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3 years ago

Justify each step in solving the equation 4x = 7(x-3) by writing a reason for each statement

1 answer:

8 0

Start with parenthesis so that will be 7x -21so then you will get 4x = 7x -21 then you will subtract 7x and 4x and you will get -3x = -21 and your answer is 7 because both numbers are a negative and that will equal a positive.

You might be interested in

The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a sta

nordsb [41]

Answer:

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

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 problem, we have that:

$\mu = 8.2, \sigma = 0.18, n = 100, s = \frac{0.18}{\sqrt{100}} = 0.018$

What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?

This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So

X = 8.22

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

By the Central Limit Theorem

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

$Z = \frac{8.22 - 8.2}{0.018}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665

X = 8.18

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

$Z = \frac{8.18 - 8.2}{0.018}$

$Z = -1.11$

$Z = -1.11$ has a pvalue of 0.1335

0.8665 - 0.1335 = 0.7330

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

8 0

3 years ago

will the inequality "7 multiplied by a number is greater than or equal to 21" have an open boundary point or a closed boundary p

ehidna [41]

Answer:

Closed boundary point

Step-by-step explanation:

It says greater than OR equal too and having a closed boundary will indicate that 21 is apart of the inequality also.

I hope this helps

5 0

3 years ago

a satelite moves at the speed of 27,000 kilometers per hour what 4 number could be the actually speed of the satelite

Anvisha [2.4K]

If the satellite moves at a speed of 27,000 km p/h, your answer depends on the question.

This could be written in an algebraic expression, such as:

27,000x = S [for S stands for the ultimate speed of the satellite]

Of course, if this is a 3rd grade level question, I highly doubt they have even gotten started to including the alphabet into math.

So, I would suggest plugging 4 into X.
To explain this to her, just say that the speed needs to be multiplied by the amount of hours it has traveled. (I got 4 because there is a '4' in the question instead of 'for').

Meaning,
27,000 x 4 = 108,000 km per 4 hours

If her teacher decides to ask why that number, have her explain the question did not make sense so she plugged in a 4 to find an answer to a certain amount of hours.

Hope that helps a bit with the confusion!

7 0

3 years ago

Ms. Willer wanted to donate 27 cans of food to each of 8 food banks each of food to each of 8 food banks each of the 23 students

Natali [406]

It will need to be 9 as 27 by 8 is 216 and 23 by 9 is 207 and the you subtract 207 from 216 and get 9

7 0

3 years ago

A local band spent $2,000 to record and make 400 CDs. They sold all of their CDs and made a profit of $500. How much did they ch

anyanavicka [17]

Answer:

$6.25 for each CD

Step-by-step explanation:

6.25 x 400 = 2,500

2,500 - 2,000 = 500

there is a 500 profit

7 0

2 years ago