Diameter=14.6 round to nearest tenth

A dump truck driver created 3 equal mounds of dirt from 1/6 of his load. What fraction of the entire load of dirt was in each mo

Lorico [155]

Lets see the answer to this question the fraction of the entire load of dirt in each mound is b.1/2 this is how i got my answer you multiply 3*1/6=1/2 so the fraction of the entire load of dirt that was in each mound is 1/2

5 0

2 years ago

Read 2 more answers

The composite scores of individual students on the ACT college entrance examination in 2009 followed a normal distribution with

Mumz [18]

Answer:

35.57% probability that a single student randomly chosen from all those taking the test scores 23 or higher.

0.41% probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher.

The lower the standard deviation, the higher the z-score, which means that the higher the pvalue of X = 23, which means there is a lower probability of scoring above 23. By the Central Limit Theorem, as the sample size increases, the standard deviation decreases, which means that Z increases.

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:

$\mu = 21.1, \sigma = 5.1$

What is the probability that a single student randomly chosen from all those taking the test scores 23 or higher?

This is the pvalue of Z when X = 23.

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

$Z = \frac{23 - 21.1}{5.1}$

$Z = 0.37$

$Z = 0.37$ has a pvalue of 0.6443

1 - 0.6443 = 0.3557

35.57% probability that a single student randomly chosen from all those taking the test scores 23 or higher.

What is the probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher?

Now we use the central limit theorem, so $n = 50, s = \frac{5.1}{\sqrt{50}} = 0.72$

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

$Z = \frac{23 - 21.1}{0.72}$

$Z = 2.64$

$Z = 2.64$ has a pvalue of 0.9959

1 - 0.9959 = 0.0041

0.41% probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher.

Why is it more likely that a single student would score this high instead of the sample of students?

The lower the standard deviation, the higher the z-score, which means that the higher the pvalue of X = 23, which means there is a lower probability of scoring above 23. By the Central Limit Theorem, as the sample size increases, the standard deviation decreases, which means that Z increases.

5 0

3 years ago

What is the sum of the interior angles of the polygon shown below?

Free_Kalibri [48]

Hope this will help u...✌☝☝

6 0

3 years ago

The original rectangle has a perimeter of 16

svet-max [94.6K]

12.4 / 6.2 = 2

so other side of enlarged rectangle = 1.8 x 2 = 3.6

Perimeter of enlarged rectangle = 2(3.6 + 12.4) = 32

Answer: 32 feet

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Another way to do:

12.4 / 6.2 = 2

SF = 2

The original rectangle has a perimeter of 16

Perimeter of the enlarged rectangle = 16 x 2 = 32

Answer: 32 feet

5 0

3 years ago

What is the slope of the line? As soon as possible please !!

mixer [17]

Answer:

$m=\frac{-8}{5}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (-1, 4)

Point (4, -4)

Step 2: Find slope m

Substitute [Slope Formula]: $m=\frac{-4-4}{4+1}$
Subtract/Add: $m=\frac{-8}{5}$

5 0

2 years ago