even number - a whole number that is able to be divided by two into two equal whole numbers

1 Die Roll

Free 1 Die Roll Calculator - Calculates the probability for the following events in the roll of one fair dice (1 dice roll calculator or 1 die roll calculator):

* Probability of any total from (1-6)

* Probability of the total being less than, less than or equal to, greater than, or greater than or equal to (1-6)

* The total being even

* The total being odd

* The total being a prime number

* The total being a non-prime number

* Rolling a list of numbers i.e. (2,5,6)

* Simulate (n) Monte Carlo die simulations.

1 die calculator

* Probability of any total from (1-6)

* Probability of the total being less than, less than or equal to, greater than, or greater than or equal to (1-6)

* The total being even

* The total being odd

* The total being a prime number

* The total being a non-prime number

* Rolling a list of numbers i.e. (2,5,6)

* Simulate (n) Monte Carlo die simulations.

1 die calculator

2 dice roll

Free 2 dice roll Calculator - Calculates the probability for the following events in a pair of fair dice rolls:

* Probability of any sum from (2-12)

* Probability of the sum being less than, less than or equal to, greater than, or greater than or equal to (2-12)

* The sum being even

* The sum being odd

* The sum being a prime number

* The sum being a non-prime number

* Rolling a list of numbers i.e. (2,5,6,12)

* Simulate (n) Monte Carlo two die simulations. 2 dice calculator

* Probability of any sum from (2-12)

* Probability of the sum being less than, less than or equal to, greater than, or greater than or equal to (2-12)

* The sum being even

* The sum being odd

* The sum being a prime number

* The sum being a non-prime number

* Rolling a list of numbers i.e. (2,5,6,12)

* Simulate (n) Monte Carlo two die simulations. 2 dice calculator

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 bag contains 19 balls numbered 1 through 19. What is the probability that a randomly selected ball

A bag contains 19 balls numbered 1 through 19. What is the probability that a randomly selected ball has an even number?
Even numbers in the bag are {2,4,6,8,10,12,14,16,18}
So we have 9 total even numbers.
Therefore, the probability of drawing an even number is [B]9/19[/B]

A bag contains 3 red marbles and 4 blue marbles. a marble is taken at random and replaced. another m

A bag contains 3 red marbles and 4 blue marbles. a marble is taken at random and replaced. Another marble is taken from the bag. Work out the probability that the two marbles taken from the bag are the same color.
[LIST]
[*]Total number of marbles in the bag is 3 + 4 = 7.
[*]The problem asks for the probability of (RR) [I]or[/I] (BB).
[*]It's worthy to note we are replacing the balls after each draw, which means we always have 7 to draw from
[/LIST]
Since each draw is independent, we take the product of each event for the total event probability.
P(RR) = 3/7 * 3/7 = 9/49
P(BB) = 4/7 * 4/7 = 16/49
We want to know P(RR) + P(BB)
P(RR) + P(BB) = 9/49 + 16/49 = 25/49
[MEDIA=youtube]26F9vjsgNGs[/MEDIA]

A bag contains 666 red balls, 444 green balls, and 333 blue balls. If we choose a ball, then another

A bag contains 666 red balls, 444 green balls, and 333 blue balls. If we choose a ball, then another ball without putting the first one back in the bag, what is the probability that the first ball will be green and the second will be red?
[U]Calculate total number of balls to start:[/U]
Total Balls = Red Balls + Green Balls + Blue Balls
Total Balls = 666 + 444 + 333
Total Balls = 1,443
[U]Calculate the probability of drawing a green ball on the first pick:[/U]
P(Green) = Green Balls / Total Balls
P(Green) = 444/1443
P(Green) = 0.30769
[U]Calculate the probability of drawing a red ball on the second pick (without replacement):[/U]
Total Balls decrease by 1, since we do not replace. So Total Balls = 1,443 - 1 = 1,442
P(Red) = Red Balls / Total Balls
P(Red) = 666/1442
P(Red) = 0.46186
Now, we want the probability of Green, Red in that order.
Since each event is independent, we multiply the event probabilities
P(Green, Red) = P(Green) * P(Red)
P(Green, Red) = 0.30769 * 0.46186
P(Green, Red) = [B]0.14211[/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 book publishing company has fixed costs of $180,000 and a variable cost of $25 per book. The books

A book publishing company has fixed costs of $180,000 and a variable cost of $25 per book. The books they make sell for $40 each.
[B][U]Set up Cost Function C(b) where b is the number of books:[/U][/B]
C(b) = Fixed Cost + Variable Cost x Number of Units
C(b) = 180,000 + 25(b)
[B]Set up Revenue Function R(b):[/B]
R(b) = 40b
Set them equal to each other
180,000 + 25b = 40b
Subtract 25b from each side:
15b = 180,000
Divide each side by 15
[B]b = 12,000 for break even[/B]

A coin is tossed and a die is rolled. Find the probability pf getting a head and a number greater th

A coin is tossed and a die is rolled. Find the probability pf getting a head and a number greater than 4.
Since each event is independent, we multiply the probabilities of each event.
P(H) = 0.5 or 1/2
P(Dice > 4) = P(5) + P(6) = 1/6 + 1/6 = 2/6 = 1/3
P(H) AND P(Dice > 4) = 1/2 * 1/3 = [B]1/6[/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 company has a fixed cost of $34,000 and a production cost of $6 for each unit it manufactures. A u

A company has a fixed cost of $34,000 and a production cost of $6 for each unit it manufactures. A unit sells for $15
Set up the cost function C(u) where u is the number of units is:
C(u) = Cost per unit * u + Fixed Cost
C(u) = [B]6u + 34000[/B]
Set up the revenue function R(u) where u is the number of units is:
R(u) = Sale price per unit * u
R(u) = [B]15u[/B]

a company has revenue given by R(x)=500x dollars and total cost given by C(x)=48,000 100x dollars, w

a company has revenue given by R(x)=500x dollars and total cost given by C(x)=48,000 + 100x dollars, where x is the number of units produced and sold. How many units will give a profit
Profit P(x) is given by:
R(x) - C(x)
So we have:
P(x) = 500x - (100x + 48,000)
P(x) = 500x - 100x - 48,000
P(x) = 400x - 48,000
A profit is found when P(x) > 0, so we have:
400x - 48000 > 0
To solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=400x-48000%3E0&pl=Solve']we type it into our search engine [/URL]and we get:
[B]x > 120[/B]

A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat.

A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat. They sell boats for $75 a piece. How many boats must be sold each month to break even?
[U]Set up Cost function C(b) where t is the number of tapestries:[/U]
C(b) = Cost per boat * number of boats + Fixed Cost
C(b) = 50b + 1500
[U]Set up Revenue function R(b) where t is the number of tapestries:[/U]
R(b) = Sale Price * number of boats
R(b) = 75b
[U]Break even is where Revenue equals Cost, or Revenue minus Cost is 0, so we have:[/U]
R(b) - C(b) = 0
75b - (50b + 1500) = 0
75b - 50b - 1500 = 0
25b - 1500 = 0
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-1500%3D0&pl=Solve']type this equation in our math engine[/URL] and we get:
b = [B]60[/B]

A company specializes in personalized team uniforms. It costs the company $15 to make each uniform a

A company specializes in personalized team uniforms. It costs the company $15 to make each uniform along with their fixed costs at $640. The company plans to sell each uniform for $55.
[U]The cost function for "u" uniforms C(u) is given by:[/U]
C(u) = Cost per uniform * u + Fixed Costs
[B]C(u) = 15u + 640[/B]
Build the revenue function R(u) where u is the number of uniforms:
R(u) = Sale Price per uniform * u
[B]R(u) = 55u[/B]
Calculate break even function:
Break even is where Revenue equals cost
C(u) = R(u)
15u + 640 = 55u
To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=15u%2B640%3D55u&pl=Solve']type this equation into our search engine[/URL] and we get:
u = [B]16
So we break even selling 16 uniforms[/B]

A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixe

A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixed costs are $110,000 per month and the feed sells for $132 per ton, how many tons should be sold each month to have a monthly profit of $560,000?
[U]Set up the cost function C(t) where t is the number of tons of cattle feed:[/U]
C(t) = Variable Cost * t + Fixed Costs
C(t) = 84t + 110000
[U]Set up the revenue function R(t) where t is the number of tons of cattle feed:[/U]
R(t) = Sale Price * t
R(t) = 132t
[U]Set up the profit function P(t) where t is the number of tons of cattle feed:[/U]
P(t) = R(t) - C(t)
P(t) = 132t - (84t + 110000)
P(t) = 132t - 84t - 110000
P(t) = 48t - 110000
[U]The question asks for how many tons (t) need to be sold each month to have a monthly profit of 560,000. So we set P(t) = 560000:[/U]
48t - 110000 = 560000
[U]To solve for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=48t-110000%3D560000&pl=Solve']type this equation into our search engine[/URL] and we get:[/U]
t =[B] 13,958.33
If the problem asks for whole numbers, we round up one ton to get 13,959[/B]

A farmer bought a number of pigs for $232. However, 5 of them died before he could sell the rest at

A farmer bought a number of pigs for $232. However, 5 of them died before he could sell the rest at a profit of 4 per pig. His total profit was $56. How many pigs did he originally buy?
Let p be the purchase price of pigs. We're given:
[LIST]
[*]Farmer originally bought [I]p [/I]pigs for 232 which is our cost C.
[*]5 of them died, so he has p - 5 left
[*]He sells 4(p - 5) pigs for a revenue amount R
[*]Since profit is Revenue - Cost, which equals 56, we have:
[/LIST]
Calculate Profit
P = R - C
Plug in our numbers:
4(p - 5) - 232 = 56
4p - 20 - 232 = 56
To solve for p, [URL='https://www.mathcelebrity.com/1unk.php?num=4p-20-232%3D56&pl=Solve']we type this equation into our search engine[/URL] and we get:
p = [B]77[/B]

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

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

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from sel

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day?
Let the number of drinks be d. Let the number of salads be s. We're given two equations:
[LIST=1]
[*]2d + 6.50s = 836.50
[*]d + s = 209
[/LIST]
We can use substitution to solve this system of equations quickly. The question asks for the number of salads (s). Therefore, we want all expressions in terms of s. Rearrange Equation 2 by subtracting s from both sides:
d + s - s = 209 - s
Cancel the s's, we get:
d = 209 - s
So we have the following system of equations:
[LIST=1]
[*]2d + 6.50s = 836.50
[*]d = 209 - s
[/LIST]
Substitute equation (2) into equation (1) for d:
2(209 - s) + 6.50s = 836.50
Multiply through to remove the parentheses:
418 - 2s + 6.50s = 836.50
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=418-2s%2B6.50s%3D836.50&pl=Solve']type it into our search engine and we get[/URL]:
s = [B]93[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produced. The product sells for $20/unit
[U]Cost Function C(u) where u is the number of units:[/U]
C(u) = cost per unit * u + fixed cost
C(u) = 12u + 100000
[U]Revenue Function R(u) where u is the number of units:[/U]
R(u) = Sale price * u
R(u) = 20u
Break even point is where C(u) = R(u):
C(u) = R(u)
12u + 100000 = 20u
To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=12u%2B100000%3D20u&pl=Solve']type this equation into our search engine[/URL] and we get:
u = [B]12,500[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $14 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $14 for each unit produced. The product sells for $20/unit.
Let u be the number of units. We have a cost function C(u) as:
C(u) = Variable cost * u + Fixed Cost
C(u) = 14u + 100000
[U]We have a revenue function R(u) with u units as:[/U]
R(u) = Sale Price * u
R(u) = 20u
[U]We have a profit function P(u) with u units as:[/U]
Profit = Revenue - Cost
P(u) = R(u) - C(u)
P(u) = 20u - (14u + 100000)
P(u) = 20u - 14u - 100000
P(u) = 6u - 1000000

A members-only speaker series allows people to join for $16 and then pay $1 for every event attended

A members-only speaker series allows people to join for $16 and then pay $1 for every event attended. What is the maximum number of events someone can attend for a total cost of $47?
Subtract the join fee from the total cost:
$47 - $16 = $31
Now divide this number by the cost per event:
$31 / $1 = [B]31 events[/B]

A motorist pays $4.75 per day in tolls to travel to work. He also has the option to buy a monthly pa

A motorist pays $4.75 per day in tolls to travel to work. He also has the option to buy a monthly pass for $80. How many days must he work (i.e. pass through the toll) in order to break even?
Let the number of days be d. Break even means both costs are equal. We want to find when:
4.75d = 80
To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=4.75d%3D80&pl=Solve']type this equation into our search engine[/URL] and we get:
d = 16.84 days
We round up to an even [B]17 days[/B].

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

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

a paper boy delivers thirteen paper to an apartment complex. if these deliveries compose one-seventh

a paper boy delivers thirteen paper to an apartment complex. if these deliveries compose one-seventh of his route, how many papers does he deliver
Let d be the total number of deliveries the paper boy makes on the route.
d
We're given, d/7 = 13
d = 13 * 7
d = [B]91
[MEDIA=youtube]HRviz-3fn5c[/MEDIA][/B]

A parking lot has seventy-one parking spaces numbered from 1 to 71. There are no cars in the parking

A parking lot has seventy-one parking spaces numbered from 1 to 71. There are no cars in the parking lot when Jillian pulls in and randomly parks. What is the probability that the number on the parking space where she parks is greater than or equal to 31?
Greater than or equal to means including 31 all the way through 71
31-71 is 40 spaces
P(s>=31) = [B]40/71[/B]

A pretzel factory has daily fixed costs of $1100. In addition, it costs 70 cents to produce each bag

A pretzel factory has daily fixed costs of $1100. In addition, it costs 70 cents to produce each bag of pretzels. A bag of pretzels sells for $1.80.
[U]Build the cost function C(b) where b is the number of bags of pretzels:[/U]
C(b) = Cost per bag * b + Fixed Costs
C(b) = 0.70b + 1100
[U]Build the revenue function R(b) where b is the number of bags of pretzels:[/U]
R(b) = Sale price * b
R(b) = 1.80b
[U]Build the revenue function P(b) where b is the number of bags of pretzels:[/U]
P(b) = Revenue - Cost
P(b) = R(b) - C(b)
P(b) = 1.80b - (0.70b + 1100)
P(b) = 1.80b = 0.70b - 1100
P(b) = 1.10b - 1100

A rental truck costs $49.95+$0.59 per mile and another costs $39.95 plus $0.99, set up an equation t

A rental truck costs $49.95+$0.59 per mile and another costs $39.95 plus $0.99, set up an equation to determine the break even point?
Set up the cost functions for Rental Truck 1 (R1) and Rental Truck 2 (R2) where m is the number of miles
R1(m) = 0.59m + 49.95
R2(m) = 0.99m + 39.95
Break even is when we set the cost functions equal to one another:
0.59m + 49.95 = 0.99m + 39.95
[URL='https://www.mathcelebrity.com/1unk.php?num=0.59m%2B49.95%3D0.99m%2B39.95&pl=Solve']Typing this equation into the search engine[/URL], we get [B]m = 25[/B].

A school spent $150 on advertising for a breakfast fundraiser. Each plate of food was sold for $8.00

A school spent $150 on advertising for a breakfast fundraiser. Each plate of food was sold for $8.00 but cost the school $2.00 to prepare. After all expenses were paid, the school raised $2,400 at the fundraiser. Which equation can be used to find x, the number of plates that were sold?
Set up the cost equation C(x) where x is the number of plates sold:
C(x) = Cost per plate * x plates
C(x) = 2x
Set up the revenue equation R(x) where x is the number of plates sold:
R(x) = Sales price per plate * x plates
C(x) = 8x
Set up the profit equation P(x) where x is the number of plates sold:
P(x) = R(x) - C(x)
P(x) = 8x - 2x
P(x) = 6x
We're told the profits P(x) for the fundraiser were $2,400, so we set 6x equal to 2400 and solve for x:
6x = 2400
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x%3D2400&pl=Solve']type it in our math engine[/URL] and we get:
x =[B]400 plates[/B]

A school theater group is selling candy to raise funds in order to put on their next performance. Th

A school theater group is selling candy to raise funds in order to put on their next performance. The candy cost the group $0.20 per piece. Plus, there was a $9 shipping and handling fee. The group is going to sell the candy for $0.50 per piece. How many pieces of candy must the group sell in order to break even?
[U]Set up the cost function C(p) where p is the number of pieces of candy.[/U]
C(p) = Cost per piece * p + shipping and handling fee
C(p) = 0.2p + 9
[U]Set up the Revenue function R(p) where p is the number of pieces of candy.[/U]
R(p) = Sale price * p
R(p) = 0.5p
Break-even means zero profit or loss, so we set the Cost Function equal to the Revenue Function
0.2p + 9 = 0.5p
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B9%3D0.5p&pl=Solve']type it in our math engine[/URL] and we get:
p = [B]30[/B]

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

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

A spinner has 3 equal sections labelled A, B, C. A bag contains 3 marbles: 1 grey, 1 black, and 1 w

A spinner has 3 equal sections labelled A, B, C. A bag contains 3 marbles: 1 grey, 1 black, and 1 white. The pointer is spun and a marble is picked at random.
a) Use a tree diagram to list the possible outcomes.
[LIST=1]
[*][B]A, Grey[/B]
[*][B]A, Black[/B]
[*][B]A, White[/B]
[*][B]B, Grey[/B]
[*][B]B, Black[/B]
[*][B]B, White[/B]
[*][B]C, Grey[/B]
[*][B]C, Black[/B]
[*][B]C, White[/B]
[/LIST]
b) What is the probability of:
i) spinning A?
P(A) = Number of A sections on spinner / Total Sections
P(A) = [B]1/3[/B]
---------------------------------
ii) picking a grey marble?
P(A) = Number of grey marbles / Total Marbles
P(A) = [B]1/3[/B]
---------------------------------
iii) spinning A and picking a white marble?
Since they're independent events, we multiply to get:
P(A AND White) = P(A) * P(White)
P(A) was found in i) as 1/3
Find P(White):
P(White) = Number of white marbles / Total Marbles
P(White) = 1/3
[B][/B]
Therefore, we have:
P(A AND White) = 1/3 * 1/3
P(A AND White) = [B]1/9[/B]
---------------------------------
iv) spinning C and picking a pink marble?
Since they're independent events, we multiply to get:
P(C AND Pink) = P(C) * P(Pink)
Find P(C):
P(C) = Number of C sections on spinner / Total Sections
P(C) = 1/3
[B][/B]
Find P(Pink):
P(Pink) = Number of pink marbles / Total Marbles
P(Pink) = 0/3
[B][/B]
Therefore, we have:
P(C AND Pink) = 1/3 * 0
P(C AND Pink) = [B]0[/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 toy company makes "Teddy Bears". The company spends $1500 for factory expenses plus $8 per bear. T

A toy company makes "Teddy Bears". The company spends $1500 for factory expenses plus $8 per bear. The company sells each bear for $12.00 each. How many bears must this company sell in order to break even?
[U]Set up the cost function C(b) where b is the number of bears:[/U]
C(b) = Cost per bear * b + factory expenses
C(b) = 8b + 1500
[U]Set up the revenue function R(b) where b is the number of bears:[/U]
R(b) = Sale Price per bear * b
R(b) = 12b
[U]Break-even is where cost equals revenue, so we set C(b) equal to R(b) and solve for b:[/U]
C(b) = R(b)
8b + 1500 = 12b
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=8b%2B1500%3D12b&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]375[/B]

Aliyah had $24 to spend on seven pencils after buying them she had $10 how much did each pencil cost

Aliyah had $24 to spend on seven pencils after buying them she had $10 how much did each pencil cost?
If Aliyah had $24 to spend, and $10 left over, then she spent $24 - $10 = $14 on pencils
Find the cost per pencil:
Cost per pencil = Pencil Spend / Number of Pencils
Cost per pencil = 14/7
Cost per pencil = [B]$2[/B]

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil co

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?
Let p be the number of pencils. We're given the following equation:
7p + 10 = 24
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B10%3D24&pl=Solve']type it in our math engine[/URL] and we get:
p = [B]2
[/B]

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil co

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?
Let the number of pencils be p. We have:
7p + 10 = 24
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B10%3D24&pl=Solve']type it in our math engine[/URL] and we get:
p = [B]2[/B]

Balls numbered 1 to 10 are placed in a bag. Two of the balls are drawn out at random. Find the proba

Balls numbered 1 to 10 are placed in a bag. Two of the balls are drawn out at random. Find the probability that the numbers on the balls are consecutive.
Build our sample set:
[LIST]
[*](1, 2)
[*](2, 3)
[*](3, 4)
[*](4, 5)
[*](5, 6)
[*](6, 7)
[*](7, 8)
[*](8, 9)
[*](9, 10)
[/LIST]
Each of these 9 possibilities has a probability of:
1/10 * 1/9
This is because we draw without replacement. To start, the bag has 10 balls. On the second draw, it only has 9. We multiply each event because each draw is independent.
We have 9 possibilities, so we have:
9 * 1/10 * 1/9
Cancelling, the 9's, we have [B]1/10[/B]

Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each p

Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each pencil
The cost per pencil is:
1560/30 = 52
Build revenue function:
Revenue = Number of Pencils * Sales Price (s)
Revenue = 30s
The profit equation is:
Profit = Revenue - Cost
Given profit is 180 and cost is 1560, we have:
30s - 1560 = 180
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=30s-1560%3D180&pl=Solve']type this equation into our search engine[/URL] and we get:
s = 58
This is sales for total profit. The question asks profit per pencil.
Profit per pencil = Revenue per pencil - Cost per pencil
Profit per pencil = 58 - 52
Profit per pencil = [B]6[/B]

Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of

Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 47 cards left. How many cards did Benny start with?
Let b be the number of baseball trading cards Benny started with. We have the following events:
[LIST=1]
[*]Benny buys 8 new cards, so we add 8 to get b + 8
[*]The dog ate half of his cards the next day, so Benny has (b + 8)/2
[*]We're told he has 47 cards left, so we set (b + 8)/2 equal to 47
[/LIST]
(b + 8)/2 = 47
[B][U]Cross multiply:[/U][/B]
b + 8 = 47 * 2
b + 8 = 94
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B8%3D94&pl=Solve']Type this equation into the search engine[/URL], we get [B]b = 86[/B].

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

Chuck-a-luck is an old game, played mostly in carnivals and county fairs. To play chuck-a-luck you p

Chuck-a-luck is an old game, played mostly in carnivals and county fairs. To play chuck-a-luck you place a bet, say $1, on one of the numbers 1 through 6. Say that you bet on the number 4. You then roll three dice (presumably honest). If you roll three 4’s, you win $3.00; If you roll just two 4’s, you win $2; if you roll just one 4, you win $1 (and, in all of these cases you get your original $1 back). If you roll no 4’s, you lose your $1. Compute the expected payoff for chuck-a-luck.
Expected payoff for each event = Event Probability * Event Payoff
Expected payoff for 3 matches:
3(1/6 * 1/6 * 1/6) = 3/216 = 1/72
Expected payoff for 2 matches:
2(1/6 * 1/6 * 5/6) = 10/216 = 5/108
Expected payoff for 1 match:
1(1/6 * 5/6 * 5/6) = 25/216
Expected payoff for 0 matches:
-1(5/6 * 5/6 * 5/6) = 125/216
Add all these up:
(3 + 10 + 25 - 125)/216
-87/216 ~ [B]-0.40[/B]

Construct a data set of seven temperature readings where the mean is positive and the median is nega

Construct a data set of seven temperature readings where the mean is positive and the median is negative.
[B]{-20,-10.-5,-2,-1,20,40}[/B]
[URL='https://www.mathcelebrity.com/statbasic.php?num1=-20%2C-10%2C-5%2C-2%2C-1%2C20%2C40&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Using our mean and median calculator[/URL], we see that:
[B]Mean = 3.142857 (positive)
Median = -2[/B]

Derek must choose a 4 digit PIN. Each Digit can be chosen from 0 to 9. Derek does not want to reuse

Derek must choose a 4 digit PIN. Each Digit can be chosen from 0 to 9. Derek does not want to reuse any digits. He also only wants an even number that begins with 5. How many possible PINS could he choose from?
[LIST=1]
[*]First digit must begin with 5. So we have 1 choice
[*]We subtract 1 possible digit from digit 3 to have 8 - 1 = 7 possible digits
[*]This digit can be anything other than 5 and the even number in the next step. So we have 0-9 is 10 digits - 2 = 8 possible digits
[*]Last digit must end in 0, 2, 4, 6, 8 to be even. So we have 5 choices
[/LIST]
Our total choices from digits 1-4 are found by multiplying each possible digit choice:
1 * 7 * 8 * 5 = [B]280 possible PINS[/B]

Diana earns $8.50 working as a lifeguard. Write an equation to find Dianas money earned m for any nu

Diana earns $8.50 working as a lifeguard. Write an equation to find Dianas money earned m for any numbers of hours h
Set up the revenue function:
[B]R = 8.5h[/B]

Erik is rolling two regular six-sided number cubes. What is the probability that he will roll an eve

Erik is rolling two regular six-sided number cubes. What is the probability that he will roll an even number on one cube and a prime number on the other?
P(Even on first cube) = (2,4,6) / 6 total choices
P(Even on first cube) = 3/6
P(Even on first cube) = 1/2 <-- [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL]
P(Prime on second cube) = (2,3,5) / 6 total choices
P(Prime on second cube) = 3/6
P(Prime on second cube) = 1/2 <-- [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL]
Since each event is independent, we have:
P(Even on the first cube, Prime on the second cube) = P(Even on the first cube) * P(Prime on the second cube)
P(Even on the first cube, Prime on the second cube) = 1/2 * 1/2
P(Even on the first cube, Prime on the second cube) = [B]1/4[/B]

Erin has 72 stamps in her stamp drawer along with a quarter, two dimes and seven pennies. She has 3

Erin has 72 stamps in her stamp drawer along with a quarter, two dimes and seven pennies. She has 3 times as many 3-cent stamps as 37-cent stamps and half the number of 5-cent stamps as 37-cent stamps. The value of the stamps and coins is $8.28. How many 37-cent stamps does Erin have?
Number of stamps:
[LIST]
[*]Number of 37 cent stamps = s
[*]Number of 3-cent stamps = 3s
[*]Number of 5-cent stamps = 0.5s
[/LIST]
Value of stamps and coins:
[LIST]
[*]37 cent stamps = 0.37s
[*]3-cent stamps = 3 * 0.03 = 0.09s
[*]5-cent stamps = 0.5 * 0.05s = 0.025s
[*]Quarter, 2 dime, 7 pennies = 0.52
[/LIST]
Add them up:
0.37s + 0.09s + 0.025s + 0.52 = 8.28
Solve for [I]s[/I] in the equation 0.37s + 0.09s + 0.025s + 0.52 = 8.28
[SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE]
(0.37 + 0.09 + 0.025)s = 0.485s
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
0.485s + 0.52 = + 8.28
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 0.52 and 8.28. To do that, we subtract 0.52 from both sides
0.485s + 0.52 - 0.52 = 8.28 - 0.52
[SIZE=5][B]Step 4: Cancel 0.52 on the left side:[/B][/SIZE]
0.485s = 7.76
[SIZE=5][B]Step 5: Divide each side of the equation by 0.485[/B][/SIZE]
0.485s/0.485 = 7.76/0.485
s = [B]16[/B]
[URL='https://www.mathcelebrity.com/1unk.php?num=0.37s%2B0.09s%2B0.025s%2B0.52%3D8.28&pl=Solve']Source[/URL]

Ethan has $9079 in his retirement account, and Kurt has $9259 in his. Ethan is adding $19per day, wh

Ethan has $9079 in his retirement account, and Kurt has $9259 in his. Ethan is adding $19per day, whereas Kurt is contributing $1 per day. Eventually, the two accounts will contain the same amount. What balance will each account have? How long will that take?
Set up account equations A(d) where d is the number of days since time 0 for each account.
Ethan A(d): 9079 + 19d
Kurt A(d): 9259 + d
The problems asks for when they are equal, and how much money they have in them. So set each account equation equal to each other:
9079 + 19d = 9259 + d
[URL='https://www.mathcelebrity.com/1unk.php?num=9079%2B19d%3D9259%2Bd&pl=Solve']Typing this equation into our search engine[/URL], we get [B]d = 10[/B].
So in 10 days, both accounts will have equal amounts in them.
Now, pick one of the account equations, either Ethan or Kurt, and plug in d = 10. Let's choose Kurt's since we have a simpler equation:
A(10) = 9259 + 10
A(10) = $[B]9,269
[/B]
After 10 days, both accounts have $9,269 in them.

Even Numbers

Free Even Numbers Calculator - Shows a set amount of even numbers and cumulative sum

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?

Find the odd number less than 100 that is divisible by 9, and when divided by 10 has a remainder of

Find the odd number less than 100 that is divisible by 9, and when divided by 10 has a remainder of 7.
From our [URL='http://www.mathcelebrity.com/divisibility.php?num=120&pl=Divisibility']divisibility calculator[/URL], we see a number is divisible by 9 if the sum of its digits is divisible by 9.
Starting from 1 to 99, we find all numbers with a digit sum of 9.
This would be digits with 0 and 9, 1 and 8, 2 and 7, 3 and 6, and 4 and 5.
9
18
27
36
45
54
63
72
81
90
Now remove even numbers since the problem asks for odd numbers
9
27
45
63
81
Now, divide each number by 10, and find the remainder
9/10 = 0
[URL='http://www.mathcelebrity.com/modulus.php?num=27mod10&pl=Calculate+Modulus']27/10[/URL] = 2 R 7
We stop here. [B]27[/B] is an odd number, less than 100, with a remainder of 7 when divided by 10.

Fixed cost 500 marginal cost 8 item sells for 30

fixed cost 500 marginal cost 8 item sells for 30.
Set up Cost Function C(x) where x is the number of items sold:
C(x) = Marginal Cost * x + Fixed Cost
C(x) = 8x + 500
Set up Revenue Function R(x) where x is the number of items sold:
R(x) = Revenue per item * items sold
R(x) = 30x
Set up break even function (Cost Equals Revenue)
C(x) = R(x)
8x + 500 = 30x
Subtract 8x from each side:
22x = 500
Divide each side by 22:
x = 22.727272 ~ 23 units for breakeven

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

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

if p=2x is even, then p^2 is also even

if p=2x is even, then p^2 is also even
p^2 = 2 * 2 * x^2
p^2 = 4x^2
This is [B]true [/B]because:
[LIST]
[*]If x is even, then x^2 is even since two evens multiplied by each other is even and 4x^2 is even
[*]If x is odd, the x^2 is odd, but 4 times the odd number is always even since even times odd is even
[/LIST]

If two consecutive even numbers are added, the sum is equal to 226. What is the smaller of the two n

If two consecutive even numbers are added, the sum is equal to 226. What is the smaller of the two numbers?
Let the smaller number be n.
The next consecutive even number is n + 2.
Add them together to equal 226:
n + n + 2 = 226
Solve for [I]n[/I] in the equation n + n + 2 = 226
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(1 + 1)n = 2n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
2n + 2 = + 226
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 2 and 226. To do that, we subtract 2 from both sides
2n + 2 - 2 = 226 - 2
[SIZE=5][B]Step 4: Cancel 2 on the left side:[/B][/SIZE]
2n = 224
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2n/2 = 224/2
n = [B]112
[URL='https://www.mathcelebrity.com/1unk.php?num=n%2Bn%2B2%3D226&pl=Solve']Source[/URL][/B]

In rolling a die, the event E is getting a number greater than or equal to 3. What is the complement

In rolling a die, the event E is getting a number greater than or equal to 3. What is the complement of the event?
The complement E' is everything but the event. So we have:
E = P(n >= 3)
E' = [B]P(n < 3)[/B]

Jazmin is a hairdresser who rents a station in a salon for daily fee. The amount of money (m) Jazmin

Jazmin is a hairdresser who rents a station in a salon for daily fee. The amount of money (m) Jazmin makes from any number of haircuts (n) a day is described by the linear function m = 45n - 30
A) A haircut costs $30, and the station rent is $45
B) A haircut costs $45, and the station rent is $30.
C) Jazmin must do 30 haircuts to pay the $45 rental fee.
D) Jazmin deducts $30 from each $45 haircut for the station rent.
[B]Answer B, since rent is only due once. Profit is Revenue - Cost[/B]

Jennifer spent $11.25 on ingredients for cookies shes making for the school bake sale. How many cook

Jennifer spent $11.25 on ingredients for cookies shes making for the school bake sale. How many cookies must she sale at $0.35 apiece to make profit?
Let x be the number of cookies she makes. To break even, she must sell:
0.35x = 11.25
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=0.35x%3D11.25&pl=Solve']equation calculator[/URL], and we get:
x = 32.14
This means she must sell [B]33[/B] cookies to make a profit.

Joelle had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil co

Joelle had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?
Subtract the $10 left over from the $24 Joelle started with.
$24 - $10 = $14
Therefore, Joelle spent $14 on seven pencils.
Cost per pencil = Total Pencil Spend / Number of pencils
Cost per pencil = 14 / 7
Cost per pencil = [B]$2[/B]

Last week at the business where you work, you sold 120 items. The business paid $1 per item and sol

Last week at the business where you work, you sold 120 items. The business paid $1 per item and sold them for $3 each. What profit did the business make from selling the 120 items?
Let n be the number of items. We have the following equations:
Cost Function C(n) = n
For n = 120, we have C(120) = 120
Revenue Function R(n) = 3n
For n = 120, we have R(120) = 3(120) = 360
Profit = Revenue - Cost
Profit = 360 - 120
Profit = [B]240[/B]

Let n be an integer. If n^2 is odd, then n is odd

Let n be an integer. If n^2 is odd, then n is odd
Proof by contraposition:
Suppose that n is even. Then we can write n = 2k
n^2 = (2k)^2 = 4k^2 = 2(2k) so it is even
[I]So an odd number can't be the square of an even number. So if an odd number is a square it must be the square of an odd number.[/I]

Let x be an integer. If x is odd, then x^2 is odd

Let x be an integer. If x is odd, then x^2 is odd
Proof: Let x be an odd number. This means that x = 2n + 1 where n is an integer.
[U]Squaring x, we get:[/U]
x^2 = (2n + 1)^2 = (2n + 1)(2n + 1)
x^2 = 4n^2 + 4n + 1
x^2 = 2(2n^2 + 2n) + 1
2(2n^2 + 2n) is an even number since 2 multiplied by any integer is even
So adding 1 is an odd number
[MEDIA=youtube]GlzV80M33x0[/MEDIA]

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. With how many did she start?
Let the number of boxes Maria started with be b. We're given the following pieces:
[LIST]
[*]She starts with b
[*]She bought 7 boxes. So we add 7 to b: b + 7
[*]If half the boxes were destroyed, she's left with 1/2. So we divide (b + 7)/2
[*]Only 22 boxes left means we set (b + 7)/2 equal to 22
[/LIST]
(b + 7)/2 = 22
Cross multiply:
b + 7 = 22 * 2
b + 7 = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B7%3D44&pl=Solve']Type this equation into our search engine[/URL] to solve for b and we get:
b = [B]37[/B]

Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she c

Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she charges $53 for each lawn, how many lawns must she service to make a profit of at $800 a month?
Melissa has a fixed cost of $264 per month in fuel. No variable cost is given. Our cost function is:
C(x) = Fixed Cost + Variable Cost. With variable cost of 0, we have:
C(x) = 264
The revenue per lawn is 53. So R(x) = 53x where x is the number of lawns.
Now, profit is Revenue - Cost. Our profit function is:
P(x) = 53x - 264
To make a profit of $800 per month, we set P(x) = 800.
53x - 264 = 800
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=53x-264%3D800&pl=Solve']equation solver[/URL], we get:
[B]x ~ 21 lawns[/B]

Number Property

Free Number Property Calculator - This calculator determines if an integer you entered has any of the following properties:

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

n^2+n = odd

n^2+n = odd
Factor n^2+n:
n(n + 1)
We have one of two scenarios:
[LIST=1]
[*]If n is odd, then n + 1 is even. The product of an odd and even number is an even number
[*]If n is even, then n + 1 is odd. The product of an even and odd number is an even number
[/LIST]

n^2-n = even

n^2-n = even
Factor n^2-n:
n(n - 1)
We have one of two scenarios:
[LIST=1]
[*]If n is odd, then n - 1 is even. The product of an odd and even number is an even number
[*]If n is even, then n - 1 is odd. The product of an even and odd number is an even number
[/LIST]

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 Friday evening a pizza shop had orders for 4 pepperoni, 97 vegetable, and 335 cheese pizzas. If

On a Friday evening a pizza shop had orders for 4 pepperoni, 97 vegetable, and 335 cheese pizzas. If the 4 cooks each made an equal number of pizzas, how many pizzas did each cook make?
Total Pizzas Made = 4 pepperoni + 97 vegetable + 335 cheese
Total Pizzas Made = 436
Equal number of pizzas per cook = 436 pizzas / 4 cooks
Equal number of pizzas per cook = [B]109[/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

positive even numbers less than 10

positive even numbers less than 10
First, list out all positive even numbers less than 10.
Less than 10 means we do [U]not[/U] include 10.
[B]{2, 4, 6, 8}
[MEDIA=youtube]5YsPQo_2dpI[/MEDIA][/B]

Product of Consecutive Numbers

Free Product of Consecutive Numbers Calculator - Finds the product of (n) consecutive integers, even or odd as well. Examples include:

product of 2 consecutive integers

product of 2 consecutive numbers

product of 2 consecutive even integers

product of 2 consecutive odd integers

product of 2 consecutive even numbers

product of 2 consecutive odd numbers

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product of 5 consecutive numbers

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product of 4 consecutive numbers

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product of five consecutive odd integers

product of five consecutive even integers

product of five consecutive numbers

product of five consecutive odd numbers

product of five consecutive even numbers

Prove sqrt(2) is irrational

Use proof by contradiction. Assume sqrt(2) is rational.
This means that sqrt(2) = p/q for some integers p and q, with q <>0.
We assume p and q are in lowest terms.
Square both side and we get:
2 = p^2/q^2
p^2 = 2q^2
This means p^2 must be an even number which means p is also even since the square of an odd number is odd.
So we have p = 2k for some integer k. From this, it follows that:
2q^2 = p^2 = (2k)^2 = 4k^2
2q^2 = 4k^2
q^2 = 2k^2
q^2 is also even, therefore q must be even.
So both p and q are even.
This contradicts are assumption that p and q were in lowest terms.
So sqrt(2) [B]cannot be rational.
[MEDIA=youtube]tXoo9-8Ewq8[/MEDIA][/B]

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a ball at random.
a. What is the probability that you choose a red or even numbered ball?
b. What is the probability you choose a green ball or a ball numbered less than 5?
a. The phrase [I]or[/I] in probability means add. But we need to subtract even reds so we don't double count:
We have 18 total balls, so this is our denonminator for our fractions.
Red and Even balls are {2, 4, 6, 8, 10, 12}
Our probability is:
P(Red or Even) = P(Red) + P(Even) - P(Red and Even)
P(Red or Even) = 13/18 + 9/18 - 6/18
P(Red or Even) = 16/18
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=16%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have:
P(Red or Even) = [B]16/18[/B]
[B][/B]
b. The phrase [I]or[/I] in probability means add. But we need to subtract greens less than 5 so we don't double count:
We have 18 total balls, so this is our denonminator for our fractions.
Green and less than 5 does not exist, so we have no intersection
Our probability is:
P(Green or Less Than 5) = P(Green) + P(Less Than 5) - P(Green And Less Than 5)
P(Green or Less Than 5) = 5/18 + 4/18 - 0
P(Green or Less Than 5) = 9/18
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have:
P(Red or Even) = [B]1/2[/B]

Sara has a box of candies. In the box there are 8 pink candies, 7 purple candies and 5 blue candies.

Sara has a box of candies. In the box there are 8 pink candies, 7 purple candies and 5 blue candies. She takes one candy and records its color. She then puts it back in the box and draws another candy. What is the probability of taking out a pink candy followed by a blue candy?
[B][U]Calculate the total number of candies:[/U][/B]
Total candies = Pink + Purple + Blue
Total candies = 8 + 7 + 5
Total candies = 20
[B][U]Calculate the probability of drawing one pink candy:[/U][/B]
P(Pink) = 8/20
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F20&frac2=3%2F8&pl=Simplify']fraction reduction calculator[/URL], we get:
P(Pink) = 2/5
[B][U]Calculate the probability of drawing one blue candy:[/U][/B]
P(Blue) = 5/20 <-- [I]20 options since Sara replaced her first draw[/I]
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F20&frac2=3%2F8&pl=Simplify']fraction reduction calculator[/URL], we get:
P(Blue) = 1/4
The problem asks for the probability of a Pink followed by a Blue. Since each event is independent, we multiply:
P(Pink, Blue) = P(Pink) * P(Blue)
P(Pink, Blue) = 2/5 * 1/4
P(Pink, Blue) = 2/20
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F20&frac2=3%2F8&pl=Simplify']fraction reduction calculator[/URL], we get:
P(Pink, Blue) = [B]1/10 or 10%[/B]

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]

Set C is the set of two-digit even numbers greater than 72 that do not contain the digit 8.

Set C is the set of two-digit even numbers greater than 72 that do not contain the digit 8.
First, two-digit numbers mean anything less than 100. Let's, list out our two-digit even numbers greater than 72 but less than 100.
C = {74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98}
The problem asks for numbers that do not contain the digit 8. Let's remove those numbers from the list.
C = {74, 76, [S]78[/S], [S]80, 82, 84, 86, 88[/S], 90, 92, 94, 96, [S]98[/S]}
[B]C = {74, 76, 90, 92, 94, 96}
[MEDIA=youtube]_O6nXX0V4zo[/MEDIA][/B]

Set C is the set of two-digit even numbers less than 56 that are divisible by 5

[U]Two digit Numbers less than 56:[/U]
{10, 11, 12, ..., 55}
[U]Two Digit Even Numbers of that Set:[/U]
{10, 12, 14, ..., 54}
[U]Two Digit Even numbers Divisible by 5[/U]
[B]C = {10, 20, 30, 40, 50}[/B]
[I]Note: Even means you can divide it by 2 with no remainder. Divisible by 5 means the number ends in 5 or 0. Since it is even numbers only, end in 0.[/I]

Set D is the set of two-digit even numbers less than 67 that are divisible by 5

Set D is the set of two-digit even numbers less than 67 that are divisible by 5
two-digit numbers start at 10. Divisible by 5 means the last digit is either 0 or 5. But even numbers don't end in 5, so we take the two-digit numbers ending in 0:
D = {[B]10, 20, 30, 40, 50, 60}[/B]

Set of 2 digit even numbers less than 40

Set of 2 digit even numbers less than 40
Knowns and givens:
[LIST]
[*]2 digit numbers start at 10
[*]Less than 40 means we do not include 40
[*]Even numbers are divisible by 2
[/LIST]
[B]{10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38}[/B]

Seven less than 1/4 of a number is 9.

Seven less than 1/4 of a number is 9.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
1/4 of a number means we multiply x by 1/4:
x/4
Seven less than this means we subtract 7 from x/4:
x/4 - 7
The word [I]is[/I] means an equation, so we set x/4 - 7 equal to 9:
[B]x/4 - 7 = 9[/B]

Seven subtracted from the product of 3 and a number is greater than or equal to -26

Seven subtracted from the product of 3 and a number is greater than or equal to -26
[LIST=1]
[*]A number means an arbitrary variable, let's call it x.
[*]The product of 3 and a number is written as 3x
[*]Seven subtracted from 3x is written as 3x - 7
[*]Finally, that entire expression is greater than or equal to -26: [B]3x - 7 >= - 26[/B]
[/LIST]

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 c

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cents of additional expense for each soda can made. Assuming all soda cans manufactured can be sold, find the break-even point.
Calculate the revenue function R(c) where s is the number of sodas sold:
R(s) = Sale Price * number of units sold
R(s) = 50s
Calculate the cost function C(s) where s is the number of sodas sold:
C(s) = Variable Cost * s + Fixed Cost
C(s) = 0.25s + 900
Our break-even point is found by setting R(s) = C(s):
0.25s + 900 = 50s
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B900%3D50s&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]18.09[/B]

Students stuff envelopes for extra money. Their initial cost to obtain the information for the job w

Students stuff envelopes for extra money. Their initial cost to obtain the information for the job was $140. Each envelope costs $0.02 and they get paid $0.03per envelope stuffed. Let x represent the number of envelopes stuffed. (a) Express the cost C as a function of x. (b) Express the revenue R as a function of x. (c) Determine analytically the value of x for which revenue equals cost.
a) Cost Function
[B]C(x) = 140 + 0.02x[/B]
b) Revenue Function
[B]R(x) = 0.03x[/B]
c) Set R(x) = C(x)
140 + 0.02x = 0.03x
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=140%2B0.02x%3D0.03x&pl=Solve']equation solver[/URL], we get x = [B]14,000[/B]

Sum of Consecutive Numbers

Free Sum of Consecutive Numbers Calculator - Finds the sum of (n) consecutive integers, even or odd as well. Examples include:

sum of 2 consecutive integers

sum of 2 consecutive numbers

sum of 2 consecutive even integers

sum of 2 consecutive odd integers

sum of 2 consecutive even numbers

sum of 2 consecutive odd numbers

sum of two consecutive integers

sum of two consecutive odd integers

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Sum of the First (n) Numbers

Free Sum of the First (n) Numbers Calculator - Determines the sum of the first (n)

* Whole Numbers

* Natural Numbers

* Even Numbers

* Odd Numbers

* Square Numbers

* Cube Numbers

* Fourth Power Numbers

* Whole Numbers

* Natural Numbers

* Even Numbers

* Odd Numbers

* Square Numbers

* Cube Numbers

* Fourth Power Numbers

Sum of two consecutive numbers is always odd

Sum of two consecutive numbers is always odd
Definition:
[LIST]
[*]A number which can be written in the form of 2 m where m is an integer, is called an even integer.
[*]A number which can be written in the form of 2 m + 1 where m is an integer, is called an odd integer.
[/LIST]
Take two consecutive integers, one even, and one odd:
2n and 2n + 1
Now add them
2n + (2n+ 1) = 4n + 1 = 2(2 n) + 1
The sum is of the form 2n + 1 (2n is an integer because the product of two integers is an integer)
Therefore, the sum of two consecutive integers is an odd number.

Suppose you write a book. The printer charges $4 per book to print it, and you spend 5500 on adverti

Suppose you write a book. The printer charges $4 per book to print it, and you spend 5500 on advertising. You sell the book for $15 a copy. How many copies must you sell to break even.
Profit per book is:
P = 15 - 4
P = 11
We want to know the number of books (b) such that:
11b = 5500 <-- Breakeven means cost equals revenue
[URL='https://www.mathcelebrity.com/1unk.php?num=11b%3D5500&pl=Solve']Typing this equation into the search engine[/URL], we get:
b = [B]500[/B]

Susan makes and sells purses. The purses cost her $15 each to make, and she sells them for $30 each.

Susan makes and sells purses. The purses cost her $15 each to make, and she sells them for $30 each. This Saturday, she is renting a booth at a craft fair for $50. Write an equation that can be used to find the number of purses Susan must sell to make a profit of $295
Set up the cost function C(p) where p is the number of purses:
C(p) = Cost per purse * p + Booth Rental
C(p) = 15p + 50
Set up the revenue function R(p) where p is the number of purses:
R(p) = Sale price * p
R(p) = 30p
Set up the profit function which is R(p) - C(p) equal to 295
30p - (15p + 50) = 295
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=30p-%2815p%2B50%29%3D295&pl=Solve']we type it into our search engine[/URL] and we get:
p = [B]23[/B]

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]

Take a look at the following sums: 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 +

Take a look at the following sums:
1 = 1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
a. Come up with a conjecture about the sum when you add the first *n* odd numbers. For example, when you added the first 5 odd numbers (1 + 3 + 5 + 7 + 9), what did you get? What if wanted to add the first 10 odd numbers? Or 100?
b. Can you think of a geometric interpretation of this pattern? If you start with one square and add on three more, what can you make? If you now have 4 squares and add on 5 more, what can you make?
c. Is there a similar pattern for adding the first n even numbers?
2 = 2
2 + 4 = 6
2 + 4 + 6 = 12
2 + 4 + 6 + 8 = 20
a. The formula is [B]n^2[/B].
The sum of the first 10 odd numbers is [B]100[/B] seen on our s[URL='http://www.mathcelebrity.com/sumofthefirst.php?num=10&pl=Odd+Numbers']um of the first calculator[/URL]
The sum of the first 100 odd numbers is [B]10,000[/B] seen on our [URL='http://www.mathcelebrity.com/sumofthefirst.php?num=100&pl=Odd+Numbers']sum of the first calculator[/URL]
b. Geometric is 1, 4, 9 which is our [B]n^2[/B]
c. The sum of the first n even numbers is denoted as [B]n(n + 1)[/B] seen here for the [URL='http://www.mathcelebrity.com/sumofthefirst.php?num=+10&pl=Even+Numbers']first 10 numbers[/URL]

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 dance committee of pine bluff middle school earns $72 from a bake sale and will earn $4 for each

The dance committee of pine bluff middle school earns $72 from a bake sale and will earn $4 for each ticket sold they sell to the Spring Fling dance. The dance will cost $400
Let t be the number of tickets sold. We have a Revenue function R(t):
R(t) = 4t + 72
We want to know t such that R(t) = 400. So we set R(t) = 400:
4t + 72 = 400
[URL='https://www.mathcelebrity.com/1unk.php?num=4t%2B72%3D400&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]t = 82[/B]

The domain of a relation is all even negative integers greater than -9. The range y of the relation

The domain of a relation is all even negative integers greater than -9. The range y of the relation is the set formed by adding 4 to the numbers in the domain. Write the relation as a table of values and as an equation.
The domain is even negative integers greater than -9:
{-8, -6, -4, -2}
Add 4 to each x for the range:
{-8 + 4 = -4, -6 + 4 = -2. -4 + 4 = 0, -2 + 4 = 2}
For ordered pairs, we have:
(-8, -4)
(-6, -2)
(-4, 0)
(-2, 2)
The equation can be written:
y = x + 4 on the domain (x | x is an even number where -8 <= x <= -2)

The fixed costs to produce a certain product are 15,000 and the variable costs are $12.00 per item.

The fixed costs to produce a certain product are 15,000 and the variable costs are $12.00 per item. The revenue for a certain product is $27.00 each. If the company sells x products, then what is the revenue equation?
R(x) = Revenue per item x number of products sold
[B]R(x) = 27x[/B]

The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for

The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for $40. Write a cost and revenue function and determine the break-even point.
[U]Calculate cost function C(b) with b as the number of books:[/U]
C(b) = Cost per book * b + Overhead
[B]C(b) = 15b + 5500[/B]
[U]Calculate Revenue Function R(b) with b as the number of books:[/U]
R(b) = Sales Price per book * b
[B]R(b) = 40b[/B]
[U]Calculate break even function E(b):[/U]
Break-even Point = Revenue - Cost
Break-even Point = R(b) - C(b)
Break-even Point = 40b - 15b - 5500
Break-even Point = 25b - 5500
[U]Calculate break even point:[/U]
Break-even point is where E(b) = 0. So we set 25b - 5500 equal to 0
25b - 5500 = 0
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-5500%3D0&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]b = 220[/B]

the set of natural numbers less than 7 that are divisible by 3

the set of natural numbers less than 7 that are divisible by 3
Natural Numbers less than 7
{1, 2, 3, 4, 5, 6}
Only 2 of them are divisible by 3. Divisible means the number is divided evenly, with no remainder:
[B]{3, 6}[/B]

The total cost to fix your bike is $45 the parts cost $10 and the labor cost seven dollars per hour

The total cost to fix your bike is $45 the parts cost $10 and the labor cost seven dollars per hour how many hours were there:
Set up a cost function where h is the number of hours:
7h + 10 = 45
To solve for h, we t[URL='https://www.mathcelebrity.com/1unk.php?num=7h%2B10%3D45&pl=Solve']ype this equation into our search engine[/URL] and we get:
h = [B]5[/B]

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash t

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 in the past, and they are making $2 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take?
Set up the earnings equation for the volleyball team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 4w + 81
Set up the earnings equation for the wrestling team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 2w + 85
If the raised the same amount in total, set both earnings equations equal to each other:
4w + 81 = 2w + 85
Solve for [I]w[/I] in the equation 4w + 81 = 2w + 85
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides
4w + 81 - 2w = 2w + 85 - 2w
[SIZE=5][B]Step 2: Cancel 2w on the right side:[/B][/SIZE]
2w + 81 = 85
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 81 and 85. To do that, we subtract 81 from both sides
2w + 81 - 81 = 85 - 81
[SIZE=5][B]Step 4: Cancel 81 on the left side:[/B][/SIZE]
2w = 4
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2w/2 = 4/2
w = [B]2 <-- How many cars it will take
[/B]
To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2:
E = 4(2) + 81
E = 8 + 81
E = [B]89 <-- Total Earnings[/B]

There are 100 people in a sport centre. 67 people use the gym. 62 people use the swimming pool. 5

There are 100 people in a sport centre. 67 people use the gym. 62 people use the swimming pool. 56 people use the track. 38 people use the gym and the pool. 31 people use the pool and the track. 33 people use the gym and the track. 16 people use all three facilities. A person is selected at random. What is the probability that this person doesn't use any facility?
WE use the compound probability formula for 3 events:
[LIST=1]
[*]Gym use (G)
[*]Swimming pool use (S)
[*]Track (T)
[/LIST]
P(G U S U T) = P(G) + P(S) + P(T) - P(G Intersection S) - P(G Intersection T) - P(S Intersection T) + P(G Intersection S Intersection T)
[LIST]
[*]Note: U means Union (Or) and Intersection means (And)
[/LIST]
Plugging our numbers in:
P(G U S U T) = 67/100 + 62/100 + 56/100 - 38/100 - 31/100 - 33/100 + 16/100
P(G U S U T) = (67 + 62 + 56 - 38 - 31 - 33 + 16)/100
P(G U S U T) = 99/100 or 0.99
What this says is, the probability that somebody uses at any of the 3 facilities is 99/100.
The problem asks for none of the 3 facilities, or P(G U S U T)'
P(G U S U T)' = 1 - P(G U S U T)
P(G U S U T)' = 1 - 99/100
P(G U S U T)' = 100/100 - 99/100
P(G U S U T)' = [B]1/100 or 0.1[/B]

There is a stack of 10 cards, each given a different number from 1 to 10. suppose we select a card r

There is a stack of 10 cards, each given a different number from 1 to 10. Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card is an odd number and the second card is greater than 7.
First Event: P(1, 3, 5, 7, 9) = 5/10 = 1/2 or 0.5
Second Event: P(8, 9, 10) = 3/10 or 0.3
Probability of both events since each is independent is 1/2 * 3/10 = 3/20 = [B]0.15 or 15%[/B]

There were 175 tickets sold for the upcoming event in the gym. If students tickets cost $5 and adult

There were 175 tickets sold for the upcoming event in the gym. If students tickets cost $5 and adult tickets are $8, tell me how many tickets were sold if gate receipts totaled $1028?
Let s be the number of student tickets and a be the number of adult tickets. We are given:
a + s = 175
8a + 5s = 1028
There are 3 ways to solve this, all of which give us:
[B]a = 51
s = 124
[/B]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Substitution']Substitution Method[/URL]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Elimination']Elimination Method[/URL]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Cramers+Method']Cramers Method[/URL]

True or False (a) The normal distribution curve is always symmetric to its mean. (b) If the variance

True or False
(a) The normal distribution curve is always symmetric to its mean.
(b) If the variance from a data set is zero, then all the observations in this data set are identical.
(c) P(A AND A^{c})=1, where A^{c} is the complement of A.
(d) In a hypothesis testing, if the p-value is less than the significance level ?, we do not have sufficient evidence to reject the null hypothesis.
(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.
[B](a) True, it's a bell curve symmetric about the mean
(b) True, variance measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical
(c) True. P(A) is the probability of an event and P(Ac) is the complement of the event, or any event that is not A. So either A happens or it does not. It covers all possible events in a sample space.
(d) False, we have sufficient evidence to reject H0.
(e) False. Volume can be a decimal or fractional. There are multiple values between 127 and 128. So it's continuous.[/B]

what is a well defined set

what is a well defined set?
A well defined set is with no ambiguity or confusion about what belongs to the set. Think of it as a collection of distinct objects:
Examples:
[LIST]
[*]Set of the first 5 even numbers: {2, 4, 6, 8, 10}
[*]Set of weekend days: {Saturday, Sunday}
[/LIST]

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

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

what’s the probability of rolling a 5 and then rolling a number less then 2

what’s the probability of rolling a 5 and then rolling a number less then 2
[U]Roll a 5:[/U]
There's only one 5 on a six sided die
P(X = 5) = 1/6
A number less than 2 is only 1:
P(X < 2) = P(X = 1)
P(X = 1) = 1/6
Since each event is independent, we multiply:
P(X = 5) * P(X = 1) = 1/6 * 1/6
P(X = 5) * P(X = 1) = [B]1/36[/B]

You and a friend want to start a business and design t-shirts. You decide to sell your shirts for $1

You and a friend want to start a business and design t-shirts. You decide to sell your shirts for $15 each and you paid $6.50 a piece plus a $50 set-up fee and $25 for shipping. How many shirts do you have to sell to break even? Round to the nearest whole number.
[U]Step 1: Calculate Your Cost Function C(s) where s is the number of t-shirts[/U]
C(s) = Cost per Shirt * (s) Shirts + Set-up Fee + Shipping
C(s) = $6.50s + $50 + $25
C(s) = $6.50s + 75
[U]Step 2: Calculate Your Revenue Function R(s) where s is the number of t-shirts[/U]
R(s) = Price Per Shirt * (s) Shirts
R(s) = $15s
[U]Step 3: Calculate Break-Even Point[/U]
Break Even is where Cost = Revenue. Set C(s) = R(s)
$6.50s + 75 = $15s
[U]Step 4: Subtract 6.5s from each side[/U]
8.50s = 75
[U]Step 5: Solve for s[/U]
[URL='https://www.mathcelebrity.com/1unk.php?num=8.50s%3D75&pl=Solve']Run this through our equation calculator[/URL] to get s = 8.824. We round up to the next integer to get [B]s = 9[/B].
[B][URL='https://www.facebook.com/MathCelebrity/videos/10156751976078291/']FB Live Session[/URL][/B]

You roll a red die and a green die. What is the size of the sample space of all possible outcomes of

You roll a red die and a green die. What is the size of the sample space of all possible outcomes of rolling these two dice, given that the red die shows an even number and the green die shows an odd number greater than 1?
[LIST]
[*]Red Die Sample Space {2, 4, 6}
[*]Green Die Sample Space {3, 5}
[*]Total Sample Space {(2, 3), (2, 5), (4, 3), (4, 5), (6, 3), (6, 5)}
[*]The sie of this is 6 elements.
[/LIST]