The Ship It Anywhere Company bought a truck for $245,000. According to the company’s accounting department, the truck will depreciate $32,500 per year. 1. Find a linear function V(t) of the form V(t) = mt + b that models the value of the truck. V is the value of the truck and t is the number of years after the truck was bought. a. What is the slope of the function? Interpret what the slope means. b. What is the V intercept? Interpret what the V intercept means. c. Give the formula for the function. 2. Usethefunctiontofindthetintercept.Interpretwhatthetinterceptmeans. 3. Graphthefunction. 4. What is the domain and range of V(t)? 5. Find V(8) and explain what it means. Does your answer make sense? 6. When will the truck have a value of $128,000? 7. When will the truck have a value between $62,000 and $140,000?
Answers
Answer:
1. [tex]V(t) = -32500t + 245000[/tex]
a. The slope of the function is m = -32500, and it means the change in the value of V(t) for each unitary change in the value of t.
b. The V-intercept is b = 245000, and it means the value of V(t) when t = 0, that is, the inicial value of V(t).
c. The formula is: [tex]V(t) = -32500t + 245000[/tex]
2. t-intercept: [tex]t = 7.5385[/tex]
The t-intercept means when the function V(t) will be zero, that is, the truck has no value anymore.
3. Graph in the image attached.
4. The domain is t = [0, 7.5385] and the range is V(t) = [245000, 0].
5. [tex]V(8) = -15000[/tex]
It means the price the truck will have after 8 years. It does not make sense, because the truck can't have a negative price.
6. After 3.6 years.
7. Between 3.23 years and 5.63 years.
Step-by-step explanation:
1.
The inicial value is 245,000, and each year the value decreases 32,500, so we can write the equation:
[tex]V(t) = -32500t + 245000[/tex]
a. The slope of the function is m = -32500, and it means the change in the value of V(t) for each unitary change in the value of t.
b. The V-intercept is b = 245000, and it means the value of V(t) when t = 0, that is, the inicial value of V(t).
c. The formula is: [tex]V(t) = -32500t + 245000[/tex]
2.
To find the t-intercept we just need to use V(t) = 0 and then find the value of t:
[tex]0 = -32500t + 245000[/tex]
[tex]32500t = 245000[/tex]
[tex]t = 7.5385[/tex]
The t-intercept means when the function V(t) will be zero, that is, the truck has no value anymore.
3.
The graph of the function is in the image attached.
4.
The domain is t = [0, 7.5385] and the range is V(t) = [245000, 0].
5.
[tex]V(8) = -32500*8 + 245000 = -15000[/tex]
It means the price the truck will have after 8 years. It does not make sense, because the truck can't have a negative price.
6.
[tex]128000 = -32500t + 245000[/tex]
[tex]32500t = 117000[/tex]
[tex]t = 3.6[/tex]
After 3.6 years.
7.
[tex]62000 = -32500t + 245000[/tex]
[tex]32500t = 183000[/tex]
[tex]t = 5.6308[/tex]
[tex]140000 = -32500t + 245000[/tex]
[tex]32500t = 105000[/tex]
[tex]t = 3.2308[/tex]
Between 3.23 years and 5.63 years.
Related Questions
What is the measure of angle ABC? Please answer quickly!
Answers
Answer:
ABC = 88
Step-by-step explanation:
Angle Formed by Two Chords = 1/2( sum of Intercepted Arcs)
ABD = 1/2 ( 131+ 53)
ABD = 1/2 (184)
=92
ABC = 180 -ABD
ABC = 88
The organization that Jones works for is running for a father son dinner for those employees is invited to attend along with his youngest son. If Jones is known to have two children, what is the condition probability that they are both boys given that he is invited to the dinner?
Answers
Answer:
25%
Step-by-step explanation:
The probability of having a boy is 50%
To calculate the probability of him having 2 boys, multiply the probabilities together
0.5(0.5) = 0.25
PLEASE HELPP! f(x)= -3x + 3
Which of the graphs represent the inverse of the function F??
Answers
Answer:
Answer is Y
Step-by-step explanation:
will give brainliest help plz i can't get back on the password won't go to my email and my little brother changed the password I am scared I lost everything PLZ HELP ME
Answers
is lmn congruent to opq if so name the postulate
Answers
Answer:
Option (A)
Step-by-step explanation:
Given:
LM ≅ OP
MN ≅ PQ
∠M ≅ ∠P
To Prove:
ΔLMN ≅ ΔOQP
Statements Reasons
1). LM ≅ OP 1). Given
2). MN ≅ PQ 2). Given
3). ∠P ≅ ∠M 3). Given
4). ΔLNM ≅ ΔOQP 4). By the SAS postulate of congruence.
[Side - Angle - Side]
Therefore, Option (A) will be the answer.
Reflected across the x-axis ? How is look in the figure
Answers
Answer:
Well a shape reflecting across the x axis will look like some thing in the image below.
Look at both images.
T or F? Is 3y=5x If x is 3 and y is 5?
Answers
Answer:
True
Step-by-step explanation:
3y=5x
Put x as 3 and y as 5.
3(5) = 5(3)
15 = 15
Hence, true.
Answer:
trueX=3
y=15
[tex]3y = 5x \\ 3 \times 5 = 5 \times 3 \\ 15 = 15[/tex]
Proved.
Hope it helps..
Select the correct answer. If g = 8, what is the value of the expression g/2+3 ? A. 8/5 B.11/2 C. 7 D. 19
Answers
Answer:
7Option C is the correct option
Step-by-step explanation:
g = 8 ( given )
Now,
[tex] \frac{g}{2} + 3[/tex]
Plugging the value of g
[tex] \frac{8}{2} + 3[/tex]
[tex] \frac{8 + 3 \times 2}{2} [/tex]
[tex] \frac{8 + 6}{2} [/tex]
[tex] \frac{14}{2} [/tex]
[tex]7[/tex]
Hope this helps...
Good luck on your assignment...
Find the value of x
Answers
Answer:
8
Step-by-step explanation:
the value of x is 8 because the sides are the same
5x is equal to 8X raise to power - 1/3
Answers
Answer:
No solutions.
Step-by-step explanation:
5x = 8x^-1/3
Divide 8 into both sides.
5/8x = x^-1/3
Divide both sides by x.
5/8 = x^-4/3
Multiply both sides by the exponent -3/4.
5/8^-3/4 = x
1.422624 = x
Plug in 1.422624 for x to check.
It does not work. There are no real solutions.
A pet store has 32 more dogs than cats. If there are a total of 144 dogs and cats altogether, then how many cats does the pet store have?
PLZ ANSWER ASAP THANKS
Answers
Answer:
56 cats
88 dogs
Step-by-step explanation:
x=cats
x+32=dogs
x+x+32=144
2x=144-32
2x=112
x=112/2
x=56 (56 cats)
x+32=88 (88 dogs)
Answer:
56
Step-by-step explanation:
In order to solve this question you need to subtract 32 by 144 then divide that answer by 2.
So we know that they're 32 more dogs then cats and there is 144 dogs and cats all together.
[tex]144 - 32 = 112[/tex]
Divide it in half
[tex]112 \div2=56[/tex]
[tex]56+32 = 88[/tex]
[tex]= 56[/tex]
Therefore they're 56 cats in the pet store.
Hope this helps.
Factor by grouping 5x^3+6x^2+25x+30
Answers
Answer:
(5x + 6) (x² + 5)
Step-by-step explanation:
5x³ + 6x² + 25x + 30
= x² (5x + 6) + 25x + 30 -- Group 5x³ and 6x²
= x² (5x + 6) + 5 (5x + 6) -- Group 25x and 30
= (5x + 6) (x² + 5) -- Both terms have a common factor of 5x + 6
which of the following descriptions represent the transformation shown in the image? Part 3c
Answers
Answer: c) rotation of 180° & shift right 1 unit and down 2 units
Step-by-step explanation:
Rotation of 180° changes the signs of x and y
(x, y) → (-x, -y)
Shift right one unit adds 1 to x, Shift two down subtracts 2 from y
(-x, -y) → (-x + 1, -y - 2)
(x, y) (-x + 1, -y - 2)
(-1, -2) → (2, 0)
(-4, -1) → (5, -1)
(-4, -3) → (5, 1)
A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 30 batteries of each type.
Required:
a. How many ways can a total inventory of 30 batteries be distributed among the eight different types.
b. How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory must include at least four A76 batteries?
c. How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory includes at most three A7b batteries?
Answers
Answer:
a. 10295472 ways
b. 4272048 ways
c. 6023424 ways
Step-by-step explanation:
Given that:
Camera shop stocks ----- 8 different types of batteries
one of which is ---- A76
Assume that there are ------ at least 30 batteries of each type.
a.
How many ways can a total inventory of 30 batteries be distributed among the eight different types.
The number of ways a total inventory of 30 batteries be distributed is :
[tex]= \left \{ {{30+8-1} \atop {30}} \right. \}[/tex]
[tex]= \left \{ {{37} \atop {30}} \right. \}[/tex]
[tex]=\dfrac{37!}{30! *7!}[/tex]
[tex]= \dfrac{37*36*35*34*33*32*31*30!}{30!*7*6*5*4*3*2*1}[/tex]
[tex]= \dfrac{37*36*35*34*33*32*31}{7*6*5*4*3*2*1}[/tex]
= 10295472 ways
b.
How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory must include at least four A76 batteries?
If we must include 4 A76 batteries; then the number of ways a total inventory of 30 batteries can be distributed among eight different types of batteries will be:
30 - 4 = 26 batteries
Now;
[tex]= \left \{ {{26+8-1} \atop {26}} \right. \}[/tex]
[tex]= \left \{ {{33} \atop {26}} \right. \}[/tex]
[tex]=\dfrac{33!}{26! \ \ 7!}[/tex]
[tex]=\dfrac{33*32*31*30*29*28*27*26!}{26! \ * \ 7*6*5*4*3*2*1}[/tex]
[tex]=\dfrac{33*32*31*30*29*28*27}{ \ 7*6*5*4*3*2*1}[/tex]
= 4272048 ways
c. If we must include at most three A7b batteries. the number of ways that a total inventory of 30 batteries can be distributed among eight different types of inventory is:
[tex]= \sum \limits ^3 _{x=0} \left \{ {{(30-x)+7-1} \atop {30-x}} \right. \} \\ \\ \\ = \sum \limits ^3 _{x=0} \left \{ {{(30-0)+7-1} \atop {30-0}} \right. \} = (^{36}_{30})+(^{35}_{29})+ (^{34}_{28})+ (^{33}_{27})[/tex]
[tex]= \dfrac{36!}{30! * 6!} + \dfrac{35!}{29! * 6!} + \dfrac{34!}{28! * 6!} + \dfrac{33!}{27! * 6!}[/tex]
= 1947792 + 1623160 + 1344904 + 1107568
= 6023424 ways
Need Help!!!! What is 1495486+73940426 Thanks!
Answers
Answer:
75435912
Step-by-step explanation:
1495486+73940426
= 75435912
Answer:
75,435,912
Step-by-step explanation:
=> 1495486 + 73940426
Using Calculator
=> 75,435,912
There are members on the board of directors for a certain non-profit institution. a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? b. If they must form an ethics subcommittee of four members, how many different subcommittees are possible?
Answers
Answer: a. 1320
b.495
Step-by-step explanation:
Complete question is provided in the attachment.
Total members on the board = 12
a. Persons to chose : chairperson, first vice chairperson, second vice chairperson, and secretary
i.e. Total 3 posts in an order.
Number of ways to choose 3 persons from 12 in an order = [tex]^{12}P_3[/tex] [By permutation]
[tex]=\dfrac{12!}{(12-3)!}\\\\=\dfrac{12!}{7!}\\\\=12\times11\times10\\\\=1320[/tex]
hence, 1320 different slates of candidates are possible .
b. number of ways to choose 4 members out of 12 ( order not matters)=[tex]^{12}C_{4}[/tex] [By combinations]
[tex]=\dfrac{12!}{4!8!}\\\\=\dfrac{12\times11\times10\times9}{24}\\\\=495[/tex]
Hence, the number of different subcommittees are possible =495
If the area to the left of x in a normal distribution is 0.187, what is the area to the right of x? (Enter an exact number as an integer, fraction, or decimal.)
Answers
Answer:
Area to the right is 0.813
Step-by-step explanation:
Since the area under the full normal distribution should render "1" (one), then the area to the right of x should be:
1 - area to the left of x = 1 - 0.187 = 0.813
The area to the right of x in this normal distribution will be 0.813.
What is a normal distribution?The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean.
The probabilities for values that are farther from the mean taper off equally in both directions. Extreme values in the distribution's two tails are likewise rare.
Not all symmetrical distributions are normal, even though the normal distribution is symmetrical.
We know that the total area described in a normal distribution is 1.
Given, that the area to the left of x in a normal distribution is 0.187.
So, the area to the right of x will be,
1 - 0.187.
= 0.813.
learn more about normal distribution here :
https://brainly.com/question/15103234
#SPJ2
Which parent function is f(x) = x^2?
O A. An exponential parent function
OB. The linear parent function
C. The absolute value parent function
D. The quadratic parent function
Answers
Answer:
D. Quadratic parent function.
Step-by-step explanation:
Juanita wants to buy 12.5 pounds of stones to decorate her garden. The stone normally sells for $1.80 a pound. The salesman offers her a total price of $21.25. How much is she saving per pound with the salesman’s offer? Round to the nearest hundredth.
Answers
Answer:
She is saving 10 cents per pound
Step-by-step explanation:
First, we need to find how much she would pay without the sale:
12.5(1.8) = 22.5
Now, we can calculate how much she saved:
22.5 - 21.25 = 1.25
To find how much she's saving per pound, we divide the difference by the number of pounds:
1.25/12.5 = 0.1
She is saving 10 cents per pound
Answer:
A
Step-by-step explanation:
I took the test and got it right
4) →BRAINLIEST & 10+ POINTS! ← A wheel with diameter 44 cm completes four revolutions in 0.5 seconds. Find the linear speed of the edge of the wheel in cm per second. ⇒Round to the nearest whole number. Linear speed = ____ cm/s
Answers
Answer:
352 cm/s
Step-by-step explanation:
circ = 44pi
speed = distance * time
distance = circ * 4 = 176pi
speed = 176pi/0.5
Answer:
≈ 1106 cm/s
Step-by-step explanation:
linear speed = angular speed x radius of the rotation
v = ωr
v = linear speed (m/s)
ω = angular speed (radians/s)
r = radius of the rotation (m)
------------
Given:
d= 44 cm ⇒ r= 44/2 cm= 22 cmω= 4 rev/0.5 s= 8 rev/s= 8*2π/s= 16π/s (converted rev to radians)Linear speed is:
v= 22*16π cm/s ≈ 1106 cm/s (rounded to full number)Simplify The square root of 5 (6-4 the square root of 3)
Answers
Answer:
7.75
Step-by-step explanation:
6-4=2
2 times the square root of 3=3.46410161514
square root of 5 times 3.46410161514=7.74596669242
to 2dp=7.75
simplify the expression into form a+bi, where rational numbers
(4-i)(-3+7i) - 7i(8+2i)
Answers
Answer:
-12+28i+3i-7i-65i+28
14 -41i
A student earned grades of B, B, A, C, and D. Those courses had these corresponding numbers of credit hours: 4, 5, 1, 5, 4. The grading system assigns quality points to letter grades as follows: Aequals=4, Bequals=3, Cequals=2, Dequals=1, and Fequals=0. Compute the grade point average (GPA) and round the result to two decimal places.
Answers
Answer:
1.69Step-by-step explanation:
Let the five courses with their corresponding credit hours be represented as shown;
FST 201 = 4
FST 203 = 5
FST 112 = 1
FST 219 = 5
FST 223 = 4
If a student earned grades of B, B, A, C, and D respectively in those courses with the following grading system A =4, B =3, C =2, D =1, and F =0, before we can get the student GPA, we need to know the total credit point for the five courses.
Credit point for each course = Number of credit hour * point for each grade
FST 201 = 4 * 4 = 16points (A)
FST 203 = 5 * 4 = 20points (A)
FST 112 = 1 * 4 = 4points (A)
FST 219 = 5 * 4 = 20points (A)
FST 223 = 4 * 4 = 16points (A)
Total credit point = 16+20+4+20+16 = 76points
Total credit point gotten by the student is calculated as thus;
FST 201 = 4 * 3 = 12points (B)
FST 203 = 5 * 3 = 15points (B)
FST 112 = 1 * 4 = 4points (A)
FST 219 = 5 * 2 = 10points (C)
FST 223 = 4 * 1 = 4points (D)
Total credit point gotten by the student = 45points.
student's Grade Point Average (GPA) = Total credit point/Total credit point gotten by the student = 76/45 = 1.69 (to 2dp)
In the figure, a//b, and both lines are intersected by transversal t. Complete the statements to prove that m<1=m<5.
Answers
Answer:
Transitive Property of EqualityAlternate Interior Angles TheoremStep-by-step explanation:
a) You're trying to justify that two sums equal to 180° are equal to each other. The Transitive Property of Equality is that justification.
__
b) You're trying to justify that angles 3 and 6 are congruent. These are between the parallel lines, so are "interior" angles. They are on opposite sides of the transversal, so are "alternate" angles. They do not share a vertex, so cannot be vertical angles. The applicable theorem is the Alternate Interior Angles Theorem.
Answer:
Step-by-step explanation:
Simplify e^ln4
A. 1/4
B. 4
C. 1n4
D. E^4
Answers
Answer:
The answer is option B.
4Step-by-step explanation:
Using the expression
[tex] {e}^{ ln(x) } = x[/tex]
[tex] {e}^{ ln(4) } = 4[/tex]
Hope this helps you
Each of 100 students in the Allen School can only take 1 CSE class each, between the four classes CSE 311, CSE 312, CSE 331, and CSE 332. Each student (independently of others) takes CSE 311 with probability 0.3, CSE 312 with probability 0.4, CSE 331 with probability 0.1, and CSE 332 with probability 0.2. What is the probability that exactly 31 sign up for CSE 311, 39 sign up for CSE 312, 7 sign up for CSE 331, and 23 sign up for CSE 332
Answers
Answer:
[tex]P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
Step-by-step explanation:
Sample space, n = 100
Let the number of students signed up for CSE 311 = a
Let the number of students signed up for CSE 312 = b
Let the number of students signed up for CSE 331 = c
Let the number of students signed up for CSE 332 = d
Probability of taking CSE 311, [tex]P_a[/tex] = 0.3
Probability of taking CSE 312, [tex]P_b[/tex] = 0.4
Probability of taking CSE 331, [tex]P_c[/tex] = 0.1
Probability of taking CSE 332, [tex]P_d[/tex] = 0.2
[tex]P(a,b,c,d) = \frac{n!}{a! b! c! d!} p_a^{a} p_b^{b} p_c^{c} p_d^{d} \\P(a=31,b=39,c=7,d=23) = \frac{100!}{31! 39! 7! 23!} * 0.3^{31} * 0.4^{39} * 0.1^{7} 0.2^{23}\\P(a=31,b=39,c=7,d=23) = \frac{4.58*10^{111}}{2.13*10^{56}* 5040 }* (1.57*10^{-55})\\P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
For the data set represented by this box plot, what is the value of the maximum? maximum:
Answers
Answer:
140
Step-by-step explanation:
The maximum is the furthest the line that goes out the furthest, the minimum would be about 83-84
Answer:
the other person is correct!
Step-by-step explanation:
Tom takes a cancer test and the test is advertised as being 99% accurate: if you have cancer you will test positive 99% of the time, and if you don't have cancer, you will test negative 99% of the time. If 1% of all people have cancer and Tom tests positive, what is the prob that Tom has the disease
Answers
Answer:
99% chance tommy has it
Step-by-step explanation:
cuz do da math
Kajol has $75. This is 3/8 of the amount she earned. How much did she earn?
Answers
Answer:
$200
I hope this helps!
Answer:
200rupees
Step-by-step explanation:
according to the question ,kajol has 75 rupees
amount earned=3/8* amount earned
=75/3*8
=200 rupees
How many gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze? Use the six step method.
Answers
Answer:
x = 270 gallons
270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze
Step-by-step explanation:
Let x represent the number of gallons of the 50% antifreeze solution.
The volume of the 10% antifreeze is = 90 gallons
The volume of the mixture that is 40% antifreeze = 90+x
The amount of antifreeze in the two solutions must be equal to the amount of anti freeze in the mixture;
50% of x + 10% of 90 = 40% of (90+x)
0.50(x) + 0.10(90) = 0.40(90+x)
0.50x + 9 = 36 + 0.40x
Collecting the like terms;
0.50x - 0.40x = 36-9
0.10x = 27
x = 27/0.10
x = 270 gallons
270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze