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lutik1710 [3]
3 years ago
11

The diameter of a circle is 16 meters. What is the angle measure of an arc bounding a sector with an area eight pi square meters

? (give the exact answer in simplest form)
Mathematics
1 answer:
Degger [83]3 years ago
5 0

Answer: 45°

Step-by-step explanation:

Diameter= 16m

Radius= 16/2 = 8m

The area of the circle= πr^2

= π8^2

= 64π square metres.

An area of 8π square metres is also 1/8 of the total area, therefore the arc must be 1/8 of the circumference.

The circumference = 2πr = 16π,

This gives us an arc length of 2π metres.

But since we are looking for the the angle.

In degrees: 360/8 = 45°

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Mrs. Hawk assigns her students an average of no more than 5 questions on each assignment. On their first 5 assignments Mrs. Hawk
bixtya [17]
Given that <span>Mrs. Hawk assigns her students an average of no more than 15 questions on each assignment. On their first 5 assignments Mrs. Hawk’s students had 11, 10, 13, 14, and 14 questions.

Let x be the number of questions she can have on the sixth assignment, then the inequality that Mrs. Hawk can use to determine the number of questions she can have on the sixth assignment is given by

\frac{11+10+13+14+14+x}{6} \leq15 \\  \\ \Rightarrow62+x\leq90 \\  \\ \Rightarrow x\leq28</span>
5 0
4 years ago
Suppose that for a typical FedEx package delivery, the cost of the shipment is a function of the weight of the package measured
Maksim231197 [3]

Answer:

The answer is "Option 5"

Step-by-step explanation:

Please find the complete question in the attached file.

Throughout the above output the regression equation is:

Delivery cost =0.469\times weight +9.617

4 0
3 years ago
One of my factors is 9. The sum of my product of my two factors is 13. What inumber am I?
timofeeve [1]
4  x+9=13 X=4 subtract 9 from the 9 and 13 and 13-9 =4 so x=4
5 0
3 years ago
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as ed
natka813 [3]
Production cost = one time cost + variable costs

Let the number of published books for equal production costs be n.

Using the first method:
production cost = 18,853 + 19.75n
Using the second method:
production cost = 64,853 + 8.25n

Now, we need the two production costs to be equal:
18,853 + 19.75n = 64,853 + 8.25n

Solve for n as follows:
18,853 + 19.75n = 64,853 + 8.25n
19.75n - 8.25n = 64,853 - 18,853
11.5n = 46000
n = 46000/11.5
n = 4000 books






6 0
3 years ago
Hotels’ use of ecolabels. Refer to the Journal of Vacation Marketing (January 2016) study of travelers’ familiarity with ecolabe
Alexxx [7]

Answer:

a) 0.7486; b) 0.6518; c) No

Step-by-step explanation:

We use z scores to answer these questions.  The formula for a z score is

z=\frac{X-\mu}{\sigma}

Our mean, μ, is 44; our standard deviation, σ, is 1.5.

For part a,

We want P(X > 43):

z = (43-44)/1.5 = -1/1.5 = -0.67

Using a z table, we see that the area under the curve to the left of this is 0.2514.  However, we want the area to the right; this means we subtract from 1:

1 - 0.2514 = 0.7486

For part b,

We want P(42 ≤ X ≤ 45):

z = (42-44)/1.5 = -2/1.5 = -1.3

z = (45-44)/1.5 = 1/1.5 = 0.67

Using a z table, the area under the curve to the left of z = -1.3 is 0.0968.  The area under the curve to the left of z = 0.67 is 0.7486.

The area between them is 0.7486 - 0.0968 = 0.6518.

For part c,

A response of 35 has a z score of

z = (35-44)/1.5 = -9/1.5 = -6

This is 6 standard deviations below the mean.  This is more than the amount required to make this an outlier, or an unlikely response.

8 0
4 years ago
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