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3 years ago

The diameter of a circle is 41 ft. Find the area of the circle.

1 answer:

5 0

The formula for area of a circle is A=πd.

So plug in 3.14 for π and 41 for d.

It should look like this A=3.14(41).

Now solve and you get 128.74.

Lastly round and your answer is 128.7

Hope this helps :-)

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To qualify for a police academy, candidates must score in the top 10% on a general abilities test. The test has a mean of 200 an

kolbaska11 [484]

Answer:

z = 1.28 < a - 200/20

And if we solve for a we got

a = 200 + 1.28 * 20 = 225.6

So the value of height that separates the bottom 90% of data from the top 10% is 225.6.

Step-by-step explanation:

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

X ~ N (200,20)

For u = 200 and o = 20

For this case we can use the z score in order to solve this problem, given by this formula:

Z = x-u/o

For this part we want to find a value a, such that we satisfy this condition:

P (X > a) = 0.1 (a)

P (X < a) = 0.9 (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

P ( X < a) = P (X-u/o < a - u/o) = 0.9

P (z < a-u/o) = 0.9

But we know which value of z satisfy the previous equation so then we can do this:

z = 1.28 < a - 200/20

And if we solve for a we got

a = 200 + 1.28 * 20 = 225.6

So the value of height that separates the bottom 90% of data from the top 10% is 225.6.

3 0

2 years ago

There are two numbers. Their GCF is 5. Their LCM is 150. The first number is 25. What is the second number?

Galina-37 [17]

Answer:

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.

alexandr402 [8]

Answer:

slope-inercept form: y = 3x + 3 point-slope form: y - 9 = 3(x - 2)

Step-by-step explanation:

slope-intercept form:

y2 - y1 / x2 - x1

9 - (-6)/ 2 - (-3)

= 3

y = 3x + b

9 = 3(2) + b

9 = 6 + b

3 = b

y = 3x + 3

point-slope form:

y - 9 = 3(x - 2)

5 0

3 years ago

The length of a rectangular frame is 5 cm more than the width. The area inside the frame is 66 square cm. Find the width of the

Ratling [72]

For this case we have that the area is given by:
A = (w) * (l)
Where,
w: width
l: long
Substituting we have:
66 = (w) * (w + 5)
Rewriting
w ^ 2 + 5w - 66 = 0
(w + 11) * (w-6) = 0
Using the positive root we have:
w = 6
Answer:
the width of the frame is:
w = 6 cm

6 0

3 years ago

Choose an American household at random, and let the random variable X be the number of cars (including SUVs and light trucks) th

PilotLPTM [1.2K]

Answer:

19% of households have more cars than the garage can hold

Step-by-step explanation:

We are given the following distribution for the number of cars owned by a family.

Number of cars X: 0 1 2 3 4 5 6

Probability: 0.07 0.31 0.43 0.12 0.04 0.02 0.01

We have to find the percentage of households have more cars than the garage can hold.

A garage can hold two cars. Thus, the household with more than two cars are the households that have more cars than the garage can hold.

The given distribution is a discrete probability distribution.

Thus, we evaluate:

$P(x\geq 3) = P(x+3) + P(x+4) + P(x+5) + P(x+6)\\P(x\geq 3) = 0.12 +0.04+ 0.02 +0.01 = 0.19\\P(x\geq 3) = 19\%$

Thus, 19% of households have more cars than the garage can hold.

4 0

3 years ago