Write the equation of the parabola with a focus (-1 4) and directrix y = 3

Answers

Answer 1

Answer: parabola
4P(y-k)=(x-h)^2
where (h,k) is vertex
P is distance from vertex to focus which is also equalt to distance from vertex to directix

we plot those points and see it opens up (don't cross directix)
P is positive
from 4 to 3 is a distace of 1
1/2=1/2
P=1/2
3+1/2=3.5
the vertex is (-1,3.5)

4(1/2)(y-3.5)=(x+1)^2
2(y-3.5)=(x+1)^2

put in vertex form (solve for y)
divide both sides by 2
y-3.5=(1/2)(x+1)^2
add 3.5
y= $(1/2)(x+1)^(2)+3.5$

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Answers

The answer to your question is 8

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. To determine the effectiveness of the advertising campaign, a sample of 49 days of sales were taken. They found that the average daily sales were $6,300 per day. From past history, the restaurant knew that its population standard deviation is about $1,000. If the level of significance is 0.01, have sales increased as a result of the advertising campaign? Multiple Choice A. Reject the null hypothesis and conclude that the mean is equal to $6,000 per day.
B. Fail to reject the null hypothesis.
C. Reject the null hypothesis and conclude the mean is lower than $6,000 per day.
D. Reject the null hypothesis and conclude the mean is higher than $6,000 per day.

Answers

Answer:

Option B) Fail to reject the null hypothesis.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $6,000

Sample mean, $\bar{x}$ = $6,300

Sample size, n = 49

Alpha, α = 0.01

Population standard deviation, σ = $1,000

First, we design the null and the alternate hypothesis

$H_(0): \mu = 6000\text{ dollars per week}\nH_A: \mu > 6000\text{ dollars per week}$

We use one-tailed(right) z test to perform this hypothesis.

Formula:

$z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }$

Putting all the values, we have

$z_(stat) = \displaystyle(6300 - 6000)/((1000)/(√(49)) ) = 2.1$

Now, $z_(critical) \text{ at 0.01 level of significance } = 2.33$

Since,

$z_(stat) < z_(critical)$

We fail to reject the null hypothesis and accept the null hypothesis. Thus, we conclude that sales have not increased as a result of the advertising campaign

Option B) Fail to reject the null hypothesis.

A software company is releasing one of their products on a CD. The manufacturer charges a $5,500 setup fee and $1.00 per CD. Approximately how many CDs must be produced so that the total cost per CD is $5.50? A) 1,222 CDs
B) 2,200 CDs
C) 1,571 CDs
D) 5,500 CDs

Answers

Given:
set-up fee 5,500
variable fee 1 per CD.

Cost per CD is $5.50

5.50 - 1= 4.50

5,500 / 4.50 = 1,222 CDs Choice A.

1*1,222 = 1,222
1,222 + 5,500 = 6,722
6,722/1,222 = 5.50

Answer:

It is actually 2,200, which is option B. I originally put option A but it said it was incorrect and told m eit was 2,200. I hope i was able to help ;)

Step-by-step explanation:

What percent of 70 is 26

Answers

26/70 = 13/35
= 0.3714
= 37.14% which is your answer.

Is 63% a real number?

Answers

No I do not believe it is.

Which is the equation of a line with the slope of -2 that passes through the point (-2,0)

Answers

y = -2x - 4

-2x is the slope and -4 is the y intercept.

The equation of a line is y = mx + b (m is the slope; b is the y-intercept)

We are given the slope of -2 so...

y = -2x + b

We must determine b. Since they give us a point, we can sub in the x and y coords (-2,0)

0 = -2(-2) + b
0 = 2 + b
[Subtract 2 from both sides]
0-2=2-2+b
-2=b

Now, go back to the original equation (before adding coordinates in) and input b.

y = -2x-2

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