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andreyandreev [35.5K]

3 years ago

15

Lamar is fertilizing his garden. The garden is in the shape of a rectangle. Its length is 16 feet and its width is 13 feet. Supp

ose each bag of fertilizer covers 26 square feet. How many bags will he need to cover the garden?

1 answer:

Vera_Pavlovna [14]3 years ago

5 0

Answer:

8

Step-by-step explanation:

16x13=208

208÷26=8

8 bags of fertilizer

You might be interested in

A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square val

Natali5045456 [20]

Answer:

$\chi^2_{\alpha/2}=43.195$

$\chi^2_{1- \alpha/2}=14.573$

b. 14.573 and 43.195.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

2) Solution to the problem

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

We need on this case to calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=28-1=27$

Since the Confidence is 0.95 or 95%, the value of $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table for the Chis square distribution with 27 degrees of freedom to find the critical values. We need a value that accumulates 0.025 of the area on the left tail and 0.025 of the area on the right tail.

The excel commands would be: "=CHISQ.INV(0.025,27)" "=CHISQ.INV(0.975,27)". so for this case the critical values are:

$\chi^2_{\alpha/2}=43.195$

$\chi^2_{1- \alpha/2}=14.573$

b. 14.573 and 43.195.

7 0

3 years ago

you deposit 10,000 in an account that pays 3% annual interest compounded monthly. How much will you have in 5 years?

Inessa [10]

Answer:

$2,833.59

Step-by-step explanation:

1 $10,000.00 $10,000.00 $511.64 $0.00 $10,511.62 $10,000.00

2 $10,000.00 $10,511.62 $537.79 $0.00 $11,049.41 $10,000.00

3 $10,000.00 $11,049.41 $565.30 $0.00 $11,614.72 $10,000.00

4 $10,000.00 $11,614.72 $594.23 $0.00 $12,208.95 $10,000.00

5 $10,000.00 $12,208.95 $624.63 $0.00 $12,833.59 $10,000.00

8 0

3 years ago

Read 2 more answers

In the diagram, find the values of a and b.

uysha [10]

Answer:

<h2> m∠a = 67° , m∠b = 42°</h2>

Step-by-step explanation:

∠a is alternate interior angle to ∠ECD

∠b is alternate interior angle to ∠BCD

so:

If AB || CD then:

m∠a = m∠ECD = 25° + 42° = 67°

m∠b = 42°

8 0

3 years ago

Adair needs $21,150 to purchase a boat. How much money will you need to invest today in a savings account earning 3.2% interest,

emmasim [6.3K]

A=x(1+r/n)^nt
21150=x(1+0.032/12)^84
21150=x(1+0.0026666)^84
21150=x(1.002666666)^84
21150=x(1.25069809)
21150/1.25069809=x
16910.56=x

Hope this helps!

8 0

3 years ago

Nadia says the hypotenuse of the right triangle has a length of 73 because the Pythagorean theorem states that (28+45)squared eq

Setler79 [48]

Answer: Her solution is incorrect. The hypotenuse is 53 units

Step-by-step explanation: The error occurred when she quoted the Pythagorean theorem. She added up both sides and squared them and made the answer equal to the square of the hypotenuse. She was supposed to have squared them first, before adding up.

The Pythagorean (or Pythagoras) theorem states that the sum of the squares of two sides of a right angled triangle equals the square of the hypotenuse of the triangle. That is, in triangle ABC, if the hypotenuse is given as line AC, the Pythagoras theorem states that

AC^2 = AB^2 + BC^2

Where AC is the hypotenuse and AB and BC are the other two sides.

In Nadia’s solution, if the hypotenuse is given as 73, and the other two sides are 28 and 45, then the Pythagorean theorem properly expressed would be as follows;

73^2 = 28^2 + 45^2

5329 = 784 + 2025

5329 ≠ 2809

As we have determined, writing out the expression as

73^2 = (28 + 45)^2 is very incorrect as this is not the Pythagorean theorem and of course, the triangle cannot have 73 as its hypotenuse as we have determined by properly writing out the Pythagorean theorem.

The correct solution is as follows;

AC^2 = AB^2 + BC^2

AC^2 = 28^2 + 45^2

AC^2 = 784 + 2025

AC^2 = 2809

Add the square root sign to both sides of the equation

AC = 53

Therefore, the hypotenuse is 53 units

4 0

3 years ago

Read 2 more answers