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Pachacha [2.7K]
3 years ago
11

On a coordinate plane, 2 triangles are shown. The first triangle has points M (negative 5, 4), N (negative 2, 3), and L (negativ

e 4, 2). The second triangle has points L prime (negative 4, negative 2), M prime (negative 5, negative 4), and N prime (negative 2, negative 3).
What is the rule for the reflection?

rx-axis(x, y) → (–x, y)
ry-axis(x, y) → (–x, y)
rx-axis(x, y) → (x, –y)
ry-axis(x, y) → (x, –y)
Mathematics
2 answers:
worty [1.4K]3 years ago
7 1

Answer:

The rule of the reflection is rx-axis(x, y) → (x, –y) ⇒ 3rd answer

Step-by-step explanation:

Let us revise the reflection on the axes

If point (x , y) reflected across the x-axis , then its image is (x , -y) , the rule of reflection is rx-axis (x , y) → (x , -y)

If point (x , y) reflected across the y-axis , then its image is (-x , y) , the rule of reflection is ry-axis (x , y) → (-x , y)

In Δ LMN

∵ L = (-4 , 2)

∵ M = (-5 , 4)

∵ N = (-2 , 3)

In ΔL'M'N'

∵ L' = (-4 , -2)

∵ M' = (-5 , -4)

∵ N' = (-2 , -3)

The signs of y-coordinates of the vertices of Δ LMN are changed, that means Δ LMN are reflected across the x-axis

∵ The y-coordinate of L is 2 and the y-coordinate of L' is -2

∵ The y-coordinate of M is 4 and the y-coordinate of M' is -4

∵ The y-coordinate of N is 3 and the y-coordinate of N' is -3

∴ Δ LMN is reflected across the x-axis

∴ The image of point (x , y) is (x , -y)

The rule of the reflection is rx-axis(x, y) → (x, –y)

Veronika [31]3 years ago
4 0

Answer:

c

Step-by-step explanation:

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Answer:

(a) The 90% confidence interval is: (0.60, 0.63) Correct interpretation is (3).

(b) The 95% confidence interval is: (0.42, 0.46) Correct interpretation is (1).

(c) First, the confidence level in part(b) is <u>more than</u> the confidence level in part(a) is, so the critical value of part(b) is <u>more than</u> the critical value of part(a), Second the <u>margin of error</u> in part(b) is <u>more than</u> than in part(a).

Step-by-step explanation:

(a)

Let <em>X</em> = number of dog owners who take more pictures of their dog than of their significant others or friends.

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CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

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Construct a 90% confidence interval for the population proportion of dog owners who take more pictures of their dog than their significant others or friends as follows:

CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.61\pm 1.645\sqrt{\frac{0.61(1-0.61}{1000}}\\=0.61\pm 0.015\\=(0.595, 0.625)\\\approx(0.60, 0.63)

Thus, the 90% confidence interval for the population proportion of dog owners who take more pictures of their dog than their significant others or friends is (0.60, 0.63).

<u>Interpretation</u>:

There is a 90% chance that the true proportion of dog owners who take more pictures of their dog than of their significant others or friends falls within the interval (0.60, 0.63).

Correct option is (3).

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Given:

<em>X</em> = 440

<em>n</em> = 1000

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The (1 - <em>α</em>)% confidence interval for population proportion is:

CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

The sample proportion is:

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The critical value of <em>z</em> for a 95% confidence level is:

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Construct a 95% confidence interval for the population proportion of dog owners who are more likely to complain to their dog than to a friend as follows:

CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.44\pm 1.96\sqrt{\frac{0.44(1-0.44}{1000}}\\=0.44\pm 0.016\\=(0.424, 0.456)\\\approx(0.42, 0.46)

Thus, the 95% confidence interval for the population proportion of dog owners who are more likely to complain to their dog than to a friend  is (0.42, 0.46).

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There is a 95% chance that the true proportion of dog owners who are more likely to complain to their dog than to a friend falls within the interval (0.42, 0.46).

Correct option is (1).

(c)

The confidence interval in part (b) is wider than the confidence interval in part (a).

The width of the interval is affected by:

  1. The confidence level
  2. Sample size
  3. Standard deviation.

The confidence level in part (b) is more than that in part (a).

Because of this the critical value of <em>z</em> in part (b) is more than that in part (a).

Also the margin of error in part (b) is 0.016 which is more than the margin of error in part (a), 0.015.

First, the confidence level in part(b) is <u>more than</u> the confidence level in part(a) is, so the critical value of part(b) is <u>more than</u> the critical value of part(a), Second the <u>margin of error</u> in part(b) is <u>more than</u> than in part(a).

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