Using an exponential function, it is found that the equation that represents the value of the car after 5 years is:
[tex]A(5) = 21800(0.905)^5 = 13234.25[/tex]
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the car is purchased for 21,800 dollars, and it's value deprecites 9.5% per year, hence the equation for it's value after t years is given by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 21800(1 - 0.095)^t[/tex]
[tex]A(t) = 21800(0.905)^t[/tex]
After 5 years, the value is given by:
[tex]A(5) = 21800(0.905)^5 = 13234.25[/tex]
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Which expression is equivalent to the expression -3(4x - 2) - 2x
A) -8x
B) -16x
C) -14x - 2
D) -14x + 6
Answer:
-14x + 6 (option D)
Step-by-step explanation:
To solve the given equation, you first need to distribute the negative 3.
So, you need to multiply
(4x)(-3) ; (-2)(-3)
(4x)(-3)= -12x
(-2)(-3)= 6
So, your new, distributed, equation would be:
-12x + 6 - 2x
If we combine like terms (-12x - 2x), our new equation will be:
-14x + 6
A cone-shaped lampshade has a height of 18 cm and a slant height of 19.5 cm. Find the lateral surface area of the lampshade.
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{19.5^2-18^2}=r\implies \sqrt{56.25}=r \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\ \stackrel{slant~height}{\sqrt{r^2+h^2}}\\[-0.5em] \hrulefill\\ r=\sqrt{56.25} \end{cases}\implies \begin{array}{llll} LA=\pi \sqrt{56.25}\stackrel{slant~height}{(19.5)} \\\\\\ LA\approx 459.46~cm^2 \end{array}[/tex]
Sam is renting one of two cars to go on a 300-mile trip. The first car can travel 75 miles on 5 gallons of gas. The second car can travel 240 miles on 20 gallons of gas. Each car costs the same to rent, and Sam wants to rent the car with the better gas mileage. Sam estimates that he will pay $49.49 for every 14 gallons of gas he has to buy. Which car should Same rent, and how much money should Sam bring for gas? Explain your reasoning
Inscribed angle
Help please
Answer:
x = 3
Step-by-step explanation:
The measure of the inscribed angle is half of measure of the intercepted arc .
Find the half of 192.
192/2 = 96
The inscribed angle is 96°.
Create an equation and solve for x.
31x + 3 = 96
31x + 3 - 3 = 96 - 3
31X = 93
31x/31 = 93/31
x = 3
HELP ME PLEASE. THIS IS MY LAST QUESTION THEN I CAN GO TO BED.
Answer:
100.
Step-by-step explanation:
The 2 smaller triangles are similar, so:
48 / (x - 64) = 64 / 48
64(x - 64) = 48^2
x - 64 = 48^2/64
x = 48^2/64 + 64
= 100.
HELP!! Using the geometric sequence 2,2/3,2/9,. ,2/243, find the approximate sum of the geometric series. Round your answer to the nearest whole number.
Answer choices:
4
3
1
6
we can always get the common ratio of a geometric sequence by simply dividing the current term by the previous term, in this case for the sake of simplicity let's divide 2/3 by 2, so
[tex]\cfrac{2}{3}\div 2\implies \cfrac{2}{3}\div \cfrac{2}{1}\implies \cfrac{2}{3}\cdot \cfrac{1}{2}\implies \cfrac{1}{3}\impliedby \textit{common ratio}[/tex]
so the sequence more or less looks like [tex]2~~,~~\cfrac{2}{3}~~,~~\cfrac{2}{9}~~,~~\cfrac{2}{81}~~,~~\cfrac{2}{243}[/tex]
so we'd want the sum of the first 5 terms
[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio} \end{cases} \\\\\\ S_5=2\left( \cfrac{1~~ - ~~(\frac{1}{3})^5}{1~~ - ~~\frac{1}{3}} \right)\implies S_5=2\left( \cfrac{~~\frac{242}{243}~~}{\frac{2}{3}} \right)\implies S_5=\cfrac{242}{81}\implies S_5=2\frac{80}{81}[/tex]
I think of a number multiply it by 2, subtract 3 and multiply by 4
Step-by-step explanation:
(2x - 3)×4
random number multiplied by 2, then minus 3 from that result, and multiply that result by 4.
please only geniussssssssssssssssss
Check the picture below.
I need this ASAP PLS
(will give brainliest)!
Answer:
The answer is A since it does the same movements twice. Think of it like flipping a coin, then actually taking the coin and flipping it back over regardless of what it lands on.
Step-by-step explanation:
Hope this helps have a good rest of your day
Identify the domain and range of the relation.
x −5 −2 1 5
y 10 11 4 10 what is the function
Answer:
Domain: -5, -2, 1, 5
Range: 10, 11, 4, 10
To get the function, you need to create an equation.
Step-by-step explanation:
For example, f(x)= 10x. "x" equals your y value, and "10" is where you plug in your range, or in other words, your y-values.
1. A wooden box is to be built so that it measures 156 cm by 122 cm by 95 cm.
How much plywood will it take to build the garbage bin?
The amount of plywood needed to build the garbage bin is the surface area. Therefore, the amount of plywood needed is 90884 cm².
How to find the surface area of a rectangular prismThe wooden box is a rectangular prism. The amount of plywood used to construct the wooden box is the surface area of the box.
Therefore,
surface area of rectangular prism = 2(lw + lh + hw)
where
l = lengthw = widthh = heightl = 156 cm
w = 122 cm
h = 95 cm
surface area of rectangular prism = 2((156 × 122) + (156 × 95) + (122 × 95))
surface area of rectangular prism = 2(19032 + 14820 + 11590)
surface area of rectangular prism = 2(45442)
surface area of rectangular prism = 90884 cm²
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21. 2n= 53
Explanation of the division please, and how you got the answer
Answer:
2n= 53
and you divide both sides by 2
2n/2 =53/2
2 divided by 2 is 1 and 53 divided 2 is 26.5
n= 26.5
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
What value of p makes the equation true?
Answer:
1/8
Step-by-step explanation:
●●○•°°°□□●○○○○○••••
please help me bro please
What is the slope of the line that passes through the points (−2,−4) and)(3,−9)? Write your answer in simplest form.
Answer:
The slope is -1
Step-by-step explanation:
Formula for finding slope: [tex]\frac{rise}{run} = \frac{y2 - y1}{x2-x1}[/tex]
we got the points:
(−2,−4) and)(3,−9)
let's plug them in.
[-9-(-4)] / [3-(-2)] =
-5 / 5 = -1
What is the image point of (5,-6)(5,−6) after the transformation r_{\text{y-axis}}\circ T_{-4,0}r
y-axis
∘T
−4,0
?
The image point of P(x,y) = (5, -6) after applying a horizontal reflection is P'(x,y) = (1, -6).
How to apply a rigid transformation in a point on a Cartesian plane
In geometry, a rigid transformation is a transformation applied onto a geometric object such that Euclidean distance in every point of it is conserved. Translations are examples of rigid transformations and are defined by this formula:
P'(x,y) = P(x,y) + T(x,y) (1)
Where:
P(x,y) - Original pointT(x,y) - Translation vectorP'(x,y) - Image pointIf we know that P(x,y) = (5, -6) and T(x,y) = (-4, 0), then the image point is:
P'(x,y) = (5, -6) + (-4, 0)
P'(x,y) = (1, -6)
The image point of P(x,y) = (5, -6) after applying a horizontal reflection is P'(x,y) = (1, -6). [tex]\blacksquare[/tex]
Remark
Statement is incorrect and poorly formatted. Correct form is shown below:
What is the image point of (x, y) = (5, -6) after the transformation of translating horizontally the point -4 units to the y-axis?
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If two men walk in opposite directions for 8 meters then turn left and walk six meters how far apart are they
Answer:
20 meters
Step-by-step explanation:
Help please cus I don't know.
Answer:
114
Step-by-step explanation:
just add all sides together.
Answer:
91 cm
Step-by-step explanation:
Perimeter is adding all of the side lengths:
8+32+10+10+4+4+23=91
Don't forget to add the unit:
91 cm
1/(x+1) divided by 4/(x+1)+6/x
Answer:
4x/(x+1)(x2+x+6)
Step-by-step explanation:
1/2x12divided by 2-2 +11= what?
Answer:
The answer is 12
Step-by-step explanation:
1/2x 12 = 6
6/2-2+11 = 12
The final answer is 12
PLEASE HELP A.S.A.P.!
Solve the equation:
|x-1|+|x-2|=3
PLS HELP
Lacey has a roll of wrapping paper with 2 3/4 yards remaining. She has six boxes to wrap, each of which requires 3/8 of a yard of paper. Will Lacey have enough wrapping paper left to also wrap a book that requires 1/2 yard of paper? Support your answer by showing your work.
Answer: Yes
Step-by-step explanation:
Step #1: Lacey has 2 3/4 yards of wrapping paper remaining. She has six boxes to wrap, each of which requires 3/8 of a yard of paper. First, you must find the total number of yards of wrapping paper needed for six boxes.
Number of boxes * Number of wrapping paper required for each box
6 x 3/8 = 9/4
Step #2: Subtract the number of yards of wrapping paper remaining by the total number of wrapping for 6 boxes.
2 3/4 - 9/4 = 1/2
Step #3: Determine and solve whether Lacey will have enough wrapping paper left to also wrap a book that requires 1/2 yard of paper. To solve, subtract the remaining amount of wrapping paper by the amount of wrapping required for a book.
1/2 - 1/2 = 0
So, yes Lacey will have just enough wrapping paper to also wrap a book that requires 1/2 yard of paper.
The correlation between two scores X and Y equals 0.75. If both scores were converted to Z-scores, then the correlation between the z-scores
for X and z-scores for Y would be
-0.75
0.25
-0.25
0.0
0.75
Answer:
(e) 0.75
Step-by-step explanation:
The correlation coefficient is not affected by translation or scaling of scores. Converting them from "raw scores" to z-scores does not affect their correlation.
The correlation coefficient of the z-scores is 0.75.
Khalil has a game board as shown below, which is a square with 20 cm sides. The area of the largest circle is 314
square centimeters
What is the probability of scoring 1, 3, or 5 points with one randomly thrown dart?
O 50%
O 62.5%
O75%
O78.5%
Answer:
78.5
Step-by-step explanation:
The probability of scoring 1 , 3 or 5 points is 78.5% ( optionD)
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 and it's 100% in percentage.
probability is expressed as;
probably = sample space/total outcome
The area of the square is expressed as;
A = l²
= 20 × 20
= 400cm²
The area of the biggest circle is 314 cm²
The probability of scoring 1, 3 or 5
= 314/400 = 0.785
in percentage = 0.785 × 100
= 78.5%
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I’m very stuck and someone give the answer
Answer:
since there are 30 students as a whole and 20 boys make up part of the class, you can assume that there are 10 girls in the class. since the mean mark for boys is 62 I think the mean mark for girls would be 8%
Step-by-step explanation:
How is the graph of the parent function, y = StartRoot x EndRoot transformed to produce the graph of y = StartRoot negative 2 x EndRoot? It is translated horizontally by 2 units and reflected over the x-axis. It is translated horizontally by 2 units and reflected over the y-axis. It is horizontally compressed by a factor of 2 and reflected over the x-axis. It is horizontally compressed by a factor of 2 and reflected over the y-axis.
Answer:
The answer is D
Step-by-step explanation:
The parent function will be reflected over the x-axis, compressed by a factor of 0.4, and translated into 2 units right.
It is given that the two functions one is the parent function [tex]\rm y = \sqrt[3]{-x}[/tex] and the transformed function [tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex].
It is required to find the transformation rules.
What is a function?It is defined as a special type of relationship and they have a predefined domain and range according to the function.
We have parent function:
[tex]\rm y = \sqrt[3]{-x}[/tex]
and transformed function:
[tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex]
If we multiply the parent function with a negative value it will f(x) over the x axis.
By the transformation rules of the function y = -f(x) reflects f(x) over x-axis.
After applying the transformation to the parent function:
[tex]\rm y = -\sqrt[3]{-x}[/tex]
By the transformation rules of the function if multiply the function with less than the unit value it will be compressed by the multiplied factor ie.
y = k f(x) and k<1, the function will be compressed by the k factor hence:
[tex]\rm y = -0.4\sqrt[3]{-x}[/tex] (after applying the second transformation)
As we can see the transformed function is subtracted by -2
By rules of transformation, for y=f(x-A) it would be a horizontal translation of 'A' unit to the right.
After applying this transformation we get:
[tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex] which is a transformed function derived after applying the transformation to the parent function.
Thus, the parent function will be reflected over the x-axis, compressed by a factor of 0.4, and translated into 2 units right.
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You put the name of all the students in your class in a paper bag. There are 14 boys and 16 girls. If
you draw a name at random, what is P(girl's name)?
A: 7/15
B: 8/7
C: 8/15
D: 7/8
21b-32+7b-20b=?
Tell fast pls
21b-32+7b-20b=
21b + 7b - 20b - 32
8b - 32
Hello!
21b-32+7b-20b=
21b +7b -20b -32
= 28b -20b - 32
= 8b -32
Ginger and Caleb each have 0.77 of a dollar. Ginger does not have any quarters. Caleb does not have any dimes. Explain how many of each type of coin each of them might have.
Ginger can have 7 dimes and 7 pennies while Caleb can have 3 quarters and 2 pennies.
What is an equation?An equation is an expression used to show the relationship between two or more numbers and variables.
Ginger and Caleb each have $0.75
Ginger does not have any quarters. He might have 7 dimes and 7 pennies.
Caleb does not have any dimes. He can have 3 quarters and 2 pennies.
Ginger can have 7 dimes and 7 pennies while Caleb can have 3 quarters and 2 pennies.
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Q10.
At work Liv puts apple pies into boxes.
Liv has 42 apple pies.
Each full box has 9 apple pies.
How many full boxes of apple pies does Liv have?
Show how many apple pies are left over.
Show your working and your answers in the box below.
Answer:
He has 4 full boxes
6 Apple pies are leftover
Step-by-step explanation:
42/9 = 4.67 How many full boxes can he fill
9 X 4 = 36 He filled out 4 full boxes
42-36=6 Total - Filled = Remainder
Answer:
she has 4 full boxes of applepies and she has 6 leftover apple pies
Step-by-step explanation: