If j||k, what must be the measure of the angle marked x?

Which representation does NOT represent y as a function of x?

siniylev [52]

<h3>Answer: Choice C</h3>

Why isn't choice C a function? It's because we have the input x = 4 lead to more than one output at the same time (y = 5 and y = -5). A function must have all allowed inputs lead to exactly one output.

The diagram for choice C shows we have the points (4,5) and (4,-5). If we plotted those two points, then a vertical line forms, which will show this relation fails the vertical line test.

Choices A, B, and D do not have this happen where a certain input leads to multiple outputs at once; therefore, these are all functions. For the tables A and D, note there aren't any repeated x values. If you were to convert choice C into table form, then you would have the x value 4 repeat itself.

7 0

2 years ago

Read 2 more answers

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 104 inches, and a standard

dsp73

Answer:

91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

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 normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 104, \sigma = 14, n = 49, s = \frac{14}{\sqrt{49}} = 2$

What is the probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

This is the pvalue of Z when X = 106.8. So

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

By the Central Limit Theorem

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

$Z = \frac{106.8 - 104}{2}$

$Z = 1.4$

$Z = 1.4$ has a pvalue of 0.9192

0.9192 = 91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

8 0

3 years ago

If the pattern rule is defined by the equation `t = 6n`, where `t` is the term value and `n` is the term number, what is the one

blagie [28]

Answer:

600

Step-by-step explanation:

Given

equation t = 6n

n is term number

we have to find 100th term.

Thus, term number is 100

substituting 100 in place of n in equation t=6n , we can find the value of 100th term

t = 6*100 = 600

Thus, 100th term is 600.

8 0

2 years ago

In a word processing document or on a separate piece of paper, use the guide to construct a two-column proof proving AC > EF

VARVARA [1.3K]

Answer:

Complete proof is written below.

Facts and explanation about the segments shown in question :

As BC = EF is a given statement in the question
AB + BC = AC because the definition of betweenness gives us a clear idea that if a point B is between points A and C, then the length of AB and the length of BC is equal to the length of AC. Also according to Segment addition postulate, AB + BC = AC. For example, if AB = 5 and BC= 7 then AC = AB + BC → AC = 12
AC > BC because the Parts Theorem (Segments) mentions that if B is a point on AC between A and C, then AC > BC and AC>AB. So, if we observe the question figure, we can realize that point B lies on the segment AC between points A and C.
AC > EF because BC is equal to EF and if AC>BC, then it must be true that the length of AC must greater than the length segment EF.

Below is the complete proof of the observation given in the question:

STATEMENT REASON 

___________________________________________________

1. BC = EF 1. Given

2. AB + BC = AC 2. Betweenness

3. AC > BC 3. Def. of segment inequality

4. AC > EF 4. Def. of congruent segments

Keywords: statement, length, reason, proof

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4 0

2 years ago

Period Posers question: Mo's number has 2 periods, in one period he has a 7 in the hundreds place in the other he has an 8 in th

Sidana [21]

780,120?

Attention:check before using this answer it may not be right.
Thank you.

4 0

2 years ago