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3 years ago

5

Hank is throwing a surprise party. The party costs $20 per person. Create an equation and graph to represent the relationship be

tween the cost of the party and the number of friends attending.
The dependent variable is ____.
A. Number of friends (f)
B. Cost of party (c)

2 answers:

Aloiza [94]3 years ago

8 0

It is the number of friends.

Gekata [30.6K]3 years ago

5 0

A.Number of friends i think

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What is the area of the trapezoid?

DanielleElmas [232]

Answer:

C) 100 m^2

Step-by-step explanation:

Area of a trapezoid= h*[(b1+b2)/2]

h=10

b1=8

b2=12

Therefore:

A=10*[(8+12)/2]

A=10*(20/2)

A=10*10

A=100

So the area of the trapezoid is 100 m^2

7 0

3 years ago

The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a sta

nordsb [41]

Answer:

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

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 problem, we have that:

$\mu = 8.2, \sigma = 0.18, n = 100, s = \frac{0.18}{\sqrt{100}} = 0.018$

What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?

This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So

X = 8.22

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

By the Central Limit Theorem

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

$Z = \frac{8.22 - 8.2}{0.018}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665

X = 8.18

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

$Z = \frac{8.18 - 8.2}{0.018}$

$Z = -1.11$

$Z = -1.11$ has a pvalue of 0.1335

0.8665 - 0.1335 = 0.7330

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

8 0

3 years ago

You’ve seen two methods for finding the area of ΔABC—using coordinate algebra (by hand) and using geometry software. How are the

Phantasy [73]

AnsweYou’ve seen two methods for finding the area of ΔABC—using coordinate algebra (by hand) and using geometry software. How are the two methods similar? How are they different? Why might coordinate algebra be important in making and using geometry software?

r:

Step-by-step explanation:

8 0

2 years ago

Alfonso is 8 years older than Ashley. Five years ago Alfonso was three times as old as Ashley. How old is Ashley now?

Pavel [41]

Answer: 9 years

Step-by-step explanation:

Let the present age of Ashley be x.

Then the present age of Alfonso =x+8

Five years ago,

Ashley's age = x-5

Alfonso's age = x+8-5 = x+3

According to the question,

$x+3=3(x-5)\\\Rightarrow\ x+3=3x-15\\\Rightarrow\ 3x-x=3+15\\\Rightarrow\ 2x=18\\\Rightarrow\ x=\frac{18}{2}\\\Rightarrow\ x=9$

Hence, the present age of Ashley =9 years

8 0

3 years ago

Read 2 more answers

Jessica has saved $50. She will add $25 to her savings each week. Ron has saved $40 and will add $25 to his savings each week.

MAVERICK [17]

Answer:

Jessica will have saved $175, and Ron will have saved $165.

Step-by-step explanation:

Jessica starts out with $50. She adds $25 each week, and it's asking how much money she would have in 5 weeks. So, you multiply $25 by 5 to get $125. Then, you add $50 to that to get $175. Same thing for Ron. Multiply $25 by 5 to get $125, but this time add $40 to it to get $165.

6 0

3 years ago

Read 2 more answers