Chantel's car originally sold for $46,600. It depreciates exponentially at a rate of 10.3% per year. Chantel put $12,000 down and pays $800 per month to pay off the balance. After how many years
will her car value equal the amount she paid to date for the car?
What will that value be?
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Answers

Answer 1

The value of the car after 4.53 years will be $19,642.64.So after 4.53 years, the value of the car will equal the amount Chantel has paid to date

To solve this problem, we need to use the formula for exponential decay:

V(t) = V(0) *

where:

V(t) is the value of the car after t years

V(0) is the initial value of the car, which is $46,600

k is the decay rate, which is 10.3% or 0.103 per year

t is the time in years

Let's first find the value of the car after t years:

V(t) = 46,600 * $e^(-0.103t)$

Now let's find the amount Chantel paid to date. She put $12,000 down and pays $800 per month, so after t years, she would have paid:

P(t) = 12,000 + 800 * 12 * t

where:

P(t) is the amount Chantel paid to date

12 * t is the number of months Chantel has been paying for (since there are 12 months in a year)

We want to find the time t when V(t) = P(t). That is, we want to find the time when the value of the car equals the amount Chantel has paid. So we can set the two equations equal to each other and solve for t:

46,600 * $e^(-0.103t)$ = 12,000 + 800 * 12 * t

Dividing both sides by 46,600, we get:

= (12,000/46,600) + (800/46,600) * 12 * t

Taking the natural logarithm of both sides, we get:

-0.103t = ln[(12,000/46,600) + (800/46,600) * 12 * t]

Simplifying, we get:

t = -ln[(12,000/46,600) + (800/46,600) * 12 * t]/0.103

Using a calculator or a computer algebra system, we can solve for t numerically. The solution is approximately 4.53 years.

, which is:

V(4.53) = 46,600 * $e^(-0.103$ * 4.53) = $19,642.64

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Related Questions

Maddie Evans drove 180 miles in the same matter I'm not detect a turbo propeller plane to travel 690 miles the speed of the plane was 170 mph faster than the speed of the car find the speed of the plane

Answers

Answer:

let

m = the speed of Mattie

d1 = 180 mi the distance Mattie traveled

p = the speed of the plane

d2 = 630 mi the distance the plane traveled

the speed of the plane was 150 mph faster than the speed of the car

p = m + 150

since speed = distance/time => time = distance/speed

d1/m = d2/p

180/m = 630/p cross multiply

180p = 630m divide both sides by 90

2p = 7m

by solving the system of equations

p = m + 150

2p = 7m

we find

p = 210 mph

The speed of the plane was 210 mph

please please help last text then finals l give brainliest

Answers

1. The x - intercepts of the parabola are

x = 2.5 s and x = 7.5 s

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

What is a parabola?

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

x = 2.5 s and x = 7.5 s

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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Question 14 (essay worth 12 points)
(writing two step equations HC)

Given the equation 6x + 18 = 72:
Part A: Write a short word problem about a purchase made to illustrate the equation. (6 points)
Part B: Solve the equation showing all work. (4 points)
Part C: Explain what the value of the variable represents. (2 points)

Answers

A. Ram spent $18 on six pens and six books. The grand total is $72.

B. The cost of each pen is $9.

C. The variable is called x.

What is an equation?

A set of variables, constants, and mathematical operations such as addition, subtraction, multiplication, or division balanced by the equal sign is known as an equation. The equation's left-hand side (LHS) is on the left side, and its right-hand side (RHS) is on the right side (RHS).

Here, we have

Given: the equation 6x + 18 = 72:

A. The issue is that Ram spent $18 on six pens and six books. The total amount he paid is $72.

B. The following equation will be used to demonstrate this:

6x + 18 = 72

Compile similar terms.

6x = 72 - 18

6x = 54

On dividing,

x = 54 / 6.

x = $9

Hence, each pen will set you back $9.

C. The variable's value is x = 9.

Hence, the pen's price is 9.

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Write a function g whose graph represents the indicated transformation of the graph of f F(x)=4-|x+1|

Answers

The function g from the indicated transformation of the graph of f is g(x) = 4 - |x - 2|

What is a function?

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The equation of the function f is given as :

F(x) = 4-|x+1|

Shifting of a graph is done by adding any arbitrary constant to the function in shifting.

For example, If shift up by 1 unit, add 1 to the function

So the function g(x) is 3 units to the right of the function f(x)

⇒ g(x) = f(x - 3)

So, F(x - 3) = 4 - |x - 3+ 1|

Evaluate both equations,

⇒ F(x - 3) = 4 - |x - 2|

⇒ g(x) = 4 - |x - 2|

Hence, the function g from the indicated transformation of the graph of f is g(x) = 4 - |x - 2|

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Help please quickly calculus

Answers

Her next step in obtaining the area of the triangle is replacing the numeric values of h and y into the area formula.

How to obtain the area of a triangle?

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Base of b = y.Height of h.

Hence the formula is:

A = 0.5yh.

Hence the actual values of y and h must be inserted into the formula to obtain the area of the triangle.

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Find the equation of the function in the graph.

A. y=x
B. y= |x|
C. y= x3
D. y= x2

Answers

D. y = x^2 because it is a parabola so the function needs to be quadratic

Answer:

Step-by-step explanation:

YEAH

In art class students are mixing black and white paint to make gray paint. Sophia mixes 3 cups of black paint and 4 cups of white paint. Jeriel mixes 9 cups of black paint and 10 cups of white paint. Use Sophia and jeriels percent of white paint to determine whose gray paint will be lighter

Answers

Answer:

Sophia's paint is lighter.

Step-by-step explanation:

percent = part/whole × 100%

Sophia:

3 cups black, 4 cups white

total: 7 cups

white percent = 4/7 × 100% = 57%

Jeriel:

9 cups black, 10 cups white

total: 19 cups

white percent = 10/19 × 100% = 53%

Sophia's paint is lighter.

Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)

Answers

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

$\\$AB = B - A = (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B = (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C = (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D = (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k [Collect like terms]

DA = -i - 4j - 3k

AC = C - A = (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD [AB is parallel to CD]

AC = BD This implies that AC || BD [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

Now let's calculate the area

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

$AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]$

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = $\sqrt{(-6)^2 + (-6)^2 + (10)^2}$

|AB X AC| = $\sqrt{172}$

|AB X AC| = 13.15

Area = 13.15 square units.

PS: ACBD is also a parallelogram. The diagram has also been attached to this response.

Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1),

Write the ratio 1.5:9 in simplest form.

Answers

Answer:

1 : 6

Step-by-step explanation:

Carley beat the school record for the 400 meter run by 1.3 seconds. If she ran the race in 55.7 seconds, what was the record.

Answers

Answer:

57 seconds

Step-by-step explanation:

55.7 + 1.3 = 57 seconds

To find the number in a square, add the numbers in the two circles
connected to it.
Fill in the missing numbers.

Answers

The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

square = circle + circle

We can deduce that :

circle = square - circle

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

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Find the quotient.
2,593 dived 4

Answers

Answer:

648.25

Step-by-step explanation:

For the following exercises, determine whether the vector field is conservative and, if it is, find the potential function. 106. F(x, y) = (6x + 5y)i + (5x + 4yj

Answers

f(x, y) = 3x + 2y + C

To know if a vector field is conservative, we have to check if it is the gradient of a scalar function.

The gradient of the function f(x, y) is given by

∇f(x, y) = (∂f/∂x, ∂f/∂y)

If a vector field F(x, y) is the gradient of a scalar function f(x, y), then the following conditions must be satisfied:

F(x, y) = ∇f(x, y)

Whether a given vector field satisfies this condition can be checked by taking the partial derivative with respect to x and y.

∂F/∂x = ∂(6x + 5y)/∂x = 6

∂F/∂y = ∂(5x + 4y)/∂y = 4

The partial derivative of a given vector field is the constant, the gradient of the scalar function. So vector fields are conservative and we can find a potential function f(x, y) such that F(x, y) = ∇f(x, y).

To find the potential function, we can integrate the partial derivative of F(x, y) with respect to x and y.

f(x, y) = ∫∂F/∂xdx + ∫∂F/∂ydy

= ∫6dx + ∫4dy

= 3x + 2y + C

where C is the constant of integration. So the potential function for a given vector field is

f(x, y) = 3x + 2y + C

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!!!! Which equation represents the graph shown? PLEASE HELP ASAP!!!

Answers

Answer:

y= 2x +1

Step-by-step explanation:

Slope-intercept form

y= mx +c, where m is the gradient and c is the slope.

Since all the slope in the options are the same, let's focus on the y-intercept. From the graph, the line cuts through the y-axis at y= 1. Thus, the y- intercept is 1.

Hence, y= 2x +1 is the correct option.

Extra notes:

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

Use the ALEKS calculator to evaluate each expression.
Round your answers to the nearest thousandth.
Do not round any intermediate computations.
log√7 =
Log 23/6=

Answers

Exponential growth is a type of growth that occurs when the rate of increase is proportional to the current amount.

Logarithmic evaluationLog√7 = 1.659Log 23/6 = 0.862It is a rapid increase in the quantity of something over a period of time. Exponential growth can be seen in populations, investments, and other areas.It is characterized by a doubling or tripling of the original amount within a specified period of time.This type of growth is often caused by compounding, where gains from one period are reinvested in the next period, leading to a rapid increase in the overall amount.Exponential growth is often seen in the early stage of a business, when it is experiencing rapid growth due to investments or other factors.However, exponential growth can also lead to rapid decline if not managed properly.This is called logarithmic evaluation, which involves using logarithms to simplify complex expressions.

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Shamin Jewelers sells diamond necklaces for $442 less 10%. Jewelers offers the same necklace for $527 less 34%, 14% What additional rate of discount must offer to meet the competitor's price

Answers

Answer:

The selling price of the diamond necklace at Shamin Jewelers after 10% discount is:

$442 * 0.9 = $397.80

The selling price of the same necklace at the competitor's store after 34% and 14% discount is:

$527 * 0.66 * 0.86 = $247.08

So, Shamin Jewelers needs to offer an additional discount to meet the competitor's price:

$397.80 - $247.08 = $150.72

To calculate the additional rate of discount, we divide the difference by the original selling price at Shamin Jewelers and multiply by 100:

($150.72 / $442) * 100 = 34.11%

Therefore, Shamin Jewelers must offer an additional 34.11% discount to meet the competitor's price.

Step-by-step explanation:

please help i’ll give brainlist

Answers

Answer:

Step-by-step explanation:

18/3 (3x4)+1

=18/3 (12)+1

=6 (12) +1

=72 +1

=73

18/3(2+4)+1

=18/3(6)+1

=6(6)+1

=36+1

=37

you have to do the brackets first and than / and x and after that do the + & -

Precious did it correctly.
Shamira made mistake by multiplying 3 by 6. She should have done the division first: 18/3.
The order of operations is from left to right.

List all factors of the number 52. SHOW ALL WORK!!!

Answers

Answer:

Factors of number 52

Factors of 52: 1, 2, 4, 13, 26 and 52.

Negative Factors of 52: -1, -2, -4, -13, -26 and -52.

Prime Factors of 52: 2, 13.

Prime Factorization of 52: 2 × 2 × 13 = 22 × 13.

Sum of Factors of 52: 98.

The graph represents the piecewise function: f (x) ={ , if -3

Answers

The domain and the range of the function are

Domain = (-∝, ∝)Range = (0, ∝)How to determine the domain and range of the function

From the question, we have the following parameters that can be used in our computation:

The graph

The graph is a piecewise function

When combined gives an absolute function

The rule of a function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is greater than the constant term

In this case, it is 0

So, the range is y > 0

Answers

The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.

What is a line segment?

A line segment in mathematics has two different points on it that define its boundaries.

A line segment is sometimes referred to as a section of a path that joins two places.

Six-year-old students at an elementary school were given a 20-yard head start in a race. The graph shows how far the average student ran in 30 seconds.

A line graph with Distance, in yards, on the x-axis and Age of the Runner on the y-axis. The x-axis has a scale from 0 to 80 in increments of 10. The y-axis has a scale of 0 to 8 in increments of 2. A straight line connecting 20, 6, and 60, 6 is drawn.

The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.

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Answer:

the correct option is D

Step-by-step explanation:

15 POINTS!!! ANSWERS NEEDED ASAP!!!!
what is the y intercept when the coordinate is -3,-3 and the slope is -1

Answers

The y-intercept is -6, when the coordinate is -3,-3 and the slope is -1

Describe Slope?

More specifically, it is defined as the ratio of the change in the y-coordinate (vertical) to the change in the x-coordinate (horizontal) between any two points on the line or surface.

The slope of a line is often denoted by the letter "m" and can be calculated using the formula:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

A positive slope indicates that the line is rising from left to right, while a negative slope indicates that the line is falling from left to right. A slope of zero indicates that the line is horizontal.

The slope of a surface can be calculated using partial derivatives. The slope of a surface at a point is the slope of the tangent plane at that point.

Slope is an important concept in mathematics, physics, and engineering, and is used to calculate rates of change, velocities, and accelerations, and to model relationships between variables. It is also used in a variety of practical applications, such as in construction and surveying, where it is necessary to determine the slope of the land.

To find the equation of the line when the coordinate is (-3, -3) and the slope is -1, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is the given point. Plugging in the values, we get:

y - (-3) = -1(x - (-3))

y + 3 = -x - 3

y = -x - 6

The y-intercept is the point where the line intersects the y-axis, which occurs when x = 0. Plugging in x = 0 into the equation, we get:

y = -0 - 6

y = -6

Therefore, the y-intercept is -6.

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Kyle puts ribbon around his rectangular bulletin board and covers it in paper board measure 4 3/4 feet by 6 1/2
Hi ow much ribbon did he use
How much paper will he need for bulleitin board?

Answers

The amount of paper, he will need for the bulletin board is 30.875 square feet.

The required amount of ribbon is 22.5 feet.

What is a rectangular perimeter?

The whole distance that a rectangle's borders, or its sides, the cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.

Given:

Kyle puts ribbon around his rectangular bulletin board and covers it in a paper board measuring 4$\frac{3}{4}$ feet by 6$\frac{1}{2}$.

That means,

the perimeter of the paper board = the perimeter of the rectangular bulletin board

The perimeter of the rectangular bulletin board = 2(4$\frac{3}{4}$ + 6$\frac{1}{2}$)

The perimeter of the rectangular bulletin board = 45/2 feet

The perimeter of the rectangular bulletin board = 22.5 feet.

The amount of paper = (4$\frac{3}{4}$ x 6$\frac{1}{2}$) = 30.875 square feet.

Therefore, the required amount of ribbon is 22.5 feet.

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Select the number that round to 387.4 when rounded to the nearest tenth.
A. 387.461
B. 387.344
C. 387.309
D. 387.352
E. 387.779

Answers

Answer:

Step-by-step explanation:

When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"

If you think my answer is the best, please mark it as the Brainliest.
Thank you! :))

what is this
x - 3 < 9

Answers

Answer:

X<12

Step-by-step explanation:

function f(x)=7^x represent exponential growth, decay or neither?

Answers

Answer:

exponential growth

Step-by-step explanation:

Please help
Picture inserted
Multiple choice
Will appreciate it if you help!

Answers

Answer:

Step-by-step explanation:

Linear; can be written in the form y = 5x + 4

Write and solve an equation to represent the situationBilly age is 10 years less than 2 times Charlie's age. If Billy is 36 years old, how old is Charlie?Charlie is__ years old

Answers

Billy age is 10 years less than 2 times Charlie's age. If Billy is 36 years old, how old is Charlie?

Billy's age = B = 36

Charlie's age= C

10 years less means minus 10, and two times means multiplied by 2.

B = 2C-10

Since B = 36

36= 2C-10

Solving for C:

36+10 = 2C

46=2C

46/2 =C

C= 23

Charlie is 23 years old.

Algebra: conic sections. Create a picture of a robot with at least 2 types of conic sections. Then explain what the key features are for the two conic section equations

Answers

Kindly check below

1) For this problem, let's start out with the Ellipse

So, the key features of an Ellipse are:

a,a = (2) Semi-major axis ( the sum of the semi-major axis yields the longer axis of an ellipse), a=6

b,b =(2) Semi-minor axis (the sum of the semi-minor axis yields the shorter axis of an ellipse), b=4

F1, F2 (Foci)=(2√5,0), (-2√5,0)

A1,A2 =(6,0), (-6,0) Vertices (the endpoints of the semi-major axis)

B1, B2 =(4,0), (-4,0) Co-vertices (the endpoints of the semi-minor axis)

Domain: [-6,6] The set of entries of a function, usually represented by x

Range: [-4,4] The set of outputs of a function, usually represented by y

$\frac{\left(x\right)^{2}}{36}+\frac{\left(y\right)^{2}}{16}=1$

The general formula for an ellipse

2) Now, let's move on to the next conic section. The Hyperbola

In this sketch, we've got the following features:

A_1, A_2: The vertices of a hyperbola are at (5,-1) and (-3,1)

F_1, F_2: Foci of a hyperbola

$\left(1+2\sqrt{13},\:1\right),\:\left(1-2\sqrt{13},\:1\right)$

In red: The asymptotes, (in this case slant ones. They set the boundaries where the hyperbola does not trespass.

$y=\frac{3\left(x-1\right)}{2}+1,\:\quad \:y=-\frac{3\left(x-1\right)}{2}+1$

Note that these asymptotes have a slope, so we need to express them as linear equations

P: Generic point on the curve.

Domain: Set of entries of a hyperbola. We can tell that this hyperbola has the following Domain:

$D=(-\infty,-3)\cup(5,\infty)$

A hyperbola can be given with a general formula as well:

$\frac{\left(x-1\right)^{2}}{16}-\frac{\left(y-1\right)^{2}}{36}=1$

This is the photo for the last question

Answers

All the angles required to complete each sentence are:

m ∠ 4 = 60, m ∠ 2 = 120m ∠ 3 = 110, m ∠ 4 = 70m ∠ 2 = x, m ∠ 1 = 180 - x

How to find measures of missing angles by Euclidean geometry

In this question we must take advantage of definitions and theorems of Euclidean geometry to complete the three sentences seen in the figure. Now we proceed to present each sentence completed in detail:

If m ∠ 5 = 60, then m ∠ 4 = 60 by alternal internal angles between parallel lines and m ∠ 2 = 120 by supplementary angles.If m ∠ 7 = 110, then m ∠ 3 = 110 by corresponding angles between parallel lines and m ∠ 4 = 70 by supplementary angles. If m ∠ 6 = x, then m ∠ 2 = x by corresponding angles and m ∠ 1 = 180 - x by supplementary angles.

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If the random variable x is normally distributed with a mean equal to .45 and a standard deviation equal to .40, then P(x ≥ .75) is:

Answers

If the random variable x is normally distributed with a mean equal to 0.45 and a standard deviation equal to 0.40, then P(x ≥ .75) is 0.9227.

What is a Z-score?

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

Given the problem above, we need to find what the z-score is when P(x ≥ .75).

The formula for calculating a z-score is given by:

$Z=\dfrac{\text{x}-\mu}{\sigma}$

Where:

x is the value of 0.75$\mu$ is the mean of 0.45And $\sigma$ is the standard deviation of 0.40

Now,

$Z=\dfrac{\text{x}-\mu}{\sigma}$

$Z=P(\text{x} \geq 0.75) = \huge \text(\dfrac{P(Z \geq (0.75 - 0.45)}{0.40}\huge \text)$

$Z= P\huge \text (\dfrac{Z \geq0.30}{0.40}\huge \text)$

$Z=P(Z \geq 0.75) = 1 - P(Z < 0.75)$

$Z=1 - 0.077337$

$Z\thickapprox 0.9227$

Therefore, the z-score of P(x ≥ .75) is 0.9227.

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