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2 years ago

what is the function rule for the transformed with vertical stretch by a factor of 2 and translated down 6

1 answer:

5 0

Answer: Thus, the equation of a function stretched vertically by a factor of 2 and then shifted 3 units up is y = 2f (x) + 6, and the equation of a function stretched horizontally by a factor of 2 and then shifted 6 units left is y = f ( (x - 6)) = f ( x - ). Example: f (x) = 2x2.

Step-by-step explanation:

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A student takes an exam containing 1414 multiple choice questions. The probability of choosing a correct answer by knowledgeable

Readme [11.4K]

Answer:

0.0082 = 0.82% probability that he will pass

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the students guesses the correct answer, or he guesses the wrong answer. The probability of guessing the correct answer for a question is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$n = 14, p = 0.3$ .

If the student makes knowledgeable guesses, what is the probability that he will pass?

He needs to guess at least 9 answers correctly. So

$P(X \geq 9) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{14,9}.(0.3)^{9}.(0.7)^{5} = 0.0066$

$P(X = 10) = C_{14,10}.(0.3)^{10}.(0.7)^{4} = 0.0014$

$P(X = 11) = C_{14,11}.(0.3)^{11}.(0.7)^{3} = 0.0002$

$P(X = 12) = C_{14,12}.(0.3)^{12}.(0.7)^{2} = 0.000024$

$P(X = 13) = C_{14,13}.(0.3)^{13}.(0.7)^{1} = 0.000002$

$P(X = 14) = C_{14,14}.(0.3)^{14}.(0.7)^{0} \cong 0$

$P(X \geq 9) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.0066 + 0.0014 + 0.0002 + 0.000024 + 0.000002 = 0.0082$

0.0082 = 0.82% probability that he will pass

6 0

2 years ago

Suppose the diameter of a circle is 4 units. What is its circumference?

Murrr4er [49]

12.5663706144 or yes, 12.57

3 0

3 years ago

Two cities are 45 miles apart. Two trains, with speeds of 70 mph and 60 mph, leave the two cities at the same time so that one i

KATRIN_1 [288]

The distance between the trains is changing at the rate of (70 -60) = 10 mph. They will be in the same place (45 mi)/(10 mi/h) = 4.5 hours after they leave their respective cities. They will be 10 miles apart both 1 hour before that time and one hour after that time.

The trains will be 10 miles apart 3.5 hours after leaving.

They will be 10 miles apart the second time 5.5 hours after leaving.

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3 years ago

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Mice21 [21]

Answer:

25 ounces of water

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2 years ago

Renata's recipe for her famous Kale 'n' Clam Quencher calls for kale juice and clam juice in a 3:1 ratio. If Renata pours 18 lit