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Paul [167]
3 years ago
10

Find the value of the variable and the measure of each labeled angle

Mathematics
1 answer:
ololo11 [35]3 years ago
8 0
Since the two angles that you have are vertical angles, we know that vertical angles are congruent, so you have to set them to equal each other.

x+24=5x-36
-4x+24=-36
-4x=-60
x=15

We now have the value of x so now we plug it in for each expression of each angle.

x+24=?
15+24=39

5x-36=?
5(15)-36=?
75-36=39
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Solve for all values of x by factoring. x^2-x-18= -4x
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Answer:

x=-6,x=3

Step-by-step explanation:

x^2-x-18=-4x

Adding both sides by 4x

x^2+3x-18=0

Factoring

(x+6)(x-3)=0

x=-6,x=3

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How many minutes are there in 600 seconds
Katen [24]
There are 10 minutes in 600 seconds

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4 0
3 years ago
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Logbase(a)b+clogbase(a)d-rlogbase(a)s
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8 0
3 years ago
Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with
Charra [1.4K]

Answer:

96.24% probability that a SRS of 25 students will spend an average of between 600 and 700 dollars

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 = 650, \sigma = 120, n = 25, s = \frac{120}{\sqrt{25}} = 24

What is the probability that a SRS of 25 students will spend an average of between 600 and 700 dollars

This is the pvalue of Z when X = 700 subtracted by the pvalue of Z when X = 600. So

X = 700

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

By the Central Limit Theorem

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

Z = \frac{700 - 650}{24}

Z = 2.08

Z = 2.08 has a pvalue of 0.9812

X = 600

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

Z = \frac{600 - 650}{24}

Z = -2.08

Z = -2.08 has a pvalue of 0.0188

0.9812 - 0.0188 = 0.9624

96.24% probability that a SRS of 25 students will spend an average of between 600 and 700 dollars

6 0
3 years ago
Read 2 more answers
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