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pav-90 [236]
3 years ago
8

Find the length of the arc on a circle of radius 12 feet intercepted by a central angle of 150°.

Mathematics
1 answer:
stich3 [128]3 years ago
5 0
Let A = arc length of circle

A = 2πr•(degree/360°)

A = 2π(12)(150°/360°)

A = 24π(150°/360°)

Calculate the right side to find A and you're done. Take it from here.
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In order to ensure efficient usage of a server, it is necessary to estimate the mean number
juin [17]

Answer:

a. [36.19;39.21]

b. Reject the null hypothesis. The population mean of users that are connected at the same time is greater than 35.

Step-by-step explanation:

Hello!

Your study variable is,

X: "number of users of one server at a time"

The objective is to estimate the mean, for this, a sample of n=100 times was taken and the standard deviation S= 9.2 and the sample mean is X[bar]= 37.7 were calculated.

You need to study the population mean, for this you need your variable to have at least normal distribution. Since you don't have information about its distribution, but the sample is big enough (n≥30) you can apply the Central Limit Theorem and approximate the distribution of the sample mean X[bar] to normal:

X[bar]≈N(μ;σ²/n)

a. With this approximation, you can construct the 90% Confidence Interval using the approximate Z

[X[bar] ± Z_{1-\alpha /2} * S/√n]

Z_{1-\alpha /2} = Z_{0.95} = 1.64

[37.7± 1.64* 9.2/√100]

[36.19;39.21]

b. You need to test if the population mean is greater than 35 with a level of significance of 1%.

The hypothesis is:

H₀: μ ≤ 35

H₁: μ > 35

α: 0.01

This is a one-tailed test so you have only one critical level (right tail):

Z_{1\alpha } = Z_{0.99} = 2.33

This means that if the value of the calculated statistic is equal or greater than 2.33 you will reject the null Hypothesis.

If the value is less than 2.33 you will support the null hypothesis.

The statistic is:

Z=<u> X[bar] - μ </u>= <u> 37.7 - 35 </u> = 2.93

       S/√n           9.2/10

The value 2.93 > 2.33, so you reject the null hypothesis. This means that the population mean of users that are connected at the same time is greater than 35.

<u><em>Note: </em></u><em>To make the decision using the interval calculated on a), the hypothesis should have been two-tailed and the confidence and significance levels complementary.</em>

I hope it helps!

7 0
3 years ago
Share 60 in the ratio 5 7
nignag [31]
If the ratio is 5:7 then the each part has a value of:

60/(5+7)=5 so from a total of 60

5:7 becomes 5*5:7*5 which is:

25:35
7 0
3 years ago
Graph the line y=−3x+b if it is known that the graph goes through point:<br> b<br> B(5, 2)
egoroff_w [7]

Answer: y=-3x+17

b = 17

4 0
3 years ago
SOMEONE HELP I WILL GIVE BRAINLIEST 6TH GRADE MATH
jasenka [17]

Answer:

1. 15%

2. 85%

Step-by-step explanation:

The graph is 100 units,

the shaded part is 15 units,

so it is 15%,

if it is 15% than the unshaded part is 85%.

3 0
3 years ago
Boris has ridden 21 miles of a bike course. The course is 30 miles long. What percentage of the course has Boris ridden so far?
snow_lady [41]

Answer:

70%

Step-by-step explanation:

21/30 * 100 = 70%

3 0
2 years ago
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