A furniture store pays a wholesale price for a mattress.
Then, the store marks up the retail price to 150% of the
wholesale price. Later, they put the mattress on sale for
50% off of the retail price. A customer just bought the
mattress on sale and paid $1,200.
a. What was the retail price of the mattress, before the
discount?

Answer:

[tex](x,y) = (-1,0)[/tex]

Step-by-step explanation:

Given

[tex](x+1)^2 = -8(y-2)[/tex]

Required

The coordinates of the focus

First, write the expression in form of: [tex]y=a(x-h)^2+k[/tex]

[tex](x+1)^2 = -8(y-2)[/tex]

[tex](x+1)^2 = -8y + 16[/tex]

[tex]-8y + 16 = (x+1)^2[/tex]

Subtract 16 from both sides

[tex]-8y = (x+1)^2 - 16[/tex]

Divide through by -8

[tex]y = -\frac{1}{8}(x+1)^2 - \frac{16}{-8}[/tex]

[tex]y = -\frac{1}{8}(x+1)^2 +2[/tex]

In this case:

[tex]a = -\frac{1}{8}[/tex]

[tex]-h = 1[/tex]         [tex]h = -1[/tex]

[tex]k = 2[/tex]

The focus of the parabola is:

[tex](x,y) = (h,k + \frac{1}{4a})[/tex]

This gives:

[tex](x,y) = (-1,2 + \frac{1}{4*-\frac{1}{8}})[/tex]

[tex](x,y) = (-1,2 + \frac{1}{-\frac{1}{2}})[/tex]

[tex](x,y) = (-1,2 -2)[/tex]

[tex](x,y) = (-1,0)[/tex]

Answer:

2% per year.

Step-by-step explanation:

Solving our equation

r = 960 / ( 12000 × 4 ) = 0.02

r = 0.02

converting r decimal to a percentage

R = 0.02 * 100 = 2%/year

The interest rate required to

accumulate simple interest of $ 960.00

from a principal of $ 12,000.00

over 4 years is 2% per year.

Answer:

A: 3.84% chance.

B: 23.08% chance

The chance of pulling out an A and then a Z and two vowels in two consecutive turns will be 1 / 650 and 2 / 65, respectively.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The letters of the alphabet are written on pieces of paper and put into a hat. they are then pulled out and not replaced.

Then the total number of letters of the alphabet will be 26.

Then the chance of pulling out an A and then a Z in two consecutive turns will be given as,

P = (1 / 26) x (1 / 25)

P = 1/650

The chance of pulling out two vowels in two consecutive turns will be given as,

P = (5 / 26) x (4 / 25)

P = 20 / 650

P = 2 / 65

The chance of pulling out an A and then a Z and two vowels in two consecutive turns will be 1 / 650 and 2 / 65, respectively.

More about the probability link is given below.

https://brainly.com/question/795909

#SPJ2

Answer:

Radius -  4

Apothem -  2

Area - [tex]12\sqrt{3}[/tex] or 20.8

Step-by-step explanation:

Try to draw out my explanation so you know what this looks like.

~~~~

This is an equilateral triangle, so all sides are the same length. The perimeter can be divided by 3 to get each side length...

[tex]12\sqrt{3} \div3 = 4\sqrt{3}[/tex]

Now that we know the side lengths, we can get this started!

~~~~

Now, an equilateral triangle has angles that all equal 60 degrees. We can bisect this into TWO special case triangles of measures 90-60-30.

4 times the square root of 3 will be the hypotenuse, and the smallest leg is always half of that. The larger leg is represented as the small leg times the square root of 3.

[tex]Small=2\sqrt{3} \\Hypotenuse = 4\sqrt{3} \\Long =6[/tex]

By the way, the formula for the area can be either of the two:

[tex]A= \frac{1}{2} bh\\or\\A = \frac{1}{2} NAS[/tex]

we can easily find the area using the first formula.

[tex]A= \frac{1}{2} (4\sqrt{3} )(6)\\A=12\sqrt{3}[/tex]

The radius is the distance from the center to the corners & the apothem is the distance from the center to a side...

So we can divide the big triangle into a mini triangle at the bottom left/right

The height (small leg) of that triangle would be the apothem

The hypotenuse of that triangle would be the radius.

I did the math really quick because this is getting long. Anyhow, the small leg is 2 so is the apothem, and the hypotenus is 4, so is the radius

Happy April Fool's btw, lol.

Answer:

8

Step-by-step explanation:

3/5 ×2=8/10

..............

Answer:

18 is 14% of 128.5714

Step-by-step explanation:

it's 77.78

Step-by-step explanation:

14: 18*100 =

(14*100): 18 =

1400: 18 = 77.78

Now we have: 14 is what percent of 18 = 77.78

Question: 14 is what percent of 18?

Percentage solution with steps:

Step 1: We make the assumption that 18 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$x.

Step 3: From step 1, it follows that $100\%=18$100%=18.

Step 4: In the same vein, $x\%=14$x%=14.

Step 5: This gives us a pair of simple equations:

$100\%=18(1)$100%=18(1).

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

$\frac{100\%}{x\%}=\frac{18}{14}$100%x%=1814

Step 7: Taking the inverse (or reciprocal) of both sides yields

$\frac{x\%}{100\%}=\frac{14}{18}$x%100%=1418

$\Rightarrow x=77.78\%$⇒x=77.78%

Therefore, $14$14 is $77.78\%$77.78% of $18$18.

Answer:

C

Step-by-step explanation:

Hello There!

x = # of cars and y = # of vans

the total amount of vehicles is 12 so

x + y = 12

each car can hold 4 students and each van can carry 12 students

there are a total amount of 72 students

so 4x + 12y = 72

so from the given information we can conclude that the answer is C

Answer:

it's 2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

The answer is 3

Step-by-step explanation:

The answer is 3 because x= 15/5 = 3

Answer:

XW in the first blank

Z in the second blank

Answer: ok i kown

Step-by-step explanation:

i kown

Step-by-step explanation:

[tex]( - \frac{3}{5} ) \times ( - 15) = \\ = \frac{3}{5} \times 15 = \\ = 3 \times 3 = 9[/tex]

Answer:

4.8ft

Step-by-step explanation:

9514 1404 393

Answer:

  J = {4, -8, 7, 3}

Step-by-step explanation:

Sets F, G, H contain fractions, so are not limited to integers.

Set J simplifies to integers, so is the one you want.

Answer:

1. Interpret (L): To explain or to give meaning to.

2. Variable: (F) Something that can change or influence the results of an experiment.

3. Observe (I): To notice what occurs during an experiment.

4. Questions (B): The inquiry or problem relating to a topic that can be answered by conducting an experiment.

5. Scientific Method (A): A method of doing research that includes the steps of identifying a problem, gathering data, forming a hypothesis, testing a hypothesis, and drawing a conclusion.

6. Ethical (E): Following the rules of being being fair and honest.

7. Hypothesis (G): An educated guess or reasonable assumption.

8. Research (D): To conduct an investigation into current information about something.

9. Experiment (C): A test or trial performed in order  to discover something.

10.  Conclusion (K): The result or outcome of something.

11. Procedure (H): A sequence of steps involved in performing an experiment.

If this helps, please consider giving a thanks, a good rating, and Brainliest! Thanks!

Answer:

(a) 20 represents the initial population and

    1.014 represents 1 + % growth of rabbits each day

(b) Average Rate of change = 0.8

Step-by-step explanation:

P.S - The exact question is -

Given - A population of rabbits in a lab, p(x), can be modeled by

            the function p(x)=20(1.014)^x, where x represents the number

            of days since the population was first counted.

To find - (a) Explain what 20 and 1.014 represent in the context of

                   the problem.

              (b) Determine, to the nearest tenth, the average rate of

                   change from day 50 to day 100.

Proof -

(a)

Given that the function p(x) is represented as

[tex]p(x) = 20(1.014)^{x}[/tex]

Here,

20 represents the initial population and

1.014 represents 1 + % growth of rabbits each day

(b)

Given,

[tex]p(x) = 20(1.014)^{x}[/tex]

When x = 50

[tex]p(50) = 20(1.014)^{50}[/tex] = 40.08000 ≈ 40.1

When x = 100

[tex]p(100) = 20(1.014)^{100}[/tex] = 80.32033 ≈ 80.3

Now,

Average Rate of change = [tex]\frac{p(100) - p(50)}{100 - 50}[/tex]

                                         = [tex]\frac{80.3 - 40.1}{50}[/tex]

                                         = [tex]\frac{40.2}{50}[/tex]

                                         = 0.804 ≈ 0.8

⇒Average Rate of change = 0.8

Answer:

Step-by-step explanation:

4x1=4, 20-4=16. 16/2=8. Lucy made 8 2 point field goals

Answer:

A

Step-by-step explanation:

Given

[tex]\frac{1}{3}[/tex] x - 8 = - 12 ( multiply through by 3 to clear the fraction )

x - 24 = - 36 ( add 24 to both sides )

x = - 12 → A

Answer:

x = 18

Step-by-step explanation:

1/2x - 7 = 1/3 (x- 12)

Multiply both sides by 3

3 * 1/2x - 3 * 7 = 3 * 1/3 (x - 12)

3/2x - 21 = x - 12

Collect like terms

3/2x - x = 21 - 12

1/2x = 9

Multiply both sides by 2

x = 2 * 9

x = 18

Answer:

x = 18

hope this helps! :)

Answer: 35000

Step-by-step explanation:

Answer: 35

Step-by-step explanation:

329/200 / 0.047

329/200 / 47/1000

35

Answer:

whatttttttttttttttttt???????????????????

Step-by-step explanation:

Answer:

$0.83

Step-by-step explanation:

Its teh only one that makes sense since the 2nd is under, 3rd is over, and 4th is for lazy people

Answer:

a

Step-by-step explanation:

Answer:

Gillmans

Step-by-step explanation:

I feel like gillmans class did better cuz their class didnt have anyone get a score less than 60 but mr athens class had people who got below 50. Although athens class has people over 95 the most were 60-90 while gillmans was 70-90

Step-by-step explanation:

To convert decimal number 639 to quinary, follow these steps:

Then just write down the remainders in the reverse order to get the answer, The decimal number 639 converted to quinary is therefore equal to :

10024

Answer:

B

Step-by-step explanation:

This asks for data from multiple people, and it not just a yes or no question

Answer:

the answer is c!

Step-by-step explanation:

:)