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RoseWind [281]
2 years ago
11

5<2y<12 where y is an integer. Write down all the possible values of y.

Mathematics
1 answer:
frozen [14]2 years ago
8 0

Answer:

y = 3, 4, or 5

Step-by-step explanation:

<u />

<u>Step 1; Simplify the Double Inequality</u>

Let's first simplify this double inequality to make answering this problem a bit easier. This means getting the middle term to be just y, without any added constant or coefficients.

In this case, this is a fairly simple process, as all we have to do to get y by itself is just divide the <em>entire inequality</em> by 2. This means that we will also divide the 5 and 12 by 2. (Note that the signs stay the same because we are not dividing by a negative number.)

Doing so gives us the following double inequality: 2.5 < y < 6.

<u>Step 2: Identify the Integers in this Range</u>

Now that we have a simplified double inequality, all we need to do is find all of the integers in its range. (Recall that an integer is <u>any number that is not a fraction when fully simplified (ex. …-1, 0, 1...)</u>.)

In other words, we need to find all of the integers <em>in between</em> 2.5 and 6. Note that we don't include 6 because of the "<" sign, which indicates that the 2.5 and 6 are not included in the set. These numbers are 3, 4, and 5, making them your answer. Hope this helps!

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A scuba diving company currently charges $100per dive. On average, there are 30 customers per day. The company performed a study
Semenov [28]

A. Total Revenue (R) is equal to price per dive (P) multiplied by number of customers (C). We can write R=PC.

Per price increase is $20. So four price increase is $20*4=$80. Hence, price per dive is 100+80=$180.

Also per price increase, 2 customers are reduced from 30. For 4 price increases, 4*2=8 customers are reduced. Hence, total customers is 30-8=22.

So Total Revenue is:

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B. Each price increase is 20. So x price increase is 20x. Hence, new price per dive would be equal to the sum of 100 and 20x.

Also per price increase, customers decrease by 2. So per x price increases, the customer decrease is 2x. Hence, new number of customers is the difference of 30 and 2x.

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C. We are looking for the point (x) at which the equation modeled in part (B) gives a maximum value of revenue (y). That x value is given as x=-\frac{b}{2a}, where a is the coefficient of x^{2} and b is the coefficient of x. So we have,

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That means, the greatest revenue is achieved after 5 price increases. Each price increase was 20, so 5 price increase would be 5*20=100. So the price that gives the greatest revenue is 100+100=200.

ANSWERS:

A. $3960

B. R=-40x^{2}+400x+3000

C. $200

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Answer:

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SOLUTION:

Step 1:

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Step 2:

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