If an asset declines in value from $5000 to $3500 over nine years, what is the mean annual growth rate in the asset's value over these nine years? Round your answer to two decimal places.

Answers

Answer 1

Mean annual growth rate in the asset’s value over the nine years is -3.8856%.

Given that an asset declines in value from $5000 to 3500 over the nine years.

To determine the mean growth rate over some period of time, compute the geometric mean of the growth factors. A growth factor less than one indicate negative growth.

The formula for the geometric mean over n periods is given by

[tex]y_n =\sqrt[n]{ {y_1 \times y_2 \times y_3 \times ......\times y_n}}[/tex]

Suppose an asset declined over nine years.

[tex]3500 = 5000\times({y_1 \times y_2\times y_3 \times ..\times y_9})[/tex]

[tex]{y_1 \times y_2\times y_3 \times ..\times y_9} = 3500/5000\\\ y_1 \times y_2\times y_3 \times ..\times y_9} = 0.7[/tex]

Then, the mean annual growth factor over these nine years is,

[tex]y_9 = \sqrt[9]{0.7}[/tex]

= 0.961144

Compute the mean annual growth rate in the asset’s value.

= (0.961144 - 1) 100%

= -3.8856%

Therefore, the mean annual growth rate in the asset’s value is -3.8856%.

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Answer 2

Final answer:

To find the mean annual growth rate of an asset declining from $5000 to $3500 over 9 years, you calculate the growth rate 'r' using the formula P(t) = P0 * e^(rt). The result is about -5.13%, indicating a depreciation in the asset's value.

Explanation:

To calculate the mean annual growth rate for an asset that declines in value, we can use the formula for the annual growth rate, which is P(t) = P0 * e(rt), where:

P(t) is the future value of the asset.P0 is the initial value of the asset.e is the base of the natural logarithm.r is the growth rate.t is the time in years.

In this case, the value of the asset declines from $5000 to $3500 over 9 years. Therefore, we have:

P0 = $5000P(t) = $3500t = 9 years

First, we need to solve for r in the equation:

3500 = 5000 * e(9r)

By dividing both sides by 5000 and taking the natural logarithm, we get:

ln(3500/5000) = ln(e(9r))

ln(0.7) = 9r

r = ln(0.7)/9

Substitute the value of ln(0.7) and divide by 9:

r = -0.0512932942

Since the result is negative, it indicates a decline, and the annual growth rate is about -5.13%, reflecting a decrease in value.

Related Questions

Can somebody plz help me

Answers

This type of proof is called a flowchart proof.

What is the measure of x?
A.36
B.72
C.144
D.360

Answers

i believe your answer would be B)72.

36° The answer is 36° because if you multiply 36 × 2 then you would get 72°.

A vending machine needs to be programmed to accept any combination of coins totaling 0.75, excluding pennies, and half dollars. How many combinations are possible?

Answers

Combination 1: 3 quarters (25 cent).

Combination 2: 2 quarters and 5 nickels.

Combination 3: 2 quarters, 2 dimes, 1 nickel.

Combination 4: 15 nickels

Combination 5: 7 dimes and 1 nickel.

Combination 6: 1 quarter, 5 dimes

Combination 7: 1 quarter, 1 dime, 7 nickels.

Combination 8: 1 quarter, 2 dimes, 6 nickels.

Combination 9: 1 quarter, 3 dimes, 4 nickels.

Combination 10: 1 quarter, 4 dimes, 2 nickels.

I believe those are all the possible combinations.

I hope that helped you! :)

Mark had $19.00 to spend on stamp packets. They sell for $1.78 each. How many packets can he buy?

Answers

just do 19.00/1.78

That equals 10.67

so you can by 10 stamps.

Answer:

[tex]10\ stamp\ packets[/tex]

Step-by-step explanation:

Let

x-----> the number of packets that mark can buy

we know that

[tex]1.78x\leq 19[/tex] -----> inequality that represent the situation

Solve for x

Divide by [tex]1.78[/tex] both sides

[tex]x\leq 19/1.78[/tex]

[tex]x\leq 10.67\ stamp\ packets[/tex]

Find the greatest common factor of 16, 27 and 20

Answers

Can you list the factors of each of those numbers (the numbers that divide evenly into them)? Of those three lists, what's the highest number present in all three?

The greatest common factor for 16, 27, and 20 is 1.
The factors for 16 are 1,2,4,8,16.
The factors for 27 are 1,3,9,27.
The factors for 20 are 1,2,4,5,10,20.

find three consecutive odd integers such that the square of the first plus the square of the third is 170

Answers

Here is the set up:

x
x + 2
x + 4

x^2 + (x + 2) + (x + 4)^2 = 170

Take it from here.

Martha took 48 pictures of flowers and 36 pictures of beautiful scenery.she wants to display the pictures so there are the same number of each kind of picture in each display.what is the greatest number of displays she can make?

Answers

Well if you have 48 pics of flowers and 36 pictures of scenery and you want an equal amount of pictures of the scenery, you want to start out by just seeing what number divides evenly into both, in this case, it is four.

15. How much less would a 25 year old male pay for a $50,000 policy of 20 y life insurance @ $5.84 per $1000, than a straight life policy @ $15.66 per $1000? (Points : 1)
$783
$491
$292
$415

Answers

The man would pay $491 less for a policy of 20 year life insurance than a straight life policy. So, the answer is the second one.

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

Amount for policy = $50,000

If he opt for life insurance @$5.84 per $1000,

then, his amount of premium will be

[tex]50000\times \frac{5.84}{1000}=\$292[/tex]

If he opt for straight policy @ $15.66 per $1000,

then, his amount of premium will be

[tex]50000\times \frac{15.66}{1000}=\$783[/tex]

Difference in both the cases will be

[tex]783-292=\$491[/tex]

Hence, Second option is correct.

Solve for x: the quantity of x plus 4 / 3 = 2.
A.x = −2 B.x = 2 C.x = 2/ 3 D. x = negative 10/ 3

Answers

i meant answer will be C.x=2/3

A web store offers two versions of a popular song. The size of the standard version is 2.5 MB. The size of the high quality is 4.3 MB. Yesterday, there was 1180 downloads of the song, for a total size of 3850 MB. How many downloads of the high quality version were there?

Answers

i believe the answer is 895.348837

Answer:

250

Step-by-step explanation:

A local hamburger shop sold a combined total of 445 hamburgers and cheeseburgers on Tuesday. There were 55 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Tuesday?

Answers

Let x represent the number of hamburgers sold, and (x - 55) represent the number of cheeseburgers sold.

Set up an equation:
hamburgers + cheeseburgers = total number of burgers

x + (x-55) = 445

solve for x:
2x - 55 = 445

2x = 445 + 55

2x = 500

x = 500÷2

x = 250

This means 250 hamburgers were sold on Tuesday.

Hope this helps!

-Jabba

To solve for the number of hamburgers sold, two equations were setup: H + C = 445 and C = H - 55. Substituting the second equation into the first and solving for H results in finding that 250 hamburgers were sold on Tuesday.

The question asks us to find out how many hamburgers were sold on Tuesday given that a total of 445 hamburgers and cheeseburgers were sold, and there were 55 fewer cheeseburgers than hamburgers. Let's denote the number of hamburgers as H and the number of cheeseburgers as C. We have two equations here: H + C = 445 and C = H - 55. Plugging in the second equation into the first, we get H + (H - 55) = 445, which simplifies to 2H - 55 = 445. Adding 55 to both sides gives us 2H = 500, and dividing both sides by 2 gives us H = 250. Therefore, on Tuesday, the hamburger shop sold 250 hamburgers.

What is the LCM of 5 and 6?

Answers

Answer: 30

Explanation: To find the least common multiple of lcm of 5 and 6, we begin by listing the first few multiples of each number.

Multiples of 5

1 x 5 = 5

2 x 5 = 10

3 x 5 = 15

4 x 5 = 20

5 x 5 = 25

6 x 5 = 30

Notice that we skipped 0 x 6 in our list of multiples. That's because 0 x 6 is 0 and our least common multiple can't be 0.

Next we list the multiples of 6. When we list the multiples of 6, it's a good idea to keep an eye on the list of multiples for 6 so that we know when we have found a least common multiple.

Multiples of 6

1 x 6 = 6

2 x 6 = 12

3 x 6 = 18

4 x 6 = 24

5 x 6 = 30

Notice that 30 appears in both lists so we can stop here.

This means that the least common multiple of 5 and 6 is 30.

Answer:

Step-by-step explanation:

both 6 and 5 go into 30 :)

You can jog around the block twice and the park once in 10 min. You can jog around the block twice and the park 3 times in 22 min. Write a system of linear equations that represents this situation. How long does it take to jog around the park?

Answers

b = block p = park

2b + p = 10 min 2 runs around the block takes 10 minutes
2b + 3p = 22 min 2 runs around the block plus 3 runs around the park takes 22 minutes

To solve, I will use substitution. First, I will divide the first equation by 2 to get b by itself and subtract p from both sides to get b by itself. Then, substitute 5 - 1/2p in for b in the second equation because they have equal values. Then, subtract 10 from both sides to eliminate it. Divide by 2 to both sides to get 'p' by itself.

2b + p = 10 min ---------→b + 1/2p = 5 ----------→ b = 5 - 1/2p

2(5 - 1/2p) + 3p = 22 ---------→ 10 -p + 3p = 22 --------→ 10 + 2p = 22

10 + 3p = 22 ----------→ 2p = 12

2p = 12 -------------→ p = 6

It takes 6 minutes to jog around the park

Hope this helps!

If c(x)= [tex] \frac{5}{x-2} [/tex] and d(x) = x + 3, what is the domain of (cd)(x)?
all real values of x
all real values of x except x = 2
all real values of x except x = –3
all real values of x except x = 2 and x = –3

Answers

[tex]\bf \begin{cases} c(x)=\cfrac{5}{x-2}\\\\ d(x)=x+3\\ ----------\\ (cd)(x)\implies c(x)\cdot d(x) \end{cases} \\\\\\ c(x)\cdot d(x)\implies \left( \cfrac{5}{x-2}\right)(x+3)\implies \cfrac{5(x+3)}{x-2}[/tex]

now, for a fraction, if its denominator ever becomes 0, the fraction becomes undefined, because it'd be a division by 0.

when does that happen? let's zero out the denominator to check,

x - 2 = 0, thus x = 2

so, if "x" ever becomes 2, the fractions goes kaput.

so, that domain is all real values except that one, that makes the fraction undefined.

Final answer:

The domain of the composite function (cd)(x), where c(x) = 5/(x-2) and d(x) = x + 3, includes all real values except x = 2 due to a division by zero condition in the function c(x).

Explanation:

In this problem, we need to figure out the domain of the combined function (cd)(x). The domain constitutes the set of all real values of x that make the function defined. The first function, c(x) = rac{5}{x-2}, isn't defined for x = 2 because it would lead to a division by zero. The second function, d(x) = x + 3, is defined for all real values since it's a linear function.

When these functions are multiplied to form (cd)(x), the domain will be the intersection of the individual function domains. This means, with c(x) having a restriction with x != 2, the composite function (cd)(x) will maintain this restriction despite d(x) being defined for all real values. So the domain for (cd)(x) is all real values except for x = 2.

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find the root of 6x-48=0

Answers

undistribute 6
(6)(-48)=0
set to zero
x-8=0
add 8 to both sides
x=8
the root is at x-8

Find the roots of 6x-48=0 by solving for x.

X=8

Simplify the expression. (4 − 4i)(−2 + 5i)

Answers

12 + 28i
is your answer

To simplify multiplying binomials, you can use two equations
4(-2+5i) + -4i(-2+5i)
Simplify - -8+20i +8i -20i²
-20i² + 28i - 8
Hope this helps- Please mark brainliest :)

20 POINTS PLEASE HELP Write an equation for a trend line and predict the value when x is 15
X 0 3 6 9 12
Y 17.5 35.4 50.5 60.6 66.3

Answers

Attached is what you can do on excel.

Add the values as presented on the image. Select the values and then go t the menu "Insert" and look for "Charts" and then "Insert scatter chart". After this, select one of the dots from the graph and then press the right button of the mouse and select "add trendline". Now you have a trend line. Format the trendline selecting the option "Display Equation on chart" (and also if you want "Display R-squared value on chart"). Now you have the equation and you can easily predict the value when X is 15, you just need to substitute on the equation the X by the 15:
y = 4.0933Χ + 21.5 <=> y = 82.8995

A garden table and a bench cost $573 combined. The garden table costs $77 less than the bench. What is the cost of the bench?

Answers

just do 573 minus 77

Because the total cost is $573.00, subtract the cost of the garden table from the total.

• 573 - 77 = 496

So, the bench costs $496.00.

Hope this helps! :D

~PutarPotato

A store sells small notebooks for $8 and large notebooks for $10. if a student buys 6 notebooks and spends $56, how many of each size did he buy?

Answers

The first thing you have to do is find a way to make the last digit 6 (since its $56). So that would be $8×2=16, so there are 2 small notebooks. Then, she needs another $40 to get $56, so 40÷10=4, so she bought 4 large notebooks.

Answer: 2 small, 4 large

I would approach this from a Guess and Check Strategy. Take combinations of two numbers when added equal six: 0 + 6 1+ 5. 2+ 4, 3 + 3, 4 + 2, 5 + 1, 6 + 0. Take a combination like 3 + 3. If the student bought 3 notebooks at $8 each and 3 notebooks at $10 each it would be $24 + $30 = $54 which is just short of $56. You could use each of the combinations in the same way until you match $56. In the end the combination of 2 + 4 would solve the problem. Two notebooks at $8 each plus four notebooks at $10 each would be: $16 + $40 which does equal $56. So the student bought 2 notebooks at $8 each and 4 notebooks at $0 each.

Macs farm has a total of 18 horses and 27 cows. what is the ratio of horses to cows in simplest form?

Answers

The ratio is basically finding the quotient of two numbers. If you want to find the ratio of horses to cows, divide the number of horses to that of cows.

Ratio = 18/27

When expressing it to its simplest form, make sure it is reduced. 18 and 27 are both factors of 9. So,

Ratio = 9*2/9*3
Cancelling out 9, the ratio at its simplest form is: 2/3

Answer:

2/3

Step-by-step explanation:

You know that you can ride your bike 8 miles in 20 minutes. At the same pace, how many miles would you go in 2 hours?

Answers

Hello there,
2 hrs= 160 minutes
20 minutes= 8 miles
160 minutes= ? miles
As you can see 20 x 8 = 160 miles
So, you need to multiply 8 in both sides (meaning- 20 x 8 & 8 x 8)
160 minutes= 64 miles

Hope this helps

~Top

i think its D but who knows HEEEEELELELLELEELEP

Answers

you plus 4 friends = 5 people

them multiply 5 by m sp you get 5m

D is the correct answer

Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%.
Alexander thought the equivalent quarterly interest rate would be 2%. Is Alexander correct? If he is, explain
why. If he is not correct, state what the equivalent quarterly interest rate is and show how you got your
answer. i need to show my work and everything

Answers

Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.

For the annually rate we have that:
[tex] V_{0} =(1+ i_{a} ) ^{1} [/tex]
Where
[tex] V_{0}[/tex] = initial investment.
[tex] i_{a} [/tex] = annually interest rate in decimal form.
And the exponent (1) represents the full year.

For the quarterly interest rate we have that:
[tex] V_{0} =(1+ i_{q} ) ^{4} [/tex]
Where
[tex] V_{0}[/tex] = initial investment.
[tex] i_{q}[/tex] = quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.

Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
[tex](1+ i_{a} )=(1+ i_{q} ) ^{4} [/tex]
Notice that we are not using the initial investment [tex] V_{0} [/tex] since they are the same.

The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
[tex](1+0.07)=(1+ i_{q} ) ^{4} [/tex]
[tex]1.07=(1+ i_{q} ) ^{4} [/tex]
[tex] \sqrt[4]{1.07} =1+ i_{q} [/tex]
[tex] i_{q} = \sqrt[4]{1.07} -1[/tex]
[tex] i_{q} =0.017[/tex]
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.

How many permutations are there of jack, queen, king, ace

Answers

[tex]\bf _nP_r=\cfrac{n!}{(n-r)!}\qquad \qquad _4P_1=\cfrac{4!}{(4-1)!}[/tex]

What point is the image of (3,4) if it is reflected over the y axis?A. (-3,-4)B. (3,-4)C. (-3,4)D. (3,4)

Answers

point is the image of (3,4) if it is reflected over the y axis is (-3,4)
answer
C. (-3,4)

If point is the image of (3,4) if it is reflected over the y axis, then the resulting point is (-3,4) (option c)

When a point is reflected over the y-axis, its x-coordinate changes sign while the y-coordinate remains the same. In other words, if we have a point (x, y), its image after reflection over the y-axis will be (-x, y).

Let's apply this rule to the given point (3, 4). When we reflect it over the y-axis, the x-coordinate changes sign, but the y-coordinate remains the same. Therefore, the image of (3, 4) after reflection over the y-axis will be (-3, 4).

So, the correct Answer: C. (-3, 4)

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Is is true that the coefficient of the expression 18z-7(-3+2z) of z is 13

Answers

18z-7(-3+2z)
= 18z + 21 - 14z
= 4z + 21

answer is False
coefficient of z is 4, not 13

One number is four times another. the greater number is xx. write an expression for the lesser number.

Answers

xx/4=y Y is the lesser number. xx is the greater number. Since xx is four times y, you need to divide xx by four to find y. To find xx, you would need to multiply y times four, and the resulting expression would be 4y=xx.

64.125 - 20.37 i need the answer

Answers

The answer is 43.755.

Answer:

43.755 what the other person said but I know that is the answer

Step-by-step explanation:

Sharon writes this sentence:

Seven less than two times a number is 29.

Enter the equation that represents Sharon's sentence into the box.

Use x for the variable.

Answers

The answer is 2x-7=29

Answer:

your answer would be 2x-7+29

Ana wants to paint her dogs doghouse. She has 4 colors: Green, Maroon, Blue and Wheat. One color will cover the walls, and another color will be used for the trim. (For example, green walls with wheat trim = GW.) Which one of these answers show all of the possible color combinations?

A. BW, BM, BG, BB, MW, MB, MG, MM, GW, GB, GM, GG
B. GM, GB, GW, MG, MB, MW, BG, BM, BW, WG, WM, WB
C. MM, MG, WB, WM, WG, BB, BG, BM, WB, GB, GM, GW

Answers

Let us take this one by one. One color can pair with three colors.

Green = Maroon, Blue, Wheat = GM, GB, GW

Maroon = Green, Blue, Wheat = MG, MB, MW

Blue = Green, Maroon, Wheat = BG, BM, BW

Wheat = Green, Maroon, Blue = WG, WM, WB

So the combinations are:

GM, GB, GW, MG, MB, MW, BG, BM, BW, WG, WM, WB

Which is letter B.

The awnser is b trust I got it right thank you for your time nd day

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