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3 years ago

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Which of the following statements are true? I. -(-6) = 6 and -(-4) > -4 III. 5 + 6 = 11 or 9 - 2 = 11 II. -(-4) < 4 or -10

> 10 - 10 IV. 17 > 2 or 6 < 9

1 answer:

scoray [572]3 years ago

8 0

IV : 17 > 2 or 6 < 9......these are true....17 is greater then 2 and 6 is less then 9

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Use the Commutative Property to write an expression equivalent to -5d + 6

Ludmilka [50]

Answer:

6 - 5d is an expression equivalent to -5d + 6 using the commutative Property of Addition.

Step-by-step explanation:

Commutative Property of Addition

We know that we can add two numbers in any order.

For example,

Let 'a' and 'b' be two numbers.

We can add 'a' and 'b' numbers in any order, such as

a + b = b + a

Thus,

a + b = b + a is represented using the commutative Property of Addition.

In our case,

-5d + 6 can be written or represented using the commutative Property of Addition, such as

-5d + 6 = 6 - 5d

It is clear that -5d + 6 can be written in any order such as 6 - 5d.

In other words, 6 - 5d is an expression equivalent to -5d + 6 using the commutative Property of Addition.

Therefore, 6 - 5d is an expression equivalent to -5d + 6 using the commutative Property of Addition.

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2 years ago

Patty is inviting her friends to a party.She has 30 snack bars and 45 juice boxes and she wants to give the same number to each

Alexeev081 [22]

Answer

15 friends

Step-by-step explanation:

The largest common factor ( meaning the biggest number that goes into both 30 and 45) is 15. Each friend could get 2 snack bars and 3 juice boxes and there would be none left over

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3 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 <em>sample mean</em>. The distribution for <em>sample means</em> follows a <em>normal distribution</em> 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 <em>z</em> follows a <em>standard normal distribution</em>, 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 <em>standard deviation</em> 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 <em>cumulative standard normal table</em> (or use some statistic program) to find the cumulative probability for <em>z</em> (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) $\\ P(z>0.48) = P(x>533.2) = 0.3156$ .

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3 years ago