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miss Akunina [59]
2 years ago
8

An apartment building has 1500 residents. Every year 10% of the residents move out and no one new moves in. How many residents w

ill live there is 7 years?
Mathematics
1 answer:
maw [93]2 years ago
7 0

Answer:

717.44535

Step-by-step explanation:

P is the population in the beginning

r = population decrease per year = 10%

n = years = 7

P*(1-r/100)^n

1500(1-(0.10)^7

pioneermathematicscomFORMULAEFORPOPULATIONGROWTHandDECREASEformulaf779146html

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Prove that if r is any rational number, then 3r2 − 2r + 4 is rational. The following properties may be used in your proof. Prope
ziro4ka [17]

Given:

Expression is

3r^2-2r+4

To prove:

If r is any rational number, then 3r^2-2r+4 is rational.

Step-by-step explanation:

Property 1: Every integer is a rational number. It is Theorem 4.3.1.

Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.

Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.  

Let r be any rational number.

We have,

3r^2-2r+4

It can be written as

3(r\times r)-2r+4

Now,

3, -2 and 4 are rational numbers by property 1.

r^2=r\times r is rational by Property 3.

3r^2\text{ and }-2r are rational by Property 3.

3r^2+(-2r)+4 is rational by property 2.

So, 3r^2-2r+4 is rational.

Hence proved.

6 0
2 years ago
FREE BRAINLIEST & 50 points bc im nice <3
Ostrovityanka [42]
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2 years ago
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What is the relationship between 962 meters and 0.962 kilometers
dem82 [27]
1 meter is equal to 0.001 kilometers so if we multiply 962 by 0.001 we would get .962 kilometers...so with that said what would the relationship be?
8 0
3 years ago
Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value
MArishka [77]

Answer:

  • y = 81-x
  • the domain of P(x) is [0, 81]
  • P is maximized at (x, y) = (54, 27)

Step-by-step explanation:

<u>Given</u>

  • x plus y equals 81
  • x and y are non-negative

<u>Find</u>

  • P equals x squared y is maximized

<u>Solution</u>

a. Solve x plus y equals 81 for y.

  y equals 81 minus x

__

b. Substitute the result from part a into the equation P equals x squared y for the variable that is to be maximized.

  P equals x squared left parenthesis 81 minus x right parenthesis

__

c. Find the domain of the function P found in part b.

  left bracket 0 comma 81 right bracket

__

d. Find dP/dx. Solve the equation dP/dx = 0.

  P = 81x² -x³

  dP/dx = 162x -3x² = 3x(54 -x) = 0

The zero product rule tells us the solutions to this equation are x=0 and x=54, the values of x that make the factors be zero. x=0 is an extraneous solution for this problem so ...

  P is maximized at (x, y) = (54, 27).

7 0
3 years ago
Solve the equation using square roots. x^2-15=34
matrenka [14]
<span>x^2-15=34
</span><span>x^2 = 34 + 15
</span><span>x^2 = 19
x = + 7  and x = -7

answer is 

</span>x = + 7  and x = -7
3 0
3 years ago
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