A charter fishing company buys a new boat for $224,000 and assumes that it will have a trade-in value of $115,200 after 16 years.
a. Find a linear model for the depreciated value V of the boat t years
after it was purchased.
b. What is the depreciated value of the boat after 10 years?
c. When will the depreciated value fall below $100,000?
d. Graph V for 0 ≤ t ≤ 30 and illustrate the answers from (b) and
(c) on the graph.
Answers
First, according to the information, we build a linear model, and then, the model is used to find the information asked.
a) The linear model is:
[tex]V(t) = 224000 - 6800t[/tex]
b) The depreciated value of the boat after 10 years is of $156,000.
c) The depreciated value falls below $100,000 after 18.24 years.
d) The sketch is given at the end of the answer.
Item a:
The initial value is of $224,000, thus, the y-intercept of the linear function is of [tex]b = 224000[/tex].The value decayed to $115,200 in 16 years, thus, the slope of the linear function is:[tex]m = \frac{115200 - 224000}{16} = -6800[/tex]
Then, the linear model is:
[tex]V(t) = 224000 - 6800t[/tex]
Item b:
The value after 10 years is V(10), so:
[tex]V(10) = 224000 - 6800(10) = 156000[/tex]
Then, the depreciated value of the boat after 10 years is of $156,000.
Item c:
This is t for which: V(t) = 100000. So
[tex]V(t) = 224000 - 6800t[/tex]
[tex]100000 = 224000 - 6800t[/tex]
[tex]6800t = 224000 - 100000[/tex]
[tex]6800t = 124000[/tex]
[tex]t = \frac{124000}{6800}[/tex]
[tex]t = 18.24[/tex]
The depreciated value falls below $100,000 after 18.24 years.
Item d:
The sketch is appended at the end of this answer.
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Related Questions
Jordan counts 53 ducks on a pond. Then she
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Answer:
Step-by-step explanation:
goes up by 1 each time
The pattern of Jordan is that, she goes up by 1 , each time.
It is given that Jordan counts 53 ducks on a pond and then she counts 3 more by following a same pattern each time.
What is the pattern that she follows ?
What will be the value if we add 1 for 4 times.
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Answer:
Step-by-step explanation:
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Answer:
$250
Step-by-step explanation:
Reverse division is multiplication. So one fifth of 50 is ?/5=50. Now reverse this to 50*5=?. This should come out to 250, because you can leave off the zero, and do 5*5, which equals 25, and add the zero back in you get 250. So your answer is $250.
¿Cuántas combinaciones se pueden
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Answers
Queremos ver cuantas combinaciones diferentes se pueden hacer con una letra del abecedario y los números 8 y 14.
La respuesta es:
Hay 162 combinaciones diferentes.
Primero dejemos la letra fija, asumamos que queremos ver las combinaciones entre la letra A, el número 8, y el número 14.
Tenemos 3 elementos, entonces el número de combinaciones será solo 3 factorial, o:
combinaciones = 3! = 3*2*1 = 6
Hay 6 combinaciones diferentes de esos 3 elementos.
Ahora recordamos que ademas de A hay 26 opciones más, entonces la letra tiene un total de 27 permutaciones posibles. Es decir, el número total de combinaciones va a ser 27 veces lo que obtuvimos arriba:
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Answer:
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Step-by-step explanation:
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Answer:
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Answers
Distance» [tex]speed \times time[/tex]
Distance» [tex]70 \times \frac{7}{2} [/tex]
Distance» [tex] \frac{490}{2} [/tex]
Distance» 245
Answer:
245 units
Step-by-step explanation:
Anna drives her car at a speed of = 70 kmph
To Find:
How much distance will she cover in 3 hours 30 minutes.
Solution:
We'll use here the formula of Speed,then plug the values which are given.
Speed = Distance/Time
Speed = 70 kmphDistance = 3 hr 3 mins = 7/2 hrs70 = D/7/2
7/2*70 = Distance
7*35 = Distance
Distance = 245
We can conclude that Anna can cover 245 units in 3 hrs 30 mins.
If sin x=0.96, find tan x
Answers
Step-by-step explanation:
sin x= P/H
sin x = 0.96 = 96/100 = 24/25.
Let the ratio of the sides be x.
B²=H²-P²
B²=(25x)²-(24x)²
B²=625x²-576x²
B²=49x²
B=√49x²
B= 7x.
cos x = 7x/25x = 7/25.
therefore, tan x = sin x / cos x = (24/25)/(7/25) = 24/25×25/7 = 24/7 .
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Answers
Answer:
(x, y) → (x, -y)Step-by-step explanation:
We can see each corresponding point of the figures is mirrored over x- axis.
This is a reflection and the rule is:
(x, y) → (x, -y)Answer:
(x,y) => (x, -y)
Step-by-step explanation:
U in -x, y -> U' in -x, -y(transformation : x to x and y to -y)
T in -x, -y -> T' in -x, y(transformation : -x to -x (stand) and -y to y)
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Answers
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Answers
Answer:
Exact = 3822
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2275/(15*20) = cost per square footage which is approx. 7.583
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Answer:
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Step-by-step explanation:
The average rate of change of f(x) on the interval is ...
(f(a) -f(1))/(a -1)
= ((4a² -6) -(4(1)² -6))/(a -1) = (4a² -4)/(a -1)
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Answer:
15.81 is the answer.
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Answers
Answer:
90 students
Step-by-step explanation:
Let u be 1 unit.
8u = 240
u = 240÷8
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3u = 30×3
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Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
As we know,
1 km = 1000 m
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I want to eat and bought a hamburger a bag of chips and a drink all the chips cost $1.25 gave the cashier $20 and received $14.39 in how what did the drink cost
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20.00 - 1.25 =18.75
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Answers
Answer:
8\sqrt2=\sqrt128
Step-by-step explanation:
[tex] \sqrt{50} = 5 \sqrt{2} \\ \sqrt{18} = 3 \sqrt{2} [/tex]
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Answers
Answer:
718
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Answer:
88
Step-by-step explanation:
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Answer:
18 + v = 67
Step-by-step explanation:
v represents Victor's age, and 18 more than it is 67.
Add 18 to Victor's age, resulting in 67.
The equation is 18 + v = 67.
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Answer: 2
Step-by-step explanation:
Sonya buys a baseball jersey for her brother on sale for 20% off. If the price she paid was $6 lower than the regular price, what was the original price of the jersey?
Answers
Answer:
30
Step-by-step explanation:
6x5
The original price of the jersey is $ 30
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
Let the original price of the jersey be = $ x
The percentage discount on the original price = 20 %
The difference between the original price and the discounted price = $ 6
So ,
By the percentage equation ,
Percentage discount on the original price = difference between the original price and the discounted price
And ,
( 20 / 100 ) of original price = $ 6
On simplifying the equation , we get
( 20/100 ) x = 6
( 1/5 ) x = 6
Multiply by 5 on both sides , we get
x = 5 x 6
x = $ 30
So , the original price of the jersey is $ 30 and the discounted price is $ 24
Hence , the original price of the jersey is $ 30
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Find the midpoint of the segment with the given endpoints.
(-10,- 6) and (-3,7)
Answers
Step-by-step explanation:
in essence, these 2 points are the Hypotenuse of a right-angled triangle. the legs are the coordinate differences between the 2 points creating the 3rd point of that triangle at (-10, 7) : the x coordinate of one point, and the y coordinate of the other.
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when we create now a similar triangle based on that "half- Hypotenuse", we need to use the same scaling factor also on the legs (the coordinate differences).
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so, the midpoint is (-6.5, 0.5)
is the product of 2 numbers always the LCM
Answers
Answer
I guess so.
To find the LCM you need to know the lowest digit as possible.
For example,
Question: What is the LCM of 8 and 6?
Answer: Table of 8: 8, 16, 24, 32, 40,48
Table of 6: 6, 12, 18, 24, 30, 36, 42, 48
Now look at the tables again and, did you see the LCM???......
If so your answer would be 24.
Step-by-step explanation:
How much money will be in an account at the end of 6 years if $8000 is deposited at 7% interest compounded 2 times per year? Assume no deposits or withdrawals are made. HELPPPPPPPPPPPP
Answers
Answer:
$12,088.55
Step-by-step explanation:
$8000(1+(0.07/2))^(2*6)
$8000(1.035)^(2*6)
$8000(1.51106865)
$12088.5492 - exact
$12088.55 - real
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Select Similar or Not Similar for each pair of rectangles.
Answers
-similar
-similar
Answer: it’s actually
A and B: similar
B and C: not similar
A and C: not similar
Step-by-step explanation:
the person below me was actually wrong, i know because i took the quiz ( thx a lot bro got my quiz wrong)
-4x - (4 - 3x) + x - 9
Answers
Answer:
5
Step-by-step explanation:
-4x-4+3x+x-9 distributive property
combine like terms which would delete x, so the answer would be 5
Terrance earned $444 in March, $523 in April and $410 in May. He divided his earnings between himself and his 4 other workers. How much did they each earn?
Answers
Answer:
$275.40
Step-by-step explanation:
Add 444+523+410=1377
divide 1377 by 5 and u get 275.4
How much would you need to deposit in an account now in order to have $3000 in the account in 10 years? Assume the account earns 4% simple interest. Round your answer to the nearest cent.
Answers
50,000
hope it helps you
HELP A CHICKEN NUGGET OUT!
What is the value of x−9? 14x−(x+2)=−14 Enter your answer in the box. x−9=
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A movie is 1 3/8 hours long. Write the mixed number 1 3/8 as a decimal.
Answers
Answer:
1 3/8 as a decimal is 1.375
Step-by-step explanation:
It's a terminating decimal.