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mixas84 [53]
4 years ago
6

To rent a certain meeting room, a college charges a reservation fee of $19 and an additional fee of $6 per hour. The chemistry c

lub wants to spend less than $91 on renting a room. What are the possible numbers of hours the chemistry club could rent the meeting room? Use t for the number of hours. Write your answer as an inequality solved for t,
Mathematics
1 answer:
ivanzaharov [21]4 years ago
3 0
T= # of rental hours


Multiply number of hours rented by the cost per hour, add that total to the reservation fee. The total needs to be less than $91.


Reservation + ($ per hr * # hrs) < $91

$19 + $6t < $91
subtract 19 from both sides

6t < 72
divide both sides by 6

t < 12


ANSWER: To spend less than $91, they need to rent the room less than 12 hours.

Hope this helps! :)
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A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per
dexar [7]

Answer:

The total revenue is TR=580x-10x^2.

The marginal revenue is MR=580-20x.

The fixed cost is $900.

The marginal cost function is MC=50x+300.

Step-by-step explanation:

The Total Revenue (TR) received from the sale of x goods at price p is given by

                                                         TR=p\cdot x

The Marginal Revenue (MR) is the derivative of total revenue with respect to demand and is given by

                                                       MR=\frac{d(TR)}{dx}

From the information given we know that the price they can sell cakes is given by the function p=580-10x, where x is the number of cakes sold per day.

So, the total revenue is

TR=(580-10x)\cdot x\\TR=580x-10x^2

And the marginal revenue is

MR=\frac{d}{dx}(580x-10x^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\MR=\frac{d}{dx}\left(580x\right)-\frac{d}{dx}\left(10x^2\right)\\\\MR=580-20x

The Fixed Cost (FC) is the amount of money you have to spend regardless of how many items you produce.

The Marginal Cost (MC) function is the derivative of the cost function and is given by

                                                   MC=\frac{d(TC)}{dx}

We know that the total cost function of the company is given by C=(30+5x)^2, which it is equal to

\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\a=30,\:\:b=5x\\\\\left(30+5x\right)^2=30^2+2\cdot \:30\cdot \:5x+\left(5x\right)^2=25x^2+300x+900\\\\C=25x^2+300x+900

From the total cost function and applying the definition of fixed cost, the fixed cost is $900.

And the marginal cost function is

MC=\frac{d}{\:dx}\left(25x^2+300x+900\right)\\\\MC=\frac{d}{dx}\left(25x^2\right)+\frac{d}{dx}\left(300x\right)+\frac{d}{dx}\left(900\right)\\\\MC=50x+300+0=50x+300

4 0
3 years ago
Which graph fits y=2x+1?
alekssr [168]

Answer:

C

Step-by-step explanation:

4 0
3 years ago
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PLEASE HELP IM TIMED<br> If 3^2x+1=3x+^5 what is the value of x
atroni [7]

The correct answer is X=6

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4 years ago
You estimate that a baby pig weighs 20 pounds. The actual weight of the baby pig is 16 pounds. Find the percent error.
WARRIOR [948]
20-16=4
16/4=4
1/4=.25
.25=25%
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3 years ago
Jen has read 4/5 of a book. The next day she read 2/3 of what she had left. What fraction of the book is left to read?
Nostrana [21]

Answer:

1/15

Step-by-step explanation:


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3 years ago
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