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Marina CMI [18]
2 years ago
10

Given a point A(-3,-1), it is dilated by some scale

Mathematics
1 answer:
Sidana [21]2 years ago
3 0

Answer:

B' = (-3, -15)

Step-by-step explanation:

Given

A = (-3,-1)

A' = (-9,-3)

B = (-1,-5)

Required

Determine the coordinates of B'

Since A' is the image of A; we need to first calculate the scale factor using

A' = A * Scale\ factor

Make Scale Factor the subject

Scale\ Factor = \frac{A'}{A}

Substitute values for A' and A

Scale\ Factor = \frac{(-9,-3)}{(-3, -1)}

Factorize the numerator

Scale\ Factor = \frac{3 * (-3,-1)}{(-3, -1)}

Scale\ Factor = \frac{3 * 1}{1}

Scale\ Factor = 3

The coordinates of B' is then calculated as follows:

B' = B * Scale\ Factor

Substitute values for B and Scale Factor

B' = (-1,-5) * 3

B' = (-3, -15)

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-100

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Assume that a spherical cell, with a diameter of 18 μm, has spherical mitochondria, each with a diameter of 0.18 μm. If mitochon
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4 0
3 years ago
"A study conducted at a certain college shows that 56% of the school's graduates find a job in their chosen field within a year
KiRa [710]

Answer:

99.27% probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they find a job in their chosen field within one year of graduating, or they do not. The probability of a student finding a job in their chosen field within one year of graduating is independent of other students. 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.

56% of the school's graduates find a job in their chosen field within a year after graduation.

This means that p = 0.56

Find the probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.

This is P(X \geq 1) when n = 6.

Either none find a job, or at least one does. The sum of the probabilities of these events is decimal 1. So

P(X = 0) + P(X \geq 1) = 1

P(X \geq 1) = 1 - P(X = 0)

In which

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

P(X = 0) = C_{6,0}.(0.56)^{0}.(0.44)^{6} = 0.0073

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0073 = 0.9927

99.27% probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.

8 0
2 years ago
When QS=6x and CS=5x-8, what is AB?
patriot [66]

Answer:

AB = x+ 8

Step-by-step explanation:

Given : QS=6x and CS=5x-8

From the given figure,

QS = QC + CS

We are given with  QS  and CS

Replace it the above equation

6x = QC + 5x -8

Solve for QC

Subtract 5x on both sides

x = QC + -8

Add 8 on both sodes

QC= x + 8

QABC is a rectangle

QC = AB

So AB = x+ 8


4 0
3 years ago
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