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Hannah M.

Successful math teacher for 5 years and counting!

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Pre-Algebra

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Question:

Four students, about to purchase concert tickets for $20 for each ticket, discover that they may purchase a block of 5 tickets for $80.00. How much would each of the four save if they can get a fifth person to join them and the five people equally divide the price of the five tickets?

Hannah M.

Answer:

If the students decide to purchase the five tickets for $80, we can find the price per ticket by dividing 80 by 5. 80/5 = 16 So, each student would pay $16 per ticket if they purchased the five pack. Without purchasing the five pack, each student will pay $20. How much would each of the four save if they can get a fifth person to join them and the five people equally divide the price of the five tickets? We find this by taking the difference between the price with four students ($20) and the price with five students ($16). $20 - $16 = $4 Each student will save $4 if they find a fifth student to go with them to the concert.

Statistics

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Question:

A bag of marbles has 7 yellow marbles, 5 red marbles, 3 blue marbles, and 6 white marbles. What is the probability of selecting a yellow marble and then a red marble if the marbles are not replaced?

Hannah M.

Answer:

Let A be the event that a yellow marble is selected first. Let B be the event that a red marble is selected next. Then we are interested in the probability of the event "A and B." We want to find the probability of event A and B, which we notatat using P(A∩B). According to the Chain Rule: P(A∩B)=P(A)P(B|A) P(A) is the probability that a yellow marble is selected first. In total, there are 21 marbles, and only 7 of them are yellow. We must assume that we are equally likely to select any of the 21 marbles. P(A) = 7/21 = .333 P (B|A) is the conditional probability that B occurs if we know that A has also occurred, or B given A. Since, A has occurred, then there must only be 20 marbles left now that we have removed a yellow one. All 5 red marbles still remain. P(B|A) = 5/20 = 0.25 Combining these two parts gives us: P(A∩B)=(7/21)⋅(5/20)= 0.333 x 0.25 = 0.0833 The probability of selecting a yellow marble and then a red marble if the marbles are not replaced is 0.0833.

Algebra

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Question:

A rectangle has perimeter X, length Y and width Z. Write an equation for the perimeter of the rectangle that represents Y in terms of X and Z.

Hannah M.

Answer:

First, you need to determine what the equation for the perimeter of a rectangle is based on the information you were given. To find the perimeter of a rectangle, you just add the sides up! I would suggest drawing a rectangle to represent the problem. Y = length (there are two long sides in a rectangle) Z = width (there are two short sides in a rectangle) X = perimeter (all the sides added together) The perimeter of a rectangle equals the two short sides added together and the two long sides added together. X = Y + Y + Z + Z To simplify this expression further, you can combine like terms. (combine the Y's and the Z's) X = 2Y + 2Z Now that we have an equation for the perimeter, we can answer the second part of the question. Write an equation for the perimeter of the rectangle that represents Y in terms of X and Z. In order to "represent Y", this means we need to rearrange the equation until we have Y alon on the left side of the equal sign. We can do this using inverse operations. X = 2Y + 2Z X - 2Y = 2Y - 2Y + 2Z (subtract 2Y from each side) X - 2Y = 2Z (simplify) X - X -2Y = 2Z - X (subtract X from each side) -2Y = 2Z - X (simplify) -2Y/-2 = (2Z/-2) - (X/-2) (divide everything by -2) Y = -Z + X/2 (simplify) or Y = x/2 - z

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