age - the length of time that a person has lived or a thing has existed

$6500 is 7/10 of a number. What is the number

The number is $9,285 from our [URL='http://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=6500&pct1=70&pcheck=2&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pof1=40&pof2=20&pl=Calculate']percentage-decimal-fraction calculator[/URL].

$8 an hour for 5 hours

$8 an hour for 5 hours
Wages = Hourly Rate * Hours Worked
Wages = $8 * 5
Wages = [B]$40[/B]

1 year from now Mike will be 40 years old. The current sum of the ages of Mike and John is 89. How o

1 year from now Mike will be 40 years old. The current sum of the ages of Mike and John is 89. How old is John right now?
If Mike will be 40 1 year from now, then he is:
40 - 1 = 39 years old today.
And if the current sum of Mike and John's age is 89, then we use j for John's age:
j + 39 = 89
[URL='https://www.mathcelebrity.com/1unk.php?num=j%2B39%3D89&pl=Solve']Type this equation into our search engine[/URL], and we get:
[B]j = 50[/B]

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

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

12 laps in 18 minutes . What is the average time per lap?

12 laps in 18 minutes . What is the average time per lap?
18/12 = [B]1.5 minutes per lap[/B]

1225 people live in a village,329 are men and 404 are women. how many are children

1225 people live in a village,329 are men and 404 are women. how many are children
We can have either men, women, or children. We have the following equation where children are "c".
239 + 404 + c = 1225
To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=239%2B404%2Bc%3D1225&pl=Solve']type this equation into our search engine[/URL] and we get:
c = [B]582[/B]

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

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

15 out of 18 students agreed. What percentage did not?

18 - 15 = 3 student disagreed.
3/18 is the fraction of student who disagreed.
[URL='http://www.mathcelebrity.com/perc.php?num=3&den=18&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']Converting to a percentage using our fraction to decimal calculator, we get:[/URL]
16.67%

19 increased by twice Vanessa's age

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

2/3 of his present age

2/3 of his present age
Let a be present age. We have:
[B]2a/3[/B]

2000 people attended a baseball game 1300 of the people attending supported the home team while 700

2000 people attended a baseball game 1300 of the people attending supported the home team while 700 supported the visiting team what percentage of people attending supported the home team
We want the percentage of 1300 out of 2000.
[URL='https://www.mathcelebrity.com/perc.php?num=1300&den=2000&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']We go to our search engine and type 1300 out of 2300 as a percent[/URL] and we get:
[B]65%[/B]

24 coloring books, 60 crayons, and 84 markers can be packaged into at most how many identical packag

24 coloring books, 60 crayons, and 84 markers can be packaged into at most how many identical packages? How many of each would each package contain?
First, determine the greatest common factor (GCF) of 24, 60, and 84 using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=24&num2=60&num3=84&pl=GCF']GCF calculator[/URL].
GCF(24, 60, 84) = 12
So we have 12 identical packages.
Now, figure out how many coloring books, crayons, and markers for each package
[LIST]
[*]24/12 = 2 coloring books
[*]60/12 = 5 crayons
[*]84/12 = 7 markers
[/LIST]
[B]So we have 12 identical packages, each containing 2 coloring books, 5 crayons, and 7 markers[/B]

24 students in a class took an algebra test and 19 of them earned a B or better. What percent of stu

24 students in a class took an algebra test and 19 of them earned a B or better. What percent of students earned a B or better?
Using our [URL='http://www.mathcelebrity.com/perc.php?num=19&den=24&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']percentage calculator[/URL], we have:
19/24 = [B]79.1667%[/B]

3 children painted a local park track of 5000m, Alex painted 70m, Dell painted 15m, and Tony painted

3 children painted a local park track of 5000m, Alex painted 70m, Dell painted 15m, and Tony painted 35m. This pattern continues to the end of the track. What percentage of the park did each child paint?
70 + 15 + 35 = 120
When we take[URL='https://www.mathcelebrity.com/modulus.php?num=5000mod120&pl=Calculate+Modulus'] 5000 divided by 120[/URL], we get:
41 remainder 80
So we have:
[LIST]
[*]Alex: 70 * 41 = 2870
[*]Dell: 15 * 41 = 615
[*]Tony: 35 * 41 = 1435
[/LIST]
Now Alex goes next, and paints the full 70. So he has:
2870 + 70 = 2940
Dell goes next, and paints the last 10
615 + 10 = 625
Now for percentages:
[LIST]
[*]Alex: 2940/5000 = [B]58.8%[/B]
[*]Dell: 625/5000 = [B]12.5%[/B]
[*]Tony: 1435/5000 = [B]28.7%[/B]
[/LIST]

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

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

300 reduced by 5 times my age is 60

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

36 PAGES AND IT 3/8CM THICK, WHAT IS THE THICKNESS OF 1 PAGE?

36 PAGES AND IT 3/8CM THICK, WHAT IS THE THICKNESS OF 1 PAGE?
Set up a proportion in pages to cm:
36 pages /3/8cm = 1 page/x cm
Cross multiply:
36x = 3/8
Divide each side by 36
x = 3/(8 * 36)
x = 1/(8*12)
x = [B]1/96 cm[/B]

4 balls in package. 8 packages of balls in a carton. how many balls would be in 125 cartons?

4 balls in package. 8 packages of balls in a carton. how many balls would be in 125 cartons?
We have 4 balls per package * 8 packages per carton * 125 cartons
[B]4,000 balls[/B]

400 reduced by 3 times my age is 214

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

401(k) Balance

Determines your 401(k) balance given a salary history per year, contribution percentage rate, employer match percentage, and a rate of return.

44 less that twice julies age

44 less that twice julies age
Let Julie's age be a. Twice Julie's age is 2a.
44 less than this is: [B]2a - 44[/B]

45.62% of Ricks home is lit at night with fluorescent bulbs and the remaining with LED lights. what

45.62% of Ricks home is lit at night with fluorescent bulbs and the remaining with LED lights. what is the percentage is lit with LED lights?
Since the remaining is lit with LED lights, fluorescent and LED make up 100% of the lighting. So we have:
Percentage of LED lights = 100% - 45.62%
Percentage of LED lights = [B]54.38%[/B]

46% of bullied students report notifying an adult at school about the incident. How much of the perc

46% of bullied students report notifying an adult at school about the incident. How much of the percentage did not notify an adult?
When it comes to bullying, either a student notified or did not notify.
If 46% notified, then:
100% - 46% = [B]54% did not notify[/B]

5 years ago Kevin was 3 times as old as Tami. Now he is twice as old as she is. How is each now?

5 years ago Kevin was 3 times as old as Tami. Now he is twice as old as she is. How is each now?
Let Kevin's age be k. Let Tami's age be t. We're given the following equations:
[LIST=1]
[*]k - 5 = 3(t - 5)
[*]k = 2t
[/LIST]
Plug equation (2) into equation (1) for k:
2t - 5 = 3(t - 5)
We p[URL='https://www.mathcelebrity.com/1unk.php?num=2t-5%3D3%28t-5%29&pl=Solve']lug this equation into our search engine[/URL] and we get:
t = [B]10. Tami's age[/B]
Now plug t = 10 into equation (2) to solve for k:
k = 2(10)
k =[B] 20. Kevin's age[/B]

5000 union members of a financially troubled company accepted a 17% pay cut. The company announced t

5000 union members of a financially troubled company accepted a 17% pay cut. The company announced that this would save them approximately $108 million annually. Based on this information, calculate the average annual pay of a single union member
Let the full salary of the union members be s. Since 17% is 0.17, We're given:
0.17s = 108000000
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.17s%3D108000000&pl=Solve']type it in our search engine[/URL] and we get:
s = 635,294,117.65
Calculate the average annual pay of a single union member:
Average Pay = Total Pay / Number of Union Members
Average Pay = 635,294,117.65 / 5000
Average Pay = [B]127,058.82[/B]

54% of students got an F, 15% of students got a D, 19% of students got a B and 12% of students got a

54% of students got an F, 15% of students got a D, 19% of students got a B and 12% of students got an A. if there were 26 students, how many got an F?
First, we check our total percentages:
54% + 15% + 19% + 12% = 100% <-- Good, we have our full sample set
F Students = 54% * 26
F Students = 14.04 -->[B] 14[/B]

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

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

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

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

63 is the sum of 24 and helenas age

Set up an equation where h is Helena's age.
h + 24 = 63
[URL='http://www.mathcelebrity.com/1unk.php?num=h%2B24%3D63&pl=Solve']Subtract 24 from each side[/URL]
h = 39

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]

67 less than twice tims age

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

70 decreased by twice Carlos's age

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

75% of a ship’s cargo was destroyed by an on-board fire. The captain of the ship sold the remaining

75% of a ship’s cargo was destroyed by an on-board fire. The captain of the ship sold the remaining cargo, which was slightly damaged, for 25% of its real value and received $1400. What was the value of the cargo before the fire? (Do not include the $ sign or commas in the answer)
So 25% of the cargo is left.
This was sold at 25% of value.
Let the starting value be s:
We have 0.25 * 0.25 * s = 1400
0.0625s = 1400
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.0625s%3D1400&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]22400[/B]

8 years from now a girls age will be 5 times her present age whats is the girls age now

8 years from now a girls age will be 5 times her present age whats is the girls age now.
Let the girl's age now be a. We're given:
a + 8 = 5a
[URL='https://www.mathcelebrity.com/1unk.php?num=a%2B8%3D5a&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]a = 2[/B]

A $650 television costs $702 after sales tax is figured in. What is the sales tax percentage?

A $650 television costs $702 after sales tax is figured in. What is the sales tax percentage?
[U]Calculate Sales Tax Amount:[/U]
Sales Tax Amount = Total Bill - Original Cost
Sales Tax Amount = 702 - 650
Sales Tax Amount = 52
[U]Calculate Sales Tax Percentage:[/U]
Sales Tax Percentage = 100% * Sales Tax Amount / Original Cost
Sales Tax Percentage = 100% * 52 / 650
Sales Tax Percentage = 100% * 0.08
Sales Tax Percentage = [B]8%[/B]

A 1.5 inch tall preying mantis will sometimes hold its ground and attempt to fight a person who is 6

A 1.5 inch tall preying mantis will sometimes hold its ground and attempt to fight a person who is 6 feet tall. If a person who is 6 feet tall is engaged in a battle with an animal that was proportionally as tall as the person is to the preying mantis, how tall would the animal be?
In terms of inches, [URL='https://www.mathcelebrity.com/linearcon.php?quant=6&pl=Calculate&type=foot']6 feet = 72 inches[/URL]
Set up a proportion of height of smaller creature to larger creature where h is the heigh of the animal
1.5/72 = 72/h
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=1.5&num2=72&den1=72&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
h = 3456 inches
In terms of feet, we have [URL='https://www.mathcelebrity.com/linearcon.php?quant=3456&pl=Calculate&type=inch']3456 inches[/URL] = [B]288 feet[/B]

A 5L juice container has 3.6L of juice left. What percentage has been used?

A 5L juice container has 3.6L of juice left. What percentage has been used?
What has been used?
5L - 3.6L = 1.4L
Now, the [URL='http://www.mathcelebrity.com/perc.php?num=1.4&den=5.4&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']percentage used[/URL] is 1.4L/5.4L = [B]25.93%[/B]

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

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

A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a func

A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a function to model the situation the value of the card in 2020.Let x be number of years since 1970
The formula for accumulated value of something with a percentage growth p and years x is:
V(x) = Initial Value * (1 + p/100)^x
Set up our growth equation where 8% = 0.08 and V(y) for the value at time x and x = 2020 - 1970 = 50, we have:
V(x) = 100 * (1 + 8/100)^50
V(x) = 100 * (1.08)^50
V(x) = 100 * 46.9016125132
V(x) = [B]4690.16[/B]

a baseball player has 9 hits in his first 60 at bats. how many consecutive hits would he need to bri

a baseball player has 9 hits in his first 60 at bats. how many consecutive hits would he need to bring his average up to 0.400?
Let the amount of consecutive hits needed be h. We have:
hits / at bats = Batting Average
Plugging in our numbers, we get:
(9 + h)/60 = 0.400
Cross multiply:
9 + h = 60 * 0.4
9 + h = 24
To solve this equation for h, [URL='https://www.mathcelebrity.com/1unk.php?num=9%2Bh%3D24&pl=Solve']we type it in our search engine[/URL] and we get:
h = [B]15[/B]

A baseball team won 40% of its first 30 games. The team then won 65% of its next 60 games. Approxima

A baseball team won 40% of its first 30 games. The team then won 65% of its next 60 games. Approximately what percent of the games did the team win?
Using our percentage calculators, we type the following statements into our search engine and get:
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=45&den1=30&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']45% of 30[/URL] = 13.5
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=65&den1=60&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']65% of 60[/URL] = 39
For a total of 52.5 games won
The team played 30 + 60 = 90 games. So we want to know the pecent:
[URL='https://www.mathcelebrity.com/perc.php?num=52&den=90&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']52/90[/URL] = [B]57.78%[/B]

A bedroom set that normally sells for $1100 is on sale for 15% off. If sales tax rate is 2%, what is

A bedroom set that normally sells for $1100 is on sale for 15% off. If sales tax rate is 2%, what is the total price of the bedroom set if it is bought while on sale?
[U]Calculate the sale price:[/U]
Sale Price = Normal Price * (1 - Sales Percentage)
[U]With our sales percentage of 15% = 0.15, we have:[/U]
Sale Price = 1100 * (1 - 0.15)
Sale Price = 1100 * (0.85)
Sale Price = 935
[U]Calculate post tax amount:[/U]
Post tax amount = Sale Price * (1 + Tax Percentage)
[U]With our tax percentage of 2% = 0.02, we have:[/U]
Post tax amount = 935 * (1 + 0.02)
Post tax amount = 935 * (1.02)
Post tax amount = [B]$953.70[/B]

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

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

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

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

a bicycle store costs $3600 per month to operate. The store pays an average of $60 per bike. the ave

a bicycle store costs $3600 per month to operate. The store pays an average of $60 per bike. the average selling price of each bicycle is $100. how many bicycles must the store sell each month to break even?
Cost function C(b) where b is the number of bikes:
C(b) = Variable Cost + Fixed Cost
C(b) = Cost per bike * b + operating cost
C(b) = 60b + 3600
Revenue function R(b) where b is the number of bikes:
R(b) = Sale price * b
R(b) = 100b
Break Even is when Cost equals Revenue, so we set C(b) = R(b):
60b + 3600 = 100b
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=60b%2B3600%3D100b&pl=Solve']type it in our math engine[/URL] and we get:
b = [B]90[/B]

A bike is purchased for $200 and sold for $150. Determine the percentage of profit or loss.

A bike is purchased for $200 and sold for $150. Determine the percentage of profit or loss.
[U]Since sale price is less than purchase price, we have a loss:[/U]
Loss = Sale Price - Purchase Price
Loss = 150 - 200
Loss = -50
[U]Calculate percent loss:[/U]
Percent Loss = 100% * Loss / Purchase Price
Percent Loss = 100% * -50/200
Percent Loss = 100% *- 1/4
Percent Loss = [B]-25%[/B]

A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find th

A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find the present age of each?
Let the boy's age be b and his brother's age be c. We're given two equations:
[LIST=1]
[*]b = c + 10
[*]b + 4 = 2(c + 4)
[/LIST]
Substitute equation (1) into equation (2):
(c + 10) + 4 = 2(c + 4)
Simplify by multiplying the right side through and grouping like terms:
c + 14 = 2c + 8
[URL='https://www.mathcelebrity.com/1unk.php?num=c%2B14%3D2c%2B8&pl=Solve']Type this equation into our search engine[/URL] and we get:
c = [B]6[/B]
Now plug c = 6 into equation (1):
b = 6 + 10
b = [B]16[/B]

A boy is 6 years older than his sister. In 3 years time he will be twice her age. What are their pre

A boy is 6 years older than his sister. In 3 years time he will be twice her age. What are their present ages?
Let b be the boy's age and s be his sister's age. We're given two equations:
[LIST=1]
[*]b = s + 6
[*]b + 3 = 2(s + 3)
[/LIST]
Plug in (1) to (2):
(s + 6) + 3 = 2(s + 3)
s + 9 = 2s + 6
[URL='https://www.mathcelebrity.com/1unk.php?num=s%2B9%3D2s%2B6&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]s = 3[/B]
We plug s = 3 into Equation (1) to get the boy's age (b):
b = 3 + 6
[B]b = 9[/B]

A boy is 6 years younger than his sister. If he is (x-9) years old, how long will it take for his si

A boy is 6 years younger than his sister. If he is (x-9) years old, how long will it take for his sister to be x years old?
If the boy is x - 9 years old, and he's 6 years younger than his sister, than the sister is older by 6 years.
Sister's Age = x - 9 + 6
Sister's Age = x - 3
In order to be x years old, we must add 3 years:
x - 3 + 3 = x
So in [B]3 years, [/B]the sister will be x years old.

A builder needs 36 nails to finish a projects. If the nails come in packages of 3, how many packages

A builder needs 36 nails to finish a projects. If the nails come in packages of 3, how many packages should the builder purchase?
Packages needed = Total Nails / Nails per package
Packages needed = 36/3
Packages needed = [B]12[/B]

A camera normally cost for $450 is on sale for $315 what is the discount rate as the percentage on t

A camera normally cost for $450 is on sale for $315 what is the discount rate as the percentage on the camera
Using our [URL='https://www.mathcelebrity.com/markup.php?p1=450&m=&p2=+315&pl=Calculate']markdown calculator[/URL], we get:
[B]-30%[/B]

A car is bought for $2400 and sold one year later $1440 find the loss as a percentage of the cost pr

A car is bought for $2400 and sold one year later $1440 find the loss as a percentage of the cost price.
(2400 - 1440)/2400
960/2400
0.4
As a percentage, we multiply by 100 to get [B]40%[/B]

A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge

A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge of 25¢ per square foot for any footage that exceeds 180 sq ft and $1.30 per step for any carpeting on a staircase. A customers cleaning bill was $253.95. This included the cleaning of a staircase with 14 steps. In addition to the staircase, how many square feet of carpet did the customer have cleaned?
Calculate the cost of the staircase cleaning.
Staircase cost = $1.30 * steps
Staircase cost = $1.30 * 14
Staircase cost = $18.20
Subtract this from the cost of the total cleaning bill of $253.95. We do this to isolate the cost of the carpet.
Carpet cost = $253.95 - $18.20
Carpet cost = $235.75
Now, the remaining carpet cost can be written as:
75 + $0.25(s - 180) = $235.75 <-- were s is the total square foot of carpet cleaned
Multiply through and simplify:
75 + 0.25s - 45 = $235.75
Combine like terms:
0.25s + 30 = 235.75
[URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B30%3D235.75&pl=Solve']Type this equation into our search engine[/URL] to solve for s, and we get:
s = [B]823[/B]

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute c

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute costs $.35. This month you used 750 minutes. How much do you owe
[U]Find the overage minutes:[/U]
Overage Minutes = Total Minutes - Free Minutes
Overage Minutes = 750 - 600
Overage Minutes = 150
[U]Calculate overage cost:[/U]
Overage Cost = Overage Minutes * Overage cost per minute
Overage Cost = 150 * 0.35
Overage Cost = $52.5
Calculate total cost (how much do you owe):
Total Cost = Monthly Fee + Overage Cost
Total Cost = $49.99 + $52.50
Total Cost = [B]$102.49[/B]

A chicken farm produces ideally 700,000 eggs per day. But this total can vary by as many as 60,000 e

A chicken farm produces ideally 700,000 eggs per day. But this total can vary by as many as 60,000 eggs. What is the maximum and minimum expected production at the farm?
[U]Calculate the maximum expected production:[/U]
Maximum expected production = Average + variance
Maximum expected production = 700,000 + 60,000
Maximum expected production = [B]760,000[/B]
[U]Calculate the minimum expected production:[/U]
Minimum expected production = Average - variance
Minimum expected production = 700,000 - 60,000
Minimum expected production = [B]640,000[/B]

A coat normally costs $100. First, there was a 20% discount. Then, later, it was marked down 30% off

A coat normally costs $100. First, there was a 20% discount. Then, later, it was marked down 30% off of the discounted priced. How much does the coat cost now?
Calculate discounted price:
Discounted Price = Full Price * (1 - Discount Percentage)
Discounted Price = 100 * (1 - 0.20) <-- Since 20% = 0.2
Discounted Price = 100 * (0.80)
Discounted Price = 80
Now calculate marked down price off the discount price:
Markdown Price = Discount Price * (1 - Markdown Percentage)
Markdown Price = 80 * (1 - 0.30) <-- Since 30% = 0.3
Markdown Price = 80 * (0.70)
Markdown Price = [B]56[/B]

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

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

A company delivered 498 packages on Monday. On Tuesday they delivered 639 and on Wednesday they deli

A company delivered 498 packages on Monday. On Tuesday they delivered 639 and on Wednesday they delivered 436. How many packages did the company deliver in all?
Add up all the packages:
498 + 639 + 436 = [B]1573[/B]

A coupon that was mailed to preferred customers of video village rentals is good for 15% on any vide

A coupon that was mailed to preferred customers of video village rentals is good for 15% on any video that is bought. How much savings is there using the coupon to purchase a $22 video?
Savings = Full Price * Coupon Amount
Savings = $22 * 0.15
Savings = $3.30

A cubical storage box has edges that are 2 feet 4 inches long. What is the volume of the storage box

A cubical storage box has edges that are 2 feet 4 inches long. What is the volume of the storage box?
Since 1 foot = 12 inches, we have:
2 feet 4 inches = 2(12) + 4
2 feet 4 inches = 24 + 4
2 feet 4 inches = 28 inches
We type [URL='https://www.mathcelebrity.com/cube.php?num=28&pl=Side&type=side&show_All=1']cube side = 28[/URL] into our search engine to get:
V = [B]21952 cubic inches[/B]

A delivery man had 3,456 bottles of water in his truck. The bottles were packages in cases. There we

A delivery man had 3,456 bottles of water in his truck. The bottles were packages in cases. There were 48 bottles in each case. The driver delivered 192 bottles to a store. How many cases were in the truck after delivery?
Total cases in the truck before delivery
3,456/48 = 72 cases
Driver delivers 192 bottles to the store.
192 bottles / 48 bottles per case = 4 cases
72 cases before delivery - 4 cases for delivery = 68 cases after delivery

A department store buys 100 shirts at a cost of $600 and sells them at a selling price of 10 each fi

A department store buys 100 shirts at a cost of $600 and sells them at a selling price of 10 each find the percentage mark up
Find Unit Cost:
Unit Cost = Cost / Number of Shirts
Unit Cost = 600 / 100
Unit Cost = 6
With a selling price of 10, our markup percentage is:
Markup % = 100 * (New Price - Old Price)/Old Price
Markup % = 100 * (10 - 6)/6
Markup % = 100 * 4/6
Markup % = 400/6
Markup % = [B]66.67%[/B]

A discount store buys a shipment of fish bowls at a cost of $3.80 each. The fish bowls will be sold

A discount store buys a shipment of fish bowls at a cost of $3.80 each. The fish bowls will be sold for $5.76 apiece. What is the mark-up, as a percentage?
Using our [URL='https://www.mathcelebrity.com/markup.php?p1=3.80&m=&p2=5.76&pl=Calculate']markup calculator[/URL], we get:
[B]51.58% markup[/B]

A dormitory manager buys 38 bed sheets and 61 towels for $791.50. The manager get another 54 bed she

A dormitory manager buys 38 bed sheets and 61 towels for $791.50. The manager get another 54 bed sheets and 50 towels for $923 from the same store. What is the cost of one bed sheet and one towel?
Let s be bed sheets and t be towels. We have two equations:
[LIST=1]
[*]38s + 61t = 791.50
[*]54s + 50t = 923
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=38s+%2B+61t+%3D+791.50&term2=54s+%2B+50t+%3D+923&pl=Cramers+Method']system of equations calculator,[/URL] we get:
[LIST]
[*]s = 12
[*]t = 5.5
[/LIST]

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over all

A farmer is taking her eggs to the market in a cart, but she hits a
pothole, which knocks over all the containers of eggs. Though she is
unhurt, every egg is broken. So she goes to her insurance agent, who
asks her how many eggs she had. She says she doesn't know, but she
remembers somethings from various ways she tried packing the eggs.
When she put the eggs in groups of two, three, four, five, and six
there was one egg left over, but when she put them in groups of seven
they ended up in complete groups with no eggs left over.
What can the farmer figure from this information about the number of
eggs she had? Is there more than one answer?
We need a number (n) that leaves a remainder of 1 when divided by 2, 3, 4, 5, 6 but no remainder when divided by 7.
217 + 84 = [B]301[/B].
Other solutions are multiples of 3 x 4 x 5 x 7, but we want the lowest one here.

A father is K years old and his son is M years younger. The sum of their ages is 53.

A father is K years old and his son is M years younger. The sum of their ages is 53.
Father's Age = K
Son's Age = K - M
and we know K + (K - M) = 53
Combine like terms:
2K - M = 53
Add M to each side:
2K - M + M = 53 + M
Cancel the M's on the left side, we get:
2K = 53+ M
Divide each side by 2:
2K/2 = (53 + M)/2
Cancel the 2's on the left side:
K = [B](53 + M)/2[/B]

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

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

A football team lost 7 yards each play for four consecutive plays. Represent the team’s total change

A football team lost 7 yards each play for four consecutive plays. Represent the team’s total change in position for the four plays as an integer.
A net loss in yardage for 7 yards is written as -7
4 plays * -7 yards equals [B]-28[/B]

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

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

A high school with 1000 students offers two foreign language courses : French and Japanese. There ar

A high school with 1000 students offers two foreign language courses : French and Japanese. There are 200 students in the French class roster, and 80 students in the Japanese class roster. We also know that 30 students enroll in both courses. Find the probability that a random selected student takes neither foreign language course.
Let F be the event a student takes French and J be the event a student takes Japanese
P(F) = 200/1000 = 0.2
P(J) = 80/1000 = 0.08
P(F ? J) = 30/1000 = 0.03
From our [URL='http://www.mathcelebrity.com/probunion2.php?pa=+0.2&pb=0.08+&paintb=+0.03&aub=+&pl=Calculate']two event calculator[/URL], we get P(F U J) = 0.25
So we want P(F U J)^C = 1 - P(F U J) = 1 - 0.25 = [B]0.75[/B]

A house sold for $200,000 and the real estate agent earned a commission of $10,200.00. Find the comm

A house sold for $200,000 and the real estate agent earned a commission of $10,200.00. Find the commission rate.
Commission Rate = 100 * Commission Amount / Sale Price
Commission Rate = 100 * 10200/20000
Commission Rate = 100 * 0.051
Commission Rate = [B]5.51%[/B]

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

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

a is 2 years older than b who is twice as old as c. if the total ages of a,b and c is 42, then how o

a is 2 years older than b who is twice as old as c. if the total ages of a,b and c is 42, then how old is b
We're given 3 equations:
[LIST=1]
[*]a = b + 2
[*]b = 2c
[*]a + b + c = 42
[/LIST]
Substituting equation (2) into equation (1), we have:
a = 2c + 2
Since b = 2c, we substitute both of these into equation (3) to get:
2c + 2 + 2c + c = 42
To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=2c%2B2%2B2c%2Bc%3D42&pl=Solve']type this equation into our math engine[/URL] and we get:
c = 8
Now take c = 8 and substitute it into equation (2) above:
b = 2(8)
b = [B]16[/B]

A jet left Nairobi and flew east at an average speed of 231 mph. A passenger plane left four hours l

A jet left Nairobi and flew east at an average speed of 231 mph. A passenger plane left four hours later and flew in the same direction but with an average speed of 385 mph. How long did the jet fly before the passenger plane caught up?
Jet distance = 231t
Passenger plane distance = 385(t - 4)
385(t - 4) = 231t
385t - 1540 = 231t
Subtract 231t from each side
154t = 1540
[URL='https://www.mathcelebrity.com/1unk.php?num=154t%3D1540&pl=Solve']Type 154t = 1540[/URL] into the search engine, we get [B]t = 10.
[/B]
Check our work:
Jet distance = 231(10) = 2,310
Passenger plane distance = 385(10 - 4) = 385 * 6 = 2,310

A job pays $56 for 8 hours of work. how much money does the job pay per hour

A job pays $56 for 8 hours of work. how much money does the job pay per hour
Hourly Wage = Total Wages / Total Hours Worked
$56/8 = [B]$7 per hour[/B].

A large bag of candy contains 84 blue candies, 96 red candies, and 120 yellow candies. What percent

A large bag of candy contains 84 blue candies, 96 red candies, and 120 yellow candies. What percent of the candies are red?
[U]Calculate total candies:[/U]
Total Candies = Blue Candies + Red Candies + Yellow Candies
Total Candies = 84 + 96 + 120
Total Candies = 300
[U]Now calculate the red candy percentage:[/U]
Red Candy Percent = 100 * Red Candies / Total Candies
Red Candy Percent = 100 * 96 / 300
Red Candy Percent = 9600 / 300
Red Candy Percent = [B]32%[/B]

A large storage container is filled with 44.9 quarts of water. One quart of water is equivalent to 3

A large storage container is filled with 44.9 quarts of water. One quart of water is equivalent to 32 fluid ounces. How many fluid ounces of water are stored in the container? Round your answer to the nearest whole number.
44.9 quarts * 32 fluid ounce / quart = 1,436.8
if we found to the nearest whole number, we round up since 0.8 is greater than 0.5, so we get:
[B]1,437 fluid ounces[/B]

a laser printer prints 9 pages per minute. how long will it take to print 288 pages?

a laser printer prints 9 pages per minute. how long will it take to print 288 pages?
288 pages / 9 pages per minute = [B]32 minutes[/B]

A laundry basket contains 30 socks, of which 9 are black. What is the probability that a randomly s

A laundry basket contains 30 socks, of which 9 are black. What is the probability that a randomly selected sock will be black?
P(Black) = 9/30
Simplifying, we can divide top and bottom by 3:
[B]3/10
3/10 as a percentage is 30%[/B]

A luncheon for 14 guests cost $468.00. What was the average cost per guest?

A luncheon for 14 guests cost $468.00. What was the average cost per guest?
Average Cost per Guest = Total Cost / Number of Guests
Average Cost per Guest = $468 / 14
Average Cost per Guest = [B]$33.43[/B]

a machine has a first cost of 13000 an estimated life of 15 years and an estimated salvage value of

a machine has a first cost of 13000 an estimated life of 15 years and an estimated salvage value of 1000.what is the book value at the end of 9 years?
Using [URL='https://www.mathcelebrity.com/depsl.php?d=&a=13000&s=1000&n=15&t=9&bv=&pl=Calculate']our straight line depreciation calculator[/URL], we get a book value at time 9, B9 of:
[B]5,800[/B]

A mail courier charges a base fee of $4.95 plus $11.90 per package being delivered. If x represents

A mail courier charges a base fee of $4.95 plus $11.90 per package being delivered. If x represents the number of packages delivered, which of the following equations could be used to find y, the total cost of mailing packages?
Set up the cost function y = C(x)
[B]C(x) = 4.95 + 11.90x[/B]

A man bought a mobile phone for $800 and sold it for $1000. What was his profit as a percentage of t

A man bought a mobile phone for $800 and sold it for $1000. What was his profit as a percentage of the cost price
Calculate Profit:
Profit = Sales Price - Cost
Profit = 1000 - 800
Profit = 200
Calculate profit percentage:
Profit Percentage = Profit * 100 / Cost
Profit Percentage = 800 * 100 / 200
Profit Percentage = [B]400%[/B]

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add the

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add their ages is equal 100
Let the man's age be m. Let the wife's age be w. Let the daughter's age be d. We're given:
[LIST=1]
[*]m = w + 5
[*]d = 0.5m
[*]d + m + w = 100
[/LIST]
Rearrange equation 1 in terms of w my subtracting 5 from each side:
[LIST=1]
[*]w = m - 5
[*]d = 0.5m
[*]d + m + w = 100
[/LIST]
Substitute equation (1) and equation (2) into equation (3)
0.5m + m + m - 5 = 100
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.5m%2Bm%2Bm-5%3D100&pl=Solve']type this equation into our search engine[/URL] to solve for m and we get:
m = [B]42
[/B]
Now, substitute m = 42 into equation 2 to solve for d:
d = 0.5(42)
d = [B]21
[/B]
Now substitute m = 42 into equation 1 to solve for w:
w = 42 - 5
w = [B]37
[/B]
To summarize our ages:
[LIST]
[*]Man (m) = 42 years old
[*]Daughter (d) = 21 years old
[*]Wife (w) = 37 years old
[/LIST]

A man is four time as old as his son. How old is the man if the sum of their ages is 60?

A man is four time as old as his son. How old is the man if the sum of their ages is 60?
Let the son's age be a. Then the man's age is 4a.
If the sum of their ages is 60, we have:
a + 4a = 60
To solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B4a%3D60&pl=Solve']type it in our math engine[/URL] and we get:
a = 12
Therefore, the man's age is:
4(12) = [B]48[/B]

A man is four times as old as his son. In five years time he will be three times as old. Find their

A man is four times as old as his son. In five years time he will be three times as old. Find their present ages.
Let the man's age be m, and the son's age be s. We have:
[LIST=1]
[*]m = 4s
[*]m + 5 = 3(s + 5)
[/LIST]
Substitute (1) into (2)
4s + 5 = 3s + 15
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=4s%2B5%3D3s%2B15&pl=Solve']equation calculator[/URL], and we get [B]s = 10[/B].
m = 4(10)
[B]m = 40[/B]

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

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

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

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

a mans age (a) ten years ago

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

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

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

A mother gives birth to a 10 pound baby. Every 2 months, the baby gains 5 pounds. If x is the age o

A mother gives birth to a 10 pound baby. Every 2 months, the baby gains 5 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight.
If the baby gains 5 pounds every 2 months, then they gain 5/2 = 2.5 pounds per month. Let x be the number of months old for the baby, we have:
The baby starts at 10 pounds. And every month (x), the baby's weight increases 2.5 pounds. Our equation is:
[B]y = 2.5x + 10[/B]

A mother gives birth to a 6 pound baby. Every 4 months, the baby gains 4 pounds. If x is the age of

A mother gives birth to a 6 pound baby. Every 4 months, the baby gains 4 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx b that describes the baby's weight.
The baby gains 4 pounds every month, where x is the number of months since birth. The baby boy starts life (time 0) at 6 pounds. So we have
[B]y = 4x + 6[/B]

A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of

A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight.
Every month, the baby gains 2/3 of a pound. So we have:
[B]y = 2/3x + 7
[/B]
The baby starts off with 7 pounds. So we add 7 pounds + 2/3 times the number of months passed since birth.

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

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

A package of cookies cost $4.00 it has 20 cookies how much does each cookie cost?

A package of cookies cost $4.00 it has 20 cookies how much does each cookie cost?
We want the cost per cookie:
$4.00/20 cookies = [B]$0.20 or 20 cents per cookie[/B]

a package of soccer accessories costs $25 for cleats, $14 for shin guards , and $12 for a ball. Writ

a package of soccer accessories costs $25 for cleats, $14 for shin guards , and $12 for a ball. Write two equivalent expressions for the total cost of 9 accessory package. Then find the cost.
Let c be the number of cleats, s be the number of shin guards, and b be the number of balls. We have the following cost function for 9 accessory packages:
[B]9(25c + 14s + 12b)[/B]
But if we multiply through, we get an equivalent expression:
[B]225c + 126s + 108b[/B]

A package that is heavier than 11 lbs and 8 oz will have a label that says HEAVY on it. Gloria packe

A package that is heavier than 11 lbs and 8 oz will have a label that says HEAVY on it. Gloria packed 6 flowerpots to send to her customers. Each of the flowerpots weighs 1 lb and 12 oz. The packing material weighs 5 oz. Will her package be labeled as HEAVY?
Calculate weight of flowerpots:
Flowerpot weight = Weight per flowerpot * number of flowerpots
Flowerpot weight = 1 lb 12 oz * 6
Flowerpot weight = 6 lb and 72 oz
Since 72oz = 72/16 = 4 lbs and 8 oz, we have:
Flowerpot weight = 6 lb 8 oz + 4 lbs and 8 oz = 12 lb 16 oz
Since 16oz = 1 lb, we have:
13lb
Add in the 5 oz of packing material, we have:
13lb 5 oz
Since this is greater than 11lb 8oz, the package [B]will be labeled as HEAVY[/B]

A packing machine can package 236 first aid kit each hour. At this rate, find the number of first ai

A packing machine can package 236 first aid kit each hour. At this rate, find the number of first aid kit package in 24 hours
Total First Aid Kits = Kits Per Hour * Number of Hours
Total First Aid Kits = 236 * 24
Total First Aid Kits = [B]5,664[/B]

A parking garage charges $5 plus $2 per hour. You have $16 to spend for parking. How many hours can

A parking garage charges $5 plus $2 per hour. You have $16 to spend for parking. How many hours can you park?
Subtract the flat rate to get the amount you have for hourly parking:
16 - 5 = 11
So we divide 11 dollars to park by 2 dollars per hour to get:
11/2
[B]5.5 hours[/B]

A passenger train left station A at 6:00 P.M. Moving with the average speed 45 mph, it arrived at st

A passenger train left station A at 6:00 P.M. Moving with the average speed 45 mph, it arrived at station B at 10:00 p.m. A transit train left from station A 1 hour later than the passenger train, but it arrived at the station B at the same time with the passenger train. What was the average speed of the transit train?
[U]Passenger Train[/U]
[LIST]
[*]45 miles per hour and it got there in 4 hours.
[/LIST]
Using our formula D = rt where:
[LIST]
[*]D = Distance
[*]r = rate
[*]t = time
[/LIST]
[LIST]
[*]D = rt
[*]D = 45(4)
[*]D = 180 miles from Station A to Station B
[/LIST]
Transit Train
[LIST]
[*]It has to go the same distance, 180 miles, so D = 180
[*]It made it there in 3 hours. This is r
[*]We want to solve for t
[/LIST]
D = rt
180 = 3r
Divide each side by 3
[B]r = 60 miles per hour[/B]

A phone company charges a $30 usage fee $15 per 1GB of data. Write an expression that describes the

A phone company charges a $30 usage fee $15 per 1GB of data. Write an expression that describes the monthly charge and use d to represent data
We multiply gigabyte fee by d and add the usage fee:
[B]15d + 30[/B]

A piece of gym equipment which cost 450 including vat last year is now selling at 500 excluding vat.

A piece of gym equipment which cost 450 including vat last year is now selling at 500 excluding vat. Calculate the percentage increase.
Increase = (New Price - Old Price)/Old Price
Increase = (500-450)/450
50/450 = 0.1111
To get the percentage, multiply by 100
[B]11.11%[/B]

A postage stamp costs $0.42. How much would a roll of 100 stamps cost?

A postage stamp costs $0.42. How much would a roll of 100 stamps cost?
100 stamps = cost per stamp *100
100 stamps = 0.42 * 100
100 stamps = [B]$42[/B]

A printer can print 25 pages per minute. At this rate, how long will it take to print 2000 pages?

A printer can print 25 pages per minute. At this rate, how long will it take to print 2000 pages?
Let m be the number of minutes it takes to print 2,000 pages. We have the equation:
25m = 2000
[URL='https://www.mathcelebrity.com/1unk.php?num=25m%3D2000&pl=Solve']Type this equation into our search engine[/URL], and we get:
m = 80

A private high school charges $52,200 for tuition, but this figure is expected to rise 7% per year.

A private high school charges $52,200 for tuition, but this figure is expected to rise 7% per year. What will tuition be in 3 years?
We have the following appreciation equation A(y) where y is the number of years:
A(y) = Initial Balance * (1 + appreciation percentage)^ years
Appreciation percentage of 7% is written as 0.07, so we have:
A(3) = 52,200 * (1 + 0.07)^3
A(3) = 52,200 * (1.07)^3
A(3) = 52,200 * 1.225043
A(3) = [B]63,947.25[/B]

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

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

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

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

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

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

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

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

A real estate agency receives 3.5% commission on the first $100,000 of a sale and 2.25% on the remai

A real estate agency receives 3.5% commission on the first $100,000 of a sale and 2.25% on the remainder. How much commission is received on the sale of a $450,000 property?
Calculate commission on first $100,000 (Commission 1):
Commission 1 = $100,000 * 0.035
Commission 1 = $3,500
Calculate commission on the remainder (Commission 2):
Commission 2 = 0.025 * ($450,000 - $100,000)
Commission 2 = 0.025 * ($350,000)
Commission 2 = $8,750
Calculate Total Commission:
Total Commission = Commission 1 + Commission 2
Total Commission = $3,500 + $8,750
Total Commission = [B]$12,250[/B]

A real estate agent has $920 to spend on newspaper ads. Each ad costs $6. After buying as many ads a

A real estate agent has $920 to spend on newspaper ads. Each ad costs $6. After buying as many ads as she can afford, how much money will the real estate agent have left over?
We want to know the remainder of 920/6. We can type 920 mod 6 into our search engine and get:
[URL='https://www.mathcelebrity.com/modulus.php?num=920mod6&pl=Calculate+Modulus']920 mod 6[/URL] = [B]2[/B]

A real estate agent sells a house for $229,605. A sales commission of 6% is charged. The agent gets

A real estate agent sells a house for $229,605. A sales commission of 6% is charged. The agent gets 45% of this commission. How much money does the agent get?
The agents Commission (C) is:
C = Sale price * sales commission percent * agent commission percent
Since 6% = 0.06 and 45% = 0.45, we have:
C = 229605 * 0.06 * 0.45
C = [B]6,199.34[/B]

A recent survey showed that 44% of recent college graduates named flexible hours as their most desir

A recent survey showed that 44% of recent college graduates named flexible hours as their most desire employment benefit. In a graduating class of 870 college students, how many would you expect to rank flexible hours as their top priority in job benefits?
Using our [URL='http://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=44&den1=870&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percentage calculator[/URL], 44% of 870 = 382.8 ~ [B]383[/B]

A recent survey showed that 49% of recent college graduates named flexible hours as their most desir

A recent survey showed that 49% of recent college graduates named flexible hours as their most desire employment benefit. In a graduating class of 820 college students, how many would you expect to rank flexible hours as their top priority in job benefits?
49% of 820, using our [URL='http://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=49&den1=820&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percentage calculator[/URL], we get:
401.8 ~ [B]402[/B]

A restaurant chain sells 15,000 pizzas each month, and 70% of the pizzas are topped with pepperoni.

A restaurant chain sells 15,000 pizzas each month, and 70% of the pizzas are topped with pepperoni. Of these, 2/3 also have peppers. How many pizzas have pepperoni and peppers?
We multiply the pizzas sold by the percentage of pepperoni times the fraction of peppers. Since 70% is 7/10, we have:
Pizzas with pepperoni and peppers = 15,000 * 7/10 * 2/3
7/10 * 2/3 = 14/30. [URL='https://www.mathcelebrity.com/fraction.php?frac1=14%2F30&frac2=3%2F8&pl=Simplify']Using our fraction simplifier calculator[/URL], we can reduce this to 7/15
Pizzas with pepperoni and peppers = 15,000 * 7/15
Pizzas with pepperoni and peppers = [B]7,000[/B]

A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the am

A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount x (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period.
Let Sunday's earnings be s. With 3 days, we divide our sum of earnings for 3 days by 3 to get our 1,000 average, so we have:
(1073 + 1108 + s)/3 = 1000
Cross multiply:
1073 + 1108 + s = 1000 * 3
1073 + 1108 + s = 3000
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=1073%2B1108%2Bs%3D3000&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]819[/B]

A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment

A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $584. What was the simple interest rate of the bonds?
For simple interest, we have:
Balance * interest rate = Interest payment
8000i = 584
Divide each side of the equation by 8000 to isolate i:
8000i/8000 = 584/8000
Cancelling the 8000's on the left side, we get:
i = 0.073
Most times, interest rates are expressed as a percentage.
Percentage interest = Decimal interest * 100%
Percentage interest = 0.073 * 100%
Multiplying by 100 is the same as moving the decimal point two places right:
Percentage interest = [B]7.3%[/B]

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

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

A road construction team built a 114 mile road over a period of 19 months what was their average bui

A road construction team built a 114 mile road over a period of 19 months what was their average building distance per a month
Average building distance = miles built / months of building
Average building distance = 114/19
Average building distance = [B]6 miles per month[/B]

A salesperson earns a commission of $364 for selling $2600 in merchandise. Find the commission rate.

A salesperson earns a commission of $364 for selling $2600 in merchandise. Find the commission rate. Write your answer as a percentage.
Commission percentage = Commission Amount / Sales Price
Commission percentage = 364 / 2600
Commission percentage = 0.14
Multiply by 100 to get the percentage:
0.14 * 100 = [B]14%[/B]

A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is

A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $24. Option B is a commission rate of 4% on weekly sales. How much does he need to sell this week to earn the same amount with the two options?
Option A payment function:
24h
With a 40 hour week, we have:
24 * 40 = 960
Option B payment function with sales amount (s):
0.04s
We want to know the amount of sales (s) where Option A at 40 hours = Option B. So we set both equal to each other:
0.04s = 960
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.04s%3D960&pl=Solve']type it in our math engine[/URL] and we get:
s = [B]24,000[/B]

a school 220 grade 9 students. 140of those students are female. what percentage of grade 9 students

a school 220 grade 9 students. 140of those students are female. what percentage of grade 9 students are female
We want [URL='https://www.mathcelebrity.com/perc.php?num=140&den=220&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']140/220 as a percent[/URL] = [B]63.64%[/B]

A ship is traveling at an average velocity of 28 miles per hour. How far will the ship travel in two

A ship is traveling at an average velocity of 28 miles per hour. How far will the ship travel in two days?
28 miles/1 hour * 24 hours/1 day * 2 days
28 * 24 * 2 = [B]1,344 miles[/B]

A shipping service charges $0.43 for the first ounce and $0.29 for each additional ounce of package

A shipping service charges $0.43 for the first ounce and $0.29 for each additional ounce of package weight. Write an equation to represent the price P of shipping a package that weighs x ounces, for any whole number of ounces greater than or equal to 1.
Set up the price function P(x)
[B]P(x) = 0.43 + 0.29(x - 1)[/B]

A shopkeeper buys a box of 20 cans of cola for $10. He sells the cans for 65 cents each. Work out hi

A shopkeeper buys a box of 20 cans of cola for $10. He sells the cans for 65 cents each. Work out his percentage profit.
[U]Calculate Revenue[/U]
Revenue = Sale price per can * number of cans
Revenue = 0.65 * 20
Revenue = 13
[U]Calculate Profit given a cost of $10:[/U]
Profit = Revenue - Cost
Profit = 13 - 10
Profit = 3
[U]Calculate Percentage Profit:[/U]
Percentage Profit = Profit/Revenue * 100%
Percentage Profit = 3/13 * 100%
Percentage Profit = 0.23076923076 * 100%
Percentage Profit = [B]23.08%[/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]

A sprinter runs 400 meters in 54 seconds. What is the runners average running rate in meters per sec

A sprinter runs 400 meters in 54 seconds. What is the runners average running rate in meters per second?
400 meters/54 seconds = [B]7.407 meters per second[/B].

A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. What is

A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. What is the height of the box?
The volume of the box is l x w x h. We're given l and w = 4. So we want height:
56 = 4 x 4 x h
16h = 56
[URL='https://www.mathcelebrity.com/1unk.php?num=16h%3D56&pl=Solve']Type this equation into our search engine[/URL] and we get:
h = [B]3.5[/B]

A store manager must calculate the total number of winter hats available to sell in the store from a

A store manager must calculate the total number of winter hats available to sell in the store from a starting number of 293. In the past month, the store sold 43 blue hats, 96 black hats, 28 red hats, and 61 pink hats. The store received a shipment of 48 blue hats, 60 black hats, 18 red hats, and 24 pink hats. How many total hats does the store have for sale?
[LIST=1]
[*]We start with 293 hats
[*]We calculate the hats sold: (43 + 96 + 28 + 61) = 228
[*]We subtract Step 2 from Step 1 to get remaining hats before the shipment: 293 - 228 = 65
[*]Now we calculate the number of hats received in the shipment: (48 + 60 + 18 + 24) = 150
[*]We add Step 4 to Step 3: 65 + 150 = [B]215 hats for sale[/B]
[/LIST]

A student has an average mark of 68 from 10 tests. What mark must be gained in the next test to rais

A student has an average mark of 68 from 10 tests. What mark must be gained in the next test to raise their average to 70?
This is a missing average problem. We use our [URL='http://www.mathcelebrity.com/missingaverage.php?num=68%2C68%2C68%2C68%2C68%2C68%2C68%2C68%2C68%2C68&avg=70&pl=Calculate+Missing+Score']missing average calculator[/URL].
The student's next score must be a [B]90[/B].

A student walks 1500 meters to school in 30 minutes. What is their average speed in meters per minut

A student walks 1500 meters to school in 30 minutes. What is their average speed in meters per minute?
1500 meters / 30 minutes
Divide top and bottom by 30
[B]50 meters / minute[/B]

A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand A aspirin. How many

A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand A aspirin. How many doctors use brand A aspirin?
We want 3/5 of 2000. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=2000&frac2=3/5&pl=Multiply']type this expression into our search engine[/URL] and we get:
[B]1,200[/B]

A taxi cab in nyc charges a pick up fee of $5.00 . The customer must also pay $2.59 for each mile th

A taxi cab in nyc charges a pick up fee of $5.00 . The customer must also pay $2.59 for each mile that the taxi must drive to reach their destination. Write an equation
Set up a cost function C(m) where m is the number of miles:
C(m) = Mileage Charge * m + pick up fee
[B]C(m) = 2.59m + 5[/B]

A teacher assumed that the average of grades for a math test was 80. Imagine 20 students took the te

A teacher assumed that the average of grades for a math test was 80. Imagine 20 students took the test and the 95% confidence interval of grades was (83, 90). Can you reject the teacher's assumption?
a. Yes
b. No
c. We cannot tell from the given information
[B]a. Yes[/B]
[I]At the 0.05 significance level, yes since 80 is not in the confidence interval.[/I]

A text message plan costs $7 per month plus $0.28 per text. Find the monthly cost for x text message

A text message plan costs $7 per month plus $0.28 per text. Find the monthly cost for x text messages.
We set up the cost function C(x) where x is the number of text messages per month:
C(x) = Cost per text * x + Monthly cost
Plugging in our given numbers, we get:
[B]C(x) = 0.28x + 7[/B]

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

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

A truck driver took 7 hours and 45 minutes to travel 426.25 miles. What was the average speed of the

A truck driver took 7 hours and 45 minutes to travel 426.25 miles. What was the average speed of the truck driver?
45/60 = 0.75 of an hour
7 hours and 45 minutes = 7.75 hours
426.25 miles / 7.75 hours miles = [B]55 miles per hour[/B]

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

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

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

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

A typist is paid a basic wage of $22.50 per hour for a 40-hour week. Calculate the typist's basic we

A typist is paid a basic wage of $22.50 per hour for a 40-hour week. Calculate the typist's basic weekly wage
Basic Weekly Wage = Hourly Rate * Hours Worked
Basic Weekly Wage = $22.50 * 40
Basic Weekly Wage = [B]$900[/B]

A virus is spreading exponentially. The initial amount of people infected is 40 and is increasing at

A virus is spreading exponentially. The initial amount of people infected is 40 and is increasing at a rate of 5% per day. How many people will be infected with the virus after 12 days?
We have an exponential growth equation below V(d) where d is the amount of days, g is the growth percentage, and V(0) is the initial infected people:
V(d) = V(0) * (1 + g/100)^d
Plugging in our numbers, we get:
V(12) = 40 * (1 + 5/100)^12
V(12) = 40 * 1.05^12
V(12) = 40 * 1.79585632602
V(12) = 71.8342530409 or [B]71[/B]

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

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

A woman earns $2400 per month and budgets $480 per month for food. What percent of her monthly incom

A woman earns $2400 per month and budgets $480 per month for food. What percent of her monthly income is spent on food?
480/2400 using our [URL='http://www.mathcelebrity.com/perc.php?num=480&den=2400&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']percentage calculator[/URL] is [B]20%[/B].

A woman is one-half as old as her mother. The sum of their ages is 75. What are their ages?

A woman is one-half as old as her mother. The sum of their ages is 75. What are their ages?
Let the woman's age be w.
Let the mother's age be m.
We're given two equations:
[LIST=1]
[*]w = m/2
[*]m + w = 75
[/LIST]
Substitute equation (1) into equation (2) for w:
m + m/2 = 75
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%2F2%3D75&pl=Solve']type this equation into our search engine [/URL]and we get:
m = [B]50
[/B]
To solve for w, we plug m = 50 into equation (1):
w = 50/2
w = [B]25[/B]

a writer can write a novel at a rate of 3 pages per 5 hour work. if he wants to finish the novel in

a writer can write a novel at a rate of 3 pages per 5 hour work. if he wants to finish the novel in x number of pages, determine a function model that will represent the accumulated writing hours to finish his novel
if 3 pages = 5 hours, then we divide each side by 3 to get:
1 page = 5/3 hours per page
So x pages takes:
5x/3 hours
Our function for number of pages x is:
[B]f(x) = 5x/3[/B]

Aaron bought a bagel and 3 muffins for $7.25. Bea bought a bagel and 2 muffins for $6. How much is b

Aaron bought a bagel and 3 muffins for $7.25. Bea bought a bagel and 2 muffins for $6. How much is bagel and how much is a muffin?
Let b be the number of bagels and m be the number of muffins. We have two equations:
[LIST=1]
[*]b + 3m = 7.25
[*]b + 2m = 6
[/LIST]
Subtract (2) from (1)
[B]m = 1.25
[/B]
Plug this into (2), we have:
b + 2(1.25) = 6
b + 2.5 = 6
Subtract 2.5 from each side
[B]b = 3.5[/B]

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

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

Age Difference

Determines the ages for an age difference word problem.

Age now and then

I brute forced this and got a wrong answer, logic tells me is right. I tried the calculator here but maybe messed up the equation using another users problem as an example. Having no luck.
Problem:
Jacob is 4 times the age of Clinton. 8 years ago Jacob was 9 times the age of Clinton. How old are they now and how old were they 8 years ago?

Age now and then

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

Age now and then

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

Age now and then

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

Age now problems

The age of the older of the two boys is twice that of the younger. 5 years ago it was three times that of the younger. Find the age of each

Age now problems

Age of the older boy is o, younger boy is y. We have the following equations:
[LIST=1]
[*]o = 2y
[*]o - 5 = 3(y - 5)
[/LIST]
Plug (1) into (2)
(2y) - 5 = 3y - 15
Plug this into our [URL='http://www.mathcelebrity.com/1unk.php?num=2y-5%3D3y-15&pl=Solve']equation solver[/URL], we get:
[B]y = 10[/B]
Plug that into (1), we get: o = 2(10), [B]o = 20[/B]

Age now problems

A father is three times as old as the son, and the daughter is 3 years younger than the son. If the sum of their ages 3 years ago was 63
Find the present age of the father

Age now problems

Let f be the age of the father and d be the age of the daughter and s be the age of the son. We have:
[LIST=1]
[*]f = 3s
[*]d = s - 3
[*]d - 3 + f - 3 + s - 3 = 63
[/LIST]
Simplify (3)
d + f + s - 9 = 63
d + f + s = 72
Now, substitute (1) and (2) into the modified (3)
(s - 3) + 3s + s = 72
Combine like terms:
5s - 3 = 72
Add 3 to each side
5s = 75
Divide each side by 5
s = 15
We want f, so we substitute s = 15 into (1)
f = 3(15)
[B]f = 45[/B]

Age Word Problems

Determines age in age word problems

Ages are consecutive integers. The sum of ages are 111. What are the ages

Ages are consecutive integers. The sum of ages are 111. What are the ages
In the search engine, we type [I][URL='http://www.mathcelebrity.com/consecintwp.php?num=111&pl=Sum']sum of 2 consecutive integers is 111[/URL][/I].
We get [B]55 and 56[/B].

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

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

Ali needs to make a total of 90 deliveries this week. So far he has completed 72 of them. What perce

Ali needs to make a total of 90 deliveries this week. So far he has completed 72 of them. What percentage of his total deliveries has Ali completed
[URL='https://www.mathcelebrity.com/perc.php?num=72&den=90&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']Enter 72/90 into our search engine and choose the percentage option[/URL] and we get [B]80%[/B].

Ali spent $60 at the grocery store. Of this amount, he spent $51 on fruit. What percentage of the to

Ali spent $60 at the grocery store. Of this amount, he spent $51 on fruit. What percentage of the total did he spend on fruit?
51/60 = 0.85
Multiply 0.85 by 100 to get the percentage
0.85 * 100 = [B]85%[/B]

Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the siste

Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara?
Let a be Alice's age, b be Barbara's age, and c be Carol's age. We have 3 given equations:
[LIST=1]
[*]a = b - 3
[*]b = c - 5
[*]a + b + c = 68
[/LIST]
Rearrange (2)
c = b + 5
Now plug in (1) and (2) revised into (3). We want to isolate for b.
a + b + c = 68
(b - 3) + b + (b + 5) = 68
Combine like terms:
(b + b + b) + (5 - 3) = 68
3b + 2 = 68
Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=3b%2B2%3D68&pl=Solve']equation calculator[/URL], and we get b = [B]22[/B]

Alice is a machinist in a shirt factory. For the first 180 shirts she is paid $2.20 and then $2.90 p

Alice is a machinist in a shirt factory. For the first 180 shirts she is paid $2.20 and then $2.90 per garment thereafter. What are her gross wages for a week in which she produces 240 shirts?
Calculate commission on the first 180 shirts (Commission 1):
Commission 1 = Shirts (up to 180) * $2.20
Commission 1 = 180 * $2.20
Commission 1 = $396
Calculate commission on the rest of the shirts about 180 (Commission 2):
Commission 2 = Shirts Above 180 * $2.90
Commission 2 = (240 - 180) * $2.90
Commission 2 = 60 * $2.90
Commission 2 = $174
Calculate Total Commission:
Total Commission = Commission 1 + Commission 2
Total Commission = $396 + $174
Total Commission = [B]$570[/B]

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

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

Alvin is 12 years younger than Elga. The sum of their ages is 60 . What is Elgas age?

Alvin is 12 years younger than Elga. The sum of their ages is 60 . What is Elgas age?
Let a be Alvin's age and e be Elga's age. We have the following equations:
[LIST=1]
[*]a = e - 12
[*]a + e = 60
[/LIST]
Plugging in (1) to (2), we get:
(e - 12) + e = 60
Grouping like terms:
2e - 12 = 60
Add 12 to each side:
2e = 72
Divide each side by 2
[B]e = 36[/B]

Alvin is 34 years younger than Elga. Elga is 3 times older than Alvin. What is Elgas age?

Alvin is 34 years younger than Elga. Elga is 3 times older than Alvin. What is Elgas age?
Let a be Alvin's age. Let e be Elga's age. We're given:
[LIST=1]
[*]a = e - 34
[*]e = 3a
[/LIST]
Substitute (2) into (1):
a = 3a - 34
[URL='https://www.mathcelebrity.com/1unk.php?num=a%3D3a-34&pl=Solve']Typing this equation into the search engine[/URL], we get
a = 17
Subtitute this into Equation (2):
e = 3(17)
e = [B]51[/B]

Alya loves to read. She reads 90 pages in half an hour. How many pages does she read per minute?

Alya loves to read. She reads 90 pages in half an hour. How many pages does she read per minute?
Set up a proportion of pages to minutes. Since 30 minutes is a half hour, we have the number of pages (p) for 1 minute as:
90/30 = p/1
To solve this proportion for p, [URL='https://www.mathcelebrity.com/prop.php?num1=90&num2=p&den1=30&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
p = [B]3[/B]

An Amazon delivery package receives a bonus if he delivers a package to a costumer in 20 minutes plu

An Amazon delivery package receives a bonus if he delivers a package to a costumer in 20 minutes plus or minus 5 minutes. Which inequality or equation represents the drivers allotted time (x) to receive a bonus
20 plus 5 minutes = 25 minutes
20 minus 5 minutes = 15 minutes
So we have the inequality:
[B]15 <= x <= 25[/B]

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

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

An elevator can hold less than 2700 pounds of extra weight. If an average person weighs 150 pounds,

An elevator can hold less than 2700 pounds of extra weight. If an average person weighs 150 pounds, what is the maximum number of people (p) that can be on the elevator at one time?
Total weight = average weight per person * Number of people
Total weight = 150p
We know from the problem that:
150p < 2700
We want to solve this inequality for p. Divide each side of the inequality by 150:
150p/150 < 2700/150
Cancel the 150's on the left side and we get:
p < [B]18[/B]

An elevator can safely lift at most 4400 1bs. A concrete block has an average weight of 41 lbs. What

An elevator can safely lift at most 4400 1bs. A concrete block has an average weight of 41 lbs. What is the maximum number of concrete blocks that the elevator can lift?
Total blocks liftable = Lift Max / Weight per block
Total blocks liftable = 4400 / 41
Total blocks liftable = 107.31
We round down to whole blocks and we get [B]107[/B]

An item cost $370 before tax, and the sales tax is 25.90 what is the percentage?

An item cost $370 before tax, and the sales tax is 25.90 what is the percentage?
Sales Tax = Tax Amount/Original Bill
Sales Tax = 25.90/370
Sales Tax = 0.07
Multiply by 100 to convert to a percent, we have[B] 7%[/B]

An item costs $470 before tax, and the sales tax is $14.10. Find the sales tax rate. Write your answ

An item costs $470 before tax, and the sales tax is $14.10. Find the sales tax rate. Write your answer as a percentage.
Sales Tax Percent = 100% * Sales Tax / Before Tax Amount
Sales Tax Percent = 100% * 14.10 / 470
Sales Tax Percent = 100% * 0.03
Sales Tax Percent = [B]3%[/B]

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

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

Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Ke

Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Kenny buys 1 software package and 1 month of game play. Each software package costs $25. If their total cost is $155, what is the cost of one month of game play.
Let s be the cost of software packages and m be the months of game play. We have:
[LIST]
[*]Angie: 2s + 4m
[*]Kenny: s + m
[/LIST]
We are given each software package costs $25. So the revised equations above become:
[LIST]
[*]Angie: 2(25) + 4m = 50 + 4m
[*]Kenny: 25 + m
[/LIST]
Finally, we are told their combined cost is 155. So we add Angie and Kenny's costs together:
4m + 50 + 25 + m = 155
Combine like terms:
5m + 75 = 155
[URL='http://www.mathcelebrity.com/1unk.php?num=5m%2B75%3D155&pl=Solve']Typing this into our search engine[/URL], we get [B]m = 16[/B]

Angie is 11, which is 3 years younger than 4 times her sister's age.

Angie is 11, which is 3 years younger than 4 times her sister's age.
Let her sister's age be a. We're given the following equation:
4a - 3 = 11
To solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=4a-3%3D11&pl=Solve']type this equation into our math engine[/URL] and we get:
[B]a = 3.5[/B]

Anita read 150 pages in 5 hours. What is her reading rate in pages per minute?

Anita read 150 pages in 5 hours. What is her reading rate in pages per minute?
150 pages / 5 hours
Divide top and bottom by 5:
150/5 = 30
5/5 = 1
So we have 30 pages per hour
And 1 hour is 60 minutes, so we have:
(30 pages / 1 hour) * (1 hour / 60 minutes)
30 pages / 60 minutes
[B]0.5 pages per minute[/B]

Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a t

Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of $5 Ann paid a total of $49.10.
Set up the cost function C(m) where m is the number of miles:
C(m) = Mileage Rate x m + Tip
2.10m + 5 = 49.10
[URL='https://www.mathcelebrity.com/1unk.php?num=2.10m%2B5%3D49.10&pl=Solve']Type 2.10m + 5 = 49.10 into the search engine[/URL], and we get [B]m = 21[/B].

Anna’s age increased by 3 times her age, the result is 72

Anna’s age increased by 3 times her age, the result is 72.
Let a be Anna's age. We have:
a + 3a = 72
Combine like terms:
(1 + 3)a = 72
4a = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=4a%3D72&pl=Solve']Type 4a = 72 into our calculator[/URL], and we get [B]a = 18[/B].

Another one...

Page 43 here, but switch q and r:
[URL]http://people.math.gatech.edu/~ecroot/2406_2012/basic_logic.pdf[/URL]

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We are engaged in the production of registered TOEFL, IELTS, ESOL, CELTA / DELTA and other English certificates.
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Arnie bought some bagels at 20 cents each. He ate 4, and sold the rest at 30 cents each. His profit

Arnie bought some bagels at 20 cents each. He ate 4, and sold the rest at 30 cents each. His profit was $2.40. How many bagels did he buy?
Let x be the number of bagels Arnie sold. We have the following equation:
0.30(x - 4) - 0.20(4) = 2.40
Distribute and simplify:
0.30x - 1.20 - 0.8 = 2.40
Combine like terms:
0.30x - 2 = 2.40
Add 2 to each side:
0.30x = 4.40
Divide each side by 0.3
[B]x = 14.67 ~ 15[/B]

Arvin is twice as old as Cory. The sum of their ages is 42. What are their ages?

Arvin is twice as old as Cory. The sum of their ages is 42. What are their ages?
Let Arvin's age be a. Let Cory's age be c. We're given two equations:
[LIST=1]
[*]a = 2c
[*]a + c = 42
[/LIST]
Plug equation (1) into equation (2):
2c + c = 42
[URL='https://www.mathcelebrity.com/1unk.php?num=2c%2Bc%3D42&pl=Solve']Plug this into our search engine[/URL] and we get:
[B]c = 14[/B]
Now, we plug c = 14 into equation 1 to solve for a:
a = 2(14)
[B]a = 28[/B]

Ashley age is 2 times Johns age. The sum of their ages is 63. What is Johns age?

Ashley age is 2 times Johns age. The sum of their ages is 63. What is Johns age?
Let Ashley's age be a.
Let John's age be j.
We have two equations:
[LIST=1]
[*]a = 2j
[*]a + j = 63
[/LIST]
Now substitute (1) into (2)
(2j) + j = 63
Combine like terms:
3j = 63
[URL='http://www.mathcelebrity.com/1unk.php?num=3j%3D63&pl=Solve']Typing 3j = 63 into our search engine[/URL], we get
[B]j = 21[/B]

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

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

At 2:18 Pm, a parachutist is 4900 feet above the ground. At 2:32 pm, the parachutist is 2100 above t

At 2:18 Pm, a parachutist is 4900 feet above the ground. At 2:32 pm, the parachutist is 2100 above the ground. Find the average rate of change in feet per minute
Average Rate of Change = Change in Distance / Change in time
Average Rate of Change = (4900 - 2100) / (2:32 - 2:18)
Average Rate of Change = 2800 / 14
Average Rate of Change = [B]200 feet per minute[/B]

at 9:30am you enter a parking garage. It cost $3.25 for each hour to park your car. You leave the ga

at 9:30am you enter a parking garage. It cost $3.25 for each hour to park your car. You leave the garage at 2:00pm. How much does it cost to park?
[U]Calculate Hours:[/U]
9:30 am to 10:00 am is 0.5 hours
10 am to 2 pm is 4 hours
So our total time is 4.5 hours
[U]Calculate Total Cost[/U]
Total Cost = Hours * Cost per hour
Total Cost = 4.5 * 3.25
Total Cost = [B]$14.63[/B]

At a certain university, 60% of the students enrolled in a math course, 50% are enrolled in an Engli

At a certain university, 60% of the students enrolled in a math course, 50% are enrolled in an English course, and 40% are enrolled in both. What percentage of the students are enrolled in an English course and/or a math course?
Let M be a math course, E be an english course, We are given:
[LIST]
[*]P(M) = 0.6
[*]P(E) = 0.5
[*]P(E AND M) = 0.4
[*]We want P(E U M)
[/LIST]
Using [URL='http://www.mathcelebrity.com/probunion2.php?pa=0.6+&pb=+0.5&paintb=+0.4&aub=+&pl=Calculate']two event probability[/URL], we get [B]P(E U M) = 0.7[/B]

At a concert, 20% of the audience members were teenagers. If the number of teenagers at the concert

At a concert, 20% of the audience members were teenagers. If the number of teenagers at the concert was 360, what was the total number of audience members?
We're looking for total audience members where [I]20% of what equals 360[/I]?
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=360&pct1=20&pcheck=2&pct2=+70&den1=+80&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Type this expression into our search engine[/URL] and we get:
Audience = [B]1,800[/B]

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

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

At Priscilla's school, the final grade for her Calculus course is weighted as follows: Tests: 50% Qu

At Priscilla's school, the final grade for her Calculus course is weighted as follows: Tests: 50% Quizzes: 30% Homework: 20% Priscilla has an average of 87% on her tests, 100% on her quizzes, and 20% on her homework. What is Priscilla's weighted average?
Weighted Average gives weights to each percent of the average as follows:
Weighted Average = Average * weighting percent
Weighted Average = Test Average * Test Weighting + Quiz Average. * Quiz Weighting + Homework Average * Homework Weighting
Weighted Average = 87% * 50% + 100% * 30% + 20% * 20%
Weighted Average = 43.5% + 30% + 4%
Weighted Average = [B]77.5%[/B]

At what simple interest rate will 4500$ amount to 8000$ in 5 years?

At what simple interest rate will 4500$ amount to 8000$ in 5 years?
Simple Interest is written as 1 + it.
With t = 5, we have:
4500(1 + 5i) = 8000
Divide each side by 4500
1 + 5i = 1.77777778
Subtract 1 from each side:
5i = 0.77777778
Divide each side by 5
i = 0.15555
As a percentage we multiply by 100 to get [B]15.5%[/B]

Ava is 4 times as old as Peter. What equation can be used to find Peter’s age?

Ava is 4 times as old as Peter. What equation can be used to find Peter’s age?
[U]Assumptions[/U]
Let a be Ava's age
Let p be Peter's age
We're given:
a = 4p
To find Peter's age, we divide each side of the equation by 4 to get:
a/4 = 4p/4
p = [B]a/4[/B]

average of 16 and x is three. find x

average of 16 and x is three. find x
Average of 16 and x is written as:
(16 + x)/2
We set this equal to 3:
(16 + x)/2 = 3
Cross multiply;
x + 16 = 6
[URL='https://www.mathcelebrity.com/1unk.php?num=x%2B16%3D6&pl=Solve']Type this equation into our search engine[/URL] and we get:
x = [B]-10[/B]

Basal Metabolic Rate (BMR)

Given a gender, an age, and a height/weight in inches/pounds or meters/kilograms, this will calculate the Basal Metabolic Rate (BMR)

Basic Statistics

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

Expected Value

Mean = μ

Variance = σ^{2}

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

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

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Expected Value

Mean = μ

Variance = σ

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

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

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Ben is 3 times as old as Daniel and is also 4 years older than Daniel.

Ben is 3 times as old as Daniel and is also 4 years older than Daniel.
Let Ben's age be b, let Daniel's age by d. We're given:
[LIST=1]
[*]b = 3d
[*]b = d + 4
[/LIST]
Substitute (1) into (2)
3d = d + 4
[URL='https://www.mathcelebrity.com/1unk.php?num=3d%3Dd%2B4&pl=Solve']Type this equation into our search engine[/URL], and we get [B]d = 2[/B].
Substitute this into equation (1), and we get:
b = 3(2)
[B]b = 6
[/B]
So Daniel is 2 years old and Ben is 6 years old.

Ben is 4 times as old as Ishaan and is also 6 years older than Ishaan.

Ben is 4 times as old as Ishaan and is also 6 years older than Ishaan.
Let b be Ben's age and i be Ishaan's age. We're given:
[LIST=1]
[*]b = 4i
[*]b = i + 6
[/LIST]
Set (1) and (2) equal to each other:
4i = i + 6
[URL='https://www.mathcelebrity.com/1unk.php?num=4i%3Di%2B6&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]i = 2[/B]
Substitute this into equation (1):
b = 4(2)
[B]b = 8
[/B]
[I]Therefore, Ishaan is 2 years old and Ben is 8 years old.[/I]

Beth is 5 years younger than celeste. Next year, their ages will have a sum equal to 57. How old is

Beth is 5 years younger than celeste. Next year, their ages will have a sum equal to 57. How old is each now?
Let b = Beth's age
Let c = Celeste's age
We are given:
[LIST=1]
[*]b = c - 5
[*]b + 1 + c + 1 = 57
[/LIST]
Substitute (1) into (2)
(c - 5) + 1 + c + 1 = 57
Group like terms:
2c - 3 = 57
[URL='https://www.mathcelebrity.com/1unk.php?num=2c-3%3D57&pl=Solve']Type 2c - 3 = 57 into our search engine[/URL], we get [B]c = 30[/B]
Substitute c = 30 into Equation (1), we get:
b = 30 - 5
[B]b = 25
[/B]
Therefore, Beth is 25 and Celeste is 30.

Binomial Option Pricing Model

This shows all 2^{t} scenarios for a stock option price on a binomial tree using (u) as an uptick percentage and (d) as a downtick percentage

Blake and Tatsu are each assigned a paper for a class they share. Blake decides to write 4 pages at

Blake and Tatsu are each assigned a paper for a class they share. Blake decides to write 4 pages at a time while Tatsu decides to write 7 pages at a time. If they end up writing the same number of pages, what is the smallest number of pages that the papers could have had?
We want the least common multiple of 4 and 7, written as LCM(4, 7). Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=7&num3=&pl=LCM']LCM Calculator[/URL], we get:
LCM(4, 7) = [B]28 pages[/B]

Blake writes 4 pages per hour. How many hours will Blake have to spend writing this week in order to

Blake writes 4 pages per hour. How many hours will Blake have to spend writing this week in order to have written a total of 16 pages?
[U]Let x = the number of hours Blake needs to write[/U]
4 pages per hour * x hours = 16
[U]Divide each side by 4[/U]
[B]x = 4 hours[/B]

Bob finished reading his book in x days. Each day, he read 4 pages. His book has 28 pages

Bob finished reading his book in x days. Each day, he read 4 pages. His book has 28 pages
Our equation for this is found by multiplying pages per day times number of days;
4x = 28
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3D28&pl=Solve']we type the equation into our search engine[/URL] and we get:
x = [B]7[/B]

Bob is twice as old as Henry. The sum of their ages is 42. How old is Henry?

Bob is twice as old as Henry. The sum of their ages is 42. How old is Henry?
Let Bob's age be b. Let Henry's age be h. We're given two equations:
[LIST=1]
[*]b = 2h
[*]b + h = 42
[/LIST]
Substitute b = 2h in equation 1 into equation 2 for b:
2h + h = 42
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2h%2Bh%3D42&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]14[/B]

Braille Translator

Given a phrase with letters, numbers, and most punctuation symbols, the calculator will perform the following duties:

1) Translate that phrase to Braille

2) Calculate the number of dots in the message

3) Calculate the number of empty spaces in the message

1) Translate that phrase to Braille

2) Calculate the number of dots in the message

3) Calculate the number of empty spaces in the message

Brian's age is 3/4 of Marcus'. The sum of their ages is 14. How old are Marcus and Brian?

Brian's age is 3/4 of Marcus'. The sum of their ages is 14. How old are Marcus and Brian?
Let Marcus's age be m.
Then Brian's age = 3/4m
The sum is:
m + 3m/4 = 14
Combine like terms
7m/4 = 14
Cross multiply:
7m = 56
[URL='http://www.mathcelebrity.com/1unk.php?num=7m%3D56&pl=Solve']Plugging this into the search engine[/URL], we get m = 8.
So Brian's age = 3(8)/4 = 24/4 = 6

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

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

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

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

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

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

Capitalized Cost and Periodic Charge

Given an Asset Value (A), a Salvage Value (S) at time (N), a sinking fund rate of (j), an effective rate of interest (i), and maintenance expense (M), this calculator solves for periodic charge (H) and capitalized cost (K)

Carlos age increased by is 16 is 62

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

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
Let m be the number of months. We have the pages written function P(m) as:
P(m) = 12m + 35
The problem asks for P(5):
P(5) = 12(5) + 35
P(5) = 60 + 35
P(5) = [B]95[/B]

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month unti

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
Set up the equation where m is the number of months:
pages per month * m + pages written already
12m + 35
The problems asks for m = 5:
12(5) + 35
60 + 35
[B]95 pages[/B]

Carol gets 5 each week for allowance. She saves 1 of her allowance. What percent of her allowance do

Carol gets 5 each week for allowance. She saves 1 of her allowance. What percent of her allowance does carol save?
[U]Calculate the decimal:[/U]
1/5 = 0.2
[U]Convert the decimal to a percentage[/U]
Percentage = Decimal * 100
Percentage = 100 * 0.2
[B]20%[/B]

Casey is 26 years old. Her daughter Chloe is 4 years old. In how many years will Casey be double her

Casey is 26 years old. Her daughter Chloe is 4 years old. In how many years will Casey be double her daughter's age
Declare variables for each age:
[LIST]
[*]Let Casey's age be c
[*]Let her daughter's age be d
[*]Let n be the number of years from now where Casey will be double her daughter's age
[/LIST]
We're told that:
26 + n = 2(4 + n)
26 + n = 8 + 2n
Solve for [I]n[/I] in the equation 26 + n = 8 + 2n
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables n and 2n. To do that, we subtract 2n from both sides
n + 26 - 2n = 2n + 8 - 2n
[SIZE=5][B]Step 2: Cancel 2n on the right side:[/B][/SIZE]
-n + 26 = 8
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 26 and 8. To do that, we subtract 26 from both sides
-n + 26 - 26 = 8 - 26
[SIZE=5][B]Step 4: Cancel 26 on the left side:[/B][/SIZE]
-n = -18
[SIZE=5][B]Step 5: Divide each side of the equation by -1[/B][/SIZE]
-1n/-1 = -18/-1
n = [B]18[/B]
Check our work for n = 18:
26 + 18 ? 8 + 2(18)
44 ? 8 + 36
44 = 44

CHEBYSHEVS THEOREM TELLS US THAT WHAT PERCENTAGE LIES BETWEEN 2.25 STANDARD DEVIATIONS?

CHEBYSHEVS THEOREM TELLS US THAT WHAT PERCENTAGE LIES BETWEEN 2.25 STANDARD DEVIATIONS?
Using our [URL='http://www.mathcelebrity.com/chebyshev.php?pl=probability&k=2.25&probk=0.75']Chebyshevs Theorem calculator[/URL], we get:
P(X - u| < k?) >= [B]0.802469[/B]

cheryl scores 68 out of 80 on her science test, nadia scores 86 out of 120 on her science test and a

cheryl scores 68 out of 80 on her science test, nadia scores 86 out of 120 on her science test and ali scores 120 out of 150 on her science test. who preforms the best in his/her science test
Cheryl: [URL='https://www.mathcelebrity.com/perc.php?num=68&den=80&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']68/80[/URL] = 85%
Nadia: [URL='https://www.mathcelebrity.com/perc.php?num=86&den=120&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&pof1=&pof2=&pl=Calculate']86/120[/URL] = 71.67%
Ali: [URL='https://www.mathcelebrity.com/perc.php?num=+120&den=+150&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&pof1=&pof2=&pl=Calculate']120/150[/URL] = 80%
[B]Cheryl[/B] has the highest percentage, so she did the best on her test.

Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse i

Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse is 6 years older than Alex. The sum of their ages is 31 years. How old is each one of them?
Set up the relational equations where a = Alex's age, c = Chris's aged and j = Jesse's age
[LIST=1]
[*]a = c + 5
[*]j = a + 6
[*]a + c + j = 31
[*]Rearrange (1) in terms of c: c = a - 5
[/LIST]
[U]Plug in (4) and (2) into (3)[/U]
a + (a - 5) + (a + 6) = 31
[U]Combine like terms:[/U]
3a + 1 = 31
[U]Subtract 1 from each side[/U]
3a = 30
[U]Divide each side by 3[/U]
[B]a = 10[/B]
[U]Plug in 1 = 10 into Equation (4)[/U]
c = 10 - 5
[B]c = 5[/B]
Now plug 1 = 10 into equation (2)
j = 10 + 6
[B]j = 16[/B]

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

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

Computer Storage Conversions

This calculator converts between the following computer storage measurements:

* byte

* kilobyte

* megabyte

* gigabyte

* terabyte

* petabyte

* exabyte

* byte

* kilobyte

* megabyte

* gigabyte

* terabyte

* petabyte

* exabyte

Confidence Interval of a Proportion

Given N, n, and a confidence percentage, this will calculate the estimation of confidence interval for the population proportion π including the margin of error. confidence interval of the population proportion

Conner earned these scores on the first three tests in science this term: 86, 88, and 78. What is th

Conner earned these scores on the first three tests in science this term: 86, 88, and 78. What is the lowest that Conner can earn on the fourth and final test of the term if he wants to have an average of at least 83?
Using our [URL='https://www.mathcelebrity.com/missingaverage.php?num=86%2C+88%2C78&avg=83&pl=Calculate+Missing+Score']missing average calculator[/URL], we find that the fourth score must be [B]80[/B]

Coupon Comparison

Given a cost of goods, a dollar off coupon, and a percentage off coupon, this calculator will compare the two deals and determine which one is of more value. If the dollar coupon wins, the calculator will project the break even price where the dollar coupon would surpass the percentage coupon

Credit Card Balance

This calculator shows 3 methods for paying off a credit card balance on a monthly installment basis given an outstanding balance and an Annual Percentage Rate (APR):

1) Minimum Payment Amount

2) Minimum Percentage Amount

3) Payoff in Years

1) Minimum Payment Amount

2) Minimum Percentage Amount

3) Payoff in Years

Cribbage

Calculates the score you would get after the deck card is flipped in a hand of cribbage.

Crypto Scams

I'd like to warn our fans about a crypto scam going around.
The site is [URL]https://crypto-fortress.com[/URL].
The scam runs like this...
[LIST]
[*]You're asked to deposit money, a minimum of $1,000 in BTC.
[*]You're given credits on the money from their mining/aribtrage plan.
[*]However, when it comes time to cash out after a week, they suddenly tell you, their is some magical agreement (which you never signed nor is on their website) where you now have to pay 25% of your profits to them and you'll get a withdrawal code for the rest.
[*]When you press them on how they pay 75% of your profits from a 25% deposit which makes no sense, they tell you that it's how things work.
[/LIST]

Dad is (y) years old. Mom is 5 years younger than Dad. What is the total of their ages

Dad is (y) years old. Mom is 5 years younger than Dad. What is the total of their ages
Dad's age:
y
Mom's age (younger means we subtract):
y - 5
The total of their ages is found by adding them together:
y + y - 5
Group like terms, and we get:
[B]2y - 5[/B]

David had 20 pencils. 5 of them are green and 15 are purple. What percentage of pencils were gr

David had 20 pencils. 5 of them are green and 15 are purple. What percentage of pencils were green?
Percentage of Green Pencils = 100* Green Pencils / Total Pencils
Percentage of Green Pencils = 100* 5/20
Percentage of Green Pencils = 500 / 20
Percentage of Green Pencils = [B]25%[/B]

David obtained 5 out of 20 votes in the election. What percentage of the votes did david receive?

David obtained 5 out of 20 votes in the election. What percentage of the votes did david receive?
5/20 is the fraction.
You can simplify by dividing top and bottom by 5 to get 1/4
As a decimal, this is 0.25
To get a percentage, multiply the decimal by 100
100 * 0.25 = 25%
You can also use our [URL='http://www.mathcelebrity.com/perc.php?num=+5&den=+20&pcheck=1&num1=6500&pct1=70&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pof1=40&pof2=20&pl=Calculate']decimal-percentage-fraction converter[/URL]

Decay

Determines decay based on an initial mass and decay percentage and time.

Dedra took a total of 6 pages of notes during 2 hours of class. After attending 3 hours of class, ho

Dedra took a total of 6 pages of notes during 2 hours of class. After attending 3 hours of class, how many total pages of notes will Dedra have in her notebook?
Set up a proportion of pages of notes to hours of class where p equals the number of pages of notes Dedra takes for 3 hours of class:
6/2 = p/3
[URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=p&den1=2&den2=3&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get:
p = [B]9[/B]

devaughn,sageis2timessydneysage,thesumoftheiragesis78,whatissydneysage

devaughn,sageis2timessydneysage,thesumoftheiragesis78,whatissydneysage
Let d be Devaughn's age. Let s be Sydney's age. We have two equations:
[LIST=1]
[*]d = 2s
[*]d + s = 78
[/LIST]
Substitute (1) into (2)
2s + s = 78
3s = 78
Entering [URL='http://www.mathcelebrity.com/1unk.php?num=3s%3D78&pl=Solve']3x = 78 into the search engine[/URL], we get [B]s = 26[/B].

Deyjiana reads 30 pages in 25 minutes. If she reads 210 pages at this rate, how long will it take he

Deyjiana reads 30 pages in 25 minutes. If she reads 210 pages at this rate, how long will it take her?
Set up a proportion of pages to minutes, were m is the number of minutes it takes to read 210 pages:
30/25 = 210/m
To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=30&num2=210&den1=25&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search engine[/URL] and we get:
m = [B]175[/B]

Dina is twice as old as Andrea. The sum of their age is 72. Find their present ages.

Dina is twice as old as Andrea. The sum of their age is 72. Find their present ages.
Let d be Dina's age. Let a be Andrea's age. We're given:
[LIST=1]
[*]d = 2a <-- Twice means multiply by 2
[*]a + d = 72
[/LIST]
Substitute equation (1) into equation (2):
a + 2a = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=a%2B2a%3D72&pl=Solve']Type this equation into our search engine[/URL] and we get:
[B]a = 24[/B]
Substitute a = 24 into equation (1):
d = 2(24)
[B]d = 48
So Andrea is 24 years old and Dina is 48 years old[/B]

Dina is twice the age of Anton. If Anton is 12, how will you represent the age of Dina?

Dina is twice the age of Anton. If Anton is 12, how will you represent the age of Dina?
Twice means multiply by 2, so we have:
Dina = 2 * Anton's age
Dina = 2 * 12
Dina = [B]24[/B]

Direct Current (Electrical Engineering) Ohms Law

Enter two of the following items from the DIRECT CURRENT(DC) electrical engineering set of variables, and this will solve for the remaining two:

* I = current(amps.)

* V = Electricity potential of voltage(volts)

* R = resistance(ohms)

* P = power(watts)

* I = current(amps.)

* V = Electricity potential of voltage(volts)

* R = resistance(ohms)

* P = power(watts)

During Michael Jordan's NBA career (1984–2003), he averaged a free throw completion percentage of 83

During Michael Jordan's NBA career (1984–2003), he averaged a free throw completion percentage of 83.5% in regular season play. If Jordan threw 8,772 free throws in his career, how many completed free throws did he make?
We want [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=83.5&den1=8772&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']83.5% of 8772[/URL] which is 7324.62.
We round down for completed free throws to get [B]7,324[/B]

Each of 6 students reported the number of movies they saw in the past year. Here is what they repor

Each of 6 students reported the number of movies they saw in the past year. Here is what they reported. 19, 9, 14, 10, 16, 17. Find the mean number of movies that the students saw. If necessary, round your answer to the nearest tenth.
The mean is the average, so we add up the 6 movie scores, and divide by 6.
[URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = Sum of 6 Movie Scores / 6
[URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = 84 / 6
[URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = 14.16666667
The problem asks us to round to the nearest tenth, which is the first decimal place.
Since the 2nd decimal place, 6 is more than 5, we round the first decimal place up one and remove the rest.
[B]14.2[/B]

Eighty percent of the employees at Rowan University have their biweekly Wages deposit directly to th

Eighty percent of the employees at Rowan University have their biweekly Wages deposit directly to their bank by electronic deposit program. Suppose we select a random samples of 8 employees. What is the probability that three of the eight (8) sampled employees use direct deposit program?
Use the [I]binomial distribution[/I]
[LIST]
[*]p = 0.8
[*]n = 8
[*]k = 3
[/LIST]
So we want P(X = 3)
Using our [URL='http://www.mathcelebrity.com/binomial.php?n=+8&p=+0.8&k=+3&t=+5&pl=P%28X+=+k%29']binomial distribution calculator[/URL], we get P(X = 3) = [B]0.0092[/B]

Ellen reads 23 pages in 40 minutes. Rob reads 9 pages in 16 minutes. Who is the faster reader? Ju

Ellen reads 23 pages in 40 minutes. Rob reads 9 pages in 16 minutes. Who is the faster reader? Justify your answer.
Compare in terms of pages per minute.
Ellen = 23 pages / 40 minutes =0.575 pages per minute
Rob = 9 pages / 16 minutes = 0.5625 pages per minute
[B]Ellen reads faster.[/B]

Emily is three years older than twice her sister Mary’s age. The sum of their ages is less than 30.

Emily is three years older than twice her sister Mary’s age. The sum of their ages is less than 30. What is the greatest age Mary could be?
Let e = Emily's age and m = Mary's age.
We have the equation e = 2m + 3 and the inequality e + m < 30
Substitute the equation for e into the inequality:
2m + 3 + m < 30
Add the m terms
3m + 3 < 30
Subtract 3 from each side of the inequality
3m < 27
Divide each side of the inequality by 3 to isolate m
m < 9
Therefore, the [B]greatest age[/B] Mary could be is 8, since less than 9 [U]does not include[/U] 9.

eric is twice as old as Shawn. The sum of their ages is 33. How old is Shawn?

eric is twice as old as Shawn. The sum of their ages is 33. How old is Shawn?
Let Eric's age be e. Let Shawn's age be s. We're given two equations:
[LIST=1]
[*]e = 2s
[*]e + s = 33
[/LIST]
Substitute equation (1) into equation (2) for e so we can solve for s:
2s + s = 33
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=2s%2Bs%3D33&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]11[/B]

Facebook provides a variety of statistics on its Web site that detail the growth and popularity of t

Facebook provides a variety of statistics on its Web site that detail the growth and popularity of the site.
On average, 28 percent of 18 to 34 year olds check their Facebook profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a standard deviation of five percent.
a. Find the probability that the percent of 18 to 34-year-olds who check Facebook before getting out of bed in the morning is at least 30.
b. Find the 95th percentile, and express it in a sentence.
a. P(X >=0.30), calculate the [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+0.30&mean=+0.28&stdev=+0.05&n=+1&pl=P%28X+%3E+Z%29']z-score[/URL] which is:
Z = 0.4
P(x>0.4) = [B]0.344578 or 34.46%[/B]
b. Inverse Normal (0.95) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.95&pl=Calculate+Critical+Z+Value']calculator[/URL] = 1.644853627
Use NORMSINV(0.95) on Excel
0.28 + 0.05(1.644853627) = [B]0.362242681 or 36.22%[/B]

Faith is 1/5 her mother's age. Their combined ages are 30. How old is faith?

Faith is 1/5 her mother's age. Their combined ages are 30. How old is faith?
Let Faith's age be f. Let her mother's age be m. We're given:
[LIST=1]
[*]f = m/5
[*]f + m = 30
[/LIST]
Rearrange (1) by cross-multiplying:
m = 5f
Substitute this into equation (2):
f + 5f = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=f%2B5f%3D30&pl=Solve']Type this equation into our search engine[/URL] and we get:
f = [B]5[/B]

final cost for a hair cut is 22.00 the tax is 2.00 what is the tax percentage

final cost for a hair cut is 22.00 the tax is 2.00 what is the tax percentage
Calculate Tax Percentage
Tax Percentage = 100% * Tax / Total Bill
Tax Percentage = 100% * 2/22
Tax Percentage = 100% * 1/11
Tax Percentage = [B]9.09%[/B]

First four exams scores were 78%, 76%, 82% and 84%. What is needed on the final exam to receive a 90

First four exams scores were 78%, 76%, 82% and 84%. What is needed on the final exam to receive a 90% exam average?
We need a missing average. [URL='https://www.mathcelebrity.com/missingaverage.php?num=78%2C+76%2C+82%2C84&avg=90&pl=Calculate+Missing+Score']Using our missing average calculator with our 4 test scores and a target average of 90%[/URL], we get:
[B]130%[/B]

Five times Kim's age plus 13 equals 58. How old is Kim?

Five times Kim's age plus 13 equals 58. How old is Kim?
Let Kim's age be a. We have:
Five times Kim's age:
5a
Plus 13 means we add 13
5a + 13
Equals 58 means we set the expression 5a + 13 equal to 58
5a + 13 = 58 <-- This is our algebraic expression
To solve this equation for a, [URL='https://www.mathcelebrity.com/1unk.php?num=5a%2B13%3D58&pl=Solve']we type it into our search engine[/URL] and get:
a = [B]9[/B]

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]

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?
So the last cousin is n years old. this means consecutive cousins are n + 2 years older than the next.
whether their ages are even or odd, we have the sum of 4 consecutive (odd|even) integers equal to 36. We [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof4consecutiveevenintegersis36&pl=Calculate']type this into our search engine[/URL] and we get the ages of:
[B]6, 8, 10, 12[/B]

Four-fifths of Kayla’s Math Notebook is filled. She has written on 48 pages. How many pages is there

Four-fifths of Kayla’s Math Notebook is filled. She has written on 48 pages. How many pages is there total in the notebook?
Let the total pages be p. WE're given:
4p/5 = 48
To solve for p, we[URL='https://www.mathcelebrity.com/prop.php?num1=4p&num2=48&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value'] type this equation into our search engine[/URL] and we get:
p = [B]60[/B]

Frank averages 1 strike for every 4 frames that he bowls. If he bowled 48 strikes in 1 season, how m

Frank averages 1 strike for every 4 frames that he bowls. If he bowled 48 strikes in 1 season, how many frames did Frank bowl?
Set up a proportion of strikes to frames:
1/4 = 48/x
Run this through our [URL='http://www.mathcelebrity.com/prop.php?num1=1&num2=48&den1=4&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL]:
x = [B]192 frames[/B]

Gas Mileage

Given miles driven and gallons of gas, this calculates your gas (fuel) mileage.

Germaine earns $800 for 40 hours of work. What is her hourly wage?

Germaine earns $800 for 40 hours of work. What is her hourly wage?
Hourly Wage = Wages / Hours worked
Hourly Wage = $800 / 40
Hourly Wage = [B]$20[/B]

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.
[IMG]http://www.mathcelebrity.com/images/math_problem_library_129.png[/IMG]
If AB = 6 and AD = 8, by the Pythagorean theorem, we have BD = 10 from our [URL='http://www.mathcelebrity.com/pythag.php?side1input=6&side2input=8&hypinput=&pl=Solve+Missing+Side']Pythagorean Theorem[/URL] Calculator
Using that, we have another right triangle which we can use the [URL='http://www.mathcelebrity.com/pythag.php?side1input=10&side2input=24&hypinput=&pl=Solve+Missing+Side']pythagorean theorem[/URL] calculator to get [B]FD = 26[/B]

Google Analytics on Steroids

This software declassifies anonymous website visitors. It tells you their company, what pages they view, and gathers the contact information for decision makers at the company. And I've negotiated a free, 7 day trial for you to try it out.
This software is best if you sell or deal with B2B transactions.
Enjoy this [URL='https://www.donsevcik.com/identify-anonymous-visitors']Google Analytics on Steroids[/URL].

Google Tag Manager Certification

Google Tag Manager Certification

Grade Point Average (GPA)

Calculates Grade Point Average (GPA) based on letter grades entered.

Grandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older tha

Grandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older than her daughter, but 31 years younger than her mother (the grandmother). How old are the three
Let grandmother's age be g. Let mother's age be m. Let daughter's age be d. We're given 3 equations:
[LIST=1]
[*]m = d + 25
[*]m = g - 31
[*]d + g + m = 150
[/LIST]
This means the daughter is:
d = 25 + 31 = 56 years younger than her grandmother. So we have:
4. d = g - 56
Plugging in equation (2) and equation(4) into equation (3) we get:
g - 56 + g + g - 31
Combine like terms:
3g - 87 = 150
[URL='https://www.mathcelebrity.com/1unk.php?num=3g-87%3D150&pl=Solve']Typing this equation into the search engine[/URL], we get:
[B]g = 79[/B]
Plug this into equation (2):
m = 79 - 31
[B]m = 48[/B]
Plug this into equation (4):
d = 79 - 56
[B]d = 23[/B]

Gretchen earns $7 per hour at the local pizza shop. If she works 3 hours in an afternoon, how much m

Gretchen earns $7 per hour at the local pizza shop. If she works 3 hours in an afternoon, how much money does she earn?
Earnings = Hourly Wage * Hours Worked
Earnings = $7 * 3
Earnings = [B]$21[/B]

Heat Index

Given a temperature in Fahrenheit and a relative humidity percentage, this calculates the Heat Index.

Heather has completed six deliveries so far this week she needs to make 40 deliveries for the week w

Heather has completed six deliveries so far this week she needs to make 40 deliveries for the week what percentage of her deliveries has Heather completed?
We want [URL='https://www.mathcelebrity.com/perc.php?num=6&den=40&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']6/40 as a percent[/URL] which is [B]15%[/B]

Help Plz

There are three siblings in a family. Their ages add to 26. Let nicks age be "x". John in half of micks age and Pip is two thirds of johns age. write an equation and solve. Find each Childs age.

Help Plz

Nick's age: x
John's age: x/2
Pip's age = 2/3 * x/2 = x/3
The sum is 26, so we have:
x + x/2 + x/3 = 26
Common denominator is (1 * 2 * 3) = 6
6x/6 + 3x/6 + 2x/6 = 26
Combine like terms:
11x/6 = 26
Cross multiply:
11x = 156
x = 14.1818
This doesn't make sense for age. Are you sure you wrote out the problem right?

HELP SOLVE

Perform a one-sample z-test for a population mean. Be sure to state the hypotheses and the significance level, to compute the value of the test statistic, to obtain the P-value, and to state your conclusion.
Five years ago, the average math SAT score for students at one school was 475. A teacher wants to perform a hypothesis test to determine whether the mean math SAT score of students at the school has changed. The mean math SAT score for a random sample of 40 students from this school is 469. Do the data provide sufficient evidence to conclude that the mean math SAT score for students at the school has changed from the previous mean of 475? Perform the appropriate hypothesis test using a significance level of 10%. Assume that ? = 73.

Here is Practical Explanation about Next Life, Purpose of Human Life, philosophical/religious facts,

Practical Explanation ( For Example ) :- `1st of all can you tell me every single seconds detail from that time when you born ?? ( i need every seconds detail ?? that what- what you have thought and done on every single second )
can you tell me every single detail of your `1 cheapest Minute Or your whole hour, day, week, month, year or your whole life ??
if you are not able to tell me about this life then what proof do you have that you didn't forget your past ? and that you will not forget this present life in the future ?
that is Fact that Supreme Lord Krishna exists but we posses no such intelligence to understand him.
there is also next life. and i already proved you that no scientist, no politician, no so-called intelligent man in this world is able to understand this Truth. cuz they are imagining. and you cannot imagine what is god, who is god, what is after life etc.
_______
for example :Your father existed before your birth. you cannot say that before your birth your father don,t exists.
So you have to ask from mother, "Who is my father?" And if she says, "This gentleman is your father," then it is all right. It is easy.
Otherwise, if you makes research, "Who is my father?" go on searching for life; you'll never find your father.
( now maybe...maybe you will say that i will search my father from D.N.A, or i will prove it by photo's, or many other thing's which i will get from my mother and prove it that who is my Real father.{ So you have to believe the authority. who is that authority ? she is your mother. you cannot claim of any photo's, D.N.A or many other things without authority ( or ur mother ).
if you will show D.N.A, photo's, and many other proofs from other women then your mother. then what is use of those proofs ??} )
same you have to follow real authority. "Whatever You have spoken, I accept it," Then there is no difficulty. And You are accepted by Devala, Narada, Vyasa, and You are speaking Yourself, and later on, all the acaryas have accepted. Then I'll follow.
I'll have to follow great personalities. The same reason mother says, this gentleman is my father. That's all. Finish business. Where is the necessity of making research? All authorities accept Krsna, the Supreme Personality of Godhead. You accept it; then your searching after God is finished.
Why should you waste your time?
_______
all that is you need is to hear from authority ( same like mother ). and i heard this truth from authority " Srila Prabhupada " he is my spiritual master.
im not talking these all things from my own.
___________
in this world no `1 can be Peace full. this is all along Fact.
cuz we all are suffering in this world 4 Problems which are Disease, Old age, Death, and Birth after Birth.
tell me are you really happy ?? you can,t be happy if you will ignore these 4 main problem. then still you will be Forced by Nature.
___________________
if you really want to be happy then follow these 6 Things which are No illicit s.ex, No g.ambling, No d.rugs ( No tea & coffee ), No meat-eating ( No onion & garlic's )
5th thing is whatever you eat `1st offer it to Supreme Lord Krishna. ( if you know it what is Guru parama-para then offer them food not direct Supreme Lord Krishna )
and 6th " Main Thing " is you have to Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare ".
_______________________________
If your not able to follow these 4 things no illicit s.ex, no g.ambling, no d.rugs, no meat-eating then don,t worry but chanting of this holy name ( Hare Krishna Maha-Mantra ) is very-very and very important.
Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare " and be happy.
if you still don,t believe on me then chant any other name for 5 Min's and chant this holy name for 5 Min's and you will see effect. i promise you it works And chanting at least 16 rounds ( each round of 108 beads ) of the Hare Krishna maha-mantra daily.
____________
Here is no Question of Holy Books quotes, Personal Experiences, Faith or Belief. i accept that Sometimes Faith is also Blind. Here is already Practical explanation which already proved that every`1 else in this world is nothing more then Busy Foolish and totally idiot.
_________________________
Source(s):
every `1 is already Blind in this world and if you will follow another Blind then you both will fall in hole. so try to follow that person who have Spiritual Eyes who can Guide you on Actual Right Path. ( my Authority & Guide is my Spiritual Master " Srila Prabhupada " )
_____________
if you want to see Actual Purpose of human life then see this link : ( triple w ( d . o . t ) asitis ( d . o . t ) c . o . m {Bookmark it })
read it complete. ( i promise only readers of this book that they { he/she } will get every single answer which they want to know about why im in this material world, who im, what will happen after this life, what is best thing which will make Human Life Perfect, and what is perfection of Human Life. ) purpose of human life is not to live like animal cuz every`1 at present time doing 4 thing which are sleeping, eating, s.ex & fear. purpose of human life is to become freed from Birth after birth, Old Age, Disease, and Death.

Here is Practical Explanation about Next Life, Purpose of Human Life, philosophical/religious facts,

Practical Explanation ( For Example ) :- `1st of all can you tell me every single seconds detail from that time when you born ?? ( i need every seconds detail ?? that what- what you have thought and done on every single second )
can you tell me every single detail of your `1 cheapest Minute Or your whole hour, day, week, month, year or your whole life ??
if you are not able to tell me about this life then what proof do you have that you didn't forget your past ? and that you will not forget this present life in the future ?
that is Fact that Supreme Lord Krishna exists but we posses no such intelligence to understand him.
there is also next life. and i already proved you that no scientist, no politician, no so-called intelligent man in this world is able to understand this Truth. cuz they are imagining. and you cannot imagine what is god, who is god, what is after life etc.
_______
for example :Your father existed before your birth. you cannot say that before your birth your father don,t exists.
So you have to ask from mother, "Who is my father?" And if she says, "This gentleman is your father," then it is all right. It is easy.
Otherwise, if you makes research, "Who is my father?" go on searching for life; you'll never find your father.
( now maybe...maybe you will say that i will search my father from D.N.A, or i will prove it by photo's, or many other thing's which i will get from my mother and prove it that who is my Real father.{ So you have to believe the authority. who is that authority ? she is your mother. you cannot claim of any photo's, D.N.A or many other things without authority ( or ur mother ).
if you will show D.N.A, photo's, and many other proofs from other women then your mother. then what is use of those proofs ??} )
same you have to follow real authority. "Whatever You have spoken, I accept it," Then there is no difficulty. And You are accepted by Devala, Narada, Vyasa, and You are speaking Yourself, and later on, all the acaryas have accepted. Then I'll follow.
I'll have to follow great personalities. The same reason mother says, this gentleman is my father. That's all. Finish business. Where is the necessity of making research? All authorities accept Krsna, the Supreme Personality of Godhead. You accept it; then your searching after God is finished.
Why should you waste your time?
_______
all that is you need is to hear from authority ( same like mother ). and i heard this truth from authority " Srila Prabhupada " he is my spiritual master.
im not talking these all things from my own.
___________
in this world no `1 can be Peace full. this is all along Fact.
cuz we all are suffering in this world 4 Problems which are Disease, Old age, Death, and Birth after Birth.
tell me are you really happy ?? you can,t be happy if you will ignore these 4 main problem. then still you will be Forced by Nature.
___________________
if you really want to be happy then follow these 6 Things which are No illicit s.ex, No g.ambling, No d.rugs ( No tea & coffee ), No meat-eating ( No onion & garlic's )
5th thing is whatever you eat `1st offer it to Supreme Lord Krishna. ( if you know it what is Guru parama-para then offer them food not direct Supreme Lord Krishna )
and 6th " Main Thing " is you have to Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare ".
_______________________________
If your not able to follow these 4 things no illicit s.ex, no g.ambling, no d.rugs, no meat-eating then don,t worry but chanting of this holy name ( Hare Krishna Maha-Mantra ) is very-very and very important.
Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare " and be happy.
if you still don,t believe on me then chant any other name for 5 Min's and chant this holy name for 5 Min's and you will see effect. i promise you it works And chanting at least 16 rounds ( each round of 108 beads ) of the Hare Krishna maha-mantra daily.
____________
Here is no Question of Holy Books quotes, Personal Experiences, Faith or Belief. i accept that Sometimes Faith is also Blind. Here is already Practical explanation which already proved that every`1 else in this world is nothing more then Busy Foolish and totally idiot.
_________________________
Source(s):
every `1 is already Blind in this world and if you will follow another Blind then you both will fall in hole. so try to follow that person who have Spiritual Eyes who can Guide you on Actual Right Path. ( my Authority & Guide is my Spiritual Master " Srila Prabhupada " )
_____________
if you want to see Actual Purpose of human life then see this link : ( triple w ( d . o . t ) asitis ( d . o . t ) c . o . m {Bookmark it })
read it complete. ( i promise only readers of this book that they { he/she } will get every single answer which they want to know about why im in this material world, who im, what will happen after this life, what is best thing which will make Human Life Perfect, and what is perfection of Human Life. ) purpose of human life is not to live like animal cuz every`1 at present time doing 4 thing which are sleeping, eating, s.ex & fear. purpose of human life is to become freed from Birth after birth, Old Age, Disease, and Death.

How many dimes must be added to a bag of 200 nickels so that the average value of the coins in the b

How many dimes must be added to a bag of 200 nickels so that the average value of the coins in the bag is 8 cents?
200 nickels has a value of 200 * 0.05 = $10.
Average value of coins is $10/200 = 0.05
Set up our average equation, where we have total value divided by total coins:
(200 * 0.05 + 0.1d)/(200 + d) = 0.08
Cross multiply:
16 + 0.08d = 10 + 0.1d
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=16%2B0.08d%3D10%2B0.1d&pl=Solve']equation solver[/URL], we get:
[B]d = 300[/B]

How old am I if 400 reduced by 2 times my age is 244?

How old am I if 400 reduced by 2 times my age is 244?
Let my age be a. We're given:
400 - 2a = 244
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D244&pl=Solve']type this equation into our search engine [/URL]and we get:
a = [B]78[/B]

How old am I if 400 reduced by 3 times my age is 124?

How old am I if 400 reduced by 3 times my age is 124?
Let my age be a. We're given an algebraic expression:
[LIST]
[*]3 times my age means we multiply a by 3: 3a
[*]400 reduced by 3 times my age means we subtract 3a from 400:
[*]400 - 3a
[*]The word [I]is[/I] mean an equation, so we set 400 - 3a equal to 124
[/LIST]
400 - 3a = 124
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D124&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]92[/B]

How old am I if: 210 reduced by 3 times my current age is 4 times my current age?

How old am I if: 210 reduced by 3 times my current age is 4 times my current age?
Let your current age be a. We're given:
[LIST]
[*]210 reduced by 3 times current age = 210 - 3a
[*]4 times current age = 4a
[*]The word [I]is[/I] means equal to. So we set 210 - 3a equal to 4a
[/LIST]
210 - 3a = 4a
To solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=210-3a%3D4a&pl=Solve']type this equation into our search engine [/URL]and we get:
a = [B]30[/B]

How old am I of 400 reduced by 2 times my age is 224

How old am I of 400 reduced by 2 times my age is 224
[LIST=1]
[*]Let my age be a.
[*]2 times my age: 2a
[*]400 reduced by 2 times my age: 400 - 2a
[*]The phrase [I]is [/I]means an equation. So we set 400 - 2a equal to 224 for our algebraic expression
[/LIST]
[B]400 - 2a = 224
[/B]
If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D224&pl=Solve']type this equation into our search engine[/URL] and we get:
a = [B]88[/B]

How old is Ruben if he was 28 years old eleven years ago?

How old is Ruben if he was 28 years old eleven years ago?
Let's Ruben's age be a. If he was 28 years old 11 years ago, then his age is expressed as:
a - 11 = 28
[URL='https://www.mathcelebrity.com/1unk.php?num=a-11%3D28&pl=Solve']Plugging this into our calculator[/URL], we get:
a = [B]39[/B]

Hubspot Agency Partner Exam

Exam answers and Study Guide for the Hubspot Agency Partner Exam

HubSpot Growth Driven Agency Exam

Exam answers and Study Guide for the HubSpot Growth Driven Agency Exam

I am 12 years old. My brother is 5 years older than me. How old is my brother?

I am 12 years old. My brother is 5 years older than me. How old is my brother?
Older means we add, so we have:
Brother's age = 12 + 5
Brother's age = [B]17[/B]

If 1/8 = y%, find y

If 1/8 = y%, find y
Using our [URL='https://www.mathcelebrity.com/perc.php?num=1&den=8&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']fraction to percentage calculation[/URL], we see that:
1/8 = [B]12.5[/B]%

If 25% of 30% of x is 9, what is x?

If 25% of 30% of x is 9, what is x?
Convert percentages to decimals when multiplying:
25% = 0.25
30% = 0.3
0.25 * 0.3 * x = 9
0.075x = 9
Using our math engine, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.075x%3D9&pl=Solve']type this equation in[/URL] and we get:
x = [B]120
[MEDIA=youtube]5EwNxiBdLu0[/MEDIA][/B]

if a city grows by 12% per month what is the yearly growth rate

if a city grows by 12% per month what is the yearly growth rate
We know that there are 12 months in a year.
12% = 0.12
Annual Growth Rate = (1 + Monthly Growth Rate)^12 - 1
Annual Growth Rate = (1 + 0.12)^12 - 1
Annual Growth Rate = (1.12)^12 - 1
Annual Growth Rate = 3.89597599255 - 1
Annual Growth Rate = 2.90
For our percentage, our annual growth rate is the Annual growth rate * 100%
2.90 * 100% = [B]290%[/B]

If Emma reads 1 page of a book in 44 seconds, how many pages will she read in 15 minutes

If Emma reads 1 page of a book in 44 seconds, how many pages will she read in 15 minutes
Convert 15 minutes to seconds:
15 minutes = 60 * 15 = 900 seconds
Set up a proportion of pages read to seconds where p is the number of pages read in 900 seconds (15 minutes):
1/44 = p/900
[URL='https://www.mathcelebrity.com/prop.php?num1=1&num2=p&den1=44&den2=900&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
p = [B]20.45[/B]

If Frank’s age is double of Willis’ age and the sum of their ages is 42. What are their ages?

If Frank’s age is double of Willis’ age and the sum of their ages is 42. What are their ages?
Let Frank's age be f. Let Willis's age be w. We're given two equations:
[LIST=1]
[*]f = 2w <-- Double means multiply by 2
[*]f + w = 42
[/LIST]
Substitute equation (1) into equation (2):
2w + w = 42
To solve for w, [URL='https://www.mathcelebrity.com/1unk.php?num=2w%2Bw%3D42&pl=Solve']type this equation into our search engine[/URL]. We get:
w = [B]14
[/B]
Now, take w = 14, and substitute it back into equation (1) to solve for f:
f = 2(14)
f = [B]28[/B]

If I have 48 days to finish a 337 page book how many pages a day will I have to read each day

If I have 48 days to finish a 337 page book how many pages a day will I have to read each day
337 pages / 48 days =[B] 7.02 pages per day[/B]

If I have a reading average of 2 hours 30 minutes 0 seconds per 93.25 pages, how long would it take

If I have a reading average of 2 hours 30 minutes 0 seconds per 93.25 pages, how long would it take me to read 58 pgs?
Set up a proportion, of reading time to pages where m is the number of minutes it takes you to read 58 pages.
2 hours and 30 minutes is:
60(2) + 30
120 + 30
150 minutes
Our proportion is:
150/93.25 = m/58
[URL='https://www.mathcelebrity.com/prop.php?num1=150&num2=m&den1=93.25&den2=58&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get:
[B]m = 93.3 minutes, or about 1 hour, 33 minutes[/B]

If Jay reads 1 & 1/8 pages per minute, how long will it take him to read 72 pages?

If Jay reads 1 & 1/8 pages per minute, how long will it take him to read 72 pages?
Calculate de
72 pages / 1 & 1/8
Converting to decimal, we have:
72 pages / 1.125 pages per minute = [B]64 minutes[/B]

If Susie is 14, what was her age x years ago?

If Susie is 14, what was her age x years ago?
x years ago means we subtract x from 14:
[B]14 - x[/B]

If Tanya eats the box of donuts before she goes to bed, she'll wake up in a fog the next day. If she

If Tanya eats the box of donuts before she goes to bed, she'll wake up in a fog the next day. If she is in a fog, she will not do well on the SAT test that she will take the next day. If she doesn't do well on that SAT test, she will not get a scholarship to college and will have to pay her own way. Can we conclude that if Tanya eats the box of donuts before she goes to age that she will not get a scholarship to college?
[B]Yes
[/B]
[LIST]
[*]IF she eats the donuts, she'll wake up in a fog.
[*]IF she is in a fog, she will not do well on the test
[*]IF she doesn't do well on the test, she will not get a scholarship
[/LIST]

If the original price of an item was $30.00 and Joan only paid $24.00 for it, what percentage discou

If the original price of an item was $30.00 and Joan only paid $24.00 for it, what percentage discount did Joan receive on her purchase?
She received 6 dollars off of a 30 dollar purchase, so we have 6/30 = 1/5 = 0.2 = [B]20%[/B]

If the probability of an event occurring is 7%, what is the probability of an event not occurring?

If the probability of an event occurring is 7%, what is the probability of an event not occurring?
The probability of all event is 1, or 100%.
If we treat the success of an event as p, then q is 1 - p.
Using percentages, we have:
q = 100% - p
Given p = 7%, we have:
q = 100% - 7%
q = [B]93%[/B]

If you buy 5 packages of noodles at $1.48 each whats the total?

If you buy 5 packages of noodles at $1.48 each whats the total?
Total = Packages x Cost Per Package
Total = 5 x 1.48
Total = [B]$7.40[/B]

If you divide my brother's age by 3 and then add 20, you will get my age, which is 31. What is my br

If you divide my brother's age by 3 and then add 20, you will get my age, which is 31. What is my brothers age?
Let b be the brother's age.
We're given the following relationship for the brother's age and my age:
b/3 + 20 = 31
Subtract 20 from each side:
b/3 + 20 - 20 = 31 - 20
Cancel the 20's on the left side and we get:
b/3 = 11
Cross multiply, and we get:
b = 3 * 11
b = [B]33
[/B]
Check our work using b = 33 for b/3 + 20 = 31:
33/3 + 20 ? 31
11 + 20 ? 31
31 = 31

Imagine a researcher posed a null hypothesis that in a certain community, the average energy expendi

Imagine a researcher posed a null hypothesis that in a certain community, the average energy expenditure should be 2,100 calories per day. He randomly sampled 100 people in that community. After he computed the t value by calculating a two-tailed t-statistic, he found that the probability value was 0.10. Thus, he concluded:
a. The average energy expenditure was bigger than 2,100 calories per day
b. The average energy expenditure was smaller than 2,100 calories per day
c. He could not reject the null hypothesis that the average energy expenditure was 2,100 calories per day
d. The average energy expenditure was either more than 2,100 calories per day or less than 2,100 calories per day
[B]c. He could not reject the null hypothesis that the average energy expenditure was 2,100 calories per day[/B]
[I]p-value is higher than 0.05[/I]

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He r

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. What's the sample [U][B]standard deviation[/B][/U]?
[B]20.79182532[/B] using stdev.s in excel or also found on our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics#standard_deviation']statistics calculator[/URL]

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He r

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. What's the [B][U]standard error of the mean[/U][/B]?
9.29839 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics#standard_error_of_the_mean']statistics calculator[/URL]

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He r

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. The researcher posed a null hypothesis that the average weight for boys in that high school should be 100 lbs. What is the [B][U]absolute value[/U][/B] of calculated t that we use for testing the null hypothesis?
Mean is 109.4 and Standard Deviation = 20.79182532 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']statistics calculator[/URL]
Now use those values and calculate the t-value
Abs(t value) = (100 - 109.4)/ 20.79182532/sqrt(5)
Abs(tvalue) = [B]1.010928029[/B]

In 1 year, a baseball player got 195 hits in 600 times. What is his batting average?

In 1 year, a baseball player got 195 hits in 600 times. What is his batting average?
Batting Average = Hits / Times at Bat
Batting Average = 195 / 600
[URL='https://www.mathcelebrity.com/perc.php?num=196&den=600&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']Batting Average[/URL] = [B]0.327[/B]

In 16 years, Ben will be 3 times as old as he is right now

In 16 years, Ben will be 3 times as old as he is right now.
Let Ben's age today be a. We're given:
a + 16 = 3a
[URL='https://www.mathcelebrity.com/1unk.php?num=a%2B16%3D3a&pl=Solve']Type this equation into the search engine[/URL], and we get:
a = [B]8[/B]

In 16 years, Ben will be 3 times as old as he is right now.

In 16 years, Ben will be 3 times as old as he is right now.
Let Ben's age right now be b.
We have, in 16 years, Ben's age will be 3 times what his age is now:
b + 16 = 3b
Subtract b from each side:
2b = 16
Divide each side by 2
[B]b = 8[/B]
Check our work:
16 years from now, Ben's age is 8 + 16 = 24
And, 8 x 3 = 24

In 1996 Ato Boldon of UCLA ran the 100-meter dash in 9.92 seconds. In 1969 John Carlos of San Jose S

In 1996 Ato Boldon of UCLA ran the 100-meter dash in 9.92 seconds. In 1969 John Carlos of San Jose State ran the 100-yard dash in 9.1 seconds. Which runner had the faster average speed?
We [URL='https://www.mathcelebrity.com/linearcon.php?quant=100&type=yard&pl=Calculate']convert yards to meters using our conversion calculator[/URL] and we get:
100 yards = 91.44 meters
Now we set up a proportion of time per meter:
[LIST]
[*]Ato Boldon: 9.92/100 = 0.992 per meter
[*]John Carlos: 9.1/91.44 = 0.995 per meter
[/LIST]
[B]Since Ato Boldon's time was [I]less per meter[/I], he had the faster average speed[/B]

In 20 years charles will be 3 times as old as he is now. How old is he now?

In 20 years charles will be 3 times as old as he is now. How old is he now?
Let Charles's age be a today. We're given:
a + 20 = 3a
[URL='https://www.mathcelebrity.com/1unk.php?num=a%2B20%3D3a&pl=Solve']If we type this equation into our search engine[/URL], we get:
[B]a = 10
[/B]
Let's check our work in our given equation:
10 + 20 ? 3(10)
30 = 30 <-- Checks out!

In 45 years, Gabriela will be 4 times as old as she is right now.

In 45 years, Gabriela will be 4 times as old as she is right now.
Let a be Gabriela's age. we have:
a + 45 = 4a
Subtract a from each side:
3a = 45
Divide each side by a
[B]a = 15[/B]

in 5 years, sarah will be old enough to vote in an election. the minimum age for voting is at least

in 5 years, sarah will be old enough to vote in an election. the minimum age for voting is at least 18 years. what can you say about how old she is now?
18 - 5 = [B]13 years old[/B]

In 56 years, Stella will be 5 times as old as she is right now.

In 56 years, Stella will be 5 times as old as she is right now.
Let Stella's age be s. We're given:
s + 56 = 5s
[URL='https://www.mathcelebrity.com/1unk.php?num=s%2B56%3D5s&pl=Solve']Type this equation into our search engine[/URL], and we get:
[B]s = 14[/B]

in 6th grade, veronica reads 45 books. in 7th grade she reads 63 books. what is the percent change?

in 6th grade, veronica reads 45 books. in 7th grade she reads 63 books. what is the percent change?
Percent Change = 100% * (New Value - Old Value)/Old Value
Percent Change = 100% * (63 - 45)/45
Percent Change = 100% * 18/45
Percent Change = 100% * 0.4
Percent Change = [B]40%[/B]
[B]
There is a percentage increase[/B]

In 8 years kelly's age will be twice what it is now. How old is kelly?

In 8 years kelly's age will be twice what it is now. How old is kelly?
Let Kelly's age be a.
In 8 years means we add 8 to a:
a + 8
Twice means we multiply a by 2:
2a
The phrase [I]will be[/I] means equal to, so we set a + 8 equal to 2a
a + 8 = 2a
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B8%3D2a&pl=Solve']type it in our math engine[/URL] and we get:
a = [B]8
[/B]
[U]Evaluate a = 8 and check our work[/U]
8 + 8 ? 2(8)
16 = 16
[MEDIA=youtube]y4jaQpkaJEw[/MEDIA]

In a 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 a sample of 80 beetles, 50 beetles had 4 spots each, and the rest had 6 spots each. What was the

In a sample of 80 beetles, 50 beetles had 4 spots each, and the rest had 6 spots each. What was the average number of spots per beetle? Show your work below.
Average spots per beetle = Total spots for all beetles / Total beetles
Average spots per beetle = (50(4) + 6(80 - 50))/80
Average spots per beetle =(200 + 6(30))/80
Average spots per beetle = (200 + 180)/80
Average spots per beetle = (380)/80
Average spots per beetle = [B]4.75 spots[/B]

In January 2017 the cost of postage stamps increased from 47 cents to 49 cents. What was the percent

In January 2017 the cost of postage stamps increased from 47 cents to 49 cents. What was the percent of increase?
[URL='https://www.mathcelebrity.com/percentage-change-calculator.php?num=thecostofpostagestampsincreasedfrom47centsto49cents.whatwasthepercentofincrease&pl=Calculate']Using our percentage change calculator[/URL], we get:
[B]4.26% increase[/B]

In order to select new board members, the French club held an election. 63 out of the 90 members of

In order to select new board members, the French club held an election. 63 out of the 90 members of the French club voted in the election. What percentage of the members voted?
Using our [URL='http://www.mathcelebrity.com/perc.php?num=63&den=90&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percentage calculator[/URL], 63 out of 90 is [B]70%[/B]

In the past year, Yoko watched 76 movies that she thought were very good. She watched 80 movies ove

In the past year, Yoko watched 76 movies that she thought were very good. She watched 80 movies over the whole year. Of the movies she watched, what percentage did she think were very good?
[URL='http://www.mathcelebrity.com/perc.php?num=76&den=80&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']Enter 76/80 into our search engine to get 95%[/URL].

In the wild, monkeys eat an average of 28 bananas a day with a standard deviation of 2 bananas. One

In the wild, monkeys eat an average of 28 bananas a day with a standard deviation of 2 bananas. One monkey eats only 21 bananas. What is the z-score for this monkey? Is the number of bananas the monkey eats unusually low?
Using [URL='https://www.mathcelebrity.com/probnormdist.php?xone=21&mean=28&stdev=2&n=1&pl=P%28X+%3C+Z%29']our z-score calculator[/URL], we get:
Z < -3.5
P(Z < -3.5) = 0.499767
Also, this [B]is unusually low as it's more than 3 deviations away from the mean[/B]

In the year 1980, Rick was twice as old as Nancy who was twice as old as Michael. In the year 1992 R

In the year 1980, Rick was twice as old as Nancy who was twice as old as Michael. In the year 1992 Ric, Nancy, and Michael ages added up to 78 years. How old was Ric in 1980?
Age in 1980:
[LIST]
[*]Let Michael's age be m
[*]Nancy's age is 2m
[*]Rick's age is 2 * 2m = 4m
[/LIST]
Age in 1992:
[LIST]
[*]Michael's age = m + 12
[*]Nancy's age is 2m + 12
[*]Rick's age is 2 * 2m = 4m + 12
[/LIST]
Total them up:
m + 12 + 2m + 12 + 4m + 12 = 78
Solve for [I]m[/I] in the equation m + 12 + 2m + 12 + 4m + 12 = 78
[SIZE=5][B]Step 1: Group the m terms on the left hand side:[/B][/SIZE]
(1 + 2 + 4)m = 7m
[SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE]
12 + 12 + 12 = 36
[SIZE=5][B]Step 3: Form modified equation[/B][/SIZE]
7m + 36 = + 78
[SIZE=5][B]Step 4: Group constants:[/B][/SIZE]
We need to group our constants 36 and 78. To do that, we subtract 36 from both sides
7m + 36 - 36 = 78 - 36
[SIZE=5][B]Step 5: Cancel 36 on the left side:[/B][/SIZE]
7m = 42
[SIZE=5][B]Step 6: Divide each side of the equation by 7[/B][/SIZE]
7m/7 = 42/7
m = 6
Rick's age = 6 * 4 = [B]24
[URL='https://www.mathcelebrity.com/1unk.php?num=m%2B12%2B2m%2B12%2B4m%2B12%3D78&pl=Solve']Source[/URL]
[/B]

In the year 1989, Luke's age was 3 times Rachel's age and Rachel's age was 3 times Dan's age. If Dan

In the year 1989, Luke's age was 3 times Rachel's age and Rachel's age was 3 times Dan's age. If Dan's age was n, how old were Rachel and Luke?
Rachel's age = 3 * Dan's age
Rachel's age = 3n
Luke's age = 3 times Rachel's age
Luke's age = 3(3n)
Luke's age = [B]9n[/B]

In x years time, Peter will be 23 years old. How old is he now?

In x years time, Peter will be 23 years old. How old is he now?
Let Peter's current age be a. In x years time means we add x to a, so we're given:
a + x = 23
We want to find a, s we subtract x from each side to get:
a + x - x = 23 - x
Cancel the x terms on the left side and we get:
a = [B]23 - x[/B]

Inclusive Number Word Problems

Given an integer A and an integer B, this calculates the following inclusive word problem questions:

1) The Average of all numbers inclusive from A to B

2) The Count of all numbers inclusive from A to B

3) The Sum of all numbers inclusive from A to B

1) The Average of all numbers inclusive from A to B

2) The Count of all numbers inclusive from A to B

3) The Sum of all numbers inclusive from A to B

Inventory Turnover and Average Inventory

Calculates inventory turnover ratio and average inventory

Is 20% equivalent to 2/5?

Is 20% equivalent to 2/5?
Let's compare fractions to fractions:
20% equals 1/5 from our [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=20&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percentage-decimal-fraction calculator[/URL].
1/5 < 2/5 so these fractions are [B][I]not equivalent[/I][/B].

Is this algebra?

Can anyone answer this equation?
You start off with 5 tickets and every 24min you get 1 extra ticket.
After you sell your first ticket you have exactly 10min to sell another ticket and so on.
How many tickets can you sell before you run out of tickets to sell?
Plz give the mathematical equation for others to know also[IMG]https://www.facebook.com/images/emoji.php/v9/f34/1/16/1f914.png[/IMG]

Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only

[SIZE=4]Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only 5 times as old as William?
[U]Express Ishaan and William's age since today where y is the number of years since today, we have:[/U]
i = 72+y
w = 4+y
[U]We want the time for Ishaan age will be 5 times William's age:[/U]
i = 5w
72 + y = 5(4 + y)
We [URL='https://www.mathcelebrity.com/1unk.php?num=72%2By%3D5%284%2By%29&pl=Solve']plug this equation into our search engine [/URL]and get:
y = [B]13[/B]
[/SIZE]

It is estimated that weekly demand for gasoline at new station is normally distributed, with an aver

It is estimated that weekly demand for gasoline at new station is normally distributed, with an average of 1,000 and standard deviation of 50 gallons. The station will be supplied with gasoline once a week. What must the capacity of its tank be if the probability that its supply will be exhausted in a week is to be no more than 0.01?
0.01 is the 99th percentile
Using our [URL='http://www.mathcelebrity.com/percentile_normal.php?mean=+1000&stdev=50&p=99&pl=Calculate+Percentile']percentile calculator[/URL], we get [B]x = 1116.3[/B]

Jack reads 90 pages of a book in six hours. What is the average number of pages he read each hour

Jack reads 90 pages of a book in six hours. What is the average number of pages he read each hour
90 pages / 6 hour = 90/6
Type [URL='https://www.mathcelebrity.com/fraction.php?frac1=90%2F6&frac2=3%2F8&pl=Simplify']90/6 in our search engine, click simplify[/URL], and we get:
[B]15 pages per hour[/B]

Jack scored a mean of 15 points per game in his first 3 basketball games. In his 4th grade, he score

Jack scored a mean of 15 points per game in his first 3 basketball games. In his 4th grade, he scored 27 points. What was Jack's mean score for the four games?
The mean is the average:
Mean = (15 + 15 + 15 + 27)/4
Mean = 72/4
[B]Mean = 18[/B]

James is four time as old as peter if their combined age is 30 how old is James.

James is four time as old as peter if their combined age is 30 how old is James.
Let j be Jame's age. Let p be Peter's age. We're given:
[LIST=1]
[*]j = 4p
[*]j + p = 30
[/LIST]
Substitute (1) into (2)
4p + p = 30
Combine like terms:
5p = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=5p%3D30&pl=Solve']Type 5p = 30 into our search engine[/URL], and we get p = 6.
Plug p = 6 into equation (1) to get James's age, we get:
j = 4(6)
j = [B]24[/B]

Jane is twice a old as Joel. If their ages total 63, how old is Joel?

Jane is twice a old as Joel. If their ages total 63, how old is Joel?
Joel = j
Jane = 2j
j + 2j = 63
3j = 63
Divide each side by 3:
3j/3 = 63/j
Cancel the 3's on the left side:
j = [B]21[/B]

Janice is looking to buy a vacation home for $185,000 near her favorite southern beach. The formula

Janice is looking to buy a vacation home for $185,000 near her favorite southern beach. The formula to compute a mortgage payment, M, is shown below, where P is the principal amount of the loan, r is the monthly interest rate, and N is the number of monthly payments. Janice's bank offers a monthly interest rate of 0.325% for a 12-year mortgage. How many monthly payments must Janice make?
12 years * 12 months per year = [B]144 mortgage payments[/B]

Jason wrote a total of 8 pages over 2 hours. How many hours will Jason have to spend writing this we

Jason wrote a total of 8 pages over 2 hours. How many hours will Jason have to spend writing this week in order to have written a total of 12 pages? Assume the relationship is directly proportional.
Set up a proportion of pages to hours
8 pages/2 hours = 12 pages/x hours
enter 8/2 = 12/x into the [URL='http://www.mathcelebrity.com/prop.php?num1=8&num2=12&den1=2&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']search engine[/URL]:
[B]x = 3[/B]

Jeff Bezos, who owns Amazon, has a net worth of approximately $143.1 billion (as of mid-2018). An em

Jeff Bezos, who owns Amazon, has a net worth of approximately $143.1 billion (as of mid-2018). An employee in the Amazon distribution center earns about $13 an hour. The estimated lifespan of the employee is 71 years. If the employee worked 24 hours a day, every day of the year from the moment of his birth, how many lifespans would it take for him to earn wages equivalent to Jeff Bezos' net worth? Round the answer to the nearest whole number.
Calculate earnings per lifespan:
Earnings per lifespan = lifespan in years * Annual Earnings
Earnings per lifespan = 71 * 13 * 24 * 365 <-- (24 hours per day * 365 days per year)
Earnings per lifespan = 8,085,480
Calculate the number of lifespans needed to match Jeff Bezos earnings:
Number of lifespans = Jeff Bezos Net Worth / Earnings Per Lifespan
Number of lifespans = 143,100,000,000 / 8,085,480
Number of lifespans = [B]17,698.39 ~ 17,699[/B]

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]

Jeremy is x years old now. How old is he 10 years from now?

Jeremy is x years old now. How old is he 10 years from now?
We add 10 years to Jeremy's current age of x:
[B]x + 10[/B]

Jerry, an electrician, worked 7 months out the year. What percent of the year did he work?

Jerry, an electrician, worked 7 months out the year. What percent of the year did he work?
We know that there are 12 months in a year.
Percentage worked = Months worked in a year / months in a year * 100%
Percentage worked = 7/12 * 100%
Percentage worked = 0.5833333 * 100%
Multiplying by 100 means we shift the decimal place 2 spaces to the right:
Percentage worked = [B]58.33%[/B]

Jessie invests $3345 in the stock market. Over the 3 years she has this invested she gets an average

Jessie invests $3345 in the stock market. Over the 3 years she has this invested she gets an average return of 7.8%. How much will her investment be worth after the 3 years?
7.8% = 0.078, so we use our compound interest formula to find our balance after 3 years.
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=3345&nval=3+&int=7.8&pl=Annually']compound interest balance calculator[/URL], we get:
[B]$4,190.37[/B]

Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82,

Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82, how old is the eldest of them
Let j be Jim's age, a be Alex's age, and u be June's age. We have 3 given equations:
[LIST=1]
[*]j + a + u = 82
[*]j = u + 9
[*]a = u - 8
[/LIST]
Substitute (2) and (3) into (1)
(u + 9) + (u - 8) + u = 82
Combine Like Terms:
3u + 1 = 82
[URL='https://www.mathcelebrity.com/1unk.php?num=3u%2B1%3D82&pl=Solve']Type this equation into the search engine[/URL], and we get u = 27.
The eldest (oldest) of the 3 is Jim. So we have from equation (2)
j = u + 9
j = 27 + 9
[B]j = 36[/B]

Jina's test score average decreased by 10 points this semester. Write a signed number to represent t

Jina's test score average decreased by 10 points this semester. Write a signed number to represent this change in average.
Let A be the original average. The new average is:
A + (-10)

John bought a painting for $600 and sold it for $648. Find the profit as a percentage of the cost.

John bought a painting for $600 and sold it for $648. Find the profit as a percentage of the cost.
[U]Calculate the profit:[/U]
Profit = Sale Price - Purchase price
Profit = 648 - 600
Profit = 48
[U]Calculate Profit percentage of cost =[/U]
Profit percentage of cost = 100% * Profit/cost
Profit percentage of cost = 100% * 48 / 600
Profit percentage of cost = [B]8%[/B]

John is n years old now. How old was he 10 years ago? What will be his age in 20 years time?

John is n years old now. How old was he 10 years ago? What will be his age in 20 years time?
10 years ago means we [I]subtract[/I] 10 from n:
[B]n - 10[/B]
20 years time or 20 years from now means we [I]add[/I] 20 to n:
[B]n + 20[/B]

John is y years old. Sarah is 9 years older than John. How old is Sarah

John is y years old. Sarah is 9 years older than John. How old is Sarah
Older means we add, so we have Sarah's age s as:
s = [B]y + 9[/B]

John read the first 114 pages of a novel, which was 3 pages less than 1/3

John read the first 114 pages of a novel, which was 3 pages less than 1/3
Set up the equation for the number of pages (p) in the novel
1/3p - 3 = 114
Add 3 to each side
1/3p = 117
Multiply each side by 3
[B]p = 351[/B]

John read the first 114 pages of a novel, which was 3 pages less than 1/3 of the novel.

John read the first 114 pages of a novel, which was 3 pages less than 1/3 of the novel.
Let n be the number of pages in the novel. We have:
1/3n - 3 = 114
Multiply each side by 3:
n - 9 = 342
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=n-9%3D342&pl=Solve']equation solver[/URL], we get [B]n = 351[/B].

John's age 4 years ago, if he will be y years old in 5 years.

John's age 4 years ago, if he will be y years old in 5 years.
Josh's age now is y - 5
Josh's age 4 years ago is y - 5 - 4 = [B]y - 9[/B]

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15%

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathan and Raymond have to sell in order to earn the same amount each month?
[U]Step 1: Set up Jonathan's sales equation S(m) where m is the amount of sales made each month:[/U]
S(m) = Commission percentage * m + Base Salary
10% written as a decimal is 0.1. We want decimals to solve equations easier.
S(m) = 0.1m + 1500
[U]Step 2: Set up Raymond's sales equation S(m) where m is the amount of sales made each month:[/U]
S(m) = Commission percentage * m + Base Salary
15% written as a decimal is 0.15. We want decimals to solve equations easier.
S(m) = 0.15m + 1200
[U]The question asks what is m when both S(m)'s equal each other[/U]:
The phrase [I]earn the same amount [/I]means we set Jonathan's and Raymond's sales equations equal to each other
0.1m + 1500 = 0.15m + 1200
We want to isolate m terms on one side of the equation.
Subtract 1200 from each side:
0.1m + 1500 - 1200 = 0.15m + 1200 - 1200
Cancel the 1200's on the right side and we get:
0.1m - 300 = 0.15m
Next, we subtract 0.1m from each side of the equation to isolate m
0.1m - 0.1m + 300 = 0.15m - 0.1m
Cancel the 0.1m terms on the left side and we get:
300 = 0.05m
Flip the statement since it's an equal sign to get the variable on the left side:
0.05m = 300
To solve for m, we divide each side of the equation by 0.05:
0.05m/0.05 = 300/0.05
Cancelling the 0.05 on the left side, we get:
m = [B]6000[/B]

JP's age is twice the age of Reyna. The sum of their ages does not exceed 51

JP's age is twice the age of Reyna. The sum of their ages does not exceed 51
Let JP's age be j. Let Reyna's age be r. We're given two expressions:
[LIST=1]
[*]w = 2r
[*]r + w <= 51. ([I]Does not exceed means less than or equal to)[/I]
[/LIST]
We substitute (1) into (2) for w to get the inequality:
r + 2r <= 51
To solve this inequality, we type it in our search engine and we get:
[B]r <= 17[/B]

Juan is going on a flight to the beach. his luggage weighs 36 pounds. The bag weighs 4 pounds more t

Juan is going on a flight to the beach. his luggage weighs 36 pounds. The bag weighs 4 pounds more than the weight of 2 small bags of beach toys. Which equation can be used to find the weight in pounds of each bag of beach toys?
Let b be the weight of each bag of beach toys. We're given the following relationship:
2b -4 = 36
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=2b-4%3D36&pl=Solve']type it in our math engine[/URL] and we get:
b = [B]20[/B]

Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and

Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and .10 cents for additional texts. How many texts did she send out?
Let m be the number of messages. We have a cost function of:
C(m) = 9 + 0.1(m - 600)
We are given C(m) = 18.20
18.20 = 9 + 0.1(m - 600)
18.20 = 9 + 0.1m - 60
Combine like terms:
18.20 = 0.1m - 51
Add 51 to each side
0.1m = 69.20
Divide each side by 0.1
[B]m = 692[/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]

kate is twice as old as her sister mars. the sum of their ages is 24. find their ages.

kate is twice as old as her sister mars. the sum of their ages is 24. find their ages.
Let k be Kate's age
Let m be Mars's age
We're given two equations:
[LIST=1]
[*]k = 2m. (Because twice means multiply by 2)
[*]k + m = 24
[/LIST]
Substitute equation (1) for k into equation (2):
2m + m = 24
T o solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=2m%2Bm%3D24&pl=Solve']type this equation into our math engine[/URL]:
m = [B]8
[/B]
We want to solve for k using m= 8. Substitute this into equation 1
k = 2(8)
k = [B]16
[/B]
Check our work for equation 1
16 = 2 * 8
16 = 16
Check our work for equation 2
16 + 8 ? 24
24 = 24
[MEDIA=youtube]TJMTRYP-Ct8[/MEDIA]

Katie is twice as old as her sister Mara. The sum of their age is 24.

Let k = Katie's age and m = Mara's age.
We have 2 equations:
(1) k = 2m
(2) k + m = 24
Substitute (1) into (2)
(2m) + m = 24
Combine like terms:
3m = 24
Divide each side of the equation by 3 to isolate m
m = 8
If m = 8, substituting into (1) or (2), we get k = 16.

Kendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. How

Kendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. How old are they?
Let k be Kendra's age, m be Morgan's age, and l be Lizzie's age. We're given:
[LIST=1]
[*]k = 0.5m
[*]k = l - 3
[*]k + l + m = 39
[/LIST]
Rearranging (1) by multiplying each side by 2, we have:
m = 2k
Rearranging (2) by adding 3 to each side, we have:
l = k + 3
Substituting these new values into (3), we have:
k + (k + 3) + (2k) = 39
Group like terms:
(k + k + 2k) + 3 = 39
4k + 3 = 39
[URL='https://www.mathcelebrity.com/1unk.php?num=4k%2B3%3D39&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]k = 9
[/B]
Substitute this back into (1), we have:
m = 2(9)
[B]m = 18
[/B]
Substitute this back into (2), we have:
l = (9) + 3
[B][B]l = 12[/B][/B]

Kent Realty Company had an annual loss of $63,408. What was the average loss per month?

Kent Realty Company had an annual loss of $63,408. What was the average loss per month?
Convert years to months
1 year = 12 months
63,408/12 = [B]5,284 per month[/B]

Kevin is 4 times old as Daniel and is also 6 years older than Daniel

Kevin is 4 times old as Daniel and is also 6 years older than Daniel.
Let k be Kevin's age and d be Daniel's age. We have 2 equations:
[LIST=1]
[*]k = 4d
[*]k = d + 6
[/LIST]
Plug (1) into (2):
4d = d + 6
Subtract d from each side:
4d - d = d - d + 6
Cancel the d terms on the right side and simplify:
3d = 6
Divide each side by 3:
3d/3 = 6/3
Cancel the 3 on the left side:
d = 2
Plug this back into equation (1):
k = 4(2)
k = 8
So Daniel is 2 years old and Kevin is 8 years old

Kiko is now 6 times as old as his sister. In 6 years, he will be 3 times as old as his sister. What

Kiko is now 6 times as old as his sister. In 6 years, he will be 3 times as old as his sister. What is their present age?
Let k be Kiko's present age
Let s be Kiko's sisters age.
We're given two equations:
[LIST=1]
[*]k = 6s
[*]k + 6 = 3(s + 6)
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for k:
6s + 6 = 3(s + 6)
[URL='https://www.mathcelebrity.com/1unk.php?num=6s%2B6%3D3%28s%2B6%29&pl=Solve']Typing this equation into our math engine[/URL] to solve for s, we get:
s = [B]4[/B]
To solve for k, we substitute s = 4 into equation (1) above:
k = 6 * 4
k = [B]24[/B]

Kim earns $30 for babysitting on Friday nights. She makes an average of $1.25 in tips per hour. Writ

Kim earns $30 for babysitting on Friday nights. She makes an average of $1.25 in tips per hour. Write the function of Kim's earnings, and solve for how much she would make after 3 hours.
Set up the earnings equation E(h) where h is the number of hours. We have the function:
E(h) = 1.25h + 30
The problem asks for E(3):
E(3) = 1.25(3) + 30
E(3) = 4.75 + 30
E(3) = [B]$34.75[/B]

Kimberly is taking three online classes during the summer. She spends 10 hours each week studying fo

Kimberly is taking three online classes during the summer. She spends 10 hours each week studying for her marketing class, 12 hours studying for her statistics class, and 8 hours studying for her business law class. What percent of her study time does she spend for her statistics class?
The percentage equals hours spent on statistics divided by total hours spent studying for everything.
[U]Calculate total study hours:[/U]
Total Study Hours = Marketing Class Study Hours + Statistics Class Study Hours + Business Law Study Hours
Total Study Hours = 10 + 8 + 12
Total Study Hours = [B]30[/B]
[U]Calculate Statistics Study Hours Percentage:[/U]
Statistics Study Hours Percentage = Statistics Class Study Hours / Total Study Hours
Statistics Class Study Hours = 8/30
Using our [URL='https://www.mathcelebrity.com/perc.php?num=8&den=30&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']fraction to decimal calculator[/URL], we get
Statistics Class Study Hours = [B]26.67%[/B]

Kimberly takes 4 pages of notes during each hour of class. Write an equation that shows the relation

Kimberly takes 4 pages of notes during each hour of class. Write an equation that shows the relationship between the time in class x and the number of pages y.
With x hours and y pages, our equation is:
[B]y = 4x [/B]

Kimberly wants to become a member of the desert squad at a big catering company very badly, but she

Kimberly wants to become a member of the desert squad at a big catering company very badly, but she must pass three difficult tests to do so. On the first Terrifying Tiramisu test she scored a 68. On the second the challenging Chocalate-Sprinkled Creme Brulee she scored a 72. If kimberly needs an average of 60 on all three tests to become a member on the squad what is the lowest score she can make on her third and final test
This is a missing average problem.
Given 2 scores of 68, 72, what should be score number 3 in order to attain an average score of 60?
[SIZE=5][B]Setup Average Equation:[/B][/SIZE]
Average = (Sum of our 2 numbers + unknown score of [I]x)/[/I]Total Numbers
60 = (68 + 72 + x)/3
[SIZE=5][B]Cross Multiply[/B][/SIZE]
68 + 72 + x = 60 x 3
x + 140 = 180
[SIZE=5][B]Subtract 140 from both sides of the equation to isolate x:[/B][/SIZE]
x + 140 - 140 = 180 - 140
x = [B]40[/B]

Lamar had N record albums that he tried to sell at a garage sale for $5 each. If the number of recor

Lamar had N record albums that he tried to sell at a garage sale for $5 each. If the number of record albums he didn't sell is called Q, how much money did Lamar get from record album sales?
Sales = Price * (Albums had - Albums sold)
[B]Sales = 5(N - Q)[/B]

Last week, a man worked 47 hours at Starbucks. Find his gross earnings for the week if he is paid

Last week, a man worked 47 hours at Starbucks. Find his gross earnings for the week if he is paid $7.80 per hour and earns time-and-a-half for all hours over 40.
[U]Step 1: Calculate regular time pay up to 40 hours:[/U]
Regular Pay = Hourly Wage * Hours up to 40
Regular Pay = $7.80 * 40
Regular Pay = $312
[U]Step 2: Calculate overtime hours above 40 hours:[/U]
Overtime Hours = Hours Worked - 40 hours
Overtime Hours = 47 - 40
Overtime Hours = 7
[U]Step 3: Calculate overtime pay above 40 hours:[/U]
Overtime Pay = 1.5 * Hourly Rate * Overtime Hours
Overtime Pay = 1.5 * $7.80 * 7
Overtime Pay = $81.90
[U]Step 4: Calculate Gross Earnings[/U]
Gross Earnings = Regular Pay + Overtime Pay
Gross Earnings = $312 + $81.90 = [B]$393.90
[URL='https://www.facebook.com/MathCelebrity/videos/10156751976078291/']FB Live Session[/URL][/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]

Lauren wrote a total of 6 pages over 2 hours. How many hours will Lauren have to spend writing this

Lauren wrote a total of 6 pages over 2 hours. How many hours will Lauren have to spend writing this week in order to have written a total of 9 pages? Solve using unit rates.
6 pages per 2 hours equals 6/2 = 3 pages per hour as a unit rate
Set up equation using h hours:
3h = 9
Divide each side by 3
[B]h = 3[/B]

Leah is 12 years older than Anna. if the age of Anna is x, what is the age of Leah?

Leah is 12 years older than Anna. if the age of Anna is x, what is the age of Leah?
Older means we add 12 to Anna's age. So if Anna's age is x, then Leah's age (l) is:
l = [B]x + 12[/B]

Lei is 15 years old, represent her age m years ago

Lei is 15 years old, represent her age m years ago
years ago means we subtract:
[B]15 - m[/B]

Leilani can read 20 pages in 2 minutes. if she can maintain this page, how many pages can she read i

Leilani can read 20 pages in 2 minutes. if she can maintain this page, how many pages can she read in an hour?
We know that 1 hour is 60 minutes.
Let p be the number of pages Leilani can read in 1 hour (60 minutes)
The read rate is constant, so we can build a proportion.
20 pages /2 minutes = p/60
We can cross multiply:
Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2
[SIZE=5][B]Solving for Numerator 2 we get:[/B][/SIZE]
Numerator 2 = Numerator 1 * Denominator 2/Denominator 1
[SIZE=5][B]Evaluating and simplifying using your input values we get:[/B][/SIZE]
p = 20 * 60/ 2
p = 1200/2
p = [B]600[/B]

Let x be the dog’s age in years. What is the dog’s age when he is thrice as old?

Let x be the dog’s age in years. What is the dog’s age when he is thrice as old?
Thrice means triple, or multiply by 3. So we have the future age as:
[B]3x[/B]

let x be the variable, an age that is at least 57 years old

let x be the variable, an age that is at least 57 years old
At least means greater than or equal to
x >= 57

Lily needs an internet connectivity package for her firm. She has a choice between CIVISIN and GOMI

Lily needs an internet connectivity package for her firm. She has a choice between CIVISIN and GOMI with the following monthly billing policies. Each company's monthly billing policy has an initial operating fee and charge per megabyte.
Operating Fee charge per Mb
CIVSIN 29.95 0.14
GOMI 4.95 0.39
(i) Write down a system of equations to model the above situation
(ii) At how many Mb is the monthly cost the same? What is the equal monthly cost of the two plans?
(i) Set up a cost function C(m) for CIVSIN where m is the number of megabytes used:
C(m) = charge per Mb * m + Operating Fee
[B]C(m) = 0.14m + 29.95[/B]
Set up a cost function C(m) for GOMI where m is the number of megabytes used:
C(m) = charge per Mb * m + Operating Fee
[B]C(m) = 0.39m + 4.95
[/B]
(ii) At how many Mb is the monthly cost the same?
Set both cost functions equal to each other:
0.14m + 29.95 = 0.39m + 4.95
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.14m%2B29.95%3D0.39m%2B4.95&pl=Solve']type this equation into our search engine[/URL] and we get:
m = [B]100[/B]
(ii) What is the equal monthly cost of the two plans?
CIVSIN - We want C(100) from above where m = 100
C(100) = 0.14(100) + 29.95
C(100) = 14 + 29.95
C(100) = [B]43.95[/B]
GOMI - We want C(100) from above where m = 100
C(100) = 0.39(100) + 4.95
C(100) = 39 + 4.95
C(100) = [B]43.95[/B]

Logan is 8 years older than 4 times the age of his nephew. Logan is 32 years old. How old is his nep

Logan is 8 years older than 4 times the age of his nephew. Logan is 32 years old. How old is his nephew?
Let the age of Logan's nephew be n. We're given:
4n + 8 = 32 (Since [I]older[/I] means we add)
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=4n%2B8%3D32&pl=Solve']type it into our search engine[/URL] and we get:
[B]n = 6[/B]

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]

Lucy has taken four tests in math class and has an average of 85. i. What score would she have to g

Lucy has taken four tests in math class and has an average of 85.
i. What score would she have to get on her fifth test to have an average of 88?
ii. Can she get an average of 90? Explain.
i. She would need a perfect score of [B]100[/B] from our [URL='http://www.mathcelebrity.com/missingaverage.php?num=+81%2C83%2C87%2C89&avg=+88&pl=Calculate+Missing+Score']Missing Average Calculator[/URL]
ii. [B]Impossible since we know from question i., a score of 100 only gets her to an 88. She cannot score higher than 100 on the fifth test, therefore, she cannot attain an average score of 90.[/B]

MAPE - MPE - MAPD

Given a time series of actual and forecasted values, this determines the following:

* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)

* Symmetric Mean Absolute Percentage Error (sMAPE)

* Mean Absolute Percentage Error (MPE)

* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)

* Symmetric Mean Absolute Percentage Error (sMAPE)

* Mean Absolute Percentage Error (MPE)

Markup Markdown

Given the 3 items of a markup word problem, cost, markup percentage, and sale price, this solves for any one of the three given two of the items. This works as a markup calculator, markdown calculator.

Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find t

Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find the ages of Martha and Harry.
Let m be Martha's age. Let h be Harry's age. We're given two equations:
[LIST=1]
[*]m = h + 18 [I](older means we add)[/I]
[*]h + m = 106
[/LIST]
Substitute equation (1) into equation (2) for m:
h + h + 18 = 106
To solve for h, [URL='https://www.mathcelebrity.com/1unk.php?num=h%2Bh%2B18%3D106&pl=Solve']we type this equation into our search engine[/URL] and we get:
h = [B]44[/B]

Martha's age 2/3 of her brother's age. Martha is 24 years old now. How old is her brother?

Martha's age 2/3 of her brother's age. Martha is 24 years old now. How old is her brother?
Let her brother's age be b. We're given:
2b/3 = 24
To solve this proportion for b, [URL='https://www.mathcelebrity.com/prop.php?num1=2b&num2=24&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
b = [B]36[/B]

Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than

Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than 11. What is the youngest age Warren can be?
Let m be Marty's age and w be Warren's age. We have two equations:
(1) m = 6w - 3
(2) m + w > 11
Plug (1) into (2)
6w - 3 + w > 11
Combine w terms
7w - 3 > 11
Add 3 to each side
7w > 14
Divide each side by 7
w > 2 which means [B]w = 3[/B] as the youngest age.

Mary is x years old. How old will she be in 9 years? How old was she 8 years ago

Mary is x years old. How old will she be in 9 years? How old was she 8 years ago
In 9 years, we add, since her age goes up, so she'll be:
[B]x + 9
[/B]
8 years ago, we subtract, since her age goes down, so she'll be:
[B][B]x - 8[/B][/B]

Mary paid 1.97 for toothpaste and a bar of soap using a discount coupon if the toothpaste cost 1.29

Mary paid 1.97 for toothpaste and a bar of soap using a discount coupon if the toothpaste cost 1.29 and the song cost 83 cents. What is the value of the discount coupon?
Find the full price package:
1.29 + 0.83 = 2.12
The value of the discount coupon is the money off, so:
2.12 - 1.97 = [B]0.15[/B]

Math Written Assignment

Im sorta confused about this question?
He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but I don't think he's right. You're going to help us settle this.
Here is (most of) the information you asked for:
[LIST]
[*]Is he redoing the whole yard or just the front?
He's redoing the whole yard
[*]How much topsoil does he need?
I'm not sure, you'll have to figure that out. Remember he's putting a new 4 inch layer down over all the area currently covered by grass in the overhead picture above.
[*]How big is the yard?
I'm not sure, but you can probably estimate it using the overhead picture.
[*]What kind of pickup truck does he drive?
A 2003 Ford F-150 XL.
[*]How much can the pickup carry?
The truck bed is 80 inches long, 69 inches wide, and 20 inches tall.
[*]How much is the delivery charge?
$30 per truckload on top of the soil cost. Each truckload can deliver up to 18 cubic yards.
[*]How much does the topsoil cost?
$18 per cubic yard (sold in 1/4 yard increments).
[*]How far is the soil store?
It is 9 miles away. It takes about 20 minutes to drive there.
[*]What gas mileage does the pickup truck get?
It averages 17 miles to the gallon.
[*]What is the current gas cost?
Assume it's $3.79/gallon.
[/LIST]
Using this information, figure out whether my neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that my neighbor pick up the soil himself, or pay for delivery?
Detail all your assumptions and calculations, and clearly write out your final conclusions.

Matilda needs at least $112 to buy an new dress. She has already saved $40. She earns $9 an hour bab

Matilda needs at least $112 to buy an new dress. She has already saved $40. She earns $9 an hour babysitting. Write and solve and inequality to find how many hours she will need to babysit to buy the dress.
Subtract remaining amount needed after savings:
112 - 40 = 72
Let h be her hourly wages for babysitting. We have the equation:
[B]9h = 72[/B]
Divide each side by 9
[B]h = 8[/B]

Max is 23 years younger than his father.Together their ages add up to 81.

Max is 23 years younger than his father.Together their ages add up to 81.
Let Max's age be m, and his fathers' age be f. We're given:
[LIST=1]
[*]m = f - 23 <-- younger means less
[*]m + f = 81
[/LIST]
Substitute Equation (1) into (2):
(f - 23) + f = 81
Combine like terms to form the equation below:
2f - 23 = 81
[URL='https://www.mathcelebrity.com/1unk.php?num=2f-23%3D81&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]f = 52[/B]
Substitute this into Equation (1):
m = 52 - 23
[B]m = 29[/B]

Max was 25 years old in 2011 what year was he born?

Max was 25 years old in 2011 what year was he born?
Year of Birth = Year - Age in Year
Year of Birth = 2011 - 25
Year of Birth = [B]1986[/B]

Max's age is 2 more than his fathers age divided by 4. Max is 13 years old. How old is his dad?

Max's age is 2 more than his fathers age divided by 4. Max is 13 years old. How old is his dad?
Let Max's father be age f. We're given:
(f + 2)/4 = 13
Cross Multiply:
f + 2 = 52
[URL='https://www.mathcelebrity.com/1unk.php?num=f%2B2%3D52&pl=Solve']Typing this equation into the search engine[/URL], we get:
f = [B]50[/B]

Midpoint formula

Midpoint formula
Given two points (x1, y1) and (x2, y2), the midpoint is found as the average distance between the 2 points:
[LIST]
[*]x value is: (x1 + x2)/2
[*]y value is: (y1 + y2)/2
[/LIST]
So our midpoint is:
((x1 + x2)/2, (y1 + y2)/2)

Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opp

Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent's serves. Assume her opponent serves 8 times. Show all work. Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution.
a) What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?
b) Find the probability that that she returns at least 1 of the 8 serves from her opponent.
(c) How many serves can she expect to return?
a) [B]n = 8
p = 0.2[/B]
q = 1 - p
q = 1 - 0.2
[B]q = 0.8
[/B]
b) [B]0.4967[/B] on our [URL='http://www.mathcelebrity.com/binomial.php?n=+8&p=0.2&k=1&t=+5&pl=P%28X+>+k%29']binomial calculator[/URL]
c) np = 8(0.2) = 1.6 ~ [B]2[/B] using the link above

Missing Average

Given a set of scores and an average, this calculates the next score necessary to attain that average

Morse Code Translator

Given a phrase with letters, numbers, and most punctuation symbols, the calculator will perform the following duties:

1) Translate that phrase to Morse Code.

2) Translate the Morse Code to a Dit-Dah message

3) Calculate the number of dots in the message

4) Calculate the number of dashes in the message

This also translates__from__ Morse Code back to English.

1) Translate that phrase to Morse Code.

2) Translate the Morse Code to a Dit-Dah message

3) Calculate the number of dots in the message

4) Calculate the number of dashes in the message

This also translates

Mr. Jones works for a wage of $15 per hour for a 40 hour week.If he worked on 40 hours what is his w

Mr. Jones works for a wage of $15 per hour for a 40 hour week.If he worked on 40 hours what is his wage for that week
Wages = Hourly Rate * Hours Worked
Wages = $15 * 40
Wages = [B]$600[/B]

Mr. Tan has two daughters. His elder daughter is 1/3 of his age while his younger daughter is 1/4 of

Mr. Tan has two daughters. His elder daughter is 1/3 of his age while his younger daughter is 1/4 of his age. If Mr. Tan’s age is 60, how old are his elder and youngest daughter?
Let Mr. Tan's age be a. We're given:
[LIST]
[*]Elder Daughter's age = 60/3 = [B]20 years old[/B]
[*]Younger Daughter's age = 60/4 = [B]15 years old[/B]
[/LIST]

Mr. Wilson wants to park his carin a parking garage that charges 3 per hour along with a flat fee of

Mr. Wilson wants to park his carin a parking garage that charges 3 per hour along with a flat fee of 6. If Mr. Wilson paid 54 to park in the garage, for how many hours did he park there?
[U]Set up an equation, where f is the flat fee, and h is the number of hours parked:[/U]
3h + f = 54
[U]Substitute f = 6 into the equation:[/U]
3h + 6 = 54
[U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3h%2B6%3D54&pl=Solve']equation solver[/URL], we get[/U]
[B]h = 16[/B]

My brother is x years old. I am 5 years older than him. Our combined age is 30 years old. How old is

My brother is x years old. I am 5 years older than him. Our combined age is 30 years old. How old is my brother
Brother's age is x:
I am 5 years older, meaning I'm x + 5:
The combined age is found by adding:
x + (x + 5) = 30
Group like terms:
2x + 5 = 30
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B5%3D30&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]12.5[/B]

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.

My son is 9 less than 1/2 my age. If I am 34 how old is my son?

1/2 of the parent age is 34/2 = 17.
9 less than that is 17 - 9 = 8.
The son is 8 years old.
You can also write this as 1/2(34) - 9 --> 17 - 9 = 8.

Nancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daug

Nancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daughter?
Declare variables for each age:
[LIST]
[*]Let Nancy's age be n
[*]Let her daughter's age be d
[/LIST]
We're given two equations:
[LIST=1]
[*]n = 3d - 10
[*]n = 41
[/LIST]
We set 3d - 10 = 41 and solve for d:
Solve for [I]d[/I] in the equation 3d - 10 = 41
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants -10 and 41. To do that, we add 10 to both sides
3d - 10 + 10 = 41 + 10
[SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE]
3d = 51
[SIZE=5][B]Step 3: Divide each side of the equation by 3[/B][/SIZE]
3d/3 = 51/3
d = [B]17[/B]

Nava is 17 years older than Edward. the sum of Navas age and Edwards ages id 29. How old is Nava?

Nava is 17 years older than Edward. the sum of Navas age and Edwards ages id 29. How old is Nava?
Let Nava's age be n and Edward's age be e. We have 2 equations:
[LIST=1]
[*]n = e + 17
[*]n + e = 29
[/LIST]
Substitute (1) into (2)
(e + 17) + e = 29
Group like terms:
2e + 17 = 29
Running this equation [URL='http://www.mathcelebrity.com/1unk.php?num=2e%2B17%3D29&pl=Solve']through our search engine[/URL], we get:
e = 6
Substitute this into equation (1)
n = 6 + 17
[B]n = 23[/B]

Need help quickly! My math skills are escaping me!

If I have 13 participants attending new hire class. 3 of them did not pass, 10 passed successfully. What is the percentage of success? What is the ratio of success? I don't believe there is a ratio, I could be wrong. Probably so, math does not agree with me! Please help!
Thank you!

Need help quickly! My math skills are escaping me!

Success Percentage: 3/13 = 0.2308 = 23.08%
Success to failure ratio = 3:10

Nick said that his sister is 4 times as old as his brother, and together their ages add to 20 comple

Nick said that his sister is 4 times as old as his brother, and together their ages add to 20 complete this equation to find his brothers age
Let b be the brother's age and s be the sister's age. We're given two equations:
[LIST=1]
[*]s =4b
[*]b + s = 20
[/LIST]
Plug (1) into (2):
b + 4b = 20
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B4b%3D20&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]b = 4[/B]

Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years?

Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years?
Let n be Nicole's age. Let d be Donald's age. We're given two equations:
[LIST=1]
[*]n = 0.5d
[*]n + d = 72
[/LIST]
Substitute equation (1) into (2):
0.5d + d = 72
1.5d = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=1.5d%3D72&pl=Solve']Typing this equation into the search engine and solving for d[/URL], we get:
d = [B]48[/B]

Nio is 20 years old and his brother Miguel is 8 years old. How old was Miguel when Nio is only 15?

Nio is 20 years old and his brother Miguel is 8 years old. How old was Miguel when Nio is only 15?
Nio is 20.
20 - 15 is 5 years ago.
So Miguel's age 5 years ago is:
8 - 5 = [B]3[/B]

Noah scores 20 points. Mai’s score was 30 points. The mean for Noah’s, Mia’s, and Clare’s was 40 poi

Noah scores 20 points. Mai’s score was 30 points. The mean for Noah’s, Mia’s, and Clare’s was 40 points. What was Clare’s score?
[URL='https://www.mathcelebrity.com/missingaverage.php?num=20%2C30&avg=40&pl=Calculate+Missing+Score']Using our missing average calculator[/URL], Claire's score was [B]70[/B].

Nolan is paid $9 per hour plus a bonus of $55 per week. If Nolan worked n hours during a week, how m

Nolan is paid $9 per hour plus a bonus of $55 per week. If Nolan worked n hours during a week, how much was he paid?
Total Wage = Hourly Wage + Bonus
Hourly wage = Hourly Rate * Hours worked
Bonus = 55
We have:
Total Wage = [B]9n + 55[/B]

Of the 800 students of a school, 600 have traveled. What percentage of the students went on a trip?

Of the 800 students of a school, 600 have traveled. What percentage of the students went on a trip?
Our percentage is found as 600/800.
Simplifying by dividing top and bottom by 100, we have:
6/8
Divide top and bottom by 2, we get:
3/4 or [B]75%
[/B]
You can also type in the [URL='http://www.mathcelebrity.com/perc.php?num=600&den=800&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']search engine[/URL]: 600/800 as percent.

Of the worlds 7.5 billion people, 1.2 billion people live on less than 4 per day. Calculate the perc

Of the worlds 7.5 billion people, 1.2 billion people live on less than 4 per day. Calculate the percent of the worlds population who lives on less than 4 per day?
We want the percentage 1.2/7.5.
[URL='https://www.mathcelebrity.com/perc.php?num=1.2&den=7.5&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 this fraction into our search engine[/URL], choose percentage, and we get:
[B]16%[/B]

ohn read the first 114 pages of a novel, which was 3 pages less than1/3 of the novel

Let p be the novel pages.
We have 1/3p - 3 = 114
Add 3 to each side
1/3p = 117
Multiply each side by 3
p = 351

Oliver earns $50 per day plus $7.50 for each package he delivers. If his paycheck for the first day

Oliver earns $50 per day plus $7.50 for each package he delivers. If his paycheck for the first day was $140, how many packages did he deliver that day?
His total earnings per day are the Flat Fee of $50 plus $7.50 per package delivered. We have:
50 + 7.50p = 140 where p = the number of packages delivered
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=50%2B7.50p%3D140&pl=Solve']equation solver[/URL], we have:
[B]p = 12[/B]

On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday

On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday they paid 15.80 for 8 cups of coffee and 14 bagels. Can you determine the cost of a bagel
Let the number of cups of coffee be c
Let the number of bagels be b.
Since cost = Price * Quantity, we're given two equations:
[LIST=1]
[*]7b + 4c = 8.77
[*]14b + 8c = 15.80
[/LIST]
We have a system of equations. We can solve this 3 ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer
[LIST]
[*]The system is inconsistent. Therefore, we have no answer.
[/LIST]

On the math test, Ralph answered 17 out of 20 problems. What percent did he get right?

On the math test, Ralph answered 17 out of 20 problems. What percent did he get right?
Using our [URL='http://www.mathcelebrity.com/perc.php?num=17&den=20&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percentage calculator or entering the phrase 17 out of 20 in the search engine[/URL], we get:
[B]85%[/B]

One third of the bagels in a bakery are sesame bagels. There are 72 sesame bagels.

One third of the bagels in a bakery are sesame bagels. There are 72 sesame bagels.
Set up our equation where b is the number of total bagels
72 = b/3
Multiply each side by 3
[B]b = 216[/B]

Overtime

Solves overtime wage problems

P-Hat Confidence Interval

Given a large sized distribution, and a success amount for a certain criteria x, and a confidence percentage, this will calculate the confidence interval for that criteria.

Par on a golf course is 72. If a golfer shot rounds of 74, 70, and 71 in a tournament, what will she

Par on a golf course is 72. If a golfer shot rounds of 74, 70, and 71 in a tournament, what will she need to shoot on the final round to average par?
Par is the word for average in golf. We have a missing average problem.
Using our [URL='http://www.mathcelebrity.com/missingaverage.php?num=74%2C70%2C71&avg=72&pl=Calculate+Missing+Score']missing average calculator[/URL], we need to shoot a [B]73[/B].

Pat starts reading at 1pm. He reads 5 pages in 15 minutes. If pat reads until 2:45 PM how many pages

Pat starts reading at 1pm. He reads 5 pages in 15 minutes. If pat reads until 2:45 PM how many pages has he read
From 1PM to 2:45 PM is 1 hour and 45 minutes. Since 1 hour is 60 minutes, Pat reads 105 minutes.
Calculate the 15 minute blocks:
Blocks = Total Minutes / 15
Blocks = 105/15
Blocks = 7
Pat reads 5 pages for every 15 minute block. So we have:
Total Pages Read = 5 pages * 7 blocks
Total Pages Read = [B]35[/B]

Paul’s age is 7 years younger than half of Marina’s age. Express their ages.

Paul’s age is 7 years younger than half of Marina’s age. Express their ages.
Assumptions:
[LIST]
[*]Let Paul's age be p
[*]Let Marina's age be m
[/LIST]
Our expression is:
[B]p = 1/2m - 7[/B]

Percent Error

Percentage error is the difference between an experimental measured value and a theoretical actual value

Percentage Appreciation

Solves for Book Value given a flat rate percentage appreciation per period

Percentage Change

Calculates the percentage change between two values. Percentage Increase or Percentage Decrease

Percentage Depreciation

Solves for Book Value given a flat rate percentage depreciation per period

Percentage of Completion

Given a sales price, total costs, and costs per period, this determines the gross profit to date using the percentage of completion method.

Percentage Word Problems

Solves percentage word problems

Percentage-Decimal-Fraction Relations

Calculates the relational items between a fraction, a decimal (including repeating decimal and terminating decimal), a percentage, and the numerator and denominator piece of that fraction. Also calculates the percentage change going from one number to another or the amount increase or decrease of a percentage above/below a number. Round decimals. decimals into fractions

Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he

Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost?
Let the cost of paper packages be p and the cost of staplers be s. We're given two equations:
[LIST=1]
[*]3p + 4s = 40
[*]5p + 6s = 62
[/LIST]
We have a system of equations. We can solve this three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get the same answer:
[LIST]
[*][B]p = 4[/B]
[*][B]s = 7[/B]
[/LIST]

Phonograms

Shows the 75 basic phonograms of the English language

Phyllis's mother has 6 pounds of candy to divide evenly among her 8 children. This is an average of

Phyllis's mother has 6 pounds of candy to divide evenly among her 8 children. This is an average of how many pounds per child?
6 pounds divide among 8 children can be represented as a fraction. We want to simplify this. So we use our [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F8&frac2=3%2F8&pl=Simplify']fraction simplify calculator[/URL], and we get:
3 pounds per 4 children, or 0.75 pounds per child.

Please help me!! I don't understand!

I don't understand this word problem: If each of these shapes in Figure 1 were separated and filled with water, could the sphere that contains the cube hold all of the water? [I]Assume in the second image the corners of the cube touch the sphere so the diagonal from one corner of the cube to the opposite diagonal corner is the diameter of the sphere. [IMG]https://classroom.ucscout.org/courses/1170/files/191225/preview?verifier=mT7v59BhdVHalyprWq0KmBEItbf4CPWFqOgwoEa8[/IMG][IMG]https://classroom.ucscout.org/courses/1170/files/191494/preview?verifier=nsLscsxToebAVXTSYsoMr7rwIl536LrCJSDGPaHp[/IMG][/I]
Could you guys help me please?

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the pho

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test, [U][B]the Type I error is[/B][/U]:
a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher

b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same

c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher [B]b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same [/B] [I]A Type I error is when you reject the null hypothesis when it is in fact true[/I]

b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same

c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher [B]b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same [/B] [I]A Type I error is when you reject the null hypothesis when it is in fact true[/I]

Price

Given a cost and a gross margin percentage, this calculator calculates price, gross profit, markup percentage

PRIVATE SAT TUTORING - LIVE FACE-TO-FACE SKYPE TUTORING

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Proportion Sample Size

This calculator determines a sample size to select to meet certain criteria related to a confidence percentage, reliability percentage, and a p value proportion. Simply enter your values not using percentage signs. This works whether p^ is known or not known.

Put the number 123456789 exactly ones in the bubble so that each edge adds up to say number

Put the number 123456789 exactly ones in the bubble so that each edge adds up to say number
[B]
Each side adds up to 17
[IMG]https://www.mathcelebrity.com/images/triangle_sum_17.png[/IMG]
[/B]

read 34 pages a day how many pages read in 2 weeks

read 34 pages a day how many pages read in 2 weeks
2 weeks = 14 days
34 pages per day * 14 days = [B]476 pages[/B]

Reagan bought t T-shirts. The shirts came in 8 packages. Write an expression that shows how many T-s

Reagan bought t T-shirts. The shirts came in 8 packages. Write an expression that shows how many T-shirts were in each package.
T-shirts per package = number of packages / number of t-shirts per package
T-shirts per package = [B]8/t[/B]

Rebound Ratio

Calculates a total downward distance traveled given an initial height of a drop and a rebound ratio percentage

Receivables Ratios

Given Net Sales, Beginning Accounts Receivable, and Ending Accounts Receivable, this determines Average Accounts Receivable, Receivables turnover ratio, and Average Collection Period.

Relevancy Page Formula

[URL]https://soundcloud.com/mathcelebrity/organic-seo-part-2-relevancy-page-formula[/URL]

Researchers in Antarctica discovered a warm sea current under the glacier that is causing the glacie

Researchers in Antarctica discovered a warm sea current under the glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate if 0.06 m per day.
Which function can be used to find the thickness of the ice shelf in meters x days since the discovery?
We want to build an function I(x) where x is the number of days since the ice shelf discovery.
We start with 450 meters, and each day (x), the ice shelf loses 0.06m, which means we subtract this from 450.
[B]I(x) = 450 - 0.06x[/B]

Resistor Color Codes

Given 3 Band level color codes and a tolerance color chosen, this calculates the resistance in ohms and the tolerance percentage

Reuben finished reading his book in x days. each day, he read 4 pages.His book has 28 pages.

Reuben finished reading his book in x days. each day, he read 4 pages.His book has 28 pages.
x (days) = Total Pages / Pages Per Day
x = 28/4
[B]x = 7 days[/B]

Richard is thrice as old as Alvin. The sum of their ages is 52 years. Find their ages

Richard is thrice as old as Alvin. The sum of their ages is 52 years. Find their ages.
Let r be Richard's age. And a be Alvin's age. We have:
[LIST=1]
[*]r = 3a
[*]a + r = 52
[/LIST]
Substitute (1) into (2)
a + 3a = 52
Group like terms:
4a = 52
[URL='https://www.mathcelebrity.com/1unk.php?num=4a%3D52&pl=Solve']Typing this into the search engine[/URL], we get [B]a = 13[/B].
This means Richard is 3(13) = [B]39[/B]

Ricks age increased by 24 is 69

Let a be Rick's age
We have a + 24 = 69
Subtract 24 from each side
[B]a = 45[/B]

Ricky reads 20 pages in 50 minutes. How many minutes does it take him to read one page

Ricky reads 20 pages in 50 minutes. How many minutes does it take him to read one page
Set up a proportion of pages per minute where m is the number of minutes to read one page:
20/50 = 1/m
To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=20&num2=1&den1=50&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
m = [B]2.5[/B]

Rico was born 6 years after Nico. The sum of their age is 36. How old is Nico?

Rico was born 6 years after Nico. The sum of their age is 36. How old is Nico?
Let Rico's age be r
Let Nico's age be n
We're given two equations:
[LIST=1]
[*]r = n + 6
[*]n + r = 36
[/LIST]
We plug equation (1) into equation (2) for r:
n + n + 6 = 36
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2Bn%2B6%3D36&pl=Solve']type it in our search engine[/URL] and we get:
[B]n = 15[/B]

Rita is mailing packages. Each small package costs her $2.80 to send. Each large package costs her

Rita is mailing packages. Each small package costs her $2.80 to send. Each large package costs her $3.40 . How much will it cost her to send 7 small packages and 5 large packages?
Total Cost = Small Package Cost * small packages + Large Package Cost * large packages
Total Cost = 2.80 * 7 + 3.40 * 5
Total Cost = 19.6 + 17
Total Cost = [B]$36.60[/B]

Rob has scores of 73,75 and 79 on three exams. what does he need on the last exam to get an average

Rob has scores of 73,75 and 79 on three exams. what does he need on the last exam to get an average of no less than 80
Using our [URL='https://www.mathcelebrity.com/missingaverage.php?num=73%2C75%2C79&avg=80&pl=Calculate+Missing+Score']missing average calculator[/URL], we find the missing score must be:
[B]93[/B]

Roberto has taken 17 photos photos are placed on each odd number page and the newspaper has 10 pages

Roberto has taken 17 photos photos are placed on each odd number page and the newspaper has 10 pages total. The pages with photographs will have 3 or 4 photos each. How many pages has 3 photos and how many pages have 4 photos?
Odd pages are 1, 3, 5, 7, 9
17/5 = 3 with 2 remaining.
So all 5 pages have 3 photos. Then with 2 left over, 2 pages get 4 photos.
So 5 pages have [B]3 photos, and 2 pages have 2 photos[/B]
3(3) + 4(2) = 9 + 8 = 17

Rose weighs 140 pounds and gains 10%. What percent of her new weight must she lose to get back to 14

Rose weighs 140 pounds and gains 10%. What percent of her new weight must she lose to get back to 140 pounds?
Find her new weight after the 10% gain:
New Weight = Starting Weight * (1 + 10%)
Since 10% is 0.1, we have:
New Weight = Starting Weight * (1 + 0.1)
New Weight = Starting Weight * (1.1)
Plug in our numbers:
New Weight = 140 * (1.1)
New Weight = 154
To get back to 140, Rose must lose 154 - 140 = 14 pounds.
As a percentage of her new weight, [URL='https://www.mathcelebrity.com/perc.php?num=14&den=154&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']we type 14/154 into our search engine[/URL], and get:
[B]9.09%
[/B]
[I]We read this as, Rose must lose 9.09% of her current body weight of 154 pounds to get back to her starting weight of 140 pounds.[/I]

Sales Tax

Given a sales price and a total bill, this calculates the sales tax amount and sales tax percentage

Sally is 4 years older than Mark. Twice Sally's age plus 5 times Mark's age is equal to 64.

Sally is 4 years older than Mark. Twice Sally's age plus 5 times Mark's age is equal to 64.
Let Sally's age be s. Let Mark's age be m. We're given two equations:
[LIST=1]
[*]s = m + 4
[*]2s + 5m = 64 <-- [I]Since Twice means we multiply by 2[/I]
[/LIST]
Substitute equation (1) into equation (2):
2(m + 4) + 5m = 64
Multiply through:
2m + 8 + 5m = 64
Group like terms:
(2 + 5)m + 8 = 64
7m + 8 = 64
[URL='https://www.mathcelebrity.com/1unk.php?num=7m%2B8%3D64&pl=Solve']Type this equation into the search engine[/URL] and we get:
m = [B]8[/B]

Sally worked for 35 hours and was paid 8 dollars per hour how much money did she earn

Sally worked for 35 hours and was paid 8 dollars per hour how much money did she earn?
Total Wages = Number of Hours Worked * Hourly Rate
Total Wages = 35 * 8
Total Wages = [B]280[/B]

Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which

Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy's age, j, if he is the younger man.
Let Sam's age be s. Let' Jeremy's age be j. We're given:
[LIST=1]
[*]s = j + 2 <-- consecutive odd integers
[*]sj = 783
[/LIST]
Substitute (1) into (2):
(j + 2)j = 783
j^2 + 2j = 783
Subtract 783 from each side:
j^2 + 2j - 783 = 0 <-- This is the equation to find Jeremy's age.
To solve this, [URL='https://www.mathcelebrity.com/quadratic.php?num=j%5E2%2B2j-783%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this quadratic equation into the search engine[/URL] and get:
j = 27, j = -29.
Since ages cannot be negative, we have:
[B]j = 27[/B]

Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is John

Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is John
Let John's age be j. We're given the following equation:
3j - 20 = 52 ([I]Less than[/I] means we subtract)
To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=3j-20%3D52&pl=Solve']type this equation into our search engine[/URL] and we get:
j = [B]24[/B]

samantha is y years old now. represent her age 5 years from now. represent her age 2 years ago

Samantha is y years old now. Represent her age 5 years from now. Represent her age 2 years ago.
5 years from now, Samantha will be [B]y + 5[/B]
2 years ago, Samantha will be [B]y - 2[/B]

Sample Size Reliability for μ

Given a population standard deviation σ, a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.

Sample Size Requirement for the Difference of Means

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.

Sharon is 17 years old. The sum of the ages of Sharon and John is 70

Sharon is 17 years old. The sum of the ages of Sharon and John is 70.
John's age is 70 - Sharon's age.
John's age is 70 - 17 = [B]53[/B]

Sherry is 31 years younger than her mom. The sum of their ages is 61. How old is Sherry?

Sherry is 31 years younger than her mom. The sum of their ages is 61. How old is Sherry?
Let Sherry's age be s. Let the mom's age be m. We're given two equations:
[LIST=1]
[*]s = m - 31
[*]m + s = 61
[/LIST]
Substitute equation (1) into equation (2) for s:
m + m - 31 = 61
To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm-31%3D61&pl=Solve']we type this equation into our search engine[/URL] and we get:
m = 46
Now, we plug m = 46 into equation (1) to find Sherry's age s:
s = 46 - 31
s = [B]15[/B]

Sine Wave

Solves for any of the 3 items of the Sine Wave: Peak Value, Average Value, and RMS value given 1 input.

Sinking Fund Depreciation Method

Using the Sinking Fund method of Depreciation, this calculator determines the following:

* Depreciation at time t (D_{t})

* Asset Value (A)

* Salvage Value (S)

* Book Value at time t (B_{t})

* Depreciation at time t (D

* Asset Value (A)

* Salvage Value (S)

* Book Value at time t (B

Six Years ago, 12.2% of registered births were to teenage mothers. A sociologist believes that the

Six Years ago, 12.2% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then.
(a) Which of the following is the hypothesis to be conducted?
A. H0: p = 0.122, H1 p > 0.122
B. H0: p = 0.122, H1 p <> 0.122
C. H0: p = 0.122, H1 p < 0.122
(b) Which of the following is a Type I error?
A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2%
B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2%
C. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage.
c) Which of the following is a Type II error?
A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage
B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage
C. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2%
(a) [B]C H0: p = 0.122, H1: p < 0.122[/B]
because a null hypothesis should take the opposite of what is being assumed. So the assumption is that nothing has changed while the hypothesis is that the rate has decreased.
(b) [B]C.[/B] The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage. Type I Error is rejecting the null hypothesis when it is true
c) [B]C.[/B] The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% Type II Error is accepting the null hypothesis when it is false.

Solution Mixture

Determines a necessary amount of a Solution given two solution percentages and 1 solution amount.

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Stephanie and her sister go bowling every weekend and have been keeping track of their wins for the

Stephanie and her sister go bowling every weekend and have been keeping track of their wins for the last couple months. So far, Stephanie has won 8 out the total 18 games that they have played. if Stephanie wishes to have an 80% winning record, how many games in a row will Stephanie have to win, without losing?
Track each game the percentage
[LIST=1]
[*]8 out of 18 = 44.44%
[*]9 out of 19 = 47.37%
[*]10 out of 20 = 50%
[*]11 out of 21 = 52.38%
[*]12 out of 22 = 54.55%
[*]13 out of 23 = 56.52%
[*]14 out of 24 = 58.33%
[*]15 out of 25 = 60%
[*]16 out of 26 = 61.54%
[*]17 out of 27 = 62.96%
[*]18 out of 28 = 64.29%
[*]19 out of 29 = 65.52%
[*]20 out of 30 = 66.67%
[*]21 out of 31 = 67.74%
[*]22 out of 32 = 68.75%
[*]23 out of 33 = 69.7%
[*]24 out of 34 = 70.59%
[*]25 out of 35 = 71.43%
[*]26 out of 36 = 72.22%
[*]27 out of 37 = 72.97%
[*]28 out of 38 = 73.68%
[*]29 out of 39 = 74.36%
[*]30 out of 40 = 75%
[*]31 out of 41 = 75.61%
[*]32 out of 42 = 76.19%
[*]33 out of 43 = 76.74%
[*]34 out of 44 = 77.27%
[*]35 out of 45 = 77.78%
[*]36 out of 46 = 78.26%
[*]37 out of 47 = 78.72%
[*]38 out of 48 = 79.17%
[*]39 out of 49 = 79.59%
[*][B]40 out of 50 = 80%[/B]
[/LIST]
[B]So our answer is 32 games in a row[/B]

Straight Line Depreciation

Solves for Depreciation Charge, Asset Value, Salvage Value, Time, N, and Book Value using the Straight Line Method.

students at East Central High School earned $384 selling car washes. They want to make $2690 for a c

Students at East Central High School earned $384 selling car washes. They want to make $2690 for a club trip. What percent of their goal has been reached?
384/2690 = [B]14.28%[/B] using our [URL='http://www.mathcelebrity.com/perc.php?num=384&den=2690&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']percentage-decimal calculator[/URL]

Suppose 5% of a package of balloons are yellow balloons. Then what percentage of balloons are a diff

Suppose 5% of a package of balloons are yellow balloons. Then what percentage of balloons are a different color than yellow?
Our total possibilities of any color balloon is 100%. So we have:
Non-yellow balloons = 100% - yellow balloons percent
Non-yellow balloons = 100% - 5%
Non-yellow balloons = [B]95%[/B]

Suppose a computer chip manufacturer knows from experience that in an average production run of 5000

Suppose a computer chip manufacturer knows from experience that in an average production run of 5000 circuit boards, 100 will be defective. How many defective circuit boards can be expected in a run of 24,000 circuit boards?
100 defective / 5000 circuit boards * 24,000 circuit boards = [B]480 defective circuit boards[/B]

Suppose a firm producing light bulbs wants to know if it can claim that its light bulbs it produces

Suppose a firm producing light bulbs wants to know if it can claim that its light bulbs it produces last 1,000 burning hours (u). To do this, the firm takes a random sample of 100 bulbs and find its average life time (X=980 hrs) and the sample standard deviation s = 80 hrs. If the firm wants to conduct the test at the 1% of significance, what's you final suggestion?
(i..e, Should the producer accept the Ho that its light bulbs have a 1,000 burning hrs. at the 1% level of significance?)
Ho: u = 1,000 hours.
Ha: u <> 1,000 hours.
[URL='http://www.mathcelebrity.com/mean_hypothesis.php?xbar=+980&n=+100&stdev=+80&ptype==&mean=+1000&alpha=+0.01&pl=Mean+Hypothesis+Testing']Perform a hypothesis test of the mean[/URL]
[B]Yes, accept null hypothesis[/B]

Suppose that previously collected traffic data indicate that, during the afternoon rush hour, an ave

Suppose that previously collected traffic data indicate that, during the afternoon rush hour, an average of 4 cars arrive at a toll bridge each second. If it is assumed that cars arrive randomly, and can thus be modeled with Poisson distribution, what is the probability that in the next second, [U][B]NO[/B][/U] cars will arrive?
Use the [I]Poisson Distribution[/I] with λ = 4 and x = 0
Using the [URL='http://www.mathcelebrity.com/poisson.php?n=+10&p=+0.4&k=+0&t=+3&pl=P%28X+=+k%29']Poisson Distribution calculator[/URL], we get P(0; 4) = [B]0.0183[/B]

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls.
a. If X = average distance in feet for 49 fly balls, then X ~ _______(_______,_______)

b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.

c. Find the 80^{th} percentile of the distribution of the average of 49 fly balls
a. N(250, 50/sqrt(49)) = [B]0.42074[/B]
b. Calculate Z-score and probability = 0.08 shown [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+240&mean=+250&stdev=+7.14&n=+1&pl=P%28X+%3C+Z%29']here[/URL]
c. Inverse of normal distribution(0.8) = 0.8416. Use NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL]
Using the Z-score formula, we have
0.8416 = (x - 250)/50
x = [B]292.08[/B]

b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.

c. Find the 80

Suppose that the manager of the Commerce Bank at Glassboro determines that 40% of all depositors hav

Suppose that the manager of the Commerce Bank at Glassboro determines that 40% of all depositors have a multiple accounts at the bank. If you, as a branch manager, select a random sample of 200 depositors, what is the probability that the sample proportion of depositors with multiple accounts is between 35% and 50%?
[URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=50&n=+100&ptype==&p=+0.4&alpha=+0.05&pl=Proportion+Hypothesis+Testing']50% proportion probability[/URL]: z = 2.04124145232
[URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=+35&n=+100&ptype==&p=+0.4&alpha=+0.05&pl=Proportion+Hypothesis+Testing']35% proportion probability[/URL]: z = -1.02062072616
Now use the [URL='http://www.mathcelebrity.com/zscore.php?z=p%28-1.02062072616

Susie bought 15 pairs of shoes last year for an avarage of 30$ per pair. She sold each pair for 1/3

Susie bought 15 pairs of shoes last year for an avarage of 30$ per pair. She sold each pair for 1/3 of the avagrage price at a consignment shop. How much money did she make at the consigment shop?
Calculate average price:
1/3 the average price is $30/3 = $10
Total money made:
Pairs of Shoes * Average Price
15 * 10 = [B]$150[/B]

Tamara can proofread 16 pages in 8 minutes. How many minutes will it take her to proofread 108 pages

Tamara can proofread 16 pages in 8 minutes. How many minutes will it take her to proofread 108 pages
Set up a proportion of pages to minutes:
16 pages/8 minutes = 108 pages / p minutes
We want to solve for p.
Type [I][URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=108&den1=8&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']16/8 = 108/p[/URL][/I] into the search engine.
We get p = [B]54 minutes[/B]

Target Heart Rate

Given an age, this calculator determines the following 5 target heart rate zones:

Healthy Heart Zone (Warm up) 50 - 60%

Fitness Zone (Fat Burning) 60 - 70%

Aerobic Zone (Endurance Training) 70 - 80%

Anaerobic Zone (Performance Training) 80 - 90%

Red Line (Maximum Effort) 90 - 100%

Healthy Heart Zone (Warm up) 50 - 60%

Fitness Zone (Fat Burning) 60 - 70%

Aerobic Zone (Endurance Training) 70 - 80%

Anaerobic Zone (Performance Training) 80 - 90%

Red Line (Maximum Effort) 90 - 100%

The age of a woman 15 years ago

The age of a woman 15 years ago
Let the woman's current age be a.
15 years ago means we subtract 15 from a:
[B]a - 15[/B]

The age of denver 3 years ago if he is x years old now

The age of denver 3 years ago if he is x years old now
3 years ago means we subtract:
[B]x - 3[/B]

The age of three sister are consecutive intergers the sum of their age is 45 what is their ages

The age of three sister are consecutive intergers the sum of their age is 45 what is their ages
Type this into the search engine: [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=thesumofthreeconsecutivenumbersis45&pl=Calculate']The sum of three consecutive numbers is 45[/URL].
We get [B]14, 15, 16[/B].

The age of woman 15 years ago

The age of woman 15 years ago
Let a be the woman's age today. 15 years ago means we subtract 15 from a:
[B]a - 15[/B]

The ages of three siblings are all consecutive integers. The sum of of their ages is 39.

The ages of three siblings are all consecutive integers. The sum of of their ages is 39.
Let the age of the youngest sibling be n. This means the second sibling is n + 1. This means the oldest/third sibling is n + 2.
So what we want is the[URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof3consecutiveintegersequalto39&pl=Calculate'] sum of 3 consecutive integers equal to 39[/URL]. We type this command into our search engine. We get:
n = 12. So the youngest sibling is [B]12[/B].
The next sibling is 12 + 1 = [B]13[/B]
The oldest/third sibling is 12 + 2 = [B]14[/B]

The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. Wha

The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. What is the value of N ?
Average of the first number set is [URL='https://www.mathcelebrity.com/statbasic.php?num1=17%2C26%2C42%2C59&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']using our average calculator[/URL] is:
36
Now, the mean (average) or 19 and N is found by adding them together an dividing by 2:
(19 + N)/2
Since both number sets have equal means, we set (19 + N)/2 equal to 36:
(19 + N)/2 = 36
Cross multiply:
19 + N = 36 * 2
19 + n = 72
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=19%2Bn%3D72&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]53[/B]

The average age of 15 men is 25 years. What is their total age in years?

The average age of 15 men is 25 years. What is their total age in years?
Average Age = Total Ages/Total Men
25 = Total Ages / 15
Cross multiply and we get:
Total Ages = 15 * 25
Total Ages = [B]375[/B]

The average cost of printing a book in a publishing company is c(x) = 5.5x+kx , where x is the numbe

The average cost of printing a book in a publishing company is c(x) = 5.5x+kx , where x is the number of books printed that day and k is a constant. Find k, if on the day when 200 were printed the average cost was $9 per book.
We are given: c(200) = 9, so we have:
9 = 5.5(200) + k(200)
200k + 1100 = 9
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=200k%2B1100%3D9&pl=Solve']equation solver[/URL], we get:
[B]k = -5.455[/B]

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height re

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height remained the same. What is the height of the mother?
[LIST]
[*]Let the height of the family without the mom be f. Let the height of the mother be m.
[*]Averages mean we add the heights and divide by the number of people who were measured.
[/LIST]
We're given two equations:
[LIST=1]
[*](f + m)/6 = 6
[*]f/5 = 6
[/LIST]
Cross multiplying equation (2), we get:
f = 5 * 6
f = 30
Plug f = 30 into equation (1), we get:
(30 + m)/6 = 6
Cross multiplying, we get:
m + 30 = 6 * 6
m + 30 = 36
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B30%3D36&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]6[/B]
[SIZE=3][FONT=Arial][COLOR=rgb(34, 34, 34)][/COLOR][/FONT][/SIZE]

The average of 16 and x is 21. Find x.

The average of 16 and x is 21. Find x.
The average of 2 numbers is the sum of the 2 numbers divided by 2. So we have:
(16 + x)/2 = 21
Cross multiply:
16 + x = 21*2
16 + x = 42
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=16%2Bx%3D42&pl=Solve']we type this expression into the search engine[/URL] and get [B]x = 26[/B].
Check our work by restating our answer:
The average of 16 and 26 is 21. TRUE.

The average of 171 and x?

The average of 171 and x?
The phrase [I]average[/I] means add up all the items in the number set, divided by the count of items in the number set.
Our number set in this case is {171, x} which has 2 elements. Therefore, our average is:
[B](171 + x)/2[/B]

The average of 20 numbers is 18 while the average of 18 numbers is 20. What is the average of the 38

The average of 20 numbers is 18 while the average of 18 numbers is 20. What is the average of the 38 numbers?
The average of averages is found by getting the sum of both groups of numbers and dividing by the count of numbers.
Calculate the sum of the first group of numbers S1:
Average = S1 / n1
18 = S1 / 20
S1 = 20 * 18
S1 =360
Calculate the sum of the second group of numbers S2:
Average = S2 / n2
20 = S2 / 18
S2 = 18 * 20
S2 =360
Our average of averages is found by the following:
A = (S1 + S2)/(n1 + n2)
A = (360 + 360)/(20 + 18)
A = 720/38
[B]A = 18.947[/B]

The average of a number and double the number is 25.5

Let x equal "a number".
Double the number is 2x.
The average is (x + 2x)/2
Combine the terms in the numerator:
3x/2
The word [I]is[/I] means equal to, so we set 3x/2 equal to 25.5
3x/2 = 25.5
Cross multiply the 2:
3x = 51
Divide each side by 3
[B]x = 17[/B]

the average of eighty-five and a number m is ninety

the average of eighty-five and a number m is ninety
Average of 2 numbers means we add both numbers and divide by 2:
(85 + m)/2 = 90
Cross multiply:
m + 85 = 90 * 2
m + 85 = 180
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B85%3D180&pl=Solve']type it in our math engine [/URL]and we get:
m = [B]95[/B]

The average of manny three tests is an 84. What must he get on a 4th test to raise his average to a

The average of manny three tests is an 84. What must he get on a 4th test to raise his average to a 87?
[URL='http://www.mathcelebrity.com/missingaverage.php?num=84%2C84%2C84&avg=87&pl=Calculate+Missing+Score']This is a missing average problem, use our missing average calculator[/URL]
His 4th test must be [B]96[/B]

the average of two numbers x and y

the average of two numbers x and y
Average is the sum divided by the count:
Sum:
x + y
We have 2 numbers, so we divide (x + y) by 2
[B](x + y)/2[/B]

the average, a, is at least 85

the average, a, is at least 85
At least is an inequality. It also means greater than or equal to, so we have:
[B]a >= 85[/B]

The book Shelly has 235 pages. she has read 110 pages. If she reads 25 pages from now on, how many m

The book Shelly has 235 pages. she has read 110 pages. If she reads 25 pages from now on, how many more days will it take her to complete the book?
Subtract the pages read to get the unread pages:
235 - 110 = 125 unread pages
Now figure out how many days, reading 25 pages per day, to read 125 pages
125/25 = [B]5 days[/B]

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognit

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the bran. How many adults must he survey in order to be 90% confident that his estimate is within seven percentage points of the true population percentage?
[IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] = 0.5
1 - [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] = 0.5
margin of error (E) = 0.07
At 90% confidence level the t is,
alpha = 1 - 90%
alpha = 1 - 0.90
alpha = 0.10
alpha / 2 = 0.10 / 2 = 0.05
Zalpha/2 = Z0.05 = 1.645
sample size = n = (Z[IMG]https://ci4.googleusercontent.com/proxy/mwhpkw3aM19oMNA4tbO_0OdMXEHt9juW214BnNpz4kjXubiVJgwolO7CLbmWXXoSVjDPE_T0CGeUxNungBjN=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Calpha[/IMG] / 2 / E )2 * [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] * (1 - [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] )
= (1.645 / 0.07)^2 *0.5*0.5
23.5^2 * 0.5 * 0.5
552.25 * 0.5 * 0.5
= 138.06
[B]sample size = 138[/B]
[I]He must survey 138 adults in order to be 90% confident that his estimate is within seven percentage points of the true population percentage.[/I]

The club uses the function S(t) = -4,500t + 54,000 to determine the salvage S(t) of a fertilizer ble

The club uses the function S(t) = -4,500t + 54,000 to determine the salvage S(t) of a fertilizer blender t years after its purchase. How long will it take the blender to depreciate completely?
Complete depreciation means the salvage value is 0.
So S(t) = 0. We need to find t to make S(t) = 0
-4,500t + 54,000 = 0
Subtract 54,000 from each side
-4,500t = -54,000
Divide each side by -4,500
[B]t = 12[/B]

The cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is the

The cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is the total cost to park for 5 hours?
Set up our equation where C is cost and h is the number of hours used to park
C = 1.5h + 2.25
With h = 5, we have:
C = 1.5(5) + 2.25
C = 7.5 + 2.25
C = 9.75

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 distribution of actual weights of 8 oz chocolate bars produced by a certain machine is normal wi

The distribution of actual weights of 8 oz chocolate bars produced by a certain machine is normal with µ=8.1 ounces and ?=0.1 ounces. A sample of 5 of these chocolate bars is selected. What is the probability that their average weight is less than 8 ounces?
Calculate Z score and probability using [URL='http://www.mathcelebrity.com/probnormdist.php?xone=8&mean=8.1&stdev=0.1&n=5&pl=P%28X+%3C+Z%29']our calculator[/URL]:
Z = -2.236
P(X < -2.236) = [B]0.012545[/B]

The 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 graph shows the average length (in inches) of a newborn baby over the course of its first 15 mon

The graph shows the average length (in inches) of a newborn baby over the course of its first 15 months. Interpret the RATE OF CHANGE of the graph.
[IMG]http://www.mathcelebrity.com/community/data/attachments/0/rate-of-change-wp.jpg[/IMG]
Looking at our graph, we have a straight line. For straight lines, rate of change [U][I]equals[/I][/U] slope.
Looking at a few points, we have:
(0, 20), (12, 30)
Using our [URL='https://www.mathcelebrity.com/slope.php?xone=0&yone=20&slope=+2%2F5&xtwo=12&ytwo=30&pl=You+entered+2+points']slope calculator for these 2 points[/URL], we get a slope (rate of change) of:
[B]5/6[/B]

The height of an object t seconds after it is dropped from a height of 300 meters is s(t)=-4.9t^2 +3

The height of an object t seconds after it is dropped from a height of 300 meters is s(t)=-4.9t^2 +300. Find the average velocity of the object during the first 3 seconds? (b) Use the Mean value Theorem to verify that at some time during the first 3 seconds of the fall the instantaneous velocity equals the average velocity. Find that time.
Average Velocity:
[ f(3) - f(0) ] / ( 3 - 0 )
Calculate f(3):
f(3) = -4.9(3^2) + 300
f(3) = -4.9(9) + 300
f(3) = -44.1 + 300
f(3) = 255.9
Calculate f(0):
f(0) = -4.9(0^2) + 300
f(0) = 0 + 300
f(0) = 300
So we have average velocity:
Average velocity = (255.9 - 300)/(3 - 0)
Average velocity = -44.1/3
Average velocity = -[B]14.7
[/B]
Velocity is the first derivative of position
s(t)=-4.9t^2 +300
s'(t) = -9.8t
So we set velocity equal to average velocity:
-9.8t = -14.7
Divide each side by -9.8 to solve for t, we get [B]t = 1.5[/B]

The holy bible contains 525 pages. A believer reads 10 pages during weekends and 15 pages during wee

The holy bible contains 525 pages. A believer reads 10 pages during weekends and 15 pages during weekdays. How long will it take him to finish reading the bible?
Take one 7 day week:
15 + 10 = 25 pages
525 pages/25 pages = [B]21 weeks[/B]

The hourly wages of employees at Rowan have a mean wage rate of $10 per hour with a standard deviati

The hourly wages of employees at Rowan have a mean wage rate of $10 per hour with a standard deviation of $1.20. What is the probability the mean hourly wage of a random sample of 36 employees will be larger than $10.50? Assume the company has a total of 1,000 employees
Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=10.5&mean=10&stdev=1.2&n=36&pl=P%28X+>+Z%29']normal distribution calculator[/URL], we get P(x > 10.5) = [B]0.00621[/B]

the left and right page numbers of an open book are two consecutive integers whose number is 235 fin

the left and right page numbers of an open book are two consecutive integers whose number is 235 find the page numbers
Using our [URL='https://www.mathcelebrity.com/consecintwp.php?pl=Sum&num=+235']consecutive integer calculator[/URL], we get:
[B]117, 118[/B]

The left and right page numbers of an open book are two consecutive integers whose sum is 403. Find

The left and right page numbers of an open book are two consecutive integers whose sum is 403. Find these page numbers.
Page numbers left and right are consecutive integers. So we want to find a number n and n + 1 where:
n + n + 1 = 403
Combining like terms, we get:
2n + 1 = 403
Typing that equation into our search engine, we get:
[B]n = 201[/B]
This is our left hand page. Our right hand page is:
201 + 1 = [B]202[/B]

The margarita is one of the most common tequila-based cocktails, made with tequila, triple sec, and

The margarita is one of the most common tequila-based cocktails, made with tequila, triple sec, and lime
juice, often served with salt on the glass rim. A manager at a local bar is concerned that the bartender is
not using the correct amounts of the three ingredients in more than 50% of margaritas. He secretly
observed the bartender and found that he used the CORRECT amounts in only 9 out of the 39
margaritas in the sample. Use the critical value approach to test if the manager's suspicion is justified
at ? = 0.10. Let p represent the proportion of all margaritas made by the bartender that have
INCORRECT amounts of the three ingredients. Use Table 1.
a. Select the null and the alternative hypotheses.
[B]H0: p ? 0.50; HA: p > 0.50[/B]
[B][/B]
b. Calculate the sample proportion. (Round your answer to 3 decimal places.)
9/39 = [B]0.231
[/B]
c. Calculate the value of test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
Using our [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=9&n=39&ptype=%3C&p=+0.5&alpha=+0.10&pl=Proportion+Hypothesis+Testing']proportion hypothesis calculator[/URL], we get:
[B]Test Stat = -3.36[/B]
[B][/B]
d. Calculate the critical value. (Round your answer to 2 decimal places.)
Using the link above, we get a critical value of [B]1.2816
[/B]
e. What is the conclusion?
[B]The manager’s suspicion is not justified since the value of the test statistic does not fall in the rejection region. Do not reject H0[/B]
[B][/B]

The mean age of 10 women in an office is 30 years old. The mean age of 10 men in an office is 29 yea

The mean age of 10 women in an office is 30 years old. The mean age of 10 men in an office is 29 years old. What is the mean age (nearest year) of all the people in the office?
Mean is another word for [U]average[/U].
Mean age of women = Sum of all ages women / number of women
We're told mean age of women is 30, so we have:
Sum of all ages women / 10 = 30
Cross multiply, and we get:
Sum of all ages of women = 30 * 10
Sum of all ages of women = 300
Mean age of men = Sum of all ages men / number of men
We're told mean age of men is 29, so we have:
Sum of all ages men / 10 = 29
Cross multiply, and we get:
Sum of all ages of men = 29 * 10
Sum of all ages of men = 290
[U]Calculate mean age (nearest year) of all the people in the office:[/U]
mean age of all the people in the office = Sum of all ages of people in the office (men and women) / Total number of people in the office
mean age of all the people in the office = (300 + 290) / (10 + 10)
mean age of all the people in the office = 590 / 20
mean age of all the people in the office = 29.5
The question asks for nearest year. Since this is a decimal, we round down to either 29 or up to 30.
Because the decimal is greater or equal to 0.5 (halfway), we round [U]up[/U] to [B]30[/B]

The mean age of 5 people in a room is 28 years. A person enters the room. The mean age is now 32. W

The mean age of 5 people in a room is 28 years. A person enters the room. The mean age is now 32. What is the age of the person who entered the room?
The sum of the 5 people's scores is S. We know:
S/5 = 28
Cross multiply:
S = 140
We're told that:
(140 + a)/6 = 32
Cross multiply:
140 + a = 192
[URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D192&pl=Solve']Type this equation into our search engine[/URL], we get:
a = [B]52[/B]

The mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. Wh

The mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. What is the age of the person who entered the room?
Mean = Sum of Ages in Years / Number of People
32 = Sum of Ages in Years / 5
Cross multiply:
Sum of Ages in Years = 32 * 5
Sum of Ages in Years = 160
Calculate new mean after the next person enters the room.
New Mean = (Sum of Ages in Years + New person's age) / (5 + 1)
Given a new Mean of 40, we have:
40 = (160 + New person's age) / 6
Cross multiply:
New Person's Age + 160 = 40 * 6
New Person's Age + 160 = 240
Let the new person's age be n. We have:
n + 160 = 240
To solve for n, [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B160%3D240&pl=Solve']we type this equation into our search engine[/URL] and we get:
n = [B]80[/B]

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. Wh

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. What is the age of the person who entered the room?
The mean formulas is denoted as:
Mean = Sum of Ages / Total People
We're given Mean = 38 and Total People = 5, so we plug in our numbers:
28 = Sum of Ages / 5
Cross multiply, and we get:
Sum of Ages = 28 * 5
Sum of Ages = 140
One more person enters the room. The mean age is now 39. Set up our Mean formula:
Mean = Sum of Ages / Total People
With a new Mean of 39 and (5 + 1) = 6 people, we have:
39 = Sum of Ages / 6
But the new sum of Ages is the old sum of ages for 5 people plus the new age (a):
Sum of Ages = 140 + a
So we have:
29 = (140 + a)/6
Cross multiply:
140 + a = 29 * 6
140 + a = 174
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D174&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]34[/B]

The mean of two numbers is 49.1. The first number is 18.3. What is the second number

The mean of two numbers is 49.1. The first number is 18.3. What is the second number
We call the second number n. Since the mean is an average, in this case 2 numbers, we have:
(18.3 + n)/2 = 49.1
Cross multiply:
18.3 + n = 98.2
[URL='https://www.mathcelebrity.com/1unk.php?num=18.3%2Bn%3D98.2&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]n = 79.9[/B]

The minimum daily requirement of vitamin C for 14 year olds is at least 50 milligrams per day. An av

The minimum daily requirement of vitamin C for 14 year olds is at least 50 milligrams per day. An average sized apple contains 6 milligrams of vitamin C. How many apples would a person have to eat each day to satisfy this requirement?
Let a be the number of apples required. The phrase [I]at least[/I] means greater than or equal to, so we have the inequality:
6a >= 50
To solve this inequality, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6a%3E%3D50&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get:
[B]a >= 8.3333 apples or rounded up to a full number, we get 9 apples[/B]

The pieces of a 500 piece puzzle are stored in three containers. 220 pieces are in the first contain

The pieces of a 500 piece puzzle are stored in three containers. 220 pieces are in the first container and 180 pieces are in the second container. What percentage of the pieces is in the third container?
[U]Calculate the number of pieces in the 3rd container:[/U]
Pieces in container 3 = Total Puzzle Pieces - Pieces in container 2 - Pieces in container 1
Pieces in container 3 = 500 - 220 - 180
Pieces in container 3 = 100
Calculate the percentage of pieces in the 3rd container:
Percentage of pieces in container 3 = 100% * Pieces in container 3 / Total puzzle pieces
Percentage of pieces in container 3 = 100% * 100 / 500
Percentage of pieces in container 3 = 100% * 0.2
Percentage of pieces in container 3 = [B]20%[/B]

The property taxes on a boat were $375. What was the tax rate if the boat was valued at $75,000?

The property taxes on a boat were $375. What was the tax rate if the boat was valued at $75,000?
Tax Rate = Tax Amount / Purchase Price
Tax Rate = 375 / 75,000
Tax Rate = 0.005
Tax Rates are generally expressed in percentages, so the percentage = 0.005 * 100 = [B]0.5%[/B].

The property taxes on a house were $810. What was the tax rate if the house was valued at $90,000

The property taxes on a house were $810. What was the tax rate if the house was valued at $90,000
Tax rate = Property Tax Amount/House Value
Tax rate = 810/90000
[B]Tax Rate = 0.009, or as a percentage, 0.9%[/B]

The relief time provided by a standard dose of a popular children’s allergy medicine averages 7.9

The relief time provided by a standard dose of a popular children’s allergy medicine averages 7.9 hours with a standard deviation of 2.2 hours. Use Table 1.
a. Determine the percentage of children who experience relief for less than 6.4 hours if the relief time follows a normal distribution. (Round your answer to 2 decimal places.)
Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=6.4&mean=7.9&stdev=2.2&n=1&pl=P%28X+%3C+Z%29']normal distribution calculator[/URL], we get
Answer = [B]0.25[/B]

The sales tax for an item was $21.50 and it cost $430 before tax. Find the sales tax rate. Write you

The sales tax for an item was $21.50 and it cost $430 before tax. Find the sales tax rate. Write your answer as a percentage.
Sales tax percentage is:
21.50/430 = 0.05
To get a percentage, multiply the decimal by 100
0.05 * 100 = [B]5%[/B]

The sum of 13 and twice janelles age

Let Janelle's age be the variable a.
So twice Janelle's age is denoted as 2a.
We want the sum of 13 and 2a.
Sum means add.
13 + 2a
or
2a + 13

the sum of 23 and victor age is 59

the sum of 23 and victor age is 59
Let's Victor's age be a.
The sum of 23 and Victor's age (a) mean we add a to 23:
23 + a
The word [I]is[/I] means an equation, so we set 23 + a equal to 59:
[B]23 + a = 59[/B] <-- This is our algebraic expression
Now if the problem asks you to take it a step further and solve this for a, [URL='https://www.mathcelebrity.com/1unk.php?num=23%2Ba%3D59&pl=Solve']we type this equation into our search engine[/URL] and we get:
[B]a = 36[/B]

The sum of 9 and victors age is 55

The sum of 9 and victors age is 55
Let v be Victor's age. We have the algebraic expression:
[B]v + 9 = 55
[/B]
If you want to solve or v, use our [URL='http://www.mathcelebrity.com/1unk.php?num=v%2B9%3D55&pl=Solve']equation calculator[/URL].

The sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present age

The sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present age. How old are they now?
Let Jocelyn's age be a
Let Joseph's age be b.
We're given two equations:
[LIST=1]
[*]a + b = 40
[*]2(a + 5) = b + 5
[/LIST]
We rearrange equation (1) in terms of a to get:
[LIST=1]
[*]a = 40 - b
[*]2a = b + 5
[/LIST]
Substitute equation (1) into equation (2) for a:
2(40 - b) = b + 5
80 - 2b = b + 5
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=80-2b%3Db%2B5&pl=Solve']type it in our search engine[/URL] and we get:
[B]b (Joseph's age) = 25[/B]
Now, substitute b = 25 into equation (1) to solve for a:
a = 40 - 25
[B]a (Jocelyn's age) = 15[/B]

The sum of Juan’s age and Sara’s age is 33 yrs. If Sara is 15 yrs old, how old is Juan?

The sum of Juan’s age and Sara’s age is 33 yrs. If Sara is 15 yrs old, how old is Juan?
Let j be Juan's age and s be Sara's age. We have the following equations:
[LIST=1]
[*]j + s = 33
[*]s = 15
[/LIST]
Substitute (2) into (1)
j + 15 = 33
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=j%2B15%3D33&pl=Solve']equation solver[/URL], we get[B] j = 18[/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]

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. Ho

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. How old is Levi now?
Let Levi's current age be l. Let Renee's current age be r. Were given two equations:
[LIST=1]
[*]l + r = 89
[*]l - 7 = 4(r - 7)
[/LIST]
Simplify equation 2 by multiplying through:
[LIST=1]
[*]l + r = 89
[*]l - 7 = 4r - 28
[/LIST]
Rearrange equation 1 to solve for r and isolate l by subtracting l from each side:
[LIST=1]
[*]r = 89 - l
[*]l - 7 = 4r - 28
[/LIST]
Now substitute equation (1) into equation (2):
l - 7 = 4(89 - l) - 28
l - 7 = 356 - 4l - 28
l - 7 = 328 - 4l
To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l-7%3D328-4l&pl=Solve']type the equation into our search engine[/URL] and we get:
l = [B]67[/B]

The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. h

The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins?
Let a be Suresh's age, h be Hakima's age, and c be Saad's age. We're given:
[LIST=1]
[*]a + h + c = 48
[*]a = 0.5h
[*]a = c + 4
[/LIST]
To isolate equations in terms of Suresh's age (a), let's do the following:
[LIST]
[*]Rewriting (3) by subtracting 4 from each side, we get c = a - 4
[*]Rewriting (2) by multiply each side by 2, we have h = 2a
[/LIST]
We have a new system of equations:
[LIST=1]
[*]a + h + c = 48
[*]h = 2a
[*]c = a - 4
[/LIST]
Plug (2) and (3) into (1)
a + (2a) + (a - 4) = 48
Group like terms:
(1 + 2 + 1)a - 4 = 48
4a - 4 = 48
[URL='https://www.mathcelebrity.com/1unk.php?num=4a-4%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]a = 13 [/B]<-- Suresh's age
This means that Hakima's age, from modified equation (2) above is:
h = 2(13)
[B]h = 26[/B] <-- Hakima's age
This means that Saad's age, from modified equation (3) above is:
c = 13 - 4
[B]c = 9[/B] <-- Saad's age
[B]
[/B]

The weight of a 9.5-inch by 6-inch paperback book published by Leaden Publications, Inc., is 16.2 oz

The weight of a 9.5-inch by 6-inch paperback book published by Leaden Publications, Inc., is 16.2 oz. The standard deviation is 2.9 oz. What is the probability that the average weight of a sample of 33 such books is less than 15.89 oz?
Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=15.89&mean=16.2&stdev=2.9&n=33&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we get:
[B]0.271[/B]

There are 24 students in a class. Three new students joined the class. Work out the percentage chang

There are 24 students in a class. Three new students joined the class. Work out the percentage change in the number of students in the class.
We want to know how much an increase of 3 people is in a class of 24:
3/24
Using [URL='https://www.mathcelebrity.com/perc.php?num=3&den=24&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']our percentage/decimal calculator[/URL], we get:
[B]12.5% increase[/B]

There are 250 boys and 150 girls in a school, if 60% of the boys and 40% of the girls play football,

There are 250 boys and 150 girls in a school, if 60% of the boys and 40% of the girls play football, what percentage of the school play football
[U]First calculate total students:[/U]
Total students = Boys + Girls
Total students = 250 + 150
Total students = 400
[U]Calculate the boys that play football:[/U]
Boys playing football = 60% * 250
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=60&den1=250&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Boys playing football [/URL]= 150
[U]Calculate the girls that play football:[/U]
Girls playing football = 40% * 150
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=40&den1=150&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Girls playing football[/URL][URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=60&den1=250&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate'] [/URL]= 60
[U]Calculate total people playing football[/U]:
Total people playing football = Boys playing football + Girls playing football
Total people playing football = 150 + 60
Total people playing football = 210
Calculate percentage of the school playing football (P):
P = 100% * Total people playing football / Total Students
P = 100% * [URL='https://www.mathcelebrity.com/longdiv.php?num1=210&num2=400&pl=Long%20Division%20%28Decimals%29']210/400[/URL]
P = 100% * 0.525
P = [B]52.5%[/B]

There are 3,742,450 men, 3,177,805 women and 21,508 children in a village. Find the total population

There are 3,742,450 men, 3,177,805 women and 21,508 children in a village. Find the total population of the village.
Total population = Men + Women + Children
Total population = 3,742,450 + 3,177,805 + 21,508
Total population = [B]6,941,763[/B]

There are 32 students in a class. Nine of those students are women. What percent are men

There are 32 students in a class. Nine of those students are women. What percent are men
[U]Find the number of male students:[/U]
Males = Total Students - Females
Males = 32 - 9
Males = 23
[U]Calculate percentage of males:[/U]
Percentage of males = 100% * Males / Total Students
Percentage of males = 100% * 23 / 32
Percentage of males = 100% * 0.71875
Percentage of males = 71.88%
[URL='https://www.mathcelebrity.com/perc.php?num=23&den=32&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']See this link as well[/URL]

Tiffany is 59 years old. The sum of the ages of Tiffany and Maria is 91. How old is Maria?

Tiffany is 59 years old. The sum of the ages of Tiffany and Maria is 91. How old is Maria?
Tiffany + Maria = 91
59 + Maria = 91
Subtract 59 from each side
Maria = 91 - 59
[B]Maria = 32[/B]

To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional po

To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional pound. To ship a package with FedEx, the cost will be $5 for the first pound and $0.30 for each additional pound. How many pounds will it take for UPS and FedEx to cost the same? If you needed to ship a package that weighs 8 lbs, which shipping company would you choose and how much would you pay?
[U]UPS: Set up the cost function C(p) where p is the number of pounds:[/U]
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.2(p - 1) + 7
[U]FedEx: Set up the cost function C(p) where p is the number of pounds:[/U]
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.3(p - 1) + 5
[U]When will the costs equal each other? Set the cost functions equal to each other:[/U]
0.2(p - 1) + 7 = 0.3(p - 1) + 5
0.2p - 0.2 + 7 = 0.3p - 0.3 + 5
0.2p + 6.8 = 0.3p + 4.7
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B6.8%3D0.3p%2B4.7&pl=Solve']type it in our search engine[/URL] and we get:
p = [B]21
So at 21 pounds, both UPS and FedEx costs are equal
[/B]
Now, find out which shipping company has a better rate at 8 pounds:
[U]UPS:[/U]
C(8) = 0.2(8 - 1) + 7
C(8) = 0.2(7) + 7
C(8) = 1.4 + 7
C(8) = 8.4
[U]FedEx:[/U]
C(8) = 0.3(8 - 1) + 5
C(8) = 0.3(7) + 5
C(8) = 2.1 + 5
C(8) = [B]7.1[/B]
[B]Therefore, FedEx is the better cost at 8 pounds since the cost is lower[/B]
[B][/B]

Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one yea

Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one year from now. Given that my age is an integer number of years, what is the smallest my age could be?
Let my current age be a. We're given:
4/5a > 3/4(a + 1)
Multiply through on the right side:
4a/5 > 3a/4 + 3/4
Let's remove fractions by multiply through by 5:
5(4a/5) > 5(3a/4) + 5(3/4)
4a > 15a/4 + 15/4
Now let's remove the other fractions by multiply through by 4:
4(4a) > 4(15a/4) + 4(15/4)
16a > 15a + 15
[URL='https://www.mathcelebrity.com/1unk.php?num=16a%3E15a%2B15&pl=Solve']Typing this inequality into our search engine[/URL], we get:
a > 15
This means the smallest [I]integer age[/I] which the problem asks for is:
15 + 1 = [B]16[/B]

Tom and Damian are shooting free throws. If Tom makes 7 free throws in 9 attempts, and Damian makes

Tom and Damian are shooting free throws. If Tom makes 7 free throws in 9 attempts, and Damian makes 5 free throws in 6 attempts, who has the higher relative performance? Answer this by calculating and comparing the free throw percentages of Tom and Damian.
Tom makes 7/9. [URL='https://www.mathcelebrity.com/perc.php?num=7&den=9&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']Using our percentage and decimal calculator[/URL], he makes 77.78% of the free throws.
Damian makes 5/6. [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+6&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&pof1=&pof2=&pl=Calculate']Using our percentage and decimal calculator[/URL], he makes 83.33% of the free throws.
[B]Damian[/B] has a better free throw percentage.

Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages and subtra

Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages and subtract 2, the sum is 20. How old is Bill?
Let t be Tom's age., s be Sue's age, and b be Bill's age. We have the following equations:
[LIST=1]
[*]t = s + 2
[*]b = 2t
[*]s + t + b - 2 = 20
[/LIST]
Get (2) in terms of s
(2) b = 2(s + 2) <-- using (1), substitute for t
So we have (3) rewritten with substitution as:
s + (s + 2) + 2(s + 2) - 2 = 20
s + (s + 2) + 2s + 4 - 2 = 20
Group like terms:
(s + s + 2s) + (2 + 4 - 2) = 20
4s + 4 = 20
Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B4%3D20&pl=Solve']equation calculator [/URL]to get s = 4
Above, we had b = 2(s + 2)
Substituting s = 4, we get:
2(4 + 2) = 2(6) = [B]12
Bill is 12 years old[/B]

Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli departm

Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli department at least 260 person-hours per week. Tom has one part-time employeewho works 20 hours per week. Each full-time employee works 40 hours per week. Write an inequality to determine n, the number of full-time employees Tom must schedule, so that his employees will work at least 260 person-hours per week.
Set up the inequality:
[LIST]
[*]Add the part-timer's hours of 20
[*]Full time hours is 40 times n employees
[*]At least means greater than or equal to, so we use the >= sign
[/LIST]
[B]40n + 20 >= 260[/B]

Tom makes $500 in a week. If his rent is $350, his bills are $75 and groceries are $45, what percent

Tom makes $500 in a week. If his rent is $350, his bills are $75 and groceries are $45, what percentage of his money does he have leftover
[U]Calculate leftover amount[/U]
Leftover amount = Weekly Salary - Rent - Bills - Groceries
Leftover amount = 500 - 350 - 75 - 45
Leftover amount = 30
Calculate leftover percentage
Leftover percentage = 100% * Leftover amount / Weekly Salary
Leftover percentage = 100% * 30 / 500
Leftover percentage = 100% * 0.06
Leftover percentage = [B]6%[/B]

Translate this phrase into an algebraic expression. 58 decreased by twice Gails age. Use the variabl

Translate this phrase into an algebraic expression. 58 decreased by twice Gails age. Use the variable g to represent Gails age.
Twice Gail's age:
2g
58 decreased by twice Gail's age
[B]58 - 2g[/B]

Translate this sentence into an equation. 43 is the sum of 17 and Gregs age. Use the variable g to

Translate this sentence into an equation. 43 is the sum of 17 and Gregs age. Use the variable g to represent Gregs age.
The sum of 17 and Greg's age:
g + 17
The word [I]is[/I] means equal to, so we set g + 17 equal to 43
[B]g + 17 = 43[/B] <-- This is our algebraic expression
If you want to solve this equation for g, use our [URL='http://www.mathcelebrity.com/1unk.php?num=g%2B17%3D43&pl=Solve']equation calculator[/URL].
[B]g = 26[/B]

Translate this sentence into an equation. 48 is the difference of Ritas age and 11 . Use the variabl

Translate this sentence into an equation. 48 is the difference of Ritas age and 11 . Use the variable r to represent Ritas age.
The difference of Rita's age and 11 is written:
r - 11
The phrase [I]is[/I] means equal to, so we set r - 11 equal to 48
r - 11 = 48

Translate this sentence into an equation. 49 is the difference of Diegos age and 17. Use the variabl

Translate this sentence into an equation. 49 is the difference of Diegos age and 17. Use the variable d to represent Diegos age.
The difference means we subtract, so we have d as Diego's age minus 17
d - 17
The word "is" means an equation, so we set d - 17 equal to 49
[B]d - 17 = 49[/B]

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].

Trimmed Mean and Winsorized Mean

Given a number set and a trimmed mean percentage, this will calculate the trimmed mean (truncated mean) or winsorized mean.

two numbers have an average of 2100 and one number is $425 more than the other number. What are the

two numbers have an average of 2100 and one number is $425 more than the other number. What are the numbers
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*](x + y)/2 = 2100 (Average)
[*]y = x + 425
[/LIST]
Rearrange equation (1) by cross multiplying
x + y = 2 * 2100
x + y = 4200
So we have our revised set of equations:
[LIST=1]
[*]x + y = 4200
[*]y = x + 425
[/LIST]
Substituting equation (2) into equation (1) for y, we get:
x + (x + 425) = 4200
Combining like terms, we get:
2x + 425 = 4200
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B425%3D4200&pl=Solve']equation solver[/URL], we get:
x = [B]1887.5[/B]
Which means using equation (2), we get
y = 1887.5 + 425
y = [B]2312.5[/B]

two pages that face each other in a book have a sum of 569

two pages that face each other in a book have a sum of 569
Pages that face each other are consecutive. Let the first page be p. The second page is p + 1.
Their sum is:
p + p + 1 = 569
[URL='https://www.mathcelebrity.com/1unk.php?num=p%2Bp%2B1%3D569&pl=Solve']Type this equation into our search engine to solve for p[/URL], and we get:
p = 284
This means p + 1 = 284 + 1 = 285
So the pages that face each other having a sum of 569 are:
[B]284, 285[/B]

Units of Output (Service Output) Depreciation

Given an asset value, salvage value, production units, and units per period, this calculates the depreciation per period using the units of output depreciation (service output depreciation)

Use c for unknown variable : Sam's age plus twice his age

Use c for unknown variable : Sam's age plus twice his age
Sam's age:
c
Twice his age means we multiply c by 2:
2c
Sam's age plus twice his age
[B]c + 2c[/B]

Vendor Discount Effective Rate of Interest

Calculates the effective rate of interest earned from a vendor discount for a prepayment of a balance within a certain amount of days for a percentage discount

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.
Let Victoria's age be v. And her neighbor's age be n. We're given:
[LIST=1]
[*]v = n + 4
[*]v + n <=14 <-- no more than means less than or equal to
[/LIST]
Substitute Equation (1) into Inequality (2):
(n + 4) + n <= 14
Combine like terms:
2n + 4 <= 14
[URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B4%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get:
n <= 5
Substituting this into inequality (2):
v + 5 <= 14
[URL='https://www.mathcelebrity.com/1unk.php?num=v%2B5%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]v <= 9[/B]

Weighted Average Cost of Capital (WACC) and Capital Asset Pricing Model (CAPM)

Calculates the Weighted Average Cost of Capital (WACC) and also calculates the return on equity if not given using the Capital Asset Pricing Model (CAPM) using debt and other inputs such as Beta and risk free rate.

What fraction lies exactly halfway between 2/3 and 3/4?

What fraction lies exactly halfway between 2/3 and 3/4?
A) 3/5
B) 5/6
C) 7/12
D) 9/16
E) 17/24
Halfway means taking the average, which is dividing the sum of the fractions by 2 for 2 fractions:
1/2(2/3 + 3/4)
1/2(2/3) + 1/2(3/4)
1/3 + 3/8
We need common denominators, so [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F3&frac2=3%2F8&pl=Add']we type this fraction sum into our search engine[/URL] and get:
[B]17/24 - Answer E[/B]

What is the average of 7 consecutive numbers if the smallest number is called n?

What is the average of 7 consecutive numbers if the smallest number is called n?
[LIST]
[*]First number = n
[*]Second number = n + 1
[*]Third number = n + 2
[*]Fourth number = n + 3
[*]Fifth number = n + 4
[*]Sixth number = n + 5
[*]Seventh number = n + 6
[/LIST]
Average = Sum of all numbers / Total numbers
Average = (n + n + 1 + n + 2 + n + 3 + n + 4 + n + 5 + n + 6)/7
Average = 7n + 21/7
Factor out a 7 from the top:
7(n + 3)/7
Cancel the 7's:
[B]n + 3[/B]

When an alligator is born it is about 8 inches long each year they grow 12 inches determine the age

When an alligator is born it is about 8 inches long each year they grow 12 inches determine the age and years of 116 inch alligator?
Calculate inches to grow to get to 116
116 - 8 = 108
Now figure out how many years it takes growing at 12 inches per year, using y as years
12y = 108
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=12y%3D108&pl=Solve']equation calculator[/URL], we get:
[B]y = 9[/B]

When m = 120 , the value of .10m + 54 is 66. Explain what this means in the context of this car rent

When m = 120 , the value of .10m + 54 is 66. Explain what this means in the context of this car rental company.
This means 0.10 is the [B]per-mileage charge[/B] and $54 is the flat rate or rental fee

Which of the following is NOT TRUE about the distribution for averages?

Which of the following is NOT TRUE about the distribution for averages?
a. The mean, median, and mode are equal.
b. The area under the curve is one.
c. The curve never touches the x-axis.
d. The curve is skewed to the right.
Answer is d, the curve is skewed to the right
For a normal distribution:
[LIST]
[*] The area under the curve for a standard normal distribution equals 1
[*] Mean media mode are equal
[*] Never touches the x-axis since in theory, all events have some probability of occuring
[/LIST]

Word Problem Help

A man is three times as old as his son was at the time when the father was twice as old as his son will ne two years from now. Find the present ages of each person.

Yael worked out at a gym for 2 hours. Her workout consisted of stretching for 21 minutes,jogging for

Yael worked out at a gym for 2 hours. Her workout consisted of stretching for 21 minutes,jogging for 45 minutes, and lifting weights for the remaining amount of time. What percentage of Yael’s workout was spent lifting weights?
Each hour is 60 minutes, so we have 2 * 60 = 120 minutes of workout time for Yael.
We subtract off the stretching and jogging time to get the time Yael lifted weights:
120 - 21 - 45 = 54 minutes

Yesterday a car rental agency rented 4 convertibles and 30 other vehicles. Considering this data, ho

Yesterday a car rental agency rented 4 convertibles and 30 other vehicles. Considering this data, how many of the first 68 vehicles rented today should you expect to be convertibles?
30 other vehicles + 4 convertibles = 34 cars
34 * 2 = 68
30 * 2 other vehicles + 4 * 2 convertibles = 68 cars
60 other vehicles and [B]8 convertibles[/B]

Yesterday, there were 100 problems assigned for math homework. Andrew got 20 problems correct and 80

Yesterday, there were 100 problems assigned for math homework. Andrew got 20 problems correct and 80 problems incorrect. What percentage did Andrew get correct?
Correct Problems = 20/100
[URL='https://www.mathcelebrity.com/perc.php?num=20&den=100&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']Using our percentage and decimal calculator[/URL], we get [B]20%[/B]

Yesterday, there were 72 problems assigned for math homework. Austen got 18 problems correct and 54

Yesterday, there were 72 problems assigned for math homework. Austen got 18 problems correct and 54 problems incorrect. What percentage did Austen get correct?
[URL='https://www.mathcelebrity.com/perc.php?num=18&den=72&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']18/72 as a percentage[/URL] is [B]25%[/B]

you and michael have the sum of 19.75. if michael has 8.25 how much more do you have

you and michael have the sum of 19.75. if michael has 8.25 how much more do you have
If you and Michael have 19.75, and Michael has 8.25, then you have:
19.75 - 8.25 = 11.50
Overage/Excess than Michael = Your Money - Michael's money
Overage/Excess than Michael = 11.50 - 8.25
Overage/Excess than Michael = [B]3.25[/B]

You are parking your car in a garage. The first hour is free but every additional hour is 2 dollars.

You are parking your car in a garage. The first hour is free but every additional hour is 2 dollars. You parked for 3.25 hours. What is the cost?
[U]Calculate the number of paid hours:[/U]
Paid Hours = Total Hours - 1 (since first hour is free)
Paid Hours = 3.25 - 1
Paid Hours = 2.25
[U]Calculate the total cost:[/U]
Total Cost = Hourly Rate * Paid Hours
Total Cost = 2 * 2.25
Paid Hours = [B]$4.50[/B]

You are researching the price of DVD players. You found an average price of $58.80. One DVD player c

You are researching the price of DVD players. You found an average price of $58.80. One DVD player costs $56 and another costs $62. Find the price of the third DVD player.
We want to find n, such that n makes the average of the 3 DVD players $58.80.
[URL='https://www.mathcelebrity.com/missingaverage.php?num=56%2C62&avg=58.80&pl=Calculate+Missing+Score']Using our missing average calculator[/URL], we get the price of the 3rd DVD player is $58.40.

You are selling fertilizer to female farmers in Ghana. There are 22,600,000 people in Ghana, and 60%

You are selling fertilizer to female farmers in Ghana. There are 22,600,000 people in Ghana, and 60% are of working age. Within that working-age group, women account for 53%. Of the working-age females, 42% of them are employed in farming. What is the total number of potential customers for your fertilizer?
[U]Our sample population is found by this product:[/U]
Female farmers of working age in Ghana = Total people in Ghana *[I] Working Age[/I] * Women of working Age * Farmers
Since 60% = 0.6, 53% = 0.53, and 42% = 0.42, we have
Female farmers of working age in Ghana = 22,600,000 * 0.6 * 0.53 * 0.42
Female farmers of working age in Ghana = [B]3,018,456[/B]

You borrowed $25 from your friend. You paid him back in full after 6 months. He charged $2 for inter

You borrowed $25 from your friend. You paid him back in full after 6 months. He charged $2 for interest. What was the annual simple interest rate that he charged you? Use the formula: I = Prt.
We have I = 2, P = 25, t = 0.5
2 = 25(r)0.5
Divide each side by 0.5
4 = 25r
Divide each side by 25
r = 4/25
[B]r = 0.16[/B]
As a percentage, this is [B]16%[/B]

You buy a book that is 540 pages long. You can read about 30 pages per hour. How long does it take y

You buy a book that is 540 pages long. You can read about 30 pages per hour. How long does it take you to read the book?
540 pages / 30 pages per hour = [B]18 hours[/B]

You get paid $8 an hour. You make $35 in tips. You make $167.00 in a week. How many hours did you wo

You get paid $8 an hour. You make $35 in tips. You make $167.00 in a week. How many hours did you work?
To figure out the hours worked, we first need the amount of hourly wages made:
Hourly Wages = Total Wages - Tips
Hourly Wages = $167 - $35
Hourly Wages = $132
Calculate Hours Worked
Hours Worked = Hourly Wages / Hourly Rate
Hourly Worked = $132 / $8
Hourly Worked = [B]16.5[/B]

you got paid $45 to babysit your nephew for 5 hours. How much did you get paid per hour?

you got paid $45 to babysit your nephew for 5 hours. How much did you get paid per hour?
Hourly Rate = Total Wages / Hours
Hourly Rate = 45/5
Hourly Rate = [B]$9[/B]

You have read 100 pages of a 250 book. You have 3 days left to finish the book. How many pages will

You have read 100 pages of a 250 book. You have 3 days left to finish the book. How many pages will you need to reach each day in order to be able to finish the book?
Calculate remaining pages to read:
Remaining Pages = 250 - 100 = 150
Now, calculate pages per day
Pages per day = Remaining Pages/Days left
Pages per day = 150/3
Pages per day = [B]50[/B]

You have read a 247 page book for a class and decide to read 18 pages a night. How many pages are le

You have read a 247 page book for a class and decide to read 18 pages a night. How many pages are left in the book if you have been reading for n nights?
Set up the remaining pages read function R(n). We have:
[B]R(n) = 247 - 18n[/B]

you must be 65 or older to join inequality

you must be 65 or older to join inequality
Let a be the age. 65 or older means greater than or equal to 65:
[B]a >=65[/B]

You pay 510.00 to rent a storage unit for 3 months the total cost includes an initial deposit plus a

You pay 510.00 to rent a storage unit for 3 months the total cost includes an initial deposit plus a monthly fee of 160.00. Write and equation that represents your total cost Y in dollars after X months.
Set up the cost function Y where x is the number of months you rent
[B]Y = 160x + 510[/B]

You rake leaves for five hours. You get paid $5.75 every hour. How much did you earn?

You rake leaves for five hours. You get paid $5.75 every hour. How much did you earn?
Total Wages = Hourly Wage * Hours Worked
Total Wages = $5.75 * 5
Total Wages = [B]$28.75[/B]

You receive $8 for raking leaves for 2 hours. What is your hourly wage?

You receive $8 for raking leaves for 2 hours. What is your hourly wage?
Hourly Wage = Total Wages / Hours Worked
Hourly Wage = $8 / 2
Hourly Wage = [B]$4[/B]

You receive 9 text messages in 12 minutes. What is the rate of text messages per hour?

You receive 9 text messages in 12 minutes. What is the rate of text messages per hour?
Set up a proportion of text messages to minutes. Remember, there are 60 minutes in an hour, so we have:
9/12 = t/60 where t is the number of text messages in 60 minutes (1 hour)
[URL='https://www.mathcelebrity.com/prop.php?num1=9&num2=t&den1=12&den2=60&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this into the search engine[/URL], we get [B]t = 45[/B].

You start reading on page 342 and end on 531. How many pages did you read?

You start reading on page 342 and end on 531. How many pages did you read?
The pages read formula is:
Pages Read = End Page - Start Page + 1
Pages Read = 531 - 342 + 1
Pages Read = [B]190[/B]

your aunts age a minus 25

your aunts age a minus 25
[B]a - 25[/B]

Your grandma gives you $10,000 to invest for college. You get an average interest rate of 5% each ye

Your grandma gives you $10,000 to invest for college. You get an average interest rate of 5% each year. How much money will you have in 5 years?
Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=10000&nval=5&int=5&pl=Annually']accumulated balance calculator[/URL], we get:
[B]12,762.82[/B]

Youre setting sales goals for next month. You base your goals on previous average sales. The actual

Youre setting sales goals for next month. You base your goals on previous average sales. The actual sales for the same month for the last four years have been 24 units, 30 units, 23 units, and 27 units. What is the average number of units you can expect to sell next month?
Find the average sales for the last four years:
Average Sales = Total Sales / 4
Average Sales = (24 + 30 + 23 + 27) / 4
Average Sales = 104 / 4
Average Sales = [B]26 units[/B]

Zach can read 7 pages of a book in 5 minutes. At this rate, how long will it take him to read the en

Zach can read 7 pages of a book in 5 minutes. At this rate, how long will it take him to read the entire 175 page book?
Set up a proportion of pages to minutes where m is the number of minutes needed to read 175 pages:
7/5 = 175/m
To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=7&num2=175&den1=5&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine [/URL]and we get:
m = [B]125 minutes or 2 hours and 5 minutes[/B]

Zyrelle is now 20 years older than her sister. Find the present age of Zyrelle

Zyrelle is now 20 years older than her sister. Find the present age of Zyrelle
Let Zyrelle's age be z.
Let her sister's age be s.
Older means we add, so we have:
[B]z = s + 20[/B]