We have been given that the value of Vishal's car is depreciating exponentially. The relationship between V, the value of his car, in dollars, and t, the elapsed time, in years, since he purchased the car is modeled by the equation [tex]V=22,500\cdot 10^{-\frac{t}{12}}[/tex]. We are asked to find the time, when Vishal's car will be worth $10,000.
To find the time, we will equate our given equation with 10,000 as:
[tex]10,000=22,500\cdot 10^{-\frac{t}{12}}[/tex]
[tex]\frac{10,000}{22,500}=\frac{22,500\cdot 10^{-\frac{t}{12}}}{22,500}[/tex]
[tex]\frac{4}{9}=10^{-\frac{t}{12}}[/tex]
Now we will take log on both sides.
[tex]log_{10}\left(\frac{4}{9}\right)=log_{10}\left(10^{-\frac{t}{12}}\right)[/tex]
[tex]log_{10}\left((\frac{2}{3})^2\right)=-\frac{t}{12}[/tex]
[tex]-\frac{t}{12}=log_{10}\left((\frac{2}{3})^2\right)[/tex]
[tex]-\frac{t}{12}(-12)=(-12)log_{10}\left((\frac{2}{3})^2\right)[/tex]
[tex]t=(-12)log_{10}\left((\frac{2}{3})^2\right)[/tex]
Using property [tex]log(a^b)=b\cdot log(a)[/tex], we will get:
[tex]t=(-12)\cdot 2log_{10}\left(\frac{2}{3}\right)[/tex]
[tex]t=-24log_{10}\left(\frac{2}{3}\right)[/tex]
Therefore, the value of Vishal's car will be $10,000 after approximately [tex]-24log_{10}\left(\frac{2}{3}\right)[/tex] years.
select all that apply.
Answer:
1st, 3rd, and 4th options
Help help help me please
Answer:
[tex]A[/tex] ≈ [tex]80.03[/tex]
Step-by-step explanation:
I used the equation [tex]A=[/tex] π[tex]r(r+h^{2}+r^{2})[/tex] to find the surface area
i hope this helps
The length of a rectangle is 8 centimetres less than its width. What are the dimensions of the rectangle if its area is 240 square centimetres?
Answer:
Well, Your best answer will be is 35.
Here's a Explain.
W-5=0
W=5 That's for the width.
L=3*5-8
L=15-8=7 And, That's for the length.
Here's proof.
35=7*5
35=35
Hope That Helps!~
[tex]^{Itsbrazts}[/tex]
What is the interquartile range of this data? a5 b8 c13 d17
0 5 10 15 20
Quick answer pleaseee
(AAAASSSSSSAAAAPPPP!)
Which expression or equation is equivalent to the following?
3(2x+1)
A) 5x +4
B) 3x +6
C) 3+6x
Which function is linear?
A). f(x) = |7x| + 2
B). f(x) = 1/7x + 2
C). f(x) = 7x − 2
D). f(x) = |7x| − 2
Answer:
C
Step-by-step explanation:
Option C is the only one that's linear because it follows all of the rules for a line to be linear. To check, use the process of elimination:
A). When x is an absolute value, the line will not be linear because an input will have two outputs.
B). x cannot be in the denominator of a fraction for the line to be linear
D). Once again, x cannot be an absolute value.
*Note: I'm assuming in option B, 7x is in the denominator and 1 is in the numerator. If the fraction is simply 1/7 multiplied by x, it is linear along with C.
Answer:
C
Step-by-step explanation:
i took the k12 test
Determine the angle at the centre of a circle with a radius of 8.0 cm for an arc length of 12.0 cm.
A. 2/3 radians
B. 1/3 radians
C. 3/2 radians
D. 3π / 2 radians
Answer:
C. 3/2 Radians
Step-by-step explanation:
As we know, a radian is defined as "the angle enclosed by an arc equal to the radius", or some variant of such.
This means 1 radian in this circle would have an arc length of 8cm.
Simple proportions should get you an answer:
[tex] \frac{1 \: radians}{8cm} = \frac{x \: radians}{12cm} \\ 8x = 12 \\ x = \frac{12}{8} \\ x = \frac{3}{2} [/tex]
In a 45-45-90 rìght triangle, what is the ratio of the length of one leg to the
length of the other leg?
Answer:
The legs of a 45 45 90 are equal
And the length of the hypotenuse equals
leg * square toot of 2
Step-by-step explanation:
In Aunt Melly’s attics there are also spiders and ants, the total of 136 legs and 20 heads. If a spider has 8 legs and an ant has 6 legs, how many spiders and how many ants are there?
HELP ASAPPP
Answer:
12 ants, 8 spiders.
Step-by-step explanation:
What is the mean absolute deviation of the data set? 8, 5, 12, 4, 5, 8, 7 1 2 5 7
The mean absolute deviation (MAD) is a measure of the spread of a data set, calculated as the average of the absolute deviations of each data point from the data set's mean. For the given data set, the MAD is approximately 2.42.
The mean absolute deviation (MAD) of a data set is a measure of variability that represents the average difference between each data point and the mean of the data set. To calculate MAD, follow these steps:
Calculate the mean (average) of the data set.Calculate the deviation of each measurement, which is the absolute value of the difference between each measurement and the mean.Sum all the absolute deviations.Divide the sum by the number of data points in the data set to get the MAD.For the data set 8, 5, 12, 4, 5, 8, 7, 1, 2, 5, 7, the mean is 5.8 (sum of all numbers divided by the number of numbers). Here are the deviations from the mean:
|8 - 5.8| = 2.2|5 - 5.8| = 0.8|12 - 5.8| = 6.2|4 - 5.8| = 1.8|5 - 5.8| = 0.8|8 - 5.8| = 2.2|7 - 5.8| = 1.2|1 - 5.8| = 4.8|2 - 5.8| = 3.8|5 - 5.8| = 0.8|7 - 5.8| = 1.2Summing all the absolute deviations gives us 26.6. With 11 data points, the MAD is 26.6 / 11 = 2.42.
Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 120.
A rectangle has a width of x and a length of x plus 4.
Answer:
Inequality : 4x+8 < 120
x<28
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Perimeter of a rectangle (P)= 2 length +2 width
Where:
Width = x
Length = x+4
Replacing with the values given
P = 2 (x+4) + 2x
P = 2x+8+2x
P=4x+8
Since the perimeter of the rectangle must be less than 120:
4x+8 < 120
Solving for x
4x<120-8
4x<112
x<112/4
x<28
Feel free to ask for more if needed or if you did not understand something.
To find the values of x for which the perimeter of a rectangle is less than 120, you would solve the equation 2*(x + (x+4)) < 120. After simplifying and solving, the result is x < 28.
Explanation:In this problem, you are asked to find the values of x for which the perimeter of a rectangle is less than 120. The rectangle has width of x and a length of x plus 4.
The perimeter of a rectangle is defined as 2*(length + width). Plugging the lengths in for our rectangle, we get 2*(x + (x+4)) < 120. Simplifying this inequality gives 2*(2x + 4) < 120
From there, you want to distribute the 2 across the equation, which gives 4x + 8 < 120. Subtract 8 from both sides to get 4x < 112, and then divide both sides by 4 to find x < 28. So, the possible values of x are those less than 28.
Learn more about Inequality problem here:https://brainly.com/question/15086723
#SPJ3
__________ and other cash crops are grown on the fertile lands of Mt. Kilimanjaro’s slopes.
A.
Oranges
B.
Rice
C.
Coffee
D.
Maize
Please select the best answer from the choices provided
A
B
C
D
Answer:
Coffee doing it rn
Step-by-step explanation:
Fatima opens an account with 1300 that earns 3.5% interest, compounded monthly. How long will it take the account value to be $2500?
Answer:
The formula to calculate the account value in future (compounded monthly):
A = Principal x (1 + rate/12)^(month)
=> 2500 = 1300 x (1 + (3.5/100)/12)^(month)
=> (1 + 0.00291)^(month) = 2500/1300
=> 1.00291^(month) = 1.923
=> month = log(1.923)/log(1.00291) = 225
=> It will take 225 months to have 2500 dollar in account.
Hope this helps!
:)
The gas tank in Feliz's car is full. Each time he drives to or from work, he uses 1 of a full
tank of gas. Which equation represents the number of times Feliz can drive to or from work
with the gas in his tank?
Answer: number of times feliz can drive to or from work with the gas in his tank is 10 times
Step-by-step explanation:
Let's start by reviewing the slope-intercept formula:
y = mx + b
At the start of the journey, we have a tank that's 5/6 full and have yet to go anywhere. That means that our b is 5/6.
Thus:
y = mx + 5/6
Now, every time he drives to or from work, be loses 1/12 of a full tank.
Thus;
y = -(1/12)x + 5/6
negative because the initial volume of gas is decreasing whenever he goes out.
Now, to get the number of times feliz can drive to or from work with the gas in his tank, y = 0.
Thus,
0 = -(1/12)x + 5/6
Add (1/12)x to both sides to give;
(1/12)x = 5/6
x = 5/6 ÷ 1/12
x = 10
Which is a factor pair of 72?
12,6
14,5
23,4
24, 2
Answer:
12,6
Step-by-step explanation:
The factor pair of 72 is 12 and 6 because, factors are the 2 numbers you multiply together to get the product. In this case, the product is 72. 12x6=72 So therefore, 12 and 6 are the factors of 72. You can figure this out simply by multiplying 12 and 6 together.
The factor pairs of 72 are (1,72), (2,36), (3,24), (4,18), and (6,12).
Explanation:To find the factor pairs of 72, we need to find pairs of numbers that multiply together to give us 72. Let's list all the factors of 72 and check which pairs multiply to give us 72:
1 x 72 = 722 x 36 = 723 x 24 = 724 x 18 = 726 x 12 = 72So, the factor pairs of 72 are (1, 72), (2, 36), (3, 24), (4, 18), and (6, 12).
Learn more about factor pairs here:
https://brainly.com/question/30391475
Complete the table for missing values of p
Answer:
The answer is 50:22 and 60:12
Step-by-step explanation:
Perimeter:
Find the missing length by looking at the sides that
are equal.
Answer:
top left perimeter is 36 top left is 28 bottom right is 72 i cant see the bottom left
Step-by-step explanation:
but yeah just take each number multiply by 2 then add both of them up
Please help me with this question
Answer:
x = 20.3
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan 55 = 29 /x
Multiply each side by x
x tan 55 = 29
Divide by tan 55
x = 29 / tan 55
x =20.30601861
To the nearest tenth
x = 20.3
An above-ground rainwater tank is rectangular and has a length of 15
feet and a height of 2 feet. It will hold 375 cubic feet of water. What is the
height of the rainwater tank?
Answer:
The width of the tank is 12.5 feet
Step-by-step explanation:
We need to find the width, not height of the rainwater tank, since the height is already given.
The volume of a rectangular prism is given as:
V = L * W * H
where L = length of the tank
W = width of tank
H = height of tank
We have its volume as 375 cubic feet and the length, L, as 15 feet and height, H, as 2 feet.
Therefore, its width is:
375 = 15 * W * 2
375 = 30W
=> W = 375 / 30
W = 12.5 feet
The width of the tank is 12.5 feet.
PLEASE ANSWER I REALLY NEED IT ASAP (30points) ZOOM IN TO SEE IT BETTER
Answer:
x = 1 ; x = 8
Step-by-step explanation:
6x² - 5x + 10 = 5x² + 4x + 2
x² - 9x + 8 = 0
x² - 8x - x + 8 = 0
x(x - 8) - (x -8) = 0
(x - 8)(x - 1) = 0
x = 1, x = 8
Answer:
x=8 x=1
Step-by-step explanation:
f(x) = g(x)
6x^2 -5x +10 = 5x^2 +4x+2
Subtract 5x^2 from each side
6x^2-5x^2 -5x +10 = 5x^2-5x^2 +4x+2
x^2 -5x +10 = 4x+2
Subtract 4x from each side
x^2 -5x-4x +10 = 4x-4x+2
x^2 -9x +10 = 2
Subtract 2 from each side
x^2 -9x +10-2 = 2-2
x^2 -9x +8 =0
Factor
What 2 numbers multiply to 8 and add to -9
-8 *-1 = 8
-8-1 = -9
(x-8) (x-1) =0
Using the zero product property
x-8 = 0 x-1 =0
x=8 x=1
Choose a fraction that makes the following sentence true. 0.1
is a rational number because it can be written as -
0.1
o
The fraction that makes the statement true is 1/10.
The sentence would be: "0.1 is a rational number because it can be written as 1/10."
The statement "0.1 is a rational number because it can be written as 0.1" is not accurate.
The decimal 0.1 is already a rational number because it can be expressed as the fraction 1/10.
Therefore, the correct sentence would be:
"0.1 is a rational number because it can be written as 1/10."
Question
Choose a fraction that makes the following sentence true. 0.1 is a rational number because it can be written as 0.1
What is 5 7/12 minus 3 11/22
Answer:
5/3 or 1.66666666 or 1 2/3
Step-by-step explanation:
Subtract like normal
Look at the attached picture
Hope it will help you...
Where can I find Gradpoint answers?????
Which of the following points is closest to (3,0)?
A) point A
B) point B
C) point C
D) point D
Answer:
B) point B
Step-by-step explanation:
It is the only one on the positive side of the X intercept, and (3,0) is positive. You can get easily confused considering they are all TECHNICALLY the same distance away but since point B is most SIMILAR that would be your answer.
Hope this helped lots and lots,
sincerely, me
As part of an experiment, 500 milligrams of chlorine is added to a tank each day for 60 days.
How many grams of chlorine is added to the tank in 60 days?
Enter your answer as a whole number or decimal in the box.
sorry i have another question
Answer:
30 grams
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
300 dollars per week equals to how many hours of work?
Answer:
= 168 hrs of work
Step-by-step explanation:
I week = 7 days
If 1 day = 24hrs
What about 7 days = ?
= 7 x 24
= 168 hrs of work
To get how much he gets per hour, you divide 300 by the number of hours
= 300 ÷ 168
= 1.785
= 1 dollar 79 cents
WILL MARK BRAINIEST PLZ HELP
Answer:
473 adult tickets and 782 student tickets
Hope this helps :)
HeLP!! will mark brainlest!
The scatter plot below shows the distances some employees of a company commute to work and the annual
salary each earnsImmersive Reader
A. As the length of the commute increases, the annual salary increases.
B. As the length of the commute increases, the annual salary decreases.
C. As the length of the commute increases, the annual salary remains constant
D. There is no relationship between the length of the commute and annual salary.
Answer:
It is a
Step-by-step explanation: I looked it up