Using an exponential function, it is found that it takes 5.42 years for the car to halve in value.
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 depreciates 12% a year in value, hence r = 0.12 and the equation is given by:
[tex]A(t) = A(0)(0.88)^t[/tex].
It halves in value at t years, for which A(t) = 0.5A(0), hence:
[tex]A(t) = A(0)(0.88)^t[/tex]
[tex]0.5A(0) = A(0)(0.88)^t[/tex]
[tex](0.88)^t = 0.5[/tex]
[tex]\log{(0.88)^t} = \log{0.5}[/tex]
[tex]t\log{0.88} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.88}}[/tex]
t = 5.42.
It takes 5.42 years for the car to halve in value.
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Help me please. I need the answer and method of how you got your answer asap.
Answer:
60 degrees
Step-by-step explanation:
a straight line is equal to 180 degrees. 180 - 120 = 60 degrees for x
Answer:
60 degrees
Step-by-step explanation:
both big angles are 120. 12x2=240, 360-240=120, half 120= 60.
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
20 units
Step-by-step explanation:
Given: Bases of the trapezoid
[tex]b_1 = 14\: units [/tex][tex]b_2 = 26\: units [/tex]To find: Length of midsegment
Solution: Formula for length of midsegment of a trapezoid is given as:
[tex] Length\: of \:midsegment =\frac{b_1+b_2}{2}[/tex]Plugging the values of [tex]b_1 \:and \: b_2 [/tex] in the above formula we find:[tex] Length\: of \:midsegment =\frac{14+26}{2}[/tex][tex]\implies Length\: of \:midsegment =\frac{40}{2}[/tex][tex]\implies Length\: of \:midsegment =20\: units[/tex](3x−4)(x+2)(3x−1) hurry pls
Answer:
Step-by-step explanation:
(3x - 1)(3x - 4) = 9x^2 - 15x + 4
(x + 2)(9x^2 - 15x + 4) = 9x^3 - 15x^2 + 4x + 18x^2 - 30x + 8
9x^3 + 3x^2 -26x + 8 is the solution
Please help with this easy problem for 30 points!!!
Answer:
x^3 + 3x^2 - 10x
Step-by-step explanation:
(x - 0)(x - 2)(x + 5)
= (x^2 - 2x)(x + 5)
= x^3 + 5x^2 - 2x^2 - 10x
= x^3 + 3x^2 - 10x
Find the shortest length of 1/2-inch conduit from which the following pieces can be cut: 7 1/8 inches, 3 1/4 inches, 6 1/2 inches, 12 1/8 inches, and 24 3/16 inches. Allow 1/ 16 inch for each saw cut.
please break it down for me:)
Answer:
106 7/8 inches
Step-by-step explanation:
Simplifying the pieces
57/8 + 13/4 + 13/2 + 97/8 + 387/16114/16 + 52/16 + 104/16 + 194/16 + 387/16 + 4/16855/16855/16 x 2855/8106 7/8 inchesHELP ME PLEASE!!!!!!!!!!!!!!!!
Answer:
40
Step-by-step explanation:
you multiply them all together
A basketball player made 70 out of 100 attempted free throws. What percent of free throws was made?
Answer:
70%
Step-by-step explanation:
To find the percent you put the part (70) out of the whole (100) and then multiply it by 100%. Like this:
[tex]\frac{70}{100} *100[/tex] = 70%
You can also look at it like this, it is already out of 100, so he made 70% of free throws because he made 70 free throws!
I hope this helps! Good luck and if you have any questions please let me know in the comments!
How many inches are in one and a half yards
Answer:
54
Step-by-step explanation:
54 inches
hope it helps...!!!
The following table represents the highest educational attainment of all adult residents in a certain town. If a resident who is 30-49 years old is chosen at random, what is the probability that they have completed a master's degree? Round your answer to the nearest thousandth.
Answer:
The required Probability =0.433
Step-by-step explanation:
number of residents who has master degree =2078
number of residents who has master degree and age group 30-49years= 455+ 445=900
900/2078
=450/1039
=0.43310
Find a1 when S7=5465, r=3, n=7 using geometric series
[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}\\[-0.5em] \hrulefill\\ n=7\\ r=3 \end{cases} \\\\\\ S_7=a_1\left( \cfrac{1-r^7}{1-r} \right)\implies 5465=a_1\left( \cfrac{1-3^7}{1-3}\right)\implies 5465=a_1(1093) \\\\\\ \cfrac{5465}{1093}=a_1\implies \boxed{5=a_1}[/tex]
Can someone help with this I don't understand
Answer:
1. B 15
2. C Hexagon
Step-by-step explanation:
1.Euler's formula tells you the relation between numbers of faces, vertices, and edges of a polyhedron is ...
F +V = E +2
Solving for the number of faces, we have ...
F = E +2 -V
For the given numbers, the missing number is ...
F = 26 +2 -13 = 15
Faces: 15
__
2.The cross section (shaded figure) is described by the number of edges it has. You can count them. There are three pairs of parallel edges, for a total of 6 edges. That makes the figure a hexagon.
The angle XYZ has and angle y which is twice the size of x. If the third angle is 20 degree what is the value of x and y
The value of angle x and y in the triangle XYZ are 53.33 degrees and 106.66 degrees, respectively.
What is triangle angle sum theorem?According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees.
The angle XYZ has an angle y which is twice the size of x. Thus,
2x=y
The third angle is 20 degree, which is Z. Thus,
z=20
By the triangle angle sum theorem,
x+y+x=180
x+2x+20=180
3x=180-20
x=160/3
x=53.33
The measure of angle y is,
y=2×53.33
y=106.66
Thus, the value of angle x and y in the triangle XYZ are 53.33 degrees and 106.66 degrees, respectively.
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PLEASE HELP WILL GIVE BRAINLIEST 60 POINTS Given the triangle congruence statement ΔUVW≅ΔABC and the triangles below, mark each of the triangles appropriately for corresponding angles and sides. Then create a list of congruent sides and angles using the table.
Corresponding Sides Corresponding Angles
Congruent triangles are those triangles which have the same size and form.
What are congruent triangles?Congruent triangles are those triangles which have the same size and form. This signifies that the matching sides and angles are the same.
The two triangles ΔUVW≅ΔABC, therefore, the corresponding sides can be written as,
WU = BAUV = ACWV = BCThe corresponding angles will be,
∠W = ∠B∠U = ∠A∠V = ∠CLearn more about Congruent Triangles:
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f p(x) = 2x2 – 4x and q(x) = x – 3, what is (p circle q) (x)
Answer:
[tex]2x^{2} - 16x + 30[/tex]
Step-by-step explanation:
Here we have to find p(q(x))
q(x) =x -3
we will plug value of q(x) in x of p(x)
p(x) =2x2-4x
p(q(x)) = 2(x-3)2-4(x-3)
= 2(x2-6x+9)-4(x-3)
=2x2-12x+18 -4x+12
[tex]2x^{2} + 16x + 30[/tex]
Express the following rate as a unit rate.
63 jumping jacks in 3 minutes
_____ jumping jacks per minute
Answer:
21 jacks/min
or 21 jacks per minute
Step-by-step explanation:
63/3 = 21
write it as ___ unit/rate
please mark brainliest
Solve for x
4(x + 6) = 3x – 7
Answer:
-31 = x
Step-by-step explanation:
Step 1 4x + 24 = 3x - 7
Step 2 x + 24 = -7
Step 3 x = -31
Hope this help!!!
Graph y=|3x| using as many points as needed
Answer:
Graph is below
Step-by-step explanation:
I am going to use 3 points to make this graph
(0,0)
(-1,3)
(1,3)
Answer:
(0,0), (-1,3), (1,3)
Step-by-step explanation:
The graph is below!
Hope this helps!!!!!!!!!!!!
use the graph of the parabola to fi in the table
Answer:
line of symmetry: x = -3
intercepts...
x - intercept: (-4, 0) and (-2, 0)
y - intercept: (0, 8)
vertex: (-3, -1)
Step-by-step explanation:
The image isn't that clear but what I can get is what listed
line of symmetry is the line straight down the middle as if the graph is reflected to the other side
intercepts...
x - intercept is when y = 0, note there is 2 of these a negative and positive root
y - intercept is when x = 0
vertex is the turning point
for an upward curve its a min
for a downward curve it a max
I attached an example of each on of these
Quadrilateral CDEF is similar to quadrilateral GHIJ. Find the measure of side
GH. Round your answer to the nearest tenth if necessary.
5
E
23.3
H
C
7
Answer: 32.6
Step-by-step explanation:
What is the median of the following data set ? {3,4,2,8,5}
4
Explanation:
3, 4, 2, 8, 5
arrange in ascending order
2, 3, 4, 5, 8
Identify the integer at the middle
median: 4
Arrange in ascending order
{2,3,4,5,8}Median term=(5+1)/2=6/2=3rd term=4
Median is 4
Suppose a plumber charges $80 for a house call and $60 for each hour it takes him to complete the repair. Write an equation in slope-intercept form to represent this situation.
Answer:
80 + 60x
Step-by-step explanation:
ANSWER FOR A BRAINLY plEASE
Answer:
91 I believe. 7x4 is 28, divide by 2, you get 14. there is two triangles that have the same area so multiply by two to get 28 for the top half. then 7x9 is 63, divided by 2 times 2 is 63. add 63 and 28 to get 91
Use Statistics to make an argument to the court on behalf of your client. Structure your essay as a paragraph that contains the following:
Your Honor,
Explain why random sampling in this situation of juror selection relates the expected sample proportion to the population proportion.
Compare the expected value to the actual sample proportion.
Show that the requirements for a binomial experiment are met in this situation, implying that the binomial distribution can be used.
Identify the values for n,p, and x for this situation
Interpret the answers to parts c. and d. and submit them as evidence.
Use this to argue that the juror selection was likely to be random or not likely to be random (depending on your answer to part c).
Request a new jury be selected or accept the selected jury (depending on your answer to part c)
Respectfully,
[Your Name]
In explaining of the random sampling situation, you tell the jury that Random sampling is a kind of sampling technique where all sample has an equal right or probability to be chosen.
What is random sampling example?An example of a simple random sample would be the names of 30 employees were chosen out of a box from a company of 300 employees. In this above scenario, the population is all 300 employees, and the sample is random based on the fact that each employee do possess an equal chance of been selected.
By using the example of the argument given above to convince the juror about why the selection is said to be likely to be random.
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what is the volume of a cylinder, in cubic with a height of 2 inches and a base diameter of 18 inches Round to the nearest place
Answer:
V = 508.938 [tex]in^{3}[/tex]
Step-by-step explanation:
The equation to find the volume of a cylinder is:
[tex]V = \pi r^{2} h[/tex]
r = radius
h = height
In the question it gives us the height (2 inches) and the diameter (18 inches).
We need to find the radius from the diameter. To do this, divide the diameter by 2:
r = 18/2 = 9
Now, plug everything into the equation and solve:
[tex]V = \pi (9)^{2} (2)[/tex]
Use a calculator to get the answer:
V = 508.938 [tex]in^{3}[/tex]
(Side note: I don't know what place to round to because in the question it says to "round to the nearest place" but doesn't say tenth, hundred, etc. If the question on your homework says tenth then the answer would be 508.9, hundredth = 508.94, thousandth = 508.938)
Hope this helps!! If you have questions please comment them under this!
The US Mint charges $25 for a limited edition coin, plus a $6 shipping charge. The
cost, c, of purchasing n coins can be found using the function c = 25n+6. There is a
limit of 5 coins per purchase. What is a reasonable domain for this function?
a. {5}
b. {1, 2, 3, 4, 5}
c. {25, 50, 75, 100, 125}
d. {31, 56, 81, 106, 131}
Answer:
b. {1, 2, 3, 4, 5}
Step-by-step explanation:
Given function:
c = 25n + 6
(where c is the total purchase cost and n is the number of coins)
Domain: input values → n-values
If there is a limit of 5 coins per purchase, this means that you can purchase up to and including 5 coins at any one time.
Therefore, the domain is: {1, 2, 3, 4, 5}
{1, 2, 3, 4, 5} is a reasonable domain for this function.
So, the correct answer is:
b. {1, 2, 3, 4, 5}.
The cost function for purchasing n coins is given by c = 25n + 6.
However, there is a limit of 5 coins per purchase.
This means that the number of coins (n) should not exceed 5,
as it is not possible to purchase more than 5 coins in a single purchase.
Therefore, a reasonable domain for this function would be the set of numbers from 1 to 5,
since n can take any value between 1 and 5, inclusive.
Hence, {1, 2, 3, 4, 5} is a reasonable domain for this function.
So, the correct answer is:
b. {1, 2, 3, 4, 5}.
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Convert the following angle from degrees to radians. Express your answer in simplest form 345 ∘
well, since we know that there are 180° in π radians, how many degrees will it be in 345°?
[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ 345&x \end{array}\implies \cfrac{180}{345}~~ = ~~\cfrac{\pi }{x}\implies \cfrac{12}{23}~~ = ~~\cfrac{\pi }{x} \\\\\\ 12x=23\pi \implies x=\cfrac{23\pi }{12}[/tex]
Tess says this shape is a rhombus. Jack says the shape is a square. Who is correct? Use the drop-down menus to explain who is correct.
Click the arrows to choose an answer from each menu.
The above shape is a quadrilateral and its a square. Therefore, Jack is correct.
What is a quadrilateral?A quadrilateral is a 2 dimensional figure with 4 sides.
Examples of quadrilaterals are rhombus , square, rectangle, parallelogram etc.
A rhombus is a quadrilateral with 4 sides same length. The angles of rhombus are not right angles.
A square is a quadrilateral with 4 sides same length and 4 square corners that a right angles.
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Identify the maximum or minimum value, domain, and range of the graph of the quadratic function.
Answer:
see explanation
Step-by-step explanation:
the graph has a maximum turning point at (- 2, 2 )
the maximum value is the value of the y- coordinate of the vertex , then
maximum at 2
the domain is the values that x takes, in this case
domain is all real numbers
the range is the values that y can have, in this case
range is y ≤ 2
Answer:
See below ~
Step-by-step explanation:
Details of Graph
Maximum = 2Domain : all real numbersRange : y ≤ 2What’s the answer????
Tanika drew a line of best fit on a scatter plot as shown below
Answer:
C. she forgot the minus sign for the first term on the right side of the equation.
Step-by-step explanation:
Tanika's work: 1.02(0.5)+7.09 = y
y = 7.6
She's missing the negative sign before 1.02. Her equation should have been -1.02(0.5)+7.09 = y
y = 6.58