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ivanzaharov [21]

3 years ago

10

Arsenios says he gets 70 utils per slice from eating pepperoni pizza versus 50 utils from eating cheese pizza. Stavros says he g

ets 60 utils from eating the same pepperoni pizza. What can we conclude

1 answer:

irina1246 [14]3 years ago

6 0

Answer:

Arsenios prefers pepperoni pizza to cheese pizza.

Step-by-step explanation:

Utils are units of utility that show the satisfaction that a consumer gets from using a product. As Arsenios assigns 70 utils per slice from eating pepperoni pizza versus 50 utils from eating cheese pizza, this indicates that he gets more satisfaction from eating pepperoni pizza and because of that, the answer is that we can conclude that Arsenios prefers pepperoni pizza to cheese pizza.

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Write a power represented with a positive base and a positive exponent whose value is less then the base

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Step-by-step explanation:

The base in this case is 5 while the exponent is simply the power to which the base is raised in which case it would be 2. Both values are positive and the exponent is less than the base.

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What is 4.89 + ? = 11.26

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The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 49 househo

KonstantinChe [14]

Answer:

a) 10.38% probability that the sample mean will be more than 59 pounds.

b) 67.72% probability that the sample mean will be more than 56 pounds.

c) 22.10% probability that the sample mean will be between 56 and 57 pounds.

d) 1.46% probability that the sample mean will be less than 53 pounds.

e) 0% probability that the sample mean will be less than 49 pounds.

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

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

In this question, we have that:

$\mu = 56.8, \sigma = 12.2, n = 49, s = \frac{12.2}{\sqrt{49}} = 1.74285$

a. More than 59 pounds

This is 1 subtracted by the pvalue of Z when X = 59. So

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

By the Central Limit Theorem

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

$Z = \frac{59 - 56.8}{1.74285}$

$Z = 1.26$

$Z = 1.26$ has a pvalue of 0.8962.

1 - 0.8962 = 0.1038

10.38% probability that the sample mean will be more than 59 pounds.

b. More than 56 pounds

This is 1 subtracted by the pvalue of Z when X = 56. So

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

$Z = \frac{56 - 56.8}{1.74285}$

$Z = -0.46$

$Z = -0.46$ has a pvalue of 0.3228.

1 - 0.3228 = 0.6772

67.72% probability that the sample mean will be more than 56 pounds.

c. Between 56 and 57 pounds

This is the pvalue of Z when X = 57 subtracted by the pvalue of Z when X = 56. So

X = 57

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

$Z = \frac{57 - 56.8}{1.74285}$

$Z = 0.11$

$Z = 0.11$ has a pvalue of 0.5438

X = 56

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

$Z = \frac{56 - 56.8}{1.74285}$

$Z = -0.46$

$Z = -0.46$ has a pvalue of 0.3228.

0.5438 - 0.3228 = 0.2210

22.10% probability that the sample mean will be between 56 and 57 pounds.

d. Less than 53 pounds

This is the pvalue of Z when X = 53.

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

$Z = \frac{53 - 56.8}{1.74285}$

$Z = -2.18$

$Z = -2.18$ has a pvalue of 0.0146

1.46% probability that the sample mean will be less than 53 pounds.

e. Less than 49 pounds

This is the pvalue of Z when X = 49.

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

$Z = \frac{49 - 56.8}{1.74285}$

$Z = -4.48$

$Z = -4.48$ has a pvalue of 0.

0% probability that the sample mean will be less than 49 pounds.

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3 years ago

"what quadrant is...." PLEASE PLEASE HELP!!!! Thank you so so much!!! *will give brainliest*

sdas [7]

Given:

$\tan \theta > 0$ and $\sec \theta$ .

To find:

The quadrant.

Solution:

We know that,

In I quadrant, all trigonometric ratios are positive.

In II quadrant, only $\sin \theta, \text{cosec}\theta$ are positive and others are negative.

In III quadrant, only $\cot \theta, \tan\theta$ are positive and others are negative.

In IV quadrant, only $\cos \theta, \sec\theta$ are positive and others are negative.

We have,

$\tan \theta > 0$ and $\sec \theta$ .

Here, $\tan \theta$ is positive and $\sec \theta$ is negative. So, $\theta$ lies in the III quadrant.

Therefore, the correct option is C, i.e., III.

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3 years ago