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2 years ago

Solve the system by substitution. x = – 4y + 6 2x + 9y = 16

Mathematics

1 answer:

GaryK [48]2 years ago

3 0

Step-by-step explanation:

x = -4y + 6

Now,

Substituting the value of x on 2x + 9y = 16, we get -.

2(-4y + 6) + 9y = 16

-8y + 12 + 9y = 16

y = 16 - 12

Now,

Substituting the value of y on 2x + 9y = 16, we get -

2x + 9(4) = 16

2x = 16 - 36

2x = -20

Hence,

The value of x is -10 and y is 4.

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The ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. If the first number in the ratio is 10, what is the second num

krek1111 [17]

Answer:

10:40

Step-by-step explanation:

7 0

3 years ago

PLEASE HELP ASAP!! WORDED QUADRATIC QUESTIONS!!!

Roman55 [17]

Answer:

x² - 5x = 14

x = -2 or x = 7

Step-by-step explanation:

x² - 5x = 14

x² - 5x - 14 = 0

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x = -2 or x = 7

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2 years ago

Elderly drivers. In January 2011, The Marist Poll published a report stating that 66% of adults nationally think licensed driver

katrin [286]

Answer:

(a) Hence, the margin of error reported by The Marist Poll was correct.

(b) Based on a 95% confidence interval the poll does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.

Step-by-step explanation:

We are given that the Marist Poll published a report stating that 66% of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age.

It was also reported that interviews were conducted on 1,018 American adults, and that the margin of error was 3% using a 95% confidence level.

(a) <u>Margin of error formula is given by;</u>

Margin of Error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

where, $\alpha$ = level of significance = 1 - 0.95 = 0.05 or 5%

Standard of error = $\sqrt{\frac{\hat p(1-\hat p)}{n} }$

Also, $\hat p$ = sample proportion of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age = 66%

n = sample of American adults = 1.018

The critical value of z for level of significance of 2.5% is 1.96.

So, <em>Margin of Error </em>= $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

= $1.96 \times \sqrt{\frac{0.66(1-0.66)}{1,018} }$ = 0.03 or 3%

Hence, the margin of error reported by The Marist Poll was correct.

(b) Now, the pivotal quantity for 95% confidence interval for the population proportion who think that licensed drivers should be required to retake their road test once they turn 65 is given by;

P.Q. = $\frac{\hat p-p}{ \sqrt{\frac{\hat p(1-\hat p)}{n} }}$ ~ N(0,1)

So, <u>95% confidence interval for p</u> = $\hat p \pm \text{Margin of error}$

= $0.66 \pm 0.03$

= [0.66 - 0.03 , 0.66 + 0.03]

= [0.63 , 0.69]

Hence, based on a 95% confidence interval the poll does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65 because the interval does not include the value of 70% or more.

7 0

3 years ago

Find the slope and y-intercept for the two linear functions. Linear Functions Identify the slope of the line given in the table:

Natalija [7]

ANSWER

See explanation

EXPLANATION

The table contains these two points (-4,-3) and (2,-4.5)

The slope of this line is given by;

$m = \frac{rise}{run}$