average - A number expressing the central value of a set

Formula: Sum of Values/n

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Adam drove the 10 miles to school at a speed of 60 mph. On his way home, due to traffic, his speed w

Adam drove the 10 miles to school at a speed of 60 mph. On his way home, due to traffic, his speed was 30 mph. What was his average speed for the round trip to school and back?
D = rt
To school:
60 miles in 60 minutes = 10 miles in 10 minutes
To home:
30 miles in 60 minutes = 10 miles in 20 minutes
Total time:
10 + 20 = 30 minutes or 0.5 hours
With a speed of s, we have:
d = st
20 = 0.5s
Divide each side by 2:
s = [B]40 mph[/B]

Alex rode his bike to school at a speed of 12 mph. He then walked home at a speed of 5 mph. What was

Alex rode his bike to school at a speed of 12 mph. He then walked home at a speed of 5 mph. What was Alex's average speed for his trip to school and back?
Say the distance was 1 mile from school to home
D = rt
To school
1 = 12t
t = 1/12
From school:
1 = 5t
t = 1/5
1/2(1/12 + 1/5)
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F24&frac2=1%2F10&pl=Add']1/24 + 1/10[/URL] = 17/120
120 = Average speed * 17
Average speed = 120/17 = [B]7.06 mph[/B]

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

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

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

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

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

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

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

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

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

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

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

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

average of 16 and x is three. find x

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

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

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

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

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

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

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

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

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]

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

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

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

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

Grade Point Average (GPA)

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

HELP SOLVE

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

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

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

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

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

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

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

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

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

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

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

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

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

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

In 1 year, a baseball player got 195 hits in 600 times. What is his batting average?
Batting Average = Hits / Times at Bat
Batting Average = 195 / 600
[URL='https://www.mathcelebrity.com/perc.php?num=196&den=600&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Batting Average[/URL] = [B]0.327[/B]

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

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

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

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

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

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

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

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

Inclusive Number Word Problems

Free Inclusive Number Word Problems Calculator - Given an integer A and an integer B, this calculates the following inclusive word problem questions:

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

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

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

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

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

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

Inventory Turnover and Average Inventory

Free Inventory Turnover and Average Inventory Calculator - Calculates inventory turnover ratio and average inventory

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

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

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

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

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

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

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

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

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

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

John has grade of 88 and 92 on his first two history test. What must he get on his third test so tha

John has grade of 88 and 92 on his first two history test. What must he get on his third test so that his average is at least 90
Using our [URL='https://www.mathcelebrity.com/missingaverage.php?num=88%2C92&avg=90&pl=Calculate+Missing+Score']missing average calculator[/URL], we get:
[B]90[/B]

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

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

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

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

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

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

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

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

Math Written Assignment

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

Midpoint formula

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

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

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

Missing Average

Free Missing Average Calculator - Given a set of scores and an average, this calculates the next score necessary to attain that average

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Receivables Ratios

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

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

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

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

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

Sine Wave

Free Sine Wave Calculator - Solves for any of the 3 items of the Sine Wave: Peak Value, Average Value, and RMS value given 1 input.

Suppose a computer chip manufacturer knows from experience that in an average production run of 5000

Suppose a computer chip manufacturer knows from experience that in an average production run of 5000 circuit boards, 100 will be defective. How many defective circuit boards can be expected in a run of 24,000 circuit boards?
100 defective / 5000 circuit boards * 24,000 circuit boards = [B]480 defective circuit boards[/B]

Suppose a firm producing light bulbs wants to know if it can claim that its light bulbs it produces

Suppose a firm producing light bulbs wants to know if it can claim that its light bulbs it produces last 1,000 burning hours (u). To do this, the firm takes a random sample of 100 bulbs and find its average life time (X=980 hrs) and the sample standard deviation s = 80 hrs. If the firm wants to conduct the test at the 1% of significance, what's you final suggestion?
(i..e, Should the producer accept the Ho that its light bulbs have a 1,000 burning hrs. at the 1% level of significance?)
Ho: u = 1,000 hours.
Ha: u <> 1,000 hours.
[URL='http://www.mathcelebrity.com/mean_hypothesis.php?xbar=+980&n=+100&stdev=+80&ptype==&mean=+1000&alpha=+0.01&pl=Mean+Hypothesis+Testing']Perform a hypothesis test of the mean[/URL]
[B]Yes, accept null hypothesis[/B]

Suppose that previously collected traffic data indicate that, during the afternoon rush hour, an ave

Suppose that previously collected traffic data indicate that, during the afternoon rush hour, an average of 4 cars arrive at a toll bridge each second. If it is assumed that cars arrive randomly, and can thus be modeled with Poisson distribution, what is the probability that in the next second, [U][B]NO[/B][/U] cars will arrive?
Use the [I]Poisson Distribution[/I] with λ = 4 and x = 0
Using the [URL='http://www.mathcelebrity.com/poisson.php?n=+10&p=+0.4&k=+0&t=+3&pl=P%28X+=+k%29']Poisson Distribution calculator[/URL], we get P(0; 4) = [B]0.0183[/B]

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

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

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

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

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

c. Find the 80

Susie bought 15 pairs of shoes last year for an avarage of 30$ per pair. She sold each pair for 1/3

Susie bought 15 pairs of shoes last year for an avarage of 30$ per pair. She sold each pair for 1/3 of the avagrage price at a consignment shop. How much money did she make at the consigment shop?
Calculate average price:
1/3 the average price is $30/3 = $10
Total money made:
Pairs of Shoes * Average Price
15 * 10 = [B]$150[/B]

The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. Wha

The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. What is the value of N ?
Average of the first number set is [URL='https://www.mathcelebrity.com/statbasic.php?num1=17%2C26%2C42%2C59&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']using our average calculator[/URL] is:
36
Now, the mean (average) or 19 and N is found by adding them together an dividing by 2:
(19 + N)/2
Since both number sets have equal means, we set (19 + N)/2 equal to 36:
(19 + N)/2 = 36
Cross multiply:
19 + N = 36 * 2
19 + n = 72
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=19%2Bn%3D72&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]53[/B]

The average age of 15 men is 25 years. What is their total age in years?

The average age of 15 men is 25 years. What is their total age in years?
Average Age = Total Ages/Total Men
25 = Total Ages / 15
Cross multiply and we get:
Total Ages = 15 * 25
Total Ages = [B]375[/B]

The average cost of printing a book in a publishing company is c(x) = 5.5x+kx , where x is the numbe

The average cost of printing a book in a publishing company is c(x) = 5.5x+kx , where x is the number of books printed that day and k is a constant. Find k, if on the day when 200 were printed the average cost was $9 per book.
We are given: c(200) = 9, so we have:
9 = 5.5(200) + k(200)
200k + 1100 = 9
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=200k%2B1100%3D9&pl=Solve']equation solver[/URL], we get:
[B]k = -5.455[/B]

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height re

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height remained the same. What is the height of the mother?
[LIST]
[*]Let the height of the family without the mom be f. Let the height of the mother be m.
[*]Averages mean we add the heights and divide by the number of people who were measured.
[/LIST]
We're given two equations:
[LIST=1]
[*](f + m)/6 = 6
[*]f/5 = 6
[/LIST]
Cross multiplying equation (2), we get:
f = 5 * 6
f = 30
Plug f = 30 into equation (1), we get:
(30 + m)/6 = 6
Cross multiplying, we get:
m + 30 = 6 * 6
m + 30 = 36
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B30%3D36&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]6[/B]
[SIZE=3][FONT=Arial][COLOR=rgb(34, 34, 34)][/COLOR][/FONT][/SIZE]

The average of 16 and x is 21. Find x.

The average of 16 and x is 21. Find x.
The average of 2 numbers is the sum of the 2 numbers divided by 2. So we have:
(16 + x)/2 = 21
Cross multiply:
16 + x = 21*2
16 + x = 42
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=16%2Bx%3D42&pl=Solve']we type this expression into the search engine[/URL] and get [B]x = 26[/B].
Check our work by restating our answer:
The average of 16 and 26 is 21. TRUE.

The average of 171 and x?

The average of 171 and x?
The phrase [I]average[/I] means add up all the items in the number set, divided by the count of items in the number set.
Our number set in this case is {171, x} which has 2 elements. Therefore, our average is:
[B](171 + x)/2[/B]

The average of 20 numbers is 18 while the average of 18 numbers is 20. What is the average of the 38

The average of 20 numbers is 18 while the average of 18 numbers is 20. What is the average of the 38 numbers?
The average of averages is found by getting the sum of both groups of numbers and dividing by the count of numbers.
Calculate the sum of the first group of numbers S1:
Average = S1 / n1
18 = S1 / 20
S1 = 20 * 18
S1 =360
Calculate the sum of the second group of numbers S2:
Average = S2 / n2
20 = S2 / 18
S2 = 18 * 20
S2 =360
Our average of averages is found by the following:
A = (S1 + S2)/(n1 + n2)
A = (360 + 360)/(20 + 18)
A = 720/38
[B]A = 18.947[/B]

The average of a number and double the number is 25.5

Let x equal "a number".
Double the number is 2x.
The average is (x + 2x)/2
Combine the terms in the numerator:
3x/2
The word [I]is[/I] means equal to, so we set 3x/2 equal to 25.5
3x/2 = 25.5
Cross multiply the 2:
3x = 51
Divide each side by 3
[B]x = 17[/B]

the average of eighty-five and a number m is ninety

the average of eighty-five and a number m is ninety
Average of 2 numbers means we add both numbers and divide by 2:
(85 + m)/2 = 90
Cross multiply:
m + 85 = 90 * 2
m + 85 = 180
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B85%3D180&pl=Solve']type it in our math engine [/URL]and we get:
m = [B]95[/B]

The average of manny three tests is an 84. What must he get on a 4th test to raise his average to a

The average of manny three tests is an 84. What must he get on a 4th test to raise his average to a 87?
[URL='http://www.mathcelebrity.com/missingaverage.php?num=84%2C84%2C84&avg=87&pl=Calculate+Missing+Score']This is a missing average problem, use our missing average calculator[/URL]
His 4th test must be [B]96[/B]

the average of two numbers x and y

the average of two numbers x and y
Average is the sum divided by the count:
Sum:
x + y
We have 2 numbers, so we divide (x + y) by 2
[B](x + y)/2[/B]

The average precipitation for the first 7 months of the year is 19.32 inches with a standard deviati

The average precipitation for the first 7 months of the year is 19.32 inches with a standard deviation of 2.4 inches. Assume that the average precipitation is normally distributed.
a. What is the probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months?
b. What is the average precipitation of 5 randomly selected years for the first 7 months?
c. What is the probability of 5 randomly selected years will have an average precipitation greater than 18 inches for the first 7 months?
[URL='https://www.mathcelebrity.com/probnormdist.php?xone=18&mean=19.32&stdev=2.4&n=1&pl=P%28X+%3E+Z%29']For a. we set up our z-score for[/URL]:
P(X>18) = 0.7088
b. We assume the average precipitation of 5 [I]randomly[/I] selected years for the first 7 months is the population mean ? = 19.32
c. [URL='https://www.mathcelebrity.com/probnormdist.php?xone=18&mean=19.32&stdev=2.4&n=5&pl=P%28X+%3E+Z%29']P(X > 18 with n = 5)[/URL] = 0.8907

the average, a, is at least 85

the average, a, is at least 85
At least is an inequality. It also means greater than or equal to, so we have:
[B]a >= 85[/B]

The difference of two numbers is 12 and their mean is 15. Find the two numbers

The difference of two numbers is 12 and their mean is 15. Find the two numbers.
Let the two numbers be x and y. We're given:
[LIST=1]
[*]x - y = 12
[*](x + y)/2 = 15. <-- Mean is an average
[/LIST]
Rearrange equation 1 by adding y to each side:
x - y + y = y + 12
Cancelling the y's on the left side, we get:
x = y + 12
Now substitute this into equation 2:
(y + 12 + y)/2 = 15
Cross multiply:
y + 12 + y = 30
Group like terms for y:
2y + 12 = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=2y%2B12%3D30&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 9[/B]
Now substitute this into modified equation 1:
x = y + 12
x = 9 + 12
[B]x = 21[/B]

The distribution of actual weights of 8 oz chocolate bars produced by a certain machine is normal wi

The distribution of actual weights of 8 oz chocolate bars produced by a certain machine is normal with µ=8.1 ounces and ?=0.1 ounces. A sample of 5 of these chocolate bars is selected. What is the probability that their average weight is less than 8 ounces?
Calculate Z score and probability using [URL='http://www.mathcelebrity.com/probnormdist.php?xone=8&mean=8.1&stdev=0.1&n=5&pl=P%28X+%3C+Z%29']our calculator[/URL]:
Z = -2.236
P(X < -2.236) = [B]0.012545[/B]

The graph shows the average length (in inches) of a newborn baby over the course of its first 15 mon

The graph shows the average length (in inches) of a newborn baby over the course of its first 15 months. Interpret the RATE OF CHANGE of the graph.
[IMG]http://www.mathcelebrity.com/community/data/attachments/0/rate-of-change-wp.jpg[/IMG]
Looking at our graph, we have a straight line. For straight lines, rate of change [U][I]equals[/I][/U] slope.
Looking at a few points, we have:
(0, 20), (12, 30)
Using our [URL='https://www.mathcelebrity.com/slope.php?xone=0&yone=20&slope=+2%2F5&xtwo=12&ytwo=30&pl=You+entered+2+points']slope calculator for these 2 points[/URL], we get a slope (rate of change) of:
[B]5/6[/B]

The height of an object t seconds after it is dropped from a height of 300 meters is s(t)=-4.9t^2 +3

The height of an object t seconds after it is dropped from a height of 300 meters is s(t)=-4.9t^2 +300. Find the average velocity of the object during the first 3 seconds? (b) Use the Mean value Theorem to verify that at some time during the first 3 seconds of the fall the instantaneous velocity equals the average velocity. Find that time.
Average Velocity:
[ f(3) - f(0) ] / ( 3 - 0 )
Calculate f(3):
f(3) = -4.9(3^2) + 300
f(3) = -4.9(9) + 300
f(3) = -44.1 + 300
f(3) = 255.9
Calculate f(0):
f(0) = -4.9(0^2) + 300
f(0) = 0 + 300
f(0) = 300
So we have average velocity:
Average velocity = (255.9 - 300)/(3 - 0)
Average velocity = -44.1/3
Average velocity = -[B]14.7
[/B]
Velocity is the first derivative of position
s(t)=-4.9t^2 +300
s'(t) = -9.8t
So we set velocity equal to average velocity:
-9.8t = -14.7
Divide each side by -9.8 to solve for t, we get [B]t = 1.5[/B]

The mean age of 10 women in an office is 30 years old. The mean age of 10 men in an office is 29 yea

The mean age of 10 women in an office is 30 years old. The mean age of 10 men in an office is 29 years old. What is the mean age (nearest year) of all the people in the office?
Mean is another word for [U]average[/U].
Mean age of women = Sum of all ages women / number of women
We're told mean age of women is 30, so we have:
Sum of all ages women / 10 = 30
Cross multiply, and we get:
Sum of all ages of women = 30 * 10
Sum of all ages of women = 300
Mean age of men = Sum of all ages men / number of men
We're told mean age of men is 29, so we have:
Sum of all ages men / 10 = 29
Cross multiply, and we get:
Sum of all ages of men = 29 * 10
Sum of all ages of men = 290
[U]Calculate mean age (nearest year) of all the people in the office:[/U]
mean age of all the people in the office = Sum of all ages of people in the office (men and women) / Total number of people in the office
mean age of all the people in the office = (300 + 290) / (10 + 10)
mean age of all the people in the office = 590 / 20
mean age of all the people in the office = 29.5
The question asks for nearest year. Since this is a decimal, we round down to either 29 or up to 30.
Because the decimal is greater or equal to 0.5 (halfway), we round [U]up[/U] to [B]30[/B]

The mean of two numbers is 49.1. The first number is 18.3. What is the second number

The mean of two numbers is 49.1. The first number is 18.3. What is the second number
We call the second number n. Since the mean is an average, in this case 2 numbers, we have:
(18.3 + n)/2 = 49.1
Cross multiply:
18.3 + n = 98.2
[URL='https://www.mathcelebrity.com/1unk.php?num=18.3%2Bn%3D98.2&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]n = 79.9[/B]

The minimum daily requirement of vitamin C for 14 year olds is at least 50 milligrams per day. An av

The minimum daily requirement of vitamin C for 14 year olds is at least 50 milligrams per day. An average sized apple contains 6 milligrams of vitamin C. How many apples would a person have to eat each day to satisfy this requirement?
Let a be the number of apples required. The phrase [I]at least[/I] means greater than or equal to, so we have the inequality:
6a >= 50
To solve this inequality, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6a%3E%3D50&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get:
[B]a >= 8.3333 apples or rounded up to a full number, we get 9 apples[/B]

The 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 weight of a 9.5-inch by 6-inch paperback book published by Leaden Publications, Inc., is 16.2 oz

The weight of a 9.5-inch by 6-inch paperback book published by Leaden Publications, Inc., is 16.2 oz. The standard deviation is 2.9 oz. What is the probability that the average weight of a sample of 33 such books is less than 15.89 oz?
Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=15.89&mean=16.2&stdev=2.9&n=33&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we get:
[B]0.271[/B]

two numbers have an average of 2100 and one number is $425 more than the other number. What are the

two numbers have an average of 2100 and one number is $425 more than the other number. What are the numbers
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*](x + y)/2 = 2100 (Average)
[*]y = x + 425
[/LIST]
Rearrange equation (1) by cross multiplying
x + y = 2 * 2100
x + y = 4200
So we have our revised set of equations:
[LIST=1]
[*]x + y = 4200
[*]y = x + 425
[/LIST]
Substituting equation (2) into equation (1) for y, we get:
x + (x + 425) = 4200
Combining like terms, we get:
2x + 425 = 4200
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B425%3D4200&pl=Solve']equation solver[/URL], we get:
x = [B]1887.5[/B]
Which means using equation (2), we get
y = 1887.5 + 425
y = [B]2312.5[/B]

Weighted Average Cost of Capital (WACC) and Capital Asset Pricing Model (CAPM)

Free Weighted Average Cost of Capital (WACC) and Capital Asset Pricing Model (CAPM) Calculator - Calculates the Weighted Average Cost of Capital (WACC) and also calculates the return on equity if not given using the Capital Asset Pricing Model (CAPM) using debt and other inputs such as Beta and risk free rate.

What fraction lies exactly halfway between 2/3 and 3/4?

What fraction lies exactly halfway between 2/3 and 3/4?
A) 3/5
B) 5/6
C) 7/12
D) 9/16
E) 17/24
Halfway means taking the average, which is dividing the sum of the fractions by 2 for 2 fractions:
1/2(2/3 + 3/4)
1/2(2/3) + 1/2(3/4)
1/3 + 3/8
We need common denominators, so [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F3&frac2=3%2F8&pl=Add']we type this fraction sum into our search engine[/URL] and get:
[B]17/24 - Answer E[/B]

What is the average of 7 consecutive numbers if the smallest number is called n?

What is the average of 7 consecutive numbers if the smallest number is called n?
[LIST]
[*]First number = n
[*]Second number = n + 1
[*]Third number = n + 2
[*]Fourth number = n + 3
[*]Fifth number = n + 4
[*]Sixth number = n + 5
[*]Seventh number = n + 6
[/LIST]
Average = Sum of all numbers / Total numbers
Average = (n + n + 1 + n + 2 + n + 3 + n + 4 + n + 5 + n + 6)/7
Average = 7n + 21/7
Factor out a 7 from the top:
7(n + 3)/7
Cancel the 7's:
[B]n + 3[/B]

Which of the following is NOT TRUE about the distribution for averages?

Which of the following is NOT TRUE about the distribution for averages?
a. The mean, median, and mode are equal.
b. The area under the curve is one.
c. The curve never touches the x-axis.
d. The curve is skewed to the right.
Answer is d, the curve is skewed to the right
For a normal distribution:
[LIST]
[*] The area under the curve for a standard normal distribution equals 1
[*] Mean media mode are equal
[*] Never touches the x-axis since in theory, all events have some probability of occuring
[/LIST]

You are researching the price of DVD players. You found an average price of $58.80. One DVD player c

You are researching the price of DVD players. You found an average price of $58.80. One DVD player costs $56 and another costs $62. Find the price of the third DVD player.
We want to find n, such that n makes the average of the 3 DVD players $58.80.
[URL='https://www.mathcelebrity.com/missingaverage.php?num=56%2C62&avg=58.80&pl=Calculate+Missing+Score']Using our missing average calculator[/URL], we get the price of the 3rd DVD player is $58.40.

Your grandma gives you $10,000 to invest for college. You get an average interest rate of 5% each ye

Your grandma gives you $10,000 to invest for college. You get an average interest rate of 5% each year. How much money will you have in 5 years?
Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=10000&nval=5&int=5&pl=Annually']accumulated balance calculator[/URL], we get:
[B]12,762.82[/B]

Youre setting sales goals for next month. You base your goals on previous average sales. The actual

Youre setting sales goals for next month. You base your goals on previous average sales. The actual sales for the same month for the last four years have been 24 units, 30 units, 23 units, and 27 units. What is the average number of units you can expect to sell next month?
Find the average sales for the last four years:
Average Sales = Total Sales / 4
Average Sales = (24 + 30 + 23 + 27) / 4
Average Sales = 104 / 4
Average Sales = [B]26 units[/B]