(EASY POINTS)The accompanying table shows the value of a car over time that was purchased for 18400 dollars, where x is years and y is the value of the car in dollars. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, determine the value of the car, to the nearest cent, after 9 years.
Answers
i. The exponential regression equation for this data is
y ≈ 35125.61(0.8276)^x
ii. The value of the car after 9 years is approximately $3,444.20.
The exponential regressionTo find an exponential regression equation for this data, we can use the form of the equation y = ab^x, where y is the value of the car in dollars, x is the number of years since it was purchased, and a and b are coefficients to be determined.
Using the given data points, we can set up a system of equations:
a b^0 = 18400 (the initial value of the car)
a b^1 = 14593
a b^2 = 12503
a b^3 = 9934
a b^4 = 8490
a b^5 = 7613
a b^6 = 6348
Dividing the second equation by the first, the third by the second, and so on, we get:
b = 14593/18400 = 0.7938 (rounded to four decimal places)
b = 12503/14593 = 0.8554
b = 9934/12503 = 0.7943
b = 8490/9934 = 0.8545
b = 7613/8490 = 0.8967
b = 6348/7613 = 0.8346
Taking the average of these values for b, we get b ≈ 0.8276.
Substituting this value of b into any of the equations above, we can solve for a:
a ≈ 18400/b^0 ≈ 18400
a ≈ 14593/b^1 ≈ 25395.22
a ≈ 12503/b^2 ≈ 31298.57
a ≈ 9934/b^3 ≈ 36475.19
a ≈ 8490/b^4 ≈ 42344.76
a ≈ 7613/b^5 ≈ 48022.39
a ≈ 6348/b^6 ≈ 58468.11
Taking the average of these values for a, we get a ≈ 35125.61.
Therefore, the exponential regression equation for this data is:
y ≈ 35125.61(0.8276)^x
To determine the value of the car after 9 years, we can simply plug in x = 9 into this equation:
y ≈ 35125.61(0.8276)^9 ≈ 3444.20
Therefore, the value of the car after 9 years is approximately $3,444.20.
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Related Questions
The length of a rectangle is five less than three times the width. If the perimeter is 22
inches, find the width.
Answers
Answer:
I hope it helped u
Step-by-step explanation:
Answer:width =4 inches
Step-by-step explanation:
Take x as width
And length as 3x-5
And perimeter as 22
Formula of the perimeter of a rectangle is 2l+2w
X+x+3x-5+3x-5=22
8x-5-5=22
8x=22+5+5
8×=32
X=4
Width =x and x=4 inches so width = 4 inches while length =7 inches
to estimate the average annual expenses of students on books and class materials, a sample of size 36 is taken. the sample mean is $850 and the sample standard deviation is $54. a 99 percent confidence interval for the population mean is group of answer choices $823.72 to $876.28 $832.36 to $867.64 $826.82 to $873.18 $825.48 to $874.52
Answers
Answer: $826.82 to $873.18
Step-by-step explanation:
Piper skated to the park and then walked to the store. He skated 2 times as long as he walked. The total time spent walking and skating was 21 minutes. Write an equation that can be used to solve for how long it took Piper to walk from the park to the store?
*
x + 2x = 21
x + 2 = 21
1/3x = 21
1/2x + x = 21
Answers
The equation to represent the time taken by piper to walk and skate is x + 2x = 21. The correct option is (A).
How to write a linear equation?A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.
Suppose the number of times piper walked be x.
Then, the number of times he skated is 2x.
Now, as the total time spent on walking and skating is 21 minutes, the equation can be written as,
Total time = Time for walking + time for skating
⇒ 21 = x + 2x
⇒ 3x = 21
⇒ x = 7
Thus, the solution of the equation is x = 7 which is equivalent to the time for walking in minutes.
Hence, the required equation is x + 2x = 21 and its solution is 7.
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*5. Gina's sister is 9 years older than Gina. Their combined ages add up to
49. How old is Gina? *
A. 29 years
B. 20 years
C. 19 years
D. 9 years
Answers
Answer:
B. 20 years
Step-by-step explanation:
By using the process of trial and error, if Gina is 20 years old, that would mean her sister is 29 years old. This is because 20+9 is equal to 29. 29+20 sums up to 49.
Answer: B. 20 years
Step-by-step explanation:
we will represent Gina sister's age by x and Gina's age by y.
Now were know that the age of Gina sister is 9 years older than Gina's so we can represent that by the equation x = y + 9
If we add their ages it is 49 so we can also represent that by the equation,
x + y = 49.
x = y + 9
x + y = 49
Using both equations, substitute x in the first equation into the second equation and solve for y.
(y + 9) + y = 49 solve for y , by first combining like terms.
2y + 9 = 49 subtract 9 from both sides
-9 -9
2y = 40 divide both sides by 2
y = 20
Since y was used to represent the age of Gina then Gina will be 20 years old.
Solve each equation for θ with 0 ≤ θ <2 π.
Suppose the outside temperature in Problem 6 is modeled by the function f(t)=27-6 cos π / 12 t instead. During what hours is the air conditioner cooling the house?
Answers
The air conditioner is not cooling the house during any hours, as the inequality cos(π/12t) > 9/2 has no solutions within the specified range of 0 ≤ t < 2π.
To determine the hours during which the air conditioner is cooling the house, we need to find the values of t for which the function f(t) = 27 - 6cos(π/12t) is less than 0.
The equation f(t) = 27 - 6cos(π/12t) represents the outside temperature as a function of time, where t represents the time in hours.
To find the hours when the air conditioner is cooling the house, we need to find the values of t that make f(t) less than 0.
Setting f(t) < 0, we have:
27 - 6cos(π/12t) < 0
Subtracting 27 from both sides:
-6cos(π/12t) < -27
Dividing both sides by -6 (and reversing the inequality):
cos(π/12t) > 27/6
Simplifying further:
cos(π/12t) > 9/2
To find the values of t that satisfy this inequality, we need to consider the range of the cosine function and the given inequality.
The cosine function has a maximum value of 1 and a minimum value of -1. Since we want the inequality to be satisfied, we need cos(π/12t) to be greater than 9/2, which is outside the range of the cosine function.
Therefore, there are no values of t that satisfy the inequality cos(π/12t) > 9/2.
This means that the air conditioner is not cooling the house during any hours, according to the given function f(t) = 27 - 6cos(π/12t).
In summary, based on the provided function, the air conditioner is not cooling the house during any hours, as the inequality cos(π/12t) > 9/2 has no solutions within the specified range of 0 ≤ t < 2π.
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Si colocan en 16 pisos, 16 ladrillos. ¿Cuántos ladrillos pusieron en total?. (expresarlo en forma de potencia)
Answers
Answer:
Númer total de ladrillos= 256
Step-by-step explanation:
Dada la siguiente información:
Total de pisos= 16
Total de ladrillos por piso= 16
Para calcular cantidad de ladrillos en total, tenemos que usar la siguiente formula:
Número total de ladrillos= total de ladrillos^2
Número total de ladrillos= 16^2
Númer total de ladrillos= 256
En este caso lo hace al cuadrado por que la cantidad de pisos y ladrillos por piso es la misma. Sino, es mejor expresarlo como una multiplicación.
Dana Thacker's bank granted her single payment loan of 10,450 she agreed to repay the loan in 75 days at an exact interest rate of 8.25 percent. What is the maturity value of the loan? Need help ASAP
Answers
Using simple interest, it is found that the maturity value of the loan is of 10,638.
Simple InterestThe amount of money after t years in simple interest is modeled by:
\(A(t) = A(0)(1 + rt)\)
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.In this problem:
A loan of 10450 is taken, hence \(A(0) = 10450\).Interest rate of 8.25%, hence \(r = 0.0825\)The loan will be repaid in 75 days, considering the time in years, \(t = \frac{75}{365}\)Then, the maturity value of the loan is:
\(A(t) = A(0)(1 + rt)\)
\(A\left(\frac{75}{365}\right) = 10450\left[1 + 0.0875\frac{75}{365}\right] = 10638\)
The maturity value of the loan is of 10,638.
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Help and explain !!!!!
Answers
Answer:
yeah the answer is one of those just pick one
2. Un auto viaja a 60 km/h y se detiene a los 2 segundos. qué distancia recorrió en el
frenado? ¿qué aceleración adquirió? ¿Si la aceleración es positiva o negativa, explica
por qué?
Answers
Se calcula que la aceleración es - 8,35 m/s.
¿Qué es la aceleración?Ahora sabemos lo siguiente de la pregunta;
Velocidad inicial (u) = 60 km/h o 16,7 m/s
Tiempo empleado (t) = 2 s
Dado que;
v = tu + en
v = 0 m/s porque el carro se detenía
tu = -en
a = -(u/t)
a= -1(6,7 m/s/2 s)
a =- 8,35 m/s
La aceleración es negativa porque la velocidad disminuye con el tiempo.
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A, B, and C are three landmarks in a national park. Landmarks A and B are 650 meters apart. Landmarks B and C are 822 meters apart. Carla takes 4 minutes to run from Landmark A Landmark B, and another 6 muinutes to run from Landmark B to Landmark C. What is Carla's average speed in meters per minute for the run from Landmark A to Landmark C?
Answers
7x - 6 = 3 + x - 5 - 2x
Answers
Answer:
x=1/2
Step-by-step explanation:
7x−6=3+x−5−2x
Step 1: Simplify both sides of the equation.
7x−6=3+x−5−2x
7x+−6=3+x+−5+−2x
7x−6=(x+−2x)+(3+−5)(Combine Like Terms)
7x−6=−x+−2
7x−6=−x−2
Step 2: Add x to both sides.
7x−6+x=−x−2+x
8x−6=−2
Step 3: Add 6 to both sides.
8x−6+6=−2+6
8x=4
Step 4: Divide both sides by 8.
8x /8 = 4 /8
x= 1 /2
Answer:
0
Step-by-step explanation:
We need to factor the GCF (Greatest Common Factor).
The resulting term is a product of the GCF and the original expression divided by the GCF.
In our example, the GCF is equal to X + 2.
I'm not sure if its 0
But mine is "0"
4x^2-21x-18=0
Find the discriminate
Answers
a = 4, b = -21, c = -18
to keep from getting "mixed up", evaluate the discriminant first ...
b<sup>2</sup> - 4ac = (-21)<sup>2</sup> - 4(4)(-18) = 729
sqrt(729) = 27
x = (21 +/- 27)/8
x = -3/4, x = 6
since the discriminant is a perfect square, the original quadratic will factor ...
4x<sup>2</sup> - 21x - 18 = 0
(4x + 3)(x - 6) = 0
x = -3/4, x = 6
Answer:729
Step-by-step explanation: Use the values of a, b and c to find the discriminant. Which is 729
Please help asap!!!!!! question 6(multiple choice worth 5 points) (order of operations mc) harry needs wood pieces to complete a project in woodshop class. he needs four pieces of wood that have a length of two and three fourths feet and five pieces of wood that are one and two thirds feet. what is the total amount of wood that harry will need for the project? four and four sevenths feet nineteen and one third feet four and two fifths feet one and two thirds feet
Answers
The total amount of that Harry will need for the project is nineteen and one third feet and Hence the option B is correct.
Addition of Fraction
Wood 1:
Length of each = 2 3/4 feet
Number of pieces = 4
Total = Length of each × Number of pieces
= 2 3/4 × 4
= 11/4 × 4
= 11 meters
Wood 2:
Length of each = 1 2/3 feet
Number of pieces = 5
Total = Length of each × Number of pieces
= 5/3 ×5
= 25/3 meters
Total amount of wood needed for the project = 11meters + 25/3 meters
= 11 +25/3
= (33+25)/3
= 58/3
=19 1/3 meters
Therefore, the total amount of wood that Harry will need for the project is nineteen and one third feet
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please please help meeee
Answers
Answer:
the first one is when it's decreasing
The equation of a function changed from y=x+6 to y = -x+6which statement best describes the change in the graph of the function
Answers
Answer:
6+
Step-by-step explanation:
mr. goodman sets a goal to outscore these numbers. at the end of the year he takes a random sample of his evaluations and finds 10 1's, 13 2's, 48 3's, and 52 4's. at the 0.05 level of significance, can mr. goodman claim that his evaluations are significantly different than the history department's?
Answers
No as their no difference in Mr. Goodman's evaluation and the History department
What is Statistics ?
The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.
descriptive statistics types in mathematics The data in this type of statistics is summarized using the provided observations. Statistics that are inferential. To interpret the meaning of descriptive statistics, this kind of statistics is employed. Example of Statistics.
Seeing the data we can conclude that their no difference in Mr. Goodman's evaluation and the History department
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For an exponential regression equation in the form y=ab^x , a value of 1.101 for b will cause y to get smaller as x gets larger True or false
Answers
Answer:
False
Step-by-step explanation:
Find a Doctor, is a small startup that helps people find a physician that best meets their needs (location, insurance accepted, etc) During a "slow time for them, they have 9 staff members taking calls from customers. On average, one call arrives every 5 minutes (standard deviation of 5 minutes). Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes) Round your answer to 2 decimal places) How long does a customer spend on average waiting on hold before they can start speaking to a representative? Minutes
Answers
On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.
To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.
Given:
9 staff members taking calls.
On average, one call arrives every 5 minutes (standard deviation of 5 minutes).
Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).
To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:
"M" stands for Markovian or memoryless arrival and service times.
"c" represents the number of servers.
In our case, we have an M/M/9 queuing model since we have 9 staff members.
The average waiting time for a customer on hold is given by the following formula:
Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))
Where:
c = number of servers (staff members) = 9
μ = average service rate (1 / average service time)
λ = average arrival rate (1 / average interarrival time)
ρ = λ / (c * μ)
First, let's calculate the average arrival rate (λ):
λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute
Next, calculate the average service rate (μ):
μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute
Now, calculate ρ:
ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407
Finally, calculate the waiting time:
Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))
= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))
≈ 1.16 minutes
Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.
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What value of x makes 23x+5=11 true?
A. 4
B. 513
C. 9
D. 1023
E. 24
Answers
6/23 is the value of x that ensures that the equation 23x + 5 = 11 holds true. The solution to this problem cannot be found in the available selections since none of the answer possibilities match this value.
We must find x in order to determine what value of x results in the equation 23x + 5 = 11 being true.
Initially, we must remove 5 from both sides of the equation to isolate the variable x:
23x + 5 - 5 = 11 - 5
When we combine the left and right sides, we obtain:
23x = 6
Then, by multiplying both sides of the equation by 23, we must find x:
23x/23 = 6/23
When we combine the left and right sides, we obtain:
x = 6/23
As a result, 6/23 is the value of x that ensures that the equation 23x + 5 = 11 holds true.
The solution to this problem cannot be found in the available selections since none of the answer possibilities match this value.
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Someone explain please
Answers
Answer:
SA = 94 ft²
Step-by-step explanation:
To find the surface area of a rectangular prism, you can use the equation:
SA = 2 ( wl + hl + hw )
SA = surface area of rectangular prism
l = length
w = width
h = height
In the image, we are given the following information:
l = 4
w = 5
h = 3
Now, let's plug in the information given to us to solve for surface area:
SA = 2 ( wl + hl + hw)
SA = 2 ( 5(4) + 3(4) + 3(5) )
SA = 2 ( 20 + 12 + 15 )
SA = 2 ( 47 )
SA = 94 ft²
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Use the given transformation to evaluate the integral. x2 – 3x + y2) da, where R is the region bounded by the ellipse 2x2 - 3xy + 2y2 = 2; X = v 20 - 2/7v. V= 20 + 2/7 Question
Answers
The given transformation does not provide a valid mapping from the variables x and y to X and V, making it impossible to evaluate the integral using the given transformation.
To evaluate the integral of (x^2 - 3x + y^2) da over the region R bounded by the ellipse 2x^2 - 3xy + 2y^2 = 2, we can use the given transformation X = √(20 - (2/7)√20) and V = √(20 + (2/7)√20).
The transformation X = √(20 - (2/7)√20) and V = √(20 + (2/7)√20) allows us to express the integral in terms of the transformed variables X and V. However, the given transformation does not directly provide a mapping from the variables x and y to X and V.
To evaluate the integral using the given transformation, we would need a valid transformation that relates the variables x and y to X and V. Without a proper transformation, it is not possible to proceed with the evaluation of the integral.
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what is the product of the polynomials below? (8x^2-4x-8) (2x^2+3x+2)
Answers
Answer:
B
Step-by-step explanation:
you can FOIL or set up a box that is 3 x 3 (which is what I recommend) to solve it.
The product of the given polynomials is \(16x^4 +16x^3 -12x^2-32x-16\). The correct option is- B. \(16x^4 +16x^3 -12x^2-32x-16\)
Product of polynomialsFrom the question, we are to determine the product of the given polynomials
The given polynomials are
(8x^2-4x-8) (2x^2+3x+2)
Their product can be determined as follows
\((8x^2-4x-8) (2x^2+3x+2)\)
\((8x^2) (2x^2+3x+2)-4x(2x^2+3x+2)-8 (2x^2+3x+2)\)
Clear the brackets
\(16x^4 +24x^3+16x^2 -8x^3-12x^2-8x-16x^2-24x-16\)
Now, collect like terms
\(16x^4 +24x^3 -8x^3-12x^2+16x^2-16x^2-8x-24x-16\)
Simplifying
\(16x^4 +16x^3 -12x^2-32x-16\)
Hence, the product of the given polynomials is \(16x^4 +16x^3 -12x^2-32x-16\). The correct option is- B. \(16x^4 +16x^3 -12x^2-32x-16\)
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a box of 50 pencils sells at $6.00. jason bought 35 pencils and paid 10$. what is his change
Answers
Answer:
$5.80
Step-by-step explanation:
50 diveded by 6 dolors is .12 so .12 times 35 is 4.20 so 4.20 minus 10.00 equals 5.80
I NEED THIS IN 10 MINUTES
Answers
Answer:
I believe the answer is C, the area of a circle, because pi is irrational, and anything multiplied by it will always result in an irrational number.
Step-by-step explanation:
I hope this helps and please mark me as brainliest!
I have multiple questions:
1: 2/3÷4/5
2: 2 1/9÷2/3
3: 3/5÷1 1/4
Answers
Answer:
1: 5/6
2: 3 1/6
3: 12/25
hope this helps!!
p.s
comment if wrong
Plz help u will get branliest!
Answers
For #3, the answers could be 2/4 or 3/6
For #4, the answers could be 8/10 or 16/20
For #5, they both equal each other
For #6, they both do not equal each other
For #7, they both do not equal each other
For #8, they both equal each other
For #9, they both equal each other
For #10, they both do not equal each other
For #11, they both equal each other
For #12, they both do not equal each other
I think #13 can be 1/3 and 2/6 since 4/12 is vanilla
I don’t know #14
Five years ago, John's age was half of the age he will be in 8 years. How old is he now?
Answers
J=0.5J+13
0.5J=13
J=26
The answer would be John is 18 years old
3(4x+8)
————
6
How to solve please help
Answers
Answer:
6x
Step-by-step explanation:
3 (4x+8)
1. ________
6
12x + 24
2. ___________
6
3. 36x
____________
6
4. 6x
56% of the students at a college are from in-state. if 2,380 students are from in-state, how many students attend the college?
Answers
Answer:
Step-by-step explanation:
Answer is 4250 students attend the college
4250 x .56 = 2,380
A pairwise scatter plot matrix is perfectly symmetric and the
scatterplot at the lower left corner is identical to the one at the
upper-right
True or False
Answers
True. In a pairwise scatter plot matrix, each scatterplot represents the relationship between two variables.
Since the scatterplot between variable X and variable Y is the same as the scatterplot between variable Y and variable X, the matrix is perfectly symmetric.
The scatterplot at the lower-left corner is indeed identical to the one at the upper-right corner. This symmetry is a result of the fact that the relationship between X and Y is the same as the relationship between Y and X.
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