Solve x2 + 4x = 4 for x by completing the square.

g A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. In a rando

Tema [17]

Answer:

We accept the null hypothesis, that is, the the mean amount of garbage per bin is not different from 50.

Step-by-step explanation:

A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50.

This means that the null hypothesis is:

$H_{0}: \mu = 50$

And the alternate hypothesis is:

$H_{a}: \mu \neq 50$

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.

50 tested at the null hypothesis:

This means that $\mu = 50$

In a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds.

This means that $n = 36, X = 50.67, \sigma = 3.9$

Value of the test statistic:

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

$z = \frac{50.67 - 50}{\frac{3.9}{\sqrt{36}}}$

$z = 1.03$

p-value:

Since we are testing if the mean is differente from a value and the z-score is positive, the pvalue is 2 multipled by 1 subtracted by the pvalue of z = 1.03.

z = 1.03 has a pvalue of 0.8485

1 - 0.8485 = 0.1515

2*0.1515 = 0.3030

0.3030 > 0.01, which means that we accept the null hypothesis, that is, the the mean amount of garbage per bin is not different from 50.

5 0

3 years ago

Carl is twice as old as Ginger. If Carl were 2 years younger and Ginger were 3 years older, the difference of their ages would b

Mashcka [7]

Ginger would be 8 years old.
8+3=11
16-2=14
16/2=8

3 0

3 years ago

Find the values of a, b and c.

valina [46]

Look at the picture.

Corresponding Angles are equal.

Alternate Angles are equal.

Consecutive Angles add up to 180°.

----------------------------------------------------------------------

3a and 45 are Consecutive Angles. Therefore

3a + 45 = 180 |subtract 45 from both sides

3a = 135 |divide both sides by 3

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(2c - 1) and 45 are Corresponding Angles. Therefore

2c - 1 = 45 |add 1 to both sides

2c = 46 |divide both sides by 2

----------------------------------------------------------------------

3a and (12b + 3) are Alternate Angles. Therefore

3(45) = 12b + 3

135 = 12b + 3 |subtract 3 from both sides

132 = 12b |divide both sides by 12

7 0

4 years ago

Two professors at a nearby university want to co-author a new textbook in either economics or statistics. They feel that if they

WARRIOR [948]

Answer:

0.3 or 30%

Step-by-step explanation:

The professors will only seek a smaller publisher if they cannot place the statistics book with a major publisher. If the probability of getting a major publisher is 40% and the probability of getting a smaller publisher is 50%, then the probability that the statistics book would wind up being placed with a smaller publisher is given by:

$P=(1-P(major))*P(minor)\\P=(1-0.4)*0.5\\P=0.3$

The probability is 0.3 or 30%.

3 0

3 years ago

Please Help <3 Please Help <3

nadezda [96]

Hey, there! For this question, we can just start by plugging in the known values. $(f + g)(x)$ can be rewritten as $(\frac{x}{2} - 3 + 3x^2 + x - 6)(x)$ .

Combine like terms: $(\frac{x}{2} + x - 3 - 6 + 3x^2)(x)$

If you add x to $\frac{x}{2}$ , x will become $\frac{2x}{2}$ , which means that x/2 + x = 3/2x.

--> $(\frac{3}{2}x - 9 + 3x^2)(x)$

If you rearrange this, then your answer will be option b. Hope this helps.

5 0

3 years ago

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