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Alchen [17]
3 years ago
7

14. Consider the following questions: give the distribution name, carefully define the random variables you use and find the fin

al answer. a) A professor has made 20 exams of which 8 are hard, 7 are reasonable, and 5 are easy. The exams are mixed up and the professor selects 4 of them at random to give to four sections of the course she is teaching. What is the probability that no sections receive a hard test
Mathematics
1 answer:
malfutka [58]3 years ago
6 0

Answer: the probability that no sections receive a hard test is 0.1022

Step-by-step explanation:

Given that;

total number of exams = 20

hard exams = 8

reasonable = 7

easy exam = 5

so total exams that are bot hard = 7 + 5 = 12

we will make use of the probability mass function of hyper geometric distribution;

so the probability that no section of the received a hard test can be determined as follows;

P( x=0; N=20, n=4, k=8 ) = [ ⁸C₀ × ²⁰⁻⁸C₄₋₀ ] / ²⁰C₄

= [1 × ¹²C₄ ] / ²⁰C₄

= [1 × (12!/(4!×(12-4)!) ] / (20!/(4!×(20-4)!)

= [1 × 495 ] / 4845

= 495 / 4845

= 0.1022

Therefore the probability that no sections receive a hard test is 0.1022

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Which expression is equivalent to log Subscript c Baseline StartFraction x squared minus 1 Over 5 x EndFraction?
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The equivalent expression of \log_c(\frac{x^2 - 1}{5x}) is \log_c(x^2 - 1) - \log_c(5x)

<h3>How to determine the equivalent expression?</h3>

The logarithmic expression is given as:

\log_c(\frac{x^2 - 1}{5x})

The law of logarithm states that:

log(a) - log(b) = log(a/b)

This means that the expression can be split as:

\log_c(\frac{x^2 - 1}{5x}) = \log_c(x^2 - 1) - \log_c(5x)

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3 years ago
- Monica goes for a 60 minute bike ride each day in the summer. Let a rep
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Answer:

m = 60a

a = Independent Variable

m = Dependent Variable.

For a = 1 day, m = 60 minutes

For a = 2 days, m = 120 minutes

For a = 3 days, m = 180 minutes

For a = 4 days, m = 240 minutes

For a = 5 days, m = 300 minutes

For a = 6 days, m = 360 minutes

For a = 7 days, m = 420 minutes

Step-by-step explanation:

Monica goes for a 60-minute bike ride each day in the summer.

If a represents the number of days Monica rides her bike and m represents the total number of minutes she spends riding her bike, then a represents the independent variable and m represents the dependent variable.

The relation between a and m can be written as an equation, m = 60a.

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For a = 4 days, m = 60 × 4 = 240 minutes

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For a = 6 days, m = 60 × 6 = 360 minutes

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