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Ganezh [65]
3 years ago
8

As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast operation,

the prospective owners have projected:
Monthly fixed cost (loan payment, taxes, insurance, maintenance) $6000
Variable cost per occupied room per night $ 20
Revenue per occupied room per night $ 75
a. Write the expression for total cost per month. Assume 30 days per month.
b. Write the expression for total revenue per month, first using the general variables, and second including the values of known variables).
c. If there are 12 guest rooms available, can they break even? What would be the profit with 12 rooms?
d. What percentage of rooms would need to be occupied, on average, to break even?
Mathematics
1 answer:
Lunna [17]3 years ago
6 0

Answer:

Instructions are below.

Step-by-step explanation:

Giving the following information:

Monthly fixed cost= $6,000

Variable cost per occupied room per night= $20

Revenue per occupied room per night= $75

Fi<u>rst, we need to structure the total cost formula:</u>

Total cost= 6,000 + 20*x

x= occupied room

<u>Now, we can find the expression for total revenue:</u>

Revenue= selling price per unit*units - fixed cost - unitary variable cost*units

Revenue= 75*x - 6,000 - 20*x

<u>I assume that the 12 rooms will be occupied for the 30 days:</u>

Revenue= 75*(12*30) - 6,000 - 20*(12*30)

Revenue= $13,800

<u>Finally, we need to determine the break-even point in units:</u>

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 6,000 / (75 - 20)

Break-even point in units= 109 rooms

On percentage= (109/360)*100= 30.28%

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You select a card at random from the cards that make up the word “replacement”. Without replacing the card, you choose a second
musickatia [10]
Replacement = 11 total

probability of choosing a consonant = 7/11
without replacing the card
probability of choosing an e = 3/10

probability of choosing both = 7/11 * 3/10 = 21/110 <===
8 0
3 years ago
A new roller coaster at an amusement park requires individuals to be at least​ 4' 8" ​(56 ​inches) tall to ride. It is estimated
Maksim231197 [3]

Answer:

a) 34.46% of​ 10-year-old boys is tall enough to ride this​ coaster.

b) 78.81% of​ 10-year-old boys is tall enough to ride this​ coaster

c) 44.35% of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 54, \sigma = 5

a. What proportion of​ 10-year-old boys is tall enough to ride the​ coaster?

This is 1 subtracted by the pvalue of Z when X = 56.

So

Z = \frac{X - \mu}{\sigma}

Z = \frac{56 - 54}{5}

Z = 0.4

Z = 0.4 has a pvalue of 0.6554

1 - 0.6554 = 0.3446

34.46% of​ 10-year-old boys is tall enough to ride this​ coaster.

b. A smaller coaster has a height requirement of 50 inches to ride. What proportion of​ 10-year-old boys is tall enough to ride this​ coaster?

This is 1 subtracted by the pvalue of Z when X = 50.

Z = \frac{X - \mu}{\sigma}

Z = \frac{50 - 54}{5}

Z = -0.8

Z = -0.8 has a pvalue of 0.2119

1 - 0.2119 = 0.7881

78.81% of​ 10-year-old boys is tall enough to ride this​ coaster.

c. What proportion of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a?

Between 50 and 56 inches, which is the pvalue of Z when X = 56 subtracted by the pvalue of Z when X = 50.

From a), when X = 56, Z has a pvalue of 0.6554

From b), when X = 50, Z has a pvalue of 0.2119

0.6554 - 0.2119 = 0.4435

44.35% of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a

5 0
3 years ago
Which graph represents 49x2 + 4y2 + 196x – 40y + 100 = 0?
GREYUIT [131]

Answer:

D

Step-by-step explanation:

8 0
3 years ago
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Ira Lisetskai [31]

Answer:

1,2 and 4 are equivalents. 3 is not equivalent

2P-I, mark that one :l

Step-by-step explanation:

3 0
2 years ago
the germination rate for zinnia seeds is 78%. this means that 78 out of every 100 seeds will sprout and grow. if james wants 60
Harlamova29_29 [7]

Answer: 77 seeds


Step-by-step explanation:

Given: The germination rate for zinnia seeds =78%

Let x be the total number of seeds he planted, then

The seeds germinated= 78% of x

⇒The seeds germinated= 0.78x

If James wants 60 zinnia plants for his yard, then it will give the equation

0.78x=60\\\Rightarrow\ x=\frac{60}{0.78}\\\Rightarrow\frac{6000}{78}\\\Rightarrow\ x=76.92307\aprrox77

Hence, he should plant 77 seeds .


5 0
3 years ago
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