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3 years ago

Find the area of the shaded region. Round to nearest hundredth.

Mathematics

1 answer:

coldgirl [10]3 years ago

5 0

210/360 = 7/12, meaning the shaded area is 7/12 of the entire circle.

The circle has radius 12 in, so its total area is π (12 in)^2 = 144π in^2.

Then the area of the shaded region is 7/12 of this, or

7/12 * (144 π in^2) = 84π in^2 ≈ 263.89 in^2

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Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Upper H 0: pequals0.6 versus U

kow [346]

Answer:

Step-by-step explanation:

From the given information:

The null and the alternative hypothesis can be well written as:

$H_o:P=0.6$

$H_1:P>0.6$

Given that:

n = 200

x = 135

Alpha ∝ = 0.05 level of significance

Then;

⇒ $n \times p\times (1-P)$

= 200 × 0.6 × (1 -0.6)

= 200 × 0.6 × 0.4

= 48 ≥ 10

The sample proportion $\hat P = \dfrac{x}{n}$

$= \dfrac{135}{200}$

= 0.675

The test statistics $Z = \dfrac{\hat P - P}{\sqrt{ \dfrac{P(1-P)}{n} }}$

$Z = \dfrac{0.675 - 0.6}{\sqrt{ \dfrac{0.6 \times 0.4}{200} }}$

$Z = \dfrac{0.075}{\sqrt{ \dfrac{0.24}{200} }}$

Z = 2.165

The P-value = P(Z > 2.165)

= 1 - P(Z < 2.165)

From the z tables

= 1 - 0.9848

= 0.0152

Reject the null hypothesis since P-Value is lesser than alpha. ( i.e. 0.0152 < 0.05).

Thus, there is enough evidence to conclude that the value of the population proportion is greater than 0.6

7 0

3 years ago

A newborn weighs 8 pounds, 5 ounces. There are 453.59 grams per pound. What is the infant's weight in grams?

Nadya [2.5K]

Convert from Oz and Lbs.

1 Pound = 453.59237 Grams

1 Ounce = 28.3495231 Grams

3628.73896 for Lbs

141.7476155 for Oz

Add them, and you get:

3770.4865755

I didn't know if you needed rounding - it was classified as college.

Hope this helped, and have a good day!

5 0

3 years ago

Gary drove to the park at a rate of 50 miles per hour if it took him 2.5 hours to get from his house to the park how far away is

Marina86 [1]

Answer:

The distance of the park from the Gary's house is 125 miles.

Step-by-step explanation:

Speed of Gary = 50 miles/hour

Time taken by Gary to reach the park from his house = 2.5 hours

Now, we know that,

Distance travelled = speed × time

So, distance between park and Gary's house = speed × time

= 50 × 2.5

= 125 miles

So, the park is 125 miles away from the Gary's house.

4 0

3 years ago

If BD and EG are parallel lines and mBCF = 50°, what is mEFH?<br> Look at this diagram:

Burka [1]

It’s hard to tell due to no labels, but these are your angles due to the equal angles theorem and a few other theorems. Hopefully with this image you can hopefully find your answer. You may need to add angles together depending on what you are looking for. And possible even figure out what angle measure would make a (180 degree) triangle.
Hope this helped

4 0

3 years ago

3x - 2y + 3z = -20<br> 4x - 3y - 2z = 7<br> -5x + 5y + z = 9

skelet666 [1.2K]

Answer:

x= 4 y= 7 z= -6

Step-by-step explanation:

solve for one and you get them all

First, I got rid of the z by multiplying common factors (multiplied z by 2) and added equations 2 and 3 together after multiplying by 2

4x - 3y - 2z = 7

-10x+10y+2z= 18

-6x+7y= 25

Then multiplied z by -3 (to get rid of the z) with the original equation 3

3x - 2y + 3z = -20

15x-15y-3z= -27

18x-17y= -47

Next find common thing between the 2 equations we got and multiply it by that and combine (we can multiply first equation by 3 to get rid of the x and solve for y)

-18x+21y= 75

18x-17y= -47

y=7

Work backwards, substitute 7 into the above equation, you get x= 4 and then same for z to get z= -6

8 0

3 years ago