Factor 28y + 36.<br><br> Write your answer as a product with a whole number greater than 1.

There are 50 students in a calculus class. The amount of time needed for the instructor to grade a randomly chosen midterm exam

natta225 [31]

Answer:

14.46% probability that the instructor can finish grading in 4 and a half hours

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.

For sums of n values from a distribution, the mean is $n\mu$ and the standard deviation is $s = \sqrt{n}\sigma$

In this problem, we have that:

$\mu = 6*50 = 300, s = \sqrt{50}*4 = 28.2843$

What is the probability that the instructor can finish grading in 4 and a half hours

Four and half hours is 4.5*60 = 270.

So this probability is the pvalue of Z when X = 270.

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

By the Central Limit Theorem

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

$Z = \frac{270 - 300}{28.2843}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446

14.46% probability that the instructor can finish grading in 4 and a half hours

8 0

3 years ago

The width of a rectangular field is 20 feet less than its length. The area of the field is 12,000 ft? What is the length of the

Scilla [17]

Answer:

The answer is 120 feet.

Step-by-step explanation:

The area of the field (A) is:

A = w · l (w - width, l - length)

It is known:

A = 12,000 ft²

l = w - 20

So, let's replace this in the formula for the area of the field:

12,000 = w · (w - 20)

12,000 = w² - 20

⇒ w² - 20w - 12,000 = 0

This is quadratic equation. Based on the quadratic formula:

ax² + bx + c = 0 ⇒

In the equation w² - 20w - 12,000 = 0, a = 1, b = -20, c = -12000

Thus:

So, width w can be either

or

Since, the width cannot be a negative number, the width of the field is 120 feet.

6 0

3 years ago

Read 2 more answers

Maxwell used the diagram below to help determine 75% of 24. Which expression could Maxwell have used to find 75% of 24?

jeka94

Answer:

C.

Step-by-step explanation:

Just finished the Unit Test Review on edge2020

8 0

3 years ago

Read 2 more answers

A submarine is positioned at 300 feet below sea level. A bird is flying 100 foot above sea

alexandr1967 [171]

Answer:

h = 400 ft

The bird is 400 ft above the submarine

Step-by-step explanation:

Given;

The submarine is 300 feet below sea level

Vertical distance between submarine and sea level h1 = 300 feet

The bird is flying at 100 feet above sea level

Vertical distance between the sea level and the bird h2 = 100 feet

The total vertical distance between the bird and the submarine is the sum of the vertical distance between submarine and sea level and the vertical distance between the sea level and the bird.

h = h1 + h2

h = 300 ft + 100 ft

h = 400 ft

The bird is 400 ft above the submarine

6 0

3 years ago

Which value is equivalent to x-7/7-x

Sholpan [36]

Answer:

$\large\boxed{\dfrac{7-x}{x-7}=-1}$