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elena55 [62]
3 years ago
11

A laptop computer is purchased for $2000. After each year, the resale value decreases by 25%. What will the resale value be afte

r years?
Use the calculator provided and round your answer to the nearest dollar.

$[]
Mathematics
1 answer:
wel3 years ago
8 0

Answer:

2000? ... assume $2000

Resale Value = $2000*(1 - 0.25)t/yr

where: t = number of year after purchase

at t = 3 yr

Resale Value = $2000*(1 - 0.25)3 = $843.75

checking: at t = 0 $2000 (purchase price)

at t = 1 yr $2000 - 0.25*$2000 = $2000 - $500 = $1500

at t = 2 yr $1500 - 0.25*$1500 = $1500 - $375 = $1125

at t = 3 yr $1125 - 0.25*$1125 = $1125 - $281.25 = $843.75

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You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). O
Neko [114]

Answer:

a)q(p)=-15p+ +300

b)R(p)=-15p²+300p

c)C(p)=-30p+1600

d.1)P(p)=-15p²+330p-1600

d.2)p=$11

Step-by-step explanation:

(a).Before getting started, we are going to consider  the cartesian plane, where x-axis corresponds to the cover charge and y-axis corresponds to number of guests per night . There, we will locate the following coordinates according to the previous information:

(9,165)  (10,150).

Remember that  the slope-intercept form of the  linear equation is y=mx+b where m is the slope and b  is te intercept.

The slope can be calculated  by the next formula:

m=\frac{y2-y1}{x2-x1}

In this case we will assign  (9,165) as the first coordinate and (10,150) as the second one. The order does not matter. At the end we get the same value for m.

Therefore:

m=\frac{150-165}{10-9} = -15

Now, we have the slope and two poitns. According to this, and taking into account that  point-slope form of the equation of a line is y-y1=m(x-x1),   find a linear demand equation.

Any of two coordintates can be selected. In this case we will select the second one.

y-150=-15(x-10)   equation 1

Solve equation 1 for y

y=-15x+150+150

y=-15x+300

Above we had defined x as cover charge (p) and y as number of guests (q). Thus, rewrite equation 1.

q(p)=-15p+ +300.  

it equation shows the number of guests per night as a function of the cover charge,

(b). The nightly revenue can be calculated multplying the price of the cover charge by  the number of guests. So, we just have to multiply the equation 1 by p.

p*q(p)=p*(-15p +300)

R(p)=-15p²+300p   equation 2

(c) To get the cost function of the nightclub  we just have to multiply the cost of the two non-alcoholic drinks   by the number of the guests ( equation 1) and add to it  nightly overheads.

C(p)=2*(-15p+300)+1000

C(p)= -30p+600+1000

C(p)=-30p+1600  equation 3

(d) In order to find the profit in terms of the cover charge we will  subtract nightly costs ( equation 3) from nightly revenue (equation 2)

P(p)=R(p)-C(p)

P(p)=-15p²+300p - (-30p+1600)

P(p)=-15p²+300p+30p-1600

P(p)=-15p²+330p-1600

To determine that  the entrance fee we should charge for a maximum profit we are going to use the first derivative test (y'(x)=0) in order to find an extremum point.

Compute the first derivative of P(p)

P'(p)=-30p+330=0

30p=330

p=330/30

p= $11

The entrance fee that we should charge for a maximum profit is p=$11 per guest.

5 0
3 years ago
GCF for 44 77 210 126
alexgriva [62]

The GCF for 44, 77,210, and 126 is 1 . I know this because other than one they have none of the same factors that go into each of the numbers.

Hope this helps!! Please rate em the brainliest answer!!!

5 0
3 years ago
IM DESPERATE I need help with #3. I would like it if you could explain how to do it because there are 2 more that are similar to
hodyreva [135]
$30 • 10%

10% = 0.10

30 • 0.10 = 3

The answer is $27. They got $3 off.

$30 - $3 = $27.
7 0
2 years ago
Read 2 more answers
True or false: Most proofs in geometry are called direct proofs because theorems and postulates are used to prove a statement us
vivado [14]

Answer:

The statement is true

Step-by-step explanation:

Most proofs are direct proofs becaue theorums & postulates prove them true straightforwardly :)

5 0
2 years ago
a trapezoidal pyramid has a volume of 3168 cm^3 and its height is 36cm the lengths of the 2 bases of the trapezoidal base are 18
galina1969 [7]
10089.67cm is your answer but dont trust m answer wait for other ones


6 0
3 years ago
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