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2 years ago

2(z+5) +5(z+ 2) = 10(z − 1)

Mathematics

1 answer:

Jlenok [28]2 years ago

4 0

Answer:

z = 10

Step-by-step explanation:

First apply multiplication to inside the parenthesis:

2(z+5) = 2z + 10

5(z+ 2) = 5z + 10

10(z − 1) = 10z - 10 now write the full equation

2z + 10 + 5z + 10 = 10z - 10 add like terms

7z + 20 = 10z - 10 transfer like terms to the same side of the equation

20 + 10 = 10z - 7z

30 = 3z divide both sides by 3

10 = z

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According to 2013 report from Population Reference Bureau, the mean travel time to work of workers ages 16 and older who did not

gregori [183]

Answer:

a) 48.80% probability that his travel time to work is less than 30 minutes

b) The mean is 30.7 minutes and the standard deviation is of 3.83 minutes.

c) 13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes

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

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:

$\mu = 30.7, \sigma = 23$

a. If a worker is selected at random, what is the probability that his travel time to work is less than 30 minutes?

This is the pvlaue of Z when X = 30. So

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

$Z = \frac{30 - 30.7}{23}$

$Z = -0.03$

$Z = -0.03$ has a pvalue of 0.4880.

48.80% probability that his travel time to work is less than 30 minutes

b. Specify the mean and the standard deviation of the sampling distribution of the sample means, for samples of size 36.

$n = 36$

Applying the Central Limit Theorem, the mean is 30.7 minutes and the standard deviation is $s = \frac{23}{\sqrt{36}} = 3.83$

c. What is the probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes?

This is 1 subtracted by the pvalue of Z when X = 35. So

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

By the Central Limit Theorem

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

$Z = \frac{35 - 30.7}{3.83}$

$Z = 1.12$

$Z = 1.12$ has a pvalue of 0.8687

1 - 0.8687 = 0.1313

13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes

8 0

3 years ago

You need 150g of flour for 12 cakes, how much flour do you need for 30 cakes?

nirvana33 [79]

If you need 150g of flour for 12 cakes, that means you need 12.5 g of flour per cake. So if you multiply that by 30 it gives you
375g of flour

3 0

3 years ago

Read 2 more answers

A concession stand charges $2.50 for a bag of popcorn. The stand has already sold 30 bags of popcorn. How many more bags x of po

vesna_86 [32]

Answer:

The concession stands needs to sell 14 or more bags.

Step-by-step explanation:

Given that:

Cost per bag of popcorn = $2.50

Number of bags already sold = 30

Cost of 30 bags = 30*2.50 = $75

Bags needs to be sold to make $110 = x

2.50x + 75 ≥ 110

2.50x ≥ 110-75

2.50x ≥ 35

Dividing both sides by 2.50

$\frac{2.50x}{2.50}\geq \frac{35}{2.50}\\x\geq 14$

Hence,

The concession stands needs to sell 14 or more bags.

3 0

3 years ago

PLEASE ANSWER ASASP FOR BRAINLEST!!!!!!!!!!!!!!

stealth61 [152]

Answer:

32 units²

Step-by-step explanation:

this shape is a trapezoid with a height of 4 and bases that are 4 and 12 units in length

formula is: 1/2(height) x (sum of bases)

A = 1/2(4)(4 + 12)

A = 2(16)

A = 32

7 0

3 years ago

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According to the properties of inequality, when should the inequality symbol be reversed when solving a two-step any quality in

Marina86 [1]

According to the properties of inequality, we reverse the inequality symbol when we add or multiply by any negative number

Given inequality is Ax + B > C

In the first step, we subtract B from both sides

Ax + B > C

Ax + B - B > C - B

Ax > C - B

Now to remove A we divide by A on both sides

If A is negative then the reverse the inequality sign

When A is negative then > symbol becomes < symbol

so the inequality symbol be reversed when the value of A is negative

3 0

3 years ago

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