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egoroff_w [7]
3 years ago
8

A company rents out 17 food booths and 26 game booths at the county fair. The fee for a food booth is $200 plus $5 per day. The

fee for a game booth is $95 plus $10 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid
Mathematics
2 answers:
natka813 [3]3 years ago
7 0
I think
d = (17x200 + 17x5) + (26x95 + 95x10)
aev [14]3 years ago
5 0

Answer:

345d+5870

Step-by-step explanation:

For reference, the * symbol is a multiplication symbol.

Let's break this problem up for simplicity.

1) We recognize that there are 17 food booths.

The fee for a single food booth is $200 up front, with a $5 bonus charge with each day that passes.

The fair lasts for <em>d</em> days, where the booths are rented out the entire time.

From these statements, we derive the equation: $(200+d*5).

For 17 booths, it would be 17 times that. Now, we have 17(200+5d).

2) Now, we recognize that there are 26 game booths.

The fee for a game booth is $95 up front, with a $10 bonus charge per day.

Using the same logic, with <em>d</em> days, for one booth, we derive the equation: $(95+10d).

For 26 booths, it would be 26 times that. We have 26(95+10d).


17(200+5d)+26(95+10d)

Multiply it out.

=> 3400+85d+2470+260d

=>345d+5870


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dangina [55]

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7. no

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3 years ago
Read 2 more answers
g A manufacturer is making cylindrical cans that hold 300 cm3. The dimensions of the can are not mandated, so to save manufactur
sdas [7]

Answer:

The dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

Step-by-step explanation:

A cylindrical can holds 300 cubic centimeters, and we want to find the dimensions that minimize the cost for materials: that is, the dimensions that minimize the surface area.

Recall that the volume for a cylinder is given by:

\displaystyle V = \pi r^2h

Substitute:

\displaystyle (300) = \pi r^2 h

Solve for <em>h: </em>

\displaystyle \frac{300}{\pi r^2} = h

Recall that the surface area of a cylinder is given by:

\displaystyle A = 2\pi r^2 + 2\pi rh

We want to minimize this equation. To do so, we can find its critical points, since extrema (minima and maxima) occur at critical points.

First, substitute for <em>h</em>.

\displaystyle \begin{aligned} A &= 2\pi r^2 + 2\pi r\left(\frac{300}{\pi r^2}\right) \\ \\ &=2\pi r^2 + \frac{600}{ r}  \end{aligned}

Find its derivative:

\displaystyle A' = 4\pi r - \frac{600}{r^2}

Solve for its zero(s):

\displaystyle \begin{aligned} (0) &= 4\pi r  - \frac{600}{r^2} \\ \\ 4\pi r - \frac{600}{r^2} &= 0 \\ \\ 4\pi r^3 - 600 &= 0 \\ \\ \pi r^3 &= 150 \\ \\ r &= \sqrt[3]{\frac{150}{\pi}} \approx 3.628\text{ cm}\end{aligned}

Hence, the radius that minimizes the surface area will be about 3.628 centimeters.

Then the height will be:

\displaystyle  \begin{aligned} h&= \frac{300}{\pi\left( \sqrt[3]{\dfrac{150}{\pi}}\right)^2}  \\ \\ &= \frac{60}{\pi \sqrt[3]{\dfrac{180}{\pi^2}}}\approx 7.25 6\text{ cm}   \end{aligned}

In conclusion, the dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

7 0
3 years ago
Is 100 t-shirts for $428.00 proportional to 3,000 t-shirts for $12,180.00?
Aleks04 [339]

No 3,000 t-shirts are = to 12,840.

8 0
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