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# Tutor profile: Hannah M.

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Hannah M.
Successful math teacher for 5 years and counting!
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## Questions

### Subject: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?

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Hannah M.

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.

### Subject: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?

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Hannah M.

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.

### Subject: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.

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Hannah M.

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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