Question

Please answer every question except no 1 and don't send any links or your question will get taken down. I need it to be in perfect detail. I will give 96 points and brainliest answer.

Answer 1

9514 1404 393

Answer:

  1a. 10h +15s ≤ 55

  1b. at most 3

  2a. p = 218 -5(t -1)

  2b. p = 186 -(t -1)

  2c. week 9 (or maybe after 8 weeks, see discussion)

  3a. 7w +5c ≤ 30

  3b. yes

  3c. no

  4a. 15x +5y ≥ 44

Step-by-step explanation:

1a. Let h and s represent the numbers of hats and shirts Stephanie buys, respectively. Their cost will be the product of the number and their price. Stephanie wants the total cost to be at most 55, so the inequality will be ...

  10h +15s ≤ 55

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1b. When h=1, the limit on s is ...

  10·1 +15s ≤ 55

  15s ≤ 45 . . . . . . . subtract 10

  s ≤ 3 . . . . . . . . . .divide by 15

Stephanie can buy at most 3 shirts.

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2a. Elton starts at 218 for week 1, drops to 213 for week 2, 208 for week 3, and so on. This is an arithmetic sequence with a first term of 218 and a common difference of -5. We can use the formula for the general term of an arithmetic sequence to find Elton's weight in week t.

  an = a1 +d(n -1) . . . . . . . n-th term of arithmetic sequence with first term a1 and common difference d

We are told to use the variables p and t, so we have for a1 = 218 and d = -5 ...

  p = 218 -5(t -1) . . . . Elton's weight on week t

  p = 223 -5t . . . . . . . simplified

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2b. Steven's weight can be described in similar fashion. His weight started at 186 and had a week-to-week difference of -1 pounds.

  p = 186 -(t -1)

  p = 187 -t . . . . . . . simplified

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2c. The weights are the same when ...

  p = p

  223 -5t = 187 -t

  36 = 4t

  9 = t

Their weights will be the same on Week 9.

Note: you need to be a little careful here. The question asks, "after how many weeks ...". That could be interpreted to mean Week 9 is after 8 weeks.

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3a. As with previous questions, the total cost is the sum of products of individual cost and number of items. Larry wants his total cost to be at most $30, so the inequality can be written as ...

  7w +5c ≤ 30

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3b, c. A graph of this inequality is attached. The combinations proposed are plotted on the graph.

• 2 watermelons and 3 chip platters: yes, a feasible purchase
• 3 watermelons and 2 chip platters: no, not a feasible purchase

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4. The inequality shown on the graph is ...

  15x +5y ≥ 44

Please note that this is not the only applicable inequality. We also require that x ≥ 1 and y ≥ 1, since Brandon wants to eat at least one serving of each. (Actually, we aren't told the serving size. Here, we have assumed it is 1 cup.) The graph with these extra restrictions is shown in the second attachment.