Are the graphs of the lines in the pair parallel? Explain.<br><br> y = 3/7x + 11<br>

A process is producing a particular part where the thickness of the part is following a normal distribution with a µ = 50 mm and

Hitman42 [59]

Answer:

0.13% probability that this selected sample has an average thickness greater than 53

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 $s = \frac{\sigma}{\sqrt{n}}$ .

In this problem, we have that:

$\mu = 50, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1$

What is the probability that this selected sample has an average thickness greater than 53?

This is 1 subtracted by the pvalue of Z when X = 53. So

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

By the Central Limit Theorem

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

$Z = \frac{53 - 50}{1}$

$Z = 3$

$Z = 3$ has a pvalue of 0.9987

1 - 0.9987 = 0.0013

0.13% probability that this selected sample has an average thickness greater than 53

5 0

3 years ago

How many square feet of out door carpet will we need for this hole

Vadim26 [7]

Hey! Let me help you on this one.

As you can see, this is a very complex shape, and this might confuse you at first. Don't fear, there is a very easy and fun way to solve it.

Take a closer look at the problem. Do you notice anything? It consists of few different shapes that might be much easier for you to find area of.

For example, as you can see on the image I have sent you, these are the shapes present in the figure.

On this image, only two types of figures are present - triangle and a rectangle. Both shapes have a very easy area formula.

Triangle - $S= \frac{a*b}{2}$

Rectangle - $S=a*b$

Using these formulas, let's find the area of this complex figure by solving for each individual shape, and then, adding everything together.

Triangle at the bottom has a side of 4 feet, and an unknown second side. We can find it by getting the difference of 12 feet and 8 feet.

Why you might ask? Well, if you look at it closer, the difference is exactly the length of the side we need.

$12-8=4$

Neat! It's four as well. Let's start solving for its area.

$S= \frac{4*4}{2}$
$S=8$

Area of the first triangle is 8 feet squared. Let's get into the second triangle. It's right above this one!

Length of its right side is 3 feet, and the length of the bottom side is the same as the one we found few steps back - four feet.

$S= \frac{4*3}{2}$
$S= 6$

Awesome! Area of the second triangle is 6 feet squared. Let's take a closer look at the last figure - rectangle.

$S=8*3$
$S=24$

Area of the rectangle is 24 feet squared. Done, we have all the areas of individual shapes. Let's add them together.

$24+6+8=38$

Answer: The area of this figure is 38 feet squared

5 0

4 years ago

18

GalinKa [24]

Answer:

18

ZAOC and ZCOB are supplementary angles.

Find the

6 0

3 years ago

Every evening Jenna empties her pockets and puts her change in a jar. At the end of the week she counts her money. One week she

Sergeeva-Olga [200]

A) .10 d + .25 q = 7.75
B) d + q = 40

Multiplying B) by -.10
B) -.10d -.10q = -4.0
Then adding this to A)
A) .10 d + .25 q = 7.75
.15q = 3.75

Quarters = 25
Therefore, dimes = 15
***************************************************
Double-Check
A) .10 d + .25 q = 7.75
A) .10 * 15 d + .25 * 25 = 7.75
A) 1.50 + 6.25 = 7.75

Correct!!

6 0

3 years ago

Paula kitten weighs 3 1/2 pounds write this weight in the boxes using pounds and ounces.

Elenna [48]

Answer:

Step by step explanation

First, we have to convert 3 1/2 into a decimal, so we have to do the following:

1/2 = 1 divided by 2 3 1/2 = 3 + (1÷2) = 0.5 (1 ÷ 2 done by long division)

Then we add the whole number.

3 + 0.5 = 3.5

Next, we multiply

3.5 x 16 = 56 ounces.

3 0

3 years ago

Read 2 more answers

Are the graphs of the lines in the pair parallel? Explain. y = 3/7x + 11 –3x + 7y = 13