Write in quadratic form f(x)=(x+2)^2

A researcher wishes to estimate, with 99% confidence, the population proportion of adults who think the president of their co

scoray [572]

Answer:

a. n=4148

b. n=3909

c. The sample size is smaller if a known proportion from prior study is used. The difference in sample sizes is 239

Step-by-step explanation:

a. For sample where no preliminary estimate is given, the minimum sample size is calculated using the formula:

$n=p(1-p)(\frac{z}{ME})^2$

Where:

$ME=$ Margin of error
$p=$ is the assumed proportion

#Let p=0.5, substitute in the formula to solve for n:

$n=0.5(1-0.5)\times (2.576/0.02)^2\\\\=4147.36\approx 4148$

Hence, the minimum sample size is 4148

b. If given a preliminary estimate p=0.38, we use the same formula but substitute p with the given value:

$n=p(1-p)(z/ME)^2\\\\=0.38(1-0.38)(2.576/0.02)^2\\\\=3908.47\approx3909$

Hence, the minimum sample size is 3909

c. Comparing the sample sizes from a and b:

$n_{0.5}>n_{0.38}\\\\n_{0.5}-n_{0.38}=4148-3909=239$

Hence, the actual sample size is smaller for a known proportion from prior a prior study.

8 0

3 years ago

Find all solutions to the equation. cos^2 x +2cosx+1=0

Schach [20]

$x= \pi$

Step-by-step explanation:

$\cos^2x+\cos x+1=0$

Let $u= \cos x$

Then $u^2+2u+1=(u+1)^2=0$

or

$\cos x = -1$

This gives us $x= \pi$ or all integer multiples of $\pi (n \pi)$

4 0

2 years ago

What is the value of y in the parallelogram below? G 108 3y D E

Arlecino [84]

Answer:

C

Step-by-step explanation:

In a parallelogram, consecutive angles are supplementary, sum to 180° , so

3y + 108 = 180 ( subtract 108 from both sides )

3y = 72 ( divide both sides by 3 )

y = 24 → C

5 0

3 years ago

At the grocery store there are two different options for buying Coke. You can buy a 12 pack for $5.49 or an 18 pack for $8.59. W

baherus [9]

Step-by-step explanation:

The 18 Pack why is because it has more Coke than the other one and it is less expensive than the other one if it had 18.

3 0

2 years ago

Solve the system with elimination 4x+3y=1 -3x-6y=3

Nuetrik [128]

Answer:

x = 1, y = -1

Step-by-step explanation:

If we have the two equations:

$4x+3y=1$ and $-3x - 6y = 3$ , we can look at which variable will be easiest to eliminate.

$y$ looks like it might be easy to get rid of, we just have to multiply $4x+3y=1$ by 2 and y is gone (as -6y + 6y = 0).

So let's multiply the equation $4x+3y=1$ by 2.

$2(4x + 3y = 1)\\8x + 6y = 2$

Now we can add these equations

$8x + 6y = 2\\-3x-6y=3\\$

------------------------

$5x = 5$

Dividing both sides by 5, we get $x = 1$ .

Now we can substitute x into an equation to find y.

$4(1) + 3y = 1\\4 + 3y = 1\\3y = -3\\y = -1$

Hope this helped!

5 0

3 years ago