Express 6 cups to 4 quarts as a fraction in simplest form.

Brent is a researcher for a food company. He is on a team creating a reduced-calorie version of its flagship cracker. The team w

Andre45 [30]

Answer:

Step-by-step explanation:

Hello!

The research team created a cracker with fewer calories. The average content of calories of the new crackers per serving of 6 should be less than 60.

To test it a random sample of 26 samples of the new cracker was taken and the calories per serving were measured.

Then the study variable is

X: calories of a 6 serve sample of the new reduced-calorie version. (cal)

The variable has a normal distribution with a population standard deviation of 0.82 cal.

To test the claim that the new crackers have on average less than 60 calories, the parameter of interest is the population mean (μ) and the hypotheses are:

H₀: μ ≥ 60

H₁: μ < 60

α: 0.01

Since the variable has a normal distribution and the population variance is known, the best statistic to use to conduct the test is a Standard Normal

$Z= \frac{(X[bar]-Mu)}{\frac{Sigma}{\sqrt{n}} } ~N(0;1)$

This test is one tailed to the left, wich means that the null hypothesis will be rejected at low levels of the statistic.

$Z_{\alpha } = Z_{0.01} = -2.334$

If Z ≤ -2.334, the decision is to reject the null hypothesis.

If Z > -2.334, the decision is to not reject the null hypothesis.

Using the data of the sample I've calculated the sample mean.

X[bar]= ∑X/n= 1548.61/26= 59.56 cal

$Z_{H_0}= \frac{(59.56-60)}{\frac{0.82}{\sqrt{26} } } = -2.736$

The observed Z value is less than the critical value, so the decision is to reject the null hypothesis.

At a level of significance of 1%, you can conclude that the population mean of calories of the samples of new crackers is less than 60 cal.

I hope it helps!

6 0

3 years ago

Add the two expressions.

Vladimir79 [104]

Your answer will be 3.7w-2

8 0

3 years ago

Read 2 more answers

How many possible outfit combinations come from 10 shirts, two slacks, and five ties? A. 17B. 25C. 100D. 20

Scilla [17]

<span>100. Since 10 shirts x 2 slacks means 20 combos with one tie and 100 with 5 ties</span>

7 0

3 years ago

Read 2 more answers

PLEASE HELP :(

Vitek1552 [10]

Than Maria needs to get a new stove

7 0

3 years ago

Please help with this question.

barxatty [35]

Answer:

Step-by-step explanation:

The first thing we have to do is find the measure of angle A using the fact that the csc A = 2.5.

Csc is the inverse of sin. So we could rewrite as

$\frac{1}{sinA}=2.5$ or more easy to work with is this:

$\frac{1}{sinA} =\frac{2.5}{1}$

and cross multiply to get

2.5 sinA = 1 and

$sinA=\frac{1}{2.5}$ which simplifies to

sin A = .4

Using the 2nd and sin keys on your calculator, you'll get that the measure of angle A is 23.58 degrees.

We can find angle B now using the Triangle Angle-Sum Theorem that says that all the angles of a triangle have to add up to equal 180. Therefore,

angle B = 180 - 23.58 - 90 so

angle B = 66.42

The area of a triangle is

$A =\frac{1}{2}bh$ where h is the height of the triangle, namely side AC; and b is the base of the triangle, namely side BC. To find first the height, use the fact that angle B, the angle across from the height, is 66.42, and the hypotenuse is 3.9. Right triangle trig applies:

$sin(66.42)=\frac{h}{3.9}$ and

3.9 sin(66.42) = h so

h = 3.57

Now for the base. Use the fact that angle A, the angle across from the base, measures 23.58 degrees and the hypotenuse is 3.9. Right triangle trig again:

$sin(23.58)=\frac{b}{3.9}$ and

3.9 sin(23.58) = b so

b = 1.56

Now we can find the area:

$A=\frac{1}{2}(1.56)(3.57)$ so

A = 2.8 cm squared

3 0

3 years ago