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Bad White [126]
3 years ago
9

In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population

fall below 1,200,000?
a. 2024
b. 2027
c. 2036
d. 2049
Mathematics
1 answer:
frez [133]3 years ago
7 0
The equation
                                            P(t) = 1405233 * (1 - 0.011)^(t)
models the population at t years after 2010. Then, when P(t) = 1,200,000, we have
                                 1200000 = 1405233 * (0.989)^t
                                  (0.989)^t = 1200000/1405233
                                                t = log(1200000/1405233)/log(0.989)
                                                t = 14.27 years
This means 14.27 years after 2010. Therefore, the answer to this question is 2024.
You might be interested in
For what values (cases) of the variables the expression does not exist: <img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4y%2B
stealth61 [152]

Answer:

y = - \frac{1}{2}

Step-by-step explanation:

Given

\frac{3}{4y+2}

The denominator of the expression cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that y cannot be, that is

4y + 2 = 0 ( subtract 2 from both sides )

4y = - 2 ( divide both sides by 4 )

y = \frac{-2}{4} = - \frac{1}{2} ← excluded value

6 0
3 years ago
Our waitress was fantastic!! Matthew decided
bearhunter [10]

Hey!

-----------------------------------------------

Steps To Solve:

~Turn into decimal

15% = 0.15

~Multiply

25.65 x 0.15 = 3.8475

-----------------------------------------------

Answer:

Matthew will give the waitress $3.8475 for a tip.

-----------------------------------------------

Hope This Helped! Good Luck!

4 0
3 years ago
What is the r^2 value of the following data to three decimal places???
GaryK [48]

Answer:

0.783

Step-by-step explanation:

To find first r and then r square for the data

correlation coefficient of x and y = Cov (x,y)/std dev x * std dev Y

Cov (x,y) = E(xy) -E(x)E(y)

Hence calculations would be as follows:

x y xy

 

1 2 2

2 10 20

5 5 25

7 18 126

10 25 250

 

Mean 5 12 84.6

 

Cov E(xy)-E(x)E(y)  24.6

r 0.884640297

r^2 0.782588454

so answre is 0.783 after rounding off.

4 0
3 years ago
Can someone help me solve this
ikadub [295]

Answer:

  1. 168.25 ft
  2. 3.125 s

Step-by-step explanation:

It is almost too easy to let a graphing calculator show you the solution. (See attached)

_____

You may be expected to use some actual algebra (or even calculus) to find the solution.

If you've spent any time with quadratics, you know the vertex of ax²+bx+c is located at x=-b/(2a). Here, that means the time to get to the highest point is ...

... t = -100/(2·(-16)) = 100/32 = 3.125 . . . . seconds

Then the highest point is ...

... h(3.125) = -16·3.125² +100·3.125 +12 = 168.25 . . . . feet

_____

Or, you can put the equation into vertex form.

... h(t) = -16t² +100t +12

... = -16(t² +6.25t) +12

... = -16(t² +6.25t +3.125²) +12 +16·3.125² . . . . . add the square of half the t coefficient inside parentheses; add the opposite of the same amount outside parentheses

... = -16(t +3.125)² +168.25 . . . . . simplify

This tells us the peak of the travel of the bullet is at 168.25 ft after 3.125 seconds.

6 0
3 years ago
Write expression of the following phrase. <br> x is at least 7
SIZIF [17.4K]

Answer:

  x ≥ 7

Step-by-step explanation:

"Is at least" means the same as "is greater than or equal to". Then "x is greater than or equal to 7" is expressed in symbols as ...

  x ≥ 7

5 0
3 years ago
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