Answer:
The decay factor is 0.88.
Step-by-step explanation:
The general form of an exponential decay function is
[tex]f(x)=ab^x[/tex]
Where, a is initial value and b is decay factor.
It is given a new truck that sells for $29,000 depreciates (decreases in value) 12% each year.
The initial value is $29,000 and decay factor is
[tex]1-r=1-\frac{12}{100}=1-0.12=0.88[/tex]
The exponential function is
[tex]f(x)=29000(0.88)^x[/tex]
Therefore the decay factor is 0.88.
The decay factor b for the truck, which depreciates 12% each year, is 0.88.
The decay factor, b, for the truck's depreciation can be calculated using the formula for exponential decay:
b = 1 - r
where r is the annual depreciation rate. In this case, the annual depreciation rate is given as 12%, or 0.12 in decimal form.
Now, let's calculate the decay factor:
b = 1 - 0.12
b = 0.88
So, the decay factor for the truck's depreciation is 0.88.
The decay factor is used to calculate the value of the truck after n years by raising b to the power of n and multiplying it by the initial value of the truck. The formula for the value of the truck after n years is:
[tex]\[ V(n) = P \cdot b^n \][/tex]
where P is the initial price of the truck, b is the decay factor, and n is the number of years.
In this case, the initial price P is $29,000, and the decay factor b is 0.88. If we want to find the value of the truck after, say, 5 years, we would use the formula:
[tex]\[ V(5) = 29000 \cdot (0.88)^5 \][/tex]
However, the question only asks for the decay factor, which we have already determined to be 0.88.
Use two or three unit fractions to convert. 1515 daysdaysequals=_______ secondsseconds
It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We need to find the unit fractions to convert 15 days into seconds.
1 day = 24 hour
1 hour = 60 minutes.
1 minutes = 60 seconds
Therefore, 24 hours = 24 x 60 x 60 = 86400 seconds
There are 86400 seconds in one day.
Then 15 days = 15 x 86400 = 1,296,000
Hence, It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.
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If HE = 3p + 7, /, LP = 5p – 19, and /, find the values of p and q for which quadrilateral HELP is a parallelogram. A. p = 18, q = 13 B. p = 13, q = 8 C. p = 8, q = 18 D. p = 13, q = 1
Which quadrilateral HELP is a parallelogram? The corrsect answer is P=13, q=18
Write the equation of the function whose graph is shown.
Answer:
[tex]y=1(x-5)^2 + 3[/tex]
Step-by-step explanation:
Given : from the graph vertex is (5,3)
Also graph passes through point (8,12)
We use vertex form of quadratic equation
General vertex form is
[tex]y=a(x-h)^2 + k[/tex]
vertex is (5,3)
h= 5 and k =3
So equation becomes [tex]y=a(x-5)^2 + 3[/tex]
Now we need to find out 'a'
We use (8,12) to find out 'a'
Plug in x=8 and y = 12
[tex]12=a(8-5)^2 + 3[/tex]
[tex]12=a(3)^2 + 3[/tex]
12= 9a + 3
subtract 3 on both sides
9 = 9a
divide both sides by 9
so a=1
Final equation is
[tex]y=1(x-5)^2 + 3[/tex]
An equation of the function of this graph is equal to [tex]y=1(x-5)^2 + 3[/tex]
Given the following data:
Points on the x and y-axis = (8, 12).Vertex (h, k)= (5, 3).How to write a function.The vertex form of a quadratic equation can be used to write an equation of the function of a graph.
Mathematically, the vertex form of a quadratic equation is given by this formula:
[tex]y=a(x-h)^2 + k[/tex]
Substituting the given parameters into the formula, we have;
[tex]12=a(8-5)^2 + 3\\\\12=(3a)^2+3\\\\9a^2=12-3\\\\9a^2=9\\\\a^2=1[/tex]
a = 1.
For the equation:
[tex]y=a(x-h)^2 + k\\\\y=1(x-5)^2 + 3[/tex]
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Find the quotient and remainder using long division. x6 + 4x4 + 4x2 + 16 x2 + 4
Can you help me solve #s 43 an 44 pleeeease
please help and explain to me!
Helpppppppppppppppppp
after 5 years what is the total amount of a compound interest investment of 32,000 at 3% interest, compounded quarterly
A.57.795.56
B.32,426.67
C.43,099.36
D.37,157.89
Joe walked of a mile in of an hour. what is his unit rate in miles per hour? (1 point) = mile per hour = miles per hour = miles per hour = mile per hour
The width of a rectangle is 2m less than the length. the area is 48m squared. find the dimensions
The length of the rectangle is 8m and the width is 6m
This question involves the area of a rectangle and we can use the formula to solve this problem.
Data given;
A = 48m^2w = (L - 2)mAreaThe area of a rectangle is given as
[tex]A = L * W[/tex]
l = lengthw = widthsubstitute the values and solve
[tex]A = lw\\48 = L * ( L - 2)\\48 = l^2 -2l\\l^2 -2l - 48 = 0[/tex]
solve this quadratic equation to find the length
a = 1, b = -2, c = -48
[tex]l = \frac{-b+-\sqrt{b^2 - 4ac} }{2a} \\l = \frac{-(-2)+-\sqrt{(-2)^2-4*1*(-48)} }{2*1} \\l = 8[/tex]
Taking only the positive value of l, l = 8
but we also know that
[tex]w = l -2\\w = 8 -2\\w= 6[/tex]
from the above, the length of the rectangle is 8m and the width is 6m
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Describe which of the two points lies on the graph of the line
Y-x=4
A. 9,5
B. 5,9
Which step should be used to prove that point a is equidistant from points c and b? (1 point)?
What are the names of the eight line section and the six line section that combine to form the 14 lines of a petrarchan sonnet?
The answer is an octave and a sestet. A sestet is the title specified to the second split of an Italian sonnet (as contrasting to an English or Spenserian sonnet), which must contain of an octave, of eight lines and must be followed by a sestet, of six lines. The first recognized user of this poetical type was the Italian poet named Petrarch.
How does the radius of a positive and negative ion compare to a neutral atom?
A neutral atom contains equal amount of proton and electron.
A negative ion contains extra electrons hence there is additional outer shell so it is expected that the radius is bigger than that of a neutral atom.
While a positive ion contains less electron so there is less outer shell so the radius is smaller than that of a neutral atom.
Arranging the radius in increasing order:
positive ion, neutral atom, negative ion
Which irrational number can be multiplied by negative square root of 41 to get a product that equals 1?
For this case we define the following variable:
x: unknown number
We then have the following equation:
[tex]- \sqrt {41} x = 1[/tex]
From here, we clear the value of x.
We have then:
[tex]x = - \frac {1} {\sqrt {41}}[/tex]
Answer:
An irrational number that can be multiplied by negative square root of 41 to get a product that equals 1 is:
[tex]x = - \frac {1} {\sqrt {41}}[/tex]
PLEASE HELP ASAP!!!!!
Carl, Brian, Dave, and Ashley want to attend the same university. Unfortunately only two spots remain and these four friends have the same GPA, as well as virtually identical community service and leadership experiences. Therefore, the two spots will be determined by their SAT and ACT scores. Carl scored 1,280 on the SAT, while Brian scored 1,325. Dave scored 28 on the ACT, while Ashley scored 30. Use z-scores to determine which two students should be admitted. The mean SAT score was 1,000 with a standard deviation of 175 and the mean ACT score was 20.6 with a standard deviation of 5.2 Both tests are normally distributed.
Determine whether 2y=3x-1 represents a direct variation. if it does, find the constant of variation.
The equation 2y=3x-1 does not represent a direct variation in its strict definition, as it includes a y-intercept. If the y-intercept is ignored, the constant of variation would be k = 3/2.
The equation 2y=3x-1 represents a direct variation if it can be written in the form y = kx, where k is the constant of variation. To determine if this equation represents a direct variation, we can solve it for y:
Divide both sides of the equation by 2 to isolate y:
y = (3/2)x - 1/2.
Since we can express y as an equation of the form y = kx + b, with b being a constant, it does not represent a pure direct variation, as direct variation should have a form y = kx without the constant term.
However, if the question is interpreted to include such linear relationships as direct variations despite the y-intercept, then the constant of variation would be k = 3/2.
The m6 = (11x + 8)° and m7 = (12x – 4)° What is the measure of 4? m4 = 40° m4 = 48° m4 = 132° m4 = 140°
The measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°
From the diagram, we can observe that angles 6 and 7 are vertically opposite angles.
From one of the angle theorems, we have that vertically opposite angles are equal
That means,
measure of ∠ 6 = measure of ∠ 7
From the question,
we have that, m6 = (11x + 8)° and m7 = (12x – 4)°
Since, the measures of angles 6 and 7 are equal, then we can write that
(11x + 8)° = (12x – 4)°
Now, determine the value of x, we will solve the equation
11x + 8 = 12x – 4
First, subtract 11x from both sides
11x - 11x + 8 = 12x - 11x - 4
8 = x - 4
Now, add 4 to both sides
8 + 4 = x -4 +4
12 = x
∴ x = 12
Now, we will determine the measure of ∠6
m ∠6 = (11x + 8)°
Put x = 12
∴ m ∠6 = (11(12) + 8)°
m ∠6 = (132 + 8)°
m ∠6 = 140°
To determine the measure of ∠4, m4, we will first determine the measure of ∠8.
From the diagram,
m ∠6 + m ∠8 = 180° (Sum of angles on a straight line)
∴ 140° + m ∠8 = 180°
Then,
m ∠8 = 180° - 140°
m ∠8 = 40°
From the diagram, we can observe that angles 4 and 8 are corresponding angles.
Also, from one of the angle theorems, we have that corresponding angles are equal.
Hence, the measure of ∠ 4 equals the measure of ∠ 8.
From above, m ∠8 = 40°
∴ m ∠4 = 40°
Hence, the measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°
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"you buy a baseball bat and a ball for $1.10. the baseball bat costs $1.00 more than the ball. how much did the ball cost?"
Pleaseeee help!!!!!!!!!
2x to the fourth power + 5x squared + 3, factored
if f(x)=2x-4 find f(q+1)
The value of f(q+1) is 2(q-1).
What is a function?A relation or expression involving one or more variables.
Given that, f(x) = 2x - 4
When x = q+1
f(q+1) = 2(q+1) - 4
f(q+1) = 2q + 2 - 4
f(q+1) = 2q - 2
f(q+1) = 2(q-1)
Hence, the value of f(x) when x = (q+1) is 2(q-1)
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Find y to the nearest tenth.
2.7
2.9
7.5
y = 8 x cos(20)
y = 7.517
y = 7.5
Which of the following statements describes the process for solving 4x ≥ -24?
Divide both sides of the inequality by -24 and flip the symbol.
Divide both sides of the inequality by -24 but don't flip the symbol.
Divide both sides of the inequality by 4 and flip the symbol.
Divide both sides of the inequality by 4 but don't flip the symbol.
Answer:
Your answer would be D.
Step-by-step explanation:
Functions f(x) and g(x) are shown below:
f(x) = -4(x - 6)^2 + 3
g(x) = 2 • cos(2 • x - pi) + 4
Using COMPLETE SENTENCES, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.
How long will it take for $2800 to grow to $24,900 at an interest rate of 5.6% if the interest is compounded continuously? round the number of years to the nearest hundredth?
terrell wants to drive his car at a speed of 50 miles per hour for 2.75 hours. his car has a fuel efficiency of 25 miles per gallon. How many gallons of fuel does terrell need for his journey
The initial balance of a mutual fund is $1800. The fund is expected to grow in value at an annual rate of 5%.
Let x represent the number of years since the fund was started. Let y represent the value of the fund x years later.
What equation models the value of the mutual fund x years after it was started?
suppose the correlation coefficient between the number of the college students in a city and the number of city buses is 0.89. which statement must be true?
Answer:
Step-by-step explanation:
Given that the correlation coefficient between the number of college students in a city and the number of city buses is 0.89.
We find that correlation coefficient is a measure of linear association between two variables.
When the absolute value of correlation coefficient is near 1, there is strong correlation. If correlation has a positive sign, there is a posiitive association between the two variables.
Here the correlation coefficient is positive and also near 1. Thus there is a strong linear correlation between the two variables.
Or whenever there is an increase in one variable there will be an increase in other variable also.
Jasmine is 23 years old. jasmine is 3 years less than half of george's age. write and solve an equation to find george's age.
take 23 and multiply by 3 then divide by 2 and your answer should be x34