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3 years ago

I need help with these two problems !!

Mathematics

1 answer:

wolverine [178]3 years ago

4 0

Not so sure about the second one, but the first one is pretty simple:

The area of a circle = pi x radius^2

Since you need to find the area of the entire dvd, I'm assuming they mean if the hole in the center wasn't there, so add that to the diameter.

12+1.5 = 13.5

Half of the diameter is the radius, so half of 13.5 = 6.75

Now, multiply pi (3.14) by the radius, but have the radius squared. You'd write the equation like this:

3.14 x 6.75^2 (or on paper, the ^2 would be a small two diagonal from the 5)

Actual answer: 143.06625

You can round that to 143.

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What happens to the image of a figure that is rotated 90° counterclockwise?

Paul [167]

I think the answer is A

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3 years ago

A trash bin has a capacity of 50 gallons. What percentage of its capacity is each of the following? Show your reasoning.

snow_lady [41]

Answer:

Step-by-step explanation:

5 gallons is 1/10 of 50 gallons; this is 10% of capacity.

30 gallons 30/50, or 60%

45 gallons 45/50, or 90%

100 gallons 200%

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3 years ago

(b) how many measurements must be averaged to get a margin of error of ±0.0001 with 98% confidence? (round your answer up to the

goblinko [34]

Given that the scale readings of the laboratory scale is normally distributed with an unknown mean and a standard deviation of 0.0002 grams.

Part A:

If the weight is weighted 5 times and the mean weight is 10.0023 grams, the 98% confidence interval for μ, the true mean of the scale readings is given by:

$98\% \ C. \ I.=\bar{x}\pm z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right) \\ \\ =10.0023\pm2.33\left(\frac{0.0002}{\sqrt{5}}\right) \\ \\ =10.0023\pm2.33(0.000089) \\ \\ =10.0023\pm0.00021 \\ \\ =(10.0023-0.00021, \ 10.0023+0.00021) \\ \\ =(10.0021, \ 10.0025)$

Thus, we are 98% confidence that the true mean of the scale readings is between 10.0021 and 10.0025.

Part B:

To get a margin of error of +/- 0.0001 with a 98% confidence, then

$\pm z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right)=\pm0.0001 \\ \\ \Rightarrow2.33\left(\frac{0.0002}{\sqrt{n}}\right)=0.0001 \\ \\ \Rightarrow\left(\frac{0.0002}{\sqrt{n}}\right)= \frac{0.0001}{2.33} =0.0000429 \\ \\ \Rightarrow\sqrt{n}= \frac{0.0002}{0.0000429} =4.66 \\ \\ \Rightarrow n=4.66^2=21.7156\approx22$

Therefore, the number of <span>measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence is 22.</span>

8 0

3 years ago

If the nominal interest rate is 4. 00% and the rate of inflation is 2. 25%, what is the real interest rate? 1. 75% 4. 50% 6. 25%

Lapatulllka [165]

Based on the information given the real interest rate is 1.75%.

Using this formula

Real interest rate =Nominal interest rate − Inflation rate

Where:

Nominal interest rate=4.00%

Inflation rate=2.25%

Let plug in the formula

Real interest rate=4.00%-2.25%

Real interest rate=1.75%

Inconclusion the real interest rate is 1.75%.

Learn more about real interest rate here:brainly.com/question/6106690

3 0

3 years ago

What is the slope of the line that passes through the points (−8,−1) and (−6,−2)? Write your answer in simplest form.

4vir4ik [10]

Answer:

m = -1/2

Step-by-step explanation:

Recall that slope = (change in y) / (change in x).

Going from (−8,−1) to (−6,−2), x increases by 2 (because -6 - (-8) = 2), and

y decreases by 1. Thus, the slope here is

m = (change in y) / (change in x) = (-1) / 2 = -1 / 2

m = -1/2

6 0

3 years ago