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3 years ago

3/2 ( x - 2 ) - 5 = 19

Mathematics

1 answer:

Gnom [1K]3 years ago

4 0

Answer:

x = 18

Step-by-step explanation:

Distribute 3/2 inside the parentheses

3/2x - 3 - 5 = 19

Combine like terms

3/2x - 8 = 19

Isolate x by adding 8 to both sides

3/2x = 27

Multiply by the reciprocal

x = 18

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The line segment between (9,6) and (-2,-1) is bisected at (3.5,2.5). Find the y-intercept of the perpendicular bisector.

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Answer:

Y-intercept is (0,8)

Step-by-step explanation:

Firstly, we need to get the equation of the line segment

We have the general equation as;

y = mx + b

m is the slope and b is the y-intercept

So for the slope between (9,6) and (-2,-1); we have

m = (y2-y1)/(x2-x1)

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7m = -11

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The equation of the second line is;

y = mx + b

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2 years ago

A power plant discharges water into a river. Regulators determine that as long as the mean temperature of the discharged water i

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Answer:

(A) Type I error in the context of this problem is chances of regulators believing that the mean temperature of the discharged water is more than 150°F but in actual the mean temperature of the discharged water was 150°F.

(B) Type II error in the context of this problem is chances of regulators believing that the mean temperature of the discharged water is no more than 150°F but in actual the mean temperature of the discharged water was more than 150°F.

(C) An environmental group will consider the Type II error more serious.

Step-by-step explanation:

We are given that a power plant discharges water into a river. Regulators determine that as long as the mean temperature of the discharged water is no more than 150°F, there will be no negative effects on the river’s ecosystem.

We are also given with the following hypothesis;

Null Hypothesis, $H_0$ : $\mu$ = 150°F

Alternate Hypothesis, $H_a$ : $\mu$ > 150°F

(A) Type I error states that Probability of rejecting null hypothesis given the fact that null hypothesis was true or in other words Probability of rejecting a true hypothesis.

So, Type I error in the context of this problem is chances of regulators believing that the mean temperature of the discharged water is more than 150°F but in actual the mean temperature of the discharged water was 150°F.

(B) Type II error states that Probability of accepting null hypothesis given the fact that null hypothesis was false or in other words Probability of accepting a false hypothesis.

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