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VARVARA [1.3K]
2 years ago
12

Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour is given by , where is the number of

hours since 10 AM, .
Mathematics
1 answer:
Elan Coil [88]2 years ago
7 0

Complete Question:

Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour is given by x(t) = -4t^2 + 20t + 60, where is the number of hours since 10 AM:

a) Find an expression for the revenue per hour as a function of x, R(x)

b) Find and simplify, R(x(t))

Answer:

a) R(x) = 2x

b) R(x(t)) = -8t^2 + 40t + 120

Step-by-step explanation:

a) This is a very trivial exercise.

x(t) = -4t^2 + 20t + 60

The number of hot dogs sold per hour is given by x

Charge per hot dog = $2

An expression of revenue per hour,R, as a function of the number of hot dogs sold per hour, x, is therefore: R(x) = 2x

b) x(t) = -4t^2 + 20t + 60

R(x(t)) = 2(x(t))

R(x(t)) = 2(-4t^2 + 20t + 60)\\R(x(t)) = -8t^2 + 40t + 120

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A company that is selling computer tablets has determined that it regularly makes a net profit of $180 for each computer tablet
Gekata [30.6K]

Answer:

Considering the prediction of people who will fill out the form and receive the refund, the company should expect its net profit to drop to:

  • <u>$174.6 per computer tablet</u>.

Step-by-step explanation:

The benefit per tablet before the rebate program is $180 per computer tablet, however, once the rebate program is implemented, 18% of people who purchase their computer tablet are expected to complete the form and obtain the VISA card, which would reduce the benefit as shown below:

  • 18% benefit from computer tablets = original benefit - refund value.
  • 18% benefit from computer tablets = $180 - $30 = $150

With this we identify that 18% of computer tablets will have a benefit reduced to $150, however, as the remaining percentage of tablets (82%) will still have the benefit of $180, the general benefit must be calculated to have a single value, as it's shown in the following:

  • Overall benefit = Percentage of tablets with reimbursement * Benefit of tablets with reimbursement + Percentage of tablets without reimbursement * Benefit of tablets without reimbursement.
  • General profit = 18% * 150 + 82% * 180
  • <u>General profit = $ 174.6 </u>

By having a $ 30 rebate on 18% of the tablets, the overall benefit drops to $174.6.

6 0
2 years ago
Find the output, yyy, when the input, xxx, is 555.<br><br> y = 5x-3y=5x−3
makkiz [27]

The output y is y=22

Explanation:

The expression is y=5 x-3

We need to determine the output y, when the value of input is x is 5.

That is, substituting x=5 in y=5 x-3, we get,

y=5(5)-3

Multiplying the value within the bracket, we have,

y=25-3

Subtracting the terms, we get,

y=22

Thus, the value of output y is y=22

4 0
1 year ago
Read 2 more answers
Identify the 17th term of a geometric sequence where a1 = 16 and a5 = 150.06. Round the common ratio and 17th term to the neares
Mashutka [201]
The geometric sequence formula is expressed as an =  a1 * r^(n-1) where n is an integer. In this case, upon substitution, 150.06 = 16 * r^(4). extracting r, r is equal to 1.75. Hence the 17th term from the formula is equal to 123802.32.


8 0
1 year ago
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The area of a square is stored in a double variable named area. write an expression whose value is length of the diagonal of the
lbvjy [14]

First of all, a bit of theory: since the area of a square is given by

A = s^2

where s is the length of the square. So, if we invert this function we have

s = \sqrt{A}.

Moreover, the diagonal of a square cuts the square in two isosceles right triangles, whose legs are the sides, so the diagonal is the hypothenuse and it can be found by

d = \sqrt{s^2+s^2} = \sqrt{2s^2} = s\sqrt{2}

So, the diagonal is the side length, multiplied by the square root of 2.

With that being said, your function could be something like this:

double diagonalFromArea(double area) {

double side = Math.sqrt(area);

double diagonal = side * Math.sqrt(2);

return diagonal;

}

3 0
1 year ago
Isaiah's family took a road trip to Mount Rushmore. Isaiah slept for the last 290 miles of the trip. If the total length of the
Leviafan [203]

Answer:

58%

Step-by-step explanation:

We need to find what percent 290 is of 500.

percent = part/whole × 100%

percent = 290/500 × 100%

percent = 58%

Answer: 58%

6 0
1 year ago
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