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3 years ago

What is the distance between -7.5 and -15.3 on a number line

1 answer:

8 0

Okay. To find the distance apart from each other, subtract 15.3 and 7.5. When you do that, you should get 7.8. -7.5 and -15.3 are 7.8 units away on a number line.

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You are to take a multiple-choice exam consisting of 100 questions with 5 possible responses to each question. Suppose that you

xeze [42]

Answer:

Step-by-step explanation:

This is a binomial distribution

n = 100; p = 1/5

E(x) = np = (100)(1/5) = 20

6 0

3 years ago

What is the area of the triangle

vesna_86 [32]

Area of triangle = base x height x 1/2

Area of the triangle:
= 12 x 15 x 1/2

= 180 x 1/2

= 90 units^2

8 0

3 years ago

Read 2 more answers

Find the value of x

GalinKa [24]

Answer:

29 degrees

Step-by-step explanation:

9: 2x - 2 + x + 5 = 90

3x + 3 = 90

3x = 90 - 3

3x = 87

x = 29 degrees

4 0

2 years ago

A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of

iris [78.8K]

Answer:

The probability that the mean battery life would be greater than 533.2 minutes (in a sample of 75 batteries) is $\\ P(z>0.48) = P(x>533.2) = 0.3156$

Step-by-step explanation:

The main thing we have to take into account in this question is that we are about to find the probability of a sample mean. The distribution for sample means follows a normal distribution with mean $\\ \mu$ and standard deviation $\\ \frac{\sigma}{\sqrt{n}}$ . Mathematically

$\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

For values of the sample $\\ n \ge 30$ , no matter the distribution the data come from.

And the variable z follows a standard normal distribution, and, as we can remember, this distribution has a mean = 0 and a standard deviation = 1. Mathematically

$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [1]

That is

$\\ z \sim N(0, 1)$

We have a variance of 3364. That is, a standard deviation of

$\\ \sigma^2 = 3364; \sigma = \sqrt{3364} = 58$

The population mean is

$\\ \mu = 530$

The sample size is $\\ n = 75$

The sample mean is $\\ \overline{x} = 533.2$

With all this information, we can solve the question

The probability that the mean battery life would be greater than 533.2 minutes

Using equation [1]

$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ z = \frac{533.2 - 530}{\frac{58}{\sqrt{75}}}$

$\\ z = \frac{3.2}{\frac{58}{8.66025}}$

$\\ z = \frac{3.2}{6.69726}$

$\\ z = 0.47780$

With this value of z we can consult a cumulative standard normal table (or use some statistic program) to find the cumulative probability for z (and remember that this variable follows a standard normal distribution).

Most standard normal tables have values for z for only two decimals, so we can round the previous value for z as z = 0.48.

Then

$\\ P(z$

However, in the question we are asked for $\\ P(z>0.48) = P(x>533.2)$ . As well as all normal distributions, the standard normal distribution is symmetrical around the mean, and we have

$\\ P(z>0.48) = 1 - P(z$

Thus

$\\ P(z>0.48) = 1 - 0.68439$

$\\ P(z>0.48) = 0.31561$

Rounding to four decimal places, we have

$\\ P(z>0.48) = 0.3156$

So, the probability that the mean battery life would be greater than 533.2 minutes is (in a sample of 75 batteries) $\\ P(z>0.48) = P(x>533.2) = 0.3156$ .

5 0

3 years ago

Choose the correct way to write a comparison of seven-twelfths and ten-twelfths.

ra1l [238]

Answer:

ok so lets work this out

Step-by-step : 10/12 is closer to 12 than 7/12 soooo its not any of the ones that have these (:) and 10 is bigger than 7 so its

7/12 < 10/12

3 0

3 years ago