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

10 times the first of 2 consecutive even integers is 8 times the second. Find the integers. Let the first integer be x. Let the second integer be y. We're given: [LIST=1] [*]10x = 8y [*]We also know a consecutive even integer means we add 2 to x to get y. y = x + 2 [/LIST] Substitute (1) into (2): 10x = 8(x + 2) Multiply through: 10x = 8x + 16 To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=10x%3D8x%2B16&pl=Solve']we type this equation into our search engine[/URL] and we get: [B]x = 8[/B] Since y = x + 2, we plug in x = 8 to get: y = 8 + 2 [B]y = 10 [/B] Now, let's check our work. Does x = 8 and y = 10 make equation 1 hold? 10(8) ? 8(10) 80 = 80 <-- Yes!

2 coins are tossed. Find the probability of getting 1 head and 1 tail We can either flip HT or TH. Let's review probabilities: [LIST] [*]HT = 1/2 * 1/2 = 1/4 <-- We multiply since each event is independent [*]TH = 1/2 * 1/2 = 1/4 <-- We multiply since each event is independent [/LIST] P(1 H, 1 T) = P(HT) + P(TH) P(1 H, 1 T) = 1/4 + 1/4 P(1 H, 1 T) = 2/4 [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F4&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we can reduce 2/4 to 1/2 P(1 H, 1 T) = [B]1/2[/B]

Let x be the first even integer. That means the next consecutive even integer must be x + 2. Set up our equation: x + (x + 2) = 118 Group x terms 2x + 2 = 118 Subtract 2 from each side 2x = 116 Divide each side by 2 x = 58 Which means the next consecutive even integer is 58 + 2 = 60 So our two consecutive even integers are [B]58, 60[/B] Check our work: 58 + 60 = 118

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

2 consecutive even integers such that the smaller added to 5 times the larger gives a sum of 70. Let the first, smaller integer be x. And the second larger integer be y. Since they are both even, we have: [LIST=1] [*]x = y - 2 <-- Since they're consecutive even integers [*]x + 5y = 70 <-- Smaller added to 5 times the larger gives a sum of 70 [/LIST] Substitute (1) into (2): (y - 2) + 5y = 70 Group like terms: (1 + 5)y - 2 = 70 6y - 2 = 70 [URL='https://www.mathcelebrity.com/1unk.php?num=6y-2%3D70&pl=Solve']Typing 6y - 2 = 70 into our search engine[/URL], we get: [B]y = 12 <-- Larger integer[/B] Plugging this into Equation (1) we get: x = 12 - 2 [B]x = 10 <-- Smaller Integer[/B] So (x, y) = (10, 12)

Since each event is independent, we have: P(T) * P(T) * P(T) 1/2 * 1/2 * 1/2 [B]1/8[/B]

6 red marbles 9 green marbles and 5 blue marbles two marbles are drawn without replacement what is the probability of choosing a green and then a blue marble First draw: there are 6 red + 9 green + 5 blue = 20 marbles We draw 9 possible green out of 20 total marbles = 9/20 Second draw: We don't replace, so we have 6 red + 8 green + 5 blue = 19 marbles We draw 5 possible blue of out 19 total marbles = 5/19 Our total probability, since each event is independent, is: [URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F20&frac2=5%2F19&pl=Multiply']9/20 * 5/19[/URL] = [B]9/76[/B]

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 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 2 red marbles, 3 blue marbles, and 4 green marbles. What is the probability of choosing a blue marble, replacing it, drawing a green marble, replacing it, and then drawing a red marble? Calculate total marbles in the bag: Total marbles in the bag = Red Marbles + Blue Marbles + Green Marbles Total marbles in the bag = 2 + 3 + 4 Total marbles in the bag = 9 [U]First choice, blue marble[/U] P(blue) = Total Blue Marbles / Total Marbles in the bag P(blue) = 3/9 [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F9&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we see: P(blue) = 1/3 [U]Second choice, green marble with all the marbles back in the bag after replacement[/U] P(green) = Total Green Marbles / Total Marbles in the bag P(green) = 4/9 [U]Third choice, red marble with all the marbles back in the bag after replacement[/U] P(red) = Total Red Marbles / Total Marbles in the bag P(red) = 2/9 Since each event is independent, we multiply each probability: P(blue, green, red) = P(blue) * P(green) * P(red) P(blue, green, red) = 1/3 * 4/9 * 2/9 P(blue, green, red) = [B]8/243[/B]

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 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 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 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 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 blue dice and a red dice are tossed what is the probability that a 6 will appear on both dice Each event is independent. P(Blue dice 6) = 1/6 P(Red Dice 6) = 1/6 P(Blue 6, Red 6) = 1/6 * 1/6 = [B]1/36[/B]

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 box contains 4 plain pencils and 4 pens. A second box contains 5 color pencils and 3 crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon from the second box are selected? [LIST] [*]First box, P(pen) = 4/8 = 1/2 = 0.5 [*]Second box, P(crayon) = 3/8 [/LIST] Since each event is independent, we have: P(Pen from Box 1) * P(Crayon from Box 2) = 1/2 * 3/8 = [B]3/16 or 0.1875[/B]

A box contains 22 red apples and 3 green apples. Three apples are selected at random, one after the other, without replacement. please show the steps. (a) The first two apples are green. What is the probability that the third apple is red? (b) What is the probability that exactly two of the three apples are red? a) You have 22 red apples left and 1 green left leaving 23 total apples left. Therefore, probability of red is [B]P(R) = 22/23[/B] b) Determine our sample space to select exactly two red apples in three picks. [LIST=1] [*]RRG [*]RGR [*]GRR [/LIST] [U]Now determine the probabilities of each event in the sample space[/U] P(RRG) = 22/25 * 21/24 * 3/23 = 0.1004 P(RGR) = 22/25 * 3/24 * 21/23 = 0.1004 P(GRR) = 3/25 * 22/24 * 21/23 = 0.1004 [U]We want the sum of the three probabilities[/U] P(RRG) + P(RGR) + P(GRR) = 0.1004 + 0.1004 + 0.1004 P(RRG) + P(RGR) + P(GRR) = 3(0.1004) P(RRG) + P(RGR) + P(GRR) = [B]0.3012[/B]

A box contains 5 black and 2 white balls. 2 balls are drawn without replacement. Find the probability of drawing 2 black balls. First draw probability of black is: Total Balls in box = Black balls + white balls Total Balls in Box = 5 + 2 Total Balls in Box = 7 P(Black) = Black Balls / Total balls in box P(Black) = 5/7 Second draw probability of black (with no replacement) is: Total Balls in box = Black balls + white balls Total Balls in Box = 4 + 2 Total Balls in Box = 6 P(Black) = Black Balls / Total balls in box P(Black) = 4/6 Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F6&frac2=3%2F8&pl=Simplify']fraction simplifier[/URL], we see that 4/6 is: 2/3 Since each event is independent, we can multiply them to find the probability of drawing 2 black balls: P(Black, Black) = 5/7 * 2/3 [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F7&frac2=2%2F3&pl=Multiply']P(Black, Black)[/URL] = 10/21 [MEDIA=youtube]HEa_G3nwgUQ[/MEDIA]

A box contains 5 plain pencils and 3 pens. A second box contains 2 color pencils and 2 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected [U]Calculate the probability of a plain pencil in the first box:[/U] P(plain pencil in the first box) = Total Pencils / Total Objects P(plain pencil in the first box) = 5 pencils / (5 pencils + 3 pens) P(plain pencil in the first box) = 5/8 [U]Calculate the probability of a color pencil in the first box:[/U] P(color in the second box) = Total Pencils / Total Objects P(color in the second box) = 2 pencils / (2 pencils + 2 crayons) P(color in the second box) = 2/4 We can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F4&frac2=3%2F8&pl=Simplify']Type 2/4 into our search engine[/URL] and we get 1/2 Now the problem asks for the probability that a plain pencil from the first box and a color pencil from the second box are selected. Since each event is independent, we multiply them together to get our answer: P(plain pencil in the first box, color in the second box) = P(plain pencil in the first box) * P(color in the second box) P(plain pencil in the first box, color in the second box) = 5/8 * 1/2 P(plain pencil in the first box, color in the second box) = [B]5/16[/B]

A box contains 5 plain pencils and 7 pens. A second box contains 4 color pencils and 4 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected? Probability of plain pencil from first box: 5/(5 + 7) = 5/12 Probability of color pencil from second box: 4/(4 + 4) = 4/8 = 1/2 Probability of both events together: Since each event is independent, we multiply probabilities: 5/12 * 1/2 = [B]5/24[/B]

A box contains 6 yellow, 3 red, 5 green, and 7 blue colored pencils. A pencil is chosen at random, it is not replaced, then another is chosen. What is the probability of choosing a red followed by a green? We have 6 + 3 + 5 + 7 = 21 total pencils P(Red on the first draw) = Total Red / Total pencils P(Red on the first draw) = 3/21 [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F21&frac2=3%2F8&pl=Simplify']P(Red on the first draw)[/URL] = 1/7 We're drawing without replacement, this means on the next draw, we have 21 - 1 = 20 pencils P(Green on the second draw) = Total Green / Total pencils P(Green on the second draw) = 5/20 [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F20&frac2=3%2F8&pl=Simplify']P(Green on the second draw) [/URL]= 1/4 Since each event is independent, we have: P(Red on first, green on second) = P(Red on First) * P(green on second) P(Red on first, green on second) = 1/7 * 1/4 P(Red on first, green on second) = [B]1/28[/B]

a card is chosen at a random from a deck of 52 cards. it is then replaced and a second card is chosen. what is the probability of getting a jack and then an eight? Calculate the probability of drawing a jack from a full deck There are 4 jacks in a deck of 52 cards P(J) = 4/52 P(J) = 1/13 <-- We simplify 4/52 by dividing top and bottom of the fraction by 4 Calculate the probability of drawing an eight from a full deck There are 4 eights in a deck of 52 cards. We[I] replaced[/I] the first card giving us 52 cards to choose from. P(8) = 4/52 P(8) = 1/13 <-- We simplify 4/52 by dividing top and bottom of the fraction by 4 Since each event is independent, we multiply: P(J, 8) = P(J) * P(8) P(J, 8) = 1/13 * 1/13 P(J, 8) = [B]1/169[/B]

A card is drawn from a pack of 52 cards. The probability that the card drawn is a red card is The deck is split evenly between red and black cards. So we have 52/2 = 26 red cards P(Red) = # of Red Cards / Total Deck Cards P(Red) = 26/52 We can simplify this fraction. [URL='https://www.mathcelebrity.com/fraction.php?frac1=26%2F52&frac2=3%2F8&pl=Simplify']Using our fraction calculator[/URL], we get: P(Red) = [B]1/2 or 0.5[/B]

A catering service offers 3 appetizers, 6 main courses, and 4 desserts. A customer is to select 2 appetizers, 3 main courses, and 3 desserts for a banquet. In how many ways can this be done? We use the combinations formula, and since each event is independent of the others, we multiply: 2 appetizers, 3 main courses, and 3 desserts = [URL='https://www.mathcelebrity.com/permutation.php?num=3&den=2&pl=Combinations']3C2[/URL] * [URL='https://www.mathcelebrity.com/permutation.php?num=6&den=3&pl=Combinations']6C3[/URL] * [URL='https://www.mathcelebrity.com/permutation.php?num=4&den=3&pl=Combinations']4C3[/URL] 2 appetizers, 3 main courses, and 3 desserts = 3 * 20 * 4 2 appetizers, 3 main courses, and 3 desserts = [B]240[/B]

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 coffee franchise is opening a new store. The company estimates that there is a 75% chance the store will have a profit of $45,000, a 10% chance the store will break even, and a 15% chance the store will lose $2,500. Determine the expected gain or loss for this store. Calculate the expected value E(x). Expected value is the sum of each event probability times the payoff or loss: E(x) = 0.75(45,000) + 0.1(0) + 0.15(-2,500) <-- Note, break even means no profit and no loss and a loss is denoted with a negative sign E(x) = 33,750 + 0 - 375 E(x) = [B]33,375 gain[/B]

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 [MEDIA=youtube]ofsbmHmQmjs[/MEDIA][/B]

A committee of 6 students are being selected from a class of 10 girls and 8 boys. How many committees are possible if three must be girls and 3 must be boys? We want combinations. How many ways can we choose 3 boys from 8 boys: [URL='https://www.mathcelebrity.com/permutation.php?num=8&den=3&pl=Combinations']8 choose 3[/URL] = 56 We want combinations. How many ways can we choose 3 girls from 10 girls: [URL='https://www.mathcelebrity.com/permutation.php?num=10&den=3&pl=Combinations']10 choose 3[/URL] = 120 Our total choices are found by multiplying each event: Total committees = (8 boys choose 3) * (10 girls choose 3) Total committees = 56 * 120 Total committees = [B]6,720[/B]

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 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, 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 is planning to manufacture a certain product. The fixed costs will be $474778 and it will cost $293 to produce each product. Each will be sold for $820. Find a linear function for the profit, P , in terms of units sold, x . [U]Set up the cost function C(x):[/U] C(x) = Cost per product * x + Fixed Costs C(x) = 293x + 474778 [U]Set up the Revenue function R(x):[/U] R(x) = Sale Price * x R(x) = 820x [U]Set up the Profit Function P(x):[/U] P(x) = Revenue - Cost P(x) = R(x) - C(x) P(x) = 820x - (293x + 474778) P(x) = 820x - 293x - 474778 [B]P(x) = 527x - 474778[/B]

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 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 company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each lamp, and the selling price is $150 per lamp. Set up the Cost Equation C(l) where l is the price of each lamp: C(l) = Variable Cost x l + Fixed Cost C(l) = 90l + 1800 Determine the revenue function R(l) R(l) = 150l Determine the profit function P(l) Profit = Revenue - Cost P(l) = 150l - (90l + 1800) P(l) = 150l - 90l - 1800 [B]P(l) = 60l - 1800[/B] Determine the break even point: Breakeven --> R(l) = C(l) 150l = 90l + 1800 [URL='https://www.mathcelebrity.com/1unk.php?num=150l%3D90l%2B1800&pl=Solve']Type this into the search engine[/URL], and we get [B]l = 30[/B]

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 desk drawer contains 10 blue pencils, 7 red pencils, and 8 green pencils. Without looking, you draw out a pencil and then draw out a second pencil without returning the first pencil. What is the probability that the first pencil and the second pencil are both green? We are drawing without replacement. Take each draw probability: [LIST=1] [*]First draw, we have a total of 10 + 7 + 8 = 25 pencils to choose from. P(Green) = 8/25 [*]Next draw, we only have 24 total pencils, and 7 green pencils since we do not replace. Therefore, we have P(Green)= 7/24 [/LIST] Since both events are independent, we have: P(Green) * P(Green) = 8/25 * 7/24 P(Green) * P(Green) = 56/600 Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=56&num2=600&num3=&pl=GCF']GCF Calculator[/URL], we see the greatest common factor of 56 and 600 is 8. So we divide top and bottom of the fraction by 8. [B]P(Green) * P(Green) = 7/75[/B]

A die and a coin are tossed. What is the probability of getting a 6 and a tail? Roll a 6: P(6) = 1/6 Flip a tail: P(T) = 1/2 Probability of getting a 6 and a tail: Since both events are independent, we have: P(6 and T) = P(6) * P(T) P(6 and T) = 1/6 * 1/2 P(6 and T) = [B]1/12[/B]

A fair coin is tossed 4 times. a) How many outcomes are there in the sample space? b) What is the probability that the third toss is heads, given that the first toss is heads? c) Let A be the event that the first toss is heads, and B be the event that the third toss is heads. Are A and B independent? Why or why not? a) 2^4 = [B]16[/B] on our [URL='http://www.mathcelebrity.comcointoss.php?hts=+HTHTHH&hct=+2&tct=+1&fct=+5>=no+more+than&nmnl=+2&htpick=heads&tossct=+4&calc=5&montect=+500&pl=Calculate+Probability']coin toss calculator[/URL] b) On the link above, 4 of those outcomes have H and H in toss 1 and 3. So it's [B]1/4 or 0.25[/B] c) [B]Yes, each toss is independent of each other.[/B]

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

a jar contains a $5 note, two $10 notes, a $20 note and a $50 note. if 2 notes are taken out by random, find the probability that their sum is $15 To get a sum of $15, we'd need to pull the $5 and the $10. Since both events are indepdenent, we have: P($5 or 10) or P(whatever is not pulled in the first pull) First Pull: 2/4 (We can pull either a $10 or a $5, so 2 choices out of 4 bills) Second Pull: 1/3 <-- since there are only 3 bills and 1 bill to pull Each pull is independent, so we multiply: 2/4 * 1/3 = 2/12 We can simply this, so [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F12&frac2=3%2F8&pl=Simplify']we type this fraction in our search engine[/URL] and we get: [B]1/6[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produced. The product sells for $22/unit. The cost function for each unit u is: C(u) = Variable Cost * Units + Fixed Cost C(u) = 10u + 100000 The revenue function R(u) is: R(u) = 22u We want the break-even point, which is where: C(u) = R(u) 10u + 100000 = 22u [URL='https://www.mathcelebrity.com/1unk.php?num=10u%2B100000%3D22u&pl=Solve']Typing this equation into our search engine[/URL], we get: u =[B]8333.33[/B]

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 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 manufacturer has a monthly fixed cost of $25,500 and a production cost of $7 for each unit produced. The product sells for $10/unit. Set up cost function where u equals each unit produced: C(u) = 7u + 25,500 Set up revenue function R(u) = 10u Break Even is where Cost equals Revenue 7u + 25,500 = 10u Plug this into our [URL='http://www.mathcelebrity.com/1unk.php?num=7u%2B25500%3D10u&pl=Solve']equation calculator[/URL] to get [B]u = 8,500[/B]

A manufacturer has a monthly fixed cost of $52,500 and a production cost of $8 for each unit produced. The product sells for $13/unit. Using our [URL='http://www.mathcelebrity.com/cost-revenue-profit-calculator.php?fc=52500&vc=8&r=13&u=20000%2C50000&pl=Calculate']cost-revenue-profit calculator[/URL], we get the following: [LIST] [*]P(x) = 55x - 2,500 [*]P(20,000) = 47,500 [*]P(50,000) = 197,500 [/LIST]

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 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 non-profit organization is having a couple�s banquet for a fundraiser. The banquet hall will only hold 250 people. The President, Vice-President, two volunteers, and a guest speaker will be working the event. How many couples will be able to attend the banquet? We subtract the 5 people working the event to get: 250 - 5 = 245 A couple is 2 people, so we have 245/2 = 122.5 We round down to [B]122 couples[/B].

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 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 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 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 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 revenue function is R(x) = 22x and a cost function is C(x) = -9x + 341. The break-even point is Break even is when C(x) = R(x). So we set them equal and solve for x: -9x + 341 = 22x Typing[URL='https://www.mathcelebrity.com/1unk.php?num=-9x%2B341%3D22x&pl=Solve'] this equation into our search engine[/URL], we get: x = [B]11[/B]

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. 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 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 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 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. 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]

A watch was bought for $250 and sold for $375. What was the profit on the sale of the watch? Profit = Revenue (Sales) - Cost Profit = $375 - $250 Profit = [B]$125[/B]

Aaron buys a bag of cookies that contains 8 chocolate chip cookies, 6 peanut butter cookies,7 sugar cookies and 6 oatmeal raisin cookies. What it�s the probability that Aaron randomly selects a peanut butter cookie from the bag, eats it,, then randomly selects another peanut butter cookie? First draw out of the bag is a peanut butter cookie: P(PB) = Total Peanut Butter Cookies / Total Cookies P(PB) = 6/27 Second draw out of the bag is a peanut butter cookie, but we have one less since Aaron ate one: P(PB) = Total Peanut Butter Cookies - 1 / Total Cookies - 1 P(PB) = (6 - 1)/(27 - 1) P(PB) = 5/26 Now, since each event is independent, we multiply them to see the probability of choosing a peanut butter cookie, eating it, then reaching in and choosing another peanut butter cookie: P(PB, PB) = 6/27 * 5/26 [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F27&frac2=5%2F26&pl=Multiply']P(PB, PB)[/URL] = [B]5/117[/B]

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

The seven pencils cost $24 - $10 = $14. $14 / 7 pencils = [B]$2 per pencil[/B].

Alex says all factors of 16 are even why is she wrong. [URL='https://www.mathcelebrity.com/factoriz.php?num=16&pl=Show+Factorization']Type in factor 16[/URL] into our search engine. We get the following factor of 16: 1, 2, 4, 8, 16 [B]All of these are even [I]except[/I] 1, which is odd. This is why Alex is wrong.[/B]

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 $1. How much did each pencil cost? Let each pencil cost p. We're given the following equation: 7p + 1 = 24 [URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B1%3D24&pl=Solve']Type this equation into our search engine[/URL] and we get: p = [B]$3.29[/B]

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 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]

An ordinary fair die is rolled twice. The face value of the rolls is added together. Compute the probability of the following events: Event A: The sum is greater than 6. Event B: The sum is divisible by 5 or 6 or both. [URL='http://www.mathcelebrity.com/2dice.php?gl=2&pl=6&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum greater than 6[/URL] = [B]7/12[/B] Sum is divisible by 5 or 6 or both This means a sum of 5, a sum of 6, a sum of 10, or a sum of 12. [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=5&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 5[/URL] = 1/9 or 4/36 [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=6&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 6[/URL] = 5/36 [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=10&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 10[/URL] = 1/12 or 3/36 [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=12&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 12[/URL] = 1/36 Adding all these up, we get: (4 + 5 + 3 + 1)/36 [B]13/36[/B]

Assume that you make random guesses for 5 true-or-false questions. (a) What is the probability that you get all 5 answers correct? (Show work and write the answer in simplest fraction form) (b) What is the probability of getting the correct answer in the 5th question, given that the first four answers are all wrong? (Show work and write the answer in simplest fraction form) (c) If event A is �Getting the correct answer in the 5th question� and event B is �The first four answers are all wrong�. Are event A and event B independent? Please explain. (a) Correct Answer on each one is 1/2 or 0.5. Since all are independent events, we have: (1/2)^5 = [B]1/32[/B] (b) We have [B]1/2[/B] (1/2)^4 * 1/2/((1/2)^4) c) [B]Independent since you could have gotten correct or wrong on any of the 4 and the probability does not change[/B]

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

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]

Free Bayes Rule Calculator - Calculates the conditional probabilities of (B given A) of 2 events and a conditional probability event using Bayes Rule

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 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].

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

Free Break Even Calculator - Given a fixed cost, variable cost, and revenue function or value, this calculates the break-even point

Carter is going away to college and is giving his collection of 531 baseball cards to his cousins. If he gives 227 cards to Lewis, 186 cards to Benny, and 18 cards to Seven, how many cards are left over? When Carter gives away cards, he subtracts from his collection. So we have: 531 - 227 - 186 - 18 = [B]100 cards leftover[/B]

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]

[INDENT]Consecutive odd integers are odd integers that differ by ______ , such as ______ and 13. Consecutive even integers are even integers that differ by ______ , such as 12 and ______ . Consecutive odd integers are odd integers that differ by ___2___ , such as ___11___ and 13. Consecutive even integers are even integers that differ by ___2___ , such as 12 and ___14___ .[/INDENT]

Consider a firm that has two assembly lines, 1 and 2, both producing calculator. Assume that you have purchased a calculator and it turns out to be defective. And the line 1 produces 60% of all calculators produced. L1: event that the calculator is produced on line 1 L2: event that the calculator is produced on line 2 Suppose that your are given the conditional information: 10% of the calculator produced on line 1 is defective 20% of the calculator produced on line 2 is defective Q: If we choose one defective, what is the probability that the defective calculator comes from Line 1 and Line2? L1 = event that the calculator is produced on line 1 = 0.6 L2 = event that the calculator is produced on line 2 = 1 - 0.6 = 0.4 D = Defective D|L1 Defective from Line 1 = 0.1 D|L2 = Defective from Line 2 = 0.20 [U]Defective from Line 1[/U] P(L1|D) = P(L1)P(D/L1) / [ P(L1)P(D/L1) + P(L2)P(D/L2)] P(L1|D) = (.60)(.10) /[(.60)(.10)+ (.40)(.20)] [B]P(L1|D) = 0.4286[/B] [U]Defective from Line 2[/U] P(L2|D) = P(L2)P(D/L2) / [ P(L1)P(D/L1) + P(L2)P(D/L2)] P(L2|D) = (.40)(.20) /[(.60)(.10)+ (.40)(.20)] [B]P(L2|D) = 0.5714[/B]

Consider a probability model consisting of randomly drawing two colored balls from a jar containing 2 red and 1 blue balls. What is the Sample Space of this experiment? (assume B= blue and R=red) The sample space is the list of all possible events [LIST] [*]RRB [*]RBR [*]BRR [/LIST]

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

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]

Free Coordinating Conjunctions Calculator - Shows the 7 coordinating conjunctions using the mnemonic FANBOYS. The seven coordinating conjunctions are (FOR, AND, NOR, BUT, OR, YET, SO)

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.

Free Cost Revenue Profit Calculator - Given a total cost, variable cost, revenue amount, and profit unit measurement, this calculates profit for each profit unit

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

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 numbers of hours h Set up the revenue function: [B]R = 8.5h[/B]

2 rules. If either of them passes, then the number is divisible by 11: [LIST=1] [*]Sum of the odd digits - Sum of the even digits is divisible by 11 [*]Sum of the odd digits - Sum of the even digits = 0 (Ex. 121) [/LIST] [MEDIA=youtube]WpV87es0WAU[/MEDIA]

Edna plans to treat her boyfriend Curt to dinner for his birthday. The costs of their date options are listed next to each possible choice. Edna plans to allow Curt to choose whether they will eat Mexican food ($25), Chinese food ($15), or Italian food ($30). Next, they will go bowling ($20), go to the movies ($30) or go to a museum ($10). Edna also is deciding between a new wallet ($12) and a cell phone case ($20) as possible gift options for Curt. What is the maximum cost of this date? Edna has 3 phases of the date: [LIST=1] [*]Dinner [*]Event after dinner [*]Gift Option [/LIST] In order to calculate the maximum cost of the date, we take the maximum cost option of all 3 date phases: [LIST=1] [*]Dinner - Max price is Italian food at $30 [*]Event after dinner - Max price is movies at $30 [*]Gift Option - Max price option is the cell phone cast at $20 [/LIST] Add all those up, we get: $30 + $30 + $20 = [B]$80[/B]

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 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, 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.

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

Free Event Likelihood Calculator - Given a probability, this determines how likely that event is

Farah rolls a fair dice and flips a fair coin. What is the probability of obtaining a 5 and a head? Give your answer in its simplest form. Probability of a 5 is 1/6 Probability of a head is 1/2 Since each event is independent, we get the total probability by multiplying both together: P(5,H) = 1/6 * 1/2 P(5,H) = [B]1/12[/B]

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 3 Even Integers with a sum of 198 Let x be the first even integer. Then y is the next, and z is the third even integer. [LIST=1] [*]y = x + 2 [*]z = x + 4 [*]x + y + z = 198 [/LIST] Substituting y and z into (3): x + x + 2 + x + 4 = 198 Group x terms 3x + 6 = 198 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B6%3D198&pl=Solve']equation solver[/URL], we get: [B]x = 64[/B] y = 64 + 2 [B]y= 66[/B] z = 64 + 4 [B]z = 68[/B]

Find the largest of three consecutive even integers when six times the first integers is equal to five times the middle integer. Let the first of the 3 consecutive even integers be n. The second consecutive even integer is n + 2. The third (largest) consecutive even integer is n + 4. We are given 6n = 5(n + 2). Multiply through on the right side, and we get: 6n = 5n + 10 [URL='https://www.mathcelebrity.com/1unk.php?num=6n%3D5n%2B10&pl=Solve']Typing 6n = 5n + 10 into the search engine[/URL], we get n = 10. Remember, n was our smallest of 3 consecutive even integers. So the largest is: n + 4 10 + 4 [B]14[/B]

Find the last digit of 4^2081 no calculator 4^1= 4 4^2 = 16 4^3 = 64 4^4 = 256 4^5 = 1024 4^6 = 4096 Notice this pattern alternates between odd exponent powers with the result ending in 4 and even exponent powers with the result ending in 6. Since 2081 is odd, the answer is [B]4. [MEDIA=youtube]ueBWAW4XW4Q[/MEDIA][/B]

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. 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? 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]

In the first hour, he sold one-half of his sticks, plus one-half of a stick. The next hour, he sold one-third of his remaining sticks plus one-third of a stick. In the third hour, he sold one-fourth of what he had left, plus three-fourths of a stick. The last hour, he sold one-fifth of the remaining sticks, plus one-fifth of a stick. He did not cut up any sticks to make these sales. He returned home with 19 sticks. How many did he originally take to the event?

Ok. To go further in this equation. It reads: ...How many did he originally take to the event? Multiply the answer by 3 and reverse the digits. This will give you the answer for ACH in the coordinates. Does that make sense to reverse 303? :-/ Thank you for your help!!

Let me post the whole equation paragraph: Brainteaser # 1: Answer for ACH A fellow geocacher decided that he would try to sell some hand-made walking sticks at the local geocaching picnic event. In the first hour, he sold one-half of his sticks, plus one-half of a stick. The next hour, he sold one-third of his remaining sticks plus one-third of a stick. In the third hour, he sold one-fourth of what he had left, plus three-fourths of a stick. The last hour, he sold one-fifth of the remaining sticks, plus one-fifth of a stick. He did not cut up any sticks to make these sales. He returned home with 19 sticks. How many did he originally take to the event? Multiply the answer by 3 and reverse the digits. This will give you the answer for ACH in the coordinates. Make sure to multiply and reverse the digits. What would the answer be?

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

If 13,754 people voted for a politician in his first election, 15,420 voted for him in his second election, and 8,032 voted for him in the first and second elections, how many people voted for this politician in the first or second election? Let P(A) be the first election votes, P(B) be the second election votes, and P(A ? B) be votes for both the first AND the second elections. We want P(A U B). Use our [URL='http://www.mathcelebrity.com/probunion2.php?pa=+13754&pb=15420&paintb=8032&aub=+&pl=Calculate']two event calculator[/URL] P(A U B) = P(A) + P(B) - P(A ? B) P(A U B) = 13,754 + 15,420 - 8032 P(A U B) = 29,174 - 8,032 P(A U B) = [B]21,142[/B]

If 4 people have the same 7 shirts, what is the chance that they will wear the same shirt on one day? [LIST=1] [*]For each person, the probability they all wear the first shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the second shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the third shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the fourth shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the fifth shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the sixth shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the seventh shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [/LIST] Now, we add up all those probabilities to get our answer, since any of the 7 scenarios above meets the criteria: (1 + 1 + 1 + 1 + 1 + 1 + 1)/256 [B]7/256[/B]

If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A U B)=? We know the following formula for the probability of 2 events: P(A U B) = P(A) + P(B) - P(A intersection B) We're told A and B are independent, which makes P(A intersection B) = 0. So we're left with: P(A U B) = P(A) + P(B) - P(A intersection B) P(A U B) = 0.2 + 0.6 - 0 P(A U B) = [B]0.8[/B]

if a and b are odd then a + b is even Let a and b be positive odd integers of the form: [LIST] [*]a = 2n + 1 [*]b = 2m + 1 [/LIST] a + b = 2n + 1 + 2m + 1 a + b = 2n + 2m + 1 + 1 Combing like terms, we get: a + b = 2n + 2m + 2 a + b = 2(n + m) + 2 Let k = n + m a + b = 2k + 2 [B]Therefore a + b is even[/B]

If a is an even integer and b is an odd integer then prove a ? b is an odd integer Let a be our even integer Let b be our odd integer We can express a = 2x (Standard form for even numbers) for some integer x We can express b = 2y + 1 (Standard form for odd numbers) for some integer y a - b = 2x - (2y + 1) a - b = 2x - 2y - 1 Factor our a 2 from the first two terms: a - b = 2(x - y) - 1 Since x - y is an integer, 2(x- y) is always even. Subtracting 1 makes this an odd number. [MEDIA=youtube]GDVuQ7bGHx8[/MEDIA]

Look at the Contrapositive: If n is even, then 3n + 2 is even... Suppose that the conclusion is false, i.e., that n is even. Then n = 2k for some integer k. Then we have: 3n + 2 = 3(2k) + 2 3n + 2 = 6k + 2 3n + 2 = 2(3k + 1). Thus 3n + 2 is even, because it equals 2j for an integer j = 3k + 1. So 3n + 2 is not odd. We have shown that �(n is odd) ? �(3n + 2 is odd), therefore, the contrapositive (3n + 2 is odd) ? (n is odd) is also true.

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

If the probability of rain is 15%, what is the probability that it won't rain? If we assign the probability of raining as event A, then A' (A complement) is the probability it won't rain. Since it either rains or doesn't rain are the only two events. There exists an axiom in statistics that states: P(A) + P(A') = 1 Rearranging this, we get: P(A') = 1 - P(A) If we assign the probability of raining as event A which is 0.15, we get: P(A') = 1 - 0.15 P(A') = [B]0.85[/B]

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 a paper bag, 7 of the 15 marbles are yellow. In a cloth bag, 2 of the 15 marbles are yellow. If Tim randomly draws one marble from each bag, what is the probability that they are both yellow? Bag 1 probability of drawing yellow is 7/15 Bag 2 probability of drawing yellow is 2/15 Since each event is independent, we multiply each draw to get our final probability: P(yellow Bag 1)(yellow Bag 2) = P(Yellow Bag 1) * P(Yellow Bag 2) P(yellow Bag 1)(yellow Bag 2) = 7/15 * 2/15 P(yellow Bag 1)(yellow Bag 2) = [B]14/225[/B] [URL='https://www.mathcelebrity.com/fraction.php?frac1=14%2F225&frac2=3%2F8&pl=Simplify']Since we cannot simplify this fraction anymore[/URL], our answer is [B]14/225[/B]

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]

In the movie Die Hard: With a Vengeance, in one of the action scenes, the characters Mc Clane and Carver were caught in a breathtaking scenario where they need to keep a bomb from exploding, and the only way to prevent explosion is to put exactly four gallons of water on a scale. How would they do it if they only have a five - gallon and a three gallon jug? [LIST=1] [*]Fill the 5-gallon jug all the way. [*]Pour water into the 3 gallon jug until it is full. [*]Now you have 2 gallons in the 5-gallon jug and a full 3 gallons in the 3-gallon jug. [*]Empty the 3-gallon jug. [*]Pour the 2 gallons of water still in the 5-gallon jug into the 3-gallon jug. [*]Now the 3-gallon jug has 2 gallons of water in it, and 1 gallon of empty space. [*]Fill up the 5 gallon jug all the way, and then pour water out of the 5-gallon jug into the 3-gallon jug until the 3-gallon jug is full. [*]This leaves exactly [B]4 gallons[/B] in the 5-gallon jug. [/LIST]

It takes Spot 2 hours to paint a fence and Steven 4 hours to paint the same fence. If they work together, how long will it take them to paint the fence? Spot paints 1/2 of a fence in an hour Steven paints 1/4 of a fence in an hour Together, in an hour, they paint 1/2 + 1/4 of a fence in an hour 1/2 = 2/4, so we have 2/4 + 1/4 = 3/4 of a fence in an hour Meaning they take another 20 minutes to pain the last 1/4 of the fence [B]1 hour + 20 minutes[/B] is the total time it takes

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 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 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]

juan sells raffle tickets at a charity event for $6 each.How many tickets does he have to sell to make $144? Tickets needed = Total Sales / Cost per ticket Tickets needed = 144/6 Tickets needed = [B]24[/B]

Julia spends $1.75 on gas for her lawn mower. She earns $16.00 mowing her neighbor's yard. What is Julia's profit? Profit = Revenue - Cost Profit = 16.00 - 1.75 Profit = [B]$14.25[/B]

Larry and his friend split the dinner bill evenly. They each paid $21.34. What was the cost of dinner? Total Bill = Larry's portion + Friend's portion Total Bill = 21.34 + 21.34 Total Bill = [B]$42.68[/B]

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 A and B be independent events with P(A) = 0.52 and P(B) = 0.62. a. Calculate P(A ? B). With independent events, the intersection probability is found by: P(A ? B) = P(A) * P(B) P(A ? B) = 0.52 * 0.62 P(A ? B) = [B]0.3224[/B]

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 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 only 22 boxes left. How many did she start with? Take this in parts [LIST=1] [*]Maria starts with b boxes. [*]She buys seven more. So she has b + 7 boxes [*]A week later, half of all her boxes are destroyed in a fire. Which means she's left with 1/2. (b + 7)/2 [*]Now she has 22 boxes. So we set (b + 7)/2 = 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']Typing this equation into our search engine and solving for b[/URL], we get: [B]b = 37[/B]

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 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]

Free Multinomial Distribution Calculator - Given a set of x_i counts and a respective set of probabilities θ_i, this calculates the probability of those events occurring.

Free Number Property Calculator - This calculator determines if an integer you entered has any of the following properties:
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* Evil Numbers or Odious Numbers
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* Prime Numbers or Composite Numbers
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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 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]

Free Odds Probability Calculator - Given an odds prediction m:n of an event success, this calculates the probability that the event will occur or not occur

olivia earns $2 for every cup of lemonade she sells. How many cups of lemonade does olivia need to sell in all to earn $16? Cups needed = Total Revenue / Cost per cup Cups needed = 16/2 [URL='https://www.mathcelebrity.com/fraction.php?frac1=16%2F2&frac2=3%2F8&pl=Simplify']Cups needed [/URL]= [B]$8[/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 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 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 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]

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

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

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]

Free Probability Calculator - This lesson walks you through the basics of probability like the probability definition, events, outcomes, experiments, and probability postulates

Free Probability (A U B U C) Calculator - Calculates the probability of a union of a three event sample space, A, B, and C, as well as P(A), P(B), P(C), P(A ∩ B), P(A ∩ C), P(B ∩ C), P(A ∩ B ∩ C).

Free Probability (A U B) Calculator - Given a 2 event sample space A and B, this calculates the probability of the following events:
P(A U B)
P(A)
P(B)
P(A ∩ B)

Free Product of Consecutive Numbers Calculator - Finds the product of (n) consecutive integers, even or odd as well. Examples include:
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Free Profit Equation Calculator - Using the Profit Equation with inputs (Revenue-Cost-Profit-Tax), this determines the relevant output including gross proft, gross profit margin, net profit, and net profit margin.

Prove P(A�) = 1 - P(A) The sample space S contains an Event A and everything not A, called A' We know P(S) = 1 P(S) = P(A U A') P(A U A') = 1 P(A) + P(A') = 1 subtract P(A) from each side: P(A�) = 1 - P(A) [MEDIA=youtube]dNLl_8vejyE[/MEDIA]

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]

Take an integer n. The next alternate consecutive integer is n + 2 Subtract the difference of the squares: (n + 2)^2 - n^2 n^2 + 4n + 4 - n^2 n^2 terms cancel, we get: 4n + 4 Factor out a 4: 4(n + 1) If n is odd, n + 1 is even. 4 * even is always even If n is even, n + 1 is odd. 4 * odd is always odd Since both cases are even, we've proven our statement. [MEDIA=youtube]J_E9lR5qFY0[/MEDIA]

Take an integer n. The next consecutive integer is n + 1 Subtract the difference of the squares: (n + 1)^2 - n^2 n^2 + 2n + 1 - n^2 n^2 terms cancel, we get: 2n + 1 2 is even. For n, if we use an even: we have even * even = Even Add 1 we have Odd 2 is even. For n, if we use an odd: we have even * odd = Even Add 1 we have Odd Since both cases are odd, we've proven our statement. [MEDIA=youtube]RAi0HbH5bqc[/MEDIA]

Take two arbitrary integers, x and y We can express the odd integer x as 2a + 1 for some integer a We can express the odd integer y as 2b + 1 for some integer b x + y = 2a + 1 + 2b + 1 x + y = 2a + 2b + 2 Factor out a 2: x + y = 2(a + b + 1) Since 2 times any integer even or odd is always even, then [B]x + y by definition is even[/B]. [MEDIA=youtube]9A-qe4yZXYw[/MEDIA]

Let us take an integer x which is both even [I]and[/I] odd. [LIST] [*]As an even integer, we write x in the form 2m for some integer m [*]As an odd integer, we write x in the form 2n + 1 for some integer n [/LIST] Since both the even and odd integers are the same number, we set them equal to each other 2m = 2n + 1 Subtract 2n from each side: 2m - 2n = 1 Factor out a 2 on the left side: 2(m - n) = 1 By definition of divisibility, this means that 2 divides 1. But we know that the only two numbers which divide 1 are 1 and -1. Therefore, our original assumption that x was both even and odd must be false. [MEDIA=youtube]SMM9ubEVcLE[/MEDIA]

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]

Sam had 120 teddy bears in his toy store. He sold 2/3 of them at $12 each. How much did he receive? Revenue = Price * Quantity 12 * 2/3 * 120 12 * 80 [B]960[/B]

Free Sample Space Probability Calculator - Given a sample space S and an Event Set E, this calculates the probability of the event set occuring.

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]

Sara wants to arrange the seven scrabble letters she has in every possible way so she can determine if she has a 7-letter word. how many different ways are there for Sara to arrange all seven letters? 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = [B]5,040 ways[/B]

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. 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]

[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. [MEDIA=youtube]aQKLVxIB-p4[/MEDIA][/I]

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 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. 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 [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 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]

Stacy sells art prints for $12 each. Her expenses are $2.50 per print, plus $38 for equipment. How many prints must she sell for her revenue to equal her expenses? Let the art prints be p Cost function is 38 + 2p Revenue function is 12p Set cost equal to revenue 12p = 38 + 2p Subtract 2p from each side 10p = 38 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=10p%3D38&pl=Solve']equation calculator[/URL] gives us [B]p = 3.8[/B]

Steven has some money. If he spends $9, then he will have 3/5 of the amount he started with. Let the amount Steven started with be s. We're given: s - 9 = 3s/5 Multiply each side through by 5 to eliminate the fraction: 5(s - 9) = 5(3s/5) Cancel the 5's on the right side and we get: 5s - 45 = 3s To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=5s-45%3D3s&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]22.5[/B]

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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]

Success in a binomial event is .15 what is the probability of failure? Success is represented as p. p = 0.15. The probability of failure q, is written as q = 1 - p q = 1 - 0.15 [B]q = 0.85[/B]

Free Sum of Consecutive Numbers Calculator - Finds the sum of (n) consecutive integers, even or odd as well. Examples include:
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Sum of N and its next consecutive even integer is 65 Next even consecutive integer is N + 2. We have N + (N + 2) = 65. Combine like terms, we have 2N + 2 = 65 [URL='http://www.mathcelebrity.com/1unk.php?num=2n%2B2%3D65&pl=Solve']Running this problem through the search engine[/URL], we get n = 31.5. Meaning this problem is impossible, it cannot be done. n is not an integer, and neither is the next consecutive even integer.

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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 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 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. 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 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 + 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]

Taylor is playing a game using a die and a spinner. The spinner is divided into 4 equal parts with colors green, red, yellow, and purple. Taylor rolls the die and spins the spinner. What is the probability the die shows a 2 and the spinner lands on purple? Probability of rolling a 2 on the die is 1/6 Probability of getting a purple on the spinner is 1/4 Since each event is independent, our joint probability is: P(2 on the die and Purple on the spinner) = P(2 on the die) x P(Purple on the Spinner) P(2 on the die and Purple on the spinner) = 1/6 x 1/4 P(2 on the die and Purple on the spinner) = [B]1/24[/B]

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 brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the bran. How many adults must he survey in order to be 90% confident that his estimate is within seven percentage points of the true population percentage? [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] = 0.5 1 - [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] = 0.5 margin of error (E) = 0.07 At 90% confidence level the t is, alpha = 1 - 90% alpha = 1 - 0.90 alpha = 0.10 alpha / 2 = 0.10 / 2 = 0.05 Zalpha/2 = Z0.05 = 1.645 sample size = n = (Z[IMG]https://ci4.googleusercontent.com/proxy/mwhpkw3aM19oMNA4tbO_0OdMXEHt9juW214BnNpz4kjXubiVJgwolO7CLbmWXXoSVjDPE_T0CGeUxNungBjN=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Calpha[/IMG] / 2 / E )2 * [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] * (1 - [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] ) = (1.645 / 0.07)^2 *0.5*0.5 23.5^2 * 0.5 * 0.5 552.25 * 0.5 * 0.5 = 138.06 [B]sample size = 138[/B] [I]He must survey 138 adults in order to be 90% confident that his estimate is within seven percentage points of the true population percentage.[/I]

The 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 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 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 Oakdale High School Speech and Debate Club hosted its annual car wash fundraiser. Each club member brought a bottle of car wash soap, so there were 8 total bottles. 6 of the bottles contained orange soap. If a club member randomly selects 5 bottles to pour into the first soap bucket, what is the probability that all of them contain orange soap? This is assumed to be draw without replacement, so we have: [LIST=1] [*]Draw 1: 6/8 [*]Draw 2: 5/7 [*]Draw 3: 4/6 [*]Draw 4: 3/5 [*]Draw 5: 2/4 [/LIST] Since they are independent events, we multiply: 6/8 * 5/7 * 4/6 * 3/5 * 2/4 (6 * 5 * 4 * 3 * 2)/(8 * 7 * 6 * 5 * 4) 720/6720 [B]0.1071[/B]

The Radio City Music Hall is selling tickets to Kayla�s premiere at the Rockettes. On the first day of ticket sales they sold 3 senior citizen tickets and 9 child tickets for a total of $75. It took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of each senior citizen ticket and each child ticket? Let the cost of child tickets be c Let the cost of senior tickets be s Since revenue = cost * quantity, we're given two equations: [LIST=1] [*]9c + 3s = 75 [*]5c + 8s = 67 [/LIST] To solve this simultaneous group of equations, we can use 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we use, we get the same answer: [LIST] [*][B]c = 7[/B] [*][B]s = 4[/B] [/LIST]

The revenue for selling x candles is given by f(x)=12x. The teams profit is $40 less than 80% of the revenue of selling x candles. write a function g to model the profit. Profit = Revenue - Cost We are given the revenue function f(x) = 12x. We are told the profit is 0.8(Revenue) - 40. Our profit function P(x) is: P(x) = 0.8(12x) - 40 Simplifying, we have: [B]P(x) = 9.6x - 40[/B]

the sample space for a coin being tossed twice Since each toss results in 2 outcomes, we have 2^2 = 4 possible events in the sample space: [LIST=1] [*]H,H [*]H,T [*]T,H [*]T,T [/LIST]

The school council began the year with a $600 credit to their account, but they spent $2,000 on new books for classrooms. How much must the PTA earn through fundraising to break even? +600 - 2000 = -1,400. Break even means no profit or loss. So the PTA must earn [B]1,400 [/B]to break even on the -1,400

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 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 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 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 10 true or false questions on a test. You do not know the answer to 4 of the questions, so you guess. What is the probability that you will get all 4 answers right? Probability you guess right is 1/2 or 0.5. Since each event is independent of the other events, we multiply 1/2 4 times: 1/2 * 1/2 * 1/2 * 1/2 = [B]1/16[/B]

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 bag filled with 3 blue, 4 red and 5 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting exactly 1 green? Calculate Total marbles Total marbles = Blue + Red + Green Total marbles = 3 + 4 + 5 Total marbles = 12 Probability of a green = 5/12 Probability of not green = 1 - 5/12 = 7/12 To get exactly one green in two draws, we either get a green, not green, or a not green, green [U]First Draw Green, Second Draw Not Green[/U] [LIST] [*]1st draw: Probability of a green = 5/12 [*]2nd draw: Probability of not green = 7/11 <-- 11 since we did not replace the first marble [*]To get the probability of the event, since each draw is independent, we multiply both probabilities [*]Probability of the event is (5/12) * (7/11) = 35/132 [/LIST] [U]First Draw Not Green, Second Draw Not Green[/U] [LIST] [*]1st draw: Probability of not a green = 7/12 [*]2nd draw: Probability of not green = 5/11 <-- 11 since we did not replace the first marble [*]To get the probability of the event, since each draw is independent, we multiply both probabilities [*]Probability of the event is (7/12) * (5/11) = 35/132 [/LIST] To get the probability of exactly one green, we add both of the events: First Draw Green, Second Draw Not Green + First Draw Not Green, Second Draw Not Green 35/132 + 35/132 = 70/132 [URL='https://www.mathcelebrity.com/fraction.php?frac1=70%2F132&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL], we get: [B]35/66[/B]

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 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]

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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]

seven plus x 7 + x Twice the quantity of seven plus x 2(7 + x) Difference of x and seven x - 7 The phrase [I]is the same as[/I] means equal to. This is our algebraic expression: [B]2(7 + x) = x - 7 [/B] If the problem asks you to solve for x, distribute 2 on the left side: 14 + 2x = x - 7 Subtract x from the right side 14 + x = -7 Subtract 14 from each side [B]x = -21[/B]

Two consecutive even integers that equal 126 Let the first integer equal x. So the next even integer must be x + 2. The sum which is equal to 126 is written as x + (x + 2) = 126 Simplify: 2x + 2 = 126 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2x%2B2%3D126&pl=Solve']equation calculator,[/URL] we get: x = 62 This means the next consecutive even integer is 62 = 2 = 64. So our two even consecutive integers with a sum of 126 are [B](62, 64)[/B]

Two dice are rolled. Enter the size of the set that corresponds to the event that both dice are odd. If dice 1 is odd, then we have the following face values: {1, 3, 5} If dice 2 is odd, then we have the following face values: {1, 3, 5} [URL='https://www.mathcelebrity.com/2dice.php?gl=1&opdice=1&pl=Both+Odd&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']From this 2 dice odds face link[/URL], we see that the size of the set is 9. [LIST=1] [*]{1, 1} [*]{1, 3} [*]{1, 5} [*]{3, 1} [*]{3, 3} [*]{3, 5} [*]{5, 1} [*]{5, 3} [*]{5, 5} [/LIST]

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now 22 boxes left. With how many did she start?

Van needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that starts with 13 and continues to add seven to each output. For now, van needs to know what the 15th output will be. Complete the steps needed to determine the 15th term in sequence. Given a first term a1 of 13 and a change amount of 7, expand the series The explicit formula for an [I]arithmetic series[/I] is an = a1 + (n - 1)d d represents the common difference between each term, an - an - 1 Looking at all the terms, we see the common difference is 7, and we have a1 = 13 Therefore, our explicit formula is an = 13 + 7(n - 1) If n = 15, then we plug it into our explicit formula above: an = 13 + 7(n - 1) a(15) = 15 + 7(15 - 1) a(15) = 15 + 7 * 14 a(15) = 15 + 98 a(15) = [B]113[/B]

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? [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 [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]

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

Wilbie had candy to give to his 3 children. He first took 5 pieces and evenly divided the rest among each child. Each child received 3 pieces. With how many pieces did he start? Let the starting candy amount be c. We're given: (c - 5)/3 = 3 Cross multiply: c - 5 = 3*3 c - 5 = 9 [URL='https://www.mathcelebrity.com/1unk.php?num=c-5%3D9&pl=Solve']Type this equation into the search engine[/URL], and we get: c = 14

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 collect stamps. You give steven 21 stamps. At the end youbhave 3. How many stamps did you start with? You start with s stamps. s You give Steven 21. Giving means you subtract from your total: s - 21 You have 3 left s - 21 = 3 To solve this equation for s, we t[URL='https://www.mathcelebrity.com/1unk.php?num=s-21%3D3&pl=Solve']ype it in our math engine[/URL] and we get: s = [B]24[/B]

You have 30 DONUTS. 1/6 of them are Boston Cream. 2/5 of them are Maple. 3/10 of them are Chocolate Dip and 1/3 are Sprinkled. IS THIS EVEN POSSIBLE?? How many donuts OVER or UNDER am I? (Show your work and use EQUIVALENTS.) We use 30 as our common denominator. Let's get [I]equivalent fraction[/I]s for each donut type with a denominator of 30: [LIST] [*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=1%2F6&pl=Equivalent+Fractions']1/6[/URL] = 5/30 [*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=2%2F5&pl=Equivalent+Fractions']2/5 [/URL]= 12/30 [*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=3%2F10&pl=Equivalent+Fractions']3/10[/URL] = 9/30 [*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=1%2F3&pl=Equivalent+Fractions']1/3[/URL] = 10/30 [/LIST] Add up our numerators of the common denominator of 30: 5 + 12 + 9 + 10 = 36 So our fraction is 36/30. This makes our scenario [B]impossible[/B]. Fractions of the donut should add up to 1. Which would mean our numerators need to sum to 1 or less. Since 36 > 30, this scenario is [B]impossible.[/B]

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]

Your profit for mowing lawns this week is $24. You are paid $8 per hour and you paid $40 for gas for the lawn mower. How many hours did you work this week? We know profit from the equation below: Revenue - Cost = Profit We're given Profit as 42, so we have: Revenue - Cost = 42 Let hours worked be h. We have revenue as: Revenue = 8h Cost = 40, so we plug these into profit to get: 8h - 40 = 42 To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h-40%3D42&pl=Solve']plug this equation into our math engine[/URL] and get: h = [B]10.25[/B]

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