Answers
Answer:
• Initial value: $26,000.
,• Value after 12 years: $1,319
Explanation:
The value of a car model that is t years old is given by the function:
[tex]v(t)=26,000(0.78)^t[/tex](a)The Initial Value
At the initial point of purchase, the value of t=0.
[tex]\begin{gathered} v(0)=26,000(0.78)^0 \\ =26000\times1 \\ =\$26,000 \end{gathered}[/tex]The initial value is $26,000.
(b)Value after 12 years
When t=12:
[tex]\begin{gathered} v(12)=26,000(0.78)^{12} \\ =1318.6 \\ =\$1,319 \end{gathered}[/tex]The value of the car after 12 years is $1,319 (correct to the nearest dollar).
Related Questions
Hello please help I don’t know what I’m doing wrong
Answers
Explanation:
The domain of a function is the input value of any function for which the function exists.
For the function;
(f+g)(x) = 2x² + x
From the given function, we can see that the function will exist for all values of x i.e. the input variable exists on all real values.
The domain of the function in interval notation will be expressed as
(-∞, ∞)
For the function (f-g)(x) = x
Similarly for this function, the input variable exists on all real values.
The domain of the function in interval notation will be expressed as
(-∞, ∞)
For the function (fg)(x) =x^4 + x^3
Also for this function, the input variable exists on all real values.
The domain of the function in interval notation will be expressed as
(-∞, ∞)
For the function given as (f/g)(x) = 1 + 1/x
The function will not exist when x = 0. The function will be undefined at this point. The required domain of this function in interval notation will be:
[tex]D=(-\infty,0)U(0,\infty)[/tex]
what is the volume of the can in cubic inches in terms of
Answers
Given data:
The height of the cylinder is h=9 in.
Th diameter of the cylinder is d=6 in.
The expression for the volume of the cylinder is,
V=(πd^2h)/4
Substitute the given values in the above expression.
[tex]\begin{gathered} V=\pi(6in)^2(9\text{ in)}\frac{1}{4} \\ =81\pi in^3 \end{gathered}[/tex]Thus, the volume of the given figure is 81 in^3. so C) option is correct.
Which one of the following equations defines the line that contains the point (1,2) and is parallel to the line 4x+3y=7?
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If Lydia invests $3000 in a certificate of deposit and d dollars in a stock, write an expression for the total amount she invested.
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ANSWER:
[tex]\text{ total amount }=3000+d[/tex]STEP-BY-STEP EXPLANATION:
The total invested is equal to 3000 investment and the previous money in stock, therefore, the expression would be:
[tex]\text{ total amount }=3000+d[/tex]What is the value of sin C? a) 15/17b) 15/8c) 8/15d) 8/17
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Answer:
d) 8/17
Explanation:
From trigonometry, we know that in a right triangle:
[tex]\sin \theta=\frac{Opposite}{\text{Hypotenuse}}[/tex]From the diagram:
• The side, opposite C, is 8.
,• The ,hypotenuse, is 17.
Therefore:
[tex]\sin C=\frac{8}{17}[/tex]So basically I have to reflect triangle STU across line ST and I need to find a valid reason of why the image of U will coincide with J. I need guidance please
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Solution
- The reflection of an object across a line implies that the distance between the object and the reflection line is the same as the distance between the image and the reflection line.
- This implies that if the distance between the point U and the reflection line ST is x, then, the distance between the reflection line and the image of U must be a distance of x as well.
- This is illustrated below:
- From the above, we can see that distance x is a perpendicular distance from point U to reflection line ST.
- However, we must not just assume that distance x lands at point J.
- We can however show that this is the case because of the SSS congruency. That is,
[tex]\begin{gathered} SU\cong SJ\text{ \lparen Given in the question\rparen} \\ UT\cong TJ\text{ \lparen Given in the question\rparen} \\ ST\text{ is a common side for both triangles SUT and SJT} \end{gathered}[/tex]- Since both triangles are congruent, we can proceed to conclude that from line ST to point J is also a distance of x.
- Therefore, the image of U will coincide with J given that ST is the reflection line
If the measures of two pair of complementary angles are added together then the sum is equal to the measures of two right anglestrue or false
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ANSWER : FALSE
EXPLANATION : The sum of two complementary angles is 90°. Adding the measure of two right angles (right angles is a 90° angle) is equal to 180°.
Therefore, adding the two pairs of complementary angles is not equal to the sum of two right angles.
The coach is building shelves to store and organize the team’s collection of 175 game videos how many shelves will be needed if one shelf holds 28 videos?
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7 shelves will need to store and organize the team's collection of 175 game videos.
Given:
The team’s collection of 175 game videos.
one shelf holds 28 videos.
Number of shelves = total videos/one shelf hold capacity.
= 175/28
= 6.25
since we cannot have 0.25 shelf we take it as 1.
So number of selves = 7 shelves.
Therefore 7 shelves will need to store and organize the team's collection of 175 game videos.
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Give the name of the parent function and describe the transformation represented.
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5 units to the left and 2 units downwards
Explanation:[tex]f(x)\text{ = |x + 5| - 2}[/tex]The parent function:
f(x) = |x|
Name of parent function is absolute value function
The transformtion from parent function to the new function:
[tex]\begin{gathered} \text{from f(x) = |x| to f(x) = |x + 5| - 2} \\ \text{For translation:} \\ f(x)\text{ = |x + a| (translation to the left)} \\ f(x)\text{ = |x - a| (translation to the right)} \\ \\ So\text{ f(x) = |x + 5| is a translation of 5 units to the left} \end{gathered}[/tex][tex]\begin{gathered} For\text{ translation: } \\ f(x)\text{ = |x| + a (translation upwards)} \\ f(x)\text{ = |x| }-\text{ a (translation downwards)} \\ \\ So\text{ f(x) = |x| - 2 is a translation downwards} \end{gathered}[/tex]Combining both transformation:
f(x) = |x + 5| - 2 is a translation of 5 units to the left and 2 units downwards
3. Brust is riding his bicycle north away from an intersection at a rate of 15 miles per hour. Sully is driving his car towards the intersection from the west at a rate of 30 miles per hour. If Brust is 0.4 miles from the intersection, and Sully is 1 mile from the intersection, at what rate is the distance between the two of them increasing or decreasing?
Answers
The graph shows the situation of Brust and Sully. The distance between them is d
If x is the distance from Sully to the intersection and y is the distance from Brust to the intersection, the distance d is
[tex]d=\sqrt[]{x^2+y^2}[/tex]The rate of change of d in time is computed by taking the derivative:
[tex]d^{\prime}=\frac{xx^{\prime}+yy^{\prime}\text{ }}{\sqrt[]{x^2+y^2}}[/tex]We have the following parameters:
x=1, y=0.4, x'=-30, y'=15
Substituting:
[tex]d^{\prime}=\frac{(1)(-30)+(0.4)(15)\text{ }}{\sqrt[]{1^2+0.4^2}}[/tex]d' = -22.3 miles per hour
Since d' is negative, the distance is decreasing
HELPPP I also have to round it yo the nearest tenth if possible
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In a circle v, UTw =50 solve for X . If mUW= (9x-34)
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Answer:
X=14.9
Step-by-step explanation:
mUW=2 . m <utw
so (9x - 34) = 2.50
9x - 34 = 100
x = 14.9
I need help with number 5. Here is the problem:Injured runners train on a special track at a rehabilitation center. The track is a square with a half circle on its left and right sides. The area of the square is 128 square feet. What is the length of the track? Use the table to help you answer the questions.
Answers
To have a pictorial representation of this problem (the track), we will have the figure below:
To find the length of the track, we will sum up the length of two sides of the square and the circumference of the two half semicircles.
We will find the length of the square thus:
[tex]\begin{gathered} A=l^2 \\ 128=l^2 \\ \sqrt[]{128}=l \\ 11.314ft=l \\ \text{Each side of the square is 11.314ft} \end{gathered}[/tex]Now we will find the circumference of a half-circle:
[tex]=\frac{\pi D}{2}[/tex]Since the length of the square is also the diameter of the half circle:
[tex]\begin{gathered} D=l=11.314 \\ \text{Circumference of half-circle:} \\ =\frac{\pi(11.314)}{2} \\ =17.772ft \end{gathered}[/tex]The length of the track will be calculated with this expression:
[tex]=\text{length of two sides of the square + circumference of two half-circles}[/tex][tex]\begin{gathered} =2(11.312ft)+2(17.772ft) \\ =22.624ft+35.544ft \\ =58.168ft \\ \text{The length of the track is 58.168ft} \end{gathered}[/tex]part A Jasmine ran 5 miles in 42 minutes at what rate did Jasmine run Jasmine ran at a rate of ? minutes per mile
Answers
We will find the rate as follows:
[tex]r=\frac{5}{42}[/tex]So the rate is the distance divided by the time it took to traverse.
100 divided by 72,144
Answers
Answer:0.00138611665
Step-by-step explanation:
what is 13 divided by 113.1
Answers
A Little League baseball diamond has four bases forming a square whose sides measure 60 feet each. The pitcher's mound is 46 feet from home plate on a line joining home plate and second base. Find the distance from the pitcher's mound to third base. Round to the nearest tenth of a foot.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Square
side = 60 feet
pitcher's mound from home plate = 46 feet
distance from the pitcher's mound to third base = ?
Step 02:
Diagram:
Step 03:
distance from the pitcher's mound to third base
side 1 = 60
side 2 = 46
angle 1 = 90 / 2 = 45
a ² = b ² + c ² - 2 * b * c* Cos A
a ² = 60² + 46² - 2(60)(46) Cos 45
a² = 1812.771
a = √1812.771
a = 42.576
The answer is:
The distance from the pitcher's mound to third base is 42.6 feet.
a cube has a volume of seven units. what is the edge length of a cube?
Answers
Given:
The volume of the cube = seven units.
Let a be the edge length of the cube.
Consider the formula for the volume of the cube.
[tex]V=a^3[/tex]Substitute V=7 in the formula, we get
[tex]7=a^3[/tex]Taking cubic root on both sides, we get
[tex]\sqrt[3]{7}=a[/tex][tex]T\text{he edge length of the given cube is }\sqrt[3]{7}\text{ units.}[/tex]or
[tex]T\text{he edge length of the given cube is }1.91\text{ units.}[/tex]Simplify the following expression by distributing and combining like terms.-5(k+6) + 7(k-4)
Answers
The given expression is
[tex]-5(k+6)+7(k-4)[/tex]To solve this, first, we use the distributive property.
[tex]-5(k+6)+7(k-4)=-5k-30+7k-28[/tex]Then, we reduce like terms.
[tex]2k-58[/tex]Therefore, the simplest form of the given expression is 2k - 58.10b-2x+6 True or False is the expression contains 3 terms
Answers
It is true because they are not similiar.
A Labrador retriever weighs 50kg. After a diet and exercise program the dog weighs 41kg. What is the percentage loss in weight.
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inital weight = 50 kg
Final weight = 41 kg
loss = 50 - 41 = 9 kg
[tex]\begin{gathered} \text{percentage loss=}\frac{9}{50}\times100 \\ \text{percentage loss=}\frac{900}{50} \\ \text{percentage loss = }18\text{\%} \end{gathered}[/tex]y=-2x + 4 3y + 6x = 12 O One Solution O No Solutions o Infinitely Many Solutions
Answers
To find the number of solutions of a system of linear equations you need to identify the slope (m) of each equation
[tex]y=mx+b[/tex]If the slope is the same in both lines the system has no solution.
If the slope is different in the lines the system has one solution.
If the equation are the same (incluided the value of b) the system has infinitely many solutions.
In the given equations the slope is:
First equation:
[tex]y=-2x+4[/tex]Slope: m=-2Second equation:
[tex]3y+6x=12[/tex]Write the equation in slope-intercept form by solving for y:
[tex]\begin{gathered} 3y+6x-6x=-6x+12 \\ 3y=-6x+12 \\ \\ y=-\frac{6}{3}x+\frac{12}{3} \\ \\ y=-2x+4 \end{gathered}[/tex]Slope: m= -2In this case as the equatinos are the same the system has infinitely many solutionsfelicia owns 80 shares of electrify us power cooperative that pay dividends of $129. at this rate, what dividend would felicia recive after buying 600 shares.
Answers
The dividend that Felicia will receive after buying 600 shares is $967.50.
How to calculate the value?Dividends are regular profit-sharing payments made by a company to its shareholders. The board of directors of a company decides on the price per share as well as when and how often dividend payments are made. Dividend stocks can provide a steady stream of income, which is especially valuable during times of inflation.
From the information, Felicia owns 80 shares of electrifying us power cooperative that pay dividends of $129. It should be noted that the dividend rate will be:
= $129 / 80
= $1.6125
Therefore, the amount for 600 shares will be:
= 600 × $1.6125
= $967.50
The dividend is $967.50.
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Find the distance between the pair of points below to the nearest tenth, if necessary (-2,3), (6,9)
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We can find the distance between the points by means of the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]where
[tex]\begin{gathered} (x_1,y_1)=(-2,3) \\ (x_2,y_2)=(6,9) \end{gathered}[/tex]By substituting these values into the distance formula, we have
[tex]d=\sqrt{(6-(-2))^2+(9-3)^2}[/tex]which gives
[tex]\begin{gathered} d=\sqrt{(6+2)^2+6^2} \\ d=\sqrt{8^2+36} \\ d=\sqrt{64+36} \end{gathered}[/tex]so we have
[tex]\begin{gathered} d=\sqrt{100} \\ d=10 \end{gathered}[/tex]Therefore, the distance between the two points is 10 units.
Jennifer. Leigh Anne, and Karyn went out to eat. Jennifer bought an entrée for $12.95 and split a $4.95 dessert with Karyn, who bought a sandwich for $7.95. Leigh Anne bought soup for $3.95, a salad for $6.95, and coffee for $1.70. Determine the total amount each should pay if tax is 6% and each one tips 15% of her individual bill rounded up to the next quarter.
Answers
The total amount Leigh Anne spent is $3.95 plus $6.95 plus $1.7, that is $12.6. Since they pay a tax of 6% and a tip of 15%, she pays a total of 21% extra; this 21% can be obtained by the tule of three:
[tex]\begin{gathered} 12.6\rightarrow100 \\ x\rightarrow21 \end{gathered}[/tex]then:
[tex]x=\frac{21\cdot12.6}{100}=2.65[/tex]Therefore, Leigh Anne spent a total of $15.25.
Assuming the dessert was split in half, then Jennifer spent a total of $15.43. To this amount we have to add the tax and tip. By the same logic as before we have:
[tex]\begin{gathered} 15.43\rightarrow100 \\ x\rightarrow21 \end{gathered}[/tex]then:
[tex]x=\frac{21\cdot15.43}{100}=3.24[/tex]Therefore, Jennifer spent $18.75
Finally Karyn spent $10.43, obtaining the extra amount we have:
[tex]\begin{gathered} 10.43\rightarrow100 \\ x\rightarrow21 \end{gathered}[/tex]Then:
[tex]x=\frac{21\cdot10.43}{100}=2.19[/tex]Therefore, Karyn spent $12.75.
Your employer promises after 6 months to give you a 15% pay raise in addition to your new pay. How much will your monthly income be after the 15% pay increase?
Answers
Lets assume that the actual pay is the 100%, if after 6 months you get a rais of 15% in addition of your new pay, then the monthly income after the raise will be the 115% of the actual pay
Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places.
Answers
In order to solve this problem, we need to change the base of the logarithm function so we can use the calculator to solve it. One possible way to do it is by writing it in base 10.
We have:
[tex]\log _ba=\frac{\log _{10}a}{\log _{10}b}[/tex]In this problem, we have:
a = 47
b = 8.1
So, we can write
[tex]\log _{8.1}47=\frac{\log _{10}47}{\log _{10}8.1}[/tex]Now, using a calculator, we obtain:
[tex]\frac{\log_{10}47}{\log_{10}8.1}\cong1.841[/tex]Therefore, the last option is correct.
A physical education teacher plans to divide the seventh graders at Wilson Middle School into teams of equal size for a year-ending mock Olympic event. He wants each team to have between 6 and 10 students, and all teams need to have the same number of students. The seventh grade at Wilson consists of three classes; one with 20 students, one with 33 , and one with 26 . How many students should be on each team?
Answers
First let's find the total number of students:
[tex]S=20+33+26=79[/tex]Now, let's divide this total by 6, 7, 8, 9 and 10, and check if the result has no remaining (that is, the result is a whole number):
[tex]\begin{gathered} \frac{79}{6}=13.167 \\ \\ \frac{79}{7}=11.286 \\ \\ \frac{79}{8}=9.875 \\ \\ \frac{79}{9}=8.778 \\ \\ \frac{79}{10}=7.9 \end{gathered}[/tex]Since none of the results is a whole number, it's impossible to divide these students in teams with the same number of students.
Therefore the correct option is the second one.
Assignment 10-1 A Triangle ABC = Triangle S B U
Answers
we know that
If two triangles are congruent, then its corresponding sides and corresponding angles are congruent
Remember that
Corresponding sides are named using pairs of letters in the same position on either side of the congruence statement
so
In this problem
ST=AB
SU=AC
UT=CB
therefore
Triangle
ABC=STU10 Find x. 30° 5V3 10 5 73 1073
Answers
Do you have a pcture of this problem?
thanks
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