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3 years ago

What is the solution to the system of equations? 5x + 4y = 8 x - 2y = 10

1 answer:

4 0

Double the second equation (multiply by 2)...
2(x-2y=10)
2x-4y=20

Bring in the second equation and add the equations:
(2x-4y=20)
+ (5x+4y=8)

7x=28
x=4

Plug in x into one of the equations to get y...
(4)-2y=10
-2y=6
y=-3

(6,-3)

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What is the solution of -27 = m/9 ? A. -243 B. -3 C. 3 D. 243

asambeis [7]

Answer: m = -243

Explanation:

• Solve

-27 = m/9

•Multiply 9 by 27

m/9 * -27

• Result

m = -243

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3 years ago

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2 years ago

A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phyl

LuckyWell [14K]

Answer:

A sample of 16577 is required.

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 z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

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

99% confidence level

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

She wants to estimate the proportion using a 99% confidence interval with a margin of error of at most 0.01. How large a sample size would be required?

We have no estimation for the proportion, and thus we use $\pi = 0.5$ , which is when the largest sample size will be needed.

The sample size is n for which M = 0.01. So

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

$0.01 = 2.575\sqrt{\frac{0.5*0.5}{n}}$

$0.01\sqrt{n} = 2.575*0.5$

$\sqrt{n} = \frac{2.575*0.5}{0.01}$

$(\sqrt{n})^2 = (\frac{2.575*0.5}{0.01})^2$

$n = 16576.6$

Rounding up:

A sample of 16577 is required.

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2 years ago

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3 years ago

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Let X be the number of Heads in 10 fair coin tosses. (a) Find the conditional PMF of X, given that the first two tosses both lan

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Answer:

Follows are the solution to the given point:

Step-by-step explanation:

For option A:

In the first point let z be the number of heads which is available on the first two trails of tosses so, the equation is:

$P(X=k | z=2 ) = \begin{pmatrix} 10-2\\ k-2\end{pmatrix} (\frac{1}{2})^{k-2} (\frac{1}{2})^{10-k}$