Final answer:
To find the solutions to the system of equations, use the substitution method. The solutions are (1/2, -3/2) and (7, 5).
Explanation:
To find the solutions to the system of equations, we can use the substitution method. First, solve one of the equations for y in terms of x. Let's solve the second equation for y:
y = x - 2
Now substitute this expression for y into the first equation:
x - 2 = 2x^2 - 8x + 5
Now we have a quadratic equation. Rearrange it into standard form:
2x^2 - 9x + 7 = 0
Next, factor the quadratic equation:
(2x - 1)(x - 7) = 0
Set each factor equal to zero and solve for x:
2x - 1 = 0, x - 7 = 0
x = 1/2, x = 7
Now substitute these values of x back into either of the original equations to find the corresponding values of y:
For x = 1/2: y = 1/2 - 2 = -3/2
For x = 7: y = 7 - 2 = 5
So the solutions to the system of equations are (1/2, -3/2) and (7, 5).
Someone please help.. plz dont skip me
Which of the following are ordered pairs for the equation y =x - 3?
(0,3) (-2,-1) (2,5)
(0,3) (2,1) (-2,-5)
(0,-3) (2,-1) (-2,-5)
(0,-3) (2,-1) (-2,5)
Mt. Vesuvius has an altitude of 3000 feet. A person stands 120 feet away from the base of the volcano. What is the angle of elevation from the person on the ground to the top of the volcano?
Answer: the angle of elevation from the person on the ground to the top of the volcano is 87.7°
Step-by-step explanation:
The person, his angle of elevation and his distance from the foot of the mountain forms a right angle triangle.
The altitude of the mountain represents the opposite side of the right angle triangle.
The distance of the person from the base of the volcano represents the opposite side of the right angle triangle.
To determine the angle of elevation from the person on the ground to the top of the volcano, we would apply the tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan θ = 3000/120 = 25
θ = Tan^-1(25)
θ = 87.7° to the nearest tenth.
Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 496 and standard deviation 115. You choose an SRS of 100 students and average their SAT reading scores. If you do this many times, the mean of the average scores will be close to:_______. A. 115.
B. 115 / square root of 100 = 1.15.
C. 115 / square of 100 = 11.5.
Answer:
496
Step-by-step explanation:
I am assuming that there are options lacking. The average score, due to the Law Of Big Numbers, using a big enough sample will be close to the mean of the random variable. Thus the mean of the average scores will be close to 496 if the process is done many times.
The mean of the average scores will be close to the population mean of 496.
Explanation:The mean of the average scores will be close to the population mean, which is 496. The Central Limit Theorem states that as the sample size increases, the sample mean approaches the population mean. In this case, since we are choosing an SRS of 100 students, the mean of the average scores will be close to the population mean of 496.
Learn more about Central Limit Theorem here:https://brainly.com/question/898534
#SPJ11
PLS HELP
f(x)=x^3−2x^2+12x−6
g(x)=4x^2−6x+4
What is (f−g)(x)?
Answer:
[tex](f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10[/tex]
Step-by-step explanation:
The given functions are:
[tex]f(x) = {x}^{3} - 2 {x}^{2} + 12x - 6[/tex]
and
[tex]g(x) = 4 {x}^{2} - 6x + 4[/tex]
We want to find
[tex](f - g)(x)[/tex]
Recall that:
[tex](f - g)(x) = f(x) - g(x)[/tex]
This implies that:
[tex](f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - (4 {x}^{2} - 6x + 4)[/tex]
[tex](f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - 4 {x}^{2} + 6x - 4[/tex]
We combine similar terms to get:
[tex](f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10[/tex]
Answer:
Solution given:
f(x)=x3−2x2+12x−6
g(x)=4x2−6x+4
now
(f-g)(x)=f(x)-f(g)=x3−2x2+12x−6-4x²+6x-4
=x³-6x²+18x-10
plzzzzzzzzzz help me somebody, anybody. my questions always get skipped over!
I believe the answer is B. Hope this helps!
What do the graphs of sine and cosine have in common with the swinging you see?
Answer:
Period of 2π
Step-by-step explanation:
The graph of sine starts at zero on the y axis while that of cosine starts at the point 1 as sin 0=0 at t=0 and cos 0=1 at t=0. We say the cosine curve is a sine curve which is shifted to the left by [tex]\frac{\pi}{{2}}\[/tex]
The basic sine and cosine functions have a period of 2π (in radians). The period is the time it takes to go through one complete cycle. It means that after every complete cycle, the graph repeats itself over and over again..
Answer:
Check
Step-by-step explanation:
The high and low points repeat in a pattern.
The cycle repeats at equal time intervals.
The swinging motion is smooth, unabrupt.
Need help
The equation yˆ=2.391x+57.420 models the taste rating of a cereal, y, in a survey, where x is the number of grams of sugar per serving.
What does the y-intercept of the equation represent in context of the situation?
A cereal with 0 grams of sugar has a rating of about 2.391.
The average number of grams of sugar is 2.
A cereal with 0 grams of sugar has a rating of about 57.
The average number of grams of sugar is 57.
Answer: A cereal with 0 grams of sugar has a rating of about 57
Step-by-step explanation:
The equation modelling the taste rating of a cereal, y, in a survey, where x is the number of grams of sugar per serving is expressed as
yˆ=2.391x + 57.420
This is a straight line graph represented in the slope intercept form which is expressed as
y = mx + c
Where
m represents the slope of the straight line
c represents the y intercept. The y intercept is the point at which x = 0.
From the given equation, the y intercept is 57.420
It means that a cereal with 0 grams of sugar has a rating of about 57
Tyler has a rectangular garden that measures 10 m wide by 13 m long. He wants to increase the area to 208 m² by increasing the width and length by the same amount. What will be the length (longer dimension) of the new garden? Enter your answer in the box.
Answer:
Step-by-step explanation:
Let x represent the constant amount by which the length and width of the garden is increased.
Tyler has a rectangular garden that measures 10 m wide by 13 m long. He wants to increase the area to 208 m² by increasing the width and length by the same amount. This means that the new length of the garden would be (13 + 2x) cm and the new width of the garden would be (10 + 2x) cm. Therefore,
(13 + 2x)(10 + 2x) = 208
130 + 26x + 20x + 4x² -208 = 0
4x² + 46x - 208 - 130 = 0
4x² + 46x - 78 = 0
Dividing through by 2, it becomes
2x² + 23x - 39 = 0
2x² + 26x - 3x - 39 = 0
2x(x + 13) - 3(x + 13) = 0
2x - 3 = 0 or x + 13 = 0
x = 3/2 or x = - 13
Since the value of x cannot be negative, then
x = 3/2 = 1.5 m
The length of the new garden is
13 + 1.5 = 14.5 m
The gas tank of Alberto's car holds a total of 42 liters of gas. At the beginning of the week, Alberto's car has 35.8 liters of gasoline in its tank. He uses 28.6 liters of gasoline during the week. Then he completely fills the tank with gas. How many liters of gas does Alberto buy?
Answer:
34.8 liters
Step-by-step explanation:
He has 35.8 liters.
He uses 28.6 liters.
Now that tanks has 35.8 liters - 28.6 liters = 7.2 liters
The capacity of the tank is 42 liters, and he has only 7.2 liters.
The fill up will be 42 liters - 7.2 liters = 34.8 liters
Answer: he bought 34.8 liters of gas.
Step-by-step explanation:
Let x represent the number of liters of gas that Alberto bought.
At the beginning of the week, Alberto's car has 35.8 liters of gasoline in its tank. He uses 28.6 liters of gasoline during the week. This means that the number of liters of gas left would be
35.8 - 28.6 = 7.2
Then he completely fills the tank with gas. If the gas tank of Alberto's car holds a total of 42 liters of gas., it means that
x + 7.2 = 42
x = 42 - 7.2
x = 34.8 liters
What is the distance between m, a negative number, and 0 on a number line?
Answer:
It depends on what negative number it is. For example -23 is 23 units or whatever to 0.
Step-by-step explanation:
Use the order of operations to evaluate the expression below.
20+7 • (5-3) = (8-6) - 4
Answer:
34 = -2
Step-by-step explanation:
20 = 7 x (5-3) = 34
(8-6) - 4 = -2
So the answer is 34 = -2
The equation 20+7 • (5-3) = (8-6) - 4, when evaluated using the order of operations, gives the result 34 = -2, which indicates that the original equation is not balanced.
Explanation:Let's evaluate the expression 20+7 • (5-3) = (8-6) - 4 using the order of operations, which can be remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
First, we solve the expressions in parentheses: 7 • (5-3) = 7 • 2 = 14 and (8-6) - 4 = 2 - 4 = -2.
Then we perform the addition: 20 + 14 = 34. At this point, we have 34 = -2, which is not correct. Therefore, the original equation is not balanced.
Learn more about Order of Operationshttps://brainly.com/question/13101102?referrer=searchResults
#SPJ2
Please help ASAP!
what is x=-b/2a?
This is the formula to solve for the vertex.
Example Question:
Find the vertex of y = -0.5x^2 + 100x
-b/2a = -100/2(-0.5) = -100/-1 = 100
The x coordinate of the vertex is 100.
Best of Luck!
P.S. this is 1000th question i've answered :)
Biking at 10 mph, it takes Kristen 1/2 hour to reach the train station to go to work. Kristen then takes the train to work, and it takes another 1/2 hour for her to get to work when the train travels 28 mph. How far does Kristen travel to work
Answer: 38 mph
Step-by-step explanation:
Add. 10 plis 28 is 38.
Answer: 19 miles
Step-by-step explanation:
Distance = speed × time
Biking at 10 mph, it takes Kristen 1/2 hour to reach the train station to go to work. This means that the distance covered on her way to the train station is
0.5 × 10 = 5 miles
Kristen then takes the train to work, and it takes another 1/2 hour for her to get to work when the train travels 28 mph. Distance covered by the train is
0.5 × 28 = 14 miles
Therefore, the distance that Kristen travels to work is
14 + 5 = 19 miles
There is 7/8 quarts of orange juice. Mrs. Mathewson would like to serve her guests 3/16 quarts orange juice. How many guests can she serve orange juice?
Mrs. Mathewson can serve orange juice to 4 guests. The solution was found by first converting the fractions to the same denominator, then dividing the total orange juice by the amount per guest, and taking into account that you can't serve fractions of a guest.
Explanation:The problem presented here is a basic division problem that requires you to divide the total amount of orange juice by the amount served to each guest. Mrs. Mathewson has 7/8 quarts of orange juice and she would like to serve each guest 3/16 quarts of orange juice.
Firstly, we'll convert both fractions to the same denominator for simplicity. As 8 is a multiple of 16, we can leave the second fraction as it is (3/16) and change the first fraction to 14/16 (which is the same as 7/8). Now, we divide 14 by 3 which gives us roughly 4.6.
This result means Mrs. Mathewson can serve orange juice to 4 guests with a bit left over. As we can't serve a fraction of a guest, it means she can only serve 4 whole guests.
Learn more about Dividing Fractions here:https://brainly.com/question/18511795
#SPJ3
Mrs. Mathewson can serve orange juice to 14 guests.
Explanation:
To determine how many guests Mrs. Mathewson can serve orange juice, we need to find the quotient of the total amount of orange juice and the amount per guest. Given that there are 7/8 quarts of orange juice and Mrs. Mathewson wants to serve 3/16 quarts per guest, we divide the total amount by the amount per guest: (7/8) ÷ (3/16) = (7/8) × (16/3) = 14 guests.
Learn more about orange here:
https://brainly.com/question/755679
#SPJ2
Find the missing length QG. Round answer to nearest tenth.
Answer:
The answer to your question is QG = 55.8 ft
Step-by-step explanation:
Data
QG = x
Process
1.- Find T
The sum of the internal angles in a triangle equals 180°
G + Q + T = 180
-Solve for T
T = 180 - G - Q
- Substitution
T = 180 - 41 - 67
-Simplification
T = 72°
2.- Use the law of sines to find QG
QG / sin T = GT / sin Q
-Solve for QG
QG = GT sinT / sin Q
-Substitution
QG = 54 sin 72 / sin 67
- Simplification
QG = 54 (0.951)/0.921
-Result
QG = 55.8 ft
Answer:
Step-by-step explanation:
Considering the given triangle QGT, to determine QG, we would apply the sine rule. It is expressed as
a/SinA = b/SinB = c/SinC
Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes
QG/SinT = GT/SinQ = QT/SinG
The sum of the angles in a triangle is 180°. It means that
T = 180 - (41 + 67) = 72°
Therefore
QG/Sin72 = 54/Sin 67
Cross multiplying, it becomes
QGSin67 = 54Sin72
0.921QG = 54 × 0.951
0.921QG = 51.354
QG = 51.354/0.921
QG = 55.8 ft
Maria received 55% of the vote in a student council election. What decimal and fraction, written in its simplest form, are equivalent to the percentage of the vote maria received
Answer:
The decimal and fraction equivalent to the percentage of the vote maria received is 0.55 and [tex]\frac{11}{20}[/tex] .
Step-by-step explanation:
Given:
Maria received 55% of the vote in a student council election.
Now, to find the decimal and fraction of the percentage of the vote maria received.
Percentage of vote Maria received = 55%.
So, the fraction and decimal of the percentage in its simplest form:
[tex]\frac{55}{100}[/tex]
On simplifying it:
[tex]=\frac{11}{20}[/tex].
Thus, the fraction is [tex]\frac{11}{20} .[/tex]
[tex]\frac{11}{20}[/tex]
[tex]=0.55.[/tex]
Hence in the decimal is [tex]0.55.[/tex]
Therefore, the decimal and fraction equivalent to the percentage of the vote maria received is 0.55 and [tex]\frac{11}{20}[/tex] .
Penelope goes to work after school for 4.5 hours on Mondays, Tuesdays, and Fridays. She doesn’t have classes on Wednesdays or Thursdays, so she works 8 hours each on those days. If she makes $413 each week, what’s her hourly rate? aner
Answer:
Her hourly rate is $14.
Step-by-step explanation:
Given:
Penelope goes to work after school for 4.5 hours on Mondays, Tuesdays, and Fridays.
She works 8 hours each on Wednesdays or Thursdays.
Now, to find her hourly rate.
So, total hours Penelope work on Mondays, Tuesdays, and Fridays:
[tex]4.5+4.5+4.5=13.5\ hours.[/tex]
And, total hours she work on Wednesdays and Thursdays:
[tex]8+8=16\ hours.[/tex]
Now, the total hours each week she work:
[tex]13.5+16=29.5\ hours.[/tex]
Total money she makes each week = $413.
Now, to get the hourly rate we divide the total hours each week she work by total money she makes each week:
[tex]413\div 29.5[/tex]
[tex]=\$14.[/tex]
Therefore, her hourly rate is $14.
An open box will be made from a rectangular piece of cardboard that is 8 in. by 10 in. The box will be cut on the dashed red lines, removing the corners, and then folded up on the dotted lines. What is the MAXIMUM possible volume for the box?A) 1.5 in3B) 5.8 in3C) 52 in3D) 64 in3
Answer:
C) 52 in^3
Step-by-step explanation:
The first is to determine the formula of the volume of the box, which would be the following:
V = height * length * width
Knowing that we have a rectangular piece we will determine the maximum volume, we will double a distance x (which will be the height) in the width and length of the piece, therefore as it is on both sides, the length and width are defined from the Following way:
length = 10 - 2 * x
width = 8 - 2 * x
height = x
Now we calculate the volume:
V = x * (10-2 * x) * (8-2 * x)
To determine the maximum volume we will give values to x in order to see how it behaves:
Let x = 2.5
V = (5) * (3) * (2.5) = 37.5
Let x = 2
V = (6) * (4) * (2) = 48
Let x = 1.5
V = (7) * (5) * (1.5) = 52.5
Let x = 1
V = (8) * (6) * (1) = 48
Let x = 0.5
V = (9) * (7) * (0.5) = 31.5
It can be seen that the greatest volume is obtained when the height is equal to 1.5 and its volume is 52.5 in ^ 3
Is my answer correct?
--> explain if it is wrong!!!
Answer: its 25 because you're adding the whole line from P to R, so 12.5 + 12.5 is 25
Step-by-step explanation:
P to T is 12.5
T to R is 12.5
Add those together
12.5 + 12.5 gives you 25
Answer:
25 in.
Step-by-step explanation:
In a rectangle the diagonals bisect each other.
Therefore PT = TR = ST = TQ = 12.5 in.
PR = PT + TR = 12.5 + 12.5
= 25 in.
Reduce each fraction to lowest terms by first factoring the numerator and denominator into product of prime factors and then dividing out any factors they have in common.
What keeps stars such as the Sun from collapsing from their own self-gravity?
A the centrifugal force created by rapid rotation
B. the electrical repulsion of nuclei in the plasma
C. the gravitational pull created by orbiting planets
D. the outward pressure created by nuclear fusion
The outward pressure created by nuclear fusion within the core of stars, like the Sun, counteracts the force of gravity, preventing them from collapsing under their own self-gravity. This delicate balance sustains the stability and longevity of stars.
The correct answer is D. The outward pressure created by nuclear fusion.
Explanation: Stars, including the Sun, are massive celestial objects formed primarily of hydrogen and helium gas. In their cores, the extreme temperatures and pressures enable nuclear fusion reactions to occur, converting hydrogen into helium and releasing tremendous amounts of energy. This energy generates an outward pressure that counteracts the inward force of gravity, maintaining the star's equilibrium and preventing it from collapsing under its own self-gravity. This balance between gravitational forces pulling inward and outward pressure pushing outward due to nuclear fusion is what keeps stars, like the Sun, stable and prevents them from collapsing.
At a refinery 144,000 tons of sand are required to produce each 125,000 barrels of a tarry material. How many tons of sand are required to produce 2,500 barrels of this tarry material?
Answer:
2,880 tons of sand
Step-by-step explanation:
In this question, we are asked to calculate the amount of tons of sand required to produce a certain amount of tarry materials if a certain amount of sand had produce an amount of tarry materials.
We work as follows:
First, we write the relation that 144,000 tons of sand produces 125,000 barrels of tarry material, then x of tons would produce 2,500 barrels of tarry materials
To find c, we cross multiply:
x * 125,000 = 2,500 * 144,000
x = (2,500 * 144,000)/125,000
x = 2,880
One maid can clean the house in 2 hours. Another maid can do the job in 8 hours. How long will it take them to do the job working together?
A 16/6 hr
B 8/5 hr
C 1/10 hr
D 1/16 hr
Answer: B 8/5 hr
Step-by-step explanation:
One maid can clean the house in 2 hours. This means that the rate at which she cleans the house per hour is 1/2
Another maid can do the job in 8 hours. This means that the rate at which the other maid cleans the house per hour is 1/8
If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be
1/2 + 1/8 = 5/8
Assuming it takes t hours for both of them to clean the room working together, the working rate per hour would be 1/t. Therefore,
5/8 = 1/t
t = 8/5 hour
Option B is correct. Working together, the two maids can clean the house in 8/5 hours.
Explanation:Let's assume that the combined rate of both maids working together is x house cleaned per hour. We can set up the equation:
1 maid's rate + another maid's rate = combined rate
1/2 + 1/8 = x
Solving for x:
4/8 + 1/8 = x
5/8 = x
The combined rate of the maids working together is 5/8 house cleaned per hour. To find how long it will take them to clean the house together, we can set up the equation:
(5/8) house per hour = 1 house
Let t be the time it takes them to clean the house together. We can write the equation:
(5/8) * t = 1
Solving for t:
t = 1 / (5/8)
t = 8/5 hours.
Learn more about Working together to complete a task here:https://brainly.com/question/34743654
#SPJ11
The central limit theorem states that sampling distributions are always the same shape as the population distribution from whence the data came. True or False
Explanation:
The sample mean is not always equal to the population mean but if we take more and more number of samples from the population then the mean of the sample would become equal to the population mean.
The Central Limit Theorem states that we can have a normal distribution of sample means even if the original population doesn't follow normal distribution, But we have to take a lot of samples.
Suppose a population doesn't follow normal distribution and is very skewed then we can still have sampling distribution that is completely normal if we take a lot of samples.
Assume a round of golf requires four hours of leisure time, and attending a concert requires two hours. If the price of a round of golf is $40 and the price of a concert is $80, ceteris paribus, Joe will play
Answer:
Step-by-step explanation:
Relatively less golf and attend relatively more concerts whenever his leisure time becomes more scarce.
- This is called the marginal utility, that with every successive unit that utility decreases. With each passing hour while playing golf Joe is less inclined to play for an extra hour. When leisure time is less than 2 hrs he is equally likely to opt out of golf for concert.
What is the value of p such that the line passing through (9,-1) and (6,p) has a slope of -1?
Answer:
p=2
Step-by-step explanation:
Use the slope formula
(p-(-1))/(6-9)=-1
(p+1)/-3=-1
p+1=3
p=2
Answer:
Step-by-step explanation:
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis represent
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
The line passes through (9,-1) and (6,p) and the slope is 1
y2 = p
y1 = - 1
x2 = 6
x1 = 9
Therefore,
(p - - 1)/(6 - 9) = - 1
(p + 1)/- 3 = - 1
(p + 1) = - 1 × - 3
p + 1 = 3
p = 3 - 1
p = 2
Your friend in your statistics class is upset about a recent increase in the price to wash and dry a load of laundry. She wants to conduct a one proportion z-test to see if more than half the residents in her dorm oppose the increase. She will poll a random sample of 30 residents. Which Normal model will she use?
Answer:
Mixed mode expression
Step-by-step explanation:
Mixed mode expression is an expression that contains or have operands that have different data types.
In this case, she has to generate values that have type equal to the operands in this situation.
Answer:
The answer to this question is N(0.50,0.091), just took a quiz with same question.
Step-by-step explanation:
You have a three year fixed rate lease of $900/month due to expire next month. Your landlord is willing to renew the three year lease with a 3% total rent increase. What is your rent over the three year life of the new lease?
Answer:
[tex]\\3 percent of 900 = 27 \\900 + 27 = 927 \\ 927 * 36 = 33372[/tex]
Step-by-step explanation:
First you have to find out the 3% of 900 (is 27)
then you add 27 to 900
then you multiply it by 3 years (36 months)
and your result is 33372 :)
The rent over the three-year term of the new lease will be $33,372, calculated with a 3% increase annually.
Step 1:
Calculate the new monthly rent after the 3% increase.
The new monthly rent will be the current rent plus 3% of the current rent.
New monthly rent = $900 + 0.03 * $900 = $900 + $27 = $927.
Step 2:
Calculate the total rent over the three-year term.
Since there are 12 months in a year and the lease is for three years, multiply the new monthly rent by the number of months in three years.
Total rent over three years = $927/month * 12 months/year * 3 years = $33,372.
So, the rent over the three-year life of the new lease will be $33,372.
Can you find x I don’t know how.
Answer:
7
Step-by-step explanation:
(x+3)/(x+8) = 2/3
3x + 9 = 2x + 16
x = 7
You buy a new stereo for $1300 and are able to sell it 4 years later for $275. Assume that the resale value of the stereo decays exponentially with time. Write an equation giving the resale value $V$ (in dollars) of the stereo as a function of the time $t$ (in years) since your bought it. Round all decimals to four decimal places.
The equation for the resale value of the stereo is V = V0 * e^(-kt), where V0 is the initial value, V is the resale value at time t, and k is the decay constant. Using the given resale value after 4 years, we can solve for k and substitute it back into the equation to find the resale value of the stereo as a function of time.
Explanation:To find an equation giving the resale value of the stereo as a function of time, we can use the formula for exponential decay: V = V0 * e^(-kt). V0 represents the initial value, V represents the resale value at time t, and k is the decay constant. The given resale value after 4 years is $275, so we can substitute these values into the equation: 275 = 1300 * e^(-4k). To solve for k, divide both sides by 1300 and take the natural logarithm of both sides: ln(275/1300) = -4k. Calculate the logarithm and solve for k to get the decay constant. Finally, substitute the value of k into the equation to get the complete equation for the resale value of the stereo.