191 results

difference - the result of one of the important mathematical operations, which is obtained by subtracting two numbers

-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]

1/2 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]

1/4 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]

18 divided by the difference of t and 9

The difference of t and 9 is:
t - 9
Now, we set up a quotient with 18 as the numerator and t - 9 as the denominator
18
------
t - 9

2 number Word Problems

Free 2 number Word Problems Calculator - This calculator handles word problems in the format below:

* Two numbers have a sum of 70 and a product of 1189 What are the numbers?

* Two numbers have a sum of 70. Their difference 32

* Two numbers have a sum of 70 and a product of 1189 What are the numbers?

* Two numbers have a sum of 70. Their difference 32

3 times the difference between t and y

3 times the difference between t and y
Difference between t and y
t - y
3 times this difference:
[B]3(t - y)[/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]

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]

48 is the difference of Chrissys height and 13 .

48 is the difference of Chrissys height and 13 .
Let Chrissy's height = h.
The difference of the height and 13 is h - 13.
We set this expression equal to 48:
[B]h - 13 = 48
[/B]
Note: To solve this, [URL='http://www.mathcelebrity.com/1unk.php?num=h-13%3D48&pl=Solve']paste this problem into the search engine[/URL].

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]

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]

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 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]

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of t

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of the two poles, what is the minimum length of cord you would need?
The difference between the 70 foot and 50 foot pole is:
70 - 50 = 20 foot height difference.
So we have a right triangle, with a height of 20, base of 30. We want to know the hypotenuse.
Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=20&side2input=30&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator to solve for hypotenuse[/URL], we get:
hypotenuse = [B]36.06 feet[/B]

A holiday in Florida costs $876. A holiday in Bali costs $394. How much more expensive is the Florid

A holiday in Florida costs $876. A holiday in Bali costs $394. How much more expensive is the Florida holiday?
We want the difference between Florida holiday costs and Bali holiday costs:
$876 - $394 = [B]$482[/B]

A pot of soup, currently 66°C above room temperature, is left out to cool. If that temperature diffe

A pot of soup, currently 66°C above room temperature, is left out to cool. If that temperature difference decreases by 10% per minute, then what will the difference be in 17 minutes?
We set up the temperature function T(m), where m is the number of minutes of cooling. With 10% = 0.1, we have:
T(m) = 66 * (1 - 0.10)^m
The problem asks for T(17) [U]and[/U] the difference temperature:
T(17) = 66 * 0.9^17
T(17) = 66 * 0.16677181699
T(17) = [B]11.01C[/B]
[B][/B]
[U]Calculate the difference in temperature[/U]
Difference = Starting Temperature - Ending Temperature
Difference = 66 - 11.01
Difference = 66 - 11.01 = [B]54.99 ~ 55[/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 4.44 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 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 set of 6 wooden chairs costs $444. A set of 8 metal chairs costs $720. How much more do the metal

A set of 6 wooden chairs costs $444. A set of 8 metal chairs costs $720. How much more do the metal chairs cost per chair?
[U]Wooden Chair Unit Cost:[/U]
Unit Cost = Total Cost / Quantity
Unit Cost = 444/6
Unit Cost = 74
[B][/B]
[U]Metal Chair Unit Cost:[/U]
Unit Cost = Total Cost / Quantity
Unit Cost = 720/8
Unit Cost = 90
[B][B][/B][/B]
Find the difference (how much more)
Difference = Metal Chair Unit Cost - Wooden Chair Unit Cost
Difference = 90 - 74
Difference = [B]16[/B]

a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age.

a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age.
Declare variables:
[LIST]
[*]Let f be the father's age
[*]Let s be the son's age
[/LIST]
We're given two equations:
[LIST=1]
[*]s = f/4
[*]f - s = 30. [I]The reason why we subtract s from f is the father is older[/I]
[/LIST]
Using substitution, we substitute equaiton (1) into equation (2) for s:
f - f/4 = 30
To remove the denominator/fraction, we multiply both sides of the equation by 4:
4f - 4f/4 = 30 *4
4f - f = 120
3f = 120
To solve for f, we divide each side of the equation by 3:
3f/3 = 120/3
Cancel the 3's on the left side and we get:
f = [B]40[/B]

Absolute Difference

Free Absolute Difference Calculator - Calculates the absolute difference between 2 numbers

Absolute Value

Free Absolute Value Calculator - Add, subtract, multiply or divide any two numbers with absolute value signs. Positive Difference.

Add r to the difference of s and t, then add q to the result

Add r to the difference of s and t, then add q to the result
the difference of s and t
s - t
Add r to the difference of s and t
s - t + r
Add r to the difference of s and t, then add q to the result
[B]s - t + r + q[/B]

Age Difference

Free Age Difference Calculator - Determines the ages for an age difference word problem.

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]

At 1:00 pm you have 24 megabytes of a movie and at 1:15 pm you have 96 megabytes of a movie. What is

At 1:00 pm you have 24 megabytes of a movie and at 1:15 pm you have 96 megabytes of a movie. What is the download rate in megabytes per minute?
First, find the number of minutes:
1:15 - 1:00 = 15 minutes
Next, determine the difference in megabytes
96 - 24 = 72
Finally, determine the download rate:
72 megabytes / 15 minutes = [B]4.8 megabytes per minute
[MEDIA=youtube]RCvs3TQMzdM[/MEDIA][/B]

Benchmark Fractions

Free Benchmark Fractions Calculator - Adds or Subtracts or Compares 2 fractions using estimating sums or estimating differences with benchmark fractions.

Confidence Interval/Hypothesis Testing for the Difference of Means

Free Confidence Interval/Hypothesis Testing for the Difference of Means Calculator - 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.

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]

Date and Time Difference

Free Date and Time Difference Calculator - Calculates the difference between two dates using the following methods

1) Difference in dates using year/month/day/hour/minute/second as the primary unit of time

2) Difference in dates in the form of years remaining, months remaining, days remaining, hours remaining, minutes remaining, seconds remaining.

1) Difference in dates using year/month/day/hour/minute/second as the primary unit of time

2) Difference in dates in the form of years remaining, months remaining, days remaining, hours remaining, minutes remaining, seconds remaining.

Death Valley in California is 282 feet below sea level. Grant Hill Park, which is right across from

Death Valley in California is 282 feet below sea level. Grant Hill Park, which is right across from our school is 167 feet above sea level. How many feet higher is Grant Hill compared to Death Valley?
Below sea level is written as a negative, so we have:
Difference in feet = 282 - (-167)
Difference in feet = [B]449 feet[/B]

difference between 2 positive numbers is 3 and the sum of their squares is 117

difference between 2 positive numbers is 3 and the sum of their squares is 117
Declare variables for each of the two numbers:
[LIST]
[*]Let the first variable be x
[*]Let the second variable be y
[/LIST]
We're given 2 equations:
[LIST=1]
[*]x - y = 3
[*]x^2 + y^2 = 117
[/LIST]
Rewrite equation (1) in terms of x by adding y to each side:
[LIST=1]
[*]x = y + 3
[*]x^2 + y^2 = 117
[/LIST]
Substitute equation (1) into equation (2) for x:
(y + 3)^2 + y^2 = 117
Evaluate and simplify:
y^2 + 3y + 3y + 9 + y^2 = 117
Combine like terms:
2y^2 + 6y + 9 = 117
Subtract 117 from each side:
2y^2 + 6y + 9 - 117 = 117 - 117
2y^2 + 6y - 108 = 0
This is a quadratic equation:
Solve the quadratic equation 2y2+6y-108 = 0
With the standard form of ax2 + bx + c, we have our a, b, and c values:
a = 2, b = 6, c = -108
Solve the quadratic equation 2y^2 + 6y - 108 = 0
The quadratic formula is denoted below:
y = -b ± sqrt(b^2 - 4ac)/2a
[U]Step 1 - calculate negative b:[/U]
-b = -(6)
-b = -6
[U]Step 2 - calculate the discriminant ?:[/U]
? = b2 - 4ac:
? = 62 - 4 x 2 x -108
? = 36 - -864
? = 900 <--- Discriminant
Since ? is greater than zero, we can expect two real and unequal roots.
[U]Step 3 - take the square root of the discriminant ?:[/U]
?? = ?(900)
?? = 30
[U]Step 4 - find numerator 1 which is -b + the square root of the Discriminant:[/U]
Numerator 1 = -b + ??
Numerator 1 = -6 + 30
Numerator 1 = 24
[U]Step 5 - find numerator 2 which is -b - the square root of the Discriminant:[/U]
Numerator 2 = -b - ??
Numerator 2 = -6 - 30
Numerator 2 = -36
[U]Step 6 - calculate your denominator which is 2a:[/U]
Denominator = 2 * a
Denominator = 2 * 2
Denominator = 4
[U]Step 7 - you have everything you need to solve. Find solutions:[/U]
Solution 1 = Numerator 1/Denominator
Solution 1 = 24/4
Solution 1 = 6
Solution 2 = Numerator 2/Denominator
Solution 2 = -36/4
Solution 2 = -9
[U]As a solution set, our answers would be:[/U]
(Solution 1, Solution 2) = (6, -9)
Since one of the solutions is not positive and the problem asks for 2 positive number, this problem has no solution

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]

Difference of a and b, divided by 2

Difference of a and b, divided by 2.
The difference of a and b is written as:
a - b
We divide this by 2:
[B](a - b)/2[/B]

Difference of Proportions Test

Free Difference of Proportions Test Calculator - Calculates a test statistic and conclusion for a hypothesis for the difference of proportions

Difference of Two Squares

Free Difference of Two Squares Calculator - Factors a difference of squares binomial in the form a^{2} - b^{2} or multiplies 2 binomials through in the form (ax + by)(ax - by).

distance between -2 and 9 on the number line

distance between -2 and 9 on the number line
Distance on the number line is the absolute value of the difference:
D = |9 - -2|
D = |11|
D = [B]11[/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 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 x and y by the difference of subtracting a from b

Divide the sum x and y by the difference of subtracting a from b
The sum x and y is written as:
x + y
The difference of subtracting a from b is written as:
b - a
We divide and get the algebraic expression:
[B](x + y)/(b - a)[/B]

Eighteen times the difference of a number and ten

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
The difference of a number and ten
x - 10
Eighteen times the difference of a number and ten
[B]18(x - 10)[/B]

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]

Factoring and Root Finding

Free Factoring and Root Finding Calculator - This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential*positive* and *negative* roots using Descarte’s Rule of Signs

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential

find the difference between a mountain with an altitude of 1,684 feet above sea level and a valley

find the difference between a mountain with an altitude of 1,684 feet above sea level and a valley 216 feet below sea level.
Below sea level is the same as being on the opposite side of zero on the number line. To get the difference, we do the following:
1,684 - (-216)
Since subtracting a negative is a positive, we have:
1,684 + 216
[B]1,900 feet[/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]

Foster is centering a photo that is 9/1/2 inches wide on a scrapbook pages that is 10 inches wide. H

Foster is centering a photo that is 9/1/2 inches wide on a scrapbook pages that is 10 inches wide. How far from each side of the pages should he put the picture? Enter your answer as a mixed number.
First, determine your margins, which is the difference between the width and photo width, divided by 2.
10 - 9 & 1/2 = 1/2
1/2 / 2 = [B]1/4[/B]

Fractions and Mixed Numbers

Free Fractions and Mixed Numbers Calculator - Given (improper fractions, proper fraction, mixed numbers, or whole numbers), this performs the following operations:

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

Gigi’s family left their house and drove 14 miles south to a gas station and then 48 miles east to a

Gigi’s family left their house and drove 14 miles south to a gas station and then 48 miles east to a water park. How much shorter would their trip to the water park have been if they hadn’t stopped at the gas station and had driven along the diagonal path instead?
[IMG]https://mathcelebrity.com/community/data/attachments/0/pythag-diagonal.jpg[/IMG]
Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=14&side2input=48&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator[/URL], we see the diagonal route would be:
50 miles
The original trip distance was:
Original Trip Distance = 14 + 48
Original Trip Distance = 62 miles
Diagonal Trip was 50 miles, so the difference is:
Difference = Original Trip Distance - Diagonal Distance
Difference = 62 - 50
Difference = [B]12 miles[/B]

Hal bought a house in 1995 for $190,000. If the value of the house appreciates at a rate of 4.5 perc

Hal bought a house in 1995 for $190,000. If the value of the house appreciates at a rate of 4.5 percent per year, how much was the house worth in 2006
[U]Calculate year difference:[/U]
Year Difference = End Year - Start Year
Year Difference = 2006 - 1995
Year Difference = 11
Using our [URL='https://www.mathcelebrity.com/apprec-percent.php?q=a+house+worth+190000+appreciates+4.5%25+for+11+years&pl=Calculate+Appreciation']appreciation calculator[/URL], we get the value of the house in 2006:
[B]$308,342.08[/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 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]

heat loss of a glass window varies jointly as the window's area and the difference between the outsi

heat loss of a glass window varies jointly as the window's area and the difference between the outside and the inside temperature. a window 6 feet wide by 3 feet long loses 1,320 btu per hour when the temperature outside is 22 degree colder than the temperature inside.
Find the heat loss through a glass window that is 3 feet wide by 5 feet long when the temperature outside is 9 degree cooler than the temperature inside.
Find k of the equation:
6*3*22*k = 1320
396k = 1,320
k = 3.33333 [URL='https://www.mathcelebrity.com/1unk.php?num=396k%3D1320&pl=Solve']per our equation solver[/URL]
Now, find the heat loss for a 3x5 window when the temperature is 9 degrees cooler than the temperature inside:
3*5*9*3.333333 = [B]450 btu per hour[/B]

If H = {(1,-4), (2,-3), (3,-2), (4,-1),...), What is H(9)?

If H = {(1,-4), (2,-3), (3,-2), (4,-1),...), What is H(9)?
It looks like each x-coordinate goes up by 1 and each y-coordinate decreases by 1. Their difference is 5. So we have:
H(9) = [B](9, 4)[/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 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 max time that John can spend on Client A ($20/hr) in one week is 32 hours, and the min time i

If the max time that John can spend on Client A ($20/hr) in one week is 32 hours, and the min time is 8 hours, while the max time on Client B ($14/hr) is 8 hours and the min 5 hours, what is the RANGE (max, min) of total pay he can earn in one week (40 hours)
[LIST]
[*]Client A Minimum = 20 x 8 hours = $160
[*]Client A Maximum = 20 x 32 hours = $640
[*]Client B Minimum = 14 x 5 hours = $70
[*]Client B Maximum = 14 x 8 hours = $112
[/LIST]
[U]The Total Maximum Pay is found by adding Client A Maximum and Client B Maximum[/U]
Total Maximum = Client A Maximum + Client B Maximum
Total Maximum = 640 + 112
Total Maximum = 752
[U]The Total Minimum Pay is found by adding Client A Minimum and Client B Minimum[/U]
Total Minimum = Client A Minimum + Client B Minimum
Total Minimum = 160 + 70
Total Minimum = 230
[U]The Range is the difference between the Total maximum and the Total minimum[/U]
Range(Total Maximum, Total Minimum) = Total Maximum - Total Minimum
Range(752, 230) = 752 - 230
Range(752, 230) = [B]522[/B]

If the P-value of a hypothesis test is 0.40, you conclude a. You accept the null hypothesis b. You r

If the P-value of a hypothesis test is 0.40, you conclude
a. You accept the null hypothesis
b. You reject the null hypothesis
c. You failed to reject the null hypothesis
d. You think there is a significant difference
[B]c. You failed to reject the null hypothesis[/B]
[I]due to a high p value, especially above 0.05[/I]

In a factory that manufactures tires, a machine responsible for molding the tire has a failure rate

In a factory that manufactures tires, a machine responsible for molding the tire has a failure rate of 0.2%. If 1,000 tires are produced in a day, of which 6 are faulty, what is the difference between the experimental probability and the theoretical probability?
Theoretical probability = Failure Rate * Tires
Theoretical probability = 0.002 * 1000
Theoretical probability = 2
The experimental probability was given as 6, so the difference is:
6 - 2 = [B]4[/B]

In a golf tournament Ned was 4 under par on Saturday and 5 over or on Sunday. What is the difference

In a golf tournament Ned was 4 under par on Saturday and 5 over or on Sunday. What is the difference in his score on Sunday compared to his score on Saturday
Givens and opening thoughts:
[LIST]
[*]Think of par as 0 or average.
[*]Under par is negative
[*]Over par is positive
[*]We have 4 under par as -4
[*]We have 5 over par as +5
[/LIST]
The difference is found by subtracting:
+5 - -4
+5 + 4
[B]9 strokes[/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]

Jennifer is twice as old as Peter. The difference between their ages is 15. What is Peters age

Jennifer is twice as old as Peter. The difference between their ages is 15. What is Peters age
Let j be Jennifer's age
Let p be Peter's age
We're given two equations:
[LIST=1]
[*]j = 2p
[*]j - p = 15
[/LIST]
Substitute equation (1) into equation (2) for j
2p - p = 15
To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=2p-p%3D15&pl=Solve']type this equation into our calculation engine[/URL] and we get:
p = [B]15[/B]

Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. Wh

Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. What age is Martina?
[U]Assumptions and givens:[/U]
[LIST]
[*]Let Justin's age be j
[*]Let Martina's age be m
[*]j > m ([I]since Justin is older than Martina[/I])
[/LIST]
We're given the following equations :
[LIST=1]
[*]j - m = 22
[*]j + m = 54
[/LIST]
Since the coefficients of m are opposites, we can take a shortcut using the [I]elimination method[/I] and add equation (1) to equation (2)
(j + j) + (m - m) = 22 + 54
2j = 76
To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=2j%3D76&pl=Solve']type this equation into our math engine[/URL] and we get:
j = 38
The question asks for Martina's age (m), so we can pick equation (1) or equation (2). Let's use equation (1):
38 - m = 22
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=38-m%3D22&pl=Solve']type it in our math engine[/URL] and we get:
m = [B]16[/B]

Kaylee had $197 in her savings now her savings is $429 . How much was her paycheck

Kaylee had $197 in her savings now her savings is $429 . How much was her paycheck
Her paycheck equals the increase in savings from $197 to $429. We want the difference:
Paycheck = Savings Now - Savings Before Paycheck
Paycheck = $429 - $197
Paycheck = [B]$232[/B]

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden or a round garden with the fencing.
Laura did some calculations and found that a circular garden would give her 1380 more square feet than a square garden. How many feet of fencing were in the roll that Laura found? (Round to the nearest foot.)
Feet of fencing = n
Perimeter of square garden = n
Each side of square = n/4
Square garden's area = (n/4)^2 = n^2/16
Area of circle garden with circumference = n is:
Circumference = pi * d
n = pi * d
Divide body tissues by pi:
d = n/pi
Radius = n/2pi
Area = pi * n/2pi * n/2pi
Area = pin^2/4pi^2
Reduce by canceling pi:
n^2/4pi
n^2/4 * 3.14
n^2/12.56
The problem says that the difference between the square's area and the circle's area is equal to 1380 square feet.
Area of Circle - Area of Square = 1380
n^2/12.56 - n^2/16 = 1380
Common denominator = 200.96
(16n^2 - 12.56n^2)/200.96 = 1380
3.44n^2/200.96 = 1380
Cross multiply:
3.44n^2 = 277,324.8
n^2 = 80,617.7
n = 283.9
Nearest foot = [B]284[/B]

Lorda is older than Kate. The sum of their ages is 30. The difference in their ages is 6. What are t

Lorda is older than Kate. The sum of their ages is 30. The difference in their ages is 6. What are their ages?
Let Lorda's age be l. Let Kate's age be k. We're given two equations:
[LIST=1]
[*]l + k = 30
[*]l - k = 6 <-- Since Lorda is older
[/LIST]
Add the 2 equations together and we eliminate k:
2l = 36
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%3D36&pl=Solve']Typing this equation into our search engine[/URL] and solving for l, we get:
l = [B]18[/B]
Now substitute l = 18 into equation 1:
18 + k = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=18%2Bk%3D30&pl=Solve']Type this equation into our search engine[/URL] and solving for k, we get:
k = [B]12[/B]

Luke drove for n hours at 55 miles per hour. Luke's mother drove for n hours at a speed of 60 miles

Luke drove for n hours at 55 miles per hour. Luke's mother drove for n hours at a speed of 60 miles per hour. How much farther than Luke did his mother drive?
Distance = Rate * Time
[LIST]
[*]Luke drove: 55n
[*]Mom drove 60n
[/LIST]
Distance difference = 60n - 55n = [B]5n[/B]

m times the difference of 2p and 4r

m times the difference of 2p and 4r
The difference of 2p and 4r:
2p - 4r
m times the difference:
[B]m(2p - 4r)[/B]

Maria leaves her house and runs west for 6 m miles. She then turns North and runs 5 miles. Maria the

Maria leaves her house and runs west for 6 miles. She then turns North and runs 5 miles. Maria then travels east for 7 miles and then south for 5 miles. How far is Maria from her house now?
Maria traveled the same distance north and south of 5 miles. These cancel each other out.
Her 7 mile eastern trip compared to the 6 mile west trip represents a net difference of [B]1 mile[/B]

Mike works in a toy store. One week, he worked 38 hours and made $220. The next week, he received a

Mike works in a toy store. One week, he worked 38 hours and made $220. The next week, he received a raise, so when he worked 30 hours he made $180. How much was his raise (to the nearest cent)?
First week, Mike earns the following in hours (h)
38h = 220
h = 5.79 [URL='https://www.mathcelebrity.com/1unk.php?num=38h%3D220&pl=Solve']using our equation calculator[/URL]
We call this his old hourly salary
Next week, Mike earns the following in hours (h)
30h = 180
h = 6 [URL='https://www.mathcelebrity.com/1unk.php?num=30h%3D180&pl=Solve']using our equation calculator[/URL]
We call this his new hourly salary
His raise is the difference between his current hourly salary and his old hourly salary:
Raise = New Hourly Salary - Old Hourly Salary
Raise = 6 - 5.79
Raise = [B]$0.21[/B]
Mike got a 21 cent hourly raise

Mount McKinley in Alaska, the highest mountain in North America, is 20,320 feet above sea level. Dea

Mount McKinley in Alaska, the highest mountain in North America, is 20,320 feet above sea level. Death Valley, the lowest point, is 280 feet below sea level. What is the difference in height between Mount McKinley and Death Valley?
Regarding height with respect to sea level...
[LIST]
[*]Above sea level is written as positive height
[*]Below sea level is written as negative height
[/LIST]
So we have:
+20,320 - -280
+20,320 + 280
[B]20,600[/B]

Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest

Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference between these two elevations?
Above sea level is listed as positive (+)
Below sea level is listed as negative (-)
We have:
Difference = +29,028 - (-1312)
Difference = 29028 + 1312
[URL='https://www.mathcelebrity.com/longdiv.php?num1=29028&num2=1312&pl=Add']Difference[/URL] = [B]30,340[/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 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]

My rent was 800.00 a month. My landlord raised my rent to 1,240.00. What percentage did he raise m

My rent was 800.00 a month. My landlord raised my rent to 1,240.00. What percentage did he raise my rent?.
First, calculate the difference between the old and new rent:
Difference = 1,240 - 800 = 440
Percentage increase = 440/800
[URL='https://www.mathcelebrity.com/perc.php?num=440&den=800&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']Type 440/800 into the search engine, and choose the percent option[/URL]
You get [B]55%[/B] increase.

n increased by the difference between 10 times n and 9

n increased by the difference between 10 times n and 9
Take this algebraic expression in pieces:
[LIST]
[*]10 times n: 10n
[*]The difference between 10 times n and 9: 10n - 9
[*]n increased by the difference...: [B]n + (10n - 9)[/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]

Narda has $250 and Ding has $170. How much money must Narda give to Ding so that each of them will h

Narda has $250 and Ding has $170. How much money must Narda give to Ding so that each of them will have an equal amount of money?
Find the difference of Narda and Ding's money:
Difference = Narda - Ding
Difference = 250 - 170
Difference = 80
Find half the difference:
Half the difference = 80/2
Half the difference = 40
So Narda must give Ding [B]$40[/B] to have equal amounts:
Narda's new total = 250 - 40 = 210
Ding's new total = 1760 + 40 = 210

On July 10, the high temperature in Phoenix, Arizona, was 109°, and the high temperature in Juneau,

On July 10, the high temperature in Phoenix, Arizona, was 109°, and the high temperature in Juneau, Alaska, was 63°. What was the difference between the temperature in Phoenix and the temperature in Juneau?
Difference is found by subtracting the lower temperature from the higher temperature:
[URL='https://www.mathcelebrity.com/longdiv.php?num1=109&num2=63&pl=Subtract']109 - 63 [/URL]= [B]46[/B]

One number is 8 times another number. The numbers are both positive and have a difference of 70.

One number is 8 times another number. The numbers are both positive and have a difference of 70.
Let the first number be x, the second number be y. We're given:
[LIST=1]
[*]x = 8y
[*]x - y = 70
[/LIST]
Substitute(1) into (2)
8y - y = 70
[URL='https://www.mathcelebrity.com/1unk.php?num=8y-y%3D70&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]y = 10[/B] <-- This is the smaller number
Plug this into Equation (1), we get:
x = 8(10)
[B]x = 80 [/B] <-- This is the larger number

One positive number is one-fifth of another number. The difference between the two numbers is 192, f

One positive number is one-fifth of another number. The difference between the two numbers is 192, find the numbers.
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*]x = y/5
[*]x + y = 192
[/LIST]
Substitute equation 1 into equation 2:
y/5 + y = 192
Since 1 equals 5/5, we rewrite our equation like this:
y/5 = 5y/5 = 192
We have fractions with like denominators, so we add the numerators:
(1 + 5)y/5 = 192
6y/5 = 192
[URL='https://www.mathcelebrity.com/prop.php?num1=6y&num2=192&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Type this equation into our search engine[/URL], and we get:
[B]y = 160[/B]
Substitute this value into equation 1:
x = 160/5
x = [B]32[/B]

Paired Means Difference

Free Paired Means Difference Calculator - Calculates an estimation of confidence interval for a small or large sample difference of data. Confidence interval for paired means

Percent Error

Free Percent Error Calculator - Percentage error is the difference between an experimental measured value and a theoretical actual value

Prove that the difference between alternate consecutive squares as always even

Take an integer n. The next alternate consecutive integer is n + 2
Subtract the difference of the squares:
(n + 2)^2 - n^2
n^2 + 4n + 4 - n^2
n^2 terms cancel, we get:
4n + 4
Factor out a 4:
4(n + 1)
If n is odd, n + 1 is even. 4 * even is always even
If n is even, n + 1 is odd. 4 * odd is always odd
Since both cases are even, we've proven our statement.
[MEDIA=youtube]J_E9lR5qFY0[/MEDIA]

Prove that the difference of two consecutive cubes is never divisible by 3

Take two consecutive integers:
n, n + 1
The difference of their cubes is:
(n + 1)^3 - n^3
n^3 + 3n^2 + 3n + 1 - n^3
Cancel the n^3
3n^2 + 3n + 1
Factor out a 3 from the first 2 terms:
3(n^2 + n) + 1
The first two terms are always divisible by 3 but then the + 1 makes this expression not divisible by 3:
3(n^2 + n) + 1 = 1 (mod 3)
[MEDIA=youtube]hFvJ3epqmyE[/MEDIA]

Prove the difference between two consecutive square numbers is always odd

Take an integer n. The next consecutive integer is n + 1
Subtract the difference of the squares:
(n + 1)^2 - n^2
n^2 + 2n + 1 - n^2
n^2 terms cancel, we get:
2n + 1
2 is even. For n, if we use an even:
we have even * even = Even
Add 1 we have Odd
2 is even. For n, if we use an odd:
we have even * odd = Even
Add 1 we have Odd
Since both cases are odd, we've proven our statement.
[MEDIA=youtube]RAi0HbH5bqc[/MEDIA]

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]

raise the difference of 8 and v to the 7th power

raise the difference of 8 and v to the 7th power
Difference of 8 and v
8 - v
To the 7th power
[B](8 - v)^7[/B]

Raise the difference of V and 7 to the 10th

Raise the difference of V and 7 to the 10th
The difference of V and 7:
V - 7
Raise this to the 10th power:
[B](V - 7)^10[/B]

Sample Size Requirement for the Difference of Means

Free Sample Size Requirement for the Difference of Means Calculator - Given a population standard deviation 1 of σ_{1}, a population standard deviation 2 of σ_{2} a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.

Set Notation

Free Set Notation Calculator - Given two number sets A and B, this determines the following:

* Union of A and B, denoted A U B

* Intersection of A and B, denoted A ∩ B

* Elements in A not in B, denoted A - B

* Elements in B not in A, denoted B - A

* Symmetric Difference A Δ B

* The Concatenation A · B

* The Cartesian Product A x B

* Cardinality of A = |A|

* Cardinality of B = |B|

* Jaccard Index J(A,B)

* Jaccard Distance J_{σ}(A,B)

* Dice's Coefficient

* If A is a subset of B

* If B is a subset of A

* Union of A and B, denoted A U B

* Intersection of A and B, denoted A ∩ B

* Elements in A not in B, denoted A - B

* Elements in B not in A, denoted B - A

* Symmetric Difference A Δ B

* The Concatenation A · B

* The Cartesian Product A x B

* Cardinality of A = |A|

* Cardinality of B = |B|

* Jaccard Index J(A,B)

* Jaccard Distance J

* Dice's Coefficient

* If A is a subset of B

* If B is a subset of A

subtract the difference of t and s from 8

subtract the difference of t and s from 8
The difference of t and s:
t - s
Subtract this from 8:
8 - (t - s)

Super Snack, a convenience store, charges $4.35 for a large chicken sandwich and two large colas. Fo

Super Snack, a convenience store, charges $4.35 for a large chicken sandwich and two large colas. For a large chicken sandwich and a large cola, they charge $4.00. How much are the Super Snack large chicken sandwiches?
The difference between the orders is $0.35 and 1 large cola. Therefore, 1 large cola = $0.35.
And if we use the first order of one large chicken sandwich and one large cola, we get:
Large Chicken Sandwich + 0.35 = 4.35
Subtract 0.35 from each side, and we get:
Large Chicken Sandwich = $[B]4.00[/B]

Suppose that Sn = 3 + 1/3 + 1/9 + ... + 1/3(n-2)

Suppose that Sn = 3 + 1/3 + 1/9 + ... + 1/3(n-2)
a) Find S10 and S?
b) If the common difference in an arithmetic sequence is twice the first term, show that Sn/Sm = n^2/m^2
a) Sum of the geometric sequence is
a = 3 and r = 1/3
(a(1 - r)^n)/(1 - r)
(3(1 - 1/3)^9)/(1 - 1/3)
[B]S10 = 4.499771376[/B]
For infinity, as n goes to infinity, the numerator goes to 1
so we have [B]S? = 3(1)/2/3 = 4.5[/B]
b) Sum of an arithmetic sequence formula is below:
n(a1 + an)/2
an = a1 + (n - 1)2a1 since d = 2a1
n(a1 + a1 + (n - 1)2a1)/2
(2a1n + n^2 - 2a1n)/2
n^2/2
For Sm
m(a1 + am)/2
am = a1 + (m - 1)2a1 since d = 2a1
m(a1 + 1 + (m - 1)2a1)/2
(2a1m + m^2 - 2a1m)/2
m^2/2
Sn/Sm = n^2/m^2 (cancel the 2's)
S10/S1 = 10^2/1^2
We know S_{1} = 3
So we have 100(3)/1
[B]S10 = 300[/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 baseball coach bought 2 new baseballs for $1 each. The basketball coach bought 7 new basketballs

The baseball coach bought 2 new baseballs for $1 each. The basketball coach bought 7 new basketballs for $10 each. How much more did the basketball coach spend than the baseball coach?
[U]Baseball coach spend:[/U]
Spend = Number of baseballs * cost per baseball
Spend= 2 * $1
Spend = $2
[U]Basketball coach spend:[/U]
Spend = Number of basketballs * cost per basketball
Spend= 7 * $10
Spend = $70
[U]Calculate the difference in spend:[/U]
Difference = Basketball coach spend - Baseball coach spend
Difference= $70 - $2
Difference= [B]$68[/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 difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. Wh?

The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. What are the numbers?
Let the smaller number be x. Let the larger number be y. We're given:
[LIST=1]
[*]y - x = 108
[*]6x = y + 2
[/LIST]
Rearrange (1) by adding x to each side:
[LIST=1]
[*]y = x + 108
[/LIST]
Substitute this into (2):
6x = x + 108 + 2
Combine like terms
6x = x +110
Subtract x from each side:
5x = 110
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D110&pl=Solve']Plugging this equation into our search engine[/URL], we get:
x = [B]22[/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 the squares of two consecutive numbers is 141. Find the numbers

The difference between the squares of two consecutive numbers is 141. Find the numbers
Take two consecutive numbers:
n- 1 and n
Given a difference (d) between the squares of two consecutive numbers, the shortcut for this is:
2n - 1 = d
Proof of this:
n^2- (n - 1)^2 = d
n^2 - (n^2 - 2n + 1) = d
n^2 - n^2 + 2n - 1 = d
2n - 1 = d
Given d = 141, we have
2n - 1 = 141
Add 1 to each side:
2n = 142
Divide each side by 2:
2n/2 = 142/2
n = [B]71[/B]
Therefore, n - 1 = [B]70
Our two consecutive numbers are (70, 71)[/B]
Check your work
70^2 = 4900
71^2 = 5041
Difference = 5041 - 4900
Difference = 141
[MEDIA=youtube]vZJtZyYWIFQ[/MEDIA]

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 between two numbers is 25. The smaller number is 1/6th of the larger number. What is

The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number
Let the smaller number be s. Let the larger number be l. We're given two equations:
[LIST=1]
[*]l - s = 25
[*]s = l/6
[/LIST]
Plug in equation (2) into equation (1):
l - l/6 = 25
Multiply each side of the equation by 6 to remove the fraction:
6l - l = 150
To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=6l-l%3D150&pl=Solve']type this equation into our search engine[/URL] and we get:
l = 30
To solve for s, we plug in l = 30 into equation (2) above:
s = 30/6
[B]s = 5[/B]

The difference between two numbers is 96. One number is 9 times the other. What are the numbers?

The difference between two numbers is 96. One number is 9 times the other. What are the numbers?
Let x be the first number
Let y be the second number
We're given two equations:
[LIST=1]
[*]x - y = 96
[*]x = 9y
[/LIST]
Substitute equation (2) into equation (1) for x
9y - y = 96
[URL='https://www.mathcelebrity.com/1unk.php?num=9y-y%3D96&pl=Solve']Plugging this equation into our math engine[/URL], we get:
y = [B]12
[/B]
If y = 12, then we plug this into equation 2:
x = 9(12)
x = [B]108[/B]

The difference between two positive numbers is 5 and the square of their sum is 169

The difference between two positive numbers is 5 and the square of their sum is 169.
Let the two positive numbers be a and b. We have the following equations:
[LIST=1]
[*]a - b = 5
[*](a + b)^2 = 169
[*]Rearrange (1) by adding b to each side. We have a = b + 5
[/LIST]
Now substitute (3) into (2):
(b + 5 + b)^2 = 169
(2b + 5)^2 = 169
[URL='https://www.mathcelebrity.com/community/forums/calculator-requests.7/create-thread']Run (2b + 5)^2 through our search engine[/URL], and you get:
4b^2 + 20b + 25
Set this equal to 169 above:
4b^2 + 20b + 25 = 169
[URL='https://www.mathcelebrity.com/quadratic.php?num=4b%5E2%2B20b%2B25%3D169&pl=Solve+Quadratic+Equation&hintnum=+0']Run that quadratic equation in our search engine[/URL], and you get:
b = (-9, 4)
But the problem asks for [I]positive[/I] numbers. So [B]b = 4[/B] is one of our solutions.
Substitute b = 4 into equation (1) above, and we get:
a - [I]b[/I] = 5
[URL='https://www.mathcelebrity.com/1unk.php?num=a-4%3D5&pl=Solve']a - 4 = 5[/URL]
[B]a = 9
[/B]
Therefore, we have [B](a, b) = (9, 4)[/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 2 positive numbers is 54. The quotient obtained on dividing the 1 by the other is

The difference of 2 positive numbers is 54. The quotient obtained on dividing the 1 by the other is 4. Find the numbers.
Let the numbers be x and y. We have:
[LIST]
[*]x - y = 54
[*]x/y = 4
[*]Cross multiply x/y = 4 to get x = 4y
[*]Now substitute x = 4y into the first equation
[*](4y) - y = 54
[*]3y = 54
[*]Divide each side by 3
[*][B]y = 18[/B]
[*]If x = 4y, then x = 4(18)
[*][B]x = 72[/B]
[/LIST]

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 9 and the sum of x and 4

The difference of 9 and the sum of x and 4
The sum of x and 4:
x + 4
The difference of 9 and the sum of x and 4:
[B]9 - (x + 4)[/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 a number times 3 and 6 is equal to 7 . Use the variable w for the unknown n

The difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown number.
The phrase a number uses the variable w.
3 times w is written as 3w
The difference of 3w and 6 is written as 3w - 6
Set this equal to 7
[B]3w - 6 = 7
[/B]
This is our algebraic expression. To solve this equation for w, we [URL='http://www.mathcelebrity.com/1unk.php?num=3w-6%3D7&pl=Solve']type the algebraic expression into our search engine[/URL].

The difference of five and five y is the same as eight and two y

The difference of five and five y
5 - 5y
eight and two y
8 + 2y
The phrase [I]is the same as[/I] means equal to. Set 5 - 5y equal to 8 + 2y for our final algebraic expression
[B]5 - 5y = 8 + 2y[/B]
[B][/B]
If the problem asks you to solve for y:
Add 5y to each side:
5 = 8 + 7y
Subtract 8 from each side:
7y = -3
Divide each side by 7:
[B]y= -3/7[/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 two numbers is 720. The smaller of the numbers is 119. What is the other number?

The difference of two numbers is 720. The smaller of the numbers is 119. What is the other number?
Let the larger number be l. We're given:
l - 119 = 720
[URL='https://www.mathcelebrity.com/1unk.php?num=l-119%3D720&pl=Solve']We type this equation into the search engine[/URL] and we get:
l = [B]839[/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 x squared

The difference of x and x squared
We subtract x^2 from x:
[B]x - x^2[/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 difference when (10x - 6y) is subtracted from (7x - 4y) In simplest form

The difference when (10x - 6y) is subtracted from (7x - 4y) In simplest form
(7x - 4y) - (10x - 6y)
7x - 4y - 10x - -6y
7x - 4y - 10x + 6y
(7 - 10)x + (-4 + 6)y
[B]-3x + 2y[/B]

The distance between X and 8 is less than 14

Distance implies the positive difference between 2 points. Therefore, we use absolute value:
|x - 8| < 14
Note, we use less than since 14 is not included.

The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered t

The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 231 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer.
Digit, Probability
1, 0.301
2, 0.176
3, 0.125
4, 0.097
5, 0.079
6, 0.067
7, 0.058
8, 0.051
9, 0.046
[B][U]Fradulent Checks[/U][/B]
Digit, Frequency
1, 36
2, 32
3, 45
4, 20
5, 24
6, 36
7, 15
8, 16
9, 7
Complete parts (a) and (b).
(a) Using the level of significance α = 0.05, test whether the first digits in the allegedly fraudulent checks obey Benford's Law. Do the first digits obey the Benford's Law?

Yes or No Based on the results of part (a), could one think that the employe is guilty of embezzlement? Yes or No Show frequency percentages Digit Fraud Probability Benford Probability 1 0.156 0.301 2 0.139 0.176 3 0.195 0.125 4 0.087 0.097 5 0.104 0.079 6 0.156 0.067 7 0.065 0.058 8 0.069 0.051 9 0.03 0.046 Take the difference between the 2 values, divide it by the Benford's Value. Sum up the squares to get the Test Stat of 2.725281277 Critical Value Excel: =CHIINV(0.95,8) = 2.733 Since test stat is less than critical value, we cannot reject, so [B]YES[/B], it does obey Benford's Law and [B]NO[/B], there is not enough evidence to suggest the employee is guilty of embezzlement.

Yes or No Based on the results of part (a), could one think that the employe is guilty of embezzlement? Yes or No Show frequency percentages Digit Fraud Probability Benford Probability 1 0.156 0.301 2 0.139 0.176 3 0.195 0.125 4 0.087 0.097 5 0.104 0.079 6 0.156 0.067 7 0.065 0.058 8 0.069 0.051 9 0.03 0.046 Take the difference between the 2 values, divide it by the Benford's Value. Sum up the squares to get the Test Stat of 2.725281277 Critical Value Excel: =CHIINV(0.95,8) = 2.733 Since test stat is less than critical value, we cannot reject, so [B]YES[/B], it does obey Benford's Law and [B]NO[/B], there is not enough evidence to suggest the employee is guilty of embezzlement.

The January record high temperature in Austin, Texas is 92 degrees. The January record low temperatu

The January record high temperature in Austin, Texas is 92 degrees. The January record low temperature is -1 degree. What is the difference between the record high and low temperatures?
Difference = High - Low
Difference = 92 - -1
Difference = 92 + 1. <-- Since minus negative equals positive
Difference = [B]93 degrees[/B]

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 population of a town doubles every 12 years. If the population in 1945 was 11,005 people, what w

The population of a town doubles every 12 years. If the population in 1945 was 11,005 people, what was the population in 1981?
Calculate the difference in years:
Difference = 1981 - 1945
Difference = 36
Calculate doubling periods:
Doubling periods = Total years / Doubling time
Doubling periods = 36/12
Doubling periods = 3
Population = Initial Population * 2^doubling periods
Population = 11005 * 2^3
Population = 11005 * 8
Population = [B]88,040[/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 the sum and difference of c and d

the quotient of the sum and difference of c and d
The sum of c and d:
c + d
The difference of c and d:
c - d
the quotient of the sum and difference of c and d
[B](c + d)/(c - d)[/B]

The ratio between the sum of a and b and the difference of a and b is equal to 5.

The ratio between the sum of a and b and the difference of a and b is equal to 5.
The sum of a and b:
a + b
The difference of a and b:
a - b
The ratio between the sum of a and b and the difference of a and b
(a + b)/(a - b)
The ratio between the sum of a and b and the difference of a and b is equal to 5.
[B](a + b)/(a - b) = 5[/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 sum of 2 numbers is 70. The difference of these numbers is 24. Write and solve a system of equat

The sum of 2 numbers is 70. The difference of these numbers is 24. Write and solve a system of equations to determine the numbers.
Let the two numbers be x and y. We have the following equations:
[LIST=1]
[*]x + y = 70
[*]x - y = 24
[/LIST]
Add (1) to (2):
2x = 94
Divide each side by 2
[B]x = 47[/B]
Plug this into (1)
47 + y = 70
Subtract 47 from each side, we have:
[B]y = 23[/B]

The sum of m and 3 divided by the difference of m minus 3

The sum of m and 3 divided by the difference of m minus 3.
Sum of m and 3:
m + 3
Difference of m minus 3
m - 3
Take a quotient of these expressions:
[B]m + 3
-------
m - 3[/B]

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]
If a = 29, then we plug this into equation (1) to get:
29 + b = 55
b = 55 - 29
b = [B]26
[MEDIA=youtube]WwkpNqPvHs8[/MEDIA][/B]

The sum of the sum of x and z and the difference of y and z

The sum of the sum of x and z and the difference of y and z
Take this algebraic expression in 3 parts:
Step 1: The sum of x and z is written as:
x + z
Step 2: The difference of y and z is written as:
y - z
Step 3: the sum of the sum and difference is written as:
x + z + (y - z)
x + z + y - z
Cancelling the z terms, we get:
[B]x + y
[MEDIA=youtube]bmoZXImYCrg[/MEDIA][/B]

The sum of two y and three is the same as the difference of three y and one

The sum of two y and three
2y + 3
the difference of three y and one
3y - 1
is the same as means equal to. Set 2y + 3 equal to 3y - 1 for our final algebraic expression:
[B]2y + 3 = 3y - 1[/B]
[B][/B]
If the problem asks you to solve for y, subtract 2y from each side:
3 = y - 1
Add 1 to each side:
y = [B]4[/B]

the sum of w and v divided by their difference

the sum of w and v divided by their difference
the sum of w and v:
w + v
their difference:
w - v
the sum of w and v divided by their difference
[B](w + v)/(w - v)[/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 temp

The temperature of a solution was -23C. After adding a substance to the solution, the temperature after adding the substance to the solution was 133C.
What is the difference between the temperature of the solution before and after adding the substance
Using our [URL='https://www.mathcelebrity.com/temp-change.php?num=thetemperatureofasolutionwas-23c.afteraddingasubstancetothesolutionthetemperaturefe133c.whatisthedifferencebetweenthetemperatureofthesolutionbeforeandafteraddingthesubstance%3E&pl=Calculate+Temp+Change']temperature difference calculator[/URL], we get:
[B]156C[/B]

The temperature in Minneapolis changed from -7 fahrenheit at 6am to 7 fahrenheit at noon. What was t

The temperature in Minneapolis changed from -7 fahrenheit at 6am to 7 fahrenheit at noon. What was the difference between high and low temperatures?
Difference = High Temp - Low Temp
Difference = 7 - -7
Difference = [B]14[/B]

The total of z and 12 multiplied by the difference of 9 and y

The total of z and 12 multiplied by the difference of 9 and y
The total of z and 12:
z + 12
The difference of 9 and y:
9 - y
Now we multiply z + 12 by 9 - y:
[B](z + 12)(9 - y)[/B]

The world record for the mile in the year 1865 was held by Richard Webster of England when he comple

The world record for the mile in the year 1865 was held by Richard Webster of England when he completed a mile in 4 minutes and 36.5 seconds. The world record in 1999 was set by Hicham El Guerrouj when he ran a mile in 3 minutes and 43.13 seconds.
If both men ran the mile together, how many feet behind would Richard Webster be when Hichem El Guerrouj crossed the finish line?
Change times to seconds:
[LIST]
[*]4 minutes and 36.5 seconds = 4*60 + 36.5 = 240 + 36.5 = 276.5 seconds
[*]3 minute and 43.13 seconds = 3*60 + 43.13 = 180 + 43.13 = 223.13 seconds
[/LIST]
Now, find the distance Richard Webster travelled in 3 minutes and 43.13 seconds which is when Hiram El Guerrouj crossed the finish line.
1 mile = 5280 feet:
Set up a proportion of distance in feet to seconds where n is the distance Richard Webster travelled
5280/276.5 = n/223.13
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5280&num2=n&den1=276.5&den2=223.13&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
n = 4260.85 feet
Distance difference = 5280 - 4260.85 = [B]1019.15 feet[/B]

There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The

There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The difference between 2 times the first number and 3 times the second number is 24. Find the two numbers.
Let the first number be x and the second number be y. We have 2 equations:
[LIST=1]
[*]4x + 3y = 24
[*]2x - 3y = 24
[/LIST]
Without doing anything else, we can add the 2 equations together to eliminate the y term:
(4x + 2x) + (3y - 3y) = (24 + 24)
6x = 48
Divide each side by 6:
[B]x = 8
[/B]
Substitute this into equation (1)
4(8) + 3y = 24
32 + 3y = 24
[URL='https://www.mathcelebrity.com/1unk.php?num=32%2B3y%3D24&pl=Solve']Type 32 + 3y = 24 into our search engine[/URL] and we get [B]y = 2.6667[/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]

Translate this sentence into an equation. The difference of Maliks age and 15 is 63 Use the variable

Translate this sentence into an equation. The difference of Maliks age and 15 is 63 Use the variable m to represent Malik's age.
[B]m - 15 = 63
[/B]
To solve this equation, use our [URL='http://www.mathcelebrity.com/1unk.php?num=m-15%3D63&pl=Solve']equation calculator[/URL].

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]

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 quantity of seven plus x is the same as the difference of x and seven

seven plus x
7 + x
Twice the quantity of seven plus x
2(7 + x)
Difference of x and seven
x - 7
The phrase [I]is the same as[/I] means equal to. This is our algebraic expression:
[B]2(7 + x) = x - 7
[/B]
If the problem asks you to solve for x, distribute 2 on the left side:
14 + 2x = x - 7
Subtract x from the right side
14 + x = -7
Subtract 14 from each side
[B]x = -21[/B]

Twice the sum of a number and 6 is equal to three times the difference of the number and 3. Find the

[SIZE=6]Twice the sum of a number and 6 is equal to three times the difference of the number and 3. Find the number.
The phrase [/SIZE][I][SIZE=7]a number[/SIZE][/I][SIZE=6] means an arbitrary variable, let's call it x.
The sum of a number and 6 means we add 6 to x:
x + 6
Twice the sum of a number and 6 means we multiply x + 6 by 2:
2(x + 6)
the difference of the number and 3 means we subtract 3 from x
x - 3
three times the difference of the number and 3 means we multiply x - 3 by 3:
3(x- 3)
The word [I]is[/I] means we set 2(x + 6) equal to 3(x - 3)
2(x + 6) = 3(x - 3)
Use the distributive property to multiply through:
2x + 12 = 3x - 9
Subtract 2x from each side:
2x - 2x + 12 = 3x - 2x - 9
x - 9 = 12
Add 9 to each side:
x - 9 + 9 = 12 + 9
x = [B]21[/B]
[B][/B]
[B][MEDIA=youtube]CeZl_oZnSiw[/MEDIA][/B][/SIZE]

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 numbers total 12, and their differences is 20. Find the two numbers.

Two numbers total 12, and their differences is 20. Find the two numbers.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x + y = 12
[*]x - y = 20
[/LIST]
Since we have y coefficients of (-1 and 1) that cancel, we add the two equations together:
(x + x) + (y - y) = 12 + 20
The y terms cancel, so we have:
2x = 32
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D32&pl=Solve']Type this equation into our search engine[/URL] and we get:
x = [B]16[/B]
Substitute this value of x = 16 back into equation 1:
16 + y = 12
[URL='https://www.mathcelebrity.com/1unk.php?num=16%2By%3D12&pl=Solve']Typing this equation into our search engine[/URL], we get:
y = [B]-4
[/B]
Now, let's check our work for both equations:
[LIST=1]
[*]16 - 4 = 12
[*]16 - -4 --> 16 + 4 = 20
[/LIST]
So these both check out.
(x, y) = ([B]16, -4)[/B]

Two numbers total 50 and have a difference of 28. Find the two numbers.

Two numbers total 50 and have a difference of 28. Find the two numbers.
Using x and y as our two numbers, we write the following 2 equations:
[LIST=1]
[*]x + y = 50
[*]x - y = 28
[/LIST]
Add the 2 rows:
2x = 78
Divide each side by 2:
[B]x = 39[/B]
If x = 39, then from (1), we have
y = 50 - 39
[B]y = 11[/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]

Van needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that s

Van needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that starts with 13 and continues to add seven to each output. For now, van needs to know what the 15th output will be. Complete the steps needed to determine the 15th term in sequence.
Given a first term a1 of 13 and a change amount of 7, expand the series
The explicit formula for an [I]arithmetic series[/I] is an = a1 + (n - 1)d
d represents the common difference between each term, an - an - 1
Looking at all the terms, we see the common difference is 7, and we have a1 = 13
Therefore, our explicit formula is an = 13 + 7(n - 1)
If n = 15, then we plug it into our explicit formula above:
an = 13 + 7(n - 1)
a(15) = 15 + 7(15 - 1)
a(15) = 15 + 7 * 14
a(15) = 15 + 98
a(15) = [B]113[/B]

Vectors

Free Vectors Calculator - Given 2 vectors A and B, this calculates:

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj_{B}A and and the vector component of A orthogonal to B → A - proj_{B}A

Also calculates the horizontal component and vertical component of a 2-D vector.

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj

Also calculates the horizontal component and vertical component of a 2-D vector.

When 3 consecutive positive integers are multiplied, the product is 16 times the sum of the 3 intege

When 3 consecutive positive integers are multiplied, the product is 16 times the sum of the 3 integers. What is the difference of the product minus the sum?
Let the 3 consecutive positive integers be:
[LIST=1]
[*]x
[*]x + 1
[*]x + 2
[/LIST]
The product is:
x(x + 1)(x + 2)
The sum is:
x + x + 1 + x + 2 = 3x + 3
We're told the product is equivalent to:
x(x + 1)(x + 2) = 16(3x + 3)
x(x + 1)(x + 2) = 16 * 3(x + 1)
Divide each side by (x + 1)
x(x + 2) = 48
x^2 + 2x = 48
x^2 + 2x - 48 = 0
Now subtract the sum from the product:
x^2 + 2x - 48 - (3x + 3)
[B]x^2 - x - 51[/B]

When the circumference of a circle is increased from 10 pi inches to 15 pi inches, by how many inche

When the circumference of a circle is increased from 10 pi inches to 15 pi inches, by how many inches is the radius increased?
C = 2pir
Smaller circle:
2pir = 10pi
Divide each side by 2pi:
r = 5
Larger circle:
2pir = 15pi
Divide each side by 2pi:
r = 7.5
Difference = 7.5 - 5 = [B]2.5 or 2&1/2
[MEDIA=youtube]HvMNNffcv78[/MEDIA][/B]

When the side of a square is doubled in length, its area increases by 432 square inches. What is the

When the side of a square is doubled in length, its area increases by 432 square inches. What is the size of the original square?
Original square side length is s
Area = s^2
Double the side lengths to 2s
New area = (2s)^2 = 4s^2
Setup the difference relation:
4s^2 - s^2 = 432
3s^2 = 432
Divide each side by 3:
3s^2/3 = 432/3
s^2 = 144
s = [B]12[/B]

When the water is turned on, a bathtub will be filled in 12 minutes. When the drain is opened it tak

When the water is turned on, a bathtub will be filled in 12 minutes. When the drain is opened it takes 20 minutes for the tub to drain. If the water is turned on and the drain is left open, how long until the tub is filled?
In one hour, the faucet will fill 5 tubs since 12 * 5 = 60 minutes.
In one hour, the drain will empty 3 tubs since 20 * 3 = 60 minutes
The difference is 2 tubs filled per hour.
Therefore, we have 1 tub filled in [B]1/2 hour or 30 minutes[/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 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]

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]

You are given a choice of taking the simple interest on $100,000 invested for 5 years at a rate of 2

You are given a choice of taking the simple interest on $100,000 invested for 5 years at a rate of 2% or the interest on $100,000 invested for 5 years at an interest rate of 2% compounded daily. Which investment earns the greater amount of interest? Give the difference between the amounts of interest earned by the two investments
[URL='http://www.mathcelebrity.com/simpint.php?av=&p=100000&int=2&t=5&pl=Simple+Interest']Simple interest balance after 5 years[/URL] at 2% is $110,000.
[URL='http://www.mathcelebrity.com/compoundint.php?bal=100000&nval=1825&int=2&pl=Daily']Daily compounded interest for 5 years[/URL] at 2% is 365 days per year * 5 years = 1,825 days = [B]$110,516.79
Compound interest earns more by $110,516.79 - $110,000 = $516.79[/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]