How many 44-element subsets containing the letter a can be formed from the set {a,b,c,d,e,f,g}{a,b,c,d,e,f,g}?

The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.

Step-by-step explanation:

A machine, when working properly, produces 5% or less defective items.

This means that the null hypothesis is:

$H_0: p \leq 0.05$

Test if the percentage of defective items produced by this machine is greater than 5%.

This means that the alternate hypothesis is:

$H_a: p > 0.05$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.05 is tested at the null hypothesis:

This means that $\mu = 0.05, \sigma = \sqrt{0.05*0.95}$

A random sample of 300 items taken from the production line contained 27 defective items.

This means that $n = 300, X = \frac{27}{300} = 0.09$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.09 - 0.05}{\frac{\sqrt{0.05*0.95}}{\sqrt{300}}}$

$z = 3.18$

Pvalue of the test:

Testing if the mean is greater than a value, which means that the pvalue of the test is 1 subtracted by the pvalue of Z = 3.18, which is the probability of a finding a sample proportion of 0.09 or higher.

Looking at the Z-table, Z = 3.18 has a pvalue of 0.9993

1 - 0.9993 = 0.0007

The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.

5 0

3 years ago

Help plsss Show me the work plsss

velikii [3]

Answer:

a) y = 6x - 3

b) 1/3y = 2x -1

The first thing you need to do is isolate (y) in the second equation

3 x (1/3y) = 3 x (2x - 1)

y =6x - 3

After isolating (y) in equation b they end up being the same.

Graphing:

In order to graph this, you have to make the first point at (0, -3) since this is the Y-intercept of the equation.

In order to graph the other points, you must move 6 units up and 1 unit to the right. Or vise versa If you need a visual I'll gladly link one.

5 0

3 years ago

Find the sum.

Strike441 [17]

You are gonna use the distributive property.

4(2.5g - 4) + 3(1.2g - 2)

So you are going to multiply 4 with everything inside the first set of parenthesis and your gonna multiply 3 with everything insides the second set of parenthesis.

4 x 2.5g - 4 x 4 + 3 x 1.2g - 3 x 2

10g - 16 + 3.6g - 6

You wanna combine like terms:

10 - 3.6g + 16 - 6

6.4g + 10

You answer is 6.4g + 10.

Hope this Helps!!

6 0

3 years ago