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3 years ago

Solve the system of equations by substitution. Show your work in the sketch and write your answer as an ordered pair.

Mathematics

1 answer:

Ede4ka [16]3 years ago

3 0

Let's solve your system by substitution.

−3x+y=−2;y=4x

Rewrite equations:

y=4x;−3x+y=−2

Step: Solvey=4xfor y:

y=4x

Step: Substitute4xforyin−3x+y=−2:

−3x+y=−2

−3x+4x=−2

x=−2(Simplify both sides of the equation)

Step: Substitute−2forxiny=4x:

y=4x

y=(4)(−2)

y=−8(Simplify both sides of the equation)

Answer:

x=−2 and y=−8

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There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote f

Ann [662]

Answer:

$0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647$

$0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753$

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

The estimated population proportion for this case is:

$\hat p = \frac{350}{500}=0.7$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647$

$0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753$

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

7 0

3 years ago

The body of a 154 pound person contains approximately 2×10-1 milligrams of gold and 6×101 milligrams of aluminum. Based on this

charle [14.2K]

Answer:

300

Step-by-step explanation:

6 × 10¹ ÷ 2 × 10-¹

= 300

no of aluminium is 300 times more than that of gold

7 0

3 years ago

ABCD is a rhombus. = 5.5 cm and = 4 cm. What is the area of the rhombus?

Angelina_Jolie [31]

The formula for solving a rhombus is A = P*Q/2

5.5×4 =22

22÷2 = 11

Awnswer: 11 cm²

3 0

3 years ago

Read 2 more answers

Solve y over negative 4 + 5 = 15. 80 −80 40 −40

Virty [35]

The answer is - 40. Observe.

y/-4 + 5 = 15
y = -40
-40/-4 = 10
10 + 5 = 15

Thus, y= -40

8 0

3 years ago

The number of hospitals in a certain country has been declining for many years. In 2014, there were 5,727 hospitals, but, in 201

Svetradugi [14.3K]

Answer:

H = -52t + 6455

Step-by-step explanation:

2014 is 14 years since 2000. That gives you the point (14, 5727).

2017 is 17 years since 2000. That gives you the point (17, 5571).

Since we have two points in the line, we can find the equation of the line.

y = mx + b

m = slope = (difference in y)/(difference in x)

m = (5571 - 5727)/(17 - 14) = -156/3 = -52

y = -52x + b

Now we use one of the points for x and y, and we solve for b.

5727 = -52(14) + b

b = 6455

The equation is

y = -52x + 6455

Using H and t, we have

H = -52t + 6455

6 0

3 years ago