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Maurinko [17]
2 years ago
15

George has opened a new store and he is monitoring its success closely. He has found that this store's revenue each month can be

modeled by r(x) = x² + 5x + 14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x) = x² - 4x + 5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r-c) (5) mean about George's new store?​
A. the new store will sell 5400 items in its fifth month in business
B. The new store will have a profit of $5400 after its fifth month in business
C. The new store will have a profit of $900 after its fifth month in business
D. The new store will sell 900 items In its fifth month in business
Mathematics
1 answer:
makvit [3.9K]2 years ago
6 0

Answer:

The new store will have a profit of $5400 after its fifth month.

(R-C)(x) = (x²+5x+14)-(x²-4x+5) = x²-x²+5x--4x+14-5 = 5x+4x+14-5=9x+9

(Use 5 for x)

(R-C)(5) = 9(5) + 9 = 45+9 = 54

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For a particular diamond mine, 81% of the diamonds fail to qualify as "gemstone grade". A random sample of 92 diamonds is analyz
Fed [463]

Answer:

68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 92, p = 0.81

So

\mu = E(X) = np = 92*0.81 = 74.52

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{92*0.81*0.19} = 3.76

Find the probability that more than 79% of the sample diamonds fail to qualify as gemstone grade.

This is 1 subtracted by the pvalue of Z when X = 0.79*92 = 72.68. So

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

Z = \frac{72.68 - 74.52}{3.76}

Z = -0.49

Z = -0.49 has a pvalue of 0.3121

1 - 0.3121 = 0.6879

68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade

4 0
3 years ago
How many times larger is the 8 in 184.36 than 9,027.83
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Answer: Thus, the number with the larger value of 8 is 184.36 and it is 100 times larger.

Step-by-step explanation:

First we can find out the place value,

Then we can write,

Define Place value :

Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value. The number 42,316 is different from 61,432 because the digits are in different positions.

                     [or]

Place value of a digit can be defined as the position of the particular digit in a given number.

For Example :

The place value of 7 in 1870 is  70

Given the data,

First we use digit is :    184.36

Second we use digit is : 9027.83

Place value of 8 in First digit is  ⇒ 184.36 is 80

Place value of 8 in Second digit is ⇒ 9027.83  is 0. 8

We can solve the Ratio is :

                      Ratio = 80/ 0.8

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Therefore,

Thus, the number with the larger value of 8 is 184.36 and it is 100 times larger.

Learn more about event correlation here: brainly.com/question/17103145

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4 0
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Answer:

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Step-by-step explanation:

Step 1- Substitute the variable

g(3)= -5(3)+13

Step 2- Multiply

g(3)= -5(3)+13

Step 3- Add

g(3)= -15+13

Conclusion-

g(3)= -2

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