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3 years ago

Which pairs make the equation x-9y=12 true

Mathematics

1 answer:

ELEN [110]3 years ago

6 0

Answer:

The pairs (12,0) , (3,-1) and (0,-4/3) make the equation x- 9 y = 12 TRUE.

Step-by-step explanation:

Here, the given equation is x - 9 y = 12

Checking for each pairs individually:

a) For (12,0):

x - 9y = (12) - 9(0) = 12

and 12 = 12 (Right Side).

Hence, (12,0) satisfies the equation.

b) For (0,12):

x - 9y = 0 - 9(12) = -118

and -118 ≠ 12 (Right Side).

Hence,(0,12) DO NOT satisfy the equation.

c) For (3,-1):

x - 9y = 3 - 9((-1) ) = 3 + 9 = 12

and 12 = 12 (Right Side).

Hence, (3,-1) satisfies the equation.

d) For (0,-4/3):

x - 9y = 0 - 9((-4/3) ) = 0 + 12 = 12

and 12 = 12 (Right Side).

Hence, (0,-4/3) satisfies the equation.

Hence, the pairs (12,0) , (3,-1) and (0,-4/3) make the equation x- 9 y = 12 TRUE.

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3 years ago

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aniked [119]

Answer:

(a) $E(X) = 0.383$

The expected number in the sample that treats hazardous waste on-site is 0.383.

(b) $P(x = 4) = 0.000169$

There is a 0.000169 probability that 4 of the 10 selected facilities treat hazardous waste on-site.

Step-by-step explanation:

Professional Geographer (Feb. 2000) reported the hazardous waste generation and disposal characteristics of 209 facilities.

N = 209

Only eight of these facilities treated hazardous waste on-site.

r = 8

a. In a random sample of 10 of the 209 facilities, what is the expected number in the sample that treats hazardous waste on-site?

n = 10

The expected number in the sample that treats hazardous waste on-site is given by

$E(X) = \frac{n \times r}{N}$

$E(X) = \frac{10 \times 8}{209}$

$E(X) = \frac{80}{209}$

$E(X) = 0.383$

Therefore, the expected number in the sample that treats hazardous waste on-site is 0.383.

b. Find the probability that 4 of the 10 selected facilities treat hazardous waste on-site

The probability is given by

$P(x = 4) = \frac{\binom{r}{x} \binom{N - r}{n - x}}{\binom{N}{n}}$

For the given case, we have

N = 209

n = 10

r = 8

x = 4

$P(x = 4) = \frac{\binom{8}{4} \binom{209 - 8}{10 - 4}}{\binom{209}{10}}$

$P(x = 4) = \frac{\binom{8}{4} \binom{201}{6}}{\binom{209}{10}}$

$$ P(x = 4) = \frac{70 \times 84944276340}{35216131179263320}$

$P(x = 4) = 0.000169$

Therefore, there is a 0.000169 probability that 4 of the 10 selected facilities treat hazardous waste on-site.

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3 years ago

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Answer:

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Step-by-step explanation:

Given the data in the question;

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Hence, the slope of the regression equation for predicting our Exam 2 scores from Exam 1 scores is 0.492

And the y-intercept of the regression equation for predicting our Exam 2 scores from Exam 1 is 33.688

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