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3 years ago

Can someone help me with this math question it involves transformation

Mathematics

1 answer:

Thepotemich [5.8K]3 years ago

3 0

Answer:

ABCD is reflected over the y-axis and translate (x + [-4] , y + [-4])

Step-by-step explanation:

* Lets explain the reflection and the translation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If the point (x , y) translated horizontally to the right by h units

∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

∴ Its image is (x , y - k)

* Now lets solve the problem

∵ The vertices of ABCD are:

A = (-5 , 2) , B = (-3 , 4) , C = (-2 , 4) , D = (-1 , 2)

- If ABCD reflected over the y-axis we will change the sign of the

x-coordinate of all the points

∴ The image of A = (5 , 2)

∴ The image of B = (3 , 4)

∴ The image of C = (2 , 4)

∴ The image of D = (1 , 2)

∴ The image of ABCD after reflection over the y-axis will be at

the first quadrant

- The figure EHGF is left and down the image of ABCD after

the reflection over the y-axis

∴ The image is translate to the left and down

∵ E = (1 , -2) and E is the image of A after reflection and translation

∵ The image of a after reflection is (5 , 2)

- That means 5 became 1 and 2 became -2

∵ 1 - 5 = -4

∴ The image of A after reflection translate 4 units to the left

∵ -2 - 2 = -4

∴ The image of A after reflection translate 4 units down

∴ ABCD is reflected over the y-axis and translate (x + [-4] , y + [-4])

* You can check the rest of points

# B with H

∵ B = (-3 , 4) after reflection over y-axis is (3 , 4) after translation is

(3 + [-4] , 4 + [-4]) = (-1 , 0) the same with point H = (-1 , 0)

# C with G

∵ C = (-2 , 4) after reflection over y-axis is (2 , 4) after translation is

(2 + [-4] , 4 + [-4]) = (-2 , 0) the same with point G = (-2 , 0)

# D with F

∵ D = (-1 , 2) after reflection over y-axis is (1 , 2) after translation is

(1 + [-4] , 2 + [-4]) = (-3 , -2) the same with point F = (-3 , -2)

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2 years ago

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Step-by-step explanation:

Splitting the Statement into two, we have

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and

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So, Statement 1 can be written as

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PS:

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Answer:

The probability of Steve agreeing with the company’s claim is 0.50502.

Step-by-step explanation:

Let X denote the number of green candies.

The probability of green candies is, p = 0.20.

Steve buys 30 bags of 30 candies, randomly selects one candy from each, and counts the number of green candies.

So, n = 30 candies are randomly selected.

All the candies are independent of each other.

The random variable X follows a binomial distribution with parameter n = 30 and p = 0.20.

It is provided that if there are 5, 6, or 7 green candies, Steve will conclude that the company’s claim is correct.

Compute the probability of 5, 6 and 7 green candies as follows:

$P(X=5)={30\choose 5}(0.20)^{5}(1-0.20)^{30-5}=0.17228\\\\P(X=6)={30\choose 6}(0.20)^{6}(1-0.20)^{30-6}=0.17946\\\\P(X=7)={30\choose 7}(0.20)^{7}(1-0.20)^{30-7}=0.15328$

Then the probability of Steve agreeing with the company’s claim is:

P (Accepting the claim) = P (X = 5) + P (X = 6) + P (X = 7)

= 0.17228 + 0.17946 + 0.15328

= 0.50502

Thus, the probability of Steve agreeing with the company’s claim is 0.50502.

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