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2 years ago

1. Gloria says the two expressions - (12x + 24) - 9x and -6(x + 1) are equivalent. Is she correc Explain how you know.

Mathematics

1 answer:

yanalaym [24]2 years ago

4 0

Answer:

No they aren't equivalent

Step-by-step explanation:

Let's take each expression

the first one is

- (12x+24) - 9x = -12x -24 -9x = -21x -24 = -3 (7x +8)

the second expression

-6 (x+1) = -6x-6

So they aren't equivalent

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It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minute

NemiM [27]

Answer:

a) 10.93% probability that the mean number of minutes of daily activity of the 5 mildly obese people exceeds 420 minutes.

b) 99.22% probability that the mean number of minutes of daily activity of the 5 lean people exceeds 420 minutes.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

Normal probability distribution

Problems of normally distributed samples can be 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.

Mildly obese

Normally distributed with mean 373 minutes and standard deviation 67 minutes. So $\mu = 373, \sigma = 67$

A) What is the probability that the mean number of minutes of daily activity of the 5 mildly obese people exceeds 420 minutes?

So $n = 5, s = \frac{67}{\sqrt{5}} = 29.96$

This probability is 1 subtracted by the pvalue of Z when X = 410.

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

$Z = \frac{410 - 373}{29.96}$

$Z = 1.23$

$Z = 1.23$ has a pvalue of 0.8907.

So there is a 1-0.8907 = 0.1093 = 10.93% probability that the mean number of minutes of daily activity of the 5 mildly obese people exceeds 420 minutes.

Lean

Normally distributed with mean 526 minutes and standard deviation 107 minutes. So $\mu = 526, \sigma = 107$

B) What is the probability that the mean number of minutes of daily activity of the 5 lean people exceeds 420 minutes?

So $n = 5, s = \frac{107}{\sqrt{5}} = 47.86$

This probability is 1 subtracted by the pvalue of Z when X = 410.

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

$Z = \frac{410 - 526}{47.86}$

$Z = -2.42$

$Z = -2.42$ has a pvalue of 0.0078.

So there is a 1-0.0078 = 0.9922 = 99.22% probability that the mean number of minutes of daily activity of the 5 lean people exceeds 420 minutes.

7 0

3 years ago

Solve the equation. 7(1 – 8x) – 6 = 169

Natalija [7]

Answer:

x=-3

Step-by-step explanation:

rearrange terms

distribute

subtract the numbers

subtract 1 from both sides of the equation

simplify

4 0

2 years ago

Read 2 more answers

Mrs. Smith's class is working on a variety of science experiments. Each

SVETLANKA909090 [29]

Answer:

Step-by-step explanation:

If there are n students, then the number of pairs is $\frac{n(n-1)}{2}$ .

With 12 students, $\frac{12(12-1)}{2} = \frac{132}{2}=66$ pairs can be formed.

The reason the formula works is this: Each of the 12 students can be paired with 11 other students (no student is paired with him/her self). But counting 12 x 11 = 132 counts each pair twice. Example: student A can be paired with student B,..., student B can be paired with student A. The pair was counted two times.

See the attached image that shows pairings of 5 students. There are

5(5 - 1)/2 = 5(4)/2 = 10 pairs.

8 0

2 years ago

Deborah has two paintings in her portfolio and paints three more each week.Kai has twelve paintings in her portfolio and paints

elena-14-01-66 [18.8K]

Well, we can set up these equations like this-
Deborah- 2+3w
Kai- 12+2w
w=number of weeks that pass
Now, we set them equal to each other:
2+3w=12+2w

Solve for w
2-12=2w-3w
-10 = -1w
w = 10
10 weeks. Hope this helped!

4 0

3 years ago

Points E, D, and H are the midpoints of the sides of ΔTUV. UV=56, TV=72, and HD=56. Find HE.

natita [175]

We need a diagram to do this

5 0

3 years ago

1. Gloria says the two expressions - (12x + 24) - 9x and -6(x + 1) are equivalent. Is she correc Explain how you know.​

1. Gloria says the two expressions - (12x + 24) - 9x and -6(x + 1) are equivalent. Is she correc Explain how you know.