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Suppose a bunny farm initally has 20 bunnies. After 2 years the population grew to 80 bunnies.
A) Find f(T)=mT+b, where f(T) is the bunny population after every 2 months. Answers must be in Exact Form, Round 3 decimals, and Change of Base
B) What is the bunny population after 16 weeks?
C) How many months will it take for the bunny population to reach 300 bunnies? Answers must be in Exact Form, Round 3 decimals, and Change of Base

The completion of the MACRS annual cost recovery on a straight-line basis is as follows:

Method Purchased  Cost      Recovery     Recovery          Cost

                                                  Class             Year           Recovery

MACRS July 20      $ 5,000           7                 6            A = $833.33

MACRS  Nov. 5      $ 11,000        20                 13           B = $846.15

Ordinarily, the MACRS (modified accelerated cost recovery system) depreciation method is the tax-allowed method that ensures that larger deductions for depreciation expense or cost recovery are made in the beginning years and lower deductions for later years.

However, the same deductions are made each year when the straight-line method is used.

The depreciation expense using the MACRS straight-line method is computed by dividing the asset's cost by the recovery year.

Method Purchased  Cost      Recovery     Recovery          Cost

                                                  Class             Year           Recovery

MACRS July 20      $ 5,000           7                 6            A = $833.33 ($5,000/6)

MACRS  Nov. 5      $ 11,000        20                 13           B = $846.15 ($11,000/13)

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Answer:

Step-by-step explanation:

Vertex of g(x) is: (-2, -4)

acc to our question:

Vertex form of a quadratic function:

f(x) = (x - h)² + k

We have (h, k) = (3, -4)

The function f(x) is:

f(x) = (x - 3)² - 4

The function g(x) is: g(x) = f(x + 5) =

Vertex of g(x) is:(-2, -4)

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The ball thrown vertically upward, the ball hits the ground after 6.719 seconds.

Quadratic equation :

To solve the quadratic equation:

h(t) = 0 = -5t² +33t+ 4

[tex]t = \frac{-b \pm\sqrt{(b)^2 - 4ac}}{2a}[/tex]

[tex]t = \frac{-33 \pm\sqrt{(33)^2 - 4(-5)(4)}}{2(-5)}[/tex]

t = {(-33) ±√(1169)}/(-10)

t = -0.1190

t = 6.719

neglecting the negative term we get :

t = 6.719 seconds

This represents that the ball hits the ground after 6.719 seconds.

The ball thrown vertically upward, the ball hits the ground after 6.719 seconds.

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Answer:

5q + 5q + 5 is equivalent to 10q + 5

Answer:

A.

Step-by-step explanation:

The time taken is obtained as 3 years.

We know that radioactivity has to do with the fact that a substances does disintegrate gradually over a period of time.

Let us recall the formula;

N/No = (1/2)^t/t1/2

N = The mass of radioactive atoms at time t

No = The mass of radioactive atoms initially present

t = time taken

t/12 = half life of the radioactive nucleus

Then;

32/50 = (1/2)^t/28

0.64 =  (1/2)^t/28

log 0.64 = t/28 log0.5

t/28 = log(0.64/0.5)

t = 28 * log(0.64/0.5)

t = 3 years

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Answer:

a lot less because 0.4 is not fully of 100%

Step-by-step explanation:

Answer:

52 is 0.4% of 130. You would expect the number to be a lot greater than 52

Step-by-step explanation:

If the number we are trying to find is x, we have to use the equation x*0.4=52 which can be rewritten as 52/0.4=x

If you solve that, you get 130.

The number is expected to be a lot greater than 52 because 0.4 is almost 0.5 and that would mean doubling 52 so the number would be almost double 52. That means it would be a lot greater.

The cost the tiles are = $182.55

acc to our question-

white tiles =W = 1/4

3/5 = yellow

each tile costs= $3

= 0.25+ 0.6+ 60

= 60.85*3

$182.55

hence,The cost the tiles are = $182.55

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Answer:

The graph of a function f is the set of points which satisfy the equation y = f(x). ... However, of these two answers, only x = −2 fits in the domain.

Step-by-step explanation:

The doubling time will be 4.4 years for a city is population is growing by 17% per year.

It's time to double down on the time-doubling equation (pun intended). On the assumption that the growth in amount remains constant from one period to the next, the equation is as follows:

Doubling time = log 2 / log (1 + increase)

It has given that the population of the city is growing back 17% per year.

Doubling time = log 2 / log (1 + increase)

Doubling time = log 2 / log (1 + 17/100)

[tex]\mathrm{Apply\:log\:rule}:\quad \frac{\log _c\left(b\right)}{\log _c\left(a\right)}=\log _a\left(b\right)[/tex]

[tex]=\log _{1+\frac{17}{100}}\left(2\right)[/tex]

Doubling time = 4.41484

Round to the nearest tenth decimal.

Doubling time = 4.4

Thus, the doubling time will be 4.4 years for a city is population is growing by 17% per year.

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Answer:

-11

Step-by-step explanation:

6(x-6)+2=8x-12

6x-36+2=8x-12 First take care of the parenthesis

6x-34=8x-12 then combine numbers

-2x-34=-12 Subtract 8 from both sides

-2x=22 Add 34 to both sides

x= -11 Divide by -2 on both sides

Answer:

Step-by-step explanation:

Solution

Steps

6(x−6) +2 = 8x−12

Expand by applying the distributive law:     a(b−c)=ab−ac

6(x−6)=6x-36

6x−36+2 = 8x−12

6x−34 = 8x−12

Add 34 to both sides

6x−34+34=8x−12+34

Simplify

6x=8x+22

Subtract 8x from both sides

6x−8x=8x+22−8x

Simplify

−2x=22

Divide both sides by −2

x=−11

Answer:

h(x)= |x-3|-4

Step-by-step explanation:

If f(x) = |x| is shifted down 4 and right 3 to create h(x), then h(x) = |x - 3| - 4

The function is given

f(x) = |x|

Translation of the shape mean the displacement of the shape from one place  to another place. Some usually used displacements are shifted to right / left and shifted to up / down etc.

First f(x) is shifted down 4

Then the function will become

f(x) = |x| - 4

Then the function shifted right 3

Then the function will be

h(x) = |x - 3| - 4

Hence, if f(x) = |x| is shifted down 4 and right 3 to create h(x), then h(x) = |x - 3| - 4

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The complete general form of the equation of the given sinusoidal function is y = 8sin[(27/2π)*(x - 4)] + c.

The general form of an equation for a sinusoidal function is presented below.

y = a×sin[b*(x - h)] + c

The variable "a" denotes the amplitude of the equation. The variable "T" represents the time period of the equation, and T = 2π/b. The variable "h" denotes the phase shift of the equation. The variable "c" denotes the vertical shift of the equation. The amplitude, period, and phase shift are 8, 27, and 4 units to the left, respectively. The general form of the equation of a sinusoidal function can be written as given below.

y = a×sin[b*(x - h)] + c

y = 8sin[(27/2π)*(x - 4)] + c

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Answer:

Loan analysis is an evaluation method that determines if loans are made on feasible terms and if potential borrowers can and are willing to pay back the loan. It checks the eligibility of the potential borrower against the criteria set forth for lending. Loan analysis helps in assessing the skills and financial knowledge of the borrower to ...

The number of trips after the cost of the plan A and plan B is 16.

According to the question,

We have the following information:

Plan 1 charges a one-time fee of $145.00 for admission plus $5.00 every trip for parking. Plan 2 charges a one-time fee of $40.00 for parking plus $12.00 every trip for admission.

So, this will make an arithmetic progression.

The formula to find nth term of an A.P:

an = a+(n-1)d where a is the first term

Now, on left hand side, we have nth term for plan A and on the right hand side, we have the nth term for plan B because their nth term will be equal.

145+(n-1)5 = 40+(n-1)12

145+5n-5 = 40+12n-12

5n+140 = 12n+28

140-28 = 12n-5n

7n = 112

n = 112/7

n = 16

Hence, the number of trips after the cost of the plan A and plan B is 16.

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Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:

Year Cost   Accumulated   Book Value  Depreciation Accumulated  Book

                  Depreciation        B.O.Y             Expense   Depreciation  Value

                       B.O.Y                                                               E.O.Y       E.O.Y

1    $30,000           $0           $30,000        $12,000          $12,000  $18,000

2   $30,000   $12,000          $18,000          $7,200         $19,200  $10,800

3   $30,000   $19,200          $10,800          $4,320         $23,520   $6,480

The double-declining-balance method is a depreciation method that allocates more cost to the earlier years of the asset's life.

The double-declining-balance method uses twice the straight-line rate and is computed as the product of 100/estimated useful life multiplied by 2.

The double rate is applied at the end of the year's balance for each year's depreciation expense.

The difference between the previous year's ending balance and the residual value is taken as the depreciation expense for the last year.

Auto = $30,000

Estimated life = 5 years

Residual value = $800

Depreciable amount = $29,200 ($30,000 - $800)

Straight-line depreciation rate = 20% (100/5)

Double-declining depreciation rate = 40% (20% x 2)

1st year = $12,000 ($30,000 x 40%)

2nd year = $7,200 ($18,000 x 40%)

3rd year =  $4,320 ($10,800 x 40%)

4th year = $2,592 ($6,480  x 40%)

5th year = $3,088 ($3,888 - $800)

Year Cost   Accumulated   Book Value  Depreciation Accumulated  Book

                  Depreciation        B.O.Y             Expense   Depreciation  Value

                       B.O.Y                                                               E.O.Y       E.O.Y

1    $30,000           $0           $30,000        $12,000          $12,000  $18,000

2   $30,000   $12,000          $18,000          $7,200         $19,200  $10,800

3   $30,000   $19,200          $10,800          $4,320         $23,520   $6,480

4   $30,000  $23,520           $6,480          $2,592           $26,112   $3,888

5  $30,000    $26,112           $3,888           $3,088          $29,200     $800

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The solutions to these system of equations are given as follows:

1. x = 1, y = 7.

2. x = 0.5, y = 2.

3. x = 6, y = -2.

4. x = 3, y = 3.

A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of a problem.

For item 1, it is already stated that the solution for x is x = 1, hence the solution for y is obtained as follows:

y = 2(1) + 5 = 7.

For item 2, we are given two equations for y, hence the solution for x is obtained as follows:

2x + 1 = 6x - 1

4x = 2

x = 2/4

x = 0.5.

Hence the solution for y is:

y = 2(0.5) + 1 = 1 + 1 = 2.

For item 3, from the second equation, we have that:

y = 4 - x.

Then the solution for x will be of:

2(x - 7) = 4 - x

2x - 14 = 4 - x

3x = 18

x = 18/3

x = 6.

The solution for y is:

y = 4 - 6 = -2.

For item 4, from the first equation, we have that:

y = 3x - 6.

Then, replacing on the second equation, the solution for x is obtained as follows:

x + 3(3x - 6) = 12

x + 9x - 18 = 12

10x = 30

x = 3.

Then the solution for y is:

y = 3x - 6 = 3(3) - 6 = 9 - 6 = 3.

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The solution to the equation using graph is x= -0.62 or x = 1.62.

What is equation?

A mathematical equation may be a formula that uses the equals sign to represent the equality of two expressions.

Main Body:

For [tex]-x^{2} +y = 1[/tex]

We make y the subject to obtain

[tex]y = x^{2} +1[/tex]

We can easily graph this function, because we just have to transform the graph [tex]y = x^{2}[/tex] of  by shifting the intercept up to 1.

As for the straight line, -x +y = 2

We find the intercepts as follows,

When y = 0 , x = -2

When x = 0 , y = 2

We plot the points (-2,0)  and (0,2).

We now draw the two graphs on the same graph sheet. The intersection of the two graphs gives the solution to be

x= -0.62 or  x= 1.62

See graph

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Answer:

156.7 m (nearest tenth)

Step-by-step explanation:

Define the variables:

If the distance needed to stop a car varies directly as the square of its speed:

[tex]\boxed{d \propto v^2 \implies d=kv^2}[/tex]

where k is the constant of proportionality.

Given:

To find the constant of proportionality, k, substitute the given values into the equation:

[tex]\begin{aligned}\implies 120&=k(70)^2\\k&=\dfrac{120}{70^2}\\k&=\dfrac{6}{245}\end{aligned}[/tex]

Substitute the found value of k back into the formula to create an equation for the given relationship:

[tex]\implies d=\dfrac{6v^2}{245}[/tex]

To find the distance (in meters) required to stop a car at 80 km/h, substitute v = 80 into the equation:

[tex]\implies d=\dfrac{6(80)^2}{245}[/tex]

[tex]\implies d=\dfrac{6\cdot 6400}{245}[/tex]

[tex]\implies d=\dfrac{7680}{49}[/tex]

[tex]\implies d=156.73469...\; \sf m[/tex]

[tex]\implies d=156.7\; \sf m\; (nearest \;tenth)[/tex]

Therefore, the distance required to stop a car at 80 km/h is:

If the temperatures on Earth continue to increase, the change in the pie graph would be C. Less than 2% of the Earth's water will be in polar ice caps.

The temperature of Earth has risen significantly in the last century as a result of human activity. This had led to the loss of polar ice caps due to them having melted into the oceans from the high temperatures.

This means that if the temperature of the planet should continue to increase, the polar ice caps we have will further be depleted. This would lead to less than 2% of the Earth comprising polar ice caps as is the case now.

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The correct expression of the inequality expression is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3

From the question, the expression is given as

18 ÷ 6 + 3 □ 6 + 12 ÷ 3

We start by converting the above expression to the same form

So, we start by solving the quotients

This gives

3 + 3 □ 6 + 4

Next, we evaluate the sum

So, we have

6 □ 10

In the above expression, we have

6 and 10

By convention, the number 6 is less than the number 10

This is so because 6 has a smaller value and 10 has a higher value

When the above numbers are compared, we have

6 is less than 10

This means that we make use of the inequality symbol <

So, we have

18 ÷ 6 + 3 < 6 + 12 ÷ 3

Hence, the complete inequality is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3

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Answer:

7 * 5 =35 because if you say 5 10 15 20 25 30 35 then that's your answer

Answer:

a) 7:13  b) 5:13

Step-by-step explanation:

There are 7 new books (-> 7:--) theres 5 used books, add the 7 new books and 5 used books together. it said "The ratio for new books to all books?" it must be in that order. with leads you to 7:13

do the same thing for b) using the same steps.

Answer: Center: (-3, 2). Radius: 4.

Step-by-step explanation:

The x-coordinate of the center of the circle is given by the constant within the parenthesis with variable x. Whatever number makes the equation x + 3 = 0 is the x-coordinate of the center of the circle, which in this case is -3.

The y-coordinate of the center of the circle is given by the constant within the parenthesis with variable y. Whatever number makes the equation y - 2 = 0 is the y-coordinate of the center of the circle, which in this case is -2.

The radius of the circle is the square root of the constant on the other side of the equation. So, r = [tex]\sqrt{16}[/tex] = 4.

The explanation is from the equation of a circle in a graph:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

h and k in this equation stand for the coordinates of the center of the circle, with h being the x-coordinate and k being the y-coordinate. IN your equation, we have:

[tex](x+3)^2 + (y-2)^2 =16[/tex]

Which can also be written as

[tex](x-(-3))^2 + (y-(2))^2=16[/tex]

See the correlation of numbers -3 and 2 with h and k?

Notice also how the equation contains [tex]r^2[/tex], so to find the radius you do [tex]\sqrt{r^2}[/tex].

Answer:

0.97m : 1.08m

Step-by-step explanation:

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Answer:

-25x-45y, because if we have got + and -, so we will write minus.

Answer:

A. REFLECTION

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The greatest common factor of 160, 320 and 480 will be 160.

The largest positive number that can be evenly divided into the supplied numbers is the most common factor. The largest number that evenly divides all the specified numbers is the greatest common factor.

In maths, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero. The greatest common divisor of two numbers x and y is represented by the symbol GCD(x,y)

Assumed to be 160, 320 and 480. The numbers are factored to determine the largest common factor.

Factorize number 160

160 = 2×2×2×2×2×5

Factorize number 320

320 = 2×2×2×2×2×2×5

Factorize number 480

480 = 2×2×2×2×2×3×5

The common number between all three numbers is 2⁵×5. Therefore, the greatest common factor of 160, 320 and 480 will be 160.

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