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mrs_skeptik [129]
3 years ago
10

Given H(6,7) and I (-7,-6) if point G lies 1/2 of the way long line segment HI, Santiago argues that point G is located at the o

rigin. Is Santiago Correct. Justify your answer
Mathematics
1 answer:
amid [387]3 years ago
4 0
A point that is half way of line segment is the midpoint

Let (6, 7) be (x₁, y₁) and (-7, -6) be (x₂, y₂)

Mid point of HI = (\frac{x_1+x_2}{2},  \frac{y_1+y_2}{2})
Mid point of HI = (\frac{6+-7}{2},  \frac{7+-6}{0})
Mid point of HI = (- \frac{1}{2} ,  \frac{1}{2})

Santiago's statement is not correct
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Triangle ABC has angle measures as shown.
sladkih [1.3K]
As with any triangle, the sum of angles is 180°.

(a)
(x -5) +(3x +30) +35 = 180 . . . . . sum of angles is 180
4x +60 = 180 . . . . . . . . . . . . . . . . collect terms
4x = 120 . . . . . . . . . . . . . . . . . . . . subtract 60
x = 30 . . . . . . . . . . . . . . . . . . . . . . divide by 4


(b)
Angle A = x -5 = 30 -5 = 25

Angle B = 3x +30 = 3*30 +30 = 120
3 0
3 years ago
The radius of a circle is 7 mm. What is the area.
Solnce55 [7]

Answer:

A= 153.94 mm

Step-by-step explanation:

A = πr²

A=π(7)²

A= 153.94 mm

7 0
2 years ago
A random sample of 40 binomial trials resulted in 14 successes. test the claim that the population proportion of successes does
mylen [45]

Using the z-distribution, since the p-value of the test is of 0.057 > 0.05, there is not enough evidence that the population proportion of successes does not equal 0.50.

<h3>What are the hypotheses tested?</h3>

At the null hypotheses, we test if the proportion of successes equals 0.5, hence:

H_0: p = 0.5

At the alternative hypotheses, we test if it does not equal, hence:

H_1: p \neq 0.5

<h3>What is the test statistic?</h3>

The test statistic is given by:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}

In which:

  • \overline{p} is the sample proportion.
  • p is the proportion tested at the null hypothesis.
  • n is the sample size.

For this problem, the parameters are given by:

n = 40, \overline{p} = \frac{14}{40} = 0.35, p = 0.5

Hence the test statistic is given by:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}

z = (0.35 - 0.5)/(0.5/sqrt(40))

z = -1.9.

<h3>What is the decision?</h3>

Using a z-distribution calculator, considering a two-tailed test, as we are testing if the proportion is different of a value, with z = -1.9, we get that the p-value of the test is of 0.057.

Since the p-value of the test is of 0.057 > 0.05, there is not enough evidence that the population proportion of successes does not equal 0.50.

More can be learned about the z-distribution at brainly.com/question/16313918

#SPJ4

5 0
1 year ago
An artist wants to frame a square painting with an area of 400 square inches . she wants
Artemon [7]
(a) x^{2} = 400
(b) \sqrt{x^2} = \sqrt{400}
x=20,-20
(c) Only the positive solution makes sense because you cannot have a negative side length.
(d) Since one side of the painting is 20 inches, all four sides together will be 20*4 = 80 inches
6 0
3 years ago
Find the probability that the hitter makes 10 outs in 10 consecutive​ at-bats, assuming​ at-bats are independent events.​ Hint:
emmainna [20.7K]

Answer:

0.037

Step-by-step explanation:

If the hitter makes an out 72​% of the time, then the probabilty that he makes hit in 1 at-bat is p=0.72 and the probabilty that he doesn't make hit in 1 at-bat is q=1-p=1-0.72=0.28.

The probability that the hitter makes 10 outs in 10 consecutive​ at-bats, assuming​ at-bats are independent events is

P=p^{10}=(0.72)^{10}\approx 0.037.

5 0
3 years ago
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