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Anvisha [2.4K]
3 years ago
13

Determine whether the three points are the vertices of a right triangle.

Mathematics
1 answer:
solniwko [45]3 years ago
7 0

Answer:

A

Step-by-step explanation:

We plot the points (x,y) in the coordinate system and the points are shown in the diagram attached.

We can draw a line y = -6 connecting the RED and BLUE points. Also, we can draw a line x = 9 connecting the BLUE and GREEN points.

The intersection of these two PERPENDICULAR LINES is at the point (9, -6) (as seen --- The blue point).  So, when two perpendicular lines intersect, that point is a right angle.

So, the 3 points given INDEED make a right triangle.

So, correct answer is A

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. (0.5 point) We simulate the operations of a call center that opens from 8am to 6pm for 20 days. The daily average call waiting
SashulF [63]

Answer:

The 95% t-confidence interval for the difference in mean is approximately (-2.61, 1.16), therefore, there is not enough statistical evidence to show that there is a change in waiting time, therefore;

The change in the call waiting time is not statistically significant

Step-by-step explanation:

The given call waiting times are;

24.16, 20.17, 14.60, 19.79, 20.02, 14.60, 21.84, 21.45, 16.23, 19.60, 17.64, 16.53, 17.93, 22.81, 18.05, 16.36, 15.16, 19.24, 18.84, 20.77

19.81, 18.39, 24.34, 22.63, 20.20, 23.35, 16.21, 21.73, 17.18, 18.98, 19.35, 18.41, 20.57, 13.00, 17.25, 21.32, 23.29, 22.09, 12.88, 19.27

From the data we have;

The mean waiting time before the downsize, \overline x_1 = 18.7895

The mean waiting time before the downsize, s₁ = 2.705152

The sample size for the before the downsize, n₁ = 20

The mean waiting time after the downsize, \overline x_2 = 19.5125

The mean waiting time after the downsize, s₂ = 3.155945

The sample size for the after the downsize, n₂ = 20

The degrees of freedom, df = n₁ + n₂ - 2 = 20 + 20  - 2 = 38

df = 38

At 95% significance level, using a graphing calculator, we have; t_{\alpha /2} = ±2.026192

The t-confidence interval is given as follows;

\left (\bar{x}_{1}- \bar{x}_{2}  \right )\pm t_{\alpha /2}\sqrt{\dfrac{s_{1}^{2}}{n_{1}}+\dfrac{s_{2}^{2}}{n_{2}}}

Therefore;

\left (18.7895- 19.5152 \right )\pm 2.026192 \times \sqrt{\dfrac{2.705152^{2}}{20}+\dfrac{3.155945^2}{20}}

(18.7895 - 19.5125) - 2.026192*(2.705152²/20 + 3.155945²/20)^(0.5)

The 95% CI = -2.6063 < μ₂ - μ₁ < 1.16025996668

By approximation, we have;

The 95% CI = -2.61 < μ₂ - μ₁ < 1.16

Given that the 95% confidence interval ranges from a positive to a negative value, we are 95% sure that the confidence interval includes '0', therefore, there is sufficient evidence that there is no difference between the two means, and the change in call waiting time is not statistically significant.

6 0
2 years ago
What is the surface area of the figure below
skad [1K]
To find the area, your just supposed to multiply
4 0
2 years ago
Identify the number that is NOT the same as the others when rounded to the nearest tenth.
Andrew [12]

Answer:

c. 34.49

Step-by-step explanation:

Note that the nearest tenth place value is directly next to the decimal point (located on the right). Round each number to the nearest tenth. Look at the number in the hundredth place value. If it is 5 or greater round up, if 4 and less, round down.

a. 34.62 rounded to the nearest tenth is 34.6

c. 34.49 rounded to the nearest tenth is 34.5

b. 34.59 rounded to the nearest tenth is 34.6

d. 34.56 rounded to the nearest tenth is 34.6

This makes it so that C. 34.49 is your answer.

~

4 0
3 years ago
Read 2 more answers
What is the value of X that makes this answer true? x-3x=2(4+x)
Andreas93 [3]

The answer is x = -2

6 0
3 years ago
Read 2 more answers
After a week of rain, tadpoles appeared in your pond. After t minutes, you have (7t + 5) tadpoles and your friend has (8t – 3) t
Zanzabum
15t +2 is the total tadpoles u and ur frnd caught
5 0
3 years ago
Read 2 more answers
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