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Dmitry_Shevchenko [17]
3 years ago
13

The function of c=p+. 07p relates the price of an item p with its cost c after 7% tax and s added. A student has $12.50. What is

the cost of the most expensive item he can buy?
Mathematics
1 answer:
disa [49]3 years ago
7 0

If you have $12.50 to spend, what is the cost of the most expensive item that you can buy? ... The sales tax in TN on nonfood items is 7%. .... Write a function rule to describe each situation The sellings price s(c) after a 45% markup ..... you want to write a program to calculate the total cost of an item that has sales tax added.


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Vaselesa [24]

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2 years ago
Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting fl
Vikki [24]

Answer:

Height: 3/2 inches

Length:  12 inches

Width: 4 inches

Step-by-step explanation:

Let x is the side length of the square

The height of the box by cutting squares off :x

  • The new length of the cardboard = 15 -2x (because we cut from 4 corners)
  • The new width of the cardboard = 7 -2x (because we cut from 4 corners)

The new volume of it is:

V = (15 -2x) (7 -2x) x

<=> V = 4x^3 -44x^2 +105x

To maximum volume, we use the first derivative of the volume

\dfrac{dV}{dx} = 0

<=> 12x^2-88x+105=0

<=> \left(2x-3\right)\left(6x-35\right) = 0

<=> 2x -3 = 0 or 6x -35 = 0

<=> x = 3/2 or x = 35/6

To determine which value of x gives a maximum, we evaluate

\dfrac{d^2V}{dx^2} = 24x -88

  • If  x = 3/2, we have:

\dfrac{d^2V}{dx^2}= 24(3/2) -88  = -52

  • If x = 35/6, we have:

\dfrac{d^2V}{dx^2} = 24(35/6) -88 = 52

We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.

So the dimensions (in inches) of the box is:

Height: 3/2 inches

Length: 15-2(3/2) = 12 inches

Width: 7 - 2(3/2) = 4 inches

5 0
2 years ago
5 b.) Bill swims 2/3 of a lap in 7 minute.<br> What is his speed in laps per minute?
Arlecino [84]

Answer:

.095 laps per minute (if you need this answer as well 10.5 minutes per lap)

Step-by-step explanation:

(2/3)/7 =.095238 this is laps per min

7/(2/3)= 10.5 this is minutes per lap

I hope this is what you were looking for.

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A survey of students' favorite sports was taken from a random sample of
White raven [17]

Answer:

129

Step-by-step explanation:

Considering the survey to be representative, you can simply multiply the share of students <em>p</em> preferring “Track & Field” with the whole school population at the same time to estimate the number of such students in the whole school.

First we need to find the relative share <em>p</em> of such answers in the study by dividing it by the sum of answers, assuming that the table is complete for that random sample:

<em>p</em> = 4/(8 + 5 + 4) = 4/17

Then for the whole school we get 550 <em>p</em> ≈ 129.4

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Write an equivalent expression by factoring.<br><br>5x + 15​
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Answer:

5(x+3)........ ...........

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