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3 years ago

Find the vertex, focus, directrix, and focal width of the parabola: -1/40x^2=y

1 answer:

3 0

For
(x-h)^2=4p(y-k)
vertex is (h,k)
distance from vertex to directix=p=distance from vertex to focus
|4p|=focal width

remember, focus is on the side of the parabola where it opens and directix is at the back
when p is negative, it opens down
when p is positive, it opens up

look at equation
-1/40(x-0)^2=(y-0)
times -40 to both sides
(x-0)^2=-40(y-0)
(x-0)^2=4(-10)(y-0)
vertex=(0,0)
p=-10,it's negative so it opens down

focus is 10 units below vertex (y direction)
focus=(0,-10)

diretix is 10 above
directix is y=10

focal width=|4p|=|4(-10)|=|-40|=40

vertex=(0,0)
focus=(0,-10)
directix is y=10
focal width=40 units

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3 years ago

10.

Kay [80]

Answer:

$\frac{(82)(2.4)^2}{104.139} \leq \sigma^2 \leq \frac{(82)(2.4)^2}{62.132}$

$4.535 \leq \sigma^2 \leq 7.602$

Now we just take square root on both sides of the interval and we got:

$2.2 \leq \sigma \leq 2.8$

And the best option would be:

A. 2.2 < σ < 2.8

Step-by-step explanation:

Information provided

$\bar X=32.1$ represent the sample mean

$\mu$ population mean

s=2.4 represent the sample standard deviation

n=83 represent the sample size

Confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The degrees of freedom are given by:

$df=n-1=83-1=82$

The Confidence is given by 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , the critical values for this case are:

$\chi^2_{\alpha/2}=62.132$

$\chi^2_{1- \alpha/2}=104.139$

And replacing into the formula for the interval we got:

$\frac{(82)(2.4)^2}{104.139} \leq \sigma^2 \leq \frac{(82)(2.4)^2}{62.132}$

$4.535 \leq \sigma^2 \leq 7.602$

Now we just take square root on both sides of the interval and we got:

$2.2 \leq \sigma \leq 2.8$

And the best option would be:

A. 2.2 < σ < 2.8

3 0

3 years ago

Solve for x. Your answer must be simplified. x+5≤−4

iren2701 [21]

Answer:

x ≤ -9

Step-by-step explanation:

to solve this equation you must subtract 5 from both sides

you get

x ≤ -9

that is your answer

4 0

2 years ago

Read 2 more answers

Determine the sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 98% c

Darina [25.2K]

Answer:

Step-by-step explanation:

You have to use fractions to show your work and I'm not going to do that but just know that it is the answer.

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2 years ago

What is the probability that a point chosen at random in the given figure will be inside the larger square and outside the small

liraira [26]

Answer:

51/100

Step-by-step explanation:

The probability that a point chosen at random in the given figure will be inside the larger square and outside the smaller square is equal to the ratio of the area of interest to the total area:

P(inside larger square and outside smaller square) = area of interest / total area

P(inside larger square and outside smaller square) = area inside the larger square and outside the smaller square / area of the larger square

Calculations:

1. Area inside the larger square: side² = (10 cm)² = 100 cm²

2. Area inside the smaller square = side² = (7cm)² = 49 cm²

3. Area inside the larger square and outside the smaller square

100 cm² - 49 cm² = 51 cm²

4. P (inside larger square and outside smaller squere)

51 cm² / 100 cm² = 51/100

5 0

2 years ago