218 results

percent - a specified amount in or for every hundred. one part in every hundred.

Formula: n% = n/100

$300 for 13 years at 8% compounded semiannually. P=principle = original funds, r=rate, in percent, w

$300 for 13 years at 8% compounded semiannually. P=principle = original funds, r=rate, in percent, written as a decimal (1%=.01, 2%=.02,etc) , n=number of times per year, t= number of years
So we have:
[LIST]
[*]$300 principal
[*]13 * 2 = 26 periods for n
[*]Rate r for a semiannual compound is 8%/2 = 4% per 6 month period
[/LIST]
Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=300&int=4&t=26&pl=Compound+Interest']compound interest with balance calculator[/URL], we get:
[B]$831.74[/B]

$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].

$8000 are invested in a bank account at an interest rate of 10 percent per year. Find the amount in

$8000 are invested in a bank account at an interest rate of 10 percent per year. Find the amount in the bank after 5 years if interest is compounded annually
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=8000&nval=5&int=10&pl=Annually']compound interest with balance calculator[/URL], we get:
[B]12,884.08[/B]

12.66 g of calcium are heated in air,17.73 g of calcium oxide is formed.The percent oxygen in the co

12.66 g of calcium are heated in air,17.73 g of calcium oxide is formed.The percent oxygen in the compound is?
17.73g Calcium oxide - 12.66g Calcium = 5.07g Oxygen
Mass of the element / Mass of the compound * 100%
= 5.07g O / 17.73g CaO2 X 100%
= 28.6% of Oxygen in the compound
[B][U]Check Your Work [/U][/B]
Mass of the element / Mass of the compound X 100%
= 12.66g Ca ÷ 17.73g CaO2 X 100%
= 71.4% Ca
71.4% Ca + 28.6% O = 100% CaO2

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%

20 percent of my class is boys. There are 30 boys in class. How many girls in my class

20 percent of my class is boys. There are 30 boys in class. How many girls in my class?
Let c be the number of people in class. Since 20% = 0.2, We're given:
0.2c = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=0.2c%3D30&pl=Solve']Type this equation into our search engine[/URL], we get:
c = 150
Since the class is made up of boys and girls, we find the number of girls in the class by this equation:
Girls = 150 - 30
Girls = [B]120[/B]

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

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

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 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]

28 students in class and 16 are boys what is percent of girls?

28 students in class and 16 are boys what is percent of girls?
Calculate the number of girls:
Girls = Total Students - Boys
Girls = 28 - 16
Girls = 12
The percent of girls is found by this formula:
Percent of Girls = 100 * Number of Girls / Number of Students
Percent of Girls = 100 * 12 / 28
Percent of Girls = 1,200 / 28
Percent of Girls = [B]42.86%[/B]

3 cases of fresh apples that cost $21.95 per case with 20% off and a 7.5% sales tax

3 cases of fresh apples that cost $21.95 per case with 20% off and a 7.5% sales tax
Figure out the total cost before the discount:
Total Cost before discount = Cases * Price per case
Total Cost before discount = 3 cases * $21.95 per case
Total Cost before discount = $65.85
Now, find the discounted value of the apples:
Discounted Apple Price = Total Cost before discount * (1 - discount percent)
Discounted ApplesPrice = $65.85 * (1 - 0.2) <-- 20% is the same as 0.2
Discounted ApplesPrice = $65.85 * 0.8
Discounted ApplesPrice = $52.68
Now, apply the sales tax to this discounted value to get the total bill:
Total Bill = Discounted Apple Price * (1 + tax rate)
Total Bill = $52.68 * (1 + .075) <-- 7.5% = 0.075
Total Bill = $52.68 * 1.075
Total Bill = [B]$56.63[/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]

35% of the houses are blue. Write the percent that do not live in blue houses as a decimal and a fra

35% of the houses are blue. Write the percent that do not live in blue houses as a decimal and a fraction in simplest form
The percent that do not live in blue houses is found by:
Not in blue = 100% - 35%
Not in blue = 65%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=65&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Typing 65% in our search engine[/URL], we see that the decimal and fraction is:
[LIST]
[*]65% as a decimal: [B]0.65[/B]
[*]65% as a fraction in simplest form: [B]13/20[/B]
[/LIST]

401(k) Balance

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

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

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

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]

52% of a town's households have children and 25% have pets. If 12% have both, what percent have neit

52% of a town's households have children and 25% have pets. If 12% have both, what percent have neither
Let C represent households with children. Let P represents households with pets. We have the formula to determine households with Children or Pets as C U P (C Union P) or (C or P):
C U P = C + P - (C and P)
C U P = 52% + 25% - 12%
C U P = 65%
Now, if we want to find what percent have neither, we use (C U P)':
(C U P)' = 100% - (C U P)
(C U P)' = 100% - 65%
(C U P)' = [B]35%[/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]

60 percent of a number minus 17 is -65

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

A $480 TV was put on sale for 30% off. It didn't sell, so the price was lowered an additional percen

A $480 TV was put on sale for 30% off. It didn't sell, so the price was lowered an additional percent off the sale price, making the new sale price $285.60. What was the second percent discount that was given?
Let the second discount be d. We're given:
480 * (1 - 0.3)(1 - d) = 285.60
480(0.7)(1 - d) = 285.60
336(1 - d) = 285.60
336 - 336d = 285.60
[URL='https://www.mathcelebrity.com/1unk.php?num=336-336d%3D285.60&pl=Solve']Type this equation into our search engine[/URL] to solve for d and we get:
d = [B]0.15 or 15%[/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 20 oz. bottle of Pepsi costs $1.60 in 2010 and $1.85 in 2014. What is the percent of increase? Rou

A 20 oz. bottle of Pepsi costs $1.60 in 2010 and $1.85 in 2014. What is the percent of increase? Round to the nearest percent if necessary.
We [URL='https://www.mathcelebrity.com/markup.php?p1=1.60&m=&p2=1.85&pl=Calculate']type 1.60 to 1.85 percent increase in our search engine[/URL] and we get:
[B]15.63% percent increase[/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 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 gets 12 hits in 40 at bats. What percent are hits, and what percent are not hits?

A baseball player gets 12 hits in 40 at bats. What percent are hits, and what percent are not hits?
Percent Hits = 12/40
Using our [URL='http://www.mathcelebrity.com/perc.php?num=12&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']percent calculator[/URL], we get [B]30%[/B]
Since you either get a hit or you don't, we subtract 30% from 100% to find the percent of not hits:
Percent Not Hits = 100 - 30% = [B]70%[/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 helmet is priced at $18.50. If it is on sale for 10% off and there is 7% sales tax, how mu

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

A 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 bill at a resturant came to $95.75. There is 7.5% sales tax added on. You want to leave a 20% tip

A bill at a resturant came to $95.75. There is 7.5% sales tax added on. You want to leave a 20% tip to the total bill, after tax. How much money will you need to leave for the bill altogether?
Since the tip is [I]after tax[/I], we have:
Total Bill = Pre-tax Bill * (1 + Sales Tax Percent) * (1 + Tip Percent)
Total Bill = $95.75 * (1 + 0.07) * (1 + 0.2)
Total Bill = $95.75 * 1.07 * 1.2
Total Bill = [B]$122.94[/B]

a book which was marked at $84 was sold for $75.60 .calculate the percent discount

a book which was marked at $84 was sold for $75.60 .calculate the percent discount
Using our [URL='https://www.mathcelebrity.com/markup.php?p1=84&m=&p2=+75.60&pl=Calculate']markdown calculator[/URL], we get:
[B]10% markdown/percent discount[/B]

A bowler knocks down at least 6 pins 70 percent of the time. Out of 200 rolls, how many times can yo

A bowler knocks down at least 6 pins 70 percent of the time. Out of 200 rolls, how many times can you predict the bowler will knock down at least 6 pins?
Expected Value of (knocking down at least 6 pins) = number of rolls * probability of knocking down at least 6 pins
Expected Value of (knocking down at least 6 pins) = 200 * 0.7
Expected Value of (knocking down at least 6 pins) = [B]140[/B]

A boy spent one-half of his money for a book and one-third of his money for a pen. The remaining $2.

A boy spent one-half of his money for a book and one-third of his money for a pen. The remaining $2.25 he saved. How much money did he originally have?
Find out what percent of money was spent
Using a common denominator of 6, we have 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Therefore, 1/6 of his money is left to save. Let the boy's original money be x. We have:
x/6 = 2.25
Cross multiply, we get x = [B]13.50[/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 certain textbook cost $94. If the price increases each year by 3% of the previous year's price, fi

A certain textbook cost $94. If the price increases each year by 3% of the previous year's price, find the price after 7 years.
Using our [URL='https://www.mathcelebrity.com/apprec-percent.php?num=acertaintextbookcost94.ifthepriceincreaseseachyearby3%ofthepreviousyearspricefindthepriceafter7years&pl=Calculate']appreciation calculator[/URL], we get:
[B]115.61[/B]

A city has a population of 240,000 people. Suppose that each year the population grows by 8%. What w

A city has a population of 240,000 people. Suppose that each year the population grows by 8%. What will the population be after 5 years?
[U]Set up our population function[/U]
P(t) = 240,000(1 + t)^n where t is population growth rate percent and n is the time in years
[U]Evaluate at t = 0.08 and n = 5[/U]
P(5) = 240,000(1 + 0.08)^5
P(5) = 240,000(1.08)^5
P(5) = 240,000 * 1.4693280768
[B]P(5) = 352638.73 ~ 352,639[/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 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 group of people was surveyed to determine what newspaper they read. 80% of those interviewed read

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

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

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

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

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

A number of dogs are to equally share a bag of dog food. If there are n dogs in the group and one do

A number of dogs are to equally share a bag of dog food. If there are [I]n[/I] dogs in the group and one dog eats its share, what percent of the bag is left?
Fraction of the bag left is:
(n - 1)/n
Multiply by 100 to get a percentage:
[B]100(n - 1)/n[/B]

A pair of jeans are priced at $129.99 there is a discount of 20% and sales tax of 8% what is the fin

A pair of jeans are priced at $129.99 there is a discount of 20% and sales tax of 8% what is the final cost
[U]Calculate discounted price:[/U]
Discounted price = Full price * (100% - discount percent)
Discounted price = 129.99 * (100% - 20%)
Discounted price = 129.99 * 80%
Since 80% = 0.8, we have:
Discounted price = 129.99 * 0.8
Discounted price = 103.99
[U]Calculate after tax cost:[/U]
Tax Rate = Tax percent/100
Tax Rate = 8/100
Tax Rate = 0.08
After Tax cost = Discounted price * (1 + Tax rate)
After Tax cost = 103.99 * (1 + 0.08)
After Tax cost = 103.99 * 1.08
After Tax cost = [B]112.31[/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 popcorn is $7.00 and a drink is $3.50 tax is 7%. how much will I pay?

a popcorn is $7.00 and a drink is $3.50 tax is 7%. how much will I pay?
Calculate pre-tax amount:
Pre-tax amount = Popcorn price + drink price
Pre-tax amount = 7 + 3.50
Pre-tax amount = $10.50
Calculate post-tax amount:
Post-tax amount = Pre-tax amount * (1 + tax percent/100)
Post-tax amount = $10.50* (1 + 7/100)
Post-tax amount = $10.50 * 1.07
Post-tax amount = [B]$11.24[/B]

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 property sold for $198,000 with a listing commission of 8%. The selling office is to receive 40% o

A property sold for $198,000 with a listing commission of 8%. The selling office is to receive 40% of the total commission. How much will the listing salesperson receive if she is paid 60% of the amount retained by listed broker.
[U]Calculate commission amount:[/U]
Commission amount = Sale Price * Commission Percent
Commission amount = 198,000 * 8%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=8&den1=198000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Commission amount [/URL]= 15,840
[U]Calculate listing salesperson commission amount:[/U]
Listing salesperson commission amount = Commission Amount * Listing salesperson Percent
Listing salesperson commission amount = 15,840 * 60%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=60&den1=15840&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Listing salesperson commission amount[/URL] = [B]9,504[/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 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 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 sales clerk receives a monthly salary of $750 plus a commission of 4% on all sales over $3900. Wha

A sales clerk receives a monthly salary of $750 plus a commission of 4% on all sales over $3900. What did the clerk earn the month that she sold $12,800 in merchandise?
[U]Calculate Commission Sales Eligible Amount:[/U]
Commission Sales Eligible Amount = Sales - 3900
Commission Sales Eligible Amount = 12800 - 3900
Commission Sales Eligible Amount = 8900
[U]Calculate Commission Amount:[/U]
Commission Amount = Commission Sales Eligible Amount * Commission Percent
Commission Amount = [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=4&den1=8900&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']8900 * 4%[/URL]
Commission Amount = 356
[U]Calculate total earnings:[/U]
Total Earnings = Base Salary + Commission Amount
Total Earnings = 750 + 356
Total Earnings = [B]1106[/B]

a sales rep can generate $1,900,000 in business annually. What rate of commission does he need to ea

a sales rep can generate $1,900,000 in business annually. What rate of commission does he need to earn $30,000?
We need a commission percent p where:
1900000 * p = 30000
To solve for p, we type this equation into our search engine and we get:
p = 0.0158 or [B]1.58%[/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 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 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 softball player had 13 hits in 25 times at bat. What percent of her times at bat resulted in hits?

We take the ratio of hits to at bats:
13/25 = 0.52
To get the percent, we multiply by 100:
100 * 0.52 = 52%

a store sells a certain toaster oven for 35. The store offers a 30% discount and charges 8% sales ta

a store sells a certain toaster oven for 35. The store offers a 30% discount and charges 8% sales tax. How much will the toaster oven cost?
[U]Calculate discounted price:[/U]
Discounted Price = Full Price * (1 - Discount Percent)
Since 30% = 0.3, we have
Discounted Price = 35 * (1 - 0.3)
Discounted Price = 35 * 0.7
Discounted Price = 24.5
Calculate after-tax amount:
After-tax amount = Discounted Price * (1 + Tax Percent)
Since 8% = 0.08, we have
Discounted Price = 24.5 * (1 + 0.08)
Discounted Price = 24.5 * 1.08
Discounted Price = [B]26.46[/B]

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

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

A survey was given to 120 6th grade students at middle school. It showed the 42 students said they l

A survey was given to 120 6th grade students at middle school. It showed the 42 students said they like playing at the park. What % of the students said they like playing there?
We want [I][URL='https://www.mathcelebrity.com/perc.php?num=42&den=120&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']42 is what percent of 120[/URL][/I]
Using our calculator above, we get [B]35%[/B]

A sweater that you love costs $32. You really want the sweater but only have $35. If there’s a sales

A sweater that you love costs $32. You really want the sweater but only have $35. If there’s a sales tax of 4% on the item, do you have enough to buy the sweater?
Calculate after-tax amount:
After tax amount = Sale Price * (1 + sales tax percent)
After tax amount = 32 * (1 + 0.04) <-- Since 4% = 0.04
After tax amount = 32 * (1.04)
After tax amount = $33.28
[B]Yes[/B], since $33.28 is less than or equal to $35, you have enough to buy the sweater.

A teacher who makes $54000 per year $8400 in taxes, and $1200 in union does what fraction of the tea

A teacher who makes $54000 per year $8400 in taxes, and $1200 in union does what fraction of the teacher’s income does she have left
Calculate Net Income:
Net income = Earnings - Taxes - Union Dues
Net income = 54000 - 8400 - 1200
Net income = 44,400
Net Income Percent = 100% * Net Income / Earnings
Net Income Percent = 100% * 44,400/54,000
Net Income Percent = 100% * 0.8222
Net Income Percent = [B]82.22%[/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 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 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 whose income for the year was $42,800 paid $10,700 in taxes. What percent of her income did

A woman whose income for the year was $42,800 paid $10,700 in taxes. What percent of her income did she pay in taxes?
Tax Percent = Tax Amount / Income * 100%
Tax Percent = $10,700 / $42,800 * 100%
Tax Percent = 0.25 * 100%
Tax Percent = [B]25%[/B]

A zoo has 15 Emperor penguins. The Emperor penguins make up 30% percent of all the penguins at the z

A zoo has 15 Emperor penguins. The Emperor penguins make up 30% percent of all the penguins at the zoo. How many penguins live at the zoo?
Let p be the total number penguins at the zoo.
We're told:
30% of p = 15
Since 30% = 0.3, we have:
0.3p = 15
Solve for [I]p[/I] in the equation 0.3p = 15
[SIZE=5][B]Step 1: Divide each side of the equation by 0.3[/B][/SIZE]
0.3p/0.3 = 15/0.3
p = [B]50[/B]

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

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

After a 33 percent reduction, you purchase a television for $281.40. What was the televisions price

After a 33 percent reduction, you purchase a television for $281.40. What was the televisions price before the reduction?
Using our [URL='http://www.mathcelebrity.com/markup.php?p1=++281.40&m=+33&p2=&pl=Calculate']markup/markdown calculator[/URL], we get:
Original Sale Price = [B]$374.26[/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]

An airplane carries 500 passengers 45% are men, 20% are children. The number of women in the airplan

An airplane carries 500 passengers 45% are men, 20% are children. The number of women in the airplane is
If we assume the sample space is either men, women, or children to get 100% of the passengers, we have:
PercentWomen = 100% - Men - Children
PercentWomen = 100% - 45% - 20%
PercentWomen = 35%
Calculate Women passengers
Women passengers = Total passengers * Percent Women
Women passengers = 500 * 35%
Women passengers = [B]175[/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 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]

As a salesperson, Laura earns a base salary of $72 per week plus a commission of 20% of sales. If sh

As a salesperson, Laura earns a base salary of $72 per week plus a commission of 20% of sales. If she had $75 in sales last week, what was her total pay?
Total Pay = Base Pay + Commission
Calculate Commission:
Commission = Commission Percent x Sales
Commission = 20% * 75
Commission = 15
Total Pay = Base Pay + Commission
Total Pay = 72 + 15
Total Pay = [B]$97[/B]

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

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

Assume you have a laptop worth 2900. There is a 3 percent chance of it getting lost what’s the fair

Assume you have a laptop worth 2900. There is a 3 percent chance of it getting lost what’s the fair premium insurance?
Fair premium Insurance = Price * probability of loss:
Fair premium Insurance = 2,900 * 3%
Fair premium Insurance = [B]87[/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 Appliance Market, a salesperson sells a dishwasher for $569. She gets a commission rate of 18 per

At Appliance Market, a salesperson sells a dishwasher for $569. She gets a commission rate of 18 percent. Which expression represents how much she will receive in commission from the sale?
Since 18 percent = 0.18, we have:
Commission = Sales * Commission Percent
Commission = 569 * 0.18
Commission = [B]$102.42[/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]

Basic Statistics

Free Basic Statistics Calculator - 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

Because of the promotion, attendance exceeded normal by 275 percent. If the normal attendance was 66

Because of the promotion, attendance exceeded normal by 275 percent. If the normal attendance was 6600 people, how many people attended?
Find the exceeded multiplier:
Exceeded Multiplier = Exceed percent / 100
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=275&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']275% as a decimal[/URL] = 2.75
We multiply as follows:
Exceeded Attendance = Normal Attendance * Exceeded Multiplier
Exceeded Attendance = 6600 * 2.75
Exceeded Attendance = [B]18,150[/B]

Bid-Ask

Free Bid-Ask Calculator - This bid ask calculator takes a bid amount and ask amount and calculates the spread and the margin percent

Binomial Option Pricing Model

Free Binomial Option Pricing Model Calculator - 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

Bond Price Formulas

Free Bond Price Formulas Calculator - Given a face value, coupon percent, yield percent, term, and redemption value, this calculates the price of a bond using the four price formulas for bonds

1) Basic

2) Premium/Discount

3) Base

4) Makeham

1) Basic

2) Premium/Discount

3) Base

4) Makeham

Bridget deposited $4500 at 6 percent simple interest. How much money was in the account at the end o

Bridget deposited $4500 at 6 percent simple interest. How much money was in the account at the end of three years?
Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=4500&int=6&t=3&pl=Simple+Interest']simple interest balance calculator[/URL], we get:
$[B]5,310[/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]

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| < kσ) >= [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.

Compare a decimeter to a meter using percents. (A decimeter is what percent of a meter?)

Compare a decimeter to a meter using percents. (A decimeter is what percent of a meter?)
1 decimeter = 0.1 meters, so [B]10%[/B]

Compare a gallon to a quart using percent. (A gallon is what percent of a quart?)

Compare a gallon to a quart using percent. (A gallon is what percent of a quart?)
[URL='https://www.mathcelebrity.com/liqm.php?quant=1&pl=Calculate&type=gallon']1 gallon [/URL]= 4 quarts
So we have [B]400%[/B]

Confidence Interval of a Proportion

Free Confidence Interval of a Proportion Calculator - 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

Consider the case of a manufacturer who has an automatic machine that produces an important part. Pa

Consider the case of a manufacturer who has an automatic machine that produces an important part. Past records indicate that at the beginning of the data the machine is set up correctly 70 percent of the time. Past experience also shows that if the machine is set up correctly it will produce good parts 90 percent of the time. If it is set up incorrectly, it will produce good parts 40 percent of the time. Since the machine will produce 60 percent bad parts, the manufacturer is considering using a testing procedure. If the machine is set up and produces a good part, what is the revised probability that it is set up correctly?
[U]Determine our events:[/U]
[LIST]
[*]C = Correctly Set Machine = 0.7
[*]C|G = Correctly Set Machine And Good Part = 0.9
[*]I = Incorrectly Set Machine = 1 - 0.7 = 0.3
[*]I|G = Incorrectly Set Machine And Good Part = 0.4
[*]B< = BAD PARTS = 0.60
[/LIST]
P[correctly set & part ok] = P(C) * P(C|G)
P[correctly set & part ok] = 70% * 90% = 63%
P[correctly set & part ok] = P(I) * P(I|G)
P[incorrectly set & part ok] = 30% *40% = 12%
P[correctly set | part ok] = P[correctly set & part ok]/(P[correctly set & part ok] + P[incorrectly set & part ok])
P[correctly set | part ok] = 63/(63+12) = [B]0.84 or 84%[/B]

Coupon Comparison

Free Coupon Comparison Calculator - 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

Free Credit Card Balance Calculator - 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

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

Free Decay Calculator - Determines decay based on an initial mass and decay percentage and time.

Denise buys a soda for 90 cents, a candy bar for $1.20 and a bag of chips for $2.90. Assuming a 3.5

Denise buys a soda for 90 cents, a candy bar for $1.20 and a bag of chips for $2.90. Assuming a 3.5 percent sales tax, how much change would she receive from a $10 bill
1. Change = $10 - Total Bill
Total Bill = (Soda + Candy Bar + Bag of Chips) * 1.035
Total Bill = ($0.90 + $1.20 + $2.90) * 1.035
Total Bill = $5 * 1.035
2. Total Bill = $5.18
Plug Equation (2) into Equation (1), we have:
Change = $10 - $5.18
Change = [B]$4.82[/B]

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]

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]

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]

Farmer Yumi has too many plants in her garden. If she starts out with 150 plants and is losing them

Farmer Yumi has too many plants in her garden. If she starts out with 150 plants and is losing them at a rate of 4% each day, how long will it take for her to have 20 plants left? Round UP to the nearest day.
We set up the function P(d) where d is the number of days sine she started losing plants:
P(d) = Initial plants * (1 - Loss percent / 100)^d
Plugging in our numbers, we get:
20 = 150 * (1 - 4/100)^d
20 = 150 * (1 - 0.04)^d
Read left to right so it's easier to read:
150 * 0.96^d = 20
Divide each side by 150, and we get:
0.96^d = 0.13333333333
To solve this logarithmic equation for d, we [URL='https://www.mathcelebrity.com/natlog.php?num=0.96%5Ed%3D0.13333333333&pl=Calculate']type it in our search engine[/URL] and we get:
d = 49.35
The problem tells us to round up, so we round up to [B]50 days[/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]

Find the total coast of four nights lodging at $62.00 per night with 8 1/2% sales tax.

Find the total coast of four nights lodging at $62.00 per night with 8 1/2% sales tax.
[U]Calculate Total lodging cost[/U]
Total lodging cost = Nightly Rate * Number of Nights
Total lodging cost = 62 * 4
Total lodging cost = 248
[U]Calculate total bill with tax[/U]
Total bill with tax = Total bill * (1 + sales tax percent)
Total bill with tax = 248 * (1 + 0.85) <-- 8 1/2% = 0.085 as a decimal
Total bill with tax = 248 * 1.085
Total bill with tax =[B] $269.08[/B]

Fractions

Free Fractions Calculator - Calculates things like fraction to percent, fraction to decimal, unit fraction, ratios, and more

Francis paid 51.12 for his dinner including tax. The cost of his dinner is 48. What percent is the t

Francis paid 51.12 for his dinner including tax. The cost of his dinner is 48. What percent is the tax?
Answer: [B]6.5%[/B] using our [URL='http://www.mathcelebrity.com/tax.php?p=48&tb=51.12&pl=Calculate+Tax']sales tax calculator[/URL].

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

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

Harjap is a salesperson at an electronic store earning a base salary of $420 per week. She also earn

Harjap is a salesperson at an electronic store earning a base salary of $420 per week. She also earns 2.0% commission on sales each month. This month she had $131600 in sales. What was harjaps gross income for this month?
[U]Calculate Monthly Gross Income:[/U]
Gross Income = Monthly Base Salary + Commissions
[U]Calculate Monthly Base Salary:[/U]
Monthly Base Salary = Weekly Base Salary * 4
Monthly Base Salary = $420 * 4
Monthly Base Salary = $1,680
[U]Calculate Commissions:[/U]
Commissions = Sales * Commission Percent
Commissions = $131,600 * 2%
Since 2% as a decimal is 0.02, we have:
Commissions = $131,600 * 0.02
Commissions = $2,632
[U]Calculate Monthly Gross Income:[/U]
Gross Income = Monthly Base Salary + Commissions
Gross Income = $1,680 + $2632
Gross Income = [B]$4,312[/B]

Heat Index

Free Heat Index Calculator - 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]

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 the distribution of IQ scores is bell-shaped, with a mean of 100 and a standard deviation of 15,

If the distribution of IQ scores is bell-shaped, with a mean of 100 and a standard deviation of 15, then approximately ____% of IQ scores are less than 55?
A bell-shaped curved implies a normal distribution. By using our [URL='https://www.mathcelebrity.com/probnormdist.php?xone=55&mean=100&stdev=15&n=1&pl=Empirical+Rule']empirical rule calculator[/URL], we see that:
99.7% of all normal distribution values lie within 3 standard deviations of the mean.
This means the percent of scores less than 55 which is 3 standard deviations away from the mean is:
100% - 99.7% = [B]0.3%[/B]

If the 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]

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 a theatre audience of 500 people, 80 percent were adults. How many children were in the audience

In a theatre audience of 500 people, 80 percent were adults. How many children were in the audience?
If 80% were adults, this means 100% - 80% = 20% were children.
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=20&den1=500&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']We type the expression 20% of 500 into our search engine[/URL] and get [B]100 children[/B]

In 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].

Ina school, out of 300 students, 70% are girls and 30% are boys. if 30 girls leave and no new boy is

Ina school, out of 300 students, 70% are girls and 30% are boys. if 30 girls leave and no new boy is admitted, what is the new% of girls in the school.
Current ratios:
[LIST]
[*]Girls = 70% of 300 = 210
[*]Boys = 30% of 300 = 90
[/LIST]
Ratios after girls leave:
[LIST]
[*]Girls = 210 - 30 = 180
[*]Boys = 90
[*]Total = 180 + 90 = 270
[*]Girls Percent = 180/270 = 2/3 = [B]66 & 2/3%[/B]
[/LIST]

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 it correct to word "10% * 50 + 50" as "10% upper 50"?

Upper meaning upper bound? Upper percentile? Upper quartile?
I need a bit more background on what lesson or concept you are working on right now.

Is it correct to word "10% * 50 + 50" as "10% upper 50"?

Yes, then if we are dealing with percentiles, I read that as 10% upper x%

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

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

It is known that 45% of men snore an 25% of women snore. A doctor looked at these numbers and made t

It is known that 45% of men snore an 25% of women snore. A doctor looked at these numbers and made the following statement:
"If you put a man and a woman together, there is a 70% chance that someone is snoring."
Explain why the doctor's math is wrong.
The doctor added the percents together: 45% + 25% = 70%.
Here's why this is incorrect:
[LIST]
[*]45% of men snore means 100% - 45% = 55% of men do not snore
[*]25% of women snore means 100% - 25% = 75% of women do not snore
[*]Both men and women not snoring is: 55% * 75% = 41.25% neither of them snore
[*]100% - 41.25% = [B]58.75%[/B] somebody is snoring
[/LIST]

Jake earns 25% commission selling ice cream. How much does he earn for each days sale? a) Friday $10

Jake earns 25% commission selling ice cream. How much does he earn for each days sale?
[LIST]
[*]a) Friday $100
[*]b) Saturday $180
[/LIST]
Commission = Sales * Commission Percent
[U]Calculate part a:[/U]
Commission = 100 * 25%
Commission = [B]$25[/B]
[U]Calculate part b:[/U]
Commission = 180 * 25%
Commission = [B]$45[/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]

Joe is paid a 4% commission on all his sales in addition to a $500 per month salary. In May, his sal

Joe is paid a 4% commission on all his sales in addition to a $500 per month salary. In May, his sales were $100,235. How much money did he earn in May?
[U]The commission and salary formula is:[/U]
Earnings = Salary + Commission Percent * Sales
Plugging in our numbers with 4% as 0.04, we get:
Earnings = 500 + 0.04 * 100235
Earnings = 500 + 4009.40
Earnings = [B]4,509.40[/B]

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]

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]

Kim read 95% of a book. What percent of the book was not yet read?

Kim read 95% of a book. What percent of the book was not yet read?
The full book is 100%. So percent unread is:
Percent Unread = 100% - Percent Read
Percent Unread = 100% - 95%
Percent Unread = [B]5%[/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]

Last year I made $50,000 working for a company. This year everyone takes a 9% pay cut. Next year eve

Last year I made $50,000 working for a company. This year everyone takes a 9% pay cut. Next year everyone is promised a 15% pay raise. How much will I make next year?
[U]Calculate pay cut amount with 9% = 0.09:[/U]
Pay cut amount = Current Salary * (1 - pay cut percent)
Pay cut amount = 50000 * (1 - 0.09)
Pay cut amount = 50000 * 0.91
Pay cut amount = 45500
[U]Calculate pay raise with 15% = 0.15[/U]
Pay raise amount = Pay Cut Salary * (1 + pay raise percent)
Pay raise amount = 45500 * (1 + 0.15)
Pay raise amount = 45500 * 1.15
Pay raise amount = [B]52,325[/B]

Last year, the 6th grade had 200 students. This year the number decreased 35% How many students are

Last year, the 6th grade had 200 students. This year the number decreased 35% How many students are in this year's 6th grade class?
[URL='https://www.mathcelebrity.com/percentoff.php?p1=&m=35&p2=200&pl=Calculate']200 decreased by 35%[/URL] is [B]130[/B]

Linda estimates that her business is growing at a rate of 6% per year. Her profits is 2002 were $30,

Linda estimates that her business is growing at a rate of 6% per year. Her profits is 2002 were $30,000. To the nearest hundred dollars, estimate her profits for 2011.
Calculate the number of years of appreciation:
Appreciation years = 2011 - 2002
Appreciation years = 9
So we want 30000 to grow for 9 years at 6%. We [URL='https://www.mathcelebrity.com/apprec-percent.php?num=30000togrowfor9yearsat6%.whatisthevalue&pl=Calculate']type this into our search engine[/URL] and we get:
[B]$50,684.37[/B]

Lois is purchasing an annuity that will pay $5,000 annually for 20 years, with the first annuity pay

Lois is purchasing an annuity that will pay $5,000 annually for 20 years, with the first annuity payment made on the date of purchase. What is the value of the annuity on the purchase date given a discount rate of 7 percent?
This is an annuity due, since the first payment is made on the date of purchase.
Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=5000&n=20&i=7&check1=2&pl=Calculate']present value of an annuity due calculator[/URL], we get [B]56,677.98[/B].

MAPE - MPE - MAPD

Free MAPE - MPE - MAPD Calculator - 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

Free Markup Markdown Calculator - 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.

Melinda is paid 17000 per year. She is also paid a sales commission of 5% of the value of her sales.

Melinda is paid 17000 per year. She is also paid a sales commission of 5% of the value of her sales. Last year she sold 344000 worth of products. What percent of her total income was her commission?
Calculate Melinda's commission:
344,000 * 0.05 = 17,200
Calculate her total income for the year
Total Income = Base Pay + Commission
Total Income = 17,000 + 17,200
Total Income = 34,200
Calculate the percent of her income which is commission:
Commission Income Percent = 100 * 17,200/34,200
Commission Income Percent = 100 * 0.5029
[B]Commission Income Percent = 50.29%[/B]

Mike writes a book and gets 15% royalty of total sales. He sells 50,000 books at a cost of $35 per b

Mike writes a book and gets 15% royalty of total sales. He sells 50,000 books at a cost of $35 per book. What is the royalty he receives? Remember to put the $ symbol in your answer. For example, if your answer is 10 dollars, write $10 in the answer box.
[U]Calculate total sales:[/U]
Total Sales = Number of Books * Price per book
Total Sales = 50,000 * $35
Total Sales = $1,750,000
[U]Now calculate Mike's royalties:[/U]
Royalties = Total Sales * Royalty Percent
Royalties = $1,750,000 * 15%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=15&den1=1750000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Royalties[/URL] = [B]$262,500[/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.

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

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]

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]

P-Hat Confidence Interval

Free P-Hat Confidence Interval Calculator - 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.

Percent Error

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

Percent Math

Free Percent Math Calculator - Simplifies expressions involving numbers and percents with respect to addition and subtraction

Percent Off Problem

Free Percent Off Problem Calculator - Given the 3 items of a percent word problem, Reduced Price, percent off, and full price, this solves for any one of the three given two of the items.

Percentage Appreciation

Free Percentage Appreciation Calculator - Solves for Book Value given a flat rate percentage appreciation per period

Percentage Change

Free Percentage Change Calculator - Calculates the percentage change between two values. Percentage Increase or Percentage Decrease

Percentage Depreciation

Free Percentage Depreciation Calculator - Solves for Book Value given a flat rate percentage depreciation per period

Percentage of Completion

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

Percentage of the Pie Word Problem

Free Percentage of the Pie Word Problem Calculator - This takes two or three fractions of ownership in some good or object, and figures out what remaining fraction is left over.

Percentage Word Problems

Free Percentage Word Problems Calculator - Solves percentage word problems

Percentage-Decimal-Fraction Relations

Free Percentage-Decimal-Fraction Relations Calculator - 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

Percentile for Normal Distribution

Free Percentile for Normal Distribution Calculator - Given a mean, standard deviation, and a percentile range, this will calculate the percentile value.

Percentiles

Free Percentiles Calculator - Given a set of scores and a target score, this will determine the percentile of the target score using two different formulas.

Price

Free Price Calculator - 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

PRIVATE SAT TUTORING - LIVE FACE-TO-FACE SKYPE TUTORING
Schedule a free consultation: [URL]https://calendly.com/soflo-sat/celeb[/URL]
Expert SAT & ACT Tutoring with a live person.
SoFlo SAT Tutoring offers face to face test prep through Skype. We provide all curriculum and create a custom plan tailored to our student’s strengths and weaknesses. Our founder Adam Shlomi had an 800 in Reading and 770 in Math on the SAT — good for the 99th percentile on both sections, went to Georgetown University, and has been tutoring for five years.
Every SAT expert scored at least a 1500/1600 on the SAT and comes from the country’s top schools like Princeton, Johns Hopkins, and Georgetown. After only 10 sessions our average student improves 120 points.
Our success comes from the individual attention we give our students. Our strategies give them confidence to succeed, plus we coach them through the SAT by creating a structured study plan. Working with our expert tutors, our students achieve amazing SAT success.
[QUOTE]Adam is the best tutor I've ever had! He really knew the material and took his time explaining concepts to me. He's also fun to sit down and study with, which is super important for me. I couldn't be happier with SoFlo SAT. -- Charlotte Forman, Bard College[/QUOTE]
[QUOTE]Because of SoFlo SAT my score increased 8 points on the ACT. He pushed me and helped me reach my goals. That 8 point boost helped me earn thousands of dollars on scholarships! SoFlo has the best SAT Tutor in South Florida. -- Jake Samuels, University of Florida[/QUOTE]
Schedule a free call today with Adam to set up SAT prep!
[URL]https://calendly.com/soflo-sat/celeb[/URL]

Proportion Sample Size

Free Proportion Sample Size Calculator - 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.

Rebound Ratio

Free Rebound Ratio Calculator - Calculates a total downward distance traveled given an initial height of a drop and a rebound ratio percentage

Resistor Color Codes

Free Resistor Color Codes Calculator - Given 3 Band level color codes and a tolerance color chosen, this calculates the resistance in ohms and the tolerance percentage

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

Free Sales Tax Calculator - Given a sales price and a total bill, this calculates the sales tax amount and sales tax percentage

Sample Size Reliability for μ

Free Sample Size Reliability for μ Calculator - 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

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

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

Free Solution Mixture Calculator - Determines a necessary amount of a Solution given two solution percentages and 1 solution amount.

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]

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 that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls.
a. If X = average distance in feet for 49 fly balls, then X ~ _______(_______,_______)

b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.

c. Find the 80^{th} percentile of the distribution of the average of 49 fly balls
a. N(250, 50/sqrt(49)) = [B]0.42074[/B]
b. Calculate Z-score and probability = 0.08 shown [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+240&mean=+250&stdev=+7.14&n=+1&pl=P%28X+%3C+Z%29']here[/URL]
c. Inverse of normal distribution(0.8) = 0.8416. Use NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL]
Using the Z-score formula, we have
0.8416 = (x - 250)/50
x = [B]292.08[/B]

b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.

c. Find the 80

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and
a standard deviation of 50 feet.
a. If X = distance in feet for a fly ball, then X ~
b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability.
c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.
a. [B]N(250, 50/sqrt(1))[/B]
b. Calculate [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+220&mean=250&stdev=50&n=+1&pl=P%28X+%3C+Z%29']z-score[/URL]
Z = -0.6 and P(Z < -0.6) = [B]0.274253[/B]
c. Inverse of normal distribution(0.8) = 0.8416 using NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL]
Z-score formula: 0.8416 = (x - 250)/50

x = [B]292.08[/B]

x = [B]292.08[/B]

tammy earns $18000 salary with 4% comission on sales. How much should she sell to earn $55,000 total

tammy earns $18000 salary with 4% comission on sales. How much should she sell to earn $55,000 total
We have a commission equation below:
Sales * Commission percent = Salary
We're given 4% commission percent and 55,000 salary. With 4% as 0.04, we have:
Sales * 0.04 = 55,000
Divide each side of the equation by 0.04, and we get:
Sales = [B]1,375,000[/B]

The astronomer found that 0.017 at the stars examined were red dwarfs. if 29,000 stars or examined,

The astronomer found that 0.017 at the stars examined were red dwarfs. if 29,000 stars or examined, how many were not red dwarfs?
[U]If 0.017 were red dwarfs, then we have a not red dwarfs percent of:[/U]
Not red dwarfs pct = 1 - red dwarfs
Not red dwarfs pct = 1 - 0.017
Not red dwarfs pct = 0.983
[U]For 29,000 stars, we have[/U]
Not red dwarfs = Starts * not red dwarfs pct
Not red dwarfs = 29000 * 0.983
Not red dwarfs = [B]28,507[/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 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 IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a) What i

The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
a) What is the probability that a randomly person has an IQ between 85 and 115?
b) Find the 90th percentile of the IQ distribution
c) If a random sample of 100 people is selected, what is the standard deviation of the sample mean?
a) [B]68%[/B] from the [URL='http://www.mathcelebrity.com/probnormdist.php?xone=50&mean=100&stdev=15&n=1&pl=Empirical+Rule']empirical rule calculator[/URL]
b) P(z) = 0.90. so z = 1.28152 using Excel NORMSINV(0.9)

(X - 100)/10 = 1.21852 X = [B]113[/B] rounded up c) Sample standard deviation is the population standard deviation divided by the square root of the sample size 15/sqrt(100) = 15/10 =[B] 1.5[/B]

(X - 100)/10 = 1.21852 X = [B]113[/B] rounded up c) Sample standard deviation is the population standard deviation divided by the square root of the sample size 15/sqrt(100) = 15/10 =[B] 1.5[/B]

The lowest score that is greater than 25% of the scores

The lowest score that is greater than 25% of the scores.
[B]This is defined as the 25th percentile.[/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 regular price of a shirt was $19.00, but it is on sale for $13.30. What is the percent that the

The regular price of a shirt was $19.00, but it is on sale for $13.30. What is the percent that the shirt has been discounted?
Using our [URL='http://www.mathcelebrity.com/markup.php?p1=19&m=&p2=++13.30&pl=Calculate']markdown calculator[/URL], we get a 30% markdown, or sale.

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]

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 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]

There are 5 orange books, 12 black books, and 8 tan books on Mr. Johnsons bookshelf. Calculate the p

There are 5 orange books, 12 black books, and 8 tan books on Mr. Johnsons bookshelf. Calculate the probability of randomly selecting a black book and then a tan book without replacement. Write your answer as a percent.
P(black book first draw)
P(black book first draw) = 12 black / (5 orange + 12 black + 8 tan)
P(black book first draw) = 12 / 25
P(tan book second draw)
P(tan book second draw) = 8 tan / (5 orange + 11 black + 8 tan) <-- 11 black because we already drew one black
P(tan book second draw) = 8 / 24
Using our fraction reduction calculator, this simplifies to 1/3
Since each draw is independent, we multiply both probabilities:
P(black book first draw, tan book second draw) = 12/25 * 1/3
P(black book first draw, tan book second draw) = 12/75
P(black book first draw, tan book second draw) = [B]16%[/B]

There is a sales tax of $5 on an item that costs $51 before tax. A second item costs $173.40 before

There is a sales tax of $5 on an item that costs $51 before tax. A second item costs $173.40 before tax. What is the sales tax on the second item?
Calculate the sales tax percent using the first item:
Sales Tax Decimal = 100% * Sales Tax / Pre-Tax Bill
Sales Tax Decimal = 100% * 5/51
Sales Tax Decimal = 0.098
Calculate the sales tax on the second item:
Sales Tax = Pre-Tax bill * (1 + Sales Tax)
Sales Tax = $173.40 (1 + 0.098)
Sales Taax = $173.40 * 1.098
Sales Tax = [B]$190.39[/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 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]

Trimmed Mean and Winsorized Mean

Free Trimmed Mean and Winsorized Mean Calculator - Given a number set and a trimmed mean percentage, this will calculate the trimmed mean (truncated mean) or winsorized mean.

Vacation is 72 days long. What percent of the entire year is summer vacation ?

Vacation is 72 days long. What percent of the entire year is summer vacation ?
Vacation day Percent = 100% * Vacation Days / Total Days in the year
Vacation day Percent = 100% * 72/365
Vacation day Percent = 100% * [URL='https://www.mathcelebrity.com/perc.php?num=72&den=365&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']0.1973[/URL]
Vacation day Percent = [B]19.73%[/B]

Vendor Discount Effective Rate of Interest

Free Vendor Discount Effective Rate of Interest Calculator - 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

What is 65% of 200?

What is 65% of 200?
Using our [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=65&den1=200&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percent of calculator[/URL], we get:
[B]130[/B]

Write .02 as a percent

Write .02 as a percent
Multiply by 100 and add a percent:
.02 * 100% = [B]2%[/B]

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, 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 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 go to your favorite restaurant. The bill for the food is $74.26. The tax on the bill will be 9%.

You go to your favorite restaurant. The bill for the food is $74.26. The tax on the bill will be 9%. You are planning on giving a tip on that total amount (bill and tax together) of 20%. What is your final bill, all taxes and tips included?
[U]Calculate the after tax amount:[/U]
After tax amount = Bill * (1 + Tax Rate)
Since 9% = 0.09, we have:
After tax amount = 74.26 * (1 + 0.09)
After tax amount = 74.26 * 1.09
After tax amount = 80.94
[U]Calculate the Tip amount:[/U]
Tip amount = After tax amount * tip percent
Since 20% = 0.2, we have:
Tip amount = 80.94 * 0.20
Tip amount = 16.19
[U]Calculate the final bill:[/U]
Final Bill = After Tax Amount + Tip Amount
Final Bill = 80.94 + 16.19
Final Bill = [B]97.13[/B]

You have a meal at a restaurant and decide to leave the server a 10 percent tip. The meal was $22.47

You have a meal at a restaurant and decide to leave the server a 10 percent tip. The meal was $22.47. How much is the tip?
The way to solve this is to realize 10% means move the decimal point one space left:
10% of 22.47 = 2.247
Rounded to 2 decimal points for currency, we have [B]$2.25[/B]