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Troyanec [42]
3 years ago
11

A company rents out 18 food booths and 27 game booths at the county fair. The fee for a food booth is $50 plus $6 per day. The f

ee for a game booth is $65 plus $8 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
1 answer:
Ymorist [56]3 years ago
7 0

Answer:

$2655 + $324d

Step-by-step explanation:

total cost of a booth = fixed cost + (variable cost x number of days)

Fixed costs are costs that do not vary with output

Variable costs are costs that vary with production

cost of 18 food booths = 18(50 + 6d) = 900 + 108d

cost of 27 game booths = 27(65 + 8d) = 1755 + 216d

Add the total cost of the food and game booths together 900 + 1755 = 2655

108d + 216d = 324d

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How many terms are in the arithmetic sequence 9, 2, −5, . . . , −187?
Fantom [35]
9, 2, -5... so is going down by 7 each time, meaning the "common difference" is -7.

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=9\\
d=-7\\
a_n=-187
\end{cases}
\\\\\\
-187=9+(n-1)(-7)\implies -187=9-7n+7
\\\\\\
7n=9+7+187\implies 7n=203\implies n=\cfrac{203}{7}\implies \boxed{n=29}
4 0
3 years ago
Max earned a 85% on his test. if there were 40 questions on the test how many did he get correct?
wel
Max would have had to have gotten 34 out of 40 questions correct. Here's why:

\frac{x}{40} =  \frac{85}{100} 

(40)(85) = (x)(100)



3400 = 100x

 \frac{3400}{100} = x


34 =x

3 0
3 years ago
A research group needs to determine a 90% confidence interval for the mean repair cost for all car insurance small claims. From
lutik1710 [3]

Answer:

a) z = 1.645

b) The should sample at least 293 small claims.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.9}{2} = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.05 = 0.95, so z = 1.645, which means that the answer of question a is z = 1.645.

Now, find  the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

(b) If the group wants their estimate to have a maximum error of $12, how many small claims should they sample?

They should sample at least n small claims, in which n is found when

M = 12, \sigma = 124.88. So

M = z*\frac{\sigma}{\sqrt{n}}

12 = 1.645*\frac{124.88}{\sqrt{n}}

12\sqrt{n} = 205.43

\sqrt{n} = \frac{205.43}{12}

\sqrt{n} = 17.12

\sqrt{n}^{2} = (17.12)^{2}

n = 293

The should sample at least 293 small claims.

8 0
3 years ago
A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in
Andreyy89
So, she has 3hrs to grade all papers, for 35 students.. alrite.

the first 5, she does them in 30minutes.. what's the speed rate? well, 5/30 or 1/6

now, she has still 2 hours and a half, or 150 minutes, to do the remaining 30 papers... she has to work at a rate of 30/150 then... which is 1/5 simplified.

now if we take 1/6 as the 100%, what is 1/5 in percentage then?

\bf \begin{array}{ccllll}
rate&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
\frac{1}{6}&100\\\\
\frac{1}{5}&x
\end{array}\implies \cfrac{\frac{1}{6}}{\frac{1}{5}}=\cfrac{100}{x}\implies \cfrac{1}{6}\cdot \cfrac{5}{1}=\cfrac{100}{x}\implies \cfrac{5}{6}=\cfrac{100}{x}
\\\\\\
x=\cfrac{6\cdot 100}{5}\implies x=120

so 1/5 is 120% in relation to 1/6... meaning the rate of 1/5 she needs to move through, namely 1 paper every 5 minutes, is 20% faster than 1/6.
8 0
3 years ago
Read 2 more answers
Would appreciate the help
raketka [301]

Answer:

x° = 37°

Step-by-step explanation:

* Lets revise some facts of a circle

- The secant is a line intersect the circle in two points

- If two secants intersect each other in a point outside the circle,

 then the measure of the angle between them is half the difference

 of the measures of their intercepted arcs

* Now lets solve the problem

- There is a circle

- Two secants of this circle intersect each other in a point outside

  the circle

∴ The measure of the angle between them = 1/2 the difference of the

  measures of their intercepted arcs

∵ The measure of the angle between them is x°

∵ The measures of their intercepted arcs are 26° and 100°

- Use the rule above to find x

∴ x° = 1/2 [ measure of the large arc - measure of small arc]

∵ The measure of the large arc is 100°

∵ The measure of the small arc is 26°

∴ x° = 1/2 [100 - 26] = 1/2 [74] = 37°

∴ x° = 37°

4 0
3 years ago
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