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V125BC [204]
2 years ago
6

A real estate company owns 120 apartments which are fully occupied when the rent is $800 per month. Analytics indicate that for

each $40 increase in rent, 5 apartments will become unoccupied. What rent should be charged in order to obtain the largest gross income?
Mathematics
1 answer:
UNO [17]2 years ago
5 0

9514 1404 393

Answer:

  $880

Step-by-step explanation:

If r is the rent charged, then the number of $40 increments of increase will be ...

  (r -800)/40

and the number of occupied apartments will be ...

  120 -5(r -800)/40

The gross income (g) will be the number of apartments times the rent charged, or ...

  g = r×(120 -5(r -800)/40) = (1/8)r(1760 -r)

The equation describes a parabola with zeros at r=0 and r=1760. The vertex will be on the line of symmetry, halfway between those zeros. The maximum gross income will be had when the rent is 1760/2 = 880.

$880 should be charged for rent to maximize gross income.

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The number of students who enroll in a psychology course is a Poisson random variable with mean 105. The professor in charge of
EleoNora [17]

Answer:

The answer is "0.096".

Step-by-step explanation:

In this question, the X is a number of the students who enroll in a psycholog y course,  follows a Poisson distribution with mean = \lambda= 105  

\therefore P(X=x)=\frac{e^{-105} 105^{x}}{x!},(x=0,1,2,3.....)\\\\\to p(teach\  two \ sections) = P(X \geq 119)\\\\=1-P(X

8 0
2 years ago
Fill in the blanks to complete the sentence.
Nikitich [7]

Answer:

Step-by-step explanation:

8 0
2 years ago
The exppreson of 10x^2-7
erica [24]

The complete question is :

Question: What is the coefficient in the expression 10x²-7?

The coefficient in the expression 10x^{2} -7 is 10

<h3>What is Coefficient?</h3>

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

According to the question,

The expression given is 10x^{2} -7

The variable given is x

We need to find the coefficient in the expression.

In the given expression x is the variable and the number before the x is coefficient which is 10 .

Hence the coefficient in the expression is 10.

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3 0
2 years ago
Let represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of is as follows.
Sindrei [870]

Answer:

a) P(X=3) = 0.1

b) P(X\geq 3) =1-P(X

And replacing we got:

P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4

c) P(X=4) = 0.3

d) P(X=0) = 0.2

e) E(X) =0*0.2 +1*0.3+2*0.1 +3*0.1 +4*0.3= 2

f) E(X^2)= \sum_{i=1}^n X^2_i P(X_i)

And replacing we got:

E(X^2) =0^2*0.2 +1^2*0.3+2^2*0.1 +3^2*0.1 +4^2*0.3= 6.4

And the variance would be:

Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4

And the deviation:

\sigma =\sqrt{2.4} = 1.549

Step-by-step explanation:

We have the following distribution

x      0     1     2   3   4

P(x) 0.2 0.3 0.1 0.1 0.3

Part a

For this case:

P(X=3) = 0.1

Part b

We want this probability:

P(X\geq 3) =1-P(X

And replacing we got:

P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4

Part c

For this case we want this probability:

P(X=4) = 0.3

Part d

P(X=0) = 0.2

Part e

We can find the mean with this formula:

E(X)= \sum_{i=1}^n X_i P(X_i)

And replacing we got:

E(X) =0*0.2 +1*0.3+2*0.1 +3*0.1 +4*0.3= 2

Part f

We can find the second moment with this formula

E(X^2)= \sum_{i=1}^n X^2_i P(X_i)

And replacing we got:

E(X^2) =0^2*0.2 +1^2*0.3+2^2*0.1 +3^2*0.1 +4^2*0.3= 6.4

And the variance would be:

Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4

And the deviation:

\sigma =\sqrt{2.4} = 1.549

4 0
3 years ago
Need help on this PLEASE It is due at 11:40!!! Today!
FrozenT [24]

Answer:

X= 75, Y=30 there you go!

Step-by-step explanation:

5 0
2 years ago
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