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MrMuchimi
3 years ago
14

A rectangular garden measures 21ft by 29ft . Surrounding (and bordering) the garden is a path 3ft wide. Find the area of this pa

th. Be sure to include the correct unit in your answer.
Mathematics
1 answer:
disa [49]3 years ago
5 0
The answer is 159.  You can just add three to the measurements and then subtract the original shape.
You might be interested in
What percent of 56 is 35 shirts
9966 [12]
62.5% of 56 is 35

Divide 35 and 56:
35 \div 56 = 0.625

Convert the decimal to a percentage:
0.625 \times 100 = 62.5
8 0
3 years ago
Many universities and colleges have instituted supplemental instruction (SI) programs, in which a student facilitator meets regu
aev [14]

Answer:

Step-by-step explanation:

Let many universities and colleges have conducted supplemental instruction(SI) programs. In that a student facilitator he meets the students group regularly who are enrolled in the course to promote discussion of course material and enhance subject mastery.

Here the students in a large statistics group are classified into two groups:

1). Control group: This group will not participate in SI and

2). Treatment group: This group will participate in SI.

a)Suppose they are samples from an existing population, Then it would be the population of students who are taking the course in question and who had supplemental instruction. And this would be same as the sample. Here we can guess that this is a conceptual population - The students who might take the class and get SI.

b)Some students might be more motivated, and they might spend the extra time in the SI sessions and do better. Here they have done better anyway because of their motivation. There is other possibility that some students have weak background and know it and take the exam, But still do not do as well as the others. Here we cannot separate out the effect of the SI from a lot of possibilities if you allow students to choose.

The random assignment guarantees ‘Unbiased’ results - good students and bad are just as likely to get the SI or control.

c)There wouldn't be any basis for comparison otherwise.

5 0
2 years ago
Will award brainliest for the correct answer!
Alex787 [66]

Answer:

<h2><em>4x³</em></h2>

Step-by-step explanation:

8x⁴y⁴ = 4×2×x³×x¹×y⁴ = 4x³×(2xy⁴)

12x³z² = 4×3×x³×z² = 4x³×(3z²)

Then the greatest common factor is of the two terms 8x⁴y⁴ and 12x³z² is:

4x³

4 0
2 years ago
Peter put $8,000 into a savings account that pays 6% interest, compounded continuously. After five years, Peter will have $in th
Dmitrij [34]
We have to calculate the amount of money Peter will have in his account after 5 years. Formula for the amount after t years with interest compounded continuously : A = P * e^(r t ). We know that r = 0.06; t = 5; e = 2.71 and P = $8,000. A = 8,000 * 2.718^( 0.06 * 5 ) = 8,000 * 2,718^( 0.3 ) = 8,000 * 1.3488158 = 10,798.53. Answer:<span> B. $10,798.53. </span>
6 0
3 years ago
A television station plans to ask a random sample of 400 city residents if they can name the news anchor on the evening news at
hodyreva [135]

Answer:

There is an 8.38% probability that the anchor will be fired.

Step-by-step explanation:

For each resident, there is only two possible outcomes. Either they can name the news anchor on the evening news at their station, or they cannot.

This means that the binomial probability distribution will be used in our solution.

However, we are working with samples that are considerably big. So i am going to aaproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

400 city residents are going to be asked. So n = 400.

Suppose that in fact 12% of city residents could name the anchor if asked. This means that p = 0.12.

So,

\mu = E(X) = 400*0.12 = 48

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.12*0.88} = 6.5.

They plan to fire the news anchor if fewer than 10% of the residents in the sample can do so.

What is the approximate probability that the anchor will be fired?

10% of the residents is 0.10*400 = 40 residents.

Fewer than 10% is 39 residents. So the probability that the anchor will be fired is the pvalue of Z when X = 39.

So:

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

Z = \frac{39 - 48}{6.5}

Z = -1.38

Z = -1.38 has a pvalue of 0.0838. This means that there is an 8.38% probability that the anchor will be fired.

5 0
3 years ago
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