Which equation represents a proportional relationship? A) y = x 8 B) y = 8 x C) y = x 8 + 8 D) y = 8 x + 8

Mathematics

1 answer:

Liula [17]3 years ago

6 0

Answer:

B y=8x

Step-by-step explanation:

A proportional relationship must go through the point x=0, y=0 and be in the form y=kx where x is a constant

A) y = x^8

B) y = 8 x

C) y = x^8 + 8

D) y = 8 x + 8

The only points that is in the form y= kx is option B

C and D do not go through x=0, y=0 and A is not in the form y=kx where k is a constant

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iren [92.7K]

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3 years ago

I need help on both problems.

matrenka [14]

1) Let, the original price = x
We know, sale price is 100 - 15 = 85% of original price.
So, x * 85% = 59
x * 0.85 = 59
x = 59/0.85
x = 69.41

In short, Your Answer would be Option B

2) Let, the original price = x
We know, sale price is 100 - 30 = 70% of original price.
x * 70% = 79
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x = 79/0.70
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In short, Your Answer would be $112.85

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3 years ago

A random sample of n = 100 observations is selected from a population with mean 20 and standard deviation 15. What is the probab

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Answer:

25.14% probability of observing a mean greater than 21

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 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 $s = \frac{\sigma}{\sqrt{n}}$ .