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3 years ago

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Joaquun is thinking hard about equations and inequalitjes an comes up with this idea: Jf 45+47=t, then t=45+47. so, If 45+47<

t, then t=45+47. Is he right? Explain Why or why not

1 answer:

timama [110]3 years ago

8 0

If 45 + 47 = t, then t = 45 + 47.....correct

if 45 + 47 < t , then t = 45 + 47....incorrect

45 + 47 < t
92 < t .....this is saying that t is greater then 92

t = 45 + 47
t = 92...this is saying t is equal to 92 (not greater)

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A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat

zmey [24]

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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 question, we have that:

$\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5$

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

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

X = 205

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

$Z = \frac{205 - 200}{5}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413.

X = 195

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

$Z = \frac{195 - 200}{5}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

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

$Z = \frac{210 - 200}{5}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772.

X = 195

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

$Z = \frac{190 - 200}{5}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

7 0

3 years ago

a small bridge sit atop for cube shaped powers that all have the same volume. The combined volume of the four pillars is 503 how

Natasha_Volkova [10]

Answer:

60 inches long are the sides of the pillars.

Step-by-step explanation:

Given : A small bridge sits atop four cube shaped pillars that all have the same volume. the combined volume of the four pillars is 500 ft cubed.

To find : How many inches long are the sides of the pillars?

Solution :

Refer the attached picture below for Clarence of question.

The volume of the cube is $V=a^3$

Where, a is the side.

The combined volume of the four pillars is 500 ft cubed.

The volume of each cube is given by,

$V=\frac{500}{4}=125\ ft^3$

Substitute in the formula to get the side,

$125=a^3$

$a=\sqrt[3]{125}$

$a=5\ ft$

We know, 1 feet = 12 inches

So, 5 feet = $5\times 12=60$ inches

Therefore, 60 inches long are the sides of the pillars.

6 0

3 years ago

The length of CD is 12 units C’D’ is the image of CD under a dilation with a scale factor of n.Which of these are true?

Korvikt [17]

Answer: FIrst option, Fourth option and Fifth option.

Step-by-step explanation:

First it is important to know the definition of "Dilation".

A Dilation is defined as a transformation in which the Image (which is the figure obtained after the transformation) and the Pre-Image (this is the original figure, before the transformations) have the same shape, but their sizes are different.

If the length of CD is dilated with a scale factor of "n" and it is centered at the origin, the length C'D' will be:

$C'D'=nCD=(n)(12\ units)$

Therefore, knowing this, you can determine that:

1. If $n=\frac{3}{2}$ , you get:

$C'D'=(\frac{3}{2})(12\ units)=18\ units$

2. If $n=4$ , then the length of C'D' is:

$C'D'=(4)(12\ units)=48\ units$

3. If $n=8$ , then:

$C'D'=(8)(12\ units)=96\ units$

4. If $n=2$ , then, you get that the lenght of C'D' is:

$C'D'=(2)(12\ units)=24\ units$

5. If $n=\frac{3}{4}$ , the length of C'D' is the following:

$C'D'=(\frac{3}{4})(12\ units)=9\ units$

8 0

3 years ago

An item that was selling for $80 is reduced to $42. Find the percent decrease in

Westkost [7]

Answer:

47.5%

Step-by-step explanation:

You have to first subtract 80 and 42 to find the decrease first. This is 38. Now, you have to divide this by the original number which is 80. So 38 divided by 80 is 0.475.

Now multiply this by 100.

You can easily move the decimal point to the right.

So you would get 47.5%

Hope this helped!

3 0

3 years ago

Plz help me help me i need help badly

Alex787 [66]

Answer:

The answer is D

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers