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3 years ago

What is the equilibrium price per DVD?

Mathematics

1 answer:

OleMash [197]3 years ago

5 0

The equilibrium referred to here is the dynamic equilibrium. It means that there is a change happening, but the opposite change are equal so they cancel out. So, we can determine the equilibrium price at the point where the demand and supply curve intersect. That would be at the quantity of 60 units. Therefore, the equilibrium price is $10.

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You have won the lottery and will receive 20 annual payments of $10,000 starting today. If you can invest these payments at 8.5%

xxTIMURxx [149]

Answer:

$102,677.20

Step-by-step explanation:

The present value of an annuity due is determined by the following expression:

$PV = P+P*(\frac{1-(1+r)^{-n+1}}{r})$

Where 'P' is the amount of each payment received, 'r' is the interest rate on the investment and 'n' is the number of yearly payments.

With 20 annual payments of $10,000 at a rate of 8.5%, the present value is:

$PV = 10,000+10,000*(\frac{1-(1+0.085)^{-20+1}}{0.085})\\PV = 10,000+ 10,000*(9.26772)\\PV=\$102,677.20$

The present value of your winnings is $102,677.20.

8 0

3 years ago

How do I find the vertex and the standard form? Plz explain

xenn [34]

Answer:

Vertex form

y = -4(x + 3)^2 + 10

Standard form;

y = -4x^2-24x - 26

Step-by-step explanation:

Mathematically, we have the vertex form as

y = a(x-h)^2 + k

(h,k) represents the vertex

We have h as -3 and k as 10

y = a(x+3)^2 + 10

To get a, we substitute any of the points

Let us use (-1,-6)

-6 = a(-1+3)^2 + 10

-6-10 = 4a

4a = -16

a = -16/4

a = -4

So we have the equation as;

y = -4(x+3)^2 + 10

For the standard form;

We expand the vertex form;

y = -4(x + 3)(x + 3) + 10

y = -4(x^2 + 6x + 9) + 10

y = -4x^2 - 24x -36 + 10

y = -4x^2 -24x -26

7 0

3 years ago

Please help solve <br><br> -2x - 4 - 7 = - 3x - 15

valentina_108 [34]

Answer:

x = -4

Step-by-step explanation:

-2x-11=-3x-15

x - 11 = -15

x = -4

8 0

3 years ago

Tony buys a pair of running shoes f 80$ he pays 9%sales tax how much does the pair of shoes cost in total?

Sindrei [870]

Answer:

$87.20

Step-by-step explanation:

5 0

3 years ago

A metal rod will be cut into pieces that are each 1/56 meters long. The rod is 7/8 meters long. How many pieces will be made fro

S_A_V [24]

The number of pieces made from rod is 49

<h3><u>Solution:</u></h3>

Given that A metal rod will be cut into pieces that are each 1/56 meters long

The rod is 7/8 meters long.

<em><u>To find: number of peices made from rod</u></em>

The number of peices made from rod can be calculated by dividing the total length of rod by length of each piece

$\text {number of pieces made }=\frac{\text {total length of rod }}{\text { length of each piece}}$

Here total length of rod = $\frac{7}{8}$ meters

length of each piece to be made = $\frac{1}{56}$ meters

Substituting the values in above formula, we get

$\text {number of pieces made }=\frac{\frac{7}{8}}{\frac{1}{56}}=\frac{7}{8} \times \frac{56}{1}$

$\text {number of pieces made }=7 \times 7=49$

So the number of pieces made from rod is 49

7 0

3 years ago