The angle of a sector of a cone is 135, and the slant height is 20 centimeters. What is the diameter of the cone?

An angle measures 54° less than the measure of a supplementary angle. What is the measure of each angle?

Katen [24]

X+x+54=180
2x+54=180
2x=126
x=63
63+54=117
one angle is 63, the other is 117

8 0

3 years ago

Nelson purchased a 3 pound bunch

sveticcg [70]

Step-by-step explanation:

you would do 3 ÷ .99 and then when you get the answer from that you would multiply it by 5.

8 0

3 years ago

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a survey amony freshman at a certain university revealed that the number of hours spent studying the week before final exams was

Marat540 [252]

Answer:

Probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.

Step-by-step explanation:

We are given that the number of hours spent studying the week before final exams was normally distributed with mean 25 and standard deviation 15.

A sample of 36 students was selected.

Let $\bar X$ = sample average time spent studying

The z-score probability distribution for sample mean is given by;

Z = $\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }$ ~ N(0,1)

where, $\mu$ = population mean hours spent studying = 25 hours

$\sigma$ = standard deviation = 15 hours

n = sample of students = 36

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the average time spent studying for the sample was between 29 and 30 hours studying is given by = P(29 hours < $\bar X$ < 30 hours)

P(29 hours < $\bar X$ < 30 hours) = P( $\bar X$ < 30 hours) - P( $\bar X$ $\leq$ 29 hours)

P( $\bar X$ < 30 hours) = P( $\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }$ < $\frac{ 30-25}{\frac{15}{\sqrt{36} } }} }$ ) = P(Z < 2) = 0.97725

P( $\bar X$ $\leq$ 29 hours) = P( $\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }$ $\leq$ $\frac{ 29-25}{\frac{15}{\sqrt{36} } }} }$ ) = P(Z $\leq$ 1.60) = 0.94520

So, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2 and x = 1.60 in the z table which has an area of 0.97725 and 0.94520 respectively.

Therefore, P(29 hours < $\bar X$ < 30 hours) = 0.97725 - 0.94520 = 0.0321

Hence, the probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.

7 0

3 years ago

Write down the exact value of cos 60 degrees

Misha Larkins [42]

Answer:

.5

Step-by-step explanation:

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3 years ago

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To survey a town about traffic concerns, Henry divided the town into eight regions and randomly chose 10 households from each re

sergeinik [125]

Given that Henry divided the town into eight regions and randomly chose 10 households from each region in order to survey about traffic concerns. This type of sample is called stratified sampling.

Stratified sampling is a type of sampling method where the researcher divides the population into separate groups, called strata and then, a probability sample (often a simple random sample ) is drawn from each group.

5 0

3 years ago