Write an algebraic equation and solve each problem.

Determine the domain and range of the graph.

nirvana33 [79]

Answer:

Domain [-4,4]

Range [-2,2]

Step-by-step explanation:

The domain is the x-values of the graph and the range in the y-values. When writing domain and range it should be from least to greatest. So to find the domain find the lowest x-value on the graph and then the highest. Next, do the same for y-values. Finally, either surround each value with parentheses or bracket, the difference is that brackets mean that value is included, while parentheses mean that value is not actually on the graph.

In this case, the lowest x-value is -4 and the highest is 4, both values are included as signified by the closed circles, therefore the domain is [-4,4]. The lowest y value is -2 and the highest is 2, both are included, therefore the range is [-2,2].

4 0

3 years ago

The scores on the GMAT entrance exam at an MBA program in the Central Valley of California are normally distributed with a mean

Kaylis [27]

Answer:

58.32% probability that a randomly selected application will report a GMAT score of less than 600

93.51% probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600

98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600

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 normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 591, \sigma = 42$

What is the probability that a randomly selected application will report a GMAT score of less than 600?

This is the pvalue of Z when X = 600. So

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

$Z = \frac{600 - 591}{42}$

$Z = 0.21$

$Z = 0.21$ has a pvalue of 0.5832

58.32% probability that a randomly selected application will report a GMAT score of less than 600

What is the probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600?

Now we have $n = 50, s = \frac{42}{\sqrt{50}} = 5.94$

This is the pvalue of Z when X = 600. So

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

$Z = \frac{600 - 591}{5.94}$

$Z = 1.515$

$Z = 1.515$ has a pvalue of 0.9351

93.51% probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600

What is the probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600?

Now we have $n = 50, s = \frac{42}{\sqrt{100}} = 4.2$

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

$Z = \frac{600 - 591}{4.2}$

$Z = 2.14$

$Z = 2.14$ has a pvalue of 0.9838

98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600

8 0

3 years ago

at a party 2/5 of the pizzas ordered had pepperoni. The kids ate only 1/3 of the pepperoni pizza while the parents ate all of th

Ahat [919]

2/5*1/3=
2/15 is the answer.

3 0

4 years ago

Read 2 more answers

Sasha sells T-shirts. Each day she earns a set amount, plus a commission. Choose the linear function f to determine Sasha's pay.

fenix001 [56]

Answer:

a. The correct option is f(x) = 3x + 65.

b. Sasha earns 146 that day.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf file for the complete question.

The explanation to the answer is now given as follows:

a. Choose the linear function f to determine Sasha's pay.

Note: See the attached excel file to see the determination of the correct linear function f to determine Sasha's pay.

From the list of linear functions f given in the question, x represents the number of T-shirts Sasha sold in one day.

Therefore, the correct linear function f to determine Sasha's pay can be determined by simply substituting number of T-shirts for x in each of the linear function f to see which one is the same as the table provided in the question.

From the attached excel file, the correct option is f(x) = 3x + 65. This is indicated in bold red color in the attached excel file.

b. If Sasha sells 27 T-shirts in one day how much money does she earn that day?

This can be calculated using f(x) = 3x + 65 which is the correct linear function f determined in part a above and substituting 27 for x as follows:

Sasha’s earning = 3(27) + 65

Sasha’s earning = (3 * 27) + 65

Sasha’s earning = 81 + 65

Sasha’s earning = 146

Therefore, Sasha earns 146 that day.

Download xlsx

5 0

3 years ago

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<img src="https://tex.z-dn.net/?f=9X%5E2-12X%2B4%3D0" id="TexFormula1" title="9X^2-12X+4=0" alt="9X^2-12X+4=0" align="absmiddle"

balu736 [363]

$9x^2-12x+4=0$

$(3x)^2-2\cdot 2\cdot3x+2^2=0$

$(3x-2)^2=0, but...(3x-2)^2 \geq 0$ , ∨ x∈R

$So, (3x-2)^2=0$

$3x-2=0$ ⇒ $3x=2$ ⇒ $\boxed { x= \frac{2}{3} }$

8 0

3 years ago

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