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Hatshy [7]
3 years ago
15

To make a profit, a company’s revenue must be greater than its operating costs. The company’s revenue is modeled by the expressi

on 7.5x – 100, where x represents the number of items sold. The company’s operation costs are modeled by the expression 79.86 + 5.8x. How many items does the company need to sell to make a profit? The inequality that will determine the number of items that need to be sold to make a profit is ? The solution to the inequality is ? The company must sell at least?  items to make a profit.
Mathematics
2 answers:
snow_lady [41]3 years ago
9 0

Answer:

1. 7.5x - 100 > 79.86 + 5.8x (Option A)

2. x > 105.8 (Option D)

3. 106 (Option D)

Step-by-step explanation:

Just completed the assignment and got 100%. Hope this helps :)

valina [46]3 years ago
8 0
Revenue = 7.5x - 100
Operation Costs = 5.8x + 79.86

To break even, operation cost = Revenue
⇒ 7.5x - 100 = 5.8x + 79.86
7.5x = 5.8x + 179.86 (Add 100 to both sides)

7.5x - 5.8x = 179.86
1.7x = 179.86
x = 105.8

This implies that the company will need to sell at least 106 items to make a profit.

The inequality that will determine the number of items at need to be sold to make a profit is x ≥ 106

The solution to the inequality is as follows

Revenue = 7.5x - 100
if x =106
Revenue = 7.5(106) - 100
Revenue = 695

Operational Cost = 5.8x + 79.86
if x = 106
Operational Cost = 5.8(106) + 79.86
Operational Cost = 694.66

Profit ≥ (695 - 694.66)
Profit ≥ 0.34

The company must sell at least 106 items to make a profit.
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What is 56 1/2% written as a fraction in the simplest form?<br>​
Eduardwww [97]

Answer:

       7 / 28

Step-by-step explanation:

7 / 28 = 0 . 28

5 0
3 years ago
Suppose monthly rental prices for a one-bedroom apartment in a large city has a distribution that is skewed to the right with a
omeli [17]

Answer:

a) Nothing, beause the distribution of the monthly rental prices are not normal.

b) 1.43% probability that the sample mean rent price will be greater than $900

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

(a) Suppose a one-bedroom rental listing in this large city is selected at random. What can be said about the probability that the listed rent price will be at least $930?

Nothing, beause the distribution of the monthly rental prices are not normal.

(b) Suppose a random sample 30 one-bedroom rental listing in this large city will be selected, the rent price will be recorded for each listing, and the sample mean rent price will be computed. What can be said about the probability that the sample mean rent price will be greater than $900?

Now we can apply the Central Limit Theorem.

\mu = 880, \sigma = 50, n = 30, s = \frac{50}{\sqrt{30}} = 9.1287

This probability is 1 subtracted by the pvalue of Z when X = 900.

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

By the Central Limit Theorem

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

Z = \frac{900 - 880}{9.1287}

Z = 2.19

Z = 2.19 has a pvalue of 0.9857

1 - 0.9857 = 0.0143

1.43% probability that the sample mean rent price will be greater than $900

8 0
3 years ago
7. A cylindrical tank can hold 2279.64 cubic feet of water. The radius of the tank is 11 feet. What is the height of the tank?
aliina [53]

Answer:

r = 8.12

Step-by-step explanation:

The volume for a cylinder is V=πr^2h therefore,

v = 2279.64

h = 11ft

r = ?

2279.64 = πr^2 * 11

\frac{2279.64}{11}= {\pi r^2} \\

207.24 = πr^2

\frac{207.24}{\pi} =r^2\\\\66 = r^2\\\\\sqrt{66} = r\\\\\\8.12 = r

3 0
2 years ago
What is 25×10 to the power of 6 in standard form
Vsevolod [243]

So, 10^6 = 1,000,000 and 25*1,000,000 is equivalent to 25,000,000.

6 0
2 years ago
Which of the following relations are not functions? Select all that apply
alekssr [168]
A,b,c, d that’s the answer
5 0
2 years ago
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