Which angle has a measure closet to 30 degrees?

Find PQ if possible

cupoosta [38]

Answer:

11 units.

Step-by-step explanation:

8 0

2 years ago

Multiplying a certain even number by 4 then subtracting 16 gives you the next consecutive even number. Find the original number

anyanavicka [17]

Let 2k represent the original even number (such that k is an integer)

then 2(k + 1) is the next consecutive even number.

4(2k) - 16 = 2(k + 1)

8k - 16 = 2k + 2

6k = 18

k = 3

since 2k represents the original number, then 2(3) = 6 is the oroginal number

Answer: 6

3 0

3 years ago

Based on historical data, your manager believes that 37% of the company's orders come from first-time customers. A random sample

fomenos

Answer:

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$