rate - the ratio between two related quantities in different units. A measure, quantity, or frequency.

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

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

$100 is invested in a bank account that gives an annual interest rate of 3%, compounded monthly. How

$100 is invested in a bank account that gives an annual interest rate of 3%, compounded monthly. How much money will be in the account after 7 years?
7 years * 12 months per year = 84 periods.
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=100&nval=84&int=3&pl=Monthly']compound interest calculator[/URL], we get an account balance of:
[B]123.34[/B]

$1000 is invested with interest at a rate of 15% per year for 9 years. Find the amount you would hav

$1000 is invested with interest at a rate of 15% per year for 9 years. Find the amount you would have, if it’s continuously compounded
Using [URL='https://www.mathcelebrity.com/simpint.php?av=&p=1000&int=15&t=9&pl=Continuous+Interest']our balance calculator[/URL], we get:
[B]$3,857.43[/B]

$13,000 is compounded semiannually at a rate of 11% for 20 years

$13,000 is compounded semiannually at a rate of 11% for 20 years
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=13000&nval=40&int=11&pl=Semi-Annually']compound interest calculator with t = 20 years * 2 semi-annual periods per year = 40[/URL], we get:
[B]110,673.01[/B]

$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]

$500 is deposited into a savings account. The bank offers a 3.5% interest rate and the money is left

$500 is deposited into a savings account. The bank offers a 3.5% interest rate and the money is left in the account for 5 years. How much interest is earned in this situation?
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=5000&nval=5&int=3.5&pl=Annually']compound interest calculator[/URL], we get interest earned as:
[B]938.43[/B]

$8 an hour for 5 hours

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

$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]

1 out of 12 homes is heated by fuel oil. At this rate, how many homes in a community of 36,000 homes

1 out of 12 homes is heated by fuel oil. At this rate, how many homes in a community of 36,000 homes are heated by fuel oil?
1/12 * 36000 = [B]3,000 homes[/B]

1089 Number Trick

Free 1089 Number Trick Calculator - Demonstrates the 1089 number trick for a 3 digit number that you enter

175 students separated into n classes is 25

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

175 students separated into n classes is 25

175 students separated into n classes is 25
175/n = 25
Cross multiply:
25n = 175
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=25n%3D175&pl=Solve']equation calculator[/URL], we get:
[B]n = 7[/B]

2200 dollars is placed in an account with an annual interest rate of 7.25%. How much will be in the

2200 dollars is placed in an account with an annual interest rate of 7.25%. How much will be in the account after 29 years
[URL='https://www.mathcelebrity.com/compoundint.php?bal=2200&nval=29&int=7.25&pl=Annually']Using our compound interest calculator[/URL], with an initial balance of 2,200, 29 years for time, and 7.25% annual interest rate, we get:
[B]16,747.28[/B]

2900 dollars is placed in an account with an annual interest rate of 9%. Hoe much will be in the acc

2900 dollars is placed in an account with an annual interest rate of 9%. Hoe much will be in the account after 13 years to the nearest cent
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=2900&nval=13&int=9&pl=Annually']compound interest with balance calculator[/URL], we get:
[B]8,890.83[/B]

2900 dollars is placed in an account with annual interest rate of 9%. How much will be in the accoun

2900 dollars is placed in an account with annual interest rate of 9%. How much will be in the account after 13 years, round to the nearest cent
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=2090&nval=13&int=9&pl=Annually']compound interest calculato[/URL]r, we get a balance of:
[B]6,407.53[/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 per ride r plus $10 to get into the park

3 per ride r plus $10 to get into the park
Cost function C(r) where r is rides:
C(r) = Rate per ride * number of rides + admission cost
[B]C(r) = 3r + 10[/B]

35 m/s for 40 s. how far does it travel?

35 m/s for 40 s. how far does it travel?
This is a distance problem. The formula to relate, distance, rate, and time is:
d = rt
We are given r = 35 m/s and t = 40s. We want d
d = 35 m/s * 40s
d = [B]1,400 meters[/B]

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.

6 mph, 2 hours what is the distance

6 mph, 2 hours what is the distance
Distance = Rate * Time
Distance = 6 mph * 2 hours
Distance = [B]12 miles
[/B]
You can also use our [URL='http://www.mathcelebrity.com/drt.php?d=+&r=+6&t=+2&pl=Calculate+the+missing+Item+from+D%3DRT']distance-rate-time calculator[/URL]

6700 dollars is placed in an account with an annual interest rate of 8%. How much will be in the acc

6700 dollars is placed in an account with an annual interest rate of 8%. How much will be in the account after 24 years, to the nearest cent?
[URL='https://www.mathcelebrity.com/intbal.php?startbal=6700&intrate=8&bstart=1%2F1%2F2000&bend=1%2F1%2F2024&pl=Annual+Credit']Using our balance with interest calculator[/URL], we get:
[B]$42,485.94[/B]

6700 dollars is placed in an account with an annual interest rate of 8%. show much will be in the ac

6700 dollars is placed in an account with an annual interest rate of 8%. show much will be in the account after 24 years, to the nearest cent ?
Using our compound interest calculator, we get:
[B]42,485.91
[MEDIA=youtube]0C25FB_4004[/MEDIA][/B]

6700 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the

6700 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 28 years, to the nearest cent?
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=6700&nval=28&int=8.25&pl=Annually']balance with interest calculator[/URL], we get:
61,667.47

7100 dollars is placed in an account with an annual interest rate of 7.75%. How much will be in the

7100 dollars is placed in an account with an annual interest rate of 7.75%. How much will be in the account after 30 years, to the nearest cent?
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7100&nval=30&int=7.75&pl=Annually']balance with compound interest calculator[/URL], we get:
66,646.40

7700 dollars is placed in an account with an annual interest rate of 5.75%. How much will be in the

7700 dollars is placed in an account with an annual interest rate of 5.75%. How much will be in the
[URL='https://www.mathcelebrity.com/compoundint.php?bal=7700&nval=5.75&int=24&pl=Annually']Using our compound balance interest calculator[/URL], we get:
[B]$26,525.61[/B]

7700 dollars is placed in an account with an annual interest rate of 5.75%. How much will be in the

7700 dollars is placed in an account with an annual interest rate of 5.75%. How much will be in the account after 24 years, to the nearest cent?
[URL='https://www.mathcelebrity.com/compoundint.php?bal=7700&nval=24&int=5.75&pl=Annually']Using our balance with interest calculator[/URL], we get:
[B]$29,459.12[/B]

7900 dollars is placed in an account with an annual interest rate of 5.5%. How much will be in the a

7900 dollars is placed in an account with an annual interest rate of 5.5%. How much will be in the account after 11 years, to the nearest cent?
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7900&nval=11&int=5.5&pl=Annually']compound interest calculator[/URL], we get:
[B]14,236.53[/B]

8300 dollars is placed in an account with an annual interest rate of 6.5%. How much will be in the a

8300 dollars is placed in an account with an annual interest rate of 6.5%. How much will be in the account after 14 years, to the nearest cent?
[URL='https://www.mathcelebrity.com/compoundint.php?bal=8300&nval=14&int=6.5&pl=Annually']Using our balance with interest calculator[/URL], we get:
[B]$20,043.46[/B]

9000 dollars is placed in an account with an annual interest rate of 8%. How much will be in the acc

9000 dollars is placed in an account with an annual interest rate of 8%. How much will be in the account after 17 years, to the nearest cent?
Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=9000&nval=17&int=8&pl=Annually']compound interest accumulated balance calculator[/URL], we get:
[B]$33,300.16[/B]

993 cold drinks bottles are to be placed in crates. Each crate can hold 9 bottles. How many crates w

993 cold drinks bottles are to be placed in crates. Each crate can hold 9 bottles. How many crates would be needed and how many bottles will remain?
Let c equal the number of crates
9 bottles per crate * c = 993
9c = 993
Solve for [I]c[/I] in the equation 9c = 993
[SIZE=5][B]Step 1: Divide each side of the equation by 9[/B][/SIZE]
9c /9 = 993/9
c = 110.33333333333
Since we can't have fractional crates, we round up 1 to the next full crate
c = [B]111[/B]

A $675 stereo receiver loses value at a rate of about $18 per month The equation y = 675 - 18x repre

A $675 stereo receiver loses value at a rate of about $18 per month The equation y = 675 - 18x represents the value of the receiver after x months. Identify and interpret the x- and y-intercepts. Explain how you can use the intercepts to help you graph the equation
y = 675 - 18x
The y-intercept is found when x is 0:
y = 675 - 18(0)
y = 675 - 0
y = 675
The x-intercept is found when y is 0:
0 = 675 - 18x
[URL='https://www.mathcelebrity.com/1unk.php?num=675-18x%3D0&pl=Solve']Typing this equation into our search engine[/URL], we get:
x = 37.5

A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an ho

A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an hour. What is the boat's speed and how long was the upstream journey?
[U]Set up the relationship of still water speed and downstream speed[/U]
Speed down stream = Speed in still water + speed of the current
Speed down stream = x+2
Therefore:
Speed upstream =x - 2
Since distance = rate * time, we rearrange to get time = Distance/rate:
15/(x+ 2) + 15 /(x- 2) = 3
Multiply each side by 1/3 and we get:
5/(x + 2) + 5/(x - 2) = 1
Using a common denominator of (x + 2)(x - 2), we get:
5(x - 2)/(x + 2)(x - 2) + 5(x + 2)/(x + 2)(x - 2)
(5x - 10 + 5x + 10)/5(x - 2)/(x + 2)(x - 2)
10x = (x+2)(x-2)
We multiply through on the right side to get:
10x = x^2 - 4
Subtract 10x from each side:
x^2 - 10x - 4 = 0
This is a quadratic equation. To solve it, [URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2-10x-4%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine[/URL] and we get:
Speed of the boat in still water =X=5 +- sq. Root of 29 kmph
We only want the positive solution:
x = 5 + sqrt(29)
x = 10.38
[U]Calculate time for upstream journey:[/U]
Time for upstream journey = 15/(10.38 - 2)
Time for upstream journey = 15/(8.38)
Time for upstream journey = [B]1.79[/B]
[U]Calculate time for downstream journey:[/U]
Time for downstream journey = 15/(10.38 + 2)
Time for downstream journey = 15/(12.38)
Time for downstream journey = [B]1.21[/B]

A 50-pound bowling ball and an 8-pound bowling ball are dropped from a tall building. Which ball wil

A 50-pound bowling ball and an 8-pound bowling ball are dropped from a tall building. Which ball will hit first?
[B]They will land at the same time[/B]
[B]How fast something falls due to gravity is determined by a number known as the "acceleration of gravity", which is 9.81 m/s^2 at the surface of our Earth. In one second, [I]any object[/I]’s downward velocity will increase by 9.81 m/s because of gravity. This is just the way gravity works - it accelerates everything at exactly the same rate.[/B]

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each pri

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $188,800?
Let x be the number of $24 tickets, and y be the number of $40 tickets. We have:
[LIST=1]
[*]24x + 40y = 188,800
[*]x + y = 6,000
[*]Rearrange (2) to solve for x: x = 6000 - y
[*]Plug in (3) to (1):
[/LIST]
24(6000 - y) + 40y = 188800
144,000 - 24y + 40y = 188,800
16y + 144,000 = 188,800
Subtract 144,000 from each side:
16y = 44,800
Divide each side by 16
y = 2,800 ($40 tickets)
Plug this into (2)
x + 2,800 = 6000
Subtract 2,800 from each side:
x = 3,200 ($24 tickets)

A baseball player gets 3 hits in the first 15 games of the season. If he continues hitting at the sa

A baseball player gets 3 hits in the first 15 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 45 games?
We set up a proportion of hits to games where h is the number of hits the player gets in 45 games:
3/15 = h/45
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=h&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']Enter this into our search engine[/URL], and we get [B]h = 9[/B].

A baseball player gets 7 hits in the first 15 games of the season. If he continues hitting at the sa

A baseball player gets 7 hits in the first 15 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 45 games?
Let's find the proportion of hits to games. Using h as the number of hits in 45 games, we have:
7/15 = h/45
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=7&num2=h&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get h = 21

A basket of goods was valued at $45.40 in January 2011. The inflation rate for the year was 4%. What

A basket of goods was valued at $45.40 in January 2011. The inflation rate for the year was 4%. What is the expected cost of the basket of goods in January 2012? Write your answer to the nearest cent.
2012 cost = 2011 cost * (1 + I/100)
2012 cost = 45.40 * (1 + 4/100)
2012 cost = 45.40 * (1 + 0.04)
2012 cost = 45.40 * (1.04)
2012 cost = [B]47.22[/B]

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

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

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

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

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

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

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

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

a boat traveled 336 km downstream with the current. The trip downstream took 12 hours. write an equa

a boat traveled 336 km downstream with the current. The trip downstream took 12 hours. write an equation to describe this relationship
We know the distance (d) equation in terms of rate (r) and time (t) as:
d = rt
We're given d = 336km and t = 12 hours, so we have:
[B]336 km = 12t [/B] <-- this is our equation
Divide each side by 12 to solve for t:
12t/12 = 336/12
t = [B]28 km / hour[/B]

A boat traveled at a constant speed for 32 hours, covering a total distance of 597 kilometers. To th

A boat traveled at a constant speed for 32 hours, covering a total distance of 597 kilometers. To the nearest hundredth of a kilometer per hour, how fast was it going?
Distance = Rate * Time
We're given t = 32, and d = 597. Using our [URL='https://www.mathcelebrity.com/drt.php?d=+597&r=+&t=32&pl=Calculate+the+missing+Item+from+D%3DRT']distance, rate, and time calculator[/URL], we get:
r = [B]18.656 km/hr[/B]

A book cost $8.50 without tax. If the tax rate is 7%, what is the total cost of the book including t

A book cost $8.50 without tax. If the tax rate is 7%, what is the total cost of the book including tax?
8.50 * 1.07 = [B]$9.10[/B]

A business owner spent $4000 for a computer and software. For bookkeeping purposes, he needs to post

A business owner spent $4000 for a computer and software. For bookkeeping purposes, he needs to post the price of the computer and software separately. The computer costs 4 times as much as the software. What is the cost of the software?
Let c be the cost of the computer and s be the cost of the software. We have two equations:
[LIST=1]
[*]c + s = 4000
[*]c = 4s
[/LIST]
Substitute (2) into (1)
(4s) + s = 4000
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=4s%2Bs%3D4000&pl=Solve']equation solver[/URL], we get [B]s = 800[/B].
Substitute this into Equation (2), we get:
c = 4(800)
[B]c = 3,200[/B]

A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drin

A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 8 minutes?
Set up a proportion of gallons of water to time where g is the number of gallons of water in 8 minutes.
15/10 = g/8
[URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=g&den1=10&den2=8&propsign=%3D&pl=Calculate+missing+proportion+value']Run this problem through our proportion calculator[/URL] to get [B]g = 12.[/B]

A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drin

A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 14 minutes?
Set up a proportion of gallons of water over minutes where g is the number of gallons the camel can drink in 14 minutes:
15/10 = g/14
[URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=g&den1=10&den2=14&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
[B]g = 21[/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 candlestick burns at a rate of 0.2 inches per hour. After eight straight hours of burning, the can

A candlestick burns at a rate of 0.2 inches per hour. After eight straight hours of burning, the candlestick is 13.4 inches tall. Write and solve a linear equation to find the original height of the candle.
Let h equal the number of hours the candlestick burns. We have a candlestick height equation of C.
C = 13.4 + 0.2(8) <-- We need to add back the 8 hours of candlestick burning
C = 13.4 + 1.6
C = [B]15 inches[/B]

A car is traveling 60 km per hour. How many hours will it take for the car to reach a point that is

A car is traveling 60 km per hour. How many hours will it take for the car to reach a point that is 180 km away?
Rate * Time = Distance so we have t for time as:
60t = 180
To solve this equation for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=60t%3D180&pl=Solve']type it in the search engine[/URL] and we get:
t = [B]3[/B]

A car repair bill was $441. This included $153 for parts and four hours of labor . Find the hourly r

A car repair bill was $441. This included $153 for parts and four hours of labor . Find the hourly rate I was charge for labor
Subtract the cost of parts from the total repair bill to get the labor cost:
Labor Cost = Total Bill - Parts Cost
Labor Cost = 441 - 153
Labor Cost = 288
Labor Cost can be broken down into Labor divided by hours
Hourly Labor Rate = Labor Cost / Labor Hours
Hourly Labor Rate = = 288 / 4
Hourly Labor Rate = [B]72[/B]

A car travels 16 m/s and travels 824 m. How long was the car moving?

A car travels 16 m/s and travels 824 m. How long was the car moving?
Distance = Rate * Time, so we have:
824m = 16m/s * t
Using our [URL='https://www.mathcelebrity.com/drt.php?d=+824&r=16&t=&pl=Calculate+the+missing+Item+from+D%3DRT']distance calculator[/URL], we get:
[B]51.5 seconds[/B]

A car travels 71 feet each second.How many feet does it travel in 12 seconds?

A car travels 71 feet each second.How many feet does it travel in 12 seconds?
Distance = Rate * Time
We're given a rate of 71 feet per second and a time of 12 seconds. So we plug this in:
Distance = 71 feet/second * 12 seconds
[URL='https://www.mathcelebrity.com/drt.php?d=+&r=71&t=+12&pl=Calculate+the+missing+Item+from+D%3DRT']Distance[/URL] = [B]852 feet[/B]

A car travels at 40 kilometers per hour. Write an expression for the distance traveled after h hours

A car travels at 40 kilometers per hour. Write an expression for the distance traveled after h hours.
Distance = rate * time, so we have:
Distance = 40km/h * h
Distance = [B]40h[/B]

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

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

A cell phone company charges a monthly rate of $12.95 and $0.25 a minute per call. The bill for m mi

A cell phone company charges a monthly rate of $12.95 and $0.25 a minute per call. The bill for m minutes is $21.20. Write an equation that models this situation.
Let m be the number of minutes. We have the cost equation C(m):
[B]0.25m + 12.95 = $21.20[/B]

A cell phone plan costs $20 a month and includes 200 free minutes. Each additional minute costs 5 ce

A cell phone plan costs $20 a month and includes 200 free minutes. Each additional minute costs 5 cents. If you use your cell phone for at least 200 minutes a month, write a function C(x) that represents the total cost per x minutes.
We add the flat rate per month to 5% of the number of minutes [U]over[/U] 200:
[B]C(x) = 20 + 0.05(x - 200)[/B]

A certain group of woman has a 0.69% rate of red/green color blindness. If a woman is randomly selec

A certain group of woman has a 0.69% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
0.69% = 0.0069.
There exists a statistics theorem for an event A that states:
P(A) + P(A') = 1 where A' is the event not happening
In this case, A is the woman having red/green color blindness. So A' is the woman [U][B][I]not[/I][/B][/U][I] having red/green color blindness[/I]
So we have:
0.0069 + P(A') = 1
Subtract 0.0069 from each side, we get:
P(A') = 1 - 0.0069
P(A') = [B]0.9931[/B]

A certain Illness is spreading at a rate of 10% per hour. How long will it take to spread to 1,200 p

A certain Illness is spreading at a rate of 10% per hour. How long will it take to spread to 1,200 people if 3 people initially exposes? Round to the nearest hour.
Let h be the number of hours. We have the equation:
3 * (1.1)^h = 1,200
Divide each side by 3:
1.1^h = 400
[URL='https://www.mathcelebrity.com/natlog.php?num=1.1%5Eh%3D400&pl=Calculate']Type this equation into our search engine [/URL]to solve for h:
h = 62.86
To the nearest hour, we round up and get [B]h = 63[/B]

A cheetah can maintain it's maximum speed of 28 m/s for 30 seconds. how far does it go in this amoun

A cheetah can maintain it's maximum speed of 28 m/s for 30 seconds. how far does it go in this amount of time?
Distance = rate * time
Distance = 28 m/s * 30 s
Distance = [B]840m[/B]

A cheetah travels at a rate of 90 feet per second. The distance d traveled by the cheetah is a func

A cheetah travels at a rate of 90 feet per second. The distance d traveled by the cheetah is a function of seconds traveled t. Write a rule for the function. How far will the cheetah travel in 25 seconds?
Distance, or D(t) is expressed as a function of rate and time below:
Distance = Rate x Time
For the cheetah, we have D(t) as:
D(t) = 90ft/sec(t)
The problem asks for D(25):
D(25) = 90(25)
D(25) = [B]2,250 feet[/B]

A circular balloon is inflated with air flowing at a rate of 10cm3/s. How fast is the radius of the

A circular balloon is inflated with air flowing at a rate of 10cm3/s. How fast is the radius of the ballon increasing when the radius is 2cm?
[U]The volume (V) of the balloon with radius (r) is:[/U]
V = 4/3?r^3
[U]Differentiating with respect to t, we get:[/U]
dV/dt = 4/3? * 3r^2 * dr/dt
dV/dt = 4?r^2 * dr/dt
The rate of change of the volume is:
dV/dt = 10cm^3s^?1
[U]So, we find dr/dt:[/U]
dr/dt = 1/4?r^2 * dV/dt
dr/dt = 10/4?r^2
dr/dt = 5/2?r^2
Therefore, dr/dt(2cm) is:
dr/dt(2cm) = 5/2?(2)^2
dr/dt(2cm) = 5/2?4
dr/dt(2cm) = [B]5?/8[/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 city’s population in the 1987 was 125,524. In 2007 the population was 436,884. Determine the popul

A city’s population in the 1987 was 125,524. In 2007 the population was 436,884. Determine the population rate of increase or decrease
[U]Find the population change:[/U]
Population Change = New Population - Old Population
Population Change = 436,884 - 125,524
Population Change = 311,360
[U]Since the population change increased, we calculate the rate of increase:[/U]
Rate of increase = 100% * Population Change / Starting Population
Rate of increase = 100% * 311,360 / 125,524
Rate of increase = 100% * 2.48
Rate of increase = [B]248%[/B]

A company has 3,100 employees and is expected to grow at a rate of 0.04 for the next six years. How

A company has 3,100 employees and is expected to grow at a rate of 0.04 for the next six years. How many employees will they have in 6 years? Round to the nearest whole number.
We build the following exponential equation:
Final Balance = Initial Balance * (1 + growth rate)^time
Final Balance = 3100(1.04)^6
Final Balance = 3100 * 1.2653190185
Final Balance = 3922.48895734
The problem asks us to round to the nearest whole number. Since 0.488 is less than 0.5, we round [U]down.[/U]
Final Balance = [B]3,922[/B]

A company has a fixed cost of $26,000 / month when it is producing printed tapestries. Each item tha

A company has a fixed cost of $26,000 / month when it is producing printed tapestries. Each item that it makes has its own cost of $34. One month the company filled an order for 2400 of its tapestries, selling each item for $63. How much profit was generated by the order?
[U]Set up Cost function C(t) where t is the number of tapestries:[/U]
C(t) = Cost per tapestry * number of tapestries + Fixed Cost
C(t) = 34t + 26000
[U]Set up Revenue function R(t) where t is the number of tapestries:[/U]
R(t) = Sale Price * number of tapestries
R(t) = 63t
[U]Set up Profit function P(t) where t is the number of tapestries:[/U]
P(t) = R(t) - C(t)
P(t) = 63t - (34t + 26000)
P(t) = 63t - 34t - 26000
P(t) = 29t - 26000
[U]The problem asks for profit when t = 2400:[/U]
P(2400) = 29(2400) - 26000
P(2400) = 69,600 - 26,000
P(2400) = [B]43,600[/B]

A computer randomly generates a whole number from 1 to 25. Find the probability that the computer ge

A computer randomly generates a whole number from 1 to 25. Find the probability that the computer generates a multiple of 5
[URL='https://www.mathcelebrity.com/factoriz.php?num=25&pl=Show+Factorization']Multiples of 5[/URL]:
{1, 5, 25}
So we have the probability of a random number multiple of 5 is
[B]3/25[/B]

A construction crew has just built a new road. They built 43.75 kilometers of road at a rate of 7 ki

A construction crew has just built a new road. They built 43.75 kilometers of road at a rate of 7 kilometers per week. How many weeks did it take them?
Let w = weeks
7 kilometers per week * w = 43.75
To solve for w, we divide each side of the equation by 7:
7w/7 = 43.75/7
Cancel the 7's, we get:
w = [B]6.25 [/B]

A construction crew has just built a new road. They built 8.75 kilometers of road in 7 weeks. At wha

A construction crew has just built a new road. They built 8.75 kilometers of road in 7 weeks. At what rate did they build the road?
Rate = Km of road / weeks
Rate = 8.75 km / 7 weeks
Rate = [B]1.25 km per week[/B]

A construction crew must build a road in 10 months or they will be penalized $500,000. It took 10 wo

A construction crew must build a road in 10 months or they will be penalized $500,000. It took 10 workers 6 months to build half of the road. How many additional workers must be added to finish the road in the remaining 4 months?
Calculate unit rate per one worker:
10 workers * 6 months = 60 months for one worker
Calculate workers needed:
60 months / 4 months = 15 workers
Calculate additional workers needed:
Additional workers needed = New workers needed - Original workers needed
Additional workers needed = 15 - 10
Additional workers needed = [B]5 additional workers[/B]

A crate contains 300 coins and stamps. The coins cost $3 each and the stamps cost $1.5 each. The tot

A crate contains 300 coins and stamps. The coins cost $3 each and the stamps cost $1.5 each. The total value of the items is $825. How many coins are there?
Let c be the number of coins, and s be the number of stamps. We're given:
[LIST=1]
[*]c + s = 300
[*]3c + 1.5s = 825
[/LIST]
We have a set of simultaneous equations, or a system of equations. We can solve this 3 ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]
No matter which way we pick, we get:
s = 50
c = [B]250[/B]

A credit plan charges interest rate of 36% compounded monthly. Find the effective rate.

A credit plan charges interest rate of 36% compounded monthly. Find the effective rate.
[U]Calculate Monthly Nominal Rate:[/U]
Monthly Nominal Rate = Annual Rate / 12 months per year
Monthly Nominal Rate = 36%/12
Monthly Nominal Rate = 3%
[U]Since there are 12 months in a year, we compound 12 times to get the effective rate below:[/U]
Effective Rate = (1 + Monthly Nominal Rate as a Decimal)^12 - 1
Since 3% = 0.03, we have:
Effective Rate = 100% * ((1 + 0.03)^12 - 1)
Effective Rate = 100% * ((1.03)^12 - 1)
Effective Rate = 100% * (1.42576088685 - 1)
Effective Rate = 100% * (0.42576088685)
Effective Rate = [B]42.58%[/B]

A dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog wa

A dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog walker charge for a 3 hour walk?
Set up the cost equation C(h) where h is the number of hours:
C(h) = Hourly rate * h + flat rate
C(h) = 30h + 6
The question asks for C(h) when h = 3:
C(3) = 30(3) + 6
C(3) = 90 + 6
C(3) = [B]96[/B]

A driver drove at a speed of 42 mph for z hours. How far did the driver go?

A driver drove at a speed of 42 mph for z hours. How far did the driver go?
Distance = Rate * Time, so we have:
Distance = [B]42z[/B]

A driver drove at a speed of 56 mph for z hours. How far did the driver go?

A driver drove at a speed of 56 mph for z hours. How far did the driver go?
Distance = Rate * time
So we have:
Distance = 56 mph * z
Distance = [B]56z[/B]

A driver drove at a speed of 58 mph for t hours. How far did the driver go?

A driver drove at a speed of 58 mph for t hours. How far did the driver go?
Since distance = rate * time, we have distance D of:
[B]D = 58t[/B]

A family decides to rent a canoe for an entire day. The canoe rental rate is $50 for the first three

A family decides to rent a canoe for an entire day. The canoe rental rate is $50 for the first three hours and then 20$ for each additional hour. Suppose the family can spend $110 for the canoe rental. What is the maximum number of hours the family can rent the canoe?
IF we subtract the $50 for the first 3 hours, we get:
110 - 50 = 60 remaining
Each additional hour is 20, so the max number of hours we can rent the canoe is
$60/20 = 3 hours additional plus the original 3 hours is [B]6 hours[/B]

A Farmer Sell products at the market in 38- pound crates. If he sells 100 crates . How many pounds o

A Farmer Sell products at the market in 38- pound crates. If he sells 100 crates . How many pounds of produce has he sold
[U]Calculate the pounds of produce:[/U]
Pounds of Produce = Number of Crates * pounds per crate
Pounds of Produce = 100 crates * 38 pounds per crates
Pounds of Produce = [B]3,800 pounds of produce[/B]3

A furniture company plans to have 25 employees at its corporate headquarters and 25 employees at eac

A furniture company plans to have 25 employees at its corporate headquarters and 25 employees at each store it opens. Let s represent the number of stores and m represent the total number of employees.
There is only one corporate headquarters. So we have the number of employees (m) as:
m = Store Employees + Corporate Employees
Each store has 25 employees. Total store employees equal 25 per store times the number of stores (s).
[B]m = 25s + 25[/B]

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

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

A girl is pedaling her bicycle at a velocity of 0.10 km/hr. How far will she travel in two hours?

A girl is pedaling her bicycle at a velocity of 0.10 km/hr. How far will she travel in two hours?
The distance formula is:
d = rt
We're given a rate (r) of 0.10km/hr
We're given time (t) of 2 hours
Plug these values into the distance formula and we get:
d= 0.1 * 2
d = [B]0.2km
[MEDIA=youtube]w80E_YM-tDA[/MEDIA][/B]

A grocery store sells chili peppers at $2.04 for a dozen. At this rate, what's the cost per pepper?

A grocery store sells chili peppers at $2.04 for a dozen. At this rate, what's the cost per pepper?
A dozen = 12 peppers, so our cost per pepper is:
Cost per pepper = Cost per dozen / 12 per dozen
Cost per pepper = 2.04/12
Cost per pepper = [B]0.17[/B]

A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A star

A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A started with 6000 cells and decreased at a constant rate of 2000 cells per hour after the chemical was applied. Strain B started with 2000 cells and decreased at a constant rate of 1000 cells per hour after the chemical was applied. When will the strains have the same number of cells? Explain.
Set up strain equations where h is the number of hours since time 0:
[LIST]
[*]Strain A: 6000 - 2000h
[*]Strain B: 2000 - 1000h
[/LIST]
Set them equal to each other
6000 - 2000h = 2000 - 1000h
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=6000-2000h%3D2000-1000h&pl=Solve']equation solver[/URL], we see that [B]h = 4[/B]

A group of workers can plant 54 acres in 6 days. What is their rate in acres per day?

A group of workers can plant 54 acres in 6 days. What is their rate in acres per day?
Acres per day = 54 acres / 6 days = [B]9 acres per day[/B]

A group of workers can plant 72 acres in 8 days what is the rate in acres per a day

A group of workers can plant 72 acres in 8 days what is the rate in acres per a day
Acres per day = Total Acres / Total Days
Acres per day = 72/8
Acres per day =[B] 9[/B]

A heating company charges $60 per hour plus $54 for a service call. Let n be the number of hours t

A heating company charges $60 per hour plus $54 for a service call. Let n be the number of hours the technician works at your house.
The cost function C(n) where n is the number of hours is:
C(n) = Hourly Rate * hours + Service Call Charge
[B]C(n) = 60n + 54[/B]

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

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

A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus

A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus $15 per hour. How long is a job for which both companies will charge the same amount?
[U]Set up the cost function for the first company C(h) where h is the number of hours:[/U]
C(h) = Hourly Rate * h + flat rate
C(h) = 12h + 376
[U]Set up the cost function for the first company C(h) where h is the number of hours:[/U]
C(h) = Hourly Rate * h + flat rate
C(h) = 15h + 280
The problem asks how many hours will it take for both companies to charge the same. So we set the cost functions equal to each other:
12h + 376 = 15h + 280
Plugging this equation [URL='https://www.mathcelebrity.com/1unk.php?num=12h%2B376%3D15h%2B280&pl=Solve']into our search engine and solving for h[/URL], we get:
h = [B]32[/B]

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

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

A hummingbird moves its wings at a rate of 5400 wingbeats a minute. Write this rate in wingbeats per

A hummingbird moves its wings at a rate of 5400 wingbeats a minute. Write this rate in wingbeats per second.
5400 wingbeats per minute * 1 minute / 60 seconds = 5400/60 = [B]90 wingbeats per second[/B]

A jet plane traveling at 550 mph over takes a propeller plane traveling at 150 mph that had a 3 hour

A jet plane traveling at 550 mph over takes a propeller plane traveling at 150 mph that had a 3 hours head start. How far from the starting point are the planes?
Use the formula D = rt where
[LIST]
[*]D = distance
[*]r = rate
[*]t = time
[/LIST]
The plan traveling 150 mph for 3 hours:
Time 1 = 150
Time 2 = 300
Time 3 = 450
Now at Time 3, the other plane starts
Time 4 = 600
Time 5 = 750
Time 6 =
450 + 150t = 550t
Subtract 150t
400t = 450
Divide each side by 400
t = 1.125
Plug this into either distance equation, and we get:
550(1.125) = [B]618.75 miles[/B]

A jet travels 832 km in 5 hours. At this rate, how far could the jet fly in 12 hours? What is the ra

A jet travels 832 km in 5 hours. At this rate, how far could the jet fly in 12 hours? What is the rate of speed of the jet?
Distance = rate * time. We're given D = 832 and t = 5. Using our [URL='https://www.mathcelebrity.com/drt.php?d=+832&r=+&t=+5&pl=Calculate+the+missing+Item+from+D%3DRT']drt calculator[/URL], we solve or rate to get:
[B]r = 166.4[/B]
The problems asks for a distance D when t = 12 hours and r = 166.4 from above. Using our [URL='https://www.mathcelebrity.com/drt.php?d=&r=+166.4&t=+12&pl=Calculate+the+missing+Item+from+D%3DRT']drt calculator solving for d[/URL], we get:
d = [B]1,996.8 km[/B]

A local radio station sells time slots for programs in 20-minute intervals. If the station operates

A local radio station sells time slots for programs in 20-minute intervals. If the station operates 24 hours per day, what is the total number of 20-minute time slots the radio station can sell for Thursday and Friday?
Thursday and Friday = 2 days
With 24 hours per day, we have 24 * 2 = 48 hours for Thursday and Friday.
Since 20 minutes is 1/3 of an hour, then we have 3 20-minute time slots per hour.
3 20-minute time slots * 48 hours = [B]144[/B] total 20-minute time slots

A machine shop employee earned $642 last week. She worked 40hours at her regular rate and 9 hours at

A machine shop employee earned $642 last week. She worked 40hours at her regular rate and 9 hours at a time and a half rate. Find her regular hourly rate.
Let the regular hourly rate be h. We're given:
40h + 40(1.5)(h - 40) = 642
Multiply through and simplify:
40h + 60h - 2400 = 642
100h - 2400 = 642
[URL='https://www.mathcelebrity.com/1unk.php?num=100h-2400%3D642&pl=Solve']To solve for h, we type this equation into our search engine[/URL] and we get:
h = [B]30.42[/B]

A man invested part of $15,000 at 12% and the remainder at 8%. If his annual income from the investm

A man invested part of $15,000 at 12% and the remainder at 8%. If his annual income from the investments is $1456, how much does he have invested at each rate?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=15000&i1=12&i2=8&itot=1456&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*]Fund 1 Investment @ 12% = [B]6,400[/B]
[*]Fund 2 Investment @ 8% =[B] [B]8,600[/B][/B]
[/LIST]

A man invests $5,200, part at 4% and the balance at 3%. If his total income for the two investments

A man invests $5,200, part at 4% and the balance at 3%. If his total income for the two investments is $194, how much money did he invest at each rate?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=5200&i1=4&i2=3&itot=194&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]Fund 1 = $3,800[/B]
[*][B]Fund 2 = $1,400[/B]
[/LIST]

A mechanic charges $45 per hour and parts cost $125. Write an expression for the total if the mechan

A mechanic charges $45 per hour and parts cost $125. Write an expression for the total if the mechanic works h hours.
Set up the cost function C(h) where h is the number of hours worked:
C(h) = Hourly Rate * h + parts
C(h) = [B]45h + 125[/B]

A mechanic charges $50 to inspect your heater, plus $80 per hour to work on it. You owe the mechani

A mechanic charges $50 to inspect your heater, plus $80 per hour to work on it. You owe the mechanic a total of $310. Write and solve an equation to find the amount of time h (in hours) the mechanic works on your heater.
We calculate the cost function C(h) as:
C(h) = Hourly Rate * hours + Flat Fee Inspection
C(h) = 80h + 50 <-- this is our cost equation
Now, we want to solve for h when C(h) = 310
80h + 50 = 310
[URL='https://www.mathcelebrity.com/1unk.php?num=80h%2B50%3D310&pl=Solve']We type this equation into our search engine[/URL] and we get:
h = [B]3.25[/B]

A mechanic will charge a new customer $45.00 for an initial diagnosis plus $20 an hour of labor. How

A mechanic will charge a new customer $45.00 for an initial diagnosis plus $20 an hour of labor. How long did the mechanic work on a car if he charged the customer $165?
We set up a cost function C(h) where h is the number of hours of labor:
C(h) = Hourly Labor Rate * h + Initial Diagnosis
C(h) = 20h + 45
The problem asks for the number of hours if C(h) = 165. So we set our cost function C(h) above equal to 165:
20h + 45 = 165
To solve for h, [URL='https://www.mathcelebrity.com/1unk.php?num=20h%2B45%3D165&pl=Solve']we plug this equation into our search engine[/URL] and we get:
h = [B]6[/B]

A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going dow

A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
[U]Assumptions:[/U]
[LIST]
[*]B = the speed of the boat in still water.
[*]S = the speed of the stream
[/LIST]
Relative to the bank, the speeds are:
[LIST]
[*]Upstream is B - S.
[*]Downstream is B + S.
[/LIST]
[U]Use the Distance equation: Rate * Time = Distance[/U]
[LIST]
[*]Upstream: (B-S)6 = 258
[*]Downstream: (B+S)6 = 330
[/LIST]
Simplify first by dividing each equation by 6:
[LIST]
[*]B - S = 43
[*]B + S = 55
[/LIST]
Solve this system of equations by elimination. Add the two equations together:
(B + B) + (S - S) = 43 + 55
Cancelling the S's, we get:
2B = 98
Divide each side by 2:
[B]B = 49 mi/hr[/B]
Substitute this into either equation and solve for S.
B + S = 55
49 + S = 55
To solve this, we [URL='https://www.mathcelebrity.com/1unk.php?num=49%2Bs%3D55&pl=Solve']type it in our search engine[/URL] and we get:
S = [B]6 mi/hr[/B]

A new car worth $24,000 is depreciating in value by $3,000 per year , how many years till the cars v

A new car worth $24,000 is depreciating in value by $3,000 per year , how many years till the cars value will be $9,000
We have a flat rate depreciation each year. Set up the function D(t) where t is the number of years of depreciation:
D(t) = 24000 - 3000t
The problem asks for the time (t) when D(t) = 9000. So we set D(t) = 9000
24000 - 3000 t = 9000
To solve for t, [URL='https://www.mathcelebrity.com/1unk.php?num=24000-3000t%3D9000&pl=Solve']we plug this function into our search engine[/URL] and we get:
t = [B]5[/B]

a new savings account starts at $700 at a rate of 1.2% yearly. how much money will be in the account

a new savings account starts at $700 at a rate of 1.2% yearly. how much money will be in the account after 8 years?
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=700&nval=8&int=1.2&pl=Annually']balance and interest calculator with annual (yearly) compounding[/URL], we have:
[B]770.09[/B]

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

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

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

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

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

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

A person invests $500 in an account that earns a nominal yearly rate of 4%. How much will this inves

A person invests $500 in an account that earns a nominal yearly rate of 4%. How much will this investment be worth in 10 years? If the interest was applied four times per year (known as quarterly compounding), calculate how much the investment would be worth after 10 years.
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=500&nval=10&int=4&pl=Annually']compound interest calculator[/URL], $500 @ 4% for 10 years is:
$[B]740.12
[/B]
Using [URL='https://www.mathcelebrity.com/compoundint.php?bal=500&nval=40&int=4&pl=Quarterly']quarterly compounding in our compound interest calculator[/URL], we have 10 years * 4 quarters per year = 40 periods, so we have:
[B]$744.43[/B]

A person is earning 600 per day to do a certain job. Express the total salary as a function of the n

A person is earning 600 per day to do a certain job. Express the total salary as a function of the number of days that the person works.
Set up the salary function S(d) where d is the number of days that the person works:
S(d) = Daily Rate * d
[B]S(d) = 600d[/B]

A person places $230 in an investment account earning an annual rate of 6.8%, compounded continuousl

A person places $230 in an investment account earning an annual rate of 6.8%, compounded continuously. Using the formula V = Pe^{rt}V=Pe^rt, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 20 years
Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=230&int=6.8&t=20&pl=Continuous+Interest']continuous compounding calculator[/URL], we get:
V = [B]896.12[/B]

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuou

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuously. Using the formula V=PertV = Pe^{rt} V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years.
Substituting our given numbers in where P = 96,300, r = 0.028, and t = 7, we get:
V = 96,300 * e^(0.028 * 7)
V = 96,300 * e^0.196
V = 96,300 * 1.21652690533
V = [B]$117,151.54[/B]

A person works 46 hours in one week and earns 440 dollars. They get time and a half for over 40 hour

A person works 46 hours in one week and earns 440 dollars. They get time and a half for over 40 hours. What is their hourly salary?
Let the hourly rate be r. Since time and a half is 1.5 the hourly rate, We're given:
40r + 6(1.5r) = 440
40r + 9r = 440
to solve this equation for r, we type it in our search engine and we get:
r = [B]$8.98[/B]

A photographer snapped 224 photos over a period of 15 days. At this rate, how many would he take in

A photographer snapped 224 photos over a period of 15 days. At this rate, how many would he take in 45 days?
Set up a proportion of photos to days where p is the number of photos snapped in 45 days:
224/15 = p/45
To solve this proportion for p, we [URL='https://www.mathcelebrity.com/prop.php?num1=224&num2=p&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get;
p = [B]672[/B]

A plumber charges $45 for a house call plus $25 for each hour worked.Let h represent the number of h

A plumber charges $45 for a house call plus $25 for each hour worked.Let h represent the number of hours worked. Write the expression that shows how much a plumber charges for a job. Then find how much the plumbers charges for a job lasting 4 hours
[U]Set up the cost function C(h) where h is the number of hours:[/U]
C(h) = Hours worked * hourly rate + house call fee
[B]C(h) = 25h + 45 <-- This is the expression for how much the plumber charges for a job
[/B]
[U]Now determine how much the plumber charges for a job lasting 4 hours[/U]
We want C(4)
C(4) = 25(4) + 45
C(4) = 100 + 45
C(4) = [B]$145[/B]

A police officer is trying to catch a fleeing criminal. The criminal is 20 feet away from the cop, r

A police officer is trying to catch a fleeing criminal. The criminal is 20 feet away from the cop, running at a rate of 5 feet per second. The cop is running at a rate of 6.5 feet per second. How many seconds will it take for the police officer to catch the criminal?
Distance = Rate * Time
[U]Criminal:[/U]
5t + 20
[U]Cop[/U]:
6.5t
We want to know when their distances are the same (cop catches criminal). So we set the equations equal to each other:
5t + 20 = 6.5t
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=5t%2B20%3D6.5t&pl=Solve']we type it in our search engine[/URL] and we get:
t = 13.333 seconds

A population of 200 doubles in size every hour. What is the rate of growth of the population after 2

A population of 200 doubles in size every hour. What is the rate of growth of the population after 2.5 hours?
Time 1: 400
Time 2: 800
Time 3: 1200 (Since it's only 1/2 of a period)

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

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

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

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

A repair will require 3 hours at $40 per hour. How much will the total/labor cost be for this job?

A repair will require 3 hours at $40 per hour. How much will the total/labor cost be for this job?
Total cost = Hourly Labor Rate * hours
Total cost = $40 * 3
Totaal cost = [B]$120[/B]

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

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

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

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

A rocket travels at a rate of 160 meters in 3 seconds. What is the speed of the rocket in meters per

A rocket travels at a rate of 160 meters in 3 seconds. What is the speed of the rocket in meters per second?
160 meters /3 seconds = [B]53.333333333 meters per second[/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 salesperson works 40 hours per week at a job where he has two options for being paid. Option A is

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

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis?
Slope is y/x,so we have 27/36.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=27%2F36&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we can reduce 27/36 to 3/4. So this is our slope.
[B]3/4[/B]

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis?
Slope = Rise/Run or y/x
Since tests are on the y-axis and time is on the x-axis, we have:
Slope = 27/36
We can simplify this, so we [URL='https://www.mathcelebrity.com/fraction.php?frac1=27%2F36&frac2=3%2F8&pl=Simplify']type in 27/36 into our search engine[/URL], and get:
[B]Slope = 3/4[/B]

A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 10

A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds later. At what rate is the scuba diver going deeper down in the water
If we take these as coordinates on a graph, where y is the depth and x is the time, we calculate our slope or rate of change where (x1, y1) = (10, 30) and (x2, y2) = (40, 100)
Rate of change = (y2 - y1)/(x2 - x1)
Rate of change = (100 - 30)/(40 - 10)
Rate of change = 70/30
Rate of change =[B] 2.333 feet per second[/B]

A service charges a $1.95 flat rate plus $0.05 per mile . Jason only has $12 to spend on a a ride

A service charges a $1.95 flat rate plus $0.05 per mile. Jason only has $12 to spend on a a ride.
Set up the cost equation C(m) where m is the number of miles:
C(m) = 0.05m + 1.95
The problems asks for the number of miles (m) when C(m) = 12:
0.05m + 1.95 = 12
[URL='https://www.mathcelebrity.com/1unk.php?num=0.05m%2B1.95%3D12&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = [B]201[/B]

A shopper paid $51.93 including tax for an item marked $48.99. What would she pay for another item m

A shopper paid $51.93 including tax for an item marked $48.99. What would she pay for another item marked $75?
Set up a proportion, assuming identical tax rates:
51.93/48.99 = 75/x where x is the after-tax amount
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=51.93&num2=75&den1=48.99&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
[B]x = 70.75[/B]

A spacecraft with a volume of 800 cubic feet is leaking air at a rate of .4 cubic feet every n minut

A spacecraft with a volume of 800 cubic feet is leaking air at a rate of .4 cubic feet every [I]n[/I] minutes. How many minutes until the spacecraft has no air?
800 cubic feet / .4 cubic feet every n minutes = 2000 (n minute parts)
Total time = [B]2000n[/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 stone mason builds 7 houses in 3 days. How many days does it take to build 11 houses?

a stone mason builds 7 houses in 3 days. How many days does it take to build 11 houses?
The build rate of houses per days is proportional. Set up a proportion of [I]houses to days[/I] where d is the number of days it takes to build 11 houses:
7/3 = 11/d
Cross multiply:
Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2
7d = 11 * 3
7d = 33
Divide each side of the equation by 7:
7d/7 = 33/7
d = [B]4.7142857142857[/B]

A sum of money doubles in 20 years on simple interest. It will get triple at the same rate in: a.

A sum of money doubles in 20 years on simple interest. It will get triple at the same rate in: a. 40 years b. 50 years c. 30 years d. 60 years e. 80 years
Simple interest formula if we start with 1 dollar and double to 2 dollars:
1(1 + i(20)) = 2
1 + 20i = 2
Subtract 1 from each side:
20i = 1
Divide each side by 20
i = 0.05
Now setup the same simple interest equation, but instead of 2, we use 3:
1(1 + 0.05(t)) = 3
1 + 0.05t = 3
Subtract 1 from each side:
0.05t = 2
Divide each side by 0.05
[B]t = 40 years[/B]

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to s

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel?
Set up the travel cost equation where m is the number of miles:
C(m) = 0.8m + 1.50
If Samantha wants to spend less than 12 per ride, we have an inequality where C(m) < 12:
[B]0.8m + 1.50 < 12[/B]

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to s

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel?
[LIST]
[*]Each ride will cost 1.50 + 0.8x where x is the number of miles per trip.
[*]This expression must be less than 12.
[/LIST]
[U]Setup the inequality:[/U]
1.5 + 0.8x < 12
[U]Subtracting 1.5 from each side of the inequality[/U]
0.8x < 10.5
[U]Simplifying even more by dividing each side of the inequality by 0.8, we have:[/U]
[B]x < 13.125[/B]

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel?
Set up a cost function C(m), where m is the number of miles:
C(m) = Cost per mile * m + flat rate
C(m) = 0.65m + 1.75
The problem asks for m when C(m) = 10
0.65m + 1.75 = 10
[URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into the search engine[/URL], we get:
m = [B]12.692 miles[/B]

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to spend on the cab ride, how far could she travel
Set up a cost function C(m), where m is the number of miles Erica can travel. We have:
C(m) = 0.65m + 1.75
If C(m) = 10, we have:
0.65m + 1.75 = 10
[URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = 12.69 miles
If the problem asks for complete miles, we round down to 12 miles.

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to spend on the cab ride, how far could she travel?
Set up the cost function C(m) where m is the number of miles:
C(m) = 0.65m + 1.75
If Erica has $10, then C(m) = 10, so we have:
0.65m + 1.75 = 10
[URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into the search engine[/URL], we get
m = 12.69
if the answer asks for whole number, then we round down to m = 12

A taxi charges a flat rate of 1.75, plus an additional 0.65 per mile. If Erica has at most 10 to spe

A taxi charges a flat rate of 1.75, plus an additional 0.65 per mile. If Erica has at most 10 to spend on the cab ride, how far could she travel?
Setup an equation where x is the number of miles traveled:
0.65x + 1.75 = 10
Subtract 1.75 from each side:
0.65x = 8.25
Divide each side by 0.65
[B]x = 12.69 miles[/B]
If we do full miles, we round down to 12.

a tomato plant has 5 leaves on day 1, 7 on day 3 and 9 on day 5. what is the rate it is growing?

a tomato plant has 5 leaves on day 1, 7 on day 3 and 9 on day 5. what is the rate it is growing?
Day 1 = 5 leaves
Day 3 = 7 leaves
Day 5 = 9 leaves
[B]Growth Rate = 2 leaves per day[/B]

A tortoise is walking in the desert. It walks at a speed of 5 meters per minute for 12.5 meters. For

A tortoise is walking in the desert. It walks at a speed of 5 meters per minute for 12.5 meters. For how many minutes does it walk?
Distance formula (d) for a rate (r) and time (t) is:
d = rt
We're given d = 12.5 and r = 5
12.5 = 5t
5t = 12.5
Solve for t. Divide each side of the equation by 5:
5t/5 = 12.5/5
Cancel the 5's on left side and we get:
t = [B]2.5[/B]

a total of $4000 is invested: part at 10% and the remainder at 15%. How much is invested at each rat

a total of $4000 is invested: part at 10% and the remainder at 15%. How much is invested at each rate if the annual interest is $430?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=4000&i1=10&i2=15&itot=430&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]3,400[/B] @ 10%
[*][B]600[/B] @ 15%
[/LIST]

A total of $4300 was invested, part of it at 6% interest and the remainder at 9%. If the total yearl

A total of $4300 was invested, part of it at 6% interest and the remainder at 9%. If the total yearly interest amounted to $315, how much was invested at each rate?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=4300&i1=6+&i2=9&itot=315&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]Fund 1: 2,400[/B]
[*][B]Fund 2: 1,900[/B]
[/LIST]

A total of $6,000 was invested, a portion at 6% and the remainder at 8%. The total amount of interes

A total of $6,000 was invested, a portion at 6% and the remainder at 8%. The total amount of interest earned was $450. How much was invested at each rate?
Using our split fund interest calculator, we get:
[LIST]
[*][B]1500 in 6% fund[/B]
[*][B]4500 in 8% fund[/B]
[/LIST]

A total of $7000 is invested: part at 7% and the remainder at 9%. How much is invested at each rate

A total of $7000 is invested: part at 7% and the remainder at 9%. How much is invested at each rate if the annual interest is $550?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=7000&i1=7&i2=9&itot=550&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]Fund 1: $4,000[/B]
[*][B]Fund 2: $3,000[/B]
[/LIST]

a total of 6000 is invested part at 8% and the remainder at 13%. how much is invested at each rate i

a total of 6000 is invested part at 8% and the remainder at 13%. how much is invested at each rate if the annual interest is 710
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=6000&i1=8&i2=13&itot=710&pl=Calculate']split fund interest calculator[/URL], we get:
1,400
4,600

A total of 7000 is invested part at 7% and the reminder at 11% .how much is invested at each rate of

A total of 7000 is invested part at 7% and the reminder at 11% .how much is invested at each rate of the annual interest is 640
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=7000&i1=7&i2=11&itot=640&pl=Calculate']split fund interest rate calculator[/URL], we get:
[LIST]
[*]Fund 1 = [B]3250[/B]
[*]Fund 2 = [B]3750[/B]
[/LIST]

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

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

A train traveled at 66km an hour for four hours. Find the distance traveled

A train traveled at 66km an hour for four hours. Find the distance traveled
Distance = Rate * Time
Distance = 66km/hr * 4 hours
Distance = [B]264 miles[/B]

A tree grows 35 cm in 2 years. If it continues to grow at the same rate determine how long it would

A tree grows 35 cm in 2 years. If it continues to grow at the same rate determine how long it would take to grow 85 cm
We set up a proportion of cm to years where y is the number of years it takes to grow 85 cm:
35/2 = 85/y
To solve this proportion for y, [URL='https://www.mathcelebrity.com/prop.php?num1=35&num2=85&den1=2&den2=y&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
[B]y = 4.86[/B]

A turtle and rabbit are in a race to see who is the first to reach a point 100 feet away. The turtle

A turtle and rabbit are in a race to see who is the first to reach a point 100 feet away. The turtle travels at a constant speed of 20 feet per minute for the entire 100 feet. The rabbit travels at a constant speed of 40 feet per minute for the first 50 feet, stops for 3 minutes, and then continuous at a constant speed of 40 feet per minute for the last 50 feet.
(i) Determine which animal won the race.
(ii). By how much time the animal won the race.
(iii) Explain one life lesson from the race.
We know the distance formula is:
d = rt
For the turtle, he has a rate (r) of 20 feet / minute and distance (d) of 100. We want to solve for time:
[URL='https://www.mathcelebrity.com/drt.php?d=+100&r=+20&t=&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 5
The rabbit has 3 parts of the race:
Rabbit Part 1: Distance (d) = 50 and rate (r) = 40
[URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 1.25
Rabbit Part 2: The rabbit stops for 3 minutes (t = 3)
Rabbit Part 3: Distance (d) = 50 and rate (r) = 40
[URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 1.25
Total time for the rabbit from the 3 parts is (t) = 1.25 + 3 + 1.25
Total time for the rabbit from the 3 parts is (t) = 5.5
[LIST]
[*](i) The [B]turtle won[/B] the race because he took more time to finish and they both started at the same time
[*](ii) We subtract the turtles time from the rabbit's time: 5.5 - 5 = [B]0.5 minutes which is also 30 seconds[/B]
[*](iii) [B]Slow and Steady wins the race[/B]
[/LIST]

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

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

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

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

A 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 water tank holds 236 gallons but is leaking at a rate of 3 gallons per week. A second water tank h

A water tank holds 236 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds 354 gallons but is leaking at a rate if 5 gallons per week. After how many weeks will the amount of water in the two tanks be the same
Let w be the number of weeks of leaking. We're given two Leak equations L(w):
[LIST=1]
[*]L(w) = 236 - 3w
[*]L(w) = 354 - 5w
[/LIST]
When the water in both tanks is the same, we can set both L(w) equations equal to each other:
236 - 3w = 354 - 5w
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=236-3w%3D354-5w&pl=Solve']type it in our search engine[/URL] and we get:
w = [B]59[/B]

A wildlife reserve has a population of 180 elephants. A group of researchers trapped 60 elephants an

A wildlife reserve has a population of 180 elephants. A group of researchers trapped 60 elephants and recorded their vital statistics. Of the trapped elephants, 12 were female. If that rate holds true for the entire population of 180 elephants, how many female elephants are on the wildlife reserve?
Set up a proportion of female to trapped elephants:
12/60 = f/180
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=12&num2=f&den1=60&den2=180&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we see that f = [B]36[/B]

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

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

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

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

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applie

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional onetime untaxed fee of $5.00 is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying [I]x[/I] nights?
[LIST]
[*]The Room cost equals 99.95 times x where x is the number of rooms
[*]We express an 8% tax by multiplying the room cost by 1.08
[*]Finally, we add on $5, which is [I]untaxed[/I]
[/LIST]
[I][/I]
Take this in pieces:
Room Cost: 99.95x
Tax on Room 1.08(99.95x)
Add on $5 which is untaxed: [B]1.08(99.95x) + 5[/B]

Accounting Rate of Return

Free Accounting Rate of Return Calculator - Given an initial investment and a set of returns, this calculates the Accounting Rate of Return

Addition Equality Property

Free Addition Equality Property Calculator - Demonstrates the Addition Equality Property
Numerical Properties

Addition Property Of Inequality

Free Addition Property Of Inequality Calculator - Demonstrates the Addition Property Of Inequality.
Numerical Properties

Additive Inverse Property

Free Additive Inverse Property Calculator - Demonstrates the Additive Inverse property using a number. A + (-A) = 0
Numerical Properties

Admir works at a coffee shop and earns $9/hour he also works at a grocery store and earns $15/hour.

Admir works at a coffee shop and earns $9/hour he also works at a grocery store and earns $15/hour. Last week he earned $500 dollars. Write an equation that represents the situation.
[LIST]
[*]Let c be the hours Admir works at the coffee shop.
[*]Let g be the hours Admir works at the grocery store.
[/LIST]
Since earnings equal hourly rate times hours, We have the following equation:
[B]9c + 15g = 500[/B]

alex burns approximately 650 calories in a 1.25-hour game. Daniellle enjoys kickboxing and burns app

alex burns approximately 650 calories in a 1.25-hour game. Daniellle enjoys kickboxing and burns approximately 420 calories in 45 minute class. who burns calories at the higher rate?
We want a calories to minutes measure.
[LIST]
[*][URL='https://www.mathcelebrity.com/timecon.php?quant=1.25&pl=Calculate&type=hour']1.25 hours[/URL] = 75 minutes
[/LIST]
Alexa's unit calorie burn:
650/75 = 8.67
Danielle's unit calorie burn:
420/45 = 9.33
So [B]Danielle[/B] burns calories at a higher rate.

Algebra Master (Polynomials)

Free Algebra Master (Polynomials) Calculator - Given 2 polynomials this does the following:

1) Polynomial Addition

2) Polynomial Subtraction

Also generates binomial theorem expansions and polynomial expansions with or without an outside constant multiplier.

1) Polynomial Addition

2) Polynomial Subtraction

Also generates binomial theorem expansions and polynomial expansions with or without an outside constant multiplier.

Amy and ryan operate a car dealing and repair service. For a car detailing (full wash outside and in

Amy and ryan operate a car dealing and repair service. For a car detailing (full wash outside and inside. Amy charges 40$ and Ryan charges 50$ . In addition they charge a hourly rate. Amy charges $35/h and ryan charges $30/h. How many hours does amy and ryan have to work to make the same amount of money?
Set up the cost functions C(h) where h is the number of hours.
[U]Amy:[/U]
C(h) = 35h + 40
[U]Ryan:[/U]
C(h) = 30h + 50
To make the same amount of money, we set both C(h) functions equal to each other:
35h + 40 = 30h + 50
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=35h%2B40%3D30h%2B50&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]2[/B]

Amy deposits 4000 into an account that pays simple interest at a rate of 6% per year. How much inter

Amy deposits 4000 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in the first 4 years?
Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=4000&int=6&t=4&pl=Simple+Interest']simple interest calculator[/URL], we get an accumulated value of 4,960
Interest Paid = Accumulated Value - Principal
Interest Paid = 4960 - 4000
Interest Paid = [B]960[/B]

An airplane flies at 250 mph. How far will it travel in 5 h at that rate of speed?

An airplane flies at 250 mph. How far will it travel in 5 h at that rate of speed?
Distance = Rate x Time
Distance = 250mph x 5h
Distance = [B]1,250 miles[/B]

An airplane is flying at 38,800 feet above sea level. The airplane starts to descend at a rate of 18

An airplane is flying at 38,800 feet above sea level. The airplane starts to descend at a rate of 1800 feet per minute. Let m be the number of minutes. Which of the following expressions describe the height of the airplane after any given number of minutes?
Let m be the number of minutes. Since a descent equals a [U]drop[/U] in altitude, we subtract this in our Altitude function A(m):
[B]A(m) = 38,800 - 1800m[/B]

An auto repair bill was $563. This includes $188 for parts and $75 for each hour of labor. Find the

An auto repair bill was $563. This includes $188 for parts and $75 for each hour of labor. Find the number of hours of labor
Let the number of hours of labor be h. We have the cost function C(h):
C(h) = Hourly Labor Rate * h + parts
Given 188 for parts, 75 for hourly labor rate, and 563 for C(h), we have:
75h + 188 = 563
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=75h%2B188%3D563&pl=Solve']type it in our search engine[/URL] and we get:
h = [B]5[/B]

an earthworm moves at distance of 45cm in 90 seconds what is the speed

an earthworm moves at distance of 45cm in 90 seconds what is the speed
Using our [URL='https://www.mathcelebrity.com/drt.php?d=45&r=+&t=90&pl=Calculate+the+missing+Item+from+D%3DRT']distance, rate, time calculator[/URL], we have:
Rate = [B]1/2cm or 0.5cm per second[/B]

An employee earns $7.00 an hour for the first 35 hours worked in a week and $10.50 for any hours ove

An employee earns $7.00 an hour for the first 35 hours worked in a week and $10.50 for any hours over 35. One weeks paycheck (before deductions) was for $308.00. How many hours did the employee work?
Let's first check to see if the employee worked overtime:
Regular Hours: 35 * 7 = 245
Since the employee made $308, they worked overtime. Let's determine how much overtime money was made:
308 - 245 = 63
Now, to calculate the overtime hours, we divide overtime pay by overtime rate
63/10.50 = 6
Now figure out the total hours worked in the week:
Total Hours = Regular Pay Hours + Overtime Hours
Total Hours = 35 + 6
[B]Total Hours = 41[/B]

An executive invests $21,000, some at 8% and the rest at 7% annual interest. If he receives an annua

An executive invests $21,000, some at 8% and the rest at 7% annual interest. If he receives an annual return of $1,600, how much is invested at each rate?
Using our [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=21000&i1=8&i2=7&itot=1600&pl=Calculate']split fund calculator[/URL], we get:
[LIST]
[*][B]Fund 1 = 13,000[/B]
[*][B]Fund 2 = 8,000[/B]
[/LIST]

An executive invests $22,000, some at 7% and the rest at 6% annual interest. If he receives an annua

An executive invests $22,000, some at 7% and the rest at 6% annual interest. If he receives an annual return of $1,420, how much is invested at each rate
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=22000&i1=7&i2=6&itot=1420&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]10,000[/B] @ 7%
[*][B]12,000[/B] @ 6%
[/LIST]

An executive invests $23,000, some at 8% and some at 4% annual interest. If he receives an annual re

An executive invests $23,000, some at 8% and some at 4% annual interest. If he receives an annual return of $1,560, how much is invested at each rate?
Let x be the amount invested at 8% and y be the amount invested at 4%. We have two equations:
[LIST=1]
[*]x + y = 23,000
[*]0.08x + 0.04y = 1,560
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y+%3D+23000&term2=0.08x+%2B+0.04y+%3D+1560&pl=Cramers+Method']system of equations calculator[/URL], we get:
[B]x = 16,000
y = 7,000[/B]

An executive invests $29,000, some at 8% and the rest at 6% annual interest. If he receives an annua

An executive invests $29,000, some at 8% and the rest at 6% annual interest. If he receives an annual return of $2,020, how much is invested at each rate?
Using our [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=29000&i1=8&i2=6&itot=2020&pl=Calculate']split fund calculator[/URL], we get:
[LIST]
[*]Fund 1: $14,000
[*]Fund 2: $15,000
[/LIST]

An investment of $200 is now valued at $315. Assuming continuous compounding has occurred for 6 year

An investment of $200 is now valued at $315. Assuming continuous compounding has occurred for 6 years, approximately what interest rate is needed to be for this to be possible?
[URL='https://www.mathcelebrity.com/simpint.php?av=315&p=200&int=&t=6&pl=Continuous+Interest']Using our continuous compounding calculator solving for interest rate[/URL], we get:
I = [B]7.57%[/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]

Angelo is paid double time for each hour he works over 40 hours in a week. Last week he worked 46 ho

Angelo is paid double time for each hour he works over 40 hours in a week. Last week he worked 46 hours and earned $624. What is his normal hourly rate?
Let h be Angelo's hourly rate. We have:
40h + (46 - 40) * 2 * h = 624
40h + 6 * 2 * h = 624
40h + 12h = 624
Combine like terms:
52h = 624
[URL='https://www.mathcelebrity.com/1unk.php?num=52h%3D624&pl=Solve']Typing this equation into our search engine[/URL], we get [B]h = 12[/B].

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

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

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

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

Anna paints a fence in 4 hours wile her brother paints it in 5 hours. If they work together, how lon

Anna paints a fence in 4 hours wile her brother paints it in 5 hours. If they work together, how long will it take them to paint the fence?
Set up unit rates per hour:
[LIST]
[*]Anna paints 1/4 of a fence per hour
[*]Brother paints 1/5 of a fence per hour
[*]Combined, they paint [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=1%2F5&pl=Add']1/4 + 1/5[/URL] = 9/20 of a fence per hour
[/LIST]
Setup a proportion of time to hours where h is the number of hours needed to paint the fence
9/20 of a fence the first hour
18/20 of a fence the second hour
2/20 is left. Each 1/20 of the fence takes 60/9 = 6 & 2/3 minutes
6 & 2/3 minutes * 2 = 13 & 1/3 minutes
Final time is:
[B]2 hours and 13 & 1/3 minutes[/B]

Annuity that pays 6.6% compounded monthly. If $950 is deposited into this annuity every month, how m

Annuity that pays 6.6% compounded monthly. If $950 is deposited into this annuity every month, how much is in the account after 7 years? How much of this is interest?
Let's assume payments are made at the end of each month, since the problem does not state it. We have an annuity immediate formula. Interest rate per month is 6.6%/12 = .55%, or 0.0055. 7 years * 12 months per year gives us 84 deposits.
Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=950&n=84&i=0.55&check1=1&pl=Calculate']present value of an annuity immediate calculator[/URL], we get the following:
[LIST=1]
[*]Accumulated Value After 7 years = [B]$101,086.45[/B]
[*]Principal = 79,800
[*]Interest Paid = (1) - (2) = 101,086.45 - 79,800 = [B]$21,286.45[/B]
[/LIST]

Approximations of Interest Rate

Free Approximations of Interest Rate Calculator - Interest Rate Approximations: Approximates a yield rate of interest based on 4 methods:

1) Max Yield denoted as i_{max}

2) Min Yield denoted as i_{min}

3) Constant Ratio denoted as i_{cr}

4) Direct Ratio denoted as i_{dr}

1) Max Yield denoted as i

2) Min Yield denoted as i

3) Constant Ratio denoted as i

4) Direct Ratio denoted as i

Arithmetic Perpetuities

Free Arithmetic Perpetuities Calculator - Solves for Present Value, First Payment, Arithmetic Payment, or Interest rate for an Arithmetic Perpetuity Immediate or Due

Associative Property

Free Associative Property Calculator - Demonstrates the associative property using 3 numbers. Covers the Associative Property of Addition and Associative Property of Multiplication. Also known as the Associative Law of Addition and Associative Law of Multiplication
Numerical Properties

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

At 1:00 pm you have 24 megabytes of a movie and at 1:15 you have 96 megabytes of a movie. What is the download rate in megabytes per minute?
First, find the number of minutes:
1:15 - 1:00 = 15 minutes
Next, determine the difference in megabytes
96 - 24 = 72
Finally, determine the download rate:
72 megabytes / 15 minutes = [B]4.8 megabytes per minute[/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 a rate of 4 gallons per min , how long will it take to fill a 300 gallon swimming pool

At a rate of 4 gallons per min , how long will it take to fill a 300 gallon swimming pool
Time to fill = Total Gallons of the Pool / Fill Rate
Time to Fill = 300 gallons / 4 gallons per minute
Time to Fill = [B]75 minutes[/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 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]

Balance with Interest

Free Balance with Interest Calculator - Calculates the final account balance given a beginning balance, interest rate, and interest crediting period.

Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, ab

Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, about 170 million. The population growth rate in Bangladesh is assumed to be linear, and is about 1.5% per year of the base 170 million. Create a linear model for population growth in Bangladesh. Assume that y is the total population in millions and t is the time in years.
At any time t, the Bangladesh population at year t is:
[B]y = 170,000,000(1.015)^t[/B]

Basal Metabolic Rate (BMR)

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

Ben can write 153 letters in 3 minutes. At this rate, how many letters can he write in 10 minutes?

Ben can write 153 letters in 3 minutes. At this rate, how many letters can he write in 10 minutes?
We set up a proportion of letters to minutes where the number of letters in 10 minutes is l:
153/3 = l/10
We [URL='https://www.mathcelebrity.com/prop.php?num1=153&num2=l&den1=3&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into a search engine[/URL] and we get:
l =[B] 510[/B]

Beth made a trip to the train station and back. On the trip there she traveled 45 km/h and on the re

Beth made a trip to the train station and back. On the trip there she traveled 45 km/h and on the return trip she went 30 km/h. How long did the trip there take if the return trip took six hours?
We use the distance formula: D = rt where D = distance, r = rate, and t = time.
Start with the return trip:
D = 45(6)
D = 270
The initial trip is:
270= 30t
Divide each side by 30
[B]t = 9 hours[/B]

Bingo Card Generator

Free Bingo Card Generator Calculator - This program generates the following two types of bingo cards

1) Random Numerical bingo cards 1-75 with a FREE Space.

2) Buzzword Bingo cards which allow you to enter words of your choice to be used on the bingo card.

1) Random Numerical bingo cards 1-75 with a FREE Space.

2) Buzzword Bingo cards which allow you to enter words of your choice to be used on the bingo card.

Binomial Distribution

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

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

Calculates moment number t using the moment generating function

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

Calculates moment number t using the moment generating function

Bond Yield Rates

Free Bond Yield Rates Calculator - Calculates the yield rate of bonds using the Yield Approximation Method or the Bond Salesman Method.

Brad has $40 in a savings account. The interest rate is 5%, compounded annually. To the nearest cen

Brad has $40 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much will he have in 3 years?
[URL='https://www.mathcelebrity.com/compoundint.php?bal=40&nval=3&int=5&pl=Annually']Using our balance with interest calculator[/URL], we get [B]$46.31[/B].

Brandon can shovel his sidewalk in 8 minutes, while his brother can shovel the walk in 12 minutes. I

Brandon can shovel his sidewalk in 8 minutes, while his brother can shovel the walk in 12 minutes. If they work together, how long will it take them to shovel the sidewalk?
Set up unit rates:
[LIST]
[*]Brandon can shovel 1/8 of a sidewalk per minute
[*]His brother can shovel 1/12 of a sidewalk per minute
[/LIST]
Together, they can shovel:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F8&frac2=1%2F12&pl=Add']1/8 + 1/12[/URL] = 5/24 of a sidewalk per minute
1 minute = 60 seconds
5/24 / 60 seconds = 1/x seconds
5/24 * 60 = 1/x
5/1440 = 1/x
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5&num2=1&den1=1440&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
x = 288
288/60 = [B]4 minutes and 48 seconds[/B]

Brenda invests $1535 in a savings account with a fixed annual interest rate of 3% compounded continu

Brenda invests $1535 in a savings account with a fixed annual interest rate of 3% compounded continuously. What will the account balance be after 8 years
Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=1535&int=3&t=8&pl=Continuous+Interest']continuous interest balance calculator[/URL], we get:
[B]1,951.37
[MEDIA=youtube]vbYV6SYXtvs[/MEDIA][/B]

Calculate the simple interest if the principal is 1500 at a rate of 7% for 3 years

Calculate the simple interest if the principal is 1500 at a rate of 7% for 3 years.
Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=1500&int=7&t=3&pl=Simple+Interest']simple interest calculator[/URL], the total interest earned over 3 years is [B]$315[/B].

Caleb has a complicated and difficult research paper due soon. What should he do to keep from feelin

Caleb has a complicated and difficult research paper due soon. What should he do to keep from feeling overwhelmed and procrastinating? A. work on the paper every day but save the bulk of the work for the night before it's due B. break down the paper into several small steps and start with the smallest one C. write down the deadline for the paper where he can see it every day so he doesn't forget D. work on the hardest parts of the paper first and take multiple breaks until he's finished
Caleb wants to avoid both overwhelm and procrastination. Let's review each option:
[LIST]
[*]A is out because saving a majority of the work will cause overwhelm [U]and[/U] demonstrates procrastination
[*]B is a good option as small steps reduce overwhelm
[*]C looks nice on paper, but will he follow through with seeing the deadline everyday?
[*]D is a good option as well. Finishing the tough parts first makes the rest of the journey seem like a downhill cruise
[/LIST]
Based on these, I'd take [B]B or D[/B]

can someone help me with how to work out this word problem?

Consider a paper cone, pointing down, with the height 6 cm and the radius 3 cm; there is currently 9/4 (pie) cubic cm of water in the cone, and the cone is leaking at a rate of 2 cubic centimeters of water per second. How fast is the water level changing, in cm per second?

can someone help me with how to work out this word problem?

Have you tried the rate of change formula?

Capitalized Cost and Periodic Charge

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

Carly grew 50 plants with 25 seed packets. With 37 seed packets, how many total plants can Carly hav

Carly grew 50 plants with 25 seed packets. With 37 seed packets, how many total plants can Carly have in her backyard? Solve using unit rates.
Set up a proportion of plants per seed packets where p is the number of plants per 37 seed packets.
50/25 = p/37
Copying and pasting this problem [URL='http://www.mathcelebrity.com/prop.php?num1=50&num2=p&den1=25&den2=37&propsign=%3D&pl=Calculate+missing+proportion+value']into our search engine[/URL], we get [B]p = 74[/B].

Cassidy is renting a bicycle on the boardwalk. The rental costs a flat fee of $10 plus an additional

Cassidy is renting a bicycle on the boardwalk. The rental costs a flat fee of $10 plus an additional $7 per hour. Cassidy paid $45 to rent a bicycle.
We set up the cost equation C(h) where h is the number of hours of rental:
C(h) = hourly rental rate * h + Flat Fee
C(h) = 7h + 10
We're told that Cassidy paid 45 to rent a bicycle, so we set C(h) = 45
7h + 10 = 45
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=7h%2B10%3D45&pl=Solve']type this equation into our math engine[/URL] and we get:
h = [B]5[/B]

Charlene wants to invest $10,000 long enough for it to grow to at least $20000. The compound interes

Charlene wants to invest $10,000 long enough for it to grow to at least $20,000. The compound interest rate is 6% p.a. How many whole number of years does she need to invest the money for so that it grows to her $20,000 target?
We want 10,000(1.06)^n = 20,000.
But what the problem asks for is how long it will take money to double. We can use a shortcut called the Rule of 72. [URL='https://www.mathcelebrity.com/rule72.php?num=6&pl=Calculate']Using the Rule of 72 at 6%[/URL], we get [B]12 years[/B].

Christopher has $25 000 to invest. He finds a bank who will pay an interest rate of 5.65% p.a compou

Christopher has $25 000 to invest. He finds a bank who will pay an interest rate of 5.65% p.a compounded annually. What will the total balance be after 6 years?
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=25000&nval=6&int=5.65&pl=Annually']compound interest balance calculator[/URL], we get:
[B]34,766.18[/B]

Cody invests $4,734 in a retirement account with a fixed annual interest rate of 4% compounded conti

Cody invests $4,734 in a retirement account with a fixed annual interest rate of 4% compounded continuously. What will the account balance be after 19 years?
Using our c[URL='http://www.mathcelebrity.com/simpint.php?av=&p=4734&int=4&t=19&pl=Continuous+Interest']ontinuous interest compounding calculator[/URL], we get:
[B]10,122.60[/B]

Commutative Property

Free Commutative Property Calculator - Demonstrates the commutative property of addition and the commutative property of multiplication using 3 numbers.
Numerical Properties

Composite Number

Free Composite Number Calculator - This calculator determines the nth composite number. Helps you generate composite numbers.

Compound Interest Accumulated Balance

Free Compound Interest Accumulated Balance Calculator - Given an interest rate per annum compounded annually (i), semi-annually, quarterly, monthly, semi-monthly, weekly, and daily, this calculates the accumulated balance after (n) periods

Compound Interest and Annuity Table

Free Compound Interest and Annuity Table Calculator - Given an interest rate (i), number of periods to display (n), and number of digits to round (r), this calculator produces a compound interest table. It shows the values for the following 4 compound interest annuity functions from time 1 to (n) rounded to (r) digits:

v^{n}

d

(1 + i)^{n}

a_{n|}

s_{n|}

ä_{n|i}

s_{n|i}

Force of Interest δ^{n}

v

d

(1 + i)

a

s

ä

s

Force of Interest δ

Consider the formula for the area of a trapezoid: A=12h(a+b) . Is it mathematically simpler to solve

Consider the formula for the area of a trapezoid: A=12h(a+b) . Is it mathematically simpler to solve for a, b, or h? Why? Solve for each of these variables to demonstrate.
The variable "h" is the easiest to solve for. Because you only have one step. Let's review:
Divide each side of the equation by 12(a + b)
h = 12(a + b)/A
Solving for "a", we two steps. Divide each side by 12h:
A/12h = a + b
Subtract b from each side
a = A/12h - b
Solving for "b" takes two steps as well. Divide each side by 12h:
A/12h = a + b
Subtract a from each side
b = A/12h - a

Corvettes are known as sporty cars that can travel at high rates of speed. It is therefore assumed t

Corvettes are known as sporty cars that can travel at high rates of speed. It is therefore assumed that they are much more dangerous than minivans. An owner of a Corvette points out that when statistics are studied, there are far more deaths each year from crashes that involve minivans than crashes that involve Corvettes, so Corvettes, so Corvettes must be safer than minivans. The statistics the Covert owner sites are correct. Is his logic faulty? Why or why not?
[B]Faulty.[/B]
There are hundreds of times more minivans on the road than Corvettes, so we expect more deaths even if they are the safest car on the road.

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

Critical Z-values

Free Critical Z-values Calculator - Given a probability from a normal distribution, this will generate the z-score critical value. Uses the NORMSINV Excel function.

Customers arrive at the claims counter at the rate of 20 per hour (Poisson distributed). What is th

Customers arrive at the claims counter at the rate of 20 per hour (Poisson distributed). What is the probability that the arrival time between consecutive customers is less than five minutes?
Use the [I]exponential distribution[/I]
20 per 60 minutes is 1 every 3 minutes
1/λ = 3 so λ = 0.333333333
Using the [URL='http://www.mathcelebrity.com/expodist.php?x=+5&l=0.333333333&pl=CDF']exponential distribution calculator[/URL], we get F(5,0.333333333) = [B]0.811124396848[/B]

d-i-v interest rate relationships

Free d-i-v interest rate relationships Calculator - Calculates d,i, or v based on 1 of the items entered.

Daisy earned 300 for a 40 hour week how much is her hourly rate

Daisy earned 300 for a 40 hour week how much is her hourly rate
Hourly Rate = Earnings / Hours Worked
Hourly Rate = 300 / 40
Hourly Rate = [B]$7.50[/B]

Dan bought a computer in a state that has a sales tax rate of 7%. If he paid $67.20 sales tax, what

Dan bought a computer in a state that has a sales tax rate of 7%. If he paid $67.20 sales tax, what did the computer cost?
Set up the equation for price p:
p * 0.07 = 67.20
p = 67.20 / 0.07
p = [B]$960[/B]

Dan earns £9.80 per hour. How much will he earn for 8 hours work?

Dan earns £9.80 per hour. How much will he earn for 8 hours work?
Calculate Total Earnings
Total Earnings = Hourly Rate * Number of Hours
Total Earnings = £9.80 * 8
Total Earnings = [B]£78.40[/B]

Dan makes 9 dollars for each hour of work. Write an equation to represent his total pay p after work

Dan makes 9 dollars for each hour of work. Write an equation to represent his total pay p after working h hours.
We know that pay (p) on an hourly basis (h) equals:
p = Hourly Rate * h
We're given an hourly rate of 9, so we have:
p = [B]9h[/B]

Daniel pays $10 to get into the parking lot and will pay a fee of $2 per hour his car will be left i

Daniel pays $10 to get into the parking lot and will pay a fee of $2 per hour his car will be left in the parking lot. He ending up paying a total of $23 for parking. How many hours was Daniels car left in the parking lot?
Calculate the amount of fees for hours:
Fees for hours = Total Bill - Entrance fee
Fees for hours = 23 - 10
Fees for hours = 13
Calculate the number of hours Daniel parked:
Number of hours = Fees for hours / Hourly Rate
Number of hours = 13/2
Number of hours = [B]6.5[/B]

data below consists of the pulse rates (in beats per minute) of 32 students. Assuming ? = 10.66,

The data below consists of the pulse rates (in beats per minute) of 32 students. Assuming ? = 10.66, obtain a 95.44% confidence interval for the population mean.
80 74 61 93 69 74 80 64
51 60 66 87 72 77 84 96
60 67 71 79 89 75 66 70
57 76 71 92 73 72 68 74

Dave paints a fence in 4 hours while Sara paints the same fence in 2 hours. If they work together, h

Dave paints a fence in 4 hours while Sara paints the same fence in 2 hours. If they work together, how long will it take them to paint the fence?
Set up unit rates:
[LIST]
[*]Dave paints 1/4 of the fence in 1 hour
[*]Sara will paint 1/2 of the fence in 1 hour
[/LIST]
So together, they paint 1/2 + 1/4 = 2/4 + 14 = 3/4 of the fence in one hour.
1 hour = 60 minutes, so we set up a proportion of time to minutes where m is the time in minutes needed to complete 1 full fence:
3/4/60 = 1/m
3/240 = 1/m
[URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3&num2=1&den1=240&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion in our math engine[/URL], we get:
m = [B]80 minutes[/B]
[B]80 minutes is also 1 hour and 20 minutes.[/B]

Dave rented a limousine for his wife's birthday. The hourly rate is $60. They used the limousine for

Dave rented a limousine for his wife's birthday. The hourly rate is $60. They used the limousine for 4 hours, plus Dave gave the driver a 20% tip. How much did he spend in total for the hourly charges plus tip?
Hourly Spend = $60 * 4 = $240
Calculate 20% tip
0.2 * $240 = $48
Calculate total:
$240 + 48 = [B]$288[/B]

David roller skates for 3 1/3 hours with a constant speed of 24 km/h and then for another 1 hour 10

David roller skates for 3 1/3 hours with a constant speed of 24 km/h and then for another 1 hour 10 minutes with constant speed of 12 km/h. What distance did he go?
Distance = Rate x Time
[U]Part 1 of his trip:[/U]
D1 = R1 x T1
D1 = 3 & 1/3 hours * 24 km/h
D1 = 80 km
[U]Part 2 of his trip:[/U]
D2 = R2 x T2
D2 = 1 & 1/6 hours * 12 km/h (Note, 10 minutes = 1/6 of an hour)
D2 = 14 km
[U]Calculate Total Distance (D)[/U]
D = D1 + D2
D = 80 + 14
D = [B]94 km[/B]

DeMorgans Laws

Free DeMorgans Laws Calculator - Demonstrates DeMorgans Laws including the proof

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

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

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time pe

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12.
Our givens are:
[LIST]
[*]I = 450
[*]P = 3000
[*]t = 3
[*]We want r
[/LIST]
450 = 3000(r)(3)
450 = 9000r
Divide each side by 9000
[B]r = 0.05[/B]

Dick invested $9538 in an account at 10% compounded annually. Calculate the total investment after

Dick invested $9538 in an account at 10% compounded annually. Calculate the total investment after 10 years. Round your answer to the nearest penny if necessary.
Annual compounding means we don't need to make adjustments to interest rate per compounding period.
[URL='https://www.mathcelebrity.com/compoundint.php?bal=9538&nval=10&int=10&pl=Annually']Using our compound interest calculator[/URL], we get our new balance after 10 years of:
[B]$24,739.12[/B]

Distance Rate and Time

Free Distance Rate and Time Calculator - Solves for distance, rate, or time in the equation d=rt based on 2 of the 3 variables being known.

Distributive Property

Free Distributive Property Calculator - Demonstrates the distributive property using 3 numbers.
Numerical Properties

Division Equality Property

Free Division Equality Property Calculator - Demonstrates the Division Equality Property Calculator
Numerical Properties

Division Property Of Inequality

Free Division Property Of Inequality Calculator - Demonstrates the Division Property Of Inequality
Numerical Properties

Dollar Weighted Interest Method

Free Dollar Weighted Interest Method Calculator - Solves for Interest Rate, Starting Asset Value, Ending Asset Value, and Expenses using the Dollar Weighted Method.

During the summer, you work 30 hours per week at a gas station and earn $8.75 per hour. You also wor

During the summer, you work 30 hours per week at a gas station and earn $8.75 per hour. You also work as a landscaper for $11 per hour and can work as many hours as you want. You want to earn a total of $400 per week. How many hours, t, must you work as a landscaper?
[U]Calculate your gas station salary:[/U]
Gas Station Salary = Hours Worked * Hourly Rate
Gas Station Salary = 30 * $8.75
Gas Station Salary = $262.50
[U]Now subtract this from the desired weekly earnings of $400[/U]
$400 - 262.50 = $137.50
The landscaper makes $11 per hour. And they want to make $137.50 from landscaping. So we have the following equation:
11t = 137.50
Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=11t%3D137.50&pl=Solve']equation calculator[/URL], and we get t = 12.5 hours.

Dwayne earn $6 for each hour of yard work. After doing a total of 3 hours of yard work, how much mon

Dwayne earn $6 for each hour of yard work. After doing a total of 3 hours of yard work, how much money will Dwayne have earned?
We're given the hourly earnings equation below:
Hourly Earnings = Hourly Rate * hours worked
Hourly Earnings = $6 * 3
Hourly Earnings = [B]$18[/B]

Dwayne wants to start a saving account at his local credit union. If he puts $8000 into a savings ac

Dwayne wants to start a saving account at his local credit union. If he puts $8000 into a savings account with an annual interest rate of 1.1%, how much simple interest will he have earned after 6 years?
Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=8000&int=1.1&t=6&pl=Simple+Interest']simple interest calculator[/URL], we get:
$528 of interest earned.

Each of letters in the word PROPER are on separate cards, face down on the table. If you pick a card

Each of letters in the word PROPER are on separate cards, face down on the table. If you pick a card at random, what is the probability that its letter will be P or R?
PROPER has 6 letters in it. It has 2 P's and 2 R's. So we have:
Pr(P or R) = Pr(P) + Pr(R)
Pr(P or R) = 2/6 + 2/6
Pr(P or R) = 4/6
We can simplify this. So [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F6&frac2=3%2F8&pl=Simplify']we type this fraction in our search engine[/URL], choose simplify, and we get:
Pr(P or R) = [B]2/3[/B]

Each of the letters in the word PLOTTING are on separate cards, face down on the table. If you pick

Each of the letters in the word PLOTTING are on separate cards, face down on the table. If you pick a card at random, what is the probability that its letter will be T or G?
PLOTTING has to 8 letters. It has 2 T'sand 1 G, so we have:
P(T or G) = P(T) + P(G)
P(T or G) = 2/8 + 1/8
P(T or G) = [B]3/8[/B]

Effective Annual Yield Rate

Free Effective Annual Yield Rate Calculator - Figures out the effective annual yield rate of interest entered by compounding daily, weekly, semi-monthly, monthly, quarterly, semi-annually, and continuously.

Eva earns $72 washing 6 cars. At this rate, how many cars did Eva wash to earn $132?

Eva earns $72 washing 6 cars. At this rate, how many cars did Eva wash to earn $132?
Set up a proportion of money to cars washed where c is the number of cars washed for $132 in earnings:
72/6 = 132/c
[URL='https://www.mathcelebrity.com/prop.php?num1=72&num2=132&den1=6&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our calculator[/URL], we get:
[B]c = 11[/B]

evelyn needs atleast $112 to buy a new dress. She has already saved $40 . She earns $9 an hour babys

evelyn needs atleast $112 to buy a new dress. She has already saved $40 . She earns $9 an hour babysitting. How many hours will she need to babysit to buy the dress?
Let the number of hours be h.
We have the earnings function E(h) below
E(h) = hourly rate * h + current savings
E(h) = 9h + 40
We're told E(h) = 112, so we have:
9h + 40 = 112
[URL='https://www.mathcelebrity.com/1unk.php?num=9h%2B40%3D112&pl=Solve']Typing this equation in our math engine[/URL] and we get:
h = [B]8[/B]

Exponential Growth

Free Exponential Growth Calculator - This solves for any 1 of the 4 items in the exponential growth equation or exponential decay equation, Initial Value (P), Ending Value (A), Rate (r), and Time (t).

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]

Fermats Little Theorem

Free Fermats Little Theorem Calculator - For any integer a and a prime number p, this demonstrates Fermats Little Theorem.

Fibonacci Sequence

Free Fibonacci Sequence Calculator - Generates a list of the first 100 Fibonacci numbers.
Also shows how to generate the nth Fibonacci number using Binet's Formula

Finance

1. Spend 8000 on a new machine. You think it will provide after tax cash inflows of 3500 per year for the next three years. The cost of funds is 8%. Find the NPV, IRR, and MIRR. Should you buy it?
2. Let the machine in number one be Machine A. An alternative is Machine B. It costs 8000 and will provide after tax cash inflows of 5000 per year for 2 years. It has the same risk as A. Should you buy A or B?
3. Spend 100000 on Machine C. You will need 5000 more in net working capital. C is three year MACRS. The cost of funds is 8% and the tax rate is 40%. C is expected to increase revenues by 45000 and costs by 7000 for each of the next three years. You think you can sell C for 10000 at the end of the three year period.
a. Find the year zero cash flow.
b. Find the depreciation for each year on the machine.
c. Find the depreciation tax shield for the three operating years.
d. What is the projects contribution to operations each year, ignoring depreciation effects?
e. What is the cash flow effect of selling the machine?
f. Find the total CF for each year.
g. Should you buy it?

Finance

1) [URL='http://www.mathcelebrity.com/npv.php?matrix1=0%2C-8000%0D%0A1%2C3500%0D%0A2%2C3500%0D%0A3%2C3500%0D%0A&irr=8&pl=NPV']Net present value[/URL] = $1,019.85
[URL='http://www.mathcelebrity.com/npv.php?matrix1=0%2C-8000%0D%0A1%2C3500%0D%0A2%2C3500%0D%0A3%2C3500&irr=8&pl=IRR']IRR[/URL] = 14%
I need a reinvestment rate from you for [URL='http://www.mathcelebrity.com/mirr.php']MIRR shown here[/URL]
Yes, we should pursue the project since NPV > 0
2) [URL='http://www.mathcelebrity.com/npv.php?matrix1=0%2C-8000%0D%0A1%2C5000%0D%0A2%2C5000&irr=8&pl=NPV']Net present value[/URL] = $916.32
Buy A as it has the higher net present value.

Find Requested Confidence Value

The data below consists of the pulse rates (in beats per minute) of 32 students. Assuming ? = 10.66, obtain a 95.44% confidence interval for the population mean.
80 74 61 93 69 74 80 64
51 60 66 87 72 77 84 96
60 67 71 79 89 75 66 70
57 76 71 92 73 72 68 74

Find 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]

find the value of $20000 invested for 7 years at an annual interest rate of 2.55% compounded continu

find the value of $20000 invested for 7 years at an annual interest rate of 2.55% compounded continuously
Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=200000&int=2.55&t=7&pl=Continuous+Interest']compound continuous interest with balance calculator[/URL] we get:
[B]239.084.58[/B]

Finite Field

Free Finite Field Calculator - Demonstrates the addition table and multiplication table for a finite field (Galois Field) of n denoted GF(n).

Football Squares

Free Football Squares Calculator - Generates a Football Squares grid

Forward Rate

Free Forward Rate Calculator - Given two times and two zero-coupon yield rates at those times, this calculates the forward rate.

Fraction Cancellation Property

Free Fraction Cancellation Property Calculator - Demonstrates the Fraction Cancellation Property also known as Cancellation Property of Fractions
Numerical Properties

Frank is a plumber who charges a $35 service charge and $15 per hour for his plumbing services. Find

Frank is a plumber who charges a $35 service charge and $15 per hour for his plumbing services. Find a linear function that expresses the total cost C for plumbing services for h hours.
Cost functions include a flat rate and a variable rate. The flat rate is $35 and the variable rate per hour is 15. The cost function C(h) where h is the number of hours Frank works is:
[B]C(h) = 15h + 35[/B]

Gabe rents a piano for $49 per month. He earns $15 per hour giving piano lessons to students. How ma

Gabe rents a piano for $49 per month. He earns $15 per hour giving piano lessons to students. How many hours of lessons per month must he give to earn a profit of $326?
Build a profit function P(h) where h is the number of hours:
P(h) = Hourly Rate * Number of Hours (h) - Cost of Piano
P(h) = 15h - 49
The problem asks for the number of hours where P(h) = $326
15h - 49 = 326
We take this equation and [URL='https://www.mathcelebrity.com/1unk.php?num=15h-49%3D326&pl=Solve']type it in our search engine[/URL] to solve for h:
h = [B]25[/B]

Gamma Constant γ

Free Gamma Constant γ Calculator - This calculator generates 5000 iterations for the development of the gamma constant γ

gretchen cycles 65 miles in one week. Find her rate of cycling in miles per day

gretchen cycles 65 miles in one week. Find her rate of cycling in miles per day
65 miles per week / 7 days per week = [B]9.29 miles per day[/B]

Guadalupe left the restaurant traveling 12 mph. Then, 3 hours later, Lauren left traveling the same

Guadalupe left the restaurant traveling 12 mph. Then, 3 hours later, Lauren left traveling the same direction at 24 mph. How long will Lauren travel before catching up with Guadalupe?
Distance = Rate x Time
Guadulupe will meet Lauren at the following distance:
12t = 24(t - 3)
12t = 24t - 72
[URL='https://www.mathcelebrity.com/1unk.php?num=12t%3D24t-72&pl=Solve']Typing that equation into our search engine[/URL], we get:
t = 6

Gym Class Team Generator

Free Gym Class Team Generator Calculator - Given a list of players, this will randomly generate two teams.

Hailey worked 32 hours at 8 dollars a hour .Taxes were 1% .How much money was left?

Hailey worked 32 hours at 8 dollars a hour .Taxes were 1% .How much money was left?
Calculate earnings:
Earnings = Hourly rate * hours worked
Earnings = 32 * 8
Earnings = 256
If taxes are 1%, then Hailey ends up with 100% - 1% = 99%
Leftover = 256 * 99%
Leftover = [B]$253.44[/B]

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

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

Hall looked at 10 websites every 35 hours. At this rate, how long, in hours, will it take to look at

Hall looked at 10 websites every 35 hours. At this rate, how long, in hours, will it take to look at 6 websites?
Set up a proportion of websites to hours where h is the number of hours it takes to look at 6 websites:
10/35 = 6/h
To solve this proportion for h, we [URL='https://www.mathcelebrity.com/prop.php?num1=10&num2=6&den1=35&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get:
h = [B]21 hours[/B]

Hannah invested $540 in an account paying an interest rate of 4.7% compounded continuously. Assuming

Hannah invested $540 in an account paying an interest rate of 4.7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 18 years?
[URL='https://www.mathcelebrity.com/simpint.php?av=&p=540&int=4.7&t=18&pl=Continuous+Interest']Using our compound interest balance calculator[/URL], we get:
[B]$1,258.37[/B]

Help

Suppose company A charges a rate of $40 per day and Company B charges a $60 fee plus $40 per day. For what number of days is the cost the same?

Hong is riding his bicycle. He rides for 22.5 kilometers at a speed of 9 kilometers per hour. For ho

Hong is riding his bicycle. He rides for 22.5 kilometers at a speed of 9 kilometers per hour. For how many hours does he ride?
Distance = Rate * Time
The problem asks for time.
[URL='https://www.mathcelebrity.com/drt.php?d=+22.5&r=+9&t=&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator[/URL], we get:
t = [B]2.5 hours[/B]

How many years will it take for an initial investment of $40,000 to go to $60,000? Assuming a rate

How many years will it take for an initial investment of $40,000 to go to $60,000? Assuming a rate of interest at 18% compounded continuously
[URL='https://www.mathcelebrity.com/simpint.php?av=60000&p=40000&int=18&t=&pl=Continuous+Interest']Using our continuous interest calculator[/URL] and solving for n, we get:
n = [B]2.2526 years[/B]

How much money will there be in an account at the end of 10 years if $8000 is deposited at a 7.5% an

How much money will there be in an account at the end of 10 years if $8000 is deposited at a 7.5% annual rate that is compounded continuously?
Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=8000&int=7.5&t=10&pl=Continuous+Interest']continuous compounding calculator[/URL], we get [B]$16,936[/B].

I need help for this question. Can someone pls help me?

The simple interests earned on the sum of money for 4 years at 7.5% p.a. exceeds that on the same sum for 3.5 years at 8% p.a. by $90.
(a)Find the original sum of money.
(b)If the original sum of money accumulates to $4612.50 in 5 months at simple interest, find the interests rate per annum.

I work 30 hours a week 50 weeks of a year and I earn a salary of 36000 what is my hourly rate

I work 30 hours a week 50 weeks of a year and I earn a salary of 36000 what is my hourly rate
30 hours per week * 50 weeks = 1,500 hours
36000 / 1500 hours = [B]$24 per hour[/B]

If $9000 grows to $9720 in 2 years find the simple interest rate.

If $9000 grows to $9720 in 2 years find the simple interest rate.
Simple interest formula is Initial Balance * (1 + tn) = Current Balance
We have
[LIST]
[*]Initial Balance = 9000
[*]Current Balance = 9720
[*]n = 2
[/LIST]
Plugging in these values, we get:
9000 * (1 + 2t) = 9720
Divide each side by 9000
1 + 2t = 1.08
Subtract 1 from each sdie
2t = 0.08
Divide each side by 2
t = [B]0.04 or 4%[/B]

if 1 person with corona spreads it to 3 people and those people spread it to 3 people, how many peop

if 1 person with corona spreads it to 3 people and those people spread it to 3 people, how many people have corona
So the spread rate is 3/1 = 3.
If 3 people have it, then they spread it to 3 x 3 = [B]9 people[/B].

If 2 inches is about 5 centimeters, how many inches are in 25 centimeters? Choose the proportions th

If 2 inches is about 5 centimeters, how many inches are in 25 centimeters? Choose the proportions that accurately represent this scenario.
We set up a proportion of inches to centimeters where i is the number of inches in 25 centimeters:
2/5 = i/25
To solve this proportion for i, we [URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=i&den1=5&den2=25&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get:
i = [B]10[/B]

If 3000 is invested at an annual interest rate of 5% and compounded annually, find the balance after

If 3000 is invested at an annual interest rate of 5% and compounded annually, find the balance after 2 years.
Use our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=3000&int=5&t=2&pl=Compound+Interest']compound interest calculator[/URL], we get:
Balance = [B]$3,307.50[/B]

If 5000 dollars is invested in a bank account at an interest rate of 10 per cent per year, find the

If 5000 dollars is invested in a bank account at an interest rate of 10 per cent per year, find the amount in the bank after 9 years if interest is compounded annually.
We assume the interest is compounded at the end of the year. Use the [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=5000&n=9&i=10&check1=1&pl=Calculate']annuity immediate formula[/URL]:
[B]67,897.39[/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 a person invests $360 In an account that pays 8% interests compounded annually, find the balance

If a person invests $360 In an account that pays 8% interests compounded annually, find the balance after 5 years
[B]$528.95[/B] per our [URL='http://www.mathcelebrity.com/intbal.php?startbal=360&intrate=8&bstart=1%2F1%2F2000&bend=1%2F1%2F2005&pl=Annual+Credit']balance calculator[/URL].

if a train travels at 80 mph for 15 mins, what is the distance traveled?

if a train travels at 80 mph for 15 mins, what is the distance traveled?
Let d = distance, r = rate, and t = time, we have the distance equation:
D = rt
Plugging in our values for r and t, we have:
D = 80mph * 15 min
Remember our speed is in miles per hour, so 15 min equal 1/4 of an hour
D = 80mph * 1/4
D = [B]20 miles[/B]

If a tutor charges $35 an hour and works for 286 minutes, what is the dollar amount she is owed?

If a tutor charges $35 an hour and works for 286 minutes, what is the dollar amount she is owed?
Dollar Amount Owed = Hourly Rate * Number of Hours Worked
Convert Minutes worked to hours worked
Hours worked = Minutes Worked / 60
Hours worked = 286 minutes / 60 minutes per hour
Hours worked = 4.77
So now back to our main formula...
Dollar Amount Owed = Hourly Rate * Number of Hours Worked
Dollar Amount Owed = $35 * 4.77
Dollar Amount Owed = [B]$166.95[/B]

If an employee starts saving with $750 and increases his savings by 8% each month, what will be his

If an employee starts saving with $750 and increases his savings by 8% each month, what will be his total savings after 10 months?
Set up the savings function S(m), where m is the number of months and I is the interest rate growth:
S(m) = Initial Amount * (1 + i)^m
Plugging in our number at m = 10 months we get:
S(10) = 750 * (1 + 0.08)^10
S(10) = 750 * 1.08^10
S(10) = [B]$1,619.19[/B]

if hose a can fill up a swimming pool in 6 hours, hose b in 3 hours, hose c in 2 hours, how long wil

if hose a can fill up a swimming pool in 6 hours, hose b in 3 hours, hose c in 2 hours, how long will it take to fill up the pool using all 3 hoses?
Let V be the pool's Volume. Each hour, the hoses fill up this much of the pool:
[LIST]
[*]Hose A, V/6 of the pool
[*]Hose B, V/3 of the pool
[*]Hose C, V/2 of the pool
[/LIST]
Effective fill rate is:
V/6 + V/3 + V/2
6V/36 + 12V/36 + 18V/36
36V/36 which is volume units per hour
Let t = units / rate
t = 1 hour, so we have:
t = units / rate
t = V (volume units) / V (volume units / hour)
t = [B]1 hour[/B]

If I make 30,000 an hour, how much will I make in 6 hours

If I make 30,000 an hour, how much will I make in 6 hours
Earnings = Hourly Rate * Hours Worked
Earnings = 30,000 per hour * 6 hours
Earnings = [B]180,000[/B]

If Juan spent $1.28 for ground beef that cost $1.92 per pound, how much ground beef did Juan buy?

If Juan spent $1.28 for ground beef that cost $1.92 per pound, how much ground beef did Juan buy?
Calculate unit rate:
$1.28 / $1.92 per pound = [B]2/3 pound or 0.6667 pounds[/B]

If the correlation between two variables is close to minus one, the association is: Strong Moderate

If the correlation between two variables is close to minus one, the association is:
Strong
Moderate
Weak
None
[B]Strong[/B] - Coefficient near +1 or -1 indicate a strong correlation

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find th

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find the time taken by aeroplane to cover 1200m initially.
We know from the distance formula (d) using rate (r) and time (t) that:
d = rt
Regular speed:
1200 = rt
Divide each side by t, we get:
r = 1200/t
Reduced speed. 20 minutes = 60/20 = 1/3 of an hour. So we multiply 1,200 by 3
3600 = (r - 40)(t + 1/3)
If we multiply 3 by (t + 1/3), we get:
3t + 1
So we have:
3600 = (r - 40)(3t + 1)
Substitute r = 1200/t into the reduced speed equation:
3600 = (1200/t - 40)(3t + 1)
Multiply through and we get:
3600 = 3600 - 120t + 1200/t - 40
Subtract 3,600 from each side
3600 - 3600 = 3600 - 3600 - 120t + 1200/t - 40
The 3600's cancel, so we get:
- 120t + 1200/t - 40 = 0
Multiply each side by t:
-120t^2 - 40t + 1200 = 0
We've got a quadratic equation. To solve for t, [URL='https://www.mathcelebrity.com/quadratic.php?num=-120t%5E2-40t%2B1200%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this in our search engine[/URL] and we get:
t = -10/3 or t = 3. Since time [I]cannot[/I] be negative, our final answer is:
[B]t = 3[/B]

If the temperature is dropping at a rate of 2° per hour, how many hours will take to drop 15°

If the temperature is dropping at a rate of 2° per hour, how many hours will take to drop 15°
Hours Needed = Total Temperature Drop / Drop per hour
Hours Needed = 15/2
Hours Needed = [B]7.5[/B]

If you have $15,000 in an account with a 4.5% interest rate, compounded quarterly, how much money wi

If you have $15,000 in an account with a 4.5% interest rate, compounded quarterly, how much money will you have in 25 years?
[URL='https://www.mathcelebrity.com/compoundint.php?bal=15000&nval=100&int=4.5&pl=Quarterly']Using our compound interest calculator[/URL] with 25 years * 4 quarters per year = 100 periods of compounding, we get:
[B]$45,913.96[/B]

if you worked for 3 hours and earned a total of $24, determine your hourly pay rate

if you worked for 3 hours and earned a total of $24, determine your hourly pay rate
Hourly Pay = Total Pay / Hours Worked
Hourly Pay = $24 /3
Hourly Pay = [B]$8 per hour[/B]

Imagine that the diabetic test accurately indicates the disease in 95% of the people who have it. Wh

Imagine that the diabetic test accurately indicates the disease in 95% of the people who have it. What's the miss rate?
Miss Rate = 1 - 0.95
[B]Miss Rate = 0.05 or 5%[/B]

In 1910, the population of math valley was 15,000. If the population is increasing at an annual rate

In 1910, the population of math valley was 15,000. If the population is increasing at an annual rate of 2.4%, what was the population in 1965?
1965 - 1910 = 55 years of growth.
P(1965) = 15,000 * (1.024)^55
P(1965) = 15,000 * 3.68551018049
P(1965) = 55282.652707 ~ [B]55,283[/B]

In 2010, the population of Greenbow, AL was 1,100 people. The population has risen at at rate of 4%

In 2010, the population of Greenbow, AL was 1,100 people. The population has risen at at rate of 4% each year since. Let x = the number of years since 2010 and y = the population of Greenbow. What will the population of Greenbow be in 2022?
P(x) = 1,100(1.04)^x
x = 2022 - 2010
x = 12 years
We want P(12):
P(12) = 1,100(1.04)^12
P(12) = 1,100(1.60103221857)
P(12) = [B]1,761.14 ~ 1,761[/B]

In 2016 the geese population was at 750. the geese population is expected to grow at a rate of 12% e

In 2016 the geese population was at 750. the geese population is expected to grow at a rate of 12% each year. What is the geese population in 2022?
12% is also 0.12. We have the population growth function:
P(t) = 750(1.12)^t
2022 - 2016 is 6 years of growth. We want P(6).
P(6) = 750(1.12)^6
P(6) = 750(1.9738)
[B]P(6) = 1,480.36 ~ 1,480[/B]

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

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

In a given year, Houston has good air quality 48% of the days, moderate air quality 41% of the days,

In a given year, Houston has good air quality 48% of the days, moderate air quality 41% of the days, and unhealthy air quality 4% of the days. How many days per year do residents have unhealthy air quality?
4% of 365 days in a year = [B]14.6 days. If we are talking full days, we have 14.[/B]

Incremental Cash Flow

Free Incremental Cash Flow Calculator - Given cash inflows, outflows, depreciable amounts, and tax rates, this determines the incremental cash flows.

Inflation and Real Rate of Interest

Free Inflation and Real Rate of Interest Calculator - Calculates Real rate of Interest, Inflation, and nominal interest rate before inflation.

Isaac invested $5000 at two different rates, 4% and 6.5% if his total interest income was $250, how

Isaac invested $5000 at two different rates, 4% and 6.5% if his total interest income was $250, how much did he invest at each rate?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=5000&i1=4&i2=6.5&itot=250&pl=Calculate']split fund calculator[/URL], we have the following investments per fund:
Fund 1: [B]$3,000[/B]
Fund 2: [B]$2,000[/B]

Isabel earns $7.50 per hour on the weekends. Write and solve an inequality to find how many hours sh

Isabel earns $7.50 per hour on the weekends. Write and solve an inequality to find how many hours she needs to work to earn at least $120.
A few things to note:
[LIST]
[*]Earnings = Rate * time
[*]Let h be the number of hours worked
[*]The phrase [I]at least[/I] means greater than or equal to, so we have the following inequality.
[/LIST]
We represent this with the following inequality:
7.5h < 120
To solve this inequality for h, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=7.5h%3C120&pl=Show+Interval+Notation']type it into our math engine[/URL] and we get:
[B]h < 16[/B]

It takes 3 city snowplows 14 hours to clear 500 miles of road. If the city wants the 500 miles of ro

It takes 3 city snowplows 14 hours to clear 500 miles of road. If the city wants the 500 miles of road to be cleared in 6 hours, how many additional snowplows must they buy?
Set up unit rate per plow:
14 hours * 3 plows = 42 hours for one plow to clear 500 miles of road
Calculate the amount of plows we need:
42 hours / 6 hours = 7 plows
Additional plows = New plows - original plows:
Additional plows = 7 - 3
Additional plows = [B]4[/B]

It takes 60 minutes for 7 people to paint 5 walls. How many minutes does it take 10 people to paint

It takes 60 minutes for 7 people to paint 5 walls. How many minutes does it take 10 people to paint 10 walls?
Rate * Time = Output
Let "Rate" (r) be the rate at which [B]one person[/B] works.
So we have:
7r * 60 = 5
Multiply through and simplify:
420r = 5
Divide each side by 5 to isolate r:
r = 1/84
So now we want to find out how many minutes it takes 10 people to paint 10 walls using this rate:
10rt = 10
With r = 1/84, we have:
10t/84 = 10
Cross multiply:
10t = 840
To solve for t, we t[URL='https://www.mathcelebrity.com/1unk.php?num=10t%3D840&pl=Solve']ype this equation into our search engine[/URL] and we get:
t = [B]84 minutes[/B]

It takes a crew of 4 painters 12 hours one house. If they wanted to paint the house in 8 hours, how

It takes a crew of 4 painters 12 hours one house. If they wanted to paint the house in 8 hours, how many additional painters must they hire?
It takes one painter 4 * 12 hours = 48 hours to paint the house.
Now we calculate the unit rate:
48 hours / 8 hours = 6 painters
6 painters - 4 original painters = [B]2 additional painters[/B]

Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling?

Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling?
Distance = Rate * Time
We're given D = 395 and t = 5
We want Rate. We divide each side of the equation by time:
Distance / Time = Rate * Time / Time
Cancel the Time's on each side and we get:
Rate = Distance / Time
Plugging our numbers in, we get:
Rate = 395/5
Rate = [B]79 kilometers[/B]

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

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

Jenny makes 9 dollars for each hour of work. Write an equation to represent her total pay p after wo

Jenny makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.
Since Jenny makes 9 dollars for each hour of work, then her total pay (p) is her hourly rate times the number of hours worked:
[B]p = 9h[/B]

Jill worked 8 hours Saturday at $8.50 per hour. How much did she earned?

Jill worked 8 hours Saturday at $8.50 per hour. How much did she earned?
Earnings = Hours worked * hourly rate
Earnings = 8 * $8.50
Earnings = [B]$68[/B]

Jim invested $25,000 at an interest rate of 2% compounded anually. Approximately how much would Jim’

Jim invested $25,000 at an interest rate of 2% compounded anually. Approximately how much would Jim’s investment be worth after 2 years
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=25000&nval=20&int=2.0&pl=Annually']compound interest calculator[/URL], we get:
[B]$37,148.68[/B]

Jocelyn invested $3,700 in an account paying an interest rate of 1.5% compounded continuously. Assum

Jocelyn invested $3,700 in an account paying an interest rate of 1.5% compounded continuously. Assuming no deposits or withdrawals are made, how much money would be in the account after 6 years?
Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=3700&int=1.5&t=6&pl=Continuous+Interest']continuous interest with balance calculator[/URL], we get:
[B]$4,048.44[/B]

Joe earns $9 per hour. He worked x hours on both Wednesday and Friday, and 8 hours on both Tuesday a

Joe earns $9 per hour. He worked x hours on both Wednesday and Friday, and 8 hours on both Tuesday and Saturday. Write an expression to represent how much joe earned.
Earnings = Hourly Rate * hours worked, so we have:
[LIST]
[*]Wednesday: 9x
[*]Friday: 9x
[*]Tuesday: 9(8) = 72
[*]Saturday: 9(8) = 72
[/LIST]
Joe's total earnings come from adding up all 4 days:
9x + 9x + 72 + 72
Combine like terms:
(9 + 9)x + (72 + 72)
[B]18x + 144[/B]

John earns $5 mowing lawns. How many hours must he work to earn $40?

John earns $5 mowing lawns. How many hours must he work to earn $40?
Let hours worked be h. We have:
Earnings = Hourly Rate * Hours Worked
40 = 5h
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=40%3D5h&pl=Solve']type it in our search engine[/URL] and we get:
h = [B]8[/B]

Johnny Rocket can run 300 meters in 90 seconds. If his speed remains constant, how far could he ru

Johnny Rocket can run 300 meters in 90 seconds. If his speed remains constant, how far could he run in 500 seconds? Round to one decimal place.
Set up the distance equation:
Distance = Rate * Time
300 = 90r
Solving this equation for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=300%3D90r&pl=Solve']type it in our search engine[/URL] and we get:
r = 3.333
For 500 seconds, we set up our distance equation again:
Distance = 500 * 3.333333
Distance = [B]1666.7 meters[/B]

Julia has a bucket of water that weighs 10lbs. The total weight is 99% water. She leaves the bucke

Julia has a bucket of water that weighs 10lbs. The total weight is 99% water. She leaves the bucket outside overnight and some of the water evaporates, in the morning the water is only 98% of the total weight. What is the new weight?
Setup the proportion:
0.99/10 = 0.98/w
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=0.99&num2=0.98&den1=10&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]w = 9.899 lbs[/B].

Kathy rans 16 miles a week. If she continues to ran at this rate how many miles will she ran in a ye

Kathy rans 16 miles a week. If she continues to ran at this rate how many miles will she ran in a year?
52 weeks / year * 16 miles / week = [B]832 miles /year[/B]

Kendra has $20 in a savings account. The interest rate is 10%, compounded annually. To the nearest

Kendra has $20 in a savings account. The interest rate is 10%, compounded annually. To the nearest cent, how much will she have in 2 years?
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=20&nval=2&int=10&pl=Annually']balance with interest calculator[/URL], we get [B]$24.20[/B].

Kevin borrowed $8000 at a rate of 7.5%, compounded monthly. Assuming he makes no payments, how much

Kevin borrowed $8000 at a rate of 7.5%, compounded monthly. Assuming he makes no payments, how much will he owe after 10 years?
We want to find 8,000(1.075)^10
Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=8000&nval=10&int=7.5&pl=Annually']balance calculator[/URL], we get:
[B]$16,488.25[/B]

Kunio puts $2,200.00 into savings bonds that pay a simple interest rate of 2.4%. How much money will

Kunio puts $2,200.00 into savings bonds that pay a simple interest rate of 2.4%. How much money will the bonds be worth at the end of 4 years?
Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=2200&int=2.4&t=4&pl=Simple+Interest']simple interest balance calculator[/URL], we his account will be worth [B]$2,411.20[/B] after 4 years

Larry Mitchell invested part of his $31,000 advance at 6% annual simple interest and the rest at 7%

Larry Mitchell invested part of his $31,000 advance at 6% annual simple interest and the rest at 7% annual simple interest. If the total yearly interest from both accounts was $2,090, find the amount invested at each rate.
Let x be the amount invested at 6%. Then 31000 - x is invested at 7%.
We have the following equation:
0.06x + (31000 - x)0.07 = 2090
Simplify:
0.06x + 2170 - 0.07x = 2090
Combine like Terms
-0.01x + 2170 = 2090
Subtract 2170 from each side
-0.01x = -80
Divide each side by -0.01
x = [B]8000 [/B]at 6%
Which means at 7%, we have:
31000 - 8000 = [B]23,000[/B]

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

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

Lauren invested $340 in an account paying an interest rate of 5.8% compounded monthly. Assuming no d

Lauren invested $340 in an account paying an interest rate of 5.8% compounded monthly. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 13 years?
13 years * 12 months per year = 156 compounding periods.
[URL='https://www.mathcelebrity.com/compoundint.php?bal=340&nval=156&int=5.8&pl=Monthly']Using our compound interest balance calculator[/URL] with 156 for t, we get:
$[B]721.35[/B]

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

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

Lebron James scored 288 points in 9 games this season. Assuming he continues to score at this consta

Lebron James scored 288 points in 9 games this season. Assuming he continues to score at this constant rate, write a linear equation that represents the scenario.
288 points / 9 games = 32 points per game
Let g be the number of games Lebron plays. We build an equation for his season score:
Lebron's Season Score = Points per game * number of games
Lebron's Season Score = [B]32g[/B]

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

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

Levi invested $630 in an account paying an interest rate of 4.6% compounded daily. Assuming no depos

Levi invested $630 in an account paying an interest rate of 4.6% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $970?
3,425 days, per the [URL='http://www.mathcelebrity.com/compoundint.php?bal=630&nval=3425&int=4.6&pl=Daily']balance calculator[/URL].

Linda can run about 6 yards in one second. About how far can she run in 12 seconds?

Linda can run about 6 yards in one second. About how far can she run in 12 seconds?
Distance = Rate * Time
Distance = 6 yds/ second * 12 seconds
Distance = [B]72 yards[/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]

Linear Congruential Generator

Free Linear Congruential Generator Calculator - Using the linear congruential generator algorithm, this generates a list of random numbers based on your inputs

Lisa wants to rent a boat and spend less than $52. The boat costs $7 per hour, and Lisa has a discou

Lisa wants to rent a boat and spend less than $52. The boat costs $7 per hour, and Lisa has a discount coupon for $4 off. What are the possible numbers of hours Lisa could rent the boat?
Calculate discounted cost:
Discounted cost = Full Cost - Coupon
Discounted cost = 52 - 7
Discounted cost = 45
Since price equals rate * hours (h), and we want the inequality (less than) we have:
7h < 52
Using our [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=7h%3C52&pl=Show+Interval+Notation']inequality calculator,[/URL] we see that:
[B]h < 7.42[/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].

Lucas Numbers

Free Lucas Numbers Calculator - Generates a list of the first 100 Lucas numbers.

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

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

luke earns $328 in 8 hours. Find luke’s hourly rate

luke earns $328 in 8 hours. Find luke’s hourly rate
luke’s hourly rate = Total Earnings / Hours Worked
luke’s hourly rate 328/8
luke’s hourly rate = [B]$41[/B]

Margaret earns 15 an hour at her job. Each week she earns at least 450 and no more than 600. How man

Margaret earns 15 an hour at her job. Each week she earns at least 450 and no more than 600. How many hours does Margaret work each week?
Let h be the hours worked
We know that hourly rate * h equals total earnings.
The phrases at least and no more than signify inequalities, so we have:
450 <= 15h <= 600
Divide each entry by 15:
[B]30 <= h <= 40[/B]
This means Margaret works at least 30 hours a week and no more than 40

Marla wants to rent a bike Green Lake Park has an entrance fee of $8 and charges $2 per hour for bik

Marla wants to rent a bike Green Lake Park has an entrance fee of $8 and charges $2 per hour for bike Oak Park has an entrance fee of $2 and charges $5 per hour for bike rentals she wants to know how many hours are friend will make the costs equal
[U]Green Lake Park: Set up the cost function C(h) where h is the number of hours[/U]
C(h) = Hourly Rental Rate * h + Entrance Fee
C(h) = 2h + 8
[U]Oak Park: Set up the cost function C(h) where h is the number of hours[/U]
C(h) = Hourly Rental Rate * h + Entrance Fee
C(h) = 5h + 2
[U]Marla wants to know how many hours make the cost equal, so we set Green Lake Park's cost function equal to Oak Parks's cost function:[/U]
2h + 8 = 5h + 2
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2h%2B8%3D5h%2B2&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]2[/B]

Mary invested $800, part at 9% per annum and the rest at 12% per annum. After 1 year, the total inte

Mary invested $800, part at 9% per annum and the rest at 12% per annum. After 1 year, the total interest earned was $79.50. How much did she invest at each rate?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=800&i1=9&i2=12&itot=79.50&pl=Calculate']split fund calculator[/URL], we get:
[LIST]
[*]Fund 1: $550
[*]Fund 2: $250
[/LIST]

Match each variable with a variable by placing the correct letter on each line.

Match each variable with a variable by placing the correct letter on each line.
a) principal
b) interest
c) interest rate
d) term/time
2 years
1.5%
$995
$29.85
[B]Principal is $995
Interest is $29.85 since 995 * .0.15 * 2 = 29.85
Interest rate is 1.5%
Term/time is 2 year[/B]s

Matthew works 45 hours at $22.10 per hour and 3 hours overtime at double time. Calculate his total e

Matthew works 45 hours at $22.10 per hour and 3 hours overtime at double time. Calculate his total earnings per week.
If Matthew gets 3 hours overtime, then his regular time is 45 - 3 = 42
[U]Calculate regular hours earnings:[/U]
Regular hours earnings = Hourly Rate * Regular hours worked
Regular hours earnings = 22.10 * 42
Regular hours earnings = 928.20
[U]Calculate overtime hours earnings:[/U]
Double time = twice the regular hourly ratre
Overtime hours earnings = Hourly Rate * 2 * Overtime hours worked
Overtime hours earnings = 22.10 * 2 * 3
Overtime hours earnings = 132.60
[U]Calculate total earnings:[/U]
Total earnings = Regular hours earnings + Overtime hours earnings
Total earnings = 928.20 + 132.60
Total earnings = [B]$1,060.80[/B]

Method of Equated Time-Exact Method-Macaulay Duration-Volatility

Free Method of Equated Time-Exact Method-Macaulay Duration-Volatility Calculator - Given a set of cash flows at certain times, and a discount rate, this will calculate t using the equated time method and the exact method, as well as the macaulay duration and volatility

Michelle and Natalie both went out to eat at a new restaurant. Michelle’s bill was $22.50, and she l

Michelle and Natalie both went out to eat at a new restaurant. Michelle’s bill was $22.50, and she left a 15% tip. Natalies bill was $24.25, and she left a 10% tip. Whose total bill was the greatest?
[U]Michelles's total bill:[/U]
Total Bill = Pre-Tax Bill * (1 + tax rate)
Since 15% = 0.15, we have:
Total Bill = 22.50 * 1.15
Total Bill = 25.88
[U]Natalie's total bill:[/U]
Total Bill = Pre-Tax Bill * (1 + tax rate)
Since 10% = 0.10, we have:
Total Bill = 24.25 * 1.10
Total Bill = 26.68
[B]Natalie's[/B] total bill was the greatest.

Michelle can paint one car in 2 hours. It takes Tyler 3 hours to paint the same car while Colton tak

Michelle can paint one car in 2 hours. It takes Tyler 3 hours to paint the same car while Colton takes 6 hours to paint the car. If they all work together, how long will it take them to paint the car?
Setup unit rates:
[LIST]
[*]Michelle can paint 1/2 of the car in one hour
[*]Tyler can paint 1/3 of the car in one hour
[*]Colton can paint 1/6 of the car in one hour
[/LIST]
In one hour using a combined effort, they can paint:
1/2 + 1/3 + 1/6 = 6/6 = 1 car in [B]one hour[/B].

mike went to canalside with $40 to spend. he rented skates for $10 and paid $3 per hour to skate.wha

mike went to canalside with $40 to spend. he rented skates for $10 and paid $3 per hour to skate.what is the greatest number of hours Mike could have skated?
Let h be the number of hours of skating. We have the cost function C(h):
C(h) = Hourly skating rate * h + rental fee
C(h) = 3h + 10
The problem asks for h when C(h) = 40:
3h + 10 = 40
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=3h%2B10%3D40&pl=Solve']type it in our search engine[/URL] and we get:
h = [B]10[/B]

Modified Internal Rate of Return (MIRR)

Free Modified Internal Rate of Return (MIRR) Calculator - Given a set of positive/negative cash flows, a finance rate, and a reinvestment rate, this calculates the modified internal rate of return

Modified Payback Period

Free Modified Payback Period Calculator - Given a set of cash inflows, outflows, and a discount rate, this calculates the modified payback period.

Mortgage

Free Mortgage Calculator - Calculates the monthly payment, APY%, total value of payments, principal/interest/balance at a given time as well as an amortization table on a __standard__ or __interest only__ home or car loan with fixed interest rate. Handles amortized loans.

Mr. Elk is secretly a huge fan of Billie Eilish, and is saving up for front row seats. He puts $250

Mr. Elk is secretly a huge fan of Billie Eilish, and is saving up for front row seats. He puts $250 in the bank that has an interest rate of 8% compounded daily. After 4 years, Billie is finally hitting up NJ on her tour. How much money does Mr. Elk have in the bank? (rounded to the nearest cent) *
4 years = 365*4 days
4 years = 1,460 days.
Using this number of compounding periods, we [URL='https://www.mathcelebrity.com/compoundint.php?bal=250&nval=1460&int=8&pl=Daily']plug this into our compound interest calculator[/URL] to get:
[B]$344.27[/B]

Mr. Johnson earned $16,000 in 4 months. At this rate, how much money did he earn in one year?

Mr. Johnson earned $16,000 in 4 months. At this rate, how much money did he earn in one year?
$16,000 / 4 months * 12 months / year = [B]$48,000 per year[/B]

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

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

Mrs diaz works 40 hours per week regularly at a rate of $15.15 per hour.When she works overtime , he

Mrs diaz works 40 hours per week regularly at a rate of $15.15 per hour.When she works overtime , her rate is time and a half of her regular rate. What is Mrs. Diaz overtime rate?
Time and a half means your hourly rate plus 50% or 1/2 of your hourly rate:
15.15 * 1.5 = $[B]22.73[/B]

Mrs. Lowe charges $45 an hour with a $10 flat fee for tutoring. Mrs. Smith charges $40 an hour wit

Mrs. Lowe charges $45 an hour with a $10 flat fee for tutoring. Mrs. Smith charges $40 an hour with a $15 flat fee to tutor. Write an equation that represents the situation when the cost is the same to be tutored by Mrs. Lowe and Mrs. Smith.
[U]Set up cost equation for Mrs. Lowe where h is the number of hours tutored:[/U]
Cost = Hourly Rate * number of hours + flat fee
Cost = 45h + 10
[U]Set up cost equation for Mrs. Smith where h is the number of hours tutored:[/U]
Cost = Hourly Rate * number of hours + flat fee
Cost = 40h + 15
[U]Set both cost equations equal to each other:[/U]
45h + 10 = 40h + 15 <-- This is our equation
To solve for h if the problem asks, we [URL='https://www.mathcelebrity.com/1unk.php?num=45h%2B10%3D40h%2B15&pl=Solve']type this equation into our search engine[/URL] and we get:
h = 1

Ms. Gonzales is investing $17000 at an annual interest rate of 6% compounded continuously. How much

Ms. Gonzales is investing $17000 at an annual interest rate of 6% compounded continuously. How much money will be in the account after 16 years? Round your answer to the nearest hundredth (two decimal places).
Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=17000&int=6&t=16&pl=Continuous+Interest']continuous interest calculator[/URL], we get:
[B]44,398.84[/B]

Multiplication Equality Property

Free Multiplication Equality Property Calculator - Demonstrates the Multiplication Equality Property
Numerical Properties

Multiplication Property Of Inequality

Free Multiplication Property Of Inequality Calculator - Demonstrates the Multiplication Property Of Inequality
Numerical Properties

Multiplicative Identity Property

Free Multiplicative Identity Property Calculator - Demonstrates the Multiplicative Identity property using a number.
Numerical Properties

Multiplicative Inverse Property

Free Multiplicative Inverse Property Calculator - Demonstrates the Multiplicative Inverse property using a number.
Numerical Properties

Murray makes $12.74 per hour. How much does he earn in 38 hours?

Murray makes $12.74 per hour. How much does he earn in 38 hours?
[U]Calculate Earnings:[/U]
Earnings = Hourly Rate * Number of hours worked
Earnings = $12.74 * 38
Earnings = [B]$484.12[/B]

Nancy shot a 16 on 4 holes of golf. At this rate, what can she expect her score to be if she plays 1

Nancy shot a 16 on 4 holes of golf. At this rate, what can she expect her score to be if she plays 18 holes? Round to the nearest whole number
Set up a proportion of score to holes of golf where s is the score for 18 holes:
16/4 = s/18
To solve this proportion for s, we [URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=s&den1=4&den2=18&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
s = [B]72[/B]

Natural Logarithm Table

Free Natural Logarithm Table Calculator - Generates a natural logarithm table for the first (n) numbers rounded to (r) digits

Net Present Value (NPV) - Internal Rate of Return (IRR) - Profitability Index

Free Net Present Value (NPV) - Internal Rate of Return (IRR) - Profitability Index Calculator - Given a series of cash flows C_{t} at times t and a discount rate of (i), the calculator will determine the Net Present Value (NPV) at time 0, also known as the discounted cash flow model.

Profitability Index

Also determines an Internal Rate of Return (IRR) based on a series of cash flows. NPV Calculator

Profitability Index

Also determines an Internal Rate of Return (IRR) based on a series of cash flows. NPV Calculator

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

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

Nominal Yield

Free Nominal Yield Calculator - Given an effective annual rate of interest based on a compounding period, this determines the nominal yield.

Oakdale School is sponsoring a canned food drive. In the first week of the drive, the students colle

Oakdale School is sponsoring a canned food drive. In the first week of the drive, the students collected 638 cans. They collected 698 cans in the second week and 758 cans in the third week. If the students continue to collect cans at this rate, in which week will they collect more than 1,000 cans?
We have an arithmetic sequence where each successive term increases by 50.
[URL='https://www.mathcelebrity.com/sequenceag.php?num=638%2C698%2C758&n=10&pl=Calculate+Series&a1=5&d=3']Using our sequence calculator[/URL], we find that week #8 is when the students cross 1,000 cans.

Oliver and Julia deposit $1,000.00 into a savings account which earns 14% interest compounded contin

Oliver and Julia deposit $1,000.00 into a savings account which earns 14% interest compounded continuously. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend? Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (?2.71828), r is the interest rate expressed as a decimal, and t is the time in years. Round your answer to the nearest cent.
[URL='https://www.mathcelebrity.com/simpint.php?av=&p=1000&int=3&t=14&pl=Continuous+Interest']Using our continuous interest calculator[/URL], we get:
A = [B]1,521.96[/B]

Oliver invests $1,000 at a fixed rate of 7% compounded monthly, when will his account reach $10,000?

Oliver invests $1,000 at a fixed rate of 7% compounded monthly, when will his account reach $10,000?
7% monthly is:
0.07/12 = .00583
So we have:
1000(1 + .00583)^m = 10000
divide each side by 1000;
(1.00583)^m = 10
Take the natural log of both sides;
LN (1.00583)^m = LN(10)
Use the identity for natural logs and exponents:
m * LN (1.00583) = 2.30258509299
0.00252458479m = 2.30258509299
m = 912.064867899
Round up to [B]913 months[/B]

Omar mows lawns for $9.25 an hour. He spends $7.50 on gas for the mower. How much does he make if he

Omar mows lawns for $9.25 an hour. He spends $7.50 on gas for the mower. How much does he make if he works h hours?
His revenue R(h) where h is the number of hours is denoted by:
R(h) = Hourly Rate * h - Gas cost
[B]R(h) = 9.25h - 7.50[/B]

Omar mows lawns for $9.25 per hour. He spends $7.50 on gas for the mower. How much does he make if h

Omar mows lawns for $9.25 per hour. He spends $7.50 on gas for the mower. How much does he make if he works h hours?
We have the following profit equation:
Profit = Revenue - Cost:
Revenue = Hourly rate * number of hours
[B]9.25h - 7.50[/B]

On a trip, a family drove 270 kilometers in 3 hours. how many kilometers were traveled in one hour.

On a trip, a family drove 270 kilometers in 3 hours. how many kilometers were traveled in one hour. Express this as a rate per hour.
270 kilometers per 3 hours
270/3
Divide top and bottom by 3 to get km/hr
[B]90 kilometers per hour[/B]

One number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a c

One number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a comma to separate your answers.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]x = 1/4y
[*]x + y = 25
[/LIST]
Substitute (1) into (2)
1/4y + y = 25
Since 1/4 = 0.25, we have:
0.25y + y = 25
[URL='https://www.mathcelebrity.com/1unk.php?num=0.25y%2By%3D25&pl=Solve']Type this equation into the search engine[/URL] to get:
[B]y = 20
[/B]
Now, substitute this into (1) to solve for x:
x = 1/4y
x = 1/4(20)
[B]x = 5
[/B]
The problem asks us to separate the answers by a comma. So we write this as:
[B](x, y) = (5, 20)[/B]

Opposite Direction Distance

Free Opposite Direction Distance Calculator - Word Problem calculator to measure distance between 2 people moving in opposite directions with rate and time solved for as well

Orange Theory is currently offering a deal where you can buy a fitness pass for $100 and then each c

Orange Theory is currently offering a deal where you can buy a fitness pass for $100 and then each class is $13, otherwise it is $18 for each class. After how many classes is the total cost with the fitness pass the same as the total cost without the fitness pass?
Let the number of classes be c.
For the fitness pass plan, we have the total cost of:
13c + 100
For the flat rate plan, we have the total cost of:
18c
The question asks for c when both plans are equal. So we set both costs equal and solve for c:
13c + 100 = 18c
We [URL='https://www.mathcelebrity.com/1unk.php?num=13c%2B100%3D18c&pl=Solve']type this equation into our math engine[/URL] and we get:
c = [B]20[/B]

Pascal-Floyd-Leibniz Triangle

Free Pascal-Floyd-Leibniz Triangle Calculator - This generates the first (n) rows of the following triangles:

Pascal's Triangle

Leibniz's Harmonic Triangle

Floyd's Triangle

Pascal's Triangle

Leibniz's Harmonic Triangle

Floyd's Triangle

Password Generator

Free Password Generator Calculator - This generates an alphanumeric password between a minimum and maximum character length that you specify.

Penny bought a new car for $25,000. The value of the car has decreased in value at rate of 3% each

Penny bought a new car for $25,000. The value of the car has decreased in value at rate of 3% each year since. Let x = the number of years since 2010 and y = the value of the car. What will the value of the car be in 2020? Write the equation, using the variables above, that represents this situation and solve the problem, showing the calculation you did to get your solution. Round your answer to the nearest whole number.
We have the equation y(x):
y(x) = 25,000(0.97)^x <-- Since a 3 % decrease is the same as multiplying the starting value by 0.97
The problem asks for y(2020). So x = 2020 - 2010 = 10.
y(10) = 25,000(0.97)^10
y(10) = 25,000(0.73742412689)
y(10) = [B]18,435.60[/B]

Percentage Appreciation

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

Percentage Depreciation

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

Perpetuities

Free Perpetuities Calculator - Solves for Present Value, Payment, or Interest rate for a Perpetuity Immediate or a Perpetuity Due.

please answer my second word problem

Distance = Rate x Time
6.4 meters = 4 meters/minute * t
Divide each side by 4
[B]t = 1.6 minutes[/B]

Please help me!! I don't understand!

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

Plutonium 241 has a decay rate of 4.8 % per year. How many years will it take a 50 kg sample to deca

Plutonium 241 has a decay rate of 4.8 % per year. How many years will it take a 50 kg sample to decay to 10 kg?
Since 4.8% is 0.048, we have decay as:
50 * (1 - 0.048)^n = 10
0.952^n = 0.2
Typing [URL='https://www.mathcelebrity.com/natlog.php?num=0.952%5En%3D0.2&pl=Calculate']this into our math engine[/URL], we get:
n = [B]32.7186 years[/B]

Poisson Distribution

Free Poisson Distribution Calculator - Calculates the probability of 3 separate events that follow a poisson distribution.

It calculates the probability of exactly k successes P(x = k)

No more than k successes P (x <= k)

Greater than k successes P(x >= k)

Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis.

Calculates moment number t using the moment generating function

It calculates the probability of exactly k successes P(x = k)

No more than k successes P (x <= k)

Greater than k successes P(x >= k)

Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis.

Calculates moment number t using the moment generating function

porportion problems

Im not really good with proportion and rates word problems and I need some help with it in my homework
If Leah walks 5 miles in 60 minutes, then Leah will walk how far in 110 minutes if she walks at the same speed the whole time? If necessary, round your answer to the nearest tenth of a mile.
I wanna know how i get this answer and copy the formula. Please help me thank you.

Portfolio Rate of Return

Free Portfolio Rate of Return Calculator - Given a portfolio of individual assets with returns and weights, this calculates the total portfolio rate of return.

Positivity Rate

Free Positivity Rate Calculator - This calculator determines the positivity rate using positive tests and total tests

principal $3000, actual interest rate 5.6%, time 3 years. what is the balance after 3 years

principal $3000, actual interest rate 5.6%, time 3 years. what is the balance after 3 years
[URL='https://www.mathcelebrity.com/compoundint.php?bal=3000&nval=3&int=5.6&pl=Annually']Using our compound interest calculator[/URL], we get a final balance of:
[B]$3,532.75[/B]

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

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Quadratic Equations and Inequalities

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax^{2} + bx + c = 0. Also generates practice problems as well as hints for each problem.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)^{2} + k

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

Rachel borrowed 8000 at a rate of 10.5%, compounded monthly. Assuming she makes no payments, how muc

Rachel borrowed 8000 at a rate of 10.5%, compounded monthly. Assuming she makes no payments, how much will she owe after 4 years?
[U]Convert annual amounts to monthly[/U]
4 years = 12 * 4 = 48 months
i = .105/12 = 0.00875 monthly
[U]Build our accumulation function A(t) where t is the time in months[/U]
A(48) = 8,000 * (1.00875)^48
A(48) = 8,000 * 1.5192
A(48) = [B]12,153.60
[/B]
[URL='http://www.mathcelebrity.com/compoundint.php?bal=8000&nval=48&int=10.5&pl=Monthly']You can also use the balance calculator[/URL]

Rachel deposits $6000 into an account that pays simple interest at a rate of 6% per year. How much i

Rachel deposits $6000 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in the first 4 years?
Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=6000&int=6&t=4&pl=Simple+Interest']simple interest calculator[/URL], we get interest paid of [B]$1,440[/B]

Rachel runs 2 miles during each track practice. Write an equation that shows the relationship betwe

Rachel runs 2 miles during each track practice. Write an equation that shows the relationship between the practices p and the distance d.
Distance equals rate * practicdes, so we have:
[B]d = 2p[/B]

Random Number Generator

Free Random Number Generator Calculator - This program generates (n) random numbers between a set of values you specify.

Example: Generate 5 random numbers between 0 and 100.

Example: Generate 5 random numbers between 0 and 100.

Rates of Return

Free Rates of Return Calculator - Given a set of stock prices and dividends if applicable, this calculates the periodic rate of return and the logarithmic rate of return

Ravi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much inte

Ravi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much interest will he be paid in the first 4 years?
The formula for [U]interest[/U] using simple interest is:
I = Prt where P = Principal, r = interest, and t = time.
We're given P = 500, r =0.04, and t = 4. So we plug this in and get:
I = 500(0.04)(4)
I = [B]80[/B]

Reece made a deposite into an account that earns 8% simple interest. After 8 years reece has earned

Reece made a deposite into an account that earns 8% simple interest. After 8 years Reece has earned 400 dollars. How much was Reece's initial deposit?
Simple interest formula:
A = P(1 + it) where P is the amount of principal to be invested, i is the interest rate, t is the time, and A is the amount accumulated with interest.
Plugging in our numbers, we get:
400 = P(1 + 0.08(8))
400 = P(1 + 0.64)
400 = 1.64P
1.64P = 400
[URL='https://www.mathcelebrity.com/1unk.php?num=1.64p%3D400&pl=Solve']Typing this problem into our search engine[/URL], we get:
P = [B]$243.90[/B]

Reflexive Property

Free Reflexive Property Calculator - Demonstrates the reflexive property of congruence using a number.
Numerical Properties

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]

Rick earns $8.50 per hour at his mothers house office. He plans on working 12.5 hours this week. How

Rick earns $8.50 per hour at his mothers house office. He plans on working 12.5 hours this week. How much money will rick earn.
Total Earnings = Hourly Rate * Hours Worked
Total Earnings = 8.50 * 12.5
Total Earnings = [B]$106.25[/B]

Rick sold a total of 75 books during the first 22 days of May. If he continues to sell books at the

Rick sold a total of 75 books during the first 22 days of May. If he continues to sell books at the same rate, how many books will he sell during the month of May?
Set up a proportion of days to books where n is the number of books sold in May:
22/31 = 75/n
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=22&num2=75&den1=31&den2=n&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] and rounding to the next integer, we get:
n = [B]106[/B]

sales 45,000 commission rate is 3.6% and salary is $275

sales 45,000 commission rate is 3.6% and salary is $275
Set up the commission function C(s) where s is the salary:
C(s) = Commission * s + salary
We're given: C(s) = 45,000, commission = 3.6%, which is 0.036 and salary = 275, so we have:
0.036s + 275 = 45000
To solve for s, we type this equation into our search engine and we get:
s = [B]1,242,361.11[/B]

Sales Tax Question

Cost of an item is $55 the total cost is $58.30 what is the sales tax rate and amount of tax ?
[URL='http://www.mathcelebrity.com/tax.php?p=55&tb=58.30&pl=Calculate+Tax']Answer[/URL]

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

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

Sam invested $48,000, some at 6% interest and the rest at 10%. How much did he invest at each rate i

Sam invested $48,000, some at 6% interest and the rest at 10%. How much did he invest at each rate if he received $4,000 in interest in one year?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=48000&i1=6&i2=10&itot=4000&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*]Fund 1 @ 6% = [B]$20,000[/B]
[*]Fund 2 @ 10% = [B]$28,000[/B]
[/LIST]

Sam's plumbing service charges a $50 diagnostic fee and then $20 per hour. How much money does he ea

Sam's plumbing service charges a $50 diagnostic fee and then $20 per hour. How much money does he earn, m, when he shows up to your house to do a job that takes h hours
[U]Set up the cost equation:[/U]
m = Hourly Rate * h + service charge
[U]Plugging in our numbers, we get:[/U]
[B]m = 20h + 50[/B]

Security Market Line and Treynor Ratio

Free Security Market Line and Treynor Ratio Calculator - Solves for any of the 4 items in the Security Market Line equation, Risk free rate, market return, Β, and expected return as well as calculate the Treynor Ratio.

Serial numbers for a product are to be using 3 letters followed by 4 digits. The letters are to be t

Serial numbers for a product are to be using 3 letters followed by 4 digits. The letters are to be taken from the first 8 letters of the alphabet with no repeats. The digits are taken from numbers 0-9 with no repeats. How many serial numbers can be generated
The serial number is organized with letters (L) and digits (D) like this:
LLLDDDD
Here's how we get the serial number:
[LIST=1]
[*]The first letter can be any of 8 letters A-H
[*]The second letter can be any 7 of 8 letters A-H
[*]The third letter can be any 6 of 8 letters A-H
[*]The fourth digit can be any of 10 digits 0-9
[*]The fifth digit can be any 9 of 10 digits 0-9
[*]The sixth digit can be any 8 of 10 digits 0-9
[*]The seventh digit can be any 7 of 10 digits 0-9
[/LIST]
We multiply all possibilities:
8 * 7 * 6 * 10 * 9 * 8 * 7
[B]1,693,440[/B]

Serial numbers for a product are to made using 4 letters followed by 4 numbers. If the letters are t

Serial numbers for a product are to made using 4 letters followed by 4 numbers. If the letters are to be taken from the first 5 letters of the alphabet with repeats possible and the numbers are taken from the digits 0 through 9 with no repeats, how many serial numbers can be generated?
First 5 letters of the alphabet are {A, B, C, D, E}
The 4 letters can be chosen as possible:
5 * 5 * 5 * 5
The number are not repeatable, so the 4 numbers can be chosen as:
10 * 9 * 8 * 7 since we have one less choice with each pick
Grouping letters and numbers together, we have the following serial number combinations:
5 * 5 * 5 * 5 * 10 * 9 * 8 * 7 = [B]3,150,000[/B]

Sharpe Ratio

Free Sharpe Ratio Calculator - Calculates the Sharpe ratio given return on assets, risk free rate, and standard deviation

Sheila loaded 21 trucks every 28 minutes. At this rate how long will it take to load 12 trucks

Sheila loaded 21 trucks every 28 minutes. At this rate how long will it take to load 12 trucks.
Let m be the number of minutes it takes Sheila to load 12 trucks. We set up a proportion of trucks to minutes:
21/28 = 12/m
[URL='https://www.mathcelebrity.com/prop.php?num1=21&num2=12&den1=28&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL],and we get:
m = [B]16[/B]

Short Sale Yield Rate

Free Short Sale Yield Rate Calculator - Calculates the Yield Rate on a short sale of stock.

Simple Discount and Compound Discount

Free Simple Discount and Compound Discount Calculator - Given a principal value, interest rate, and time, this calculates the Accumulated Value using Simple Discount and Compound Discount

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.

Split Fund Interest

Free Split Fund Interest Calculator - Given an initial principal amount, interest rate on Fund 1, interest rate on Fund 2, and a total interest paid, calculates the amount invested in each fund.

Sports Pool Generator

Free Sports Pool Generator Calculator - This generator produces the following two sports (office) pools with shuffled scoring numbers (0 - 9):

1) Blank Sports Pool: This button generates a blank sports pool grid with shuffled numbers

2) Sports Pool with Names: This sports pool allows you to enter up to 100 names which will be randomly dropped into the blank grid boxes from Option 1 above.

This is easily copied and pasted into a program like Microsoft Word so that you can format it to your liking.

1) Blank Sports Pool: This button generates a blank sports pool grid with shuffled numbers

2) Sports Pool with Names: This sports pool allows you to enter up to 100 names which will be randomly dropped into the blank grid boxes from Option 1 above.

This is easily copied and pasted into a program like Microsoft Word so that you can format it to your liking.

Square Root Table

Free Square Root Table Calculator - Generates a square root table for the first (n) numbers rounded to (r) digits

Standard Normal Distribution

Free Standard Normal Distribution Calculator - Givena normal distribution z-score critical value, this will generate the probability. Uses the NORMSDIST Excel function.

Strategy then Tactics

[URL]https://soundcloud.com/mathcelebrity/organic-seo-part-1-strategy-then-tactics[/URL]

Stuart traveled n miles at a speed of 72 miles per hour. How many seconds did it take Stuart to trav

Stuart traveled n miles at a speed of 72 miles per hour. How many seconds did it take Stuart to travel the n miles?
Distance = Rate * Time
Time = Distance/Rate
Time = n/72 hours
3600 seconds per hour so we have:
3600n/72
[B]50n[/B]

Subtraction Equality Property

Free Subtraction Equality Property Calculator - Demonstrates the Subtraction Equality Property
Numerical Properties

Subtraction Property Of Inequality

Free Subtraction Property Of Inequality Calculator - Demonstrates the Subtraction Property Of Inequality
Numerical Properties

Sue has $25,000 to invest. She deposits some in stocks and the rest in annuities. If the stocks are

Sue has $25,000 to invest. She deposits some in stocks and the rest in annuities. If the stocks are at a rate of 6% and the annuities are at a rate of 3% and Sue wants to earn $1200 by the end of the year, find how much Sue deposited into each.
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=25000&i1=6&i2=3&itot=1200&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]15,000 in stocks[/B]
[*][B]10,000 in annuities[/B]
[/LIST]

Suppose Rocky Mountain have 72 centimeters of snow. Warmer weather is melting at the rate of 5.8 cen

Suppose Rocky Mountain have 72 centimeters of snow. Warmer weather is melting at the rate of 5.8 centimeters a day. If snow continues to melt at this rate, after seven days of warm weather, how much snow will be left?
Snow remaining = Starting snow - melt rate * days
Snow remaining = 72 - 5.8(7)
Snow remaining = 72 - 40.6
Snow remaining = [B]31.4 cm[/B]

Suppose that 17 inches of wire costs 51 cents at the same rate, how many inches of wire can be bough

Suppose that 17 inches of wire costs 51 cents at the same rate, how many inches of wire can be bought for 42 cents?
Set up a proportion of inches of wire to cost, were w equals the inches of wire at 42 cents. We have:
17/51 = w/42
[URL='https://www.mathcelebrity.com/prop.php?num1=17&num2=w&den1=51&den2=42&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], we get:
[B]w = 14[/B]

Suppose that Candidates A and B have moderate political positions, while Candidate C is quite libera

Suppose that Candidates A and B have moderate political positions, while Candidate C is quite liberal. Voter opinions about the candidates are as follows. 35% want A as their first choice, but would also approve of B. 31% want B as their first choice, but would also approve of A. 20% want B as their first choice, and approve of neither A nor C. 10% want C as their first choice, and approve of neither A nor B.
[LIST=1]
[*]If all voters could vote only for their first choice, which candidate would win by plurality?
[*]Which candidate wins by an approval vote?
[/LIST]
[U]Plurality Voting:[/U]
[LIST]
[*]A: 35%
[*]B: 31% + 20% = 51%
[*]C: 10%
[/LIST]
[B]Candidate B wins[/B] using the plurality voting method and a majority
[U]Approval Voting:[/U]
[LIST]
[*]A: 35% + 31% = 2 approvals
[*]B: 35% + 31% + 20% = 3 approvals
[*]C: 10% = 1 approval
[/LIST]
Therefore, [B]Candidate B wins[/B] using the approval voting method

Suppose you deposited $1200 in an account paying a compound interest rate of 6.25% quarterly, what w

Suppose you deposited $1200 in an account paying a compound interest rate of 6.25% quarterly, what would the account balance be after 10 years?
[URL='https://www.mathcelebrity.com/compoundint.php?bal=1200&nval=40&int=6.25&pl=Quarterly']Using our compound interest with balance calculator[/URL], we get:
[B]$2,231.09[/B]

Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will

Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years?
Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=1600&int=4.6&t=4&pl=Continuous+Interest']continuous compound calculator[/URL], we get $1,923.23

Survival Rates

Free Survival Rates Calculator - Given a set of times and survival population counts, the calculator will determine the following:

Survival Population l_{x}

Mortality Population d_{x}

Survival Probability p_{x}

Mortality Probability q_{x}

In addition, the calculator will determine the probability of survival from t_{x} to t_{x + n}

Survival Population l

Mortality Population d

Survival Probability p

Mortality Probability q

In addition, the calculator will determine the probability of survival from t

Symmetric Property

Free Symmetric Property Calculator - Demonstrates the Symmetric property using a number.
Numerical Properties

T-Bill

Free T-Bill Calculator - Calculates any of the four items of the T-Bill (Treasury Bill or TBill) formula:

1) Price (P)

2) Face Value (F)

3) Number of Weeks (w)

4) Yield Rate (y)

1) Price (P)

2) Face Value (F)

3) Number of Weeks (w)

4) Yield Rate (y)

T-shirts sell for $19.97 and cost $14.02 to produce. Which equation represents p, the profit, in ter

T-shirts sell for $19.97 and cost $14.02 to produce. Which equation represents p, the profit, in terms of x, the number of t-shirts sold?
A) p = $19.97x - $14.02
B) p = x($19.97 - $14.02)
C) p = $19.97 + $14.02x
D) p = x($19.97 + $14.02)
[B]B) p = x($19.97 - $14.02)[/B]
[B][/B]
[LIST]
[*]Profit is Revenue - Cost
[*]Each shirt x generates a profit of 19.97 - 14.02
[/LIST]

Target Heart Rate

Free Target Heart Rate Calculator - Given an age, this calculator determines the following 5 target heart rate zones:

Healthy Heart Zone (Warm up) 50 - 60%

Fitness Zone (Fat Burning) 60 - 70%

Aerobic Zone (Endurance Training) 70 - 80%

Anaerobic Zone (Performance Training) 80 - 90%

Red Line (Maximum Effort) 90 - 100%

Healthy Heart Zone (Warm up) 50 - 60%

Fitness Zone (Fat Burning) 60 - 70%

Aerobic Zone (Endurance Training) 70 - 80%

Anaerobic Zone (Performance Training) 80 - 90%

Red Line (Maximum Effort) 90 - 100%

Tarzan looked at 48 websites in 4 hours. At that rate, how many would he look at in 10 minutes?

Tarzan looked at 48 websites in 4 hours. At that rate, how many would he look at in 10 minutes?
48 websites per hour / 4 hours = 12 websites / hour
Since an hour is 60 minutes, we have 12 / websites per 60 minutes = w / 10 minutes
or
[URL='https://www.mathcelebrity.com/prop.php?num1=12&num2=w&den1=60&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']12/60 = w/10[/URL]
Solving the proportion in our calculator above, we get
[B]w = 2[/B]

The auto repair shop took 2.5 hours to repair Victoria’s car. The cost of parts was $93, and the tot

The auto repair shop took 2.5 hours to repair Victoria’s car. The cost of parts was $93, and the total bill was $248. What is the shops charge per hour.
Calculate Labor Cost:
Labor Cost = Total bill - Parts
Labor Cost = $248 - $93
Labor Cost = $155
Calculate labor hourly rate:
Labor Hourly Rate = Labor Cost / Number of Labor Hours
Labor Hourly Rate = 155/2.5
Labor Hourly Rate = [B]$62[/B]

The blue star publishing company produces daily "Star news". It costs $1200 per day to operate regar

The blue star publishing company produces daily "Star news". It costs $1200 per day to operate regardless of whether any newspaper are published. It costs 0.20 to publish each newspaper. Each daily newspaper has $850 worth of advertising and each newspaper is sold for $.30. Find the number of newspaper required to be sold each day for the Blue Star company to 'break even'. I.e all costs are covered.
Build our cost function where n is the number of newspapers sold:
C(n) = 1200+ 0.2n
Now build the revenue function:
R(n) = 850 + 0.3n
Break even is where cost and revenue are equal, so set C(n) = R(n)
1200+ 0.2n = 850 + 0.3n
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=1200%2B0.2n%3D850%2B0.3n&pl=Solve']equation solver[/URL], we get:
[B]n = 3,500[/B]

The Canucks lost 6 of their first 24 games. At this rate how many would the lose in an 84 game sched

The Canucks lost 6 of their first 24 games. At this rate how many would the lose in an 84 game schedule?
Set up a proportion of losses to games where l is the number of losses for 84 games:
6/24 = l/84
[URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=l&den1=24&den2=84&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
l = [B]21[/B]

The distance traveled in t hours by a car traveling at 65 miles per hour

The distance traveled in t hours by a car traveling at 65 miles per hour.
Distance = Rate * Time
Distance = 65 mph * t hours
Distance = [B]65t[/B]

The flu is starting to hit Lanberry. Currently, there are 894 people infected, and that number is gr

The flu is starting to hit Lanberry. Currently, there are 894 people infected, and that number is growing at a rate of 5% per day. Overall, how many people will have gotten the flu in 5 days?
Our exponential equation for the Flu at day (d) is:
F(d) = Initial Flu cases * (1 + growth rate)^d
Plugging in d = 5, growth rate of 5% or 0.05, and initial flu cases of 894 we have:
F(5) = 894 * (1 + 0.05)^5
F(5) = 894 * (1.05)^5
F(5) = 894 * 1.2762815625
F(5) = [B]1141[/B]

the fuel tank of a jet used gas at a constant rate of 300 gallons for each hour of flight. the tank

the fuel tank of a jet used gas at a constant rate of 300 gallons for each hour of flight. the tank can hold a maximum of 2400 gallons of gas. write an equation representing the amount of fuel left in the tank as a function of the number of hours spent flying.
We have an equation F(h) where h is the number of hours since the flight took off:
[B]F(h) = 2400 - 300h[/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 hourly wages of employees at Rowan have a mean wage rate of $10 per hour with a standard deviati

The hourly wages of employees at Rowan have a mean wage rate of $10 per hour with a standard deviation of $1.20. What is the probability the mean hourly wage of a random sample of 36 employees will be larger than $10.50? Assume the company has a total of 1,000 employees
Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=10.5&mean=10&stdev=1.2&n=36&pl=P%28X+>+Z%29']normal distribution calculator[/URL], we get P(x > 10.5) = [B]0.00621[/B]

the initial deposit in a bank account was $6000 and it has an annual interest rate of 4.5%. Find the

the initial deposit in a bank account was $6000 and it has an annual interest rate of 4.5%. Find the amount of money in the bank after 3 years
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=6000&nval=4.5&int=3&pl=Annually']balance and interest calculator[/URL], we get:
[B]$6,853.60[/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 business office were $960. What was the tax rate if the business office was

The property taxes on a business office were $960. What was the tax rate if the business office was valued at $80,000?
Tax Rate = 100% * Tax Amount / Office Value
Tax Rate = 100% * 960 / 80000
Tax Rate = 100% * 0.012
Tax Rate = [B]1.2%[/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 rent for an apartment is $6600 per year and increases at a rate of 4% each year. Find the rent o

The rent for an apartment is $6600 per year and increases at a rate of 4% each year. Find the rent of the apartment after 5 years. Round your answer to the nearest penny.
Our Rent R(y) where y is the number of years since now is:
R(y) = 6600 * (1.04)^y <-- Since 4% is 0.04
The problem asks for R(5):
R(5) = 6600 * (1.04)^5
R(5) = 6600 * 1.2166529024
R(5) = [B]8,029.91[/B]

The sales tax for an item was $21.50 and it cost $430 before tax. Find the sales tax rate. Write you

The sales tax for an item was $21.50 and it cost $430 before tax. Find the sales tax rate. Write your answer as a percentage.
Sales tax percentage is:
21.50/430 = 0.05
To get a percentage, multiply the decimal by 100
0.05 * 100 = [B]5%[/B]

The sales tax on a computer was $33.60. If the sales tax rate is 7%, how much did the computer cost

The sales tax on a computer was $33.60. If the sales tax rate is 7%, how much did the computer cost without tax?
Let the cost of the computer be c. We have:
0.07c = 33.60
Solve for [I]c[/I] in the equation 0.07c = 33.60
[SIZE=5][B]Step 1: Divide each side of the equation by 0.07[/B][/SIZE]
0.07c/0.07 = 33.60/0.07
c = $[B]480[/B]
[URL='https://www.mathcelebrity.com/1unk.php?num=0.07c%3D33.60&pl=Solve']Source[/URL]

The sales tax rate in a city is 7.27%. How much sales tax is charged on a purchase of 5 headphones

The sales tax rate in a city is 7.27%. How much sales tax is charged on a purchase of 5 headphones at $47.44 each? What is the total price?
[U]First, calculate the pre-tax price:[/U]
Pre-tax price = Price per headphone * Number of Headphones
Pre-tax price = $47.44 * 5
Pre-tax price = $237.20
Now calculate the tax amount:
Tax Amount = Pre-Tax Price * (Tax Rate / 100)
Tax Amount = $237.20 * 7.27/100
Tax Amount = $237.20 * 0.0727
Tax Amount = [B]$17.24
[/B]
Calculate the total price:
Total Price = Pre-Tax price + Tax Amount
Total Price = $237.20 + $17.24
Total Price = [B]$254.44[/B]

The senior class at high school A and high school B planned separate trips to the state fair. There

The senior class at high school A and high school B planned separate trips to the state fair. There senior class and high school A rented and filled 10 vans and 6 buses with 276 students. High school B rented and filled 5 vans and 2 buses with 117 students. Every van had the same number of students in them as did the buses. How many students can a van carry?? How many students can a bus carry??
Let b be the number of students a bus can carry. Let v be the number of students a van can carry. We're given:
[LIST=1]
[*]High School A: 10v + 6b = 276
[*]High School B: 5v + 2b = 117
[/LIST]
We have a system of equations. We can solve this 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get:
[LIST]
[*][B]b = 21[/B]
[*][B]v = 15[/B]
[/LIST]

the university of california tuition in 1990 was $951 and tuition has been increasing by a rate of 2

the university of california tuition in 1990 was $951 and tuition has been increasing by a rate of 26% each year, what is the exponential formula
Let y be the number of years since 1990. We have the formula T(y):
[B]T(y) = 951 * 1.26^y[/B]

The value of a company van is $15,000 and decreased at a rate of 4% each year. Approximate how much

The value of a company van is $15,000 and decreased at a rate of 4% each year. Approximate how much the van will be worth in 7 years.
Each year, the van is worth 100% - 4% = 96%, or 0.96. We have the Book value equation:
B(t) = 15000(0.96)^t where t is the time in years from now.
The problem asks for B(7):
B(7) = 15000(0.96)^7
B(7) = 15000(0.7514474781)
B(7) = [B]11,271.71[/B]

There is a sales tax of $15 on an item that costs $153 before tax. A second item costs $81.60 before

There is a sales tax of $15 on an item that costs $153 before tax. A second item costs $81.60 before tax. What is the sales tax on the second item?
We assume the goods are bought in the same store, so tax rates are the same:
Tax Rate = Tax Amount / Cost before tax
Tax Rate = 15/153
Tax Rate = 0.098 or 9.8%
Calculate sales tax on the second item
Sales Tax = Cost before Tax * Tax Rate
Sales Tax = 81.60 * 0.098
Sales Tax = 7.9968
We round to 2 decimals for dollars and cents and we get:
Sales Tax = [B]$8.00[/B]

Time Weighted Interest Method

Free Time Weighted Interest Method Calculator - Solves for Interest Rate based on 2 annual asset value events other than beginning or ending value using the Time Weighted Method

To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional po

To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional pound. To ship a package with FedEx, the cost will be $5 for the first pound and $0.30 for each additional pound. How many pounds will it take for UPS and FedEx to cost the same? If you needed to ship a package that weighs 8 lbs, which shipping company would you choose and how much would you pay?
[U]UPS: Set up the cost function C(p) where p is the number of pounds:[/U]
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.2(p - 1) + 7
[U]FedEx: Set up the cost function C(p) where p is the number of pounds:[/U]
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.3(p - 1) + 5
[U]When will the costs equal each other? Set the cost functions equal to each other:[/U]
0.2(p - 1) + 7 = 0.3(p - 1) + 5
0.2p - 0.2 + 7 = 0.3p - 0.3 + 5
0.2p + 6.8 = 0.3p + 4.7
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B6.8%3D0.3p%2B4.7&pl=Solve']type it in our search engine[/URL] and we get:
p = [B]21
So at 21 pounds, both UPS and FedEx costs are equal
[/B]
Now, find out which shipping company has a better rate at 8 pounds:
[U]UPS:[/U]
C(8) = 0.2(8 - 1) + 7
C(8) = 0.2(7) + 7
C(8) = 1.4 + 7
C(8) = 8.4
[U]FedEx:[/U]
C(8) = 0.3(8 - 1) + 5
C(8) = 0.3(7) + 5
C(8) = 2.1 + 5
C(8) = [B]7.1[/B]
[B]Therefore, FedEx is the better cost at 8 pounds since the cost is lower[/B]
[B][/B]

Today a car is valued at $42000. the value is expected to decrease at a rate of 8% each year. what i

Today a car is valued at $42000. the value is expected to decrease at a rate of 8% each year. what is the value of the car expected to be 6 years from now.
Depreciation at 8% per year means it retains (100% - 8%) = 92% of it's value. We set up our depreciation function D(t), where t is the number of years from right now.
D(t) = $42,000(0.92)^t
The problem asks for D(6):
D(6) = $42,000(0.92)^6
D(6) = $42,000(0.606355)
D(6) = [B]$25,466.91[/B]

Transitive Property of Equality

Free Transitive Property of Equality Calculator - Demonstrates the Transitive property of equality using a number.
Numerical Properties

Triangular Number

Free Triangular Number Calculator - This calculator determines the nth triangular number. Generates composite numbers.

Trichotomy Property

Free Trichotomy Property Calculator - Demonstrates the Trichotomy Property with 2 numbers.
Numerical Properties

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worke

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. together they charged a total of 1225. what was the rate charged per hour by each mechanic if the sum of the two rates was 170 per hour?
Set up two equations:
(1) 10x + 5y = 1225
(2) x + y = 170
Rearrange (2)
x = 170 - y
Substitute that into (1)
10(170 - y) + 5y = 1225
1700 - 10y + 5y = 1225
1700 - 5y = 1225
Move 5y to the other side
5y + 1225 = 1700
Subtract 1225 from each side
5y =475
Divide each side by 5
[B]y = 95[/B]
Which means x = 170 - 95, [B]x = 75[/B]

Two mechanics worked on a car. the first mechanic worked for 5 hours snd the second mechanic worked

Two mechanics worked on a car. the first mechanic worked for 5 hours snd the second mechanic worked for 15 hours. Together they charged a total of $2375. What was the rate charged per hour by each mechanic if the sum of the two rates was $235 per hour?
Setup equations where x is the rate of the first mechanic and y is the rate of the second mechanic:
[LIST]
[*]5x + 15y = 2375
[*]x + y = 235
[/LIST]
Using Cramers method with our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=5x+%2B+15y+%3D+2375&term2=x+%2B+y+%3D+235&pl=Cramers+Method']simultaneous equations calculator[/URL], we get:
[LIST]
[*][B]x = 115[/B]
[*][B]y = 120[/B]
[/LIST]

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

Volatility

Free Volatility Calculator - Given a set of stock prices, this determines expected rates of return and volatility

Water flows from tank A to tank B at the rate of 2 litres per minute.

Water flows from tank A to tank B at the rate of 2 litres per minute. Initially tank A has 200 litres in it and tank B has 100 Litres in it. Water drains from tank B at 0.5 litres per minute.
After how many minutes are there equal volumes of water in the 2 tanks?
Write an equation and solve it.

Water flows from tank A to tank B at the rate of 2 litres per minute.

[QUOTE="Jahn, post: 78, member: 5"]Water flows from tank A to tank B at the rate of 2 litres per minute. Initially tank A has 200 litres in it and tank B has 100 Litres in it. Water drains from tank B at 0.5 litres per minute.
After how many minutes are there equal volumes of water in the 2 tanks?
Write an equation and solve it.[/QUOTE]
Tank A: V = 200 - 2x
Tank B: V = 100 - 0.5x
Where x is the number of minutes passed.
Set them equal to each other
200 - 2x = 100 - 0.5x
Subtract 100 from each side:
100 - 2x = -0.5x
Add 2x to each side:
1.5x = 100
Divide each side of the equation by x:
x = 66.66666667

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 is a Variable

Free What is a Variable Calculator - This lesson walks you through what a variable is and how to use it.
Also demonstrates the let statement.

What is the annual nominal rate compounded daily for a bond that has an annual yield of 5.4%? Round

What is the annual nominal rate compounded daily for a bond that has an annual yield of 5.4%? Round to three decimal places. Use a 365 day year.
[U]Set up the accumulation equation:[/U]
(1+i)^365 = 1.054
[U]Take the natural log of each side[/U]
365 * Ln(1 + i) = 1.054
Ln(1 + i) = 0.000144089
[U]Use each side as a exponent to eulers constant e[/U]
(1 + i) = e^0.000144089
1 + i = 1.000144099
i = 0.000144099 or [B].0144099%[/B]

When a dog noticed a fox, they were 60 meters apart. The dog immediately started to chase the fox at

When a dog noticed a fox, they were 60 meters apart. The dog immediately started to chase the fox at a speed of 750 meters per minute. The fox started to run away at a speed of 720 meters per minute. How soon will the dog catch the fox?
The dog sits a position p.
Distance = Rate x Time
The dogs distance in minutes is D = 720t
The fox sits at position p + 60
Distance = Rate x Time
The fox's distance in minutes is D = 750t - 60 <-- Subtract 60 since the fox is already ahead 60 meters.
We want to know when their distance (location) is the same. So we set both distance equations equal to each other:
720t = 750t - 60
[URL='https://www.mathcelebrity.com/1unk.php?num=720t%3D750t-60&pl=Solve']Using our equation calculator[/URL], we get [B]t = 2[/B].
Let's check our work:
Dog's distance is 720(2) = 1440
Fox's distance is 750(2) - 60 = 1,440

When m = 120 , the value of .10m + 54 is 66. Explain what this means in the context of this car rent

When m = 120 , the value of .10m + 54 is 66. Explain what this means in the context of this car rental company.
This means 0.10 is the [B]per-mileage charge[/B] and $54 is the flat rate or rental fee

When Ms. Thelma turned on her oven, the temperature inside was 70 degrees F. The temperature began t

When Ms. Thelma turned on her oven, the temperature inside was 70 degrees F. The temperature began to rise at a rate of 20 degrees per minute. How Long did it take for the oven to reach 350 degrees F?
Figure out how many degrees we have left:
350 - 70 = 280
Let m = minutes
20m = 280
Divide each side by m
[B]m = 14[/B]

When the drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened, it tak

When the drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened, it takes 5 hours to empty the pool. The pool is being filled, but the drain was accidentally left open. How long until the pool is completely filled?
Set up unit fill rates per hour:
[LIST]
[*]1/4 of the pool is filled each hour
[*]1/5 of the pool is drained away each hour
[/LIST]
The amount left over after an hour of filling minus draining is:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=1%2F5&pl=Subtract']1/4 - 1/5[/URL] = 1/20
Therefore, it take [B]20 hours to fill the pool[/B]

Which of the following could reduce the rate of Type I error? a. Making the significant level from

Which of the following could reduce the rate of Type I error?
a. Making the significant level from 0.01 to 0.05
b. Making the significant level from 0.05 to 0.01
c. Increase the Β level
d. Increase the power
[B]a. Making the significant level from 0.01 to 0.05[/B]
[I]This widens the space under the graph and makes the test less strict.[/I]

Which of the following is the probability that subjects do not have the disease, but the test result

Which of the following is the probability that subjects do not have the disease, but the test result is positive?
a. Miss rate
b. False positive rate
c. Base rate
d. Disease rate
[B]b. [URL='http://sites.stat.psu.edu/~lsimon/stat250/sp00/solutions/misc/diagtests.htm']False positive rate[/URL][/B]

Will earned 9.50 an hour. He worked 40 hours one week, how much will he make?

Earnings = Hours Worked * Hourly Rate
Earnings = 40 * 9.50
Earnings = [B]380[/B]

Yolanda is riding her bicycle. She rides for 5 hours at a speed of 12.5 kilometers per hours. For ho

Yolanda is riding her bicycle. She rides for 5 hours at a speed of 12.5 kilometers per hours. For how many kilometers does she ride?
This is a distance problem, where distance = rate * time. We are given time of 5 hours, at a rate of 12.5km/hour.
Using our [URL='http://www.mathcelebrity.com/drt.php?d=+&r=12.5&t=5&pl=Calculate+the+missing+Item+from+D%3DRT']distance calculator[/URL], we get D = [B]62.5km[/B].

Yolanda wants to rent a boat and spend less than $41. The boat costs $8 per hour, and Yolanda has a

Yolanda wants to rent a boat and spend less than $41. The boat costs $8 per hour, and Yolanda has a discount coupon for $7 off. What are the possible numbers of hours Yolanda could rent the boat?
A few things to build this problem:
[LIST=1]
[*]Discount subtracts from our total
[*]Cost = Hourly rate * hours
[*]Less than means an inequality using the < sign
[/LIST]
Our inequality is:
8h - 7 < 41
To solve this inequality for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h-7%3C41&pl=Solve']type it in our math engine[/URL] and we get:
h < [B]6[/B]

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

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

You are parking your car in a garage. The first hour is free but every additional hour is 2 dollars.

You are parking your car in a garage. The first hour is free but every additional hour is 2 dollars. You parked for 3.25 hours. What is the cost?
[U]Calculate the number of paid hours:[/U]
Paid Hours = Total Hours - 1 (since first hour is free)
Paid Hours = 3.25 - 1
Paid Hours = 2.25
[U]Calculate the total cost:[/U]
Total Cost = Hourly Rate * Paid Hours
Total Cost = 2 * 2.25
Paid Hours = [B]$4.50[/B]

You borrowed $25 from your friend. You paid him back in full after 6 months. He charged $2 for inter

You borrowed $25 from your friend. You paid him back in full after 6 months. He charged $2 for interest. What was the annual simple interest rate that he charged you? Use the formula: I = Prt.
We have I = 2, P = 25, t = 0.5
2 = 25(r)0.5
Divide each side by 0.5
4 = 25r
Divide each side by 25
r = 4/25
[B]r = 0.16[/B]
As a percentage, this is [B]16%[/B]

You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase

You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase is $19.08, which includes 6% sales tax. Write and solve an equation to find the cost of the cat food.
Our purchase includes at cat litter and cat food. Adding those together, we're given:
12.25 + x = 19.08
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=12.25%2Bx%3D19.08&pl=Solve']we type this equation into our search engine[/URL], and we get:
x = 6.83
Since the cat food includes sales tax, we need to remove the sales tax of 6% to get the original purchase price.
Original purchase price = After tax price / (1 + tax rate)
Original purchase price = 6.83/1.06
Original purchase price = [B]$6.44[/B]

You can get 2 different moving companies to help you move. The first one charges $150 up front then

You can get 2 different moving companies to help you move. The first one charges $150 up front then $38 an hour. The second one charges $230 then $30 an hour, at what exact time will Both companies cost the same
[U]Company 1: We set up the cost equation C(h) where h is the number of hours[/U]
C(h) = Hourly Rate * h + up front charge
C(h) = 38h + 150
[U]Company 2: We set up the cost equation C(h) where h is the number of hours[/U]
C(h) = Hourly Rate * h + up front charge
C(h) = 30h + 230
The question asks for h when both cost equations C(h) are equal. So we set both C(h) equations equal to other:
38h + 150 = 30h + 230
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=38h%2B150%3D30h%2B230&pl=Solve']type this equation into our search engine [/URL]and we get:
h = [B]10[/B]

You conduct 50,000 tests, 1500 people test positive, what's the positivity rate?

You conduct 50,000 tests, 1500 people test positive, what's the positivity rate?
[U]Our Positivity Rate formula is below:[/U]
Positivity Rate = 100% * positive tests / Total tests
[U]Plugging in our numbers from the problem, we get:[/U]
Positivity Rate = 100% * 1500/50000
Positivity Rate = 100% * 0.03
Positivity Rate = [B]3%[/B]

You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must yo

You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must you leave the money in the account to earn $500 in interest?
The simple interest formula for the accumulated balance is:
I = Prt
We are given P = 2,000, r = 0.04, and I = 500.
500 = 2000(0.04)t
80t = 500
Divide each side by 80
t = 6.25 years.

You deposit $750 in an account that earns 5% interest compounded quarterly. Show and solve a functio

You deposit $750 in an account that earns 5% interest compounded quarterly. Show and solve a function that represents the balance after 4 years.
The Accumulated Value (A) of a Balance B, with an interest rate per compounding period (i) for n periods is:
A = B(1 + i)^n
[U]Givens[/U]
[LIST]
[*]4 years of quarters = 4 * 4 = 16 quarters. So this is t.
[*]Interest per quarter = 5/4 = 1.25%
[*]Initial Balance (B) = 750.
[/LIST]
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=750&nval=16&int=5&pl=Quarterly']compound balance interest calculator[/URL], we get the accumulated value A:
[B]$914.92[/B]

You get paid $8 an hour. You make $35 in tips. You make $167.00 in a week. How many hours did you wo

You get paid $8 an hour. You make $35 in tips. You make $167.00 in a week. How many hours did you work?
To figure out the hours worked, we first need the amount of hourly wages made:
Hourly Wages = Total Wages - Tips
Hourly Wages = $167 - $35
Hourly Wages = $132
Calculate Hours Worked
Hours Worked = Hourly Wages / Hourly Rate
Hourly Worked = $132 / $8
Hourly Worked = [B]16.5[/B]

You 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 got paid $45 to babysit your nephew for 5 hours. How much did you get paid per hour?

you got paid $45 to babysit your nephew for 5 hours. How much did you get paid per hour?
Hourly Rate = Total Wages / Hours
Hourly Rate = 45/5
Hourly Rate = [B]$9[/B]

You have saved $50 over the last two weeks and decide to treat yourself by buying some new clothes.

You have saved $50 over the last two weeks and decide to treat yourself by buying some new clothes. You go to the store and find two shirts and three pairs of jeans you like. The two shirts are buy-one-get-one half off, at $22.35 each. The three pairs of jeans are buy-two-get-one-free, at $23.70.
Tax Rate for Harmonized Sales Tax is 13%
a. What would be the total for the two shirts (don’t forget to include taxes)?
b. What would be the total for the three pairs of jeans (don’t forget to include taxes)?
c. Which would you buy and why?
a. Half of 22.35 is 11.18
So two shirts cost:
22.35 + 11.18 = 33.53
Cost with Tax of 13% is:
33.53 * 1.13 = [B]37.89
[/B]
b. Three pairs of jeans are calculated by cost of 1 pair times 2 jeans and you get the third one free:
23.70 * 2 = 47.40
Cost with Tax of 13% is:
47.40 * 1.13 = [B]53.56
[/B]
c. Calculate unit cost, which is cost per item
Unit cost of Shirts = 37.89 / 2 = [B]18.95[/B]
Unit cost of Jeans = 53.56 / 3 = [B]17.85
Buy the jeans since they have a lower unit cost[/B]

You invest $1,300 in an account that has an annual interest rate of 5%, compounded annually. How muc

You invest $1,300 in an account that has an annual interest rate of 5%, compounded annually. How much money will be in the account after 10 years?
Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=1300&nval=10&int=5&pl=Annually']compound interest balance calculator[/URL], we get:
[B]$2,117.56[/B]

You purchase a car for $23,000. The car depreciates at a rate of 15% per year. Determine the value

You purchase a car for $23,000. The car depreciates at a rate of 15% per year. Determine the value of the car after 7 years. Round your answer to the nearest cent.
Set up the Depreciation equation:
D(t) = 23,000/(1.15)^t
We want D(7)
D(7) = 23,000/(1.15)^7
D(7) = 23,000/2.66002
D(7) = [B]8,646.55[/B]

You purchase a new car for $35,000. The value of the car depreciates at a rate of 8.5% per year. If

You purchase a new car for $35,000. The value of the car depreciates at a rate of 8.5% per year. If the rate of decrease continues, what is the value of your car in 5 years?
Set up the depreciation function D(t), where t is the time in years from purchase. We have:
D(t) = 35,000(1 - 0.085)^t
Simplified, a decrease of 8.5% means it retains 91.5% of it's value each year, so we have:
D(t) = 35,000(0.915)^t
The problem asks for D(5)
D(5) = 35,000(0.915)^5
D(5) = 35,000(0.64136531607)
D(5) = $[B]22,447.79[/B]

You receive 9 text messages in 12 minutes. What is the rate of text messages per hour?

You receive 9 text messages in 12 minutes. What is the rate of text messages per hour?
Set up a proportion of text messages to minutes. Remember, there are 60 minutes in an hour, so we have:
9/12 = t/60 where t is the number of text messages in 60 minutes (1 hour)
[URL='https://www.mathcelebrity.com/prop.php?num1=9&num2=t&den1=12&den2=60&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this into the search engine[/URL], we get [B]t = 45[/B].

You rent skates for $5 and pay $1 an hour for skating per person. Write an equation.

You rent skates for $5 and pay $1 an hour for skating per person. Write an equation.
Let the number of hours be h. Our cost function C(h) is:
C(h) = Cost per hour * hourly rate + rental fee
Plugging in our numbers, we get:
[B]C(h) = h + 5[/B]

You use 4 gallons of water on 30 plants in your garden. At that rate, how much water will it take to

You use 4 gallons of water on 30 plants in your garden. At that rate, how much water will it take to water 45 plants?
Set up a proportion of gallons to plants:
4/30 = x/45 where x is the gallons of water needed for 45 plants.
Use our [URL='http://www.mathcelebrity.com/prop.php?num1=4&num2=x&den1=30&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL]:
[B]x = 6[/B]

You were able to send 30 snapchat stories in 9 minutes. At this rate, how many snapchat stories can

You were able to send 30 snapchat stories in 9 minutes. At this rate, how many snapchat stories can you send in 21 minutes?
Set up a proportion of stories to minutes where s is the number of Snapchat stories you can send in 21 minutes:
30/9 = s/21
To solve this proportion for s, we [URL='https://www.mathcelebrity.com/prop.php?num1=30&num2=s&den1=9&den2=21&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get:
s = [B]70[/B]

Your grandfather gave you $12,000 a a graduation present. You decided to do the responsible thing an

Your grandfather gave you $12,000 a a graduation present. You decided to do the responsible thing and invest it. Your bank has a interest rate of 6.5%. How much money will you have after 10 years if the interest is compounded monthly?
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=12000&nval=120&int=6.5&pl=Monthly']compound interest calculator[/URL], we have 10 years * 12 months = 120 months.
[B]$22,946.21[/B]

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

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

Your job pays you $7 per hour. What is the algebraic expression if you worked h hours?

Your job pays you $7 per hour. What is the algebraic expression if you worked h hours?
If your pay is rate times hours, we have:
[B]7h[/B]

Zach can read 7 pages of a book in 5 minutes. At this rate, how long will it take him to read the en

Zach can read 7 pages of a book in 5 minutes. At this rate, how long will it take him to read the entire 175 page book?
Set up a proportion of pages to minutes where m is the number of minutes needed to read 175 pages:
7/5 = 175/m
To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=7&num2=175&den1=5&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine [/URL]and we get:
m = [B]125 minutes or 2 hours and 5 minutes[/B]

Zero Multiplication Property

Free Zero Multiplication Property Calculator - Demonstrates the Zero Multiplication property using a number. Also called the Zero Product Property.
Numerical Properties

Zero-Coupon Bond Price

Free Zero-Coupon Bond Price Calculator - This calculator calculates the price of a zero-coupon bond given a face value, yield rate, and term.

Zoey invested $230 in an account paying an interest rate of 6.3% compounded daily. Assuming no depos

Zoey invested $230 in an account paying an interest rate of 6.3% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 12 years?
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=230&nval=4380&int=6.3&pl=Daily']compound interest calculator with 12*365 = 4380 for days,[/URL] we have a balance of:
[B]$489.81[/B]