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sertanlavr [38]
3 years ago
14

A pound of fertilizer covers 37 square feet of lawn. Vivian​'s lawn measure 9110.1 square feet. How much​ fertilizer, to the nea

rest tenth of a​ pound, does she need to​ buy?
(round to the nearest tenth)
Mathematics
1 answer:
LenKa [72]3 years ago
7 0

To solve this problem you must apply the proccedure shown below:

1. You have the following information given in the problem above:

- A pound of fertilizer covers 37 square feet of lawn.

- Vivian​ has 9110.1 square feet of lawn.

2. Therefore, to calculate the pounds of fertilizer needed, you must multiply  the area of lawn that she has by one pound and divide this by the area convered by a pound:

\frac{(1 lb)(9110.1ft^{2}) }{37ft^{2} } =246.2lb

Then, the answer is: 246.2 pounds.

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The 90% confidence interval for the difference between means is (4.189, 8.011).

The point estimate is the difference between sample means and has a value of Md=6.1.

Step-by-step explanation:

We have to calculate a 90% confidence interval for the difference between means.

The sample 1 (American students), of size n1=12 has a mean of 69.4 and a standard deviation of 2.79.

The sample 2 (non-American students), of size n2=17 has a mean of 63.3 and a standard deviation of 3.22.

The difference between sample means is Md=6.1.

M_d=M_1-M_2=69.4-63.3=6.1

The estimated standard error of the difference between means is computed using the formula:

s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.79^2}{12}+\dfrac{3.22^2}{17}}\\\\\\s_{M_d}=\sqrt{0.649+0.61}=\sqrt{1.259}=1.12

The critical t-value for a 90% confidence interval is t=1.703.

The margin of error (MOE) can be calculated as:

MOE=t\cdot s_{M_d}=1.703 \cdot 1.12=1.911

Then, the lower and upper bounds of the confidence interval are:

LL=M_d-t \cdot s_{M_d} = 6.1-1.911=4.189\\\\UL=M_d+t \cdot s_{M_d} = 6.1+1.911=8.011

The 90% confidence interval for the difference between means is (4.189, 8.011).

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