City A had a population of 10000 in the year 1990. City A’s population grows at a constant rate of 3% per year. City B has a population that is growing exponentially. In the year 2000, there were half as many people in B as in A. In the year 2010, the population of A was 20% more than the population of B.
When will the populations be equal? Give your answer in years after 1990.

Answer:

36 minutes

Step-by-step explanation:

The equation to determine the time together is

1/a + 1/b = 1/c  where a and b are the times alone and c is the time together

1/90  + 1/ 60 = 1/c

Multiply each side by 180c to clear the fractions

180c( 1/90  + 1/ 60 = 1/c)

2c + 3c = 180

5c = 180

Divide each side by 5

5c/5 = 180/5

c =36

9514 1404 393

Answer:

  B

Step-by-step explanation:

If the probability of event "A" is 'p', then the probability of the event "not A" is

  P(not A) = 1 - P(A) = 1 - p

For p=0.5, this is ...

  P(not A) = 1 -0.5 = 0.5 . . . . . matches choice B

Answer:

○B. 0.5 is the proof the outcome (not A).

Question:

If the measure of arc CB is [tex]\frac{8}{3} \pi[/tex] units, what is the measure of ∠CAB?

Answer:

120°

Step-by-step explanation:

The figure has been attached to this response.

The figure shows a circle centered at A and has a radius of 4 units.

Also, the length of the arc CB (as given in the question) is  [tex]\frac{8}{3} \pi[/tex] units.

The length L of an arc is given by;

L = [tex]\frac{\beta }{360} * 2\pi * r[/tex]         -----------------(i)

Where;

β = angle subtended by the arc at the center of the circle and measured in degrees

r = radius of the circle

From the question;

β = ∠CAB

r = 4 units

L =  [tex]\frac{8}{3} \pi[/tex]

Substitute these values into equation (i) as follows;

[tex]\frac{8}{3} \pi[/tex] = [tex]\frac{\beta }{360} * 2\pi * 4[/tex]

=>  [tex]\frac{8}{3} \pi[/tex] = [tex]\frac{\beta }{360} * 8\pi[/tex]

Cancel 8[tex]\pi[/tex] on both sides    

[tex]\frac{1}{3}[/tex] = [tex]\frac{\beta }{360}[/tex]

Cross multiply

3 x β = 360 x 1

3β = 360

Divide both sides by 3

[tex]\frac{3\beta }{3} = \frac{360}{3}[/tex]

β = 120°

Therefore, the measure of ∠CAB is 120°

Answer:

35

Step-by-step explanation:

the whole line is 49 and line DB is 30.

minus 16 from 30 so 30-16=14

then you minus line CB from EB so 49-14=35

that makes line EC 35

Answer:

[tex]x = 3\ or\ x = 7[/tex]

Step-by-step explanation:

Given

[tex]x^{2}-8x+14=2x-7[/tex]

Required

Solve

Equate to 0

[tex]x^{2}-8x-2x+14+7=0[/tex]

[tex]x^{2}-10x+21=0[/tex]

Expand

[tex]x^{2}-7x-3x+21=0[/tex]

Factorize

[tex]x(x-7)-3(x-7)=0[/tex]

Factor out x - 7

[tex](x-3)(x-7)=0[/tex]

Split

[tex]x - 3 = 0\ \ x - 7 = 0[/tex]

Solve

[tex]x = 3\ or\ x = 7[/tex]

Answer:

g = -8, 6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

g² + 2g - 48 = 0

Step 2: Solve for g

the sum of two numbers that is 45 and their difference is 7 it is 39 and 6 more like 39+6

Answer:

20 = x

Step-by-step explanation:

All interiror angles in this triangle will equal 180

Set your formula up as 180 = x+5+7x-5+x then solve for x

180 = x+5+7x-5+x

180 = x + 7x + x +5 - 5

180 - 5 + 5 = 9x

180 = 9x

180 / 9 = x

20 = x

You can check your result by pluging in 20 for all x

180 = 20+5+7*20-5+20

180 = 180

Answer:

a.8y³-6y

taking common

2y(4y²-3)

is a required answer

b.

3x²-20x+12

doing middle term factorization

3x²-18x-2x+12

3x(x-6)-2(x-6)

(x-6)(3x-2)

is a required answer .

Answer:

What is 1/3 of 814

Step-by-step explanation:

What is 1/3 of 814

Answer: I think C

Step-by-step explanation:

Answer:

a= 250

b= 50

250 + 50 = 300

Step-by-step explanation:

There's many solutions but this was the first one I could come up with.

Answer:

my opinion is seince a+b=300 then the sqaure of 300= 17.3?

Step-by-step explanation:

Answer:

x-intercept = 5

y-intercept = 15

Step-by-step explanation:

Change the equation to slope-intercept form: y = -3x + 15

You have the y-intercept in that equation already, so you know it's 15. To find the x-intercept, substitute 0 in for y and solve algebraically.

0 = -3x + 15

-15 = -3x

5=x

Answer:

A. 21

Step-by-step explanation:

Recall: inscribed angle in a semicircle equals 90°

m<K is an inscribed angle in a semicircle = (4x + 6)°

Therefore,

4x + 6 = 90°

Solve for x. Subtract both sides by 6

4x + 6 - 6 = 90 - 6

4x = 84

Divide both sides by 4

4x/4 = 84/4

x = 21

Answer:

i believe it is 497 after the 30% mark down

Step-by-step explanation:

i subtracted 30% from 710

Answer:

d 243

Step-by-step explanation:

The solution of given function is 243

A limit defined as the value which a function approaches as that function's inputs get closer and closer to some number

[tex]lim\ (3x-3)^\frac{5}{2} \\x\to 4[/tex]

[tex](3(4)-3)^\frac{5}{2}[/tex]

[tex](12-3)^\frac{5}{2}[/tex]

[tex](9)^\frac{5}{2}[/tex]

[tex](3^2)^\frac{5}{2}[/tex]

[tex]3^5[/tex]

243

Hence, the solution of given function is 243

Learn more about limit of function

https://brainly.com/question/23008590

#SPJ2

Answer:

24 1/2 cups

Step-by-step explanation:

we can change 6 1/8 into 49/4

there are 2 cups in 1 quart

now we can set up a proportion:

2÷1 = 'c'÷ 49/4

cross-multiply to get:

49/4 × 2 = c

49/2 = c

c = 24.5

Answer:

the quotient of w and 7

is it correct?

Step-by-step explanation:

On expanding the expression, we get - 7x + 21.

We have the following expression -

f(x) = 7(x + 3)

We have to write its equivalent expression.

Expanding we get -

f(x) = [tex]$\pi \sqrt{x} + 5\pi[/tex]

According to the question, we have -

7(x + 3)

On expanding, we get -

7(x + 3) = 7x + 21

Hence, on expanding the expression, we get - 7x + 21.

To solve more questions on expanding expressions, visit the link below -

https://brainly.com/question/12308727

#SPJ2

9514 1404 393

Answer:

  infinite number of solutions

Step-by-step explanation:

The two equations describe the same line.

Adding 9y+15 to the second equation makes it be ...

  15 = 6x +9y

Dividing that by 3 gives you ...

  5 = 2x +3y . . . . . . identical to the first equation

The lines intersect at every point, so there are an infinite number of solutions.

Answer:$6.25

Step-by-step explanation:we have that

x------------------> represent the number of hours Steven babysits

y----------------- > represent the amount he charges

for x=6 hours

y=$37.50 ----------------> y/x=37.5/6=6.25

for x=8 hours

y=$50---------------------> y/x=50/8=6.25

therefore

y=6.25x

Answer:

? = 1

Step-by-step explanation:

4/8 = ?/2

Change the ? into a variable so it's easier to calculate:

Variable x = ?

4/8 = x/2

Cross multiply:

4 × 2 = 8 × x

8 = 8x

Divide both sides by 8 to isolate the variable:

1 = x

Check your work:

4/8 = 1/2

4 × 2 = 8 × 1

8 = 8

Correct!

Answer:

4.5 cm²

Step-by-step explanation:

The given shape is a parallelogram , and the area of a parallelogram is ,

Area :-

So , that,

=> A = 1/2 * 2.5 * 1.8

=> A = 4.5 cm²

Answer:

A = 4.5 m²

Step-by-step explanation:

The area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

Here b = 2.5 and h = 1.8 , then

A = 2.5 × 1.8 = 4.5 m²

Answer:

The answer is below

Step-by-step explanation:

Given that k(x) = -125x² +670x - 125, where x is the charge per cone and P = k(x) is the weekly profit

a) The maximum profit is at P'(x) = 0. Therefore we have to find the derivative of the profit equation and equate it to 0.

P'(x) = k'(x) = 0

k'(x) = -250x + 670 = 0

-250x + 670 = 0

250x = 670

x = $2.68

P = k(2.68) = -125(2.68²) + 670(2.68) - 125 = $772.8

Hence the maximum profit is $772.8 when the price of each ice cream cone is $2.68

b) At break even, the profit is 0. Hence P= k(x) = 0

-125x² + 670x - 125 = 0

x = 5.17 or x = 0.19

Therefore to break even, the price of the ice cream cone needs to be $0.19 or $5.17

c) g(x) = k(x - 2)

g(x) = -125(x - 2)² + 670 (x -2) - 125

Maximum profit is at g'(x) = 0

g'(x) = -250(x-2) + 670

-250(x-2) + 670 = 0

-250x + 500 + 670 = 0

250x = 1170

x = 4.68

g(4.68) = -125(4.68 - 2)² + 670(4.68 -2) - 125 = $772.8

Therefore function g has the same maximum value as function k

Answer:

what is your question friend? :)

[tex]\huge\boxed{Answer\hookleftarrow}[/tex]

Answer:

✐ The integers from 6 to 25 are ⎆ [tex]\large\bold{7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22,23, 24}[/tex]

Step-by-step explanation:

Natural numbers are numbers that are greater than 0 (all numbers starting from positive 1). All natural numbers are integers. So, in this case ⎇ integers = natural numbers (note :- only in this case)

Answer:

[tex]x - 2y=5[/tex]

Step-by-step explanation:

Given

[tex]x = -5; y=-5[/tex]

[tex]x - 2y[/tex] --- missing from question

Required

Evaluate

We have:

[tex]x - 2y[/tex]

Substitute for x and y

[tex]x - 2y=-5 - 2*-5[/tex]

[tex]x - 2y=-5 +10[/tex]

[tex]x - 2y=5[/tex]

Answer:

0

Step-by-step explanation:

5x+10-4=13-7x-7

5x+6=6-7x

5x+0= -7x

0=-12x

Divide and u get x=0

Answer:

Using the formula

an = a of 1 + (n-1)(d)

an = -28 + (n-1)(-17)

simplify

an = -17n - 11

Now that we have the formula, we just plug in 66 for n

a66 = -17(66) - 11

a66 = -1133