A friend lends you $360 which you agree to repay with 3% interest. How much will you have to repay?

The producer of a certain bottling equipment claims that the variance of all its filled bottles is .027 or less. A sample of 30

o-na [289]

Answer:

$p_v = P(\chi^2_{29}>42.963)=1-0.954=0.0459$

b. between .025 and .05

Step-by-step explanation:

Previous concepts and notation

The chi-square test is used to check if the standard deviation of a population is equal to a specified value. We can conduct the test "two-sided test or a one-sided test".

$\bar X$ represent the sample mean

n = 30 sample size

s= 0.2 represent the sample deviation

$\sigma_o =\sqrt{0.027}=0.164$ the value that we want to test

$p_v$ represent the p value for the test

t represent the statistic

$\alpha=$ significance level

State the null and alternative hypothesis

On this case we want to check if the population standard deviation is less than 0.027, so the system of hypothesis are:

H0: $\sigma \leq 0.027$

H1: $\sigma >0.027$

In order to check the hypothesis we need to calculate the statistic given by the following formula:

$t=(n-1) [\frac{s}{\sigma_o}]^2$

This statistic have a Chi Square distribution distribution with n-1 degrees of freedom.

What is the value of your test statistic?

Now we have everything to replace into the formula for the statistic and we got:

$t=(30-1) [\frac{0.2}{0.164}]^2 =42.963$

What is the approximate p-value of the test?

The degrees of freedom are given by:

$df=n-1= 30-1=29$

For this case since we have a right tailed test the p value is given by:

$p_v = P(\chi^2_{29}>42.963)=1-0.954=0.0459$

And the best option would be:

b. between .025 and .05

6 0

3 years ago

How much does a glass cube with a side of 5-cm weigh if 1cm3 of glass weighs 2 2/5 grams?

PtichkaEL [24]

The weight of galss cube with side 5 cm is 300 grams

Solution:

A glass cube is of side length 5 cm

Let us first find the volume of glass cube

The volume of cube is given as:

$volume = (side)^3\\\\volume =5^3 = 125$

Thus volume of cube is 125 $cm^3$

Given that,

$1 cm^3 = 2\frac{2}{5} \text{ grams }\\\\1 cm^3 =\frac{12}{5} \text{ grams}$

So, weight of 125 cubic centimeter of glass cube is found by multiplying weight of 1 cubic centimeter of glass cube by 125

$\text{ Weight of 125 } cm^3 \text{ cube } = \text{ Weight of 1 } cm^3 \text{ cube } \times 125$

$\text{ Weight of 125 } cm^3 \text{ cube } = \frac{12}{5} \times 125 = 25 \times 12 = 300$

Thus weight of galss cube with side 5 cm is 300 grams

3 0

3 years ago

Read 2 more answers

Help I need it I’m almost done

sesenic [268]

Answer:

E

Step-by-step explanation:

3 0

2 years ago

Please help me in this question.Tell me if it is good. And if it is not good then do it for me please.

Orlov [11]

Answer:

Y = 170, Z = 64.

Step-by-step explanation:

Since y is the external angle to x, which you got right, it is in fact, 180-10, = 170 degrees. And since z is the external to our unknown angle, that means it is equal to the sum of the other two angles in the triangle. That means z is 54 + 10, which is 64.

6 0

3 years ago

Geometry: Write a formal proof, ASAP!!!

yulyashka [42]

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