In 2000, the moose population in a park was measured to be 650. By 2010, the population was measured to be 750. Assume the population continues to change exponentially. Find a formula for the moose population, P(x), where x is the number of years after 2000

Recall the definition of absolute value:

[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]

Then we have a few cases to consider:

• If [tex]4x-5\ge0[/tex] and [tex]-x+5\ge0[/tex], the equation simplifies to

[tex]4x-5 = -x+5 \implies 5x=10 \implies \boxed{x=2}[/tex]

• If [tex]4x-5<0[/tex] and [tex]-x+5\ge0[/tex], we get

[tex]-(4x-5) = -x + 5 \implies -3x = 0 \implies \boxed{x=0}[/tex]

• If [tex]4x-5\ge0[/tex] and [tex]-x+5<0[/tex], then

[tex]4x-5 = -(-x+5) \implies 3x=0 \implies x=0[/tex]

but we already have this solution.

• If [tex]4x-5<0[/tex] and [tex]-x+5<0[/tex], then

[tex]-(4x-5) = -(-x+5) \implies -5x = -10 \implies x=2[/tex]

which we also already found.

the answer is 64 multiplication can be done with calculator or normal

The height and width of the outline (perimeter) of the mirror, as well as the

center in relation to the plane of the edges are given.

[tex]\displaystyle The \ mirror \ can \ be \ \mathbf{ represented} \ by \ the \ equation; \underline{\frac{(y - 60)^2}{144} + \frac{x^2}{100} = 1}[/tex]

Reasons:

Width of the elliptical mirror = 20 inches

Height of the elliptical mirror = 24 inches

Center of the ellipse = (0, 60)

The equation of an ellipse is;  [tex]\displaystyle \mathbf{\frac{(x - h)^2}{b^2} + \frac{(y - k)^2}{a^2}} = 1[/tex]

Where;

(h, k) = Coordinates of the center;

a = Semi major axis

b = Semi minor axis

In the mirror, we have;

(h, k) = (0, 60)

a = 24 ÷ 2 = 12

b = 20 ÷ 2 = 10

Which gives;

[tex]\displaystyle \frac{(x - 0)^2}{10^2} + \frac{(y - 60)^2}{12^2} = \frac{x ^2}{100} + \frac{(y - 60)^2}{144} = \mathbf{\frac{(y - 60)^2}{144} + \frac{x^2}{100}} = 1[/tex]

Therefore;

[tex]\displaystyle The \ equation \ that \ represent \ the \ mirror \ is; \underline{ \frac{(y - 60)^2}{144} + \frac{x^2}{100} = 1}[/tex]

Learn more about the equation of an ellipse here:

https://brainly.com/question/1306753

Work Shown:

tan(angle) = opposite/adjacent

tan(x) = 13/101

x = arctan(13/101)

x = 7.334379 approximately

x = 7.33

Answer:

14/10

OR

7/5

Step-by-step explanation:

(7*2)/(2*5) = 14/10

(14/2) / (10/2) = 7/5

Answer:

Mixed fraction: 1 2/5

Decimal form: 1.4

Hope this helps :)

Answer:

232.820513

Step-by-step explanation:

Let the number you are looking for is x,

equation,

90.8 * x = 39

90.8/39 = 2.32820513

Now we multiply 100 because we are dealing with percentages so,

2.32820513 * 100 = 232.820513

So, the answer is 232.820513

Hope this helps! Good luck to everyone!

Answer:

163 miles

Step-by-step explanation:

set up a ratio based on 49 miles in 1 hour (60 minutes):

let 'd' = distance in 3hrs, 20 min

3hrs, 20 min = 200 minutes

49/60 = d/200

cross-multiply:

60d = 9800

d = 163.3

The distance you can travel in 3 hours 20 minutes if you drive on average 49 miles per hour will be 163.33 miles.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

The speed of the vehicle is 49 miles per hour. And the time is 3 hours 20 minutes.

Convert the time completely hours. Then we have

T = 3 + 20/60

T = 3.33 hours

The distance you can travel in 3 hours 20 minutes if you drive on average 49 miles per hour will be

D = 49 x 3.33

D = 163.33 miles

The distance you can travel in 3 hours 20 minutes if you drive on average 49 miles per hour will be 163.33 miles.

More about the speed link is given below.

https://brainly.com/question/7359669

#SPJ2

Answer:

25%

Step-by-step explanation:

8-6=2

2/8=0.25

0.25×100=25%

Answer:

an employee working on commission plus salary.

Step-by-step explanation:

salary is the hourly rate

commission is tips

Answer:

B - An employee working on commission plus salary

Step-by-step explanation:

Answer:

Step-by-step explanation:

You already have the slope. It is + 1 as in y = (+1)x when you have been given

y = x + b

That means all you need do is subtract to find out what  b is

y =   x + b

x = 5

y = 11

Difference is 11 - 5 = 6

Try it a couple more times.

x = 10

y = 16

y = x + b

16 = 10 + b        Subtract 10

16 - 10 = b

b = 6 just as it did before.

y = x + b

x = 20

y = 26

26 = 20 + b      Subtract 20

26-20 = b

b = 6

So ? = 6

Answer:

Both Oscar and Kim will have enough to purchase the book.

Step-by-step explanation:

Oscar takes 30% of the normal price and subtracts it from the normal price. Out of 100% price he takes 30% so the result is: 100-30%= 70% of the normal price. Oscar's first step has the same result as Kim.

Oscar takes 10% of the discounted price (70%) and adds it back. The price will become 70% + 10%*70%= 77% of original price. Kim multiplies the discounted price with 110%, so the price will be: 70% * 110%= 77%. Both also give the same result.

The final price is 77% of the original, it will be: $28.50* 77%= $21.945

Oscar :

28.50 - 0.30(28.50) = 28.50 - 8.55 = 19.95

0.10(19.95) + 19.95 = 2 + 19.95 = 21.95

Kim :

0.7(28.50) = 19.95

1.10(19.95) = 21.95

Answer:

Both Oscar and Kim got the same amount and they both had enough money to buy the book.

Given that,

Oscar and Kim have money to spend at a book fair = $22

Discount for all the students = 30% = 0.30

They both want to purchase a copy of the same book, which normally sells for $28.50 plus 10% sales tax.

Book normally sells for = $ 28.50 + 10% sales tax

According to the question,

Oscar takes 30% of $28.50 and subtracts that amount from the normal price. He takes 10% of the discounted selling price and adds it back to find the purchase amount.

28.50 - 0.30(28.50) = 28.50 - 8.55 = 19.95

0.10(19.95) + 19.95 = 2 + 19.95 = $21.95

Kim takes 70% = 0.7 of the normal purchase price and then computes 110% = 1.10 of the reduced price.

0.7(28.50) = 19.95

1.10(19.95) = $21.95

Hence, Both Oscar and Kim got the same amount and they both had enough money to buy the book.

Step-by-step explanation:

Answer:

1260°

Step-by-step explanation:

The sum of the measures of the interior angles of a polygon of n sides is

(n - 2)180°

This polygon has 9 sides, so n = 9

sum = (9 - 2)180°

sum = 7(180°)

sum = 1260°

Answer:

D) p > -2

Step-by-step explanation:

5 + p > 3

5 + p - 5 > 3 - 5

p > -2

Answer:

2.72 inches

Step-by-step explanation:

1040/8.5=122.35

1 inch on the map = 122.35 miles actual distance

333/122.35=2.72

Answer:

It's a good question I seen thank you so much for your help and support me in the morning and have a talk

Answer: 5+ba*7= 88

Step-by-step explanation:

Answer: For in the inequality to be true, X must be less than or equal to 1. That represented as an in equality is X < 1.

x<1 true

Step-by-step explanation:

3(1+x)<+6= 3×1+3×X<+6=3+3x<6 then3x=6-3 solution 3x=3 devide by 3 both sides the answer is x=1 hence x<1 verified

1470.27

v = pi r^2 (H)

v = 3.14 (6^2) (13)

v = 3.14 (36) (13)

v = 1470.27 (about)

Answer:

V = 1470

Step-by-step explanation:

V = πr²h

V = (3.14)(6²)(13)

V = (3.14)(36)(13)

V = 1469.52

Answer:

check online for more information

Answer:

A

D

B

C

Step-by-step explanation:

We can simplify the expressions for easier comprehension:

A. 60.7 x 10^-1 = 6.07

B. 6.07 x 10^3 = 6,070

C. 0.67 x 10^4 = 6,700

D. 6.7 x 10^2 = 670

Now, we can order them in ascending order (least to greatest):

A

D

B

C

Answer:

60%

Step-by-step explanation:

15 out of 25 is 60%

25 is the total people in the club

Hope this helps

Answer:

Answer below

Step-by-step explanation:

Time can not be negative from any perspective. Hence, the correct answer is 10.16 seconds.

The equation of the path of a rocket is given that is  y= x^2 + 153x + 98

We need to determine the time that the rocket will hit the ground.

Now, if the rocket hits the ground after the launching then the overall displacement at the time of hitting the ground will be zero.

Therefore, the value of y is 0.

Thus,  -16x^2 +153x + 98 = 0

Now, the formula for finding the roots of the quadratic equation  

 ax^2 +bx +c = 0 is given as:

 [tex]x^{1} =\frac{-b+\sqrt{b^2 -4ac} }{2a}[/tex]

[tex]x^2 = \frac{-b -\sqrt{b^2 -4ac} }{2a}[/tex]

Comparing the expression with the standard form of the equation.

a = -16b = 153 and c = 98

By applying the formula there are two values are come that is,

x^1 = -0.602555

x^2 = 10.1651  

Time can not be negative from any perspective.

Hence, the correct answer is 10.16 seconds.

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(Hope this helps can I pls have brainlist (crown)☺️)

.7 is the nearest tenth to the number .6752 because of the 1-4 rounds down and 5-9 round up.

Answer:

Step-by-step explanation:

6750

Answer:

A is a 2 in the tenth place of the difference

5 pounds - 1.89

3 pounds - 1.99

1 pound - 2.05

In this case, the 5 pounds of chicken is the cheapest by exactly one dime.

Answer: please read the explanation :)

Step-by-step explanation:

Make the precent a whole number then subtract it form 100 then the answer turn it to a percent :)

1) 100 - 65 = 35 = 35% of boys in the class

2) 100 - 27 = 63 = 63% of skirts that are not red

3) 100 - 78 = 22 = 22% non swimmers

4) 100 - 43 = 57 = 57% what he got wrong

5) 100 - 45+42 = 13 = 13% the games they tied

6) 100 - 28+35 = 37 = 37% who chose football

7) 100 - 38 = 62 = 62% are dogs

8) 100 -35 = 65 = 65% scored over average

9) 100 -12 = 88 = 88% percent

10) 100 - 6 = 94 = 94% can ride the bike

Hope that helps if you need more explanation please send me :)

Answer:

1,350-670=R

Step-by-step explanation:

R means Raffle

Answer:

113

Step-by-step explanation:

The supplement of angle 3 is congruent to 67, because they are corresponding angles. After you subtract the supplement from 180, you should get angle 3

180-67=113

Answer:

∠3 measures 113°

Step-by-step explanation:

These are consecutive interior angles. It's difficult to explain in words because none of the lines are marked in any way, but I marked the angles in the attached image. Because both downward facing lines are parallel, both sets of corresponding red and blue angles are congruent.

∠3 corresponds to the angle supplementary to the 67° angle. Supplementary angles add up to 180°, so ∠3 and 67° also have to add up to 180°. Hopefully my image makes that a little more clear.

[tex]x+67=180\\x=113[/tex]

∠3 measures 113°

Answer:

358.9 I think

Step-by-step explanation: