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1 year ago

Consider circle O, in which arc XY measures 16π cm. The length of a radius of the circle is 32 cm.

Mathematics

2 answers:

natali 33 [55]1 year ago

8 0

Answer:

Circumference: 64π

Ratio: 1 : 4

Measure of ∠xoy: π/2

Step-by-step explanation:

We are given an arc length of 16π. Since it's in terms of pi, we use the formula

S = rФ where r is the radius, and Ф is the measure of the angle in radians (in terms of pi)

We are given S = 16π and r = 32, plug those in and find Ф

16π = 32Ф

16π/32 = Ф

π/2 = Ф

This is the measure of the central angle.

The angle is π/2 radians. There are 2π radians in the circumference, so the circumference is 4 times the arc length created by the central angle. (There are 4 halves in 2) so the ratio of the arc length tothe circumference is 1 : 4

The formula for circumference is C = 2πr, where r is the radius, so we hace

C = 2π(32) = 64π

Vesna [10]1 year ago

4 0

Answer:

1/4

90 degrees

Step-by-step explanation:

just took it! :)

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Two number cubes are rolled to determine how a token moves on a game board. The sides of

ahrayia [7]

Answer:

D. The mathematical expectation of Option A is 1. The mathematical expectation of Option B is 1.5. Option B offers a greater likelihood of advancing to the finish line.

Step-by-step explanation:

The result of a product is odd only when the two numbers are odds.

There are 6*6 = 36 possible outcomes when two dice are rolled. Only 9 of them are a combination of two odd numbers: {1, 1} {1, 3} {1, 5} {3, 1} {3, 3} {3, 5} {5, 1} {5, 3} {5, 5}. Then 36 - 9 = 27 outcomes are even.

P(even) = 27/36 = 0.75

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Option B) Mathematical expectation: 0.75*5 + 0.25*(-9) = 1.5

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2 years ago

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2 years ago

The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv

Rina8888 [55]

Answer:

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=14.42$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=6.95$ represent the population standard deviation

n=36 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

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2 years ago

If two lines are perpendicular describe the relationship between their slopes

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1 year ago

On the surface of the moon, the value of g is 1.67 m/s2. What is the horizontal distance traveled during a 2.00-meter high jump

rodikova [14]

To solve this question, you need to find how long jump is. For 2m high with <span>1.67 m/s2 it would be:

h= 1/2 gt^2
2= 1/2 * (1.67) t^2
t^2= 1.67
t= 1.29

If the speed is 20 mph and the jump is 2 second, the distance traveled would be:
20 miles/ hour * 1.29 second * (1 hour/3600second)= 0.007179 miles

If you need to convert it to meter then: </span>0.007179 mile * 1609.34meter/ mile= 11.55 meter

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1 year ago