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4 years ago

[6.03] What is the value of the x variable in the solution to the following system of equations?

1 answer:

8 0

We multiply both equations by a constant term so that when we subtract the equations, the y values cancel out:

4(4x - 3y = 3)
3(5x - 4y = 3)

16x - 12y = 12
15x -12y = 9; subtracting the second equation from the first:

x = 3

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Work out the shaded area of this shape.

aliina [53]

Answer:

Step-by-step explanation:

5 0

3 years ago

The dwarves of the Grey Mountains wish to conduct a survey of their pick-axes in order to construct a 99% confidence interval ab

Dmitry_Shevchenko [17]

Answer:

The minimum sample size needed is 125.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

$\pi = 0.25$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 25 percent of the pick-axes are in need of repair?

This minimum sample size is n.

n is found when $M = 0.1$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.1 = 2.575\sqrt{\frac{0.25*0.75}{n}}$

$0.1\sqrt{n} = 2.575{0.25*0.75}$

$\sqrt{n} = \frac{2.575{0.25*0.75}}{0.1}$

$(\sqrt{n})^{2} = (\frac{2.575{0.25*0.75}}{0.1})^{2}$

$n = 124.32$

Rounding up

The minimum sample size needed is 125.

5 0

4 years ago

nikhil has RS 80000 from this,he gives 30% to his wife and 20% to his father. Find the amount received by wife and father

muminat

Answer:

Amount received by wife = RS 24000

Amount received by father = RS 16000

Step-by-step explanation:

His income is RS 80000

He gave 30% of his income to his wife

That's

$\frac{30}{100} \times RS \: \: 80000$

Which is RS 24000

He gave 20% of his income to his father

That's

$\frac{20}{100} \times RS \: \: 80000$

Which is RS 16000

Hope this helps you

8 0

3 years ago

Read 2 more answers

Solve square root <br> (2x+3)^2=36

REY [17]

X=3/2 btw its a fraction

6 0

4 years ago

Read 2 more answers

80=-8a please I need the answer

Free_Kalibri [48]

80=-8a
We are trying to solve for a. So we need to get a alone. To do that we have to divide each side by -8.
80/-8= -8a/-8
Once you have solved each side you will get the following.
-10=a

6 0

3 years ago