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mylen [45]
3 years ago
9

What happens to the Law of Cosines if the known angle is 90 degrees?

Mathematics
1 answer:
poizon [28]3 years ago
8 0

Answer:

See below.

Step-by-step explanation:

It transforms  to the Pythagoras theorem.

c^2  = a^2 + b^2 - 2ab cos C

If C = 90,  cos C = zero so the last term disappears.

c^2  = a^2 + b^2 - 2ab * 0

c^2 = a^2 + b^2.

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The length is 14 cm :)
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The scores of students on the ACT college entrance exam in a recent year had the normal distribution with mean  =18.6 and stand
Maurinko [17]

Answer:

a) 33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.

b) 0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher

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 random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 18.6, \sigma = 5.9

a) What is the probability that a single student randomly chosen from all those taking the test scores 21 or higher?

This is 1 subtracted by the pvalue of Z when X = 21. So

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

Z = \frac{21 - 18.6}{5.4}

Z = 0.44

Z = 0.44 has a pvalue of 0.67

1 - 0.67 = 0.33

33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.

b) The average score of the 76 students at Northside High who took the test was x =20.4. What is the probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher?

Now we have n = 76, s = \frac{5.9}{\sqrt{76}} = 0.6768

This probability is 1 subtracted by the pvalue of Z when X = 20.4. So

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

By the Central Limit Theorem

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

Z = \frac{20.4 - 18.6}{0.6768}

Z = 2.66

Z = 2.66 has a pvalue of 0.9961

1 - 0.9961 = 0.0039

0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher

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2 years ago
An employee receives a 2% raise once per year. If the employee's initial salary is $60,000.00, what will
satela [25.4K]

Answer:

The employee's salary after 9 years will be$70800

Step-by-step explanation:

find the % raise of the salary per year:2%×$60000=$1200

Then multiply the raise by the number of years:$1200×9=$10800

finally add the product with the initial salary:$10800+$60000=$70800

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Maria is mailing packages. each small package costs her $2.20 to send. each large package costs her $2.90. how much will it cost
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2 years ago
Please i need help with this question asap
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Answer:

I'm pretty sure it's C

Step-by-step explanation:

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2 years ago
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