5 * 6
f = 30
Plug f = 30 into equation (1), we get:
(30 + m)/6 = 6
Cross multiplying, we get:
m + 30 = 6 * 6
m + 30 = 36
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B30%3D36&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]6[/B]
[SIZE=3][FONT=Arial][COLOR=rgb(34, 34, 34)][/COLOR][/FONT][/SIZE]

The average of 171 and x?

The average of 171 and x?
The phrase [I]average[/I] means add up all the items in the number set, divided by the count of items in the number set.
Our number set in this case is {171, x} which has 2 elements. Therefore, our average is:
[B](171 + x)/2[/B]

The average of a number and double the number is 25.5

Let x equal "a number".
Double the number is 2x.
The average is (x + 2x)/2
Combine the terms in the numerator:
3x/2
The word [I]is[/I] means equal to, so we set 3x/2 equal to 25.5
3x/2 = 25.5
Cross multiply the 2:
3x = 51
Divide each side by 3
[B]x = 17[/B]

the average of eighty-five and a number m is ninety

the average of eighty-five and a number m is ninety
Average of 2 numbers means we add both numbers and divide by 2:
(85 + m)/2 = 90
Cross multiply:
m + 85 = 90 * 2
m + 85 = 180
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B85%3D180&pl=Solve']type it in our math engine [/URL]and we get:
m = [B]95[/B]

the average, a, is at least 85

the average, a, is at least 85
At least is an inequality. It also means greater than or equal to, so we have:
[B]a >= 85[/B]

the balance of an account after $40 withdrawal

the balance of an account after $40 withdrawal
Let the balance be b.
A withdrawal means a [U]reduction[/U][I] in the balance[/I]. So we have
[B]b - 40[/B]

The club uses the function S(t) = -4,500t + 54,000 to determine the salvage S(t) of a fertilizer ble

The club uses the function S(t) = -4,500t + 54,000 to determine the salvage S(t) of a fertilizer blender t years after its purchase. How long will it take the blender to depreciate completely?
Complete depreciation means the salvage value is 0.
So S(t) = 0. We need to find t to make S(t) = 0
-4,500t + 54,000 = 0
Subtract 54,000 from each side
-4,500t = -54,000
Divide each side by -4,500
[B]t = 12[/B]

The cost of a field trip is $220 plus $7 per student. If the school can spend at most $500, how many

The cost of a field trip is $220 plus $7 per student. If the school can spend at most $500, how many students can go on the field trip?
Set up the inequality where s is the number of students:
C(s) = 220 + 7s
We want C(s) <= 500, since at most means no more than
220 + 7s <= 500
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=220%2B7s%3C%3D500&pl=Solve']inequality calculator[/URL], we get:
[B]s <= 40[/B]

The cost of purchasing a hockey stick and puck if the stick costs 6 less than twice the cost of the

The cost of purchasing a hockey stick and puck if the stick costs 6 less than twice the cost of the puck.
Let the hockey stick cost h, and puck cost p.
Twice the cost of the puck means we multiply p by 2:
2p
6 less than this means we subtract 6:
h = 2p - 6
[B][/B]
The total cost of the hockey stick and puck is:
p + 2p - 6
[B]3p - 6[/B]

the cube of c decreased by a^2

the cube of c decreased by a^2
The cube of means we raise the variable c to the power of 3:
c^3
The phrase [I]decreased by[/I] means we subtract:
[B]c^3 - a^2[/B]

The cube of g plus the square of m

The cube of g plus the square of m
The cube of g means we raise g to the 3rd power:
g^3
The square of m means we raise m to the 2nd power:
m^2
The word [I]plus[/I] means we add them both
[B]g^3 + m^2[/B]

The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y

The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y
Take this in algebraic expression in parts:
[U]Term 1[/U]
[LIST]
[*]The square of y means we raise y to the 2nd power: y^2
[*]5 times the square of y: 5y^2
[/LIST]
[U]Term 2[/U]
[LIST]
[*]2 times y: 2y
[*]The square of 2 times y: (2y)^2 = 4y^2
[*]7 divide by the square of 2 times y: 7/4y^2
[/LIST]
[U]The difference of these terms is written as Term 1 minus Term 2:[/U]
[LIST]
[*]5y^2/4y^2
[/LIST]
[U]The cube of the difference means we raise the difference to the power of 3:[/U]
[B](5y^2/4y^2)^3[/B]

the cube of the difference of 5 times x and 4

the cube of the difference of 5 times x and 4
Take this algebraic expression in pieces:
5 times x:
5x
The difference of 5x and 4 means we subtract 4 from 5x:
5x - 4
We want to cube this difference, which means we raise the difference to the power of 3.
[B](5x - 4)^3[/B]

the cube of the product of 3 and x

the cube of the product of 3 and x
The product of 3 and x:
3x
Cube this product means raise it to the power of 3:
(3x)^3 = [B]27x^3[/B]

the cube of the sum of 2a and 3b

the cube of the sum of 2a and 3b
Sum of 2a and 3b:
(2a + 3b)
The cube of the sum mean we raise the sum to the power of 3:
[B](2a + 3b)^3[/B]

The cube of x is less than 15

The cube of x is less than 15
The cube of x means we raise x to the 3rd power:
x^3
Less than 15 means we setup the following inequality
[B]x^3 < 15[/B]

The denominator of a fraction is 4 more than the numerator. If 4 is added to the numerator and 7 is

The denominator of a fraction is 4 more than the numerator. If 4 is added to the numerator and 7 is added to the denominator, the value of the fraction is 1/2. Find the original fraction.
Let the original fraction be n/d.
We're given:
[LIST=1]
[*]d = n + 4
[*](n + 4) / (d + 7) = 1/2
[/LIST]
Cross multiply Equation 2:
2(n + 4) = d + 7
2n + 8 = d + 7
Now substitute equation (1) into tihs:
2n + 8 = (n + 4) + 7
2n + 8 = n + 11
[URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B8%3Dn%2B11&pl=Solve']Type this equation into our search engine[/URL], and we get:
n = 3
This means from equation (1), that:
d = 3 + 4
d = 7
So our original fraction n/d = [B]3/7[/B]

The difference between 3 times x and 4

[U]3 times x:[/U]
3x
[U]The difference between 3x and 4 means we subtract:[/U]
3x - 4

the difference between 7 times a number and 9 less than a number

the difference between 7 times a number and 9 less than a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
7 times a number means we multiply x by 7
7x
9 less than a number means we subtract 9 from x
x - 9
The difference between the two expressions means we subtract (x - 9) from 7x
7x - (x - 9)
Simplifying this, we have:
7x - x + 9
Grouping like terms, we get:
[B]6x + 9[/B]

The difference between a and b is 10

The difference between a and b is 10.
The problem asks for an algebraic expression. Let's take each piece one by one:
[I]Difference between[/I] means we subtract:
a - b
The phrase [I]is [/I]means an equation, so we set a - b equal to 10
[B]a - b = 10[/B]

The difference between A and B is no less than 30

The difference between A and B is no less than 30
The difference between means we subtract.
No less than means greater than or equal to, so we have the following inequality;
[B]A - B >= 30[/B]

the difference between A and B is no less than 30.

the difference between A and B is no less than 30.
The difference between a and b:
a - b
The phrase [I]no less than[/I] means an inequality. You can also say this as [I]greater than or equal to[/I].
[B]a - b >= 30[/B]

The difference between a number and 9 is 27. Find that number

The difference between a number and 9 is 27. Find that number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The difference between a number and 9
x - 9
The word [I]is[/I] means equal to, so we set x - 9 equal to 27:
x - 9 = 27
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-9%3D27&pl=Solve']type it in our math engine[/URL] and we get:
x = [B]36[/B]

The difference between sixty-four and y

The difference between sixty-four and y
The difference between means we subtract y from 64:
[B]64 - y[/B]

The difference between the opposite of a number and 6.

The difference between the opposite of a number and 6.
The phrase [I]a number means[/I] an arbitrary variable, let's call it x.
x
The opposite of a number means we multiply by x by -1
-x
The phrase [I]the difference between[/I] means we subtract 6 from -x:
[B]-x - 6[/B]

The difference between the product of 4 and a number and the square of a number

The difference between the product of 4 and a number and the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The product of 4 and a number:
4x
The square of a number means we raise x to the power of 2:
x^2
The difference between the product of 4 and a number and the square of a number:
[B]4x - x^2[/B]

The difference between the quotient of x and y, and twice z

The difference between the quotient of x and y, and twice z
The quotient of x and y means we divide x by y:
x/y
Twice z means we multiply z by 2:
2z
The difference between the quotient of x and y, and twice z means we subtract 2z from x/y
[B]x/y - 2z[/B]

The difference between the square of b and the total of b and 9

The difference between the square of b and the total of b and 9
The square of b means we raise b to the power of 2:
b^2
The total of b and 9 means we add 9 to b:
b + 9
The difference means we subtract:
[B]b^2 - (b + 9)[/B]

The difference between the square of b and the total of d and g

The difference between the square of b and the total of d and g
Square of b means we raise b to the 2nd power:
b^2
Total of d and g:
d + g
The difference between the square of b and the total of d and g
[B]b^2 - (d + g)[/B]

the difference between triple a number and double a number

the difference between triple a number and double a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Triple a number means we multiply x by 3:
3x
Double a number means we multiply x by 2:
2x
The difference means we subtract 2x from 3x:
3x - 2x
Simplifying like terms, we have:
(3 - 2)x = [B]x[/B]

The difference in Julies height and 9 is 48 letting j be Julie's height

The difference in Julies height and 9 is 48 letting j be Julie's height
Step 1: If Julie's height is represented with the variable j, then we subtract 9 from j since the phrase [I]difference[/I] means we subtract:
j - 9
Step 2: The word [I]is[/I] means an equation, so we set j - 9 equal to 48 for our final algebraic expression:
[B]j - 9 = 48[/B]

The difference of 100 and x is 57

The difference of 100 and x means we subtract x from 100:
100 - x
Is means equal to, so we set our expression above equal to 57
[B]100 - x = 57
[/B]
If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=100-x%3D57&pl=Solve']equation calculator[/URL]

The difference of 25 and a number added to triple another number

The difference of 25 and a number added to triple another number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x:
x
The difference of 25 and a number means we subtract x from 25:
25 - x
The phrase [I]another number[/I] means a different arbitrary variable, let's call it y:
y
Triple another number means we multiply y by 3:
3y
The phrase [I]added to[/I] means we add 25 - x to 3y
[B]25 - x + 3y[/B]

the difference of 4 and the quotient of 18 and a number

the difference of 4 and the quotient of 18 and a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The quotient of 18 and a number means we divide 18 by the variable x.
18/x
The difference of 4 and the quotient above means we subtract 18/x from 4:
[B]4 - 18/x[/B]

the difference of 5 and the cube of the sum of x and y

the difference of 5 and the cube of the sum of x and y
The sum of x and y:
x + y
The cube of the sum of x and y means we raise x + y to the 3rd power:
(x + y)^3
The difference of 5 and the cube of the sum of x and y
[B]5 - (x + y)^3[/B]

The difference of 6 and the sum a and b

The difference of 6 and the sum a and b
The sum of a and b means we add b to a:
a + b
The difference of 6 and the sum of a and b:
[B]6 - (a + b)[/B]

The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the num

The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?
We have two expressions:
[U]Expression 1: [I]The difference of a number and 6[/I][/U]
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The difference of a number and 6 means we subtract 6 from x:
x - 6
[U]Expression 2: [I]5 times the sum of the number and 2[/I][/U]
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The sum of a number and 2 means we add 2 to x:
x + 2
5 times the sum means we multiply x + 2 by 5
5(x + 2)
[U]For the last step, we evaluate the expression [I]is the same as[/I][/U]
This means equal to, so we set x - 6 equal to 5(x + 2)
[B]x - 6 = 5(x + 2)[/B]

The difference of twice a number and 4 is at least -27

The difference of twice a number and 4 is at least -27.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Twice a number means multiply the number by 2
2x
[I]and 4[/I] means we add 4 to our expression:
2x + 4
[I]Is at least[/I] means an inequality. In this case, it's greater than or equal to:
[B]2x + 4 >= -27
[/B]
To solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B4%3E%3D-27&pl=Solve']type it in the search engine[/URL].

The difference of twice a number and 6 is at most 28

The difference of twice a number and 6 is at most 28
This is an algebraic expression. Let's take it in parts:
[LIST=1]
[*]The phrase [I]a number[/I], means an arbitrary variable, let's call it x
[*]Twice this number means we multiply x by 2: 2x
[*][I]The difference of[/I] means subtract, so we subtract 6 to 2x: 2x - 6
[*][I]Is at most [/I]means less than or equal to, so we create an inequality where 2x - 6 is less than or equal to 28, using the <= sign
[/LIST]
[B]2x - 6 <= 28
[/B]
If you wish to solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=2x-6%3C%3D28&pl=Solve']click this link[/URL].

the difference of twice a number and 8 is at most -30

the difference of twice a number and 8 is at most -30.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Twice this number means we multiply by 2, so we have 2x.
We take the difference of 2x and 8, meaning we subtract 8:
2x - 8
Finally, the phrase [I]at most[/I] means an inequality, also known as less than or equal to:
[B]2x - 8 <= 30 <-- This is our algebraic expression
[/B]
To solve this, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x-8%3C%3D30&pl=Solve']type it into the search engine[/URL] and get x <= 19.

The difference of twice a number and 9 is less than 22

The difference of twice a number and 9 is less than 22
The phrase a number, means an arbitrary variable, let's call it x.
x
Twice a number
2x
The difference of twice a number and 9
2x - 9
Is less than 22
[B]2x - 9 < 22[/B]

The difference of two numbers is 12 and their mean is 15. Find the two numbers

The difference of two numbers is 12 and their mean is 15. Find the two numbers.
Let the two numbers be x and y. We're given:
[LIST=1]
[*]x - y = 12
[*](x + y)/2 = 15. <-- Mean is an average
[/LIST]
Rearrange equation 1 by adding y to each side:
x - y + y = y + 12
Cancelling the y's on the left side, we get:
x = y + 12
Now substitute this into equation 2:
(y + 12 + y)/2 = 15
Cross multiply:
y + 12 + y = 30
Group like terms for y:
2y + 12 = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=2y%2B12%3D30&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 9[/B]
Now substitute this into modified equation 1:
x = y + 12
x = 9 + 12
[B]x = 21[/B]

the difference of x and 5 is 2 times of x

the difference of x and 5 is 2 times of x
The difference of x and 5 means we subtract 5 from x
x - 5
The word [I]is[/I] means an equation, so we set x - 5 equal to 2 times x
[B]x - 5 = 2x[/B]

the difference of x and y added to twice the sum of a and b

the difference of x and y added to twice the sum of a and b
Take this algebraic expression in parts:
[LIST]
[*]The difference of x and y: x - y
[*]The sum of a and b: a + b
[*]Twice the sum of a and b means we multiply a + b by 2: 2(a + b)
[*]The phrase [I]added to[/I] means we add:
[/LIST]
[B]x - y + 2(a + b)[/B]

The distribution of actual weights of 8 oz chocolate bars produced by a certain machine is normal wi

The distribution of actual weights of 8 oz chocolate bars produced by a certain machine is normal with µ=8.1 ounces and ?=0.1 ounces. A sample of 5 of these chocolate bars is selected. What is the probability that their average weight is less than 8 ounces?
Calculate Z score and probability using [URL='http://www.mathcelebrity.com/probnormdist.php?xone=8&mean=8.1&stdev=0.1&n=5&pl=P%28X+%3C+Z%29']our calculator[/URL]:
Z = -2.236
P(X < -2.236) = [B]0.012545[/B]

the elevation of this lake is -513 if you are standing 442 above the lake what is your elevation

the elevation of this lake is -513 if you are standing 442 above the lake what is your elevation
Standing above means we add:
-513 + 442 = -[B]71[/B]

The enrollment at High School R has been increasing by 20 students per year. High School R currently

The enrollment at High School R has been increasing by 20 students per year. High School R currently has 200 students. High School T has 400 students and is decreasing 30 students per year. When will the two school have the same enrollment of students?
Set up the Enrollment function E(y) where y is the number of years.
[U]High School R:[/U]
[I]Increasing[/I] means we add
E(y) = 200 + 20y
[U]High School T:[/U]
[I]Decreasing[/I] means we subtract
E(y) = 400 - 30y
When the two schools have the same enrollment, we set the E(y) functions equal to each other
200 + 20y = 400 - 30y
To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=200%2B20y%3D400-30y&pl=Solve']type it in our search engine[/URL] and we get:
y = [B]4[/B]

The famous mathematician Pythagoras founded the Mathematical Brotherhood in 530 BC. About how many y

The famous mathematician Pythagoras founded the Mathematical Brotherhood in 530 BC. About how many years ago did this happen?
BC means before year 0. So we take the current year, which at the time of this post, is 2021. We [U]add[/U] 530 years to that since BC is before year 0, and we get:
2021 + 530 = [B]2551 years ago[/B]

The height of an object t seconds after it is dropped from a height of 300 meters is s(t)=-4.9t^2 +3

The height of an object t seconds after it is dropped from a height of 300 meters is s(t)=-4.9t^2 +300. Find the average velocity of the object during the first 3 seconds? (b) Use the Mean value Theorem to verify that at some time during the first 3 seconds of the fall the instantaneous velocity equals the average velocity. Find that time.
Average Velocity:
[ f(3) - f(0) ] / ( 3 - 0 )
Calculate f(3):
f(3) = -4.9(3^2) + 300
f(3) = -4.9(9) + 300
f(3) = -44.1 + 300
f(3) = 255.9
Calculate f(0):
f(0) = -4.9(0^2) + 300
f(0) = 0 + 300
f(0) = 300
So we have average velocity:
Average velocity = (255.9 - 300)/(3 - 0)
Average velocity = -44.1/3
Average velocity = -[B]14.7
[/B]
Velocity is the first derivative of position
s(t)=-4.9t^2 +300
s'(t) = -9.8t
So we set velocity equal to average velocity:
-9.8t = -14.7
Divide each side by -9.8 to solve for t, we get [B]t = 1.5[/B]

The Henson family cleaned out all their drawers. They found 47 black pens and 39 blue pens. They als

The Henson family cleaned out all their drawers. They found 47 black pens and 39 blue pens. They also found 6 pens in other colors. How many pens did they find in all?
The phrase [I]in all[/I] means we add, so we have:
Total pens = Black Pens + Blue Pens + Other color pens
Total pens = 47 + 39 + 6
Total pens = [B]92[/B]

The hourly wages of employees at Rowan have a mean wage rate of $10 per hour with a standard deviati

The hourly wages of employees at Rowan have a mean wage rate of $10 per hour with a standard deviation of $1.20. What is the probability the mean hourly wage of a random sample of 36 employees will be larger than $10.50? Assume the company has a total of 1,000 employees
Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=10.5&mean=10&stdev=1.2&n=36&pl=P%28X+>+Z%29']normal distribution calculator[/URL], we get P(x > 10.5) = [B]0.00621[/B]

The income i is directly proportional to working hours h

The income i is directly proportional to working hours h
The phrase [I]directly proportional[/I] means there exists a constant k such that:
[B]I = kh[/B]

The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a) What i

The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
a) What is the probability that a randomly person has an IQ between 85 and 115?
b) Find the 90th percentile of the IQ distribution
c) If a random sample of 100 people is selected, what is the standard deviation of the sample mean?
a) [B]68%[/B] from the [URL='http://www.mathcelebrity.com/probnormdist.php?xone=50&mean=100&stdev=15&n=1&pl=Empirical+Rule']empirical rule calculator[/URL]
b) P(z) = 0.90. so z = 1.28152 using Excel NORMSINV(0.9)

(X - 100)/10 = 1.21852 X = [B]113[/B] rounded up c) Sample standard deviation is the population standard deviation divided by the square root of the sample size 15/sqrt(100) = 15/10 =[B] 1.5[/B]

(X - 100)/10 = 1.21852 X = [B]113[/B] rounded up c) Sample standard deviation is the population standard deviation divided by the square root of the sample size 15/sqrt(100) = 15/10 =[B] 1.5[/B]

The larger number b exceeds the smaller number c by 45.

The larger number b exceeds the smaller number c by 45.
Exceeds means greater than or more than, so we have:
[B]b = c + 45[/B]

The larger of 2 numbers is 1 more than 3 times the smaller number

The larger of 2 numbers is 1 more than 3 times the smaller number.
Let the larger number be l. Let the smaller number be s. The algebraic expression is:
3 times the smaller number is written as:
3s
1 more than that means we add 1
3s + 1
Our final algebraic expression uses the word [I]is[/I] meaning an equation. So we set l equal to 3s + 1
[B]l = 3s + 1[/B]

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. Find the dimensions of Sally’s garden.
Gardens have a rectangle shape. Perimeter of a rectangle is 2l + 2w. We're given:
[LIST=1]
[*]l = 3w + 4 [I](3 times the width Plus 4 since greater means add)[/I]
[*]2l + 2w = 72
[/LIST]
We substitute equation (1) into equation (2) for l:
2(3w + 4) + 2w = 72
Multiply through and simplify:
6w + 8 + 2w = 72
(6 +2)w + 8 = 72
8w + 8 = 72
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B8%3D72&pl=Solve']type it in our search engine[/URL] and we get:
w = [B]8
[/B]
To solve for l, we substitute w = 8 above into Equation (1):
l = 3(8) + 4
l = 24 + 4
l = [B]28[/B]

The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length a

The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length and width.
A flag is a rectangle shape. So we have the following equations
Since P = 2l + 2w, we have 2l + 2w = 60
l = 7w - 2
Substitute Equation 1 into Equation 2:
2(7w -2) + 2w = 60
14w - 4 + 2w = 60
16w - 4 = 60
Add 4 to each side
16w = 64
Divide each side by 16 to isolate w
w = 4
Which means l = 7(4) - 2 = 28 - 2 = 26

The mean age of 10 women in an office is 30 years old. The mean age of 10 men in an office is 29 yea

The mean age of 10 women in an office is 30 years old. The mean age of 10 men in an office is 29 years old. What is the mean age (nearest year) of all the people in the office?
Mean is another word for [U]average[/U].
Mean age of women = Sum of all ages women / number of women
We're told mean age of women is 30, so we have:
Sum of all ages women / 10 = 30
Cross multiply, and we get:
Sum of all ages of women = 30 * 10
Sum of all ages of women = 300
Mean age of men = Sum of all ages men / number of men
We're told mean age of men is 29, so we have:
Sum of all ages men / 10 = 29
Cross multiply, and we get:
Sum of all ages of men = 29 * 10
Sum of all ages of men = 290
[U]Calculate mean age (nearest year) of all the people in the office:[/U]
mean age of all the people in the office = Sum of all ages of people in the office (men and women) / Total number of people in the office
mean age of all the people in the office = (300 + 290) / (10 + 10)
mean age of all the people in the office = 590 / 20
mean age of all the people in the office = 29.5
The question asks for nearest year. Since this is a decimal, we round down to either 29 or up to 30.
Because the decimal is greater or equal to 0.5 (halfway), we round [U]up[/U] to [B]30[/B]

The mean age of 5 people in a room is 28 years. A person enters the room. The mean age is now 32. W

The mean age of 5 people in a room is 28 years. A person enters the room. The mean age is now 32. What is the age of the person who entered the room?
The sum of the 5 people's scores is S. We know:
S/5 = 28
Cross multiply:
S = 140
We're told that:
(140 + a)/6 = 32
Cross multiply:
140 + a = 192
[URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D192&pl=Solve']Type this equation into our search engine[/URL], we get:
a = [B]52[/B]

The mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. Wh

The mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. What is the age of the person who entered the room?
Mean = Sum of Ages in Years / Number of People
32 = Sum of Ages in Years / 5
Cross multiply:
Sum of Ages in Years = 32 * 5
Sum of Ages in Years = 160
Calculate new mean after the next person enters the room.
New Mean = (Sum of Ages in Years + New person's age) / (5 + 1)
Given a new Mean of 40, we have:
40 = (160 + New person's age) / 6
Cross multiply:
New Person's Age + 160 = 40 * 6
New Person's Age + 160 = 240
Let the new person's age be n. We have:
n + 160 = 240
To solve for n, [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B160%3D240&pl=Solve']we type this equation into our search engine[/URL] and we get:
n = [B]80[/B]

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. Wh

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. What is the age of the person who entered the room?
The mean formulas is denoted as:
Mean = Sum of Ages / Total People
We're given Mean = 38 and Total People = 5, so we plug in our numbers:
28 = Sum of Ages / 5
Cross multiply, and we get:
Sum of Ages = 28 * 5
Sum of Ages = 140
One more person enters the room. The mean age is now 39. Set up our Mean formula:
Mean = Sum of Ages / Total People
With a new Mean of 39 and (5 + 1) = 6 people, we have:
39 = Sum of Ages / 6
But the new sum of Ages is the old sum of ages for 5 people plus the new age (a):
Sum of Ages = 140 + a
So we have:
29 = (140 + a)/6
Cross multiply:
140 + a = 29 * 6
140 + a = 174
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D174&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]34[/B]

The mean height of a class of 20 children is 1.27 the mean height of 12 boys in the class is 1.29 wh

The mean height of a class of 20 children is 1.27 the mean height of 12 boys in the class is 1.29 what is the mean height of the girls in the class?
The mean of sums is the sum of means. So we have:
Total Height / 20 = 1.27
Cross multiplying, we get:
Total Height = 20 * 1.27
Total Height = 25.4
Boys Height / 12 = 1.29
Cross multiplying, we get:
Boys Height = 12 * 1.29
Boys Height = 15.48
The Problem asks for mean height for girls. The formula is:
Girls Height / # of Girls = Mean of Girls Height
# of Girls = Total children - # of boys
# of Girls = 20 - 12
# of Girls = 8
Girls Height = Total Height - Boys Height
Girls Height = 25.4 - 15.48
Girls Height = 9.92
Plugging this into the Mean of girls height, we get:
9.92 /8 = [B]1.24[/B]

the mean of 12 scores is 8.8 . what is the sum of the scores ?

the mean of 12 scores is 8.8 . what is the sum of the scores ?
The Mean is denoted as:
Mean = Sum / count
We're given:
8.8 = Sum / 12
Cross multiply and we get:
Sum = 8.8*12
Sum = [B]105.6[/B]

The mean of 3 numbers is 20. Two of the numbers are 21, and 35. What is the 3rd number?

The mean of 3 numbers is 20. Two of the numbers are 21, and 35. What is the 3rd number?
The mean of 3 numbers is the sum of 3 numbers divided by 3. Let the 3rd number be n. We have:
Mean = (21 + 35 + n) / 3
The Mean is given as 20, so we have:
20 = (n + 56) / 3
Cross multiply:
n + 56 = 20 * 3
n + 56 = 60
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B56%3D60&pl=Solve']type this number in our search engine [/URL]and we get:
n = [B]4[/B]

The mean of two numbers is 49.1. The first number is 18.3. What is the second number

The mean of two numbers is 49.1. The first number is 18.3. What is the second number
We call the second number n. Since the mean is an average, in this case 2 numbers, we have:
(18.3 + n)/2 = 49.1
Cross multiply:
18.3 + n = 98.2
[URL='https://www.mathcelebrity.com/1unk.php?num=18.3%2Bn%3D98.2&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]n = 79.9[/B]

The minimum daily requirement of vitamin C for 14 year olds is at least 50 milligrams per day. An av

The minimum daily requirement of vitamin C for 14 year olds is at least 50 milligrams per day. An average sized apple contains 6 milligrams of vitamin C. How many apples would a person have to eat each day to satisfy this requirement?
Let a be the number of apples required. The phrase [I]at least[/I] means greater than or equal to, so we have the inequality:
6a >= 50
To solve this inequality, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6a%3E%3D50&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get:
[B]a >= 8.3333 apples or rounded up to a full number, we get 9 apples[/B]

The monthly earnings of a group of business students are are normally distributed with a standard de

The monthly earnings of a group of business students are are normally distributed with a standard deviation of 545 dollars. A researcher wants to estimate the mean monthly earnings of all business students. Find the sample size needed to have a confidence level of 95% and a margin of error of 128 dollars.

The monthly earnings of a group of business students are are normally distributed with a standard de

The monthly earnings of a group of business students are are normally distributed with a standard deviation of 545 dollars. A researcher wants to estimate the mean monthly earnings of all business students. Find the sample size needed to have a confidence level of 95% and a margin of error of 128 dollars.

The negative of the sum of C and D is equal to the difference of the negative of C and D

The negative of the sum of C and D is equal to the difference of the negative of C and D
The negative of the sum of C and D means -1 times the sum of C and D
-(C + D)
Distribute the negative sign:
-C - D
the difference of the negative of C and D means we subtract D from negative C
-C - D
So this statement is [B]true[/B] since -C - D = -C - D

The opposite of the difference of h and 5

The opposite of the difference of h and 5
The difference of h and 5
h - 5
The opposite of the difference of h and 5 means we multiply the difference of h and 5 by -1:
-(h - 5)
Distribute the negative sign:
[B]5 - h[/B]

the output is double the input

the output is double the input
Double means multiply by 2. So this means a function with input of x and output of y such that:
[B]y = 2x[/B]

The patient recovery time from a particular surgical procedure is normally distributed with a mean o

The patient recovery time from a particular surgical
procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.
What is the median recovery time?
a. 2.7
b. 5.3
c. 7.4
d. 2.1
[B]b. 5.3 (mean, median, and mode are all the same in a normal distribution)[/B]

The perimeter of a garden is 70 meters. Find its actual dimensions if its length is 5 meters longer

The perimeter of a garden is 70 meters. Find its actual dimensions if its length is 5 meters longer than twice its width.
Let w be the width, and l be the length. We have:
P = l + w. Since P = 70, we have:
[LIST=1]
[*]l + w = 70
[*]l = 2w + 5
[/LIST]
Plug (2) into (1)
2w + 5 + w = 70
Group like terms:
3w + 5 = 70
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=3w%2B5%3D70&pl=Solve']equation calculator[/URL], we get [B]w = 21.66667[/B]. Which means length is:
l = 2(21.6667) + 5
l = 43.33333 + 5
[B]l = 48.3333[/B]

The population of goats on a particular nature reserve t years after the initial population was sett

The population of goats on a particular nature reserve t years after the initial population was settled is modeled by p(t) = 4000 - 3000e^-0.2t. How many goats were initially present?
[U]Initially present means at time 0. Substituting t = 0, p(0), we get:[/U]
p(0) = 4000 - 3000e^-0.2(0)
p(0) = 4000 - 3000e^0
p(0) = 4000 - 3000(1)
p(0) = 4000 - 3000
[B]p(0) = 1000[/B]

The price of a baseball glove is no more than $38.95

The price of a baseball glove is no more than $38.95.
Let p be the price of the baseball glove. The phrase "no more than" means less than or equal to. Our inequality is:
p <= $38.95

The principal randomly selected six students to take an aptitude test. Their scores were: 87.4 86.9

The principal randomly selected six students to take an aptitude test.
Their scores were: 87.4 86.9 89.9 78.3 75.1 70.6
Determine a 90% confidence interval for the mean score for all students.

The principal randomly selected six students to take an aptitude test. Their scores were: 87.4 86.9

First, determine the [URL='http://www.mathcelebrity.com/statbasic.php?num1=87.4%2C86.9%2C89.9%2C78.3%2C75.1%2C70.6&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']mean and standard deviation[/URL] for the [I]sample[/I]
Mean = 81.3667
SD = 7.803
Next, use our [URL='http://www.mathcelebrity.com/normconf.php?n=6&xbar=81.3667&stdev=7.803&conf=90&rdig=4&pl=Small+Sample']confidence interval for the mean calculator[/URL] with these values and n = 6
[B]74.9478 < u < 87.7856[/B]

the product of 2 less than a number and 7 is 13

the product of 2 less than a number and 7 is 13
Take this algebraic expression in [U]4 parts[/U]:
Part 1 - The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Part 2 - 2 less than a number means we subtract 2 from x
x - 2
Part 3 - The phrase [I]product[/I] means we multiply x - 2 by 7
7(x - 2)
Part 4 - The phrase [I]is[/I] means an equation, so we set 7(x - 2) equal to 13
[B]7(x - 2) = 13[/B]

the product of 3 and the sum of m and 2n

the product of 3 and the sum of m and 2n
The sum of m and 2n means we add 2n to m:
m + 2n
The product of 3 means we multiply the sum m + 2n by 3:
[B]3(m + 2n)[/B]

the product of 8 and 15 more than a number

the product of 8 and 15 more than a number.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
15 more than x means we add 15 to x:
x + 15
The product of 8 and 15 more than a number means we multiply 8 by x + 15
[B]8(x + 15)[/B]

The product of 8 and a number k is greater than 4 and no more than 16

Let's take this by pieces.
The product of 8 and a number k is written as: 8k.
Since it's greater than 4, but not more than 16, we include this in the middle of an inequality statement.
4 < 8k <= 16
Notice no more than has an equal sign, it means less than or equal to.
Greater does not include an equal sign.

The product of a number b and 3 is no less than 12.

The product of a number b and 3 is no less than 12.
A number b is just written as b. So we have:
The product of b and 3 is no less than 12.
take this in parts:
[LIST]
[*]The product of b and 3: 3b
[*]The phrase [I]is no less than[/I] means an inequality, so we have greater than or equal to. We set 3b greater than or equal to 12
[/LIST]
[B]3b >= 12[/B]

the product of k and 70, minus 15

the product of k and 70, minus 15
Take this algebraic expression in pieces:
The product of k and 70 means we multiply 70 times k
70k
The word [I]minus[/I] means we subtract 15 from 70k
[B]70k - 15[/B]

The product of the 2 numbers x and y

The product of the 2 numbers x and y
The phrase [I]product [/I]means we multiply the two variables, x and y.
[B]xy[/B]

The product of x and 7 is not greater than 21

The product of x and 7 is not greater than 21
The product of x and 7:
7x
Is not greater than means less than or equal to, so we have our algebraic expression:
7x <= 21
If you want to solve this inequality and interval notation, use our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=7x%3C%3D21&pl=Show+Interval+Notation']calculator[/URL].

The product of x and u is not greater than 21

The product of x and u is not greater than 21
The product of x and u
xu
Not greater than means less than or equal to:
xu <= 21

The quotient of 2 and the sum of a number and 1

The quotient of 2 and the sum of a number and 1.
The phrase [I]a number[/I] represents an arbitrary variable, let's call it x.
The sum of a number and 1 is written as:
x + 1
The word [I]quotient[/I] means a fraction. So we divide 2 by x + 1
2
--------
( x + 1)

the quotient of 3 and u is equal to 52 divided by u

the quotient of 3 and u is equal to 52 divided by u
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The quotient of 3 and u means we divide 3 by u: 3/u
[*]52 divided by u means we divide 52 by u: 52/u
[*]The phrase [I]is equal to[/I] means an equation, so we set (1) equal to (2)
[/LIST]
[B]3/u = 52/u[/B]

the quotient of 4 more than a number and 7 is 10

the quotient of 4 more than a number and 7 is 10
Take this algebraic expression in pieces:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
4 more than a number means we add 4 to x:
x + 4
The quotient of 4 more than a number and 7 means we divide x + 4 by 7
(x + 4)/7
The word [I]is[/I] means an equation, so we set (x + 4)/7 equal to 10
[B](x + 4)/7 = 10[/B]

the quotient of 77 and x

the quotient of 77 and x
Quotient means we have a fraction where 77 is the numerator and x is the denominator:
[B]77/x[/B]

the quotient of 8 and the difference of x and m

The difference of x and m means we subtract:
x - m
Quotient means a fraction. 8 is the numerator, and x - m is the denominator:
[B] 8
------
x - m[/B]

The quotient of 9-x and twice x

The quotient of 9-x and twice x
Twice x means we multiply x by 2:
2x
The quotient of 9 - x and twice x is formed by the fraction:
[B](9 - x)/2x[/B]

the quotient of a number and twice another number

the quotient of a number and twice another number
The phrase[I] a number [/I]means an arbitrary variable, let's call it x.
The phrase[I] another number [/I]means another arbitrary variable, let's call it y.
Twice means we multiply y by 2:2y
The quotient means we divide x by 2y:
[B]x/2y[/B]

the quotient of a variable and 7

the quotient of a variable and 7.
A variable means an arbitrary number, let's call it x.
A quotient means a fraction, where x is the numerator and 7 is the denominator:
[B] x
---
7[/B]

the quotient of d and 182 is the same as w minus 137

The quotient of d and 182 is the same as w minus 137
Take this algebraic expression in 3 parts:
The quotient of d and 182
d/182
w minus 137
w - 137
The phrase [I]is the same as[/I] means we set d/182 equal to w - 137
[B]d/182 = w - 137[/B]

The quotient of m and -2 is greater than 24

We write the quotient: m/-2, but move the negative sign to the top.
-m/2
Next, greater than 24 means we use the > sign
-m/2 > 24

the quotient of m and the sum of n and p.

the quotient of m and the sum of n and p.
The sum of n and p means we add p to n:
n + p
The quotient means a fraction, so we divide m by (n + p)
[B]m/(n + p)[/B]

the quotient of m squared and a squared

the quotient of m squared and a squared
[U]m squared means we raise m to the power of 2:[/U]
m^2
[U]a squared means we raise a to the power of 2:[/U]
a^2
[U]The [I]quotient[/I] means we divide m^2 by a^2:[/U]
[B]m^2/a^2[/B]

The quotient of t and 12 is the sum of s and r.

The quotient of t and 12 is the sum of s and r.
Step 1: The quotient of t and 12 is:
t/12
Step 2: The Sum of s and r is
s + r
Step 3: The word [I]is[/I] means equal to, so we set t/12 equal to s + r
[B]t/12 = s + r[/B]

the quotient of the cube of a number x and 5

the quotient of the cube of a number x and 5
[LIST]
[*]A number means an arbitrary variable, let's call it x
[*]The cube of a number means raise it to the 3rd power, so we have x^3
[*]Quotient means we have a fraction, so our numerator is x^3, and our denominator is 5
[/LIST]
[B]x^3
----
5[/B]

the quotient of triple m and n squared

the quotient of triple m and n squared
Triple m means we multiply m by 3:
3m
n squared means we raise n to the 2nd power:
n^2
The quotient is formed as follows:
[B]3m/n^2[/B]

the quotient of x and y is equal to the sum of a and b

the quotient of x and y is equal to the sum of a and b
The quotient of x and y:
x/y
The sum of a and b:
a + b
The phrase [I]is equal to[/I] means an equation, so we set x/y equal to a + b:
[B]x/y = a + b[/B]

the ratio of 50 and a number added to the quotient of a number and 10

the ratio of 50 and a number added to the quotient of a number and 10
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The ratio of 50 and x means we divide by 50 by x
50/x
The quotient of a number and 10 means we have a fraction:
x/10
The phrase [I]added to[/I] means we add 50/x to x/10
[B]50/x + x/10[/B]

the ratio of a number x and 4 added to 2

the ratio of a number x and 4 added to 2
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The ratio of this number and 4 means we have a fraction:
x/4
The phrase [I]added to[/I] means we add 2 to x/4
[B]x/4 + 2[/B]

the ratio of ten to a number

the ratio of ten to a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The ratio of 10 and this number x is written as:
[B]10/x[/B]

the ratio of twice c to d

the ratio of twice c to d
Twice c means we multiply c by 2:
2c
The ratio is formed by the quotient:
[B]2c/d[/B]

the ratio of yellow to red balloons is 2:1 respectively. if there are 7 red balloons, how many yello

the ratio of yellow to red balloons is 2:1 respectively. if there are 7 red balloons, how many yellow balloons are there?
7 red balloons means we have twice as many yellow balloons. So 7 * 2 = [B]14[/B].
Written as a proportion, of yellow to red, we have:
2/1 = y/7 where y is the number of yellow balloons.
[URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=y&den1=1&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']Run this proportion through our search engine[/URL] to get [B]y = 14[/B].

the reciprocal of the product a and b

the reciprocal of the product a and b
Take this algebraic expression in pieces:
The product a and b means we multiply a times b
ab
The [I]reciprocal[/I] means we take 1 over ab
[B]1/ab[/B]

The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk con

The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk [I]m[/I] and cups of juice [I]j[/I] a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?
Total calcium = Milk calcium + Juice Calcium
Calculate Milk Calcium:
Milk Calcium = 299m where m is the number of cups of milk
Calculate Juice Calcium:
Juice Calcium = 261j where j is the number of cups of juice
The phrase [I]meet or exceed[/I] means greater than or equal to, so we have an inequality, where Total Calcium is greater than or equal to 1000. So we write our inequality as:
Milk calcium + Juice Calcium >= Total Calcium
[B]299m + 261j >= 1000[/B]

The relief time provided by a standard dose of a popular children’s allergy medicine averages 7.9

The relief time provided by a standard dose of a popular children’s allergy medicine averages 7.9 hours with a standard deviation of 2.2 hours. Use Table 1.
a. Determine the percentage of children who experience relief for less than 6.4 hours if the relief time follows a normal distribution. (Round your answer to 2 decimal places.)
Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=6.4&mean=7.9&stdev=2.2&n=1&pl=P%28X+%3C+Z%29']normal distribution calculator[/URL], we get
Answer = [B]0.25[/B]

the result of increasing n by six

the result of increasing n by six
Increasing means we add:
[B]n + 6[/B]

the result of quadrupling a number is 80

the result of quadrupling a number is 80
Let our number be x. Quadrupling any number means multiplying it by 4. We have:
4x = 80
[URL='https://www.mathcelebrity.com/1unk.php?num=4x%3D80&pl=Solve']Typing this problem into our search engine[/URL], we get:
[B]x = 20[/B]

The school council began the year with a $600 credit to their account, but they spent $2,000 on new

The school council began the year with a $600 credit to their account, but they spent $2,000 on new books for classrooms. How much must the PTA earn through fundraising to break even?
+600 - 2000 = -1,400.
Break even means no profit or loss. So the PTA must earn [B]1,400 [/B]to break even on the -1,400

The science club charges 4.50 per car at their car wash. Write and solve and inequality to find how

The science club charges 4.50 per car at their car wash. Write and solve and inequality to find how many cars they have to wash to earn at least 300
Let x be the number of cars they wash. Set up our inequality. Note, at least 300 means 300 or greater, so we use greater than or equal to.
[U]Inequality:[/U]
[B]4.50x >= 300
[/B]
[U]So solve for x, divide each side by 4[/U]
[B]x >= 66.67[/B]

the set of natural numbers less than 7 that are divisible by 3

the set of natural numbers less than 7 that are divisible by 3
Natural Numbers less than 7
{1, 2, 3, 4, 5, 6}
Only 2 of them are divisible by 3. Divisible means the number is divided evenly, with no remainder:
[B]{3, 6}[/B]

The square of a number added to its reciprocal

The square of a number added to its reciprocal
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
the square of x mean we raise x to the power of 2. It's written as:
x^2
The reciprocal of x is 1/x
We add these together to get our final algebraic expression:
[B]x^2 + 1/x[/B]

The square of a number increased by 7 is 23

The square of a number increased by 7 is 23
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
x
The square of a number means we raise x to the power of 2:
x^2
[I]Increased by[/I] means we add 7 to x^2
x^2 + 7
The word [I]is[/I] means an equation. So we set x^2 + 7 equal to 23:
[B]x^2 + 7 = 23[/B]

The square of the difference of a number and 4

The square of the difference of a number and 4
A number means an arbitrary variable, let's call it x
The difference of a number and 4:
x - 4
The square of this difference:
[B](x - 4)^2[/B]

The square of the difference of n and 2, increased by twice n

The square of the difference of n and 2, increased by twice n
The difference of n and 2:
n - 2
The square of the difference of n and 2 means we raise (n - 2) to the 2nd power:
(n - 2)^2
Twice n means we multiply n by 2:
2n
The square of the difference of n and 2, increased by twice n
[B](n - 2)^2 + 2n[/B]

The square of the radius r

The square of the radius r
The square means you raise r to the power of 2:
[B]r^2[/B]

the square of the sum of 2a and 3b

the square of the sum of 2a and 3b
the sum of 2a and 3b
2a + 3b
The square of this sum means we raise 2a + 3b to the 2nd power:
[B](2a + 3b)^2[/B]

The square of the sum of twice a number x and y

The square of the sum of twice a number x and y
Take this in algebraic expression in 3 parts:
[LIST=1]
[*]Twice a number x means we multiply x by 2: 2x
[*]The sum of twice a number x and y means we add y to 2x above: 2x + y
[*]The square of the sum means we raise the sum (2x + y) to the second power below:
[/LIST]
[B](2x + y)^2[/B]

the square of the sum of x and y is less than 20

the square of the sum of x and y is less than 20
The sum of x and y means we add y to x:
x + y
the square of the sum of x and y means we raise the term x + y to the 2nd power:
(x + y)^2
The phrase [I]is less than[/I] means an inequality, so we write this as follows:
[B](x + y)^2 < 20[/B]

the square root of twice a number is 4 less than the number

Write this out, let the number be x.
sqrt(2x) = x - 4 since 4 less means subtract
Square each side:
sqrt(2x)^2 = (x - 4)^2
2x = x^2 - 8x + 16
Subtract 2x from both sides
x^2 - 10x + 16 = 0
Using the [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2+-+10x+%2B+16+%3D+0&pl=Solve+Quadratic+Equation&hintnum=0']quadratic calculator[/URL], we get two potential solutions
x = (2, 8)
Well, 2 does not work, since sqrt(2*2) = 2 which is not 4 less than 2
However, 8 does work:
sqrt(2*8) = sqrt(16) = 4, which is 4 less than the number 8.

The sum is greater than 7, the sum is divisible by 2

The sum is greater than 7, the sum is divisible by 2
2 dice sum greater than 7 means 8, 9, 10, 11, 12.
Now take this set, and intersect it with sums divisible by 2.
[B]8, 10, 12[/B]

The sum of -4x^2 - 5x + 7 and 2x^2 + 8x - 11 can be written in the form ax^2 + bx + c, where a, b, a

The sum of -4x^2 - 5x + 7 and 2x^2 + 8x - 11 can be written in the form ax^2 + bx + c, where a, b, and c are constants. What is the value of a + b + c?
The sum means we add the polynomials together. We do this by adding the like terms:
-4x^2 - 5x + 7 + 2x^2 + 8x - 11
(-4 +2)x^2 + (-5 + 8)x +(7 - 11)
-2x^2 + 3x - 4
We have (a, b, c) = (-2, 3, -4)
The question asks for a + b + c
a + b + c = -2 + 3 - 4
a + b + c = [B]-3[/B]

The sum of 13 and twice janelles age

Let Janelle's age be the variable a.
So twice Janelle's age is denoted as 2a.
We want the sum of 13 and 2a.
Sum means add.
13 + 2a
or
2a + 13

The sum of 2 and w is less than or equal to 27.

The sum of 2 and w is less than or equal to 27.
Take this algebraic expression in parts:
[LIST]
[*]The sum of 2 and w: 2 + w
[*]The phrase [I]less than or equal to[/I] means an inequality, using the <= sign.
[/LIST]
[B]2 + w <= 27[/B]

The sum of 2 consecutive numbers is 3 less than 3 times the first number. What are the numbers?

The sum of 2 consecutive numbers is 3 less than 3 times the first number. What are the numbers?
Let the first number be x. And the second number be y. We're given:
[LIST=1]
[*]y = x + 1
[*]x + y = 3x - 3 (less 3 means subtract 3)
[/LIST]
Substitute (1) into (2):
x + x + 1 = 3x - 3
Combine like terms:
2x + 1 = 3x - 3
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B1%3D3x-3&pl=Solve']Type this equation into the search engine[/URL], we get:
x = 4
Substituting x = 4 into equation 1:
y = 4 + 1
y = 5
So (x, y) = [B](4, 5)[/B]

the sum of 2 times a number and -2, added to 4 times a number

the sum of 2 times a number and -2, added to 4 times a number.
The phrase, [I]a number[/I], means an arbitrary variable, let's call it x.
2 times a number
2x
The sum of means add, so we add -2, which is the same as subtracting 2
2x - 2
Now, we add 4 times x
2x - 2 + 4x
Combining like terms, we have:
(2 + 4)x - 2
[B]6x - 2[/B]

The sum of 2 times x and 5 times y is 7

The sum of 2 times x and 5 times y is 7
2 times x:
2x
5 times y:
5y
The sum of 2 times x and 5 times y:
2x + 5y
The word [I]is[/I] means equal to, so we set 2x + 5y equal to 7:
[B]2x + 5y = 7[/B]

the sum of 23 and victor age is 59

the sum of 23 and victor age is 59
Let's Victor's age be a.
The sum of 23 and Victor's age (a) mean we add a to 23:
23 + a
The word [I]is[/I] means an equation, so we set 23 + a equal to 59:
[B]23 + a = 59[/B] <-- This is our algebraic expression
Now if the problem asks you to take it a step further and solve this for a, [URL='https://www.mathcelebrity.com/1unk.php?num=23%2Ba%3D59&pl=Solve']we type this equation into our search engine[/URL] and we get:
[B]a = 36[/B]

The sum of 24 and twice Chau’s score . Use c to represent Chau’s score.

The sum of 24 and twice Chau’s score . Use c to represent Chau’s score.
Twice Chau's score means we multiply his score of c by 2:
2c
The sum of 24 and 2c means we add:
[B]24 + 2c[/B]

The sum of 2x and y is at least 20

The sum of 2x and y is at least 20
The sum of 2x and y:
2x + y
The phrase [I]is at least[/I] means an inequality. We write this as >= or greater than or equal to:
[B]2x + y >= 20[/B]

the sum of 3 and 2x is 10

the sum of 3 and 2x is 10
The sum of 3 and 2x means we add 2x to 3:
3 + 2x
The word [I]is[/I] means an equation, so we set 3 + 2x equal to 10
[B]3 + 2x = 10[/B]

The sum of 3 consecutive integers is greater than 30.

The sum of 3 consecutive integers is greater than 30.
Let the first consecutive integer be n
The second consecutive integer is n + 1
The third consecutive integer is n + 2
The sum is written as:
n + n + 1 + n + 2
Combine like terms:
(n + n + n) + (1 + 2)
3n + 3
The phrase [I]greater than[/I] means an inequality, which we write as:
[B]3n + 3 > 30[/B]

the sum of 3 numbers

Since no variable name is defined, we pick 3 arbitrary variables. Let's pick x, y, and z.
The sum of 3 numbers means we add them together:
x + y + z

the sum of 3 numbers divided by its product

the sum of 3 numbers divided by its product
The phrase [I]3 numbers[/I] means we choose [I]3[/I] arbitrary variables. Let's call them x, y, z.
The sum of of these 3 numbers is:
x + y + z
The phrase [I]its product[/I] means we multiply all 3 arbitrary variables together:
xyz
Now, the phrase [I]divided by[/I] means we divide x + y + z by xyz:
[B](x + y + z)/xyz[/B]

The sum of 3 times the square of a number and negative 7

The sum of 3 times the square of a number and negative 7
[U]The phrase [I]a number[/I] means an arbitrary variable, let's call it x:[/U]
x
[U]The square of a number means we raise x to the power of 2:[/U]
x^2
[U]3 times the square of a number:[/U]
3x^2
[U]The sum of 3 times the square of a number and negative 7[/U]
[B]3x^2 - 7[/B]

The sum of 3, 7, and a number amounts to 16

The sum of 3, 7, and a number amounts to 16
Let the number be n. A sum means we add. We're given:
3 + 7 + n = 16
Grouping like terms, we get:
n + 10 = 16
[URL='https://www.mathcelebrity.com/1unk.php?num=n%2B10%3D16&pl=Solve']Typing this equation into our search engine[/URL], we get:
n = [B]6 [/B]

The sum of 3w and 5 cubed

The sum of 3w and 5 cubed
The sum of 3w and 5:
3w + 5
The word [I]cubed[/I] means we raise 3w + 5 to the power 3:
[B](3w + 5)^3[/B]

the sum of 4 and x split into 5 equal parts

the sum of 4 and x split into 5 equal parts
The sum of x and 4 means we add 4 to x:
x + 4
Whenever you see the phrase [I]split into[/I], think of divide or divided by:
[B](x + 4)/5[/B]

The sum of 5 and 2x is at most 27

The sum of 5 and 2x is at most 27
The sum of 5 and 2x means we add 2x to 5:
5 + 2x
The phrase [I]at most[/I] means less than or equal to, so we have an inequality where 5 + 2x is less than or equal to 27
[B]5 + 2x <= 27[/B]

the sum of 5 and y is less than or equal to -21

the sum of 5 and y is less than or equal to -21
Take this algebraic expression in parts:
The sum of 5 and y means we add y to 5
5 + y
The phrase [I]less than or equal to[/I] -21 means an inequality. We use the <= sign to relate 5 + y to -21
[B]5 + y <= -21[/B]

the sum of 5 times p and 10

the sum of 5 times p and 10
5 times p
5p
and 10 means add 10
[B]5p + 10[/B]

The sum of 5x and 2x is at least 70

[I]Is at least [/I]means greater than or equal to:
5x + 2x >= 70
If we combine like terms, we have:
7x >=70
We can further simplify by dividing each side of the inequality by 7
x >=10
If you want the interval notation for that, use the [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=x%3E%3D10&pl=Show+Interval+Notation']interval notation calculator[/URL].

the sum of 6 and 7, plus 5 times a number, is -12

the sum of 6 and 7, plus 5 times a number, is -12
The sum of 6 and 7 means we add the two numbers:
6 + 7
This evaluates to 13
Next, we take 5 times a number. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So we multiply x by 5:
5x
The first two words say [I]the sum[/I], so we add 13 and 5x
13 + 5x
The word [I]is[/I] means an equation, so we set 13 + 5x equal to -12
[B]13 + 5x = -12[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=13%2B5x%3D-12&pl=Solve']type this algebraic expression into our search engine[/URL] and you get:
[B]x = -5[/B]

The sum of 6 times a number and -8, added to 3 times a number

The sum of 6 times a number and -8, added to 3 times a number
The phrase "a number", means an arbitrary variable, let's call it x.
6 times a number:
6x
And means we add, so we have
6x - 8
Added to 3 times a number
6x - 8 + 3x
Combine like terms:
[B]9x - 8[/B]

the sum of 7 times y and 3 is equal to 2

the sum of 7 times y and 3 is equal to 2
7 times y:
7y
The sum of 7 times y and 3 means we add 3 to 7y
7y + 3
The phrase [I]is equal to[/I] means an equation, so we set 7y + 3 equal to 2
[B]7y + 3 = 2[/B]

The sum of a and b added with the quotient of x and y.

The sum of a and b added with the quotient of x and y.
The sum of a and b is written as:
a + b
The quotient of x and y is written as:
x/y
The phrase [I]added with[/I] means we add x/y to a + b:
[B]a + b + x/y[/B]

The sum of a and b divided by their product

The sum of a and b divided by their product
The sum of a and b means we add b to a:
a + b
The product of a and b means we multiply a by b:
ab
To get our final algebraic expression, we divide the sum (a + b) by the product ab:
[B](a + b)/ab[/B]

the sum of a and b minus 4 is 12

the sum of a and b minus 4 is 12
the sum of a and b
a + b
the sum of a and b minus 4
a + b - 4
The word [I]is[/I] means equal to, so we set a + b - 4 equal to 12:
a + b - 4 = 12

the sum of a and b, divided by the product of c and d

the sum of a and b, divided by the product of c and d
The sum of a and b, means we add b to a
a + b
The product of c and d means we multiply c by d
cd
Divided by means we divide a + b by cd
[B](a + b)/cd[/B]

the sum of a number and 16 is e

A number means an arbitrary variable, let's call it x.
The sum of x and 16 means we add:
x + 16
Is, means equal to, so we set x + 16 = e
x + 16 = e

The sum of a number and 34 times the number

The sum of a number and 34 times the number
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
34 times the number:
34x
The sum of a number and 34 times the number means we add both terms together:
x + 34x

The sum of a number and 5 all divided by 2 is 17

The sum of a number and 5 all divided by 2 is 17
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The sum of a number and 5:
x + 5
All divided by 2:
(x + 5)/2
The word [I]is[/I] means equal to, so we set (x + 5)/2 equal to 17:
[B](x + 5)/2 = 17[/B]

The sum of a number and 5 divided by 8

The sum of a number and 5 divided by 8.
Let's take this algebraic expression in parts.
Part 1: The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Part 2: The sum of a number and 5 means we add 5 to the number x
x + 5
Part 3: Next, we divide this expression by 8
[B](x + 5)/8[/B]

the sum of a number and its reciprocal is 5/2

the sum of a number and its reciprocal is 5/2
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The reciprocal of the number means 1/x.
The sum means we add them:
x + 1/x
The word [I]is[/I] means an equation, so we set x + 1/x equal to 52
[B]x + 1/x = 52[/B]

The sum of a number and its reciprocal is 72

The sum of a number and its reciprocal is 72
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The reciprocal of the number is written as:
1/x
The sum of a number and its reciprocal means we add:
x + 1/x
The word [I]is[/I] means an equation, so we set x + 1/x equal to 72
[B]x + 1/x = 72[/B]

The sum of a number and its reciprocal is five.

The sum of a number and its reciprocal is five.
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
The reciprocal of the number is 1/x.
The sum means we add them together:
x + 1/x
The word [I]is[/I] means an equation, so we set x + 1/x equal to 5
[B]x + 1/x = 5[/B]

the sum of a number and itself is 8

A number means an arbitrary variable, let's call it x.
The sum of a number and itself means adding the number to itself
x + x
Simplified, we have 2x
The word is means equal to, so we have an algebraic expression of:
[B]2x= 8
[/B]
IF you need to solve this equation, divide each side by 2
[B]x = 4[/B]

The sum of a number and twice its reciprocal is 3

The sum of a number and twice its reciprocal is 3
the phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The reciprocal of a number means we take 1 over that number:
1/x
Twice the reciprocal means we multiply 1/x by 2:
2/x
The sum of a number and twice its reciprocal
x + 2/x
The word [I]is[/I] means equal to, so we set x + 2/x equal to 3
[B]x + 2/x = 3[/B]

The sum of a number b and 3 is greater than 4 and no more than 16

The sum of a number b and 3 is greater than 4 and no more than 16
The sum of a number b and 3:
b + 3
Greater than 4 and no more than 16 means we have a combo inequality:
[LIST]
[*]Greater than 4 means we use a > sign
[*]No more than 16 means less than or equal to, so <=
[/LIST]
[B]4 < b + 3 <= 16[/B]

the sum of a number divided by 8 and 3 equals 6

"A Number" means an arbitrary variable, let's call it x.
x divide d by 8 is written as a quotient
x/8
The sum of x/8 and 3 means we add:
x/8 + 3
Finally, equals means we have an equation, so we set our expression above equal to 6
x/8 + 3 = 6

The sum Of a number squared and 14

The sum Of a number squared and 14.
A number means an arbitrary variable, let's call it x.
Squared means we raise x to the 2nd power: x^2
The sum means we add x^2 to 14 to get our algebraic expression below:
[B]x^2 + 14[/B]

the sum of a number times 3 and 30 is less than 17

the sum of a number times 3 and 30 is less than 17
A number is denoted as an arbitrary variable, let's call it x.
x
Times 3 means we multiply x by 3:
3x
The sum of a number times 3 and 30 means we add 30 to 3x above
3x + 30
Is less than 17 means we have an inequality, so we set 3x + 30 less than 17
3x + 30 < 17
To solve for x and see the interval notation, use [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B30%3C17&pl=Solve']our calculator[/URL]:

the sum of d and twice g

Twice g means we multiply g by 2.
2g
The sum of d and twice g means we add:
d + 2g

the sum of doubling a number and 100 which totals to 160

the sum of doubling a number and 100 which totals to 160
Take this algebraic expression in pieces:
[LIST=1]
[*]Let the number be n.
[*]Double it, means we multiply n by 2: 2n
[*]The sum of this and 100 means we add 100 to 2n: 2n + 100
[*]The phrase [I]which totals[/I] means we set 2n + 100 equal to 160
[/LIST]
[B]2n + 100 = 160[/B] <-- This is our algebraic expression
If the question asks you to solve for n, then we [URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B100%3D160&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]n = 30[/B]

the sum of five -sixths of m and 7

the sum of five -sixths of m and 7
five-sixths of m:
5/6m
The word [I]and[/I] means we add, so we have:
[B]5/6m + 7[/B]

The sum of five and twice a number is 17

The sum of five and twice a number is 17
[U]The phrase a number means an arbitrary variable, let's call it x[/U]
x
[U]Twice a number means we multiply x by 2:[/U]
2x
[U]The sum of five and twice a number means we add 5 to 2x:[/U]
2x + 5
[U]The phrase [I]is[/I] means an equation, so we set 2x + 5 equal to 17 to get our algebraic expression[/U]
[B]2x + 5 = 17[/B]
[B][/B]
As a bonus, if the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B5%3D17&pl=Solve']type in this algebraic expression into our math engine[/URL] and we get:
x = 6

The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages?

The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages?
[U]Givens[/U]
[LIST]
[*]Let Mr. Adam's age be a
[*]Let Mrs. Benson's age be b
[*]We're given two equations where [I]sum[/I] means we add and [I]difference[/I] means we subtract:
[/LIST]
[LIST=1]
[*]a + b = 55
[*]a - b = 3
[/LIST]
Since we have opposite coefficients for b, we can take a shortcut and add equation 1 to equation 2:
(a + a) + (b - b) = 55 + 3
Combining like terms and simplifying, we get:
2a = 58
To solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=2a%3D58&pl=Solve']type it in our search engine[/URL] and we get:
a = [B]29[/B]

the sum of n and twice n is 12

Twice n means we multiply n by 2
2n
The sum of n and twice n means we add
n + 2n
The word [I]is[/I] means equal to, so we set that expression above equal to 12
n + 2n = 12
Combine like terms:
3n = 12
Divide each side of the equation by 3 to isolate n
n = 4
Check our work
Twice n is 2*4 = 8
Add that to n = 4
8 + 4
12

The sum of six times a number and 1 is equal to five times the number. Find the number.

The sum of six times a number and 1 is equal to five times the number. Find the number.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
6 times a number is written as:
6x
the sum of six times a number and 1 is written as:
6x + 1
Five times the number is written as:
5x
The phrase [I]is equal to[/I] means an equation, so we set 6x + 1 equal to 5x:
6x + 1 = 5x
[URL='https://www.mathcelebrity.com/1unk.php?num=6x%2B1%3D5x&pl=Solve']Plugging this into our search engine[/URL], we get:
x = [B]-1[/B]

the sum of the cube of a number and 12

the sum of the cube of a number and 12
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The cube of a number means we raise x to the power of 3:
x^3
Finally, we take the sum of x^3 and 12. Meaning, we add 12 to x^3. This is our final algebraic expression.
[B]x^3 + 12[/B]

The sum of the length l and 17

The sum of the length l and 17
The word [I]sum[/I] means we add:
[B]l + 17[/B]

the sum of the reciprocal of x and the reciprocal of y

the sum of the reciprocal of x and the reciprocal of y
Reciprocal of x means 1 over x:
1/x
Reciprocal of y means 1 over y:
1/y
The sum means we add the two reciprocals together:
[B]1/x + 1/y[/B]

The sum of the reciprocals of x and y

The sum of the reciprocals of x and y
The reciprocal of a variable is found by taking 1 over the variable.
[LIST]
[*]Reciprocal of x = 1/x
[*]Reciprocal of y = 1/y
[/LIST]
The sum means we add the reciprocals together
[B]1/x + 1/y[/B]

The sum of the square of a number and 7 times a number

The sum of the square of a number and 7 times a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Square the number:
x^2
7 times the number means we multiply x by 7:
7x
The sum means we add x^2 and 7x
[B]x^2 + 7x[/B]

the sum of the squares of a and b

the sum of the squares of a and b
Square of a means we raise a to the 2nd power:
a^2
Square of b means we raise b to the 2nd power:
b^2
The sum of squares means we add these terms together to get our algebraic expression:
[B]a^2 + b^2[/B]

The sum of the squares of c and d is 25

The sum of the squares of c and d is 25
The square of c means we we raise c to the power of 2:
c^2
The square of d means we we raise d to the power of 2:
d^2
The sum of the squares of c and d means we add d^2 to c^2:
c^2 + d^2
The word [I]is[/I] means equal to, so we set c^2 + d^2 equal to 25:
[B]c^2 + d^2 = 25[/B]

The sum of the squares of two consecutive positive integers is 61. Find these two numbers.

The sum of the squares of two consecutive positive integers is 61. Find these two numbers.
Let the 2 consecutive integers be x and x + 1. We have:
x^2 + (x + 1)^2 = 61
Simplify:
x^2 + x^2 + 2x + 1 = 61
2x^2 + 2x + 1 = 61
Subtract 61 from each side:
2x^2 + 2x - 60 = 0
Divide each side by 2
x^2 + x - 30
Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-30&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL], we get:
x = 5 and x = -6
The question asks for [I]positive integers[/I], so we use [B]x = 5. [/B]This means the other number is [B]6[/B].

The Sum of three times a number and 18 is -39. Find the number

The Sum of three times a number and 18 is -39. Find the number.
A number means an arbitrary variable, let us call it x.
Three times x:
3x
The sum of this and 18:
3x + 18
Is means equal to, so we set 3x + 18 = -39
3x + 18 = -39
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']equation solver[/URL], we get [B]x = -19[/B]

the sum of twice a and b

the sum of twice a and b
Twice a means multiply a by 2
2a
The sum of means add Twice a to b
[B]2a + b[/B]

The sum of twice an integer and 3 times the next consecutive integer is 48

The sum of twice an integer and 3 times the next consecutive integer is 48
Let the first integer be n
This means the next consecutive integer is n + 1
Twice an integer means we multiply n by 2:
2n
3 times the next consecutive integer means we multiply (n + 1) by 3
3(n + 1)
The sum of these is:
2n + 3(n + 1)
The word [I]is[/I] means equal to, so we set 2n + 3(n + 1) equal to 48:
2n + 3(n + 1) = 48
Solve for [I]n[/I] in the equation 2n + 3(n + 1) = 48
We first need to simplify the expression removing parentheses
Simplify 3(n + 1): Distribute the 3 to each term in (n+1)
3 * n = (3 * 1)n = 3n
3 * 1 = (3 * 1) = 3
Our Total expanded term is 3n + 3
Our updated term to work with is 2n + 3n + 3 = 48
We first need to simplify the expression removing parentheses
Our updated term to work with is 2n + 3n + 3 = 48
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(2 + 3)n = 5n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
5n + 3 = + 48
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 3 and 48. To do that, we subtract 3 from both sides
5n + 3 - 3 = 48 - 3
[SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE]
5n = 45
[SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE]
5n/5 = 45/5
Cancel the 5's on the left side and we get:
n = [B]9[/B]

The sum of two consecutive integers if n is the first integer.

The sum of two consecutive integers if n is the first integer.
consecutive means immediately after, so we have:
n
n + 1
[U]The sum is written as:[/U]
n + n + 1
[U]Grouping like terms, we have:[/U]
(n + n) + 1
[B]2n + 1[/B]

The sum of two consecutive integers plus 18 is 123

The sum of two consecutive integers plus 18 is 123.
Let our first integer be n and our next integer be n + 1. We have:
n + (n + 1) + 18 = 123
Group like terms to get our algebraic expression:
2n + 19 = 123
If we want to solve the algebraic expression using our [URL='http://www.mathcelebrity.com/1unk.php?num=2n%2B19%3D123&pl=Solve']equation solver[/URL], we get n = 52. This means the next integer is 52 + 1 = 53

The sum of two-fifths and f is one-half.

The sum of two-fifths and f is one-half.
We write two-fifths as 2/5.
The sum of two-fifths and f is written by adding f to two-fifths using the + sign:
2/5 + f
one-half is written as 1/2
The word [I]is[/I] means equals, so we set up an equation where 2/5 + f equal to 1/2
[B]2/5 + f = 1/2[/B]

The sum of x and 10 equals the sum of 2 times x and 12

The sum of x and 10 equals the sum of 2 times x and 12
The sum of x and 10 means we add 10 to x:
x + 10
2 times x means we multiply x by 2:
2x
the sum of 2 times x and 12 means we add 12 to 2x:
2x + 12
The sum of x and 10 equals the sum of 2 times x and 12:
x + 10 + (2x + 12)
Distribute the parentheses, and we get:
x + 10 + 2x + 12
Group like terms:
(1 + 2)x + 10 + 12
[B]3x + 22[/B]

the sum of x and 96 equals half of x

the sum of x and 96 equals half of x
half of x means we divide x by 2:
x/2
The sum of x and 96:
x + 96
The phrase equals means we set x + 96 equal to x/2:
[B]x + 96 = x/2[/B]

the sum of x and its cube

the sum of x and its cube
The cube of x means we raise x to the power of 3:
x^3
The sum of x and it's cube means we add x^3 to x:
[B]x + x^3[/B]

the sum of x and its reciprocal

the sum of x and its reciprocal
The reciprocal of x is found by dividing 1 by x:
1/x
the sum of x and its reciprocal means we add 1/x to x:
[B]x + 1/x[/B]

The sum of x and twice y is equal to m.

The sum of x and twice y is equal to m.
Twice y means we multiply y by 2:
2y
The sum of x and twice y:
x + 2y
The phrase [I]is equal to[/I] means an equation, so we set x + 2y equal to m
[B]x + 2y = m[/B]

The sum of x and two

Sum means we add, so we have:
Two is written as 2.
x + 2

The sum of x and y is at most 10

The sum of x and y is at most 10
The sum of x and y:
x + y
Is at most 10 means we have an inequality, at most means 10 or less, so less than or equal to
[B]x + y <= 10[/B]

the sum of x squared plus y squared

the sum of x squared plus y squared
x squared means we raise x to the power of 2:
x^2
y squared means we raise y to the power of 2:
y^2
The sum means we add both terms together:
[B]x^2 + y^2[/B]

The sum of y and z decreased by the difference of m and n

The sum of y and z decreased by the difference of m and n.
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The sum of y and z means we add z to y: y + z
[*]The difference of m and n means we subtract n from m: m - n
[*]The phrase [I]decreased by[/I] means we subtract the quantity (m - n) from the sum (y + z)
[/LIST]
[B](y + z) - (m - n)[/B]

The temperature in Chicago was five (5) degrees Celsius in the morning and is expected to drop by as

The temperature in Chicago was five (5) degrees Celsius in the morning and is expected to drop by as much as 12 degrees during the day. What is the lowest temperature in Chicago for the day?
We start with 5 celsius
A drop in temperature means we subtract
5 - 12 = [B]-7 or 7 degrees below zero[/B]

The temperature was 7? below zero. The temperature drops by 6?. What is the temperature now

The temperature was 7? below zero. The temperature drops by 6?. What is the temperature now
Below zero means negative. A drop means we subtract, so we have:
[LIST]
[*]7 below zero = -7
[*]Drops by 6 = -6
[*]-7 - 6 = [B]-13[/B]
[/LIST]

The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. h

The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins?
Let a be Suresh's age, h be Hakima's age, and c be Saad's age. We're given:
[LIST=1]
[*]a + h + c = 48
[*]a = 0.5h
[*]a = c + 4
[/LIST]
To isolate equations in terms of Suresh's age (a), let's do the following:
[LIST]
[*]Rewriting (3) by subtracting 4 from each side, we get c = a - 4
[*]Rewriting (2) by multiply each side by 2, we have h = 2a
[/LIST]
We have a new system of equations:
[LIST=1]
[*]a + h + c = 48
[*]h = 2a
[*]c = a - 4
[/LIST]
Plug (2) and (3) into (1)
a + (2a) + (a - 4) = 48
Group like terms:
(1 + 2 + 1)a - 4 = 48
4a - 4 = 48
[URL='https://www.mathcelebrity.com/1unk.php?num=4a-4%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]a = 13 [/B]<-- Suresh's age
This means that Hakima's age, from modified equation (2) above is:
h = 2(13)
[B]h = 26[/B] <-- Hakima's age
This means that Saad's age, from modified equation (3) above is:
c = 13 - 4
[B]c = 9[/B] <-- Saad's age
[B]
[/B]

The total cost of 100 dresses is $1,500.00. The mark-up is estimated at 20% of the unit cost, the pr

The total cost of 100 dresses is $1,500.00. The mark-up is estimated at 20% of the unit cost, the price of a single dress using the cost-plus method will be
The phrase [I]unit cost[/I] means price per one unit.
[U]Unit cost for one dress is:[/U]
Price of dresses / Number of dresses
1500/100
15
Each dress cost $15 which is the unit cost
[U]Cost plus method:[/U]
Cost plus price = Unit price + Unit price * markup
Cost plus price = 15 + 15 * 20%
Cost plus price = 15 + 3
Cost plus price = [B]$18
[MEDIA=youtube]H9rOp592y5s[/MEDIA][/B]

the total number of fish if you had 8 and bought 4 more

the total number of fish if you had 8 and bought 4 more
If you have 8, and buy 4 more, this means you add. So we have:
8 fish + 4 fish = [B]12 fish[/B].

the total of 3 times the cube of u and the square of u

the total of 3 times the cube of u and the square of u
[U]The cube of u means we raise u to the power of 3:[/U]
u^3
[U]The square of u means we raise u to the power of 2:[/U]
u^2
The total of both of these is found by adding them together:
[B]u^3 + u^2[/B]

the total of a and 352 equals a divided by 195

the total of a and 352 equals a divided by 195
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The total of a and 352 means we add 352 to a: a + 352
[*]a divided by 195: a/195
[*]The phrase [I]equals[/I] means we set (1) equal to (2) to get our final algebraic expression:
[/LIST]
[B]a + 352 = a/195[/B]

The weight of a 9.5-inch by 6-inch paperback book published by Leaden Publications, Inc., is 16.2 oz

The weight of a 9.5-inch by 6-inch paperback book published by Leaden Publications, Inc., is 16.2 oz. The standard deviation is 2.9 oz. What is the probability that the average weight of a sample of 33 such books is less than 15.89 oz?
Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=15.89&mean=16.2&stdev=2.9&n=33&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we get:
[B]0.271[/B]

There are 1 carrot, 3 onions, and 2 potatoes in a sink. What fraction of the vegetables are onions

There are 1 carrot, 3 onions, and 2 potatoes in a sink. What fraction of the vegetables are onions?
We have 1 + 3 + 2 = 6 total vegetables.
Which means we have 3/6 onions. But, we can reduce this fraction.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Simplifying 3/6 using our fraction simplifier[/URL], we get 1/2.

There are 100 people in a sport centre. 67 people use the gym. 62 people use the swimming pool. 5

There are 100 people in a sport centre. 67 people use the gym. 62 people use the swimming pool. 56 people use the track. 38 people use the gym and the pool. 31 people use the pool and the track. 33 people use the gym and the track. 16 people use all three facilities. A person is selected at random. What is the probability that this person doesn't use any facility?
WE use the compound probability formula for 3 events:
[LIST=1]
[*]Gym use (G)
[*]Swimming pool use (S)
[*]Track (T)
[/LIST]
P(G U S U T) = P(G) + P(S) + P(T) - P(G Intersection S) - P(G Intersection T) - P(S Intersection T) + P(G Intersection S Intersection T)
[LIST]
[*]Note: U means Union (Or) and Intersection means (And)
[/LIST]
Plugging our numbers in:
P(G U S U T) = 67/100 + 62/100 + 56/100 - 38/100 - 31/100 - 33/100 + 16/100
P(G U S U T) = (67 + 62 + 56 - 38 - 31 - 33 + 16)/100
P(G U S U T) = 99/100 or 0.99
What this says is, the probability that somebody uses at any of the 3 facilities is 99/100.
The problem asks for none of the 3 facilities, or P(G U S U T)'
P(G U S U T)' = 1 - P(G U S U T)
P(G U S U T)' = 1 - 99/100
P(G U S U T)' = 100/100 - 99/100
P(G U S U T)' = [B]1/100 or 0.1[/B]

There are 144 people in an audience. The ratio of adults to children is 5 to 3. How many are adults?

There are 144 people in an audience. The ratio of adults to children is 5 to 3. How many are adults?
We set up an equation to represent this:
5x + 3x = 144
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3x%3D144&pl=Solve']Typing this equation into our search engine[/URL], we get:
x = 18
This means we have:
Adults = 5(18)
[B]Adults = 90[/B]
Children = 3(18)
[B]Children = 54[/B]

There are 144 people in the audience. The ratio of adults to children is 5 to 3. How many adults are

[SIZE=6]There are 144 people in the audience. The ratio of adults to children is 5 to 3. How many adults are there?
Let x be the number of people, we have:
5x + 3x = 144
[/SIZE]
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3x%3D144&pl=Solve'][SIZE=6]Typing this problem in our search[/SIZE][/URL][SIZE=6][URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3x%3D144&pl=Solve'] engine[/URL], we get x = 18.
Which means we have 5(18) = [B]90 adults[/B][/SIZE]

There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much

There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much time should we spend sleeping?
3/8 of the day means we take 3/8 of 24 also written as:
3/8 * 24
We [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F8&frac2=24&pl=Multiply']type this expression into our search engine [/URL]and get:
[B]9 hours[/B]

There are 4 fewer peaches than lemons on a table. If there are x lemons, how many peaches are there?

There are 4 fewer peaches than lemons on a table. If there are x lemons, how many peaches are there?
Fewer means subtract:
[B]x - 4[/B]

There are 5 pencil-cases on the desk. Each pencil-case contains at least 10 pencils, but not more th

[SIZE=4]There are 5 pencil-cases on the desk. Each pencil-case contains at least 10 pencils, but not more than 14 pencils. Which of the following could be the total number of pencils in all 5 cases?
A) 35
B) 45
C) 65
D) 75
[U]Determine the minimum amount of pencils (At least means greater than or equal to):[/U]
Minimum Amount of pencils = Cases * Min Quantity
Minimum Amount of pencils = 5 * 10
Minimum Amount of pencils = 50
[SIZE=4][U]Determine the maximum amount of pencils (Not more than means less than or equal to):[/U]
Maximum Amount of pencils = Cases * Min Quantity
Maximum Amount of pencils = 5 * 14
Maximum Amount of pencils = 70[/SIZE]
So our range of pencils (p) is:
50 <= p <= 70
Now take a look at our answer choices. The only answer which fits in this inequality range is [B]C, 65[/B].
[B][/B][/SIZE]

There are 5 red and 4 black balls in a box. If you pick out 2 balls without replacement, what is the

There are 5 red and 4 black balls in a box. If you pick out 2 balls without replacement, what is the probability of getiing at least one red ball?
First list out our sample space. At least one means 1 or 2 red balls, so we have 3 possible draws:
[LIST=1]
[*]Red, Black
[*]Black, Red
[*]Red, Red
[/LIST]
List out the probabilities:
[LIST=1]
[*]Red (5/9) * Black (4/8) = 5/18
[*]Black (4/9) * Red (5/8) = 5/18
[*]Red (5/9) * Red (4/8) = 5/18
[/LIST]
Add these up:
3(5)/18 = [B]5/6[/B]

There are 7 more jeeps than vans.

There are 7 more jeeps than vans.
[U]Define variables[/U]
[LIST]
[*]Let j be the number of jeeps
[*]Let v be the number of vans
[/LIST]
7 more jeeps than vans means we add 7 to the number of vans:
[B]j = v + 7[/B]

There are thrice as many girls (g) as there are boys (b)

There are thrice as many girls (g) as there are boys (b)
Thrice means we multiply by 3, so we have the following algebraic expression:
[B]g = 3b[/B]

There are two bells in the school. Bell A rings every 2 minutes. Bell B rings every 3 minutes. If bo

There are two bells in the school. Bell A rings every 2 minutes. Bell B rings every 3 minutes. If both bells ring together at 8.02 p.m., when will they ring together again?
Using our[URL='http://www.mathcelebrity.com/gcflcm.php?num1=2&num2=3&num3=&pl=LCM'] least common multiple calculator,[/URL] we find the LCM(2, 3) = 6.
Which means the next time both bells ring together is 6 minutes from now.
8:02 p.m. + 6 minutes = [B]8:08 p.m.[/B]

There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the b

There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting exactly 1 blue?
Find the total number of marbles in the bag:
Total marbles = 5 blue + 6 red + 2 green
Total marbles = 13
The problem asks for exactly one blue in 2 draws [I]with replacement[/I]. Which means you could draw as follows:
Blue, Not Blue
Not Blue, Blue
The probability of drawing a blue is 5/13, since we replace the marbles in the bag each time.
The probability of not drawing a blue is (6 + 2)/13 = 8/13
And since each of the 2 draws are independent of each other, we multiply the probability of each draw:
Blue, Not Blue = 5/13 * 8/13 =40/169
Not Blue, Blue = 8/13 * 5/13 = 40/169
We add both probabilities since they both count under our scenario:
40/169 + 40/169 = 80/169
Checking our [URL='https://www.mathcelebrity.com/fraction.php?frac1=80%2F169&frac2=3%2F8&pl=Simplify']fraction simplification calculator[/URL], we see you cannot simplify this fraction anymore.
So our probability stated in terms of a fraction is 80/169
[URL='https://www.mathcelebrity.com/perc.php?num=80&den=169&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Stated in terms of a decimal[/URL], it's 0.4734

Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quo

Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quotient will be 20. What is the number
Let's call our number n.
Double the number means we multiply n by 2:
2n
Subtract 6 from the result means we subtract 6 from 2n:
2n - 6
Divide the answer by 2:
(2n - 6)/2
We can simplify this as n - 3
The quotient will be 20. This means the simplified term above is set equal to 20:
[B]n - 3 = 20 [/B] <-- This is our algebraic expression
If you want to take it a step further, and solve for n in the algebraic expression above, we [URL='https://www.mathcelebrity.com/1unk.php?num=n-3%3D20&pl=Solve']type this expression into our calculator[/URL], and get:
n = 23

Thirty is half of the sum of 4 and a number

Thirty is half of the sum of 4 and a number.
The phrase [I]a number[/I] represents an arbitrary variable, let's call it x.
The sum of 4 and a number:
4 + x
Half of this sum means we divide by 2:
(4 + x)/2
Set this equal to 30:
[B](4 + x)/2 = 30[/B] <-- This is our algebraic expression

Three days before the day after tomorrow is Monday. What day is today?

Three days before the day after tomorrow is Monday. What day is today?
List out days of the week:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday
Three days before the day after tomorrow means we start 2 days from now, and go back three days to get to Monday.
Which means it's a +1 day gain. Monday + 1 = [B]Tuesday[/B]

Three more than 2x is greater than or equal to 1 and less than or equal to 11

This is a two-part inequality. Let's take it piece by piece.
Three more than 2x means we add.
2x + 3
It's greater than or equal to 1, denoted below:
1 <= 2x + 3
It's also less than or equal to 11, denoted below
2x + 3 <= 11
Piece these two inequalities together:
1 <= 2x + 3 <= 11

Three subtracted from triple a number

Three subtracted from triple a number
A number means an arbitrary variable, let's call it x
x
Triple it
3x
Three subtracted from this
[B]3x - 3[/B]

Three-fourths of 500

Three-fourths of 500
Three-fourths is written as 3/4
3/4 of 500 means we multiply 3/4 by 500
3 * 500/4
500/4 = 125, so we have:
3 * 125
[B]375[/B]

thrice the sum of x y and z

thrice the sum of x y and z
The sum of x, y, and z
x + y + z
Thrice the sum means multiply by 3
[B]3(x + y + z)[/B]

thrice the sum of x y and z

thrice the sum of x y and z
The sum of x, y, and z means we add all 3 variables together:
x + y + z
The word [I]thrice[/I] means we multiply the sum of x, y, and z by 3:
3(x + y +z)

thrice the sum of x y and z

thrice the sum of x y and z
The sum of x, y, and z:
x + y + z
Thrice means multiply the sum by 3:
[B]3(x + y + z)[/B]

thrice y plus x minus 2z

thrice y plus x minus 2z
Thrice y means we multiply y by 3:
3y
plus x
3y + x
minus 2z
[B]3y + x - 2z[/B]

To make an international telephone call, you need the code for the country you are calling. The code

To make an international telephone call, you need the code for the country you are calling. The code for country A, country B, and C are three consecutive integers whose sum is 90. Find the code for each country.
If they are three consecutive integers, then we have:
[LIST=1]
[*]B = A + 1
[*]C = B + 1, which means C = A + 2
[*]A + B + C = 90
[/LIST]
Substitute (1) and (2) into (3)
A + (A + 1) + (A + 2) = 90
Combine like terms
3A + 3 = 90
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3a%2B3%3D90&pl=Solve']equation calculator[/URL], we get:
[B]A = 29[/B]
Which means:
[LIST]
[*]B = A + 1
[*]B = 29 + 1
[*][B]B = 30[/B]
[*]C = A + 2
[*]C = 29 + 2
[*][B]C = 31[/B]
[/LIST]
So we have [B](A, B, C) = (29, 30, 31)[/B]

Today a car is valued at $42000. the value is expected to decrease at a rate of 8% each year. what i

Today a car is valued at $42000. the value is expected to decrease at a rate of 8% each year. what is the value of the car expected to be 6 years from now.
Depreciation at 8% per year means it retains (100% - 8%) = 92% of it's value. We set up our depreciation function D(t), where t is the number of years from right now.
D(t) = $42,000(0.92)^t
The problem asks for D(6):
D(6) = $42,000(0.92)^6
D(6) = $42,000(0.606355)
D(6) = [B]$25,466.91[/B]

Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one yea

Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one year from now. Given that my age is an integer number of years, what is the smallest my age could be?
Let my current age be a. We're given:
4/5a > 3/4(a + 1)
Multiply through on the right side:
4a/5 > 3a/4 + 3/4
Let's remove fractions by multiply through by 5:
5(4a/5) > 5(3a/4) + 5(3/4)
4a > 15a/4 + 15/4
Now let's remove the other fractions by multiply through by 4:
4(4a) > 4(15a/4) + 4(15/4)
16a > 15a + 15
[URL='https://www.mathcelebrity.com/1unk.php?num=16a%3E15a%2B15&pl=Solve']Typing this inequality into our search engine[/URL], we get:
a > 15
This means the smallest [I]integer age[/I] which the problem asks for is:
15 + 1 = [B]16[/B]

Tom has 6 fewer pencils than ari. Tom has 7 pencils. How many pencils does Ari have?

Tom has 6 fewer pencils than ari. Tom has 7 pencils. How many pencils does Ari have?
6 fewer means less. Let a = Ari's pencils. We have:
a - 6 = 7
Add 6 to each side
[B]a = 13[/B]

Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli departm

Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli department at least 260 person-hours per week. Tom has one part-time employeewho works 20 hours per week. Each full-time employee works 40 hours per week. Write an inequality to determine n, the number of full-time employees Tom must schedule, so that his employees will work at least 260 person-hours per week.
Set up the inequality:
[LIST]
[*]Add the part-timer's hours of 20
[*]Full time hours is 40 times n employees
[*]At least means greater than or equal to, so we use the >= sign
[/LIST]
[B]40n + 20 >= 260[/B]

total of a number and the square of a number

total of a number and the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The square of a number means we raise x to the power of 2. x^2
The total means we add x squared to x:
[B]x + x^2[/B]

Total of a number v and 1

[I]Total[/I] means we add
[B]v + 1[/B]

translate the product of -1 and a number in mathematics expression

translate the product of -1 and a number in mathematics expression
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
The product of -1 and the number;
[B]-x[/B]

Translate the sentence into an inequality. Twice y is less than 21.

Translate the sentence into an inequality. Twice y is less than 21.
Twice y
2y
Is less than 21 means we have an inequality:
[B]2y < 21[/B]

Translate this phrase into an algebraic expression. 57 decreased by twice Mais savings Use the varia

Translate this phrase into an algebraic expression. 57 decreased by twice Mais savings Use the variable m to represent Mais savings.
Twice means multiply by 2
2m
57 decreased by means subtract 2m from 57
[B]57 - 2m[/B]

Translate this sentence into an equation. 43 is the sum of 17 and Gregs age. Use the variable g to

Translate this sentence into an equation. 43 is the sum of 17 and Gregs age. Use the variable g to represent Gregs age.
The sum of 17 and Greg's age:
g + 17
The word [I]is[/I] means equal to, so we set g + 17 equal to 43
[B]g + 17 = 43[/B] <-- This is our algebraic expression
If you want to solve this equation for g, use our [URL='http://www.mathcelebrity.com/1unk.php?num=g%2B17%3D43&pl=Solve']equation calculator[/URL].
[B]g = 26[/B]

Translate this sentence into an equation. 48 is the difference of Ritas age and 11 . Use the variabl

Translate this sentence into an equation. 48 is the difference of Ritas age and 11 . Use the variable r to represent Ritas age.
The difference of Rita's age and 11 is written:
r - 11
The phrase [I]is[/I] means equal to, so we set r - 11 equal to 48
r - 11 = 48

Translate this sentence into an equation. 49 is the difference of Diegos age and 17. Use the variabl

Translate this sentence into an equation. 49 is the difference of Diegos age and 17. Use the variable d to represent Diegos age.
The difference means we subtract, so we have d as Diego's age minus 17
d - 17
The word "is" means an equation, so we set d - 17 equal to 49
[B]d - 17 = 49[/B]

Trimmed Mean and Winsorized Mean

Given a number set and a trimmed mean percentage, this will calculate the trimmed mean (truncated mean) or winsorized mean.

triple 5, raise the result to the 10th power, then divide p by what you have

triple 5, raise the result to the 10th power, then divide p by what you have
Triple 5, means multiply 5 by 3
3 * 5 --> Simplified, this is 15
Raise the result to the 10th power, means we raise 15 to the 10 power:
15^10
Then divide it by p:
[B]15^10/p[/B]

triple a number and another number

triple a number and another number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Triple a number means we multiply x by 3:
3x
The phrase [I]another number[/I] means another arbitrary variable, let's call it y:
y
The word [I]and[/I] means we add y to 3x:
[B]3x + y[/B]

triple c divide the result by a

triple c divide the result by a
Take this algebraic expression in pieces.
Triple c means we multiply the variable c by 3
3c
Divide the result by a, means we take 3c, and divide by a
[B]3c/a[/B]

triple c, multiply the result by a, then subtract b

triple c, multiply the result by a, then subtract b
Triple c means we multiply c by 3:
3c
Multiply the result by a means we multiply 3c by a
3ac
Then, we subtract b from 3ac:
[B]3ac - b[/B]

triple h then raise the result to the 8th power

triple h then raise the result to the 8th power
[U]Triple h means we multiply h by 3:[/U]
3h
[U]Raise the result to the 8th power:[/U]
[B](3h)^8[/B]

triple s add the result to q then divide what you have by r

triple s add the result to q then divide what you have by r.
Triple s means multiply s by 3:
3s
Add the result to q:
3s + q
Divide what you have by r:
[B](3s + q)/r[/B]

triple t multiply g

triple t multiply g
triple t means we multiply t by 3:
3t
Multiply g:
[B]3tg[/B]

triple the sum of 36 and 6 then add 4

triple the sum of 36 and 6 then add 4
Take this algebraic expression in parts:
The sum of 36 and 6:
36 + 6
Triple the sum means we multiply the sum by 3:
3(36 + 6)
Then add 4:
[B]3(36 + 6) + 4[/B]
If the problem asks you to simplify the algebraic expression, we have:
3(42) + 4
126 + 4
[B]130[/B]

Triple the sum of 4 and y

The sum of 4 and y is written as (4 + y)
Triple that means we multiply that entire sum by 3.
3(4 + y)

Triple the sum of 7 and m

The sum of 7 and m is written as 7 + m
Triple that means multiply by 3:
3(7 + m)

triple the value of c plus 3 is 84

Triple the value of c means we multiply c by 3
3c
Plus 3 means we add 3
3c + 3
Is, means equal to, so we set our expression equal to 84
[B]3c +3 = 84
[/B]
If you want to solve that equation, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3c%2B3%3D84&pl=Solve']equation solver[/URL]:
c = 27

tripled square of the difference of a and b

The difference of a and b is written as:
a - b
Square the difference means raise the difference to the power of 2
(a - b)^2
Triple this expression means multiply by 3:
[B]3(a - b)^2[/B]

True or False (a) The normal distribution curve is always symmetric to its mean. (b) If the variance

True or False
(a) The normal distribution curve is always symmetric to its mean.
(b) If the variance from a data set is zero, then all the observations in this data set are identical.
(c) P(A AND A^{c})=1, where A^{c} is the complement of A.
(d) In a hypothesis testing, if the p-value is less than the significance level ?, we do not have sufficient evidence to reject the null hypothesis.
(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.
[B](a) True, it's a bell curve symmetric about the mean
(b) True, variance measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical
(c) True. P(A) is the probability of an event and P(Ac) is the complement of the event, or any event that is not A. So either A happens or it does not. It covers all possible events in a sample space.
(d) False, we have sufficient evidence to reject H0.
(e) False. Volume can be a decimal or fractional. There are multiple values between 127 and 128. So it's continuous.[/B]

True or False: The standard deviation of the chi-square distribution is twice the mean.

True or False: The standard deviation of the chi-square distribution is twice the mean.
[B]False[/B], the variance is twice the mean. Mean is k, Variance is 2k

twice a number subtracted from the square root of the same number

twice a number subtracted from the square root of the same number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Twice a number means we multiply x by 2:
2x
Square root of the same number:
sqrt(x)
twice a number subtracted from the square root of the same number
[B]sqrt(x) - 2x[/B]

twice the difference between x and 28 is 3 times a number

twice the difference between x and 28 is 3 times a number
The difference between x and 28:
x - 28
Twice the difference means we multiply x - 28 by 2:
2(x - 28)
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
3 times a number:
3x
The word [I]is[/I] means equal to, so we set 2(x - 28) equal to 3x:
[B]2(x - 28) = 3x[/B]

twice the difference of a number and 3 is equal to 3 times the sum of a number and 2

twice the difference of a number and 3 is equal to 3 times the sum of a number and 2.
We've got 2 algebraic expressions here. Let's take them in parts.
Left side algebraic expression: twice the difference of a number and 3
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]The word [I]difference[/I] means we subtract 3 from the variable x
[*]x - 3
[*]Twice this difference means we multiply (x - 3) by 2
[*]2(x - 3)
[/LIST]
Right side algebraic expression: 3 times the sum of a number and 2
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]The word [I]sum[/I] means we add 2 to the variable x
[*]x + 2
[*]3 times the sum means we multiply (x + 2) by 3
[*]3(x + 2)
[/LIST]
Now, we have both algebraic expressions, the problem says [I]is equal to[/I]
This means we have an equation, where we set the left side algebraic expression equal to the right side algebraic expression using the equal sign (=) to get our answer
[B]2(x - 3) = 3(x + 2)[/B]

twice the difference of a number and 55 is equal to 3 times the sum of a number and 8

twice the difference of a number and 55 is equal to 3 times the sum of a number and 8
Take this algebraic expression in pieces.
Left side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The difference of this number and 55 means we subtract 55 from x
x - 55
Twice the difference means we multiply x - 55 by 2
2(x - 55)
Right side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 8 means we add 8 to x
x + 8
3 times the sum means we multiply x + 8 by 3
3(x + 8)
Now that we have the left and right side of the expressions, we see the phrase [I]is equal to[/I]. This means an equation, so we set the left side equal to the right side:
[B]2(x - 55) = 3(x + 8)[/B]

twice the product of p q and r

twice the product of p q and r
The product of p q and r means we multiply all 3 variables together:
pqr
The word [I]twice[/I] means we multiply pqr by 2:
[B]2pqr[/B]

twice the product of p q and r

twice the product of p q and r
The product of p q and r:
pqr
Twice means we multiply pqr by 2:
[B]2pqr[/B]

twice the square of the product of x and y

twice the square of the product of x and y
Take this algebraic expression in pieces:
[LIST]
[*]The product of x and y means we multiply x and y: xy
[*]The square of the product means we raise xy to the power of 2: (xy)^2 = x^2y^2
[*]Twice the square means we multiply the square by 2: [B]2x^2y^2[/B]
[/LIST]

twice the square of the product of x and y

twice the square of the product of x and y
[LIST]
[*]The product of x and y: xy
[*]The square of the product means we raise xy to the power of 2: (xy)^2
[*]Twice the square means we multiply by 2
[/LIST]
[B]2(xy)^2
or
2x^2y^2[/B]

twice the square root of a number increased by 5 is 23

twice the square root of a number increased by 5 is 23
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The square root of a number means we raise x to the 1/2 power:
sqrt(x)
the square root of a number increased by 5 means we add 5 to sqrt(x):
sqrt(x) + 5
twice the square root of a number increased by 5 means we multiply sqrt(x) + 5 by 2:
2(sqrt(x) + 5)
The phrase [I]is 23[/I] means we set 2(sqrt(x) + 5) equal to 23:
[B]2(sqrt(x) + 5) = 23[/B]

twice the sum of a and b is thrice c

twice the sum of a and b is thrice c
The sum of a and b:
a + b
twice the sum of a and b means we multiply the sum of a and b by 2:
2(a + b)
Thrice c means we multiply c by 3:
3c
The word [I]is[/I] means equal to, so we set 2(a + b) equal to 3c:
[B]2(a + b) = 3c[/B]

Twice x increased by the cube of y equals z

Twice x increased by the cube of y equals z
[LIST]
[*]Twice x means we multiply x by 2: 2x
[*]Increased this by the cube of y which is y^3. So we have 2x + y^3
[*]Now, we set this entire expression equal to z: 2x + y^3 = z
[/LIST]

Two consecutive even integers that equal 126

Two consecutive even integers that equal 126
Let the first integer equal x. So the next even integer must be x + 2.
The sum which is equal to 126 is written as x + (x + 2) = 126
Simplify:
2x + 2 = 126
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2x%2B2%3D126&pl=Solve']equation calculator,[/URL] we get:
x = 62
This means the next consecutive even integer is 62 = 2 = 64.
So our two even consecutive integers with a sum of 126 are [B](62, 64)[/B]

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worke

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. together they charged a total of 1225. what was the rate charged per hour by each mechanic if the sum of the two rates was 170 per hour?
Set up two equations:
(1) 10x + 5y = 1225
(2) x + y = 170
Rearrange (2)
x = 170 - y
Substitute that into (1)
10(170 - y) + 5y = 1225
1700 - 10y + 5y = 1225
1700 - 5y = 1225
Move 5y to the other side
5y + 1225 = 1700
Subtract 1225 from each side
5y =475
Divide each side by 5
[B]y = 95[/B]
Which means x = 170 - 95, [B]x = 75[/B]

two numbers have an average of 2100 and one number is $425 more than the other number. What are the

two numbers have an average of 2100 and one number is $425 more than the other number. What are the numbers
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*](x + y)/2 = 2100 (Average)
[*]y = x + 425
[/LIST]
Rearrange equation (1) by cross multiplying
x + y = 2 * 2100
x + y = 4200
So we have our revised set of equations:
[LIST=1]
[*]x + y = 4200
[*]y = x + 425
[/LIST]
Substituting equation (2) into equation (1) for y, we get:
x + (x + 425) = 4200
Combining like terms, we get:
2x + 425 = 4200
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B425%3D4200&pl=Solve']equation solver[/URL], we get:
x = [B]1887.5[/B]
Which means using equation (2), we get
y = 1887.5 + 425
y = [B]2312.5[/B]

Two numbers that total 44 and have a difference of 6

Two numbers that total 44 and have a difference of 6.
Let the two numbers be x and y. We're given the following equations:
[LIST=1]
[*]x + y = 44 <-- Total means a sum
[*]x - y = 6
[/LIST]
Add the two equations together:
(x + x) + (y - y) = 44 + 6
Cancelling the y terms, we have:
2x = 50
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D50&pl=Solve']Typing this equation into the search engine[/URL], we get:
[B]x = 25
[/B]
Rearranging equation (2) above, we get:
y = x - 6
Substituting x = 25 into this, we get:
y = 25 - 6
[B]y = 19[/B]

two pages that face each other in a book have a sum of 569

two pages that face each other in a book have a sum of 569
Pages that face each other are consecutive. Let the first page be p. The second page is p + 1.
Their sum is:
p + p + 1 = 569
[URL='https://www.mathcelebrity.com/1unk.php?num=p%2Bp%2B1%3D569&pl=Solve']Type this equation into our search engine to solve for p[/URL], and we get:
p = 284
This means p + 1 = 284 + 1 = 285
So the pages that face each other having a sum of 569 are:
[B]284, 285[/B]

two thirds of a number is no more than -10

two thirds of a number is no more than -10
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Two thirds of a number mean we multiply x by 2/3:
2x/3
The phrase [I]no more than[/I] -10 means less than or equal to -10, so we have an inequality:
[B]2x/3 <= -10[/B]

two-thirds the difference of c and d

two-thirds the difference of c and d
The difference of c and d:
c - d
two-thirds the difference means we multiply c - d by 2/3:
[B]2(c - d)/3[/B]

Tyrese’s sister is 41 inches tall. A ride at the amusement park states that riders must be at least

Tyrese’s sister is 41 inches tall. A ride at the amusement park states that riders must be at least 52 inches tall to ride. Which statements describe how much taller Tyrese’s sister must be to ride?
Let h be the required additional height.
The phrase [I]at least[/I] means an inequality, using the >= sign, so we have:
h + 41 >= 52
If we want another way to express this, we [URL='https://www.mathcelebrity.com/1unk.php?num=h%2B41%3E%3D52&pl=Solve']type this inequality into our math engine[/URL] and we get:
[B]h >= 11[/B]

u and 201 more equals q

201 more means we add:
u + 201
We set that expression equal to q
u + 201 = q

u cubed equals nine

u cubed equals nine
u cubed means we raise u to the 3rd power:
u^3
We set this equal to 9:
[B]u^3 = 9[/B]

u more than the quotient of 8 and 5

u more than the quotient of 8 and 5
The quotient of 8 and 5:
8/5
u more means we add u
8/5 + u

u varies jointly as q and the square of m

u varies jointly as q and the square of m
Varies jointly means we multiply. There exists a constant k such that:
[B]u = kqm^2[/B]

Uniform Distribution

This calculates the following items for a uniform distribution

* Probability Density Function (PDF) ƒ(x)

* Cumulative Distribution Function (CDF) F(x)

* Mean, Variance, and Standard Deviation

Calculates moment number t using the moment generating function

* Probability Density Function (PDF) ƒ(x)

* Cumulative Distribution Function (CDF) F(x)

* Mean, Variance, and Standard Deviation

Calculates moment number t using the moment generating function

Use c for unknown variable : Sam's age plus twice his age

Use c for unknown variable : Sam's age plus twice his age
Sam's age:
c
Twice his age means we multiply c by 2:
2c
Sam's age plus twice his age
[B]c + 2c[/B]

v equals 66 decreased by d

66 decreased by d means we subtract:
66 - d
v equals means we set our entire expression equal to v
[B]66 - d = v[/B]

Vanessa is packing her bags for her vacation. She has 5 unique action figures, but only 3 fit in her

Vanessa is packing her bags for her vacation. She has 5 unique action figures, but only 3 fit in her bag. How many different groups of 3 action figures can she take?
The key word here is [U]different[/U]. This means combinations.
We use our [URL='http://www.mathcelebrity.com/permutation.php?num=5&den=3&pl=Combinations']combinations calculator[/URL] to find 5 C 3 which equals [B]10[/B].

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.
Let Victoria's age be v. And her neighbor's age be n. We're given:
[LIST=1]
[*]v = n + 4
[*]v + n <=14 <-- no more than means less than or equal to
[/LIST]
Substitute Equation (1) into Inequality (2):
(n + 4) + n <= 14
Combine like terms:
2n + 4 <= 14
[URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B4%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get:
n <= 5
Substituting this into inequality (2):
v + 5 <= 14
[URL='https://www.mathcelebrity.com/1unk.php?num=v%2B5%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]v <= 9[/B]

Wayne’s widget world sells widgets to stores for $10.20 each (wholesale price). A local store marks

Wayne’s widget world sells widgets to stores for $10.20 each (wholesale price). A local store marks them up $6.79. What is the retail price at this store?
[I]Note: Markup means we add to the wholesale price. [/I]
Calculate Retail Price:
Retail Price = Wholesale Price + Markup Amount
Retail Price = $10.20 + $6.79
Retail Price = [B]$16.99[/B]

What does y=f(x) mean

What does y=f(x) mean
It means y = a function of the variable x.
x is the independent variable and y is the dependent variable.
f(x) means a function in terms of x

What fraction lies exactly halfway between 2/3 and 3/4?

What fraction lies exactly halfway between 2/3 and 3/4?
A) 3/5
B) 5/6
C) 7/12
D) 9/16
E) 17/24
Halfway means taking the average, which is dividing the sum of the fractions by 2 for 2 fractions:
1/2(2/3 + 3/4)
1/2(2/3) + 1/2(3/4)
1/3 + 3/8
We need common denominators, so [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F3&frac2=3%2F8&pl=Add']we type this fraction sum into our search engine[/URL] and get:
[B]17/24 - Answer E[/B]

what integer is tripled when 9 is added to 3 fourths of it?

what integer is tripled when 9 is added to 3 fourths of it?
Let the integer be n. Tripling an integer means multiplying it by 3. We're given:
3n = 3n/4 + 9
Since 3 = 12/4, we have:
12n/4 = 3n/4 + 9
Subtract 3n/4 from each side:
9n/4 = 9
[URL='https://www.mathcelebrity.com/prop.php?num1=9n&num2=9&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this equation into the search engine[/URL], we get:
[B]n = 4[/B]

what integer is used for losing 10 yards

what integer is used for losing 10 yards
A loss means a negative, so a 10 yard loss is written as [B]-10[/B]

what is 3 degrees below zero

what is 3 degrees below zero
Below zero means negative, so we write this as:
[B]-3[/B]

What is the sample space for a 10 sided die?

What is the sample space for a 10 sided die?
Sample space means the set of all possible outcomes. For a 10-sided die, we have:
[B]{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}[/B]

WHAT SHOULD BE SUBTRACTED FROM -9876 TO OBTAIN -9512

WHAT SHOULD BE SUBTRACTED FROM -9876 TO OBTAIN -9512
We set up an arbitrary number x.
Subtracted from is written as
-9876 - x
The phrase [I]to obtain[/I] means an equation, so we set -9876 - x equal to -9512
-9876 - x = -9512
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=-9876-x%3D-9512&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]364[/B]

When 20 is subtracted from 3 times a certain number, the result is 43

A certain number means an arbitrary variable, let's call it x
x
3 times x
3x
20 is subtracted from 3 time x
3x - 20
The result is means equal to, so we set 3x - 20 equal to 43 for our algebraic expression
[B]3x - 20 = 43
[/B]
If you need to solve this, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3x-20%3D43&pl=Solve']equation calculator[/URL]:
[B]x = 21[/B]

When 28 is subtracted from the square of a number, the result is 3 times the number. Find the negati

When 28 is subtracted from the square of a number, the result is 3 times the number. Find the negative solution.
Let the number be n.
Square of a number:
n^2
28 is subtracted from the square of a number:
n^2 - 28
3 times the number:
3n
[I]The result is[/I] mean an equation, so we set n^2 - 28 = 3n
n^2 - 28 = 3n
Subtract 3n from each side:
n^2 - 3n - 28 = 3n - 3n
The right side cancels to 0, so we have:
n^2 - 3n - 28 = 0
This is a quadratic equation in standard form, so we [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-3n-28%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']use our quadratic calculator[/URL] to solve:
We get two solutions for n:
n = (-4, 7)
The question asks for the negative solution, so our answer is:
[B]n = -4[/B]

When 39 is added to a number, the result is 40 times the number. Find the number. Let n be the unkn

When 39 is added to a number, the result is 40 times the number. Find the number. Let n be the unknown number. Write the translated equation below.
[LIST=1]
[*]39 added to a number is written as n + 39
[*]40 times the number is written as 40n
[*]The result is means we have an equation, so set (1) equal to (2)
[/LIST]
n+ 39 = 40n
Running [URL='http://www.mathcelebrity.com/1unk.php?num=n%2B39%3D40n&pl=Solve']n + 39 = 40n through the search engine[/URL], we get[B] n = 1[/B].

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the num

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. Find the number
The phrase [I]a number, [/I]means an arbitrary variable, let's call it "x".
4 times a number, increased by 40, means we multiply 4 times x, and then add 40
4x + 40
100 decreased by the number means we subtract x from 100
100 - x
The problem tells us both of these expressions are the same, so we set them equal to each other:
4x + 40 = 100 - x
Add x to each side:
4x + x + 40 = 100 - x + x
The x's cancel on the right side, so we have:
5x + 40 = 100
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B40%3D100&pl=Solve']Typing this equation into the search engine[/URL], we get [B]x = 12[/B].

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the num

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
4 times a number means we multiply x by 4:
4x
Increased by 40 means we add 40 to 4x:
4x + 40
100 decreased by the number means we subtract x from 100:
100 - x
The phrase [I]is the same as[/I] means equal to, so we set 4x + 40 equal to 100 - x
4x + 40 = 100 - x
Solve for [I]x[/I] in the equation 4x + 40 = 100 - x
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 4x and -x. To do that, we add x to both sides
4x + 40 + x = -x + 100 + x
[SIZE=5][B]Step 2: Cancel -x on the right side:[/B][/SIZE]
5x + 40 = 100
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 40 and 100. To do that, we subtract 40 from both sides
5x + 40 - 40 = 100 - 40
[SIZE=5][B]Step 4: Cancel 40 on the left side:[/B][/SIZE]
5x = 60
[SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE]
5x/5 = 60/5
x = [B]12[/B]
Check our work for x = 12:
4(12) + 40 ? 100 - 12
48 + 40 ? 100 - 12
88 = 88

When 54 is subtracted from the square of a number, the result is 3 times the number.

When 54 is subtracted from the square of a number, the result is 3 times the number.
This is an algebraic expression. Let's take it in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it "x".
x
Square the number, means raise it to the 2nd power:
x^2
Subtract 54:
x^2 - 54
The phrase [I]the result[/I] means an equation, so we set x^2 - 54 equal to 3
[B]x^2 - 54 = 3[/B]

When 9 is subtracted from 5 times a number ,the result is 31

When 9 is subtracted from 5 times a number ,the result is 31
A number means an arbitrary variable, let's call it x.
5 times this number is written as 5x.
9 subtracted from this is written as 5x - 9
[I]The result[/I] means we have an equation, so we set [B]5x - 9 = 31[/B]. This is our algebraic expression.
Now if we want to solve for x, we [URL='http://www.mathcelebrity.com/1unk.php?num=5x-9%3D31&pl=Solve']plug this equation into the search engine [/URL]and get [B]x = 8[/B].

When a circle's radius triples, what happens to its area?

When a circle's radius triples, what happens to its area?
A = ?r^2
When r = 3r, then we have:
a = ?(3r)^2
A = 9(?r^2)
This means Area increases by [B]9x
[MEDIA=youtube]j5aqShSh4uE[/MEDIA][/B]

When m = 120 , the value of .10m + 54 is 66. Explain what this means in the context of this car rent

When m = 120 , the value of .10m + 54 is 66. Explain what this means in the context of this car rental company.
This means 0.10 is the [B]per-mileage charge[/B] and $54 is the flat rate or rental fee

When Mike uses a riding mower, it takes him 3 hours to mow his lawn. When he uses a push mower, it t

When Mike uses a riding mower, it takes him 3 hours to mow his lawn. When he uses a push mower, it takes him 6 hours to mow the lawn. (His sister also can mow the lawn with the push mower in 6 hours.). Mike wanted to get the lawn mowed as quickly as possible, so he paid his sister $10 to mow with the push mower while he used the riding mower. How long will it take Mike an his sister to mow the lawn if they worked together?
Mike can mow 1/3 of the lawn in an hour.
Mike's sister can mow 1/6 the lawn in an hour.
together, they can mow [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F3&frac2=1%2F6&pl=Add']1/3 + 1/6 [/URL]= 1/2 of the lawn in one hour.
Which means it would take [B]2 hours [/B](2 * 1/2) = 1 to mow the full lawn.

When twice a number is reduced by 15 you get 95 what is the number

When twice a number is reduced by 15 you get 95 what is the number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
[I]Twice[/I] x means we multiply x by 2
2x
[I]Reduced by[/I] 15 means we subtract 15
2x - 15
[I]You get[/I] means equal to, as in an equation. Set 2x - 15 = 95
2x - 15 = 95 <-- This is our algebraic expression.
[URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D95&pl=Solve']Type 2x - 15 = 95 into the search engine[/URL] and we get [B]x = 55[/B].

Which of the following can increase power?

Which of the following can increase power?
a. Increasing standard deviation
b. Decreasing standard deviation
c. Increasing both means but keeping the difference between the means constant
d. Increasing both means but making the difference between the means smaller
[B]b. Decreasing standard deviation[/B]
[LIST=1]
[*]Power increases if the standard deviation is smaller.
[*]If the difference between the means is bigger, the power is bigger.
[*]Sample size increase also increases power
[/LIST]

Which of the following involves making pairwise comparisons? a. Comparing the standard deviation of

Which of the following involves making pairwise comparisons?
a. Comparing the standard deviation of GRE grades between two states
b. Comparing the variance of the amount of soda consumed by boys and girls in a high school
c. Comparing the mean weight between children in grades 2, 3, 4 and 5
d. Comparing the number of restaurants in New York and Boston
[B]c. Comparing the mean weight between children in grades 2, 3, 4 and 5[/B]
Pairwise comparison generally refers to any process of comparing entities in pairs to judge which of each entity is preferred, or has a greater amount of some quantitative property

Which of the following is NOT TRUE about the distribution for averages?

Which of the following is NOT TRUE about the distribution for averages?
a. The mean, median, and mode are equal.
b. The area under the curve is one.
c. The curve never touches the x-axis.
d. The curve is skewed to the right.
Answer is d, the curve is skewed to the right
For a normal distribution:
[LIST]
[*] The area under the curve for a standard normal distribution equals 1
[*] Mean media mode are equal
[*] Never touches the x-axis since in theory, all events have some probability of occuring
[/LIST]

Which of the followings can increase the value of t? (select all the apply) a. Increase the standar

Which of the followings can increase the value of t? (select all the apply)
a. Increase the standard deviation of difference scores
b. Decrease the standard deviation of difference scores
c. Increase the difference between means
d. Decrease the difference between means
[B]b. Decrease the standard deviation of difference scores
c. Increase the difference between means[/B]
[I]Increase numerator or decrease denominator of the t-value formula[/I]

William has 75 peppermints. Viana has p fewer peppermints than William

William has 75 peppermints. Viana has p fewer peppermints than William
Fewer means less, so we subtract to get Viana's total peppermints:
[B]75 - p[/B]

Write an algebraic expression for 8 multiplied by the result of u reduced by 11.

Write an algebraic expression for 8 multiplied by the result of u reduced by 11.
u [I]reduced by[/I] 11
Reduced by means subtract 11 from u. So we have:
u - 11
We multiply this expression by 8 to get our algebraic expression of:
[B]8(u - 11)[/B]

Write an equation that relates the quantities. G varies jointly with t and q and inversely with the

Write an equation that relates the quantities. G varies jointly with t and q and inversely with the cube of w . The constant of proportionality is 8.25 .
[LIST]
[*]Varies jointly or directly means we multiply
[*]Varies inversely means divide
[*]The cube of w means we raise w to the 3rd power: w^3
[/LIST]
Using k = 8.25 as our constant of proportionality, we have:
[B]g = 8.25qt/w^3[/B]

Write the sentence as an equation. 19 is equal to c less than 321

Write the sentence as an equation. 19 is equal to c less than 321
c less than 321:
321 - c
The phrase [I]is equal to[/I] means an equation, so we set 321 - c equal to 19:
[B]321 - c = 19[/B]

X bisects WY. XY=32 and WY=2x. Find x and WY

X bisects WY. XY=32 and WY=2x. Find x and WY\
Bisects means split into two equal parts. So we have:
XY = 32
WX = XY
If XY = 32, then:
WY = 2 * 32 =[B] 64[/B]
So x = [B]32[/B]

x cubed plus x squared decreased by 7

x cubed plus x squared decreased by 7
[U]x cubed means we raise x to the power of 3:[/U]
x^3
[U]x squared means we raise x to the power of 2:[/U]
x^2
[U]x cubed plus x squared[/U]
x^3 + x^2
[U]Decreased by 7:[/U]
[B]x^3 + x^2 - 7[/B]

X is at least as large as 4

X is at least as large as 4.
This is an algebraic expression, where the phrase [I]at least as large as[/I] means greater than or equal to:
[B]x >=4[/B]

X is the speed limit is a maximum 65 mph

X is the speed limit is a maximum 65 mph
A maximum of means less than or equal to. Or, no more than. So we have the inequality:
[B]X <= 65[/B]

x is tripled and then 2 is added

x is tripled and then 2 is added
Tripled means multiply x by 3:
3x
Then add 2 to this:
[B]3x + 2[/B]

X plus 9 is equal to 3 times x minus 4

X plus 9 is equal to 3 times x minus 4
x plus 9:
x + 9
3 times x minus 4:
3x - 4
The phrase [I]is equal to[/I] means an equation, so we set x + 9 equal to 3x - 4:
[B]x + 9 = 3x - 4[/B]

x plus y times x minus y

x plus y times x minus y
Plus means we add. Minus means we subtract. So we have:
[B](x + y)(x - y)[/B]

x squared plus a minus b

x squared plus a minus b
x squared means we raise x to the power of 2:
x^2
Plus a:
x^2 + a
Minus b:
[B]x^2 + a - b[/B]

x squared times the difference of x and y

x squared times the difference of x and y
x squared means we raise x to the power of 2:
x^2
The difference of x and y
x - y
x squared times the difference of x and y
[B]x^2(x - y)[/B]

X to the 9th is less than or equal to 38

X to the 9th is less than or equal to 38:
x to the 9th means 9th power:
x^9
We set this less than or equal 38:
[B]x^9 <= 38[/B]

x tripled less two is 5

x tripled less two is 5
x tripled means we multiply x by 3
3x
Less two means we subtract 2 from 3x
3x - 2
[I]Is[/I] means equal to, so we set 3x - 2 equal to 5
[B]3x - 2 = 5[/B]
[B][/B]
To solve this equation, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3x-2%3D5&pl=Solve']equation solver[/URL].

X varies directly with the cube root of y when x=1 y=27. Calculate y when x=4

X varies directly with the cube root of y when x=1 y=27. Calculate y when x=4
Varies directly means there is a constant k such that:
x = ky^(1/3)
When x = 1 and y = 27, we have:
27^1/3(k) = 1
3k = 1
To solve for k, we[URL='https://www.mathcelebrity.com/1unk.php?num=3k%3D1&pl=Solve'] type in our equation into our search engine[/URL] and we get:
k = 1/3
Now, the problem asks for y when x = 4. We use our variation equation above with k = 1/3 and x = 4:
4 = y^(1/3)/3
Cross multiply:
y^(1/3) = 4 * 3
y^(1/3) =12
Cube each side:
y^(1/3)^3 = 12^3
y = [B]1728[/B]

Y add z then divide by x

Y add z then divide by x
y add z:
y + z
Then divide by x means we divide the sum (y + z) by x
[B](y + z)/x[/B]

y is the sum of twice a number and 3

y is the sum of twice a number and 3
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
twice a number means we multiply x by 2:
2x
the sum of twice a number and 3:
2x + 3
The word [I]is[/I] means equal to, so we set 2x + 3 equal to y
[B]y = 2x + 3[/B]

y minus 10 is equal to the product of y and 8

y minus 10 is equal to the product of y and 8.
Take this algebraic expression in 3 parts:
Part 1: y minus 10
Subtract 10 from the variable y
y - 10
Part 2: The product of y and 8
We multiply 8 by the variable y
8y
Part 3: The phrase [I]is equal to[/I] means an equation, so we set y - 10 equal to 8y
[B]y - 10 = 8y[/B]

y varies directly as the reciprocal of x

y varies directly as the reciprocal of x
The reciprocal of x is written as:
1/x
The phrase [I]varies directly[/I] means there exists a constant k such that
[B]y = k/x[/B]

y varies directly as x and inversely as i

y varies directly as x and inversely as I
Note:
Direct variation means we multiply. Inverse variation means we divide.
There exists a constant k such that:
[B]y = kx/i[/B]

Yesterday, Boris had 144 baseball cards. Today, he got m more. Using m, write an expression for the

Yesterday, Boris had 144 baseball cards. Today, he got m more. Using m, write an expression for the total number of baseball cards he has now.
144 and m more means we add
[B]144 + m[/B]

Yesterday, Kareem had n baseball cards. Today, he got 9 more. Using n, write an expression for the t

Yesterday, Kareem had n baseball cards. Today, he got 9 more. Using n, write an expression for the total number of baseball cards he has now.
9 more means we add 9 to n
[B]n + 9[/B]

Yolanda wants to rent a boat and spend less than $41. The boat costs $8 per hour, and Yolanda has a

Yolanda wants to rent a boat and spend less than $41. The boat costs $8 per hour, and Yolanda has a discount coupon for $7 off. What are the possible numbers of hours Yolanda could rent the boat?
A few things to build this problem:
[LIST=1]
[*]Discount subtracts from our total
[*]Cost = Hourly rate * hours
[*]Less than means an inequality using the < sign
[/LIST]
Our inequality is:
8h - 7 < 41
To solve this inequality for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h-7%3C41&pl=Solve']type it in our math engine[/URL] and we get:
h < [B]6[/B]

You and 6 friends went out for pizza. When the total amount was split, each person paid $3. How much

You and 6 friends went out for pizza. When the total amount was split, each person paid $3. How much was the total bill?
You and 6 friends means 7 total people. If the bill was split, everybody paid the same. We have:
7 people * $3 per person = [B]$21 total bill[/B]

You and five friends are planning a trip. You want to keep the cost less than $85 per person.

You and five friends are planning a trip. You want to keep the cost less than $85 per person.
You and five friends means you have: 5 + 1 = 6 people.
If you want a cost per person less than 85, then we have a cost c such that:
[B]c/6 < 85[/B]

You and your friend are playing a number-guessing game. You ask your friend to think of a positive n

You and your friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the result by 2, and then add three. If your friend's final answer is 53, what was the original number chosen?
Let n be our original number.
Square the number means we raise n to the power of 2:
n^2
Multiply the result by 2:
2n^2
And then add three:
2n^2 + 3
If the friend's final answer is 53, this means we set 2n^2 + 3 equal to 53:
2n^2 + 3 = 53
To solve for n, we subtract 3 from each side, to isolate the n term:
2n^2 + 3 - 3 = 53 - 3
Cancel the 3's on the left side, and we get:
2n^2 = 50
Divide each side of the equation by 2:
2n^2/2 = 50/2
Cancel the 2's, we get:
n^2 = 25
Take the square root of 25
n = +-sqrt(25)
n = +-5
We are told the number is positive, so we discard the negative square root and get:
n = [B]5[/B]

You can spend at most $35. If you buy 5 tickets, how much can you spend on each ticket

You can spend at most $35. If you buy 5 tickets, how much can you spend on each ticket
We're given the number of tickets as 5.
We know cost = price * quantity
Let p = price
The phrase [B]at most[/B] means less than or equal to, so we have:
5p <= 35
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=5p%3C%3D35&pl=Show+Interval+Notation']Plugging this inequality into our search engine[/URL], we have:
[B]p <= 7[/B]

You collect stamps. You give steven 21 stamps. At the end youbhave 3. How many stamps did you start

You collect stamps. You give steven 21 stamps. At the end youbhave 3. How many stamps did you start with?
You start with s stamps.
s
You give Steven 21. Giving means you subtract from your total:
s - 21
You have 3 left
s - 21 = 3
To solve this equation for s, we t[URL='https://www.mathcelebrity.com/1unk.php?num=s-21%3D3&pl=Solve']ype it in our math engine[/URL] and we get:
s = [B]24[/B]

You have $110 saved in your bank account. You want to save $15 every week. Let x be the amount of we

You have $110 saved in your bank account. You want to save $15 every week. Let x be the amount of weeks and y be the total amount saved.
Savings mean we add to the bank balance, so we have:
[B]y = 15x + 110[/B]

You have 30 DONUTS. 1/6 of them are Boston Cream. 2/5 of them are Maple. 3/10 of them are Chocolate

You have 30 DONUTS. 1/6 of them are Boston Cream. 2/5 of them are Maple. 3/10 of them are Chocolate Dip and 1/3 are Sprinkled. IS THIS EVEN POSSIBLE?? How many donuts OVER or UNDER am I? (Show your work and use EQUIVALENTS.)
We use 30 as our common denominator. Let's get [I]equivalent fraction[/I]s for each donut type with a denominator of 30:
[LIST]
[*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=1%2F6&pl=Equivalent+Fractions']1/6[/URL] = 5/30
[*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=2%2F5&pl=Equivalent+Fractions']2/5 [/URL]= 12/30
[*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=3%2F10&pl=Equivalent+Fractions']3/10[/URL] = 9/30
[*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=1%2F3&pl=Equivalent+Fractions']1/3[/URL] = 10/30
[/LIST]
Add up our numerators of the common denominator of 30:
5 + 12 + 9 + 10 = 36
So our fraction is 36/30. This makes our scenario [B]impossible[/B]. Fractions of the donut should add up to 1. Which would mean our numerators need to sum to 1 or less. Since 36 > 30, this scenario is [B]impossible.[/B]

You have a total of 42 math and science problems for homework. You have 10 more math problems than s

You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject?
Let m be the math problems and s be the science problems. We have two equations:
(1) m + s = 42
(2) m = s + 10
Substitute (2) into (1)
(s + 10) + s = 42
Combine like terms
2s + 10 = 42
Subtract 10 from each side
2s = 32
Divide each side by 2
[B]s = 16[/B]
So that means m = 16 + 10 --> [B]m = 26
(m, s) = (26, 16)[/B]

you must be 65 or older to join inequality

you must be 65 or older to join inequality
Let a be the age. 65 or older means greater than or equal to 65:
[B]a >=65[/B]

you own 15 CDs. you buy 7 more.How many CDs do you own now?

you own 15 CDs. you buy 7 more.How many CDs do you own now?
Start with 15
You buy 7 more, which means you [U]add[/U] 7 to your total:
15 + 7 = [B]22[/B]

You prepare 18 scoops of dog food for 6 dogs, and prepare 24 scoops of dog food for 8 dogs. What is

You prepare 18 scoops of dog food for 6 dogs, and prepare 24 scoops of dog food for 8 dogs. What is the constant of proportionality for the amount of dog food to the number of dogs? How many scoops of dog food should you prepare for 9 dogs?
18/6 = 24/8 = 3 as the constant of proportionality for the amount of dog food to the number of dogs.
What this means is for every dog, we give them 3 scoops of food.
So for 9 dogs, we give 9 dogs * 3 scoops of food per dog = 27 scoops

You purchase a new car for $35,000. The value of the car depreciates at a rate of 8.5% per year. If

You purchase a new car for $35,000. The value of the car depreciates at a rate of 8.5% per year. If the rate of decrease continues, what is the value of your car in 5 years?
Set up the depreciation function D(t), where t is the time in years from purchase. We have:
D(t) = 35,000(1 - 0.085)^t
Simplified, a decrease of 8.5% means it retains 91.5% of it's value each year, so we have:
D(t) = 35,000(0.915)^t
The problem asks for D(5)
D(5) = 35,000(0.915)^5
D(5) = 35,000(0.64136531607)
D(5) = $[B]22,447.79[/B]

You roll a die. Find the probability of rolling a number less than 4 AND rolling an odd number.

P(X = 4) AND P(X is odd)
Which means P(X = 1) + P(X = 3)
[LIST]
[*]P(X = 1) = 1/6
[*]P(X = 3) = 1/6
[*]P(X = 1) + P(X = 3) = 1/6 + 1/6 = 2/6 = [B]1/3[/B]
[/LIST]

You split $1,500 between two savings accounts. Account A pays 5% annual interest and Account B pays

You split $1,500 between two savings accounts. Account A pays 5% annual interest and Account B pays 4% annual interest. After one year, you have earned a total of $69.50 in interest. How much money did you invest in each account. Explain.
Let a be the amount you invest in Account A. So this means you invested 1500 - A in account B. We have the following equation:
05a + (1500 - a).04 = 69.50
Simplifying, we get:
0.05a + 1560 - 0.04a = 69.50
0.01a + 60 = 69.50
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.01a%2B60%3D69.50&pl=Solve']equation solver[/URL], we get:
[B]a = 950[/B]
So this means Account B is b = 1500 - 950 = [B]550[/B]

you start at a point on the number line and move 4 units left. If you are now at 10, then what was y

you start at a point on the number line and move 4 units left. If you are now at 10, then what was your original point?
Work backwards. If we're at 10, and we moved left, this means we add 4 to get back to our starting point:
10 + 4 = [B]14[/B]

Your grade must be at least 60 to pass this class

Your grade must be at least 60 to pass this class
Assumptions and givens:
[LIST]
[*]The phrase [I]at least[/I] means greater than or equal to.
[*]Let g be your grade
[/LIST]
We have:
[B]g >= 60[/B]

Your salary after a 9% salary increase if your salary before the increase was s

Your salary after a 9% salary increase if your salary before the increase was s
9% increase means we multiply s by 1.09
[B]1.09s[/B]

z , subtract 5 then times by 3

z , subtract 5 then times by 3
Take this algebraic expression two parts:
[LIST]
[*]z subtract 5: z - 5
[*][I]Then times by 3[/I] means we multiply the expression z - 5 by 3
[/LIST]
[B]3(z - 5)[/B]

z fewer than the difference of 5 and y

z fewer than the difference of 5 and y
Take this algebraic expression in parts:
The difference of 5 and y means we subtract y from 5
5 - y
z fewer than this difference means we subtract z from 5 - y
[B]5 - y - z[/B]

z is directly proportional to the square of x and y

z is directly proportional to the square of x and y
Directly proportional means there exists a constant k such that:
z = [B]kx^2y
[MEDIA=youtube]J3ByZkcX38E[/MEDIA][/B]

z is jointly proportional to the square of x and the cube of y

z is jointly proportional to the square of x and the cube of y
The square of x means we raise x to the power of 2:
x^2
The cube of y means we raise y to the power of 3:
y^3
The phrase [I]jointly proportional[/I] means we have a constant k such that:
[B]z = kx^2y^3[/B]

z varies directly with x and inversely with y

z varies directly with x and inversely with y
[LIST]
[*]The phrase directly means we multiply.
[*]The phrase inversely means we divide
[*]Variation means there exists a constant k such that:
[/LIST]
[B]z = kx/y[/B]

z varies inversely as the square of t. if z=4 when t=2, find z when t is 10

z varies inversely as the square of t. if z=4 when t=2, find z when t is 10
Varies inversely means there exists a constant k such that:
z = k/t^2
If z = 4 when t = 2, we have:
4 = k/2^2
4 = k/4
Cross multiply and we get:
k = 4 * 4
k = 16
Now the problem asks to find z when t is 10:
z = k/t^2
z = 16/10^2
z = 16/100
z = [B]0.16[/B]

z varies inversely with w, x, and y

z varies inversely with w, x, and y
Inversely means their exists a constant k such that:
[B]z = k/wxy[/B]

Z varies jointly as the 4th power of x and the 5th power of y

Z varies jointly as the 4th power of x and the 5th power of y
The 4th power of x means we raise x to the power of 4:
x^4
The 5th power of y means we raise y to the power of 5:
y^5
The phrase [I]varies jointly[/I] means we have a constant k such that:
z = [B]kx^4y^5[/B]

z varies jointly as x and y. If z=3 when x=3 and y=15, find z when x=6 and y=9

z varies jointly as x and y. If z=3 when x=3 and y=15, find z when x=6 and y=9
Varies jointly means there exists a constant k such that:
z = kxy
We're given z = 3 when x = 3 and y = 15, so we have:
3 = 15 * 3 * k
3 = 45k
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=3%3D45k&pl=Solve']equation solver,[/URL] we see that:
k = 1/15
So our joint variation equation is:
z = xy/15
Then we're asked to find z when x = 6 and y = 9
z = 6 * 9 / 15
z = 54/15
[URL='https://www.mathcelebrity.com/search.php?q=54%2F15&x=0&y=0']z =[/URL] [B]18/5[/B]

Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same a

Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same as subtracting 5 from the number then multiplying by 4.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We're given two expressions in relation to this number (x):
[U]She subtracts 6 then multiplies the result by 5[/U]
[LIST]
[*]Subtract 6: x - 6
[*]Multiply the result by 5: 5(x - 6)
[/LIST]
[U]She subtracts 5 from the number then multiplying by 4[/U]
[LIST]
[*]Subtract 6: x - 5
[*]Multiply the result by 5: 4(x - 5)
[/LIST]
Finally, the expression [I]is the same as[/I] means an equation, so we set the first expression equal to the second expression to make the following equation:
5(x - 6) = 4(x - 5)
Now, let's solve the equation for x. To do this, we [URL='https://www.mathcelebrity.com/1unk.php?num=5%28x-6%29%3D4%28x-5%29&pl=Solve']type this equation into our search engine [/URL]and we get:
x = [B]10[/B]

Zyrelle is now 20 years older than her sister. Find the present age of Zyrelle

Zyrelle is now 20 years older than her sister. Find the present age of Zyrelle
Let Zyrelle's age be z.
Let her sister's age be s.
Older means we add, so we have:
[B]z = s + 20[/B]

? = 5, ? = 4 ; calculate P(0 < x < 8)

? = 5, ? = 4 ; calculate P(0 < x < 8)
This is the same as P(x < 8) - P(x < 0).
P(x < 8) [URL='https://www.mathcelebrity.com/probnormdist.php?xone=8&mean=5&stdev=4&n=1&pl=P%28X+%3C+Z%29']using our calculator[/URL] is 0.773373
P(x < 0) [URL='https://www.mathcelebrity.com/probnormdist.php?xone=0&mean=5&stdev=4&n=1&pl=P%28X+%3C+Z%29']using our calculator[/URL] is 0.10565
So we have 0.773373 - 0.10565 = [B]0.667723[/B]