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GREYUIT [131]
1 year ago
11

A rectangular garden has a walkway around it. The area of the garden is 6(6.5x + 2.5). The combined area of the garden and the w

alkway is 6.5(8x + 6). Find the area of the walkway around the garden as the sum of two terms.
Mathematics
1 answer:
Rasek [7]1 year ago
7 0

According to the information given in the exercise, the following expression represents the area of the rectangular garden:

6\mleft(6.5x+2.5\mright)

And the following expression represents the combined area of the walkway around the rectangular garden and the area of the garden:

6.5\mleft(8x+6\mright)

You can identify that the word "combined" indicates that that expression was obtained by adding both areas.

Knowing the above, you can set up the following equation:

6(6.5x+2.5)+A=6.5(8x+6)

Where "A" is the area of the walkway around the rectangular garden.

Solving for "A", you get the following expression:

\begin{gathered} A=6.5(8x+6)-6(6.5x+2.5) \\ A=52x+39-39x-15 \\ A=13x+24 \end{gathered}

The answer is:

13x+24

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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
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kati45 [8]

Answer: dont know just search it up

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2 years ago
Jen received 60% on her science quiz.She got 9 question correct.How many total questions were on the science test
andriy [413]
There were 15 questions on the science test.
9 divided by 15 is .60%
4 0
3 years ago
Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
jarptica [38.1K]

Answer: IRT WOULD BE C bc likw look da chaer i dont gotta epsxlain

Step-by-step explanation:

6 0
3 years ago
Is this correct? if not what is the answer
LenaWriter [7]

Answer:

x = 50

Step-by-step explanation:

You are correct.

x + m<PQS + m<PSQ = 180

m<PQS = m<QRT = 70

m<QST + m<PSQ = 180

120 + m<PSQ = 180

m<PSQ = 60

x + 70 + 60 = 180

x + 130 = 180

x = 50

Great job!

4 0
3 years ago
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