He art teacher has 1 gallon of paint, which is enough for \frac{2}{3} of the class to complete a project.

Mathematics

2 answers:

enyata [817]3 years ago

6 0

Answer:

1 and 1/2

Step-by-step explanation:

denpristay [2]3 years ago

5 0

1 and 1/2.................

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It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken to estimate

Hitman42 [59]

Answer:

The minimum sample size is n = 75 so that the desired margin of error is 5 or less.

Step-by-step explanation:

We are given the following in the question:

Population variance = 484

Standard deviation =

$\sigma^2 = 484\\\sigma =\sqrt{484} = 22$

Confidence level = 0.95

Significance level = 0.05

Margin of error = 5

Formula:

Margin of error =

$E = z\times \dfrac{\sigma}{\sqrt{n}}\\\\n = (\dfrac{z\times \sigma}{E})^2$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting values, we get

$E\leq 5\\\\1.96\times \dfrac{22}{\sqrt{n}} \leq 5\\\\\sqrt{n} \geq 1.96\times \dfrac{22}{5}\\\\n \geq (1.96\times \dfrac{22}{5})^2\\\\n \geq 74.373$

Thus, the minimum sample size is n = 75 so that the desired margin of error is 5 or less.

3 0

3 years ago

Endpoint: (1,7), midpoint: (-10,10)

algol [13]

The answer is (-21, 13) for The second endpoint.

Let's start by calling the known endpoint L and the unknown K. We'll call the midpoint M. In order to find this, we must first note that to find a midpoint we need to take the average of the endpoints. To do this we add them together and then divide by 2. So, using that, we can write a formula and solve for each part of the k coordinates. We'll start with just x values.

(Kx + Lx)/2 = Mx

(Kx + 1)/2 = -10

Kx + 1 = -20

Kx = -21

And now we do the same thing for y values

(Ky + Ly)/2 = My

(Ky + 7)/2 = 10

Ky + 7 = 20

Ky = 13

This gives us the final point of (-21, 13)

5 0

3 years ago