Explain how to use partial quotients to divide 235 by 5

Solve each system of equations algebraically. For each one, explain what the solution (or lack thereof) tells you

Paul [167]

Answer:

a: no solutions

b: (2, 3)

Step-by-step explanation:

a:

In both equations, the slope of x is the same, but the y-intercept is not, which means they are parallel. Therefore, this system of equations has no solutions.

b:

Since both of the equations are equal to y, we can set them equal to each other:

$\frac{1}{2}x^2+1= 2x-1\\x^2 + 2 = 4x - 2\\x^2-4x+4=0$

We can solve by factoring (by finding a number that multiplies to 4 and adds up to -4):

(x-2)^2 = 0

x = 2

Now, to find y, plug-in x to any of the equations:

y = 2*2-1 = 3

Therefore, the solution to this system of equation is (2, 3)

I hope this helped.

4 0

3 years ago

Please help! I don't understand how to solve this problem

Ilia_Sergeevich [38]

Using the z-distribution, a sample of 142,282 should be taken, which is not practical as it is too large of a sample.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

$\overline{x} \pm z\frac{\sigma}{\sqrt{n}}$

The margin of error is:

$M = z\frac{\sigma}{\sqrt{n}}$

In which:

$\overline{x}$ is the sample mean.

z is the critical value.

n is the sample size.

$\sigma$ is the standard deviation for the population.

Assuming an uniform distribution, the standard deviation is given by:

$S = \sqrt{\frac{(4 - 0)^2}{12}} = 1.1547$

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.