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3 years ago

Given that (9,-8) is on the graph of f(x), find the corresponding point for the function f(3/4x)

Mathematics

1 answer:

Ilia_Sergeevich [38]3 years ago

5 0

Answer:

The corresponding point for the function f(3/4 x) is (12 , -8)

Step-by-step explanation:

* Lets revise the horizontal stretch or compress

- A horizontal stretching is the stretching of the graph away from

the y-axis

- A horizontal compression is the squeezing of the graph toward

the y-axis.

# if k > 1, the graph of y = f(k•x) is the graph of f(x) horizontally

compressed by dividing each of its x-coordinates by k.

# if 0 < k < 1 (a fraction), the graph y = f(k·x) is the graph of f(x)

horizontally stretched by dividing each of its x-coordinates by k.

* Now lets solve the problem

- The function f(x) will be the function f(3/4 x)

∵ The x multiplied by a constant

∴ f(x) stretched or compressed horizontally

∵ f(x) ⇒ f(k · x)

∵ f(x) ⇒ f(3/4 x)

∴ k = 3/4 ⇒ less than 1

∵ 0 < k < 1

∴ f(x) starched horizontally

∴ Divide each of its x-coordinates by k

∵ k = 3/4

∴ Divide each of its x-coordinates by 3/4

∵ Point (9 , -8) is on the graph of f(x)

- Find the corresponding point on the graph f(3/4 x) by dividing

x-coordinate by 3/4

∵ x = 9

∴ The corresponding x = 9 ÷ 3/4 = 9 × 4/3 = 36/3 = 12

∴ The corresponding point is (12 , -8)

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Sauron [17]

Answer:

$\large\boxed{-9y^5}$

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3 years ago

In a certain clinical study, 15% of participants were classified as heavy smokers, 25% as light-smokers, and the rest as non-smo

Natasha_Volkova [10]

Answer:

There is a 28.57% probability that a randomly selected participant who died by the end of the study was a non-smoker.

Step-by-step explanation:

We have the following probabilities:

A 15% probability that a participant is classified as a heavy smoker.

A 25% probability that a participant is classified as a light smoker.

A 100% - 25% - 15% = 60% probability that a participant is classified as a non smoker.

A x% probability that a non smoker dies.

A 3x% probability that a light smoker dies.

A 5x% probability that a heavy smoker dies.

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

This problem is:

What is the probability of the participant being a non-smoker, given that he died?

P(B) is the probability that the participant is a non smoker. So

$P(B) = 0.6$

P(A/B) is the probability that the participant dies, given that he is a non smoker. So:

$P(A/B) = x$

P(A) is the probability that the participant dies:

$P(A) = P_{1} + P_{2} + P_{3}$

$P_{1}$ is the probability that a heavy smoker is selected and that he dies. So:

$P_{1} = 0.15*5x = 0.75x$

$P_{2}$ is the probability that a light smoker is selected and that he dies. So:

$P_{2} = 0.25*3x = 0.75x$

$P_{3}$ is the probability that a non-smoker is selected and that he dies. So:

$P_{3} = 0.60*x = 0.60x$

The probability that a participant dies is:

$P(A) = P_{1} + P_{2} + P_{3} = 0.75x + 0.75x + 0.60x = 2.10x$

The probability of the participant being a non-smoker, given that he died, is:

$P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.6x}{2.10x} = \frac{0.6}{2.10} = 0.2857$

There is a 28.57% probability that a randomly selected participant who died by the end of the study was a non-smoker.

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3 years ago