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3 years ago

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Mrs. Gustafsson's English class is taking an exam that is made up of short-response questions and essay questions. There are 22

questions that are worth 100 points in total. Each short-response question is worth 4 points, and each essay question is worth 10 points. How many short-response question are on the exam? Select one: A. 14 B. 2 C. 18 D. 2
I need help with this ASAP, 99 points

1 answer:

mestny [16]3 years ago

5 0

Answer:

Short-response question = 20.

Step-by-step explanation:

Let x be number of short response questions and y be the number of essay questions.

We have been given that there are 22 questions that are worth 100 points in total. Each short-response question is worth 4 points, and each essay question is worth 10 points. Using our given information we can form a system of equations as:

$x+y=22...(1)$

$4x+10y=100...(2)$

Now we will solve our system of equations using substitution method.

From equation 1 we will get,

$y=22-x$

Upon substituting $y=22-x$ in equation 2 we will get,

$4x+10(22-x)=100$

$4x+220-10x=100$

$4x-10x=100-220$

$-6x=-120$

$x=\frac{-120}{-6}$

$x=20$

Therefore, there are 20 short-response questions on the exam.

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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

The function h(x) is given below:

g100num [7]

Step-by-step explanation:

The domain and range of a function and its inverse are inverted i.e. The domain of the function will become range of its inverse and the range of the function will become the domain of its inverse.

When representing the function in ordered pairs, the first values in the pair represents the domain and second values represent the range of the function.

h(x) = {3,5),(5,-7)(6,-9)(10,-12)(12,16)}

Domain of h(x) is: {3, 5, 6, 10, 12}

Range of h(x) is: (5, -7, -9, -12, 16}

So,

Domain of $h^{-1}(x)$ = Range of h(x) = (5, -7, -9, -12, 16}

Range of $h^{-1}(x)$ = Domain of h(x) = {3, 5, 6, 10, 12}

Therefore, $h^{-1}(x)$ will be represented as:

{(5,3), (-7,5), (-9, 6), (-12, 10), (16,12)}

It seems like you have made some error while writing the original function because of which we are not getting an exact match in the answer. However by looking at the answers, option B is the nearest most and seems the correct answer.

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3 years ago

Nik and his friend bought shares of stock at the rate of $32 per share. For $3,520, Nik's friend bought 10 fewer shares than Nik

Svetradugi [14.3K]

Answer:

#1-List all outcomes for choosing the digit. *

0)

O

A: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

O

B: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

O

C: 1, 2, 3, 4, 5, 6, 7, 8, 9

OD: a number

O

Both B and C

Step-by-step explanation:

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I would really like to have some help and know how to do this

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If K=C+273.15
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3 years ago

A hungry elf ate 14 of your muffins Thats was 7/10 of all of them! how many are left?

Dennis_Churaev [7]

6 muffins are left. Here's how you do it:
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Then multiply it by 3 which equals 6
hope this helps!

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3 years ago