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3 years ago

Determine and state the vertex of f(x) = x2 - 2x - 8 using the method of completing the square

Mathematics

1 answer:

Elza [17]3 years ago

3 0

Answer:

vertex = (1, - 9 )

Step-by-step explanation:

The equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

f(x) = x² - 2x - 8

To complete the square

add/ subtract ( half the coefficient of the x- term )² to x² - 2x

f(x) = x² + 2(- 1)x + 1 - 1 - 8

= (x - 1)² - 9 ← in vertex form

with vertex = (1, - 9 )

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A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained p

Studentka2010 [4]

Using the z-distribution, it is found that the needed sample sizes are:

a) 242

b) 1842

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , 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 $\frac{1+\alpha}{2}$ .

The margin of error is:

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

99% confidence level, hence $\alpha = 0.99$ , z is the value of Z that has a p-value of $\frac{1+0.99}{2} = 0.995$ , so $z = 2.575$ .

Item a:

The estimate is:

$\pi = 0.223 - 0.189 = 0.034$

The sample size is n for which M = 0.03, then:

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

$0.03 = 2.575\sqrt{\frac{0.034(0.966)}{n}}$

$0.03\sqrt{n} = 2.575\sqrt{0.034(0.966)}$

$\sqrt{n} = \frac{2.575\sqrt{0.034(0.966)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.034(0.966)}}{0.03}\right)^2$

$n = 241.97$

Rounding up, a sample of 242 is needed.

Item b:

No prior estimates, hence $\pi = 0.5$ is used.

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

$0.03 = 2.575\sqrt{\frac{0.5(0.5)}{n}}$

$0.03\sqrt{n} = 2.575\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{2.575\sqrt{0.5(0.5)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.5(0.5)}}{0.03}\right)^2$

$n = 1841.8$

Rounding up, a sample of 1842 is needed.

For more on the z-distribution, you can check brainly.com/question/25404151

5 0

3 years ago

Translate the sentence into a mathematical expression: “Twice x is 5”

Black_prince [1.1K]

Answer:

2x = 5

Step-by-step explanation:

5 0

4 years ago

Read 2 more answers

0.25a + 0.5 =4.5 Solve for a

lys-0071 [83]

Answer:

A = 16

Step-by-step explanation:

subtract .5 for both sides --> .25a = 4.5 - .5

.25a = 4

now divide .25 by both sides

A = 16

5 0

3 years ago

Read 2 more answers

Write the equation of the given circle. center (1, -5) radius of 10

Naddika [18.5K]

Answer:

$(x-1)^2+(y+5)^2=100$

Step-by-step explanation:

The equation of a circle has the following form:

$(x-h)^2+(y-k)^2=r^2$ where (h,k) is the center of a circle with radius r.

Our equation center is (1.-5) and radius is 10.

$(x-1)^2+(y--5)^2=10^2$

$(x-1)^2+(y+5)^2=100$

3 0

3 years ago

Factor each expression 22x-11y+44

Mkey [24]

11(2x-y+4)
The GCF is 11

6 0

3 years ago