The value of car after 2 years is $17,008.8, as percent it is 28.2% and depreciation is 27.75%
Value of car after two years will be calculated by calculating the depreciation each year.
Depreciation after first year = 60,320 - 15%×60,320
Depreciation after first year = 60,320 - 9,048
Depreciation after first year = $51,272
Depreciation after second year = 51,272 - 15%×51,272
Depreciation after second year = 51,272 - 7690.8
Depreciation after second year = $43,311.2
Value after depreciation = 60,320 - 43,311.2
Value after depreciation = $17,008.8
Value of car as percentage = 17008.8/60320×100
Value of car as percentage = 28.2%
Depreciation after two years period = 9048 + 7690.8
Depreciation after two years period = 16,738.8
Depreciation as percentage = 16738.8/60320×100
Depreciation as percentage = 27.75%
The correct answers are a) $17008.8, b) 28.2% and c) 27.75%.
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What is the measure of m? 28 n 7 m = 7√ [?] Give your answer in simplest form. I would really appreciate your help.
Answer:
[tex]7\sqrt{5}[/tex]
Step-by-step explanation:
Using the geometric mean theorem, [tex]n=\sqrt{28 \cdot 7}=14[/tex].
Using the Pythagorean theorem, [tex]m=\sqrt{7^2+14^2}=7\sqrt{5}[/tex]
is the statement a valid null hypothesis?
A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations.
What is meant by null hypothesis?A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations. The use of sample data in hypothesis testing allows one to judge a hypothesis' veracity.
The null hypothesis states that the estimate is only based on chance. If the observed data (in the sample) do not differ from what would be predicted solely by chance, then the null hypothesis is true. The alternative hypothesis is what the null hypothesis has as its counterpart.
Two population parameters, such as an independent variable and a dependent variable, are said to be unrelated under the null hypothesis. It's possible that an experimental or sampling error caused the result if the hypothesis indicates a relationship between the two parameters.
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JE
Write an equation for a line perpendicular to y = 3a + 3 and passing through the point (-6,6)
Answer:
Step-by-step explanation:
A line that is perpendicular to another will have the opposite slope.
y = [tex]-\frac{1}{3}[/tex]a + b
To find b, substitute y and a with the given values
6 = [tex]-\frac{1}{3}[/tex](-6) + b
6 = 2 + b
-2 -2
4 = b
thus
y = [tex]-\frac{1}{3}[/tex]a + 4
What does y equal?
Will Give Brianlest!
Answer:
[tex]\boxed{\tt y=48}[/tex]
Step-by-step explanation:
[tex]\tt \cfrac{3}{16}=\cfrac{9}{y}[/tex]
Cross multiply:-
[tex]\tt 3 \times y=(9)\times (16)[/tex]
[tex]\tt 3y=144[/tex]
Divide both sides by 3:-
[tex]\tt \cfrac{3y}{3}=\cfrac{144}{3}[/tex]
Simplify:-
[tex]\tt y=48[/tex]
_________________
Hope this helps!
Answer:y=48 I hope this is helpful good luck have a good day
Step-by-step explanation:
3/16 = 9/y
Determine the defined range
3/16=9/y y=0 cross out the equal sign y=0
Simplify the equation using cross-multiplication
3y=144
Divide both sides of the equation by 3
y=48
Check if the solution is in the defined range
Jack raied 45 dollar. He raied 3 time more than Tamara. How much did Tamar raie?
Tamar raise $15
What is division ?
One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.
A group is divided into equal portions when it is divided. For a game or activity, division can be used to divide a class into equal groups. It can also be used to divide a pizza among friends in equal pieces. Divided into partitive and quotative, there are two forms of division.
There are 2 ways one by writing equation and the other by using logic
1. by using equation
3*x=45
x=45/3
= 15
2. Logically
If Jack has $45 which is 3 times Tamara's we can reverse the statement:
45/3
=15
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State all integer values of x in the interval 1 ≤ x ≤ 6 that satisfy the following
inequality:
2x - 4 ≥1
The value of x≥2 are: 2,4,5,6
What is meant by inequality ?Inequality—the state of not being equal, particularly in status, rights, and opportunities1—is central to social justice theories. However, it is prone to misunderstanding in public debate because it means different things to different people. Some distinctions, however, are universal.
An inequality compares two values to determine whether one is less than, greater than, or simply not equal to the other. a b indicates that a is not equal to b.
Given ,
2x - 4≥1
State the values of x within 1 and 6
2x - 4≥1
2x ≥ 1 +4
2x ≥ 5
Divide both sides by 2
2x/2 ≥ 5/2
x = 2
(1,6) is an open interval which means that 1 and 6are not inclusive of the values of x.
So:
therefore the values of x≥2 are: 2,4,5,6
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find the area of the region that lies inside both curves. r2 = 50 sin(2θ), r = 5
The area under the curve r²=50sin2Θ is (15.71)unit square
How to find the area under the parabola?A parabola is defined as a plane curve that is mirror-symmetrical and approximately U-shaped.
The given parabola is r²=50sin2∅,
where r=5
Where r=radius of the circle of the parabola
Substitute r=5 in the parabola
5²=50sin2∅
Simplifying the equation to find the value of ∅25=50sin2∅[tex]\frac{25}{50}[/tex]=sin2∅
Finding the sine inverse, we havesin[tex]^{-1} 0.5=2[/tex]∅30⁰=2∅∅=15⁰
The angle made by the parabola is 15⁰
note r=5
Area = 22/7 × 5
Area = 15.71 unit²
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The line graph below displays the average value of a 2000 Toyota Camry since the year 2000. A trendline has been added to the data. V represents value in dollars of the car and t represents the time in years since 2000.
a. Consider the variables “Value” and “time”. Which variable is the independent variable and which variable is the dependent variable?
b. Find an equation for the value as a function of the number of years since 2000.
c. Write a sentence that identifies and interprets the y intercept of the trendline. Use
appropriate units.
d. Write a sentence that identifies and interprets the slope of the trendline. Use
appropriate units.
e. Use the equation of the trendline to predict the value of the car in 2017. Use your
appropriate units. Show your work.
The evaluation of the trendline in line graph of the trendline displaying the value of a 2000 Toyota Camry since the year 2000 are as follows;
a. Independent variable; Time
Dependent variable; Value
b. The equation is; V = 22,500 - 1,166.[tex]\overline 6[/tex]·t
c. The y-intercept is at the point (0, 22,500), which indicates that the value of the 2000 Toyota Camry in the year 2,000 is $22,500
d. The slope of the trendline is -1,166.[tex]\overline {6}[/tex], which indicates that the annual reduction in the price of the 2000 Toyota Camry is $1,166.[tex]\overline 6[/tex]
e. The value of the car in 2017 based on the trendline is $2,666.[tex]\overline{6}[/tex]
What is a trendline in a graph or chart?A trendline is a line drawn through a scatterplot, minimizing the distances between the points in the chart and the line itself, and shows the trend of the scatterplot.
a. The independent variable is the variable that is the input variable of the function, which the researcher can vary or the value that is controlled.
Therefor;
The independent variable is the ''time''The dependent variable is the value under study, therefore;
The dependent variable is the ''Value''b. The points on the line graph are; (0, 22,500), and (15, 5,000), the slope is therefore;
m = (5,000 - 22,500)/(15 - 0) = -3,500/3
The equation is therefore;
V - 22,500 = -3,500/3·t
V = -3,500/3·t + 22,500
The equation for the value is; V = (22,500 -(3,500/3)·tc. The y-intercept of the trend line is (0, 22,500), which indicates that in the year 2,000, the price of the 2,000 Toyota Camry was $22,500
d. The slope of the trend line is -3,500/3 = -1,166.[tex]\overline 6[/tex], which indicates that the value of the Toyota Camry, 2000, reduces at a rate of $1,166.[tex]\overline 6[/tex], each year.
e. In the year 2017, t = 17, therefore;
V = 22,500 - (3,500/3) × 17 = 2,666.[tex]\overline {6}[/tex]
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Composition of functions worksheet
using f(x) = 8x squared and g(x) (2x+8), find:
The composition of the function are as follows:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10
What is a Composite Function?
If we are given two functions, we can compose one function into the other to produce a third function. The steps needed to complete this operation are the same as those needed to solve any function for any given value. These are referred to as composite functions.
We have,
i] f(x) = 8x and
g(x) = (2x+8)
(g ∘ g) (x) = g[g(x)]
Substitute x with (2x+8) in the function g(x) = (2x+8).
= 2((2x+8))+8
= 4x + 16
(f ∘ g) (x) = f [g (x)]
Substitute x with (2x+8) in the function f(x) = 8x.
(f ∘ g) (x) = 8(2x+8)
= 16x + 64
ii] f(x) = 6x + 2 and g(x) = x -5
f [g(7)] = 6(x-5) + 2
= 6x - 28
g [f(3)] = (6x + 2 ) - 5
= -30x - 10
Hence, the composition of the function is:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10
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A Pharmacist needs 100 gallons of 50% solution. She has available a 30% solution and an 80%. How much of each should she use? (Step-by-step answer)
Answer:
look below
Step-by-step explanation:
Step 1: Determine the amount of pure solvent needed.
100 gallons x 0.5 (50%) = 50 gallons of pure solvent
Step 2: Determine the amount of each solution to use.
30% solution: 50 gallons of pure solvent / 0.3 = 166.67 gallons of 30% solution
80% solution: 50 gallons of pure solvent / 0.8 = 62.5 gallons of 80% solution
Step 3: Total the amount of solution used.
166.67 gallons of 30% solution + 62.5 gallons of 80% solution = 229.17 gallons total
The table shows the weights of apples at a grocery store.
Answer:
Is that all
_______
_______
Read and try to solve the problem below.
Are -(-3m +6 - 12 + 15m) and 2(1 − 2m) equivalent expressions?
Show why or why not.
The given expressions are equivalent.
What is equivalent expression?
Expressions that function identically despite having different appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).
Consider the given expressions,
-(-3m + 6 - 12 + 15m) and 2(1 - 2m)
First simplify the expression -(-3m + 6 - 12 + 15m)
= 3m - 6 + 12 - 15m
= -12m + 6
Divide the expression by 3,
= -4m + 2
= 2 + 4m ..(1)
Now, consider the expression, 2(1 - 2m)
Simplifying this,
2(1 - 2m) = 2 - 4m ..(2)
From (1) and (2) we can see that the expressions are equivalent.
Hence, the given expressions are equivalent.
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Write each number in standard notation. 1.2 X 10^-3
Answer:3940
Step-by-step explanation:
Find the solution(s) of the system of equations. y = x2 + 4x y + x2 = –4x
A)
(0, 0)
B)
(–4, 0) and (4, 0)
C)
(–4, 0) and (0, 0)
D)
(0, 0) and (4, 0)
PLEASE HELP ME
...This is my homework and I don't understand how to do it.
The probability that a point chosen at random lies in the shaded region is 0.28
Calculating the area of a shaded region and probabilityFrom the question, we are to find the probability that a point chosen at random lies in the shaded region.
The shaded region is a triangle.
The probability that a point chosen at random lies in the shaded region = Area of the triangle / Area of the circle
First, we will calculate the unknown side of the triangle
Let the unknown side be x.
Then, from the Pythagorean theorem, we can write that
12² = 6² + x²
144 = 36 + x²
x² = 144 - 36
x² = 108
x = √108
x = 6√3
From formula,
Area of a triangle = 1/2 × base × height
Area of the triangle = 1/2 × 6 × 6√3
Area of the triangle = 18√3 square units
Now, we will determine the area of the circle
Area of a circle = πr²
Where r is the radius
From the given information,
Diameter of the circle = 12
But,
Radius = Diameter / 2
Therefore,
r = 12/2
r = 6
Thus,
Area of the circle = 3.14 × 6²
Area of the circle = 113.04 square units
Now,
The probability that a point chosen at random lies in the shaded region = 18√3 / 113.04
The probability that a point chosen at random lies in the shaded region = 0.2758
The probability that a point chosen at random lies in the shaded region ≈ 0.28
Hence, the probability is 0.28
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An empty cubical carton i of ide 9cm. Can you fit in 1000 1cm cube in it? Jutify
Answer: Side of an empty cubicle carton = 9 cm.
Now as we know that volume of the cube is the cube of its side.
So the volume of an empty cubicle carton having side 9 cm, V = (9)3=729 cm3.
Now we have to find out can 1000 cubes of side 1cm fit in it.
So the volume of the cube of side 1 cm is, V’ = (1)3=1 cm3
So the volume of the 1000 such cubes = 1000 (1) = 1000 cubic centimeters.
Now if the ratio of the volume of the empty cubicle carton to the volume of 1000 cubes of 1 cm is greater than 1 then we can will 1000 cubes of side 1 cm into an empty cubicle carton otherwise not.
So the ratio of the volume of the empty cubicle carton to the volume of the 1000 cubes is,
⇒VV′=7291000=0.729 < 1
So as we see that the ratio is less than one so we cannot fit 1000 cubes of side 1 cm into an empty cubicle carton of side 9 cm.
Step-by-step explanation:
I really hope this works!
Hope you Have a Great Day!! :)
Quick Someone Help!!! Please!
The endpoints of line segment AB are A (9,4) and B (5,-4). Then endpoints of its image after dilation are A' (6,3) and B' (3,-3). Find the scale factor and explain step by step
The image with line segment AB is dilated from (6, 3) and (3, 3) with scale factor of 1.8
DilationDilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape. Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor.
In this case, the image with endpoints of line segments AB which are (9, 4) and (5, -4) and dilated to become (6, 3) and (3, 3) would have a scale factor of;
scale factor = 9 * x = 5
x = 9 / 5 = 1.8
The scale factor is 1.8
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25.92x +5.15²* = 12.25²* ;
2-10 how do you solve this?
idddddddddddddddkkkkkkkkkkkkkkkkkkkkkkkk annnnthinggggggg
When 14 is subtracted from 6 times a number, 40 is left. What is half the number?.
The half of the number is 4.5 .
Given in question as 14 is subtracted from 6 times a number.
Let us suppose a number is x.
First find 6 times of a number = 6*x.
6 times can be defined as x + x + x + x + x + x = 6*x.
We have to subtract from 6 times a number.
14 is subtracted from 6 times a number means 6x - 14.
After subtracting 14 is left.
So 6x - 14 = 40.
Add 14 both side of equal sign.
6x-14+14 = 40+14.
6x = 54.
x = 54/6.
x = 9.
Half of the number x is 9/2 = 4.5.
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The speed of a space shuttle orbiting the earth is 17{,}600\,\text{mph}17,600mph17, comma, 600, start text, m, p, h, end text.
The graph below shows the distance ddd (in thousands of miles) traveled in ttt hours by a weather satellite orbiting the earth.
Which orbits the earth at a greater speed, the space shuttle or the weather satellite?
Answer: the space shuttle
Step-by-step explanation:
(1.5x10^-5) divided (3.0x10^4)
Answer:
1/2 x 1/10^-9
Step-by-step explanation:
(1.5x10^-5)/(3.0x10^4)
=> 1.5/3 x 10^-5/10^4
=> 1/2 x 10^-9
Answer:
= 5
Step-by-step explanation:
(1.5*10⁵) / (3.0*10⁴)
1.5*10⁵ = 15*10⁴
Then:
(1.5*10⁵) / (3.0*10⁴) = (15*10⁴) / (3*10⁴) = 15/3
= 5
answer these for slope the following questions or do I need to get a better picture?
The graph y = - 0.5x + 12 has a slope of - 0.5 and decreases in nature.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, harper created a graph of a line by y = - 0.5x + 12.
∴ The graph will have a slope of - 0.5 which is decreasing in nature.
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Clip 136 Rearranging Simple Formulae - Question 4
Standard Questions
Question Progress
Make r the subject of x=e+r/d
Answer:
r = d(x-e)
or r = dx - de
Step-by-step explanation:
x = e + [tex]\frac{r}{d}[/tex] subtract e from both sides.
x - e = [tex]\frac{r}{d}[/tex] Multiply both sides by d
d(x -e) = r
or
dx -de = r
Under his cell phone plan, liam pays a flat cost of $69. 50 per month and $5 per gigabyte. He wants to keep his bill under $90 per month. Write and solve an inequality which can be used to determine xx, the number of gigabytes liam can use while staying within his budget.
The inequality given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
Let the number of gigabytes consumed be x,
The total cost per month will be 69.50 + 5x
accoding to the question the bill would not exceed $90.
So the inequality,
69.50 + 5x ≤ 90
Simplification for the maximum gigabyte he can buy,
5x ≤ 90 - 59.90
5x ≤ 20.5
x ≤ 4.1
Hence, the required inequality is given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.
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In five years Angela will be the age that Khalil is now. In three years, Khalil will be twice as old as Angela. How old are they now?
The current age of Angela and Khali by the formation of the equation will be 2 and 7 years old.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Suppose the current age of Angela is A while Khali is K.
In 5 years,
A + 5 = K
In 3 years,
K + 3 = 2(A + 3)
K + 3 = 2A + 6
K + 3 = 2(K - 5) + 6
K + 3 = 2K - 10 + 6
2K - K = 3 + 4
K = 7 years old,
A = 7 - 5 = 2 years old.
Hence "The current age of Angela and Khali by the formation of the equation will be 2 and 7 years old".
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does a gasoline additive improve mileage? drivers logged their mileage on a tank of gas with and without the additive. the sample of 10 drivers had an average difference (with additive - without) in mileage of 4.1 mpg with a standard deviation of 5 mpg. what is the test statistic for this test?
The test statistic for the given test is t = 2.59.
What is a standard deviation?
The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.
Given data:
[tex]\bar D[/tex] = 4.1, Sd = 5, n = 10, μd = 0
Now the test statistic can be computed as
[tex]t=\frac{\bar D-\mu_d}{S_d/\sqrt{n} }[/tex]
[tex]t=\frac{4.10-0}{5/\sqrt{10}} \\\\t=2.59[/tex]
Hence, the test statistic for the given test would be t = 2.59.
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Factorise fully the following:
4x³ + 24x²
Answer:
4 x^3 + 24 x^2 = 4 (x^3 + 6 x^2) = 4 x^2 (x + 6)
4 x^2 (x + 6) seems to be the lowest factor
Scott bought a desktop computer and a laptop computer. Before finance charges and the laptop cost $350 more than the desktop. He paid for the computers using two different financial plans. For the desktop the interest rate was 6.5% per year and for the laptop it was 9% per year. The total finance charges for one year for $388. How much did each computer cost before finance charges
The cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.
What are mathematics operations?A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value.
From the question , we are given that the laptop costs $350 more than the desktop, therefore,
let x represent the cost of the laptop thus, x-350 will be the cost of the desktop .
The total finance charge of $388 is equal to 8% of the cost of the laptop and 7.5% of the cost of the desktop, we solve as;
388 = 0.08(x) + 0.075(x - 350)
252 = 0.08x + 0.075x - 26.25
278.75 = 0.155x
x = 278.75/0.155
x = 1798
Recall that the cost of desktop = x -350
therefore:
1,798- 350 = 1448
The cost of laptop = $1798
The cost of desktop = $1448
Thus, the cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.
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find the perimeter of the triangle. a triangle is drawn. all the angles of the triangle are marked with a single arc. three sides of a triangle are labeled (x plus 5 )inches, (2 x minus 3 )inches and (21 minus x )inches.
If the three sides of the triangle is (x + 5), (2x - 3), (21 - x), then the perimeter of the triangle is 23 + 2x
The perimeter of the triangle is the summation of all three sides of the triangle
Perimeter = a + b + c
= (x + 5) + (2x - 3) + (21 - x)
= 2x + 23
= 23 + 2x
Therefore, if the three sides of the triangle is (x + 5), (2x - 3), (21 - x) then the perimeter of the triangle 23 + 2x.
Any two-dimensional figure's perimeter is determined by the space surrounding it. By adding the lengths of the sides, we can determine the perimeter of any closed shape.
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The best fitting line is one where the intercept of the regression equation: a, is closest to zero. slope of the regression equation,
b, is closest to zero. residual sum of squares is closest to zero.
c. variance of Y is large.
The best fitting line is one where the intercept of the regression equationrResidual sum of squares is closest to zero. So the option c is correct.
In the given question,
The best fitting line is one where the intercept of the regression equation:
Intercept of the regression equation, a, is closest to zero. Slope of the regression equation, b, is closest to zero. Residual sum of squares is closest to zero.variance of Y is large.As we know that;
The slope of the line of best fit is the coefficient in a simple regression with a single independent variable. The slope is a mixture of the two coefficients in this example and in any regression with two independent variables. The y-intercept of the line of best fit is constant C.
So, the best fitting line is one where the intercept of the regression equationrResidual sum of squares is closest to zero. So the option c is correct.
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