Answer:
Range = {5, 8, 11}
Step-by-step explanation:
On the function f(x) = 3x + 2
For the first domain, when x = 1, f(x) = 3(1) + 2 = 3 + 2 = 5
For the second, when x = 2, f(x) = 3(2) + 2 = 6 + 2 = 8
For the third domain, when x = 3, f(x) = 3(3) + 2 = 9 + 2 = 11
f(x) = x2 - x - 1
What is the average rate of change of f over the interval -1 < x < 1?
Answer:
-1
Step-by-step explanation:
The average rate of change is the ratio of the difference in y-values to the difference in x-values of corresponding points.
At x=-1, f(x) = (-1)^2 -(-1) -1 = 1
At x=1, f(x) = (1)^2 -(1) -1 = -1
So, points on the graph are (-1, 1) and (1, -1).
Then the change in y over that interval is -1 -1 = -2.
The change in x over that interval is 1 -(-1) = 2.
The average rate of change is ...
∆y/∆x = -2/2 = -1 . . . . average rate of change on (-1, 1)
A company employs six women and eight men. The company randomly selects one employee to receive additional vacation time. Using the classical approach, what is the probability that the selected employee will be a woman
Answer: 6/14 or 3/7
Step-by-step explanation:
There are a total of 14 employees hired so it would like like this: 1/14 if you were to chose one of all 6 women and 8 men hired.
There are 6 women that may be chosen out of all 14 employees of which 8 are men, now what this would look like is : 6?14 or simplified, (3/7).
This means there is a 6/14 chance of choosing a woman instead of a man in these 14 hired employees. just because the question asks, "what is the chance of a woman getting chosen", of the other 5 women and 8 men hired, so the answer is 6/14 or 3/7 to chosen as a women instead of men in all the 14 employees that may/might be chosen. hope this helps love yawl!!
STAY SAFE !!! LOVE YOU !!! <3 <3 <3 <3
..... <3 <3 <3 <3 <3 <3 <3 .....
What is the value of x in the equation
5x - y = 30, when y = 157
Answer:
x = 37.4
Step-by-step explanation:
Answer:
37.4
Step-by-step explanation:
If you plug in 157, we get 5x-157=30. Then we will add 157 to both sides to get 5x=187 and then divide by 5 on both sides leaving x on one side and the answer on the other so, 187/5=37.4.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
What is the area of this polygon?
coordinates are -5,2(-2,3)(3,3)(3,-3)(-2,-3)
Enter your answer in the box.
Answer:
30
Step-by-step explanation:
Simplify the radical expression √100/2
Answer: 5
Step-by-step explanation:
sqrt of 100 = 10
10/2 = 5
The speed of an object in space is shown in the graph.
What is the slope of the line?
(picture) please and thank you
Answer:
1 / 15
Step-by-step explanation:
The vertical change (rise) is 6 - 3, or just 3. The horizontal change (run) is 0.4 - 0.2, or 0.2. Thus the slope of this line is m = rise / run = 0.2 / 3 = 2 / 30 = 1 / 15
Brady and JaQuan were selling cupcakes together at a bake sale. They hope to make $100 so they can both go on the band field trip to New York City. In the first hour Brady sold 1/3 of the cupcakes and Jaquan sold 3/8...
Answer:
The initial amount of cupcakes = 48
If they sold each cupcake for $2.75, they would make $132 which is more than the required $100 to go on band field trip to New York.
The excess money available for spending is thus $32
Step-by-step explanation:
The complete question is presented in the attached image to this answer.
They need to make $100
Let x be the initial amount of cupcakes
During the first hour, Brady sold (1/3) of the cupcakes and Jaquan sold (3/8)
Total amount of cupcakes sold in the first hour = [(1/3) × x] + [(3/8) × x] = (17x/24)
Amount of cupcakes remaining after the first hour = x - (17x/24) = (7x/24)
After the first hour, they sold 2 cupcakes
Amount of cupcakes left after the first hour = (7x/24) - 2 = (0.292x - 2)
During the second hour, they sold 75% of the remaining cupcakes, meaning they had 25% of the remaining cupcakes left.
Amount of cupcakes left = 25% × (0.292x - 2)
= (0.07292x - 0.5)
During the third hour, they sold the remaining 3 cupcakes
Meaning that the amount of cupcakes left from the second hour = 3
(0.07292x - 0.5) = 3
0.07292x = 3.5
x = (3.5/0.07292) = 47.998 = 48 cupcakes.
Hence, the initial amount of cupcakes = 48.
If they sold each cupcake for $2.75, they would make 2.75 × 48 = $132
Which is more than the required $100 to go on band field trip to New York.
The excess money available for spending is thus $132 - $100 = $32.
Hope this Helps!!!
Xavier invests $100 each month for 6 months in an account that pays 6% APR compounded monthly. What is the future value of Xavier's account after 6 months?
Answer:
$607.57
Step-by-step explanation:
The size of a slow-growing bacteria strain increases continuously over time. This equation describes the predicted size of the bacteria strain, in square millimeters, after t minutes: y = 112(1.58)t. According to the equation, what will the approximate size of the bacteria strain be after 5 minutes?
Answer:
1102.8 mm^2
Step-by-step explanation:
We presume your equation is intended to be ...
y = 112(1.58)^t
Since t is in minutes, fill in the given value and do the arithmetic:
y = 112(1.58)^5 = 112(9.84658) ≈ 1102.8
The approximate size of the bacteria strain will be 1102.8 mm^2 after 5 minutes.
Answer:
Explanation:
To find the size of bacteria in five minutes, substitute 5 for t in the equation and simplify:
y = 112(1.58)5
= 112 ∙ 9.85
= 1,103.2.
Round the answer to the closest integer to get 1,103.
Step-by-step explanation:
Solve the inequality 7x ≥ –7
Answer:
x ≥ -1
Step-by-step explanation:
Divide everything by 7 to isolate x and you have your answer!
Answer:
x ≥ –1
Step-by-step explanation:
7x ≥ –7
Divide by 7
7x /7≥ –7/7
x ≥ –1
The shaded region below is called an annulus sector. Calculate the area (in square feet) of the shaded region if the inner circle has radius 7 ft and the outer circle has radius 14 ft. Round your answer to the nearest square foot.
Answer:
462 ft²
Step-by-step explanation:
The area of the annulus sector is given by the area of the outer circle (radius of 14 ft) minus the area of the inner circle (radius of 7 ft).
The area of a circle is:
[tex]A=\pi r^2[/tex]
Therefore, the area of the annulus sector is:
[tex]A_A=A_O-A_I\\A_A=\pi*14^2-(\pi*7^2)\\A_A=147\pi\\A_A= 462\ ft^2[/tex]
The area, rounded to the nearest square foot, is 462 ft².
Consider the function.
f(x) = -x-24
Which conclusions can be drawn about f'(x)? Select two options.
F1(x) has a slope of -
f'(x) has a restricted domain.
f(x) has a y-intercept of (0, -36).
F'(x) has an x-intercept of (-36,0).
f'(x) has a range of all real numbers.
Answer:
f(x) has a slope of -1 and has a range of all real numbers.
Step-by-step explanation:
A linear function is a continuous function, so that exist a range value for all value of the domain, which corresponds to all real numbers. Regarding the function described above, the y- and x-intercepts are, respectively:
x-Intercept
[tex]0 = - x-24[/tex]
[tex]x = -24[/tex]
f(x) has a x-intercept of (-24,0).
y-Intercept
[tex]f(x) = 0 - 24[/tex]
[tex]f(x) = -24[/tex]
f(x) has a y-intercept of (0, -24).
Lastly, the linear function has a slope of -1.
Answer:
D AND E
Step-by-step explanation:
edu I took it
The US Department of Agriculture reports that the mean cost of raising a child from birth to age 2 in a rural area is $10,460. A team of economists believes this value is incorrect, so they select a random sample of 900 children (age 2) and find that the sample mean cost is $10,345 with a sample standard deviation of $1540. Is this significantly different than the US Department of Agriculture reports
Answer:
[tex]t=\frac{10345-10460}{\frac{1540}{\sqrt{900}}}=-2.24[/tex]
The degrees of freedom are given by:
[tex]df=n-1=900-1=899[/tex]
The p value for this case would be given by:
[tex]p_v =2*P(t_{(899)}<-2.24)=0.0127[/tex]
The p value is low and if we use a significance level of 0.05 we can reject the null hypothesis and we can conclude tha the true mean is different from 10460
Step-by-step explanation:
Information given
[tex]\bar X=10345[/tex] represent the mean height for the sample
[tex]s=1540[/tex] represent the sample standard deviation for the sample
[tex]n=900[/tex] sample size
[tex]\mu_o =10460[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
Hypothesis to test
We want to verify if the true mean is equal to 10460, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 10460[/tex]
Alternative hypothesis:[tex]\mu \neq 10460[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{10345-10460}{\frac{1540}{\sqrt{900}}}=-2.24[/tex]
The degrees of freedom are given by:
[tex]df=n-1=900-1=899[/tex]
The p value for this case would be given by:
[tex]p_v =2*P(t_{(899)}<-2.24)=0.0127[/tex]
The p value is low and if we use a significance level of 0.05 we can reject the null hypothesis and we can conclude tha the true mean is different from 10460
Question: I had $5.00 My Mom gave me $10.00 while my Dad gave me $30.00. My Aunt and Uncle gave me 100.00. I had another $5.00 How much money did I really have?
Answer:
I had $10
I have $150
Step-by-step explanation:
This is a riddle and not a math question
So
I had $5I received $10+$30+$100= $140I had another $5The answer to the question how much I had is:
$5 + $5 = $10The answer to the question how much I have is:
$5+ $10 + $30 + $100 + $5 = $150Here we need to perform an addition of several numbers.
We will find that the total amount of money that you have is $150.
We know that:
You had $5.00
Your mom gave you $10.00
Your dad gave you $30.00
Your aunt and uncle gave you $100.00
You had another $5.00
Now you want to find how much money do you have, so you just need to add these numbers.
We can add it as:
$5 + $10 + $30 + $100 + $5
We can perform the addition in any order we want, for example:
($5 + $5) + $10 + $30 + $100
$10 + $10 + $30 + $100
($10 + $10) + $30 + $100
$20 + $30 + $100
($20 + $30) + $100
$50 + $100 = $150
You have $150.
If you want to learn more, you can read:
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00:00
Use the Distributive Property to find the product of 6 x 3,584. Enter your answer in the box.
Answer:
21,504
Step-by-step explanation:
This is the usual method multiplication is done "by hand."
6 × 3584 = 6 × (3000 +500 +80 +4)
= 6×3000 +6×500 +6×80 +6×4
= 18000 +3000 +480 +24
= 21000 +504
= 21,504
_____
Many of us are taught in grade school to do the multiplication right to left:
= 6×4 +6×80 +6×500 +6×3000
... writing down the digit corresponding to the place value of the product, and "carrying" any more significant digits to add to the next product.
Here, that looks like 6×4 = 24, write down 4, carry 2. 6×8 = 48, add 2 to get 50, write down 0, carry 5. 6×5 = 30, add 5 to get 35, write down 5, carry 3. 6×3 = 18, add 3 to get 21, write down 21. Then the product is 21504.
__
When doing mental calculation, or using an abacus or soroban, it often works better to do the multiplication left to right, as shown in the answer above.
Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs if he will earn at least $90 the job. He writes this inequality to determine x, the number of hours he must work during each job in order to accomplish this. 30 + 15 x greater-than-or-equal-to 90 Which best describes the restrictions on the jobs Deepak will accept? He only accepts jobs that last 4 or more hours. He only accepts jobs that last 5 or more hours. He only accepts jobs that last 8 or more hours. He only accepts jobs that last 9 or more hours.
Answer:
(A)He only accepts jobs that last 4 or more hours.
Step-by-step explanation:
Deepak charges $30 for each job plus an additional $15 for each hour he works.
Let the number of hours =x
Deepak's Total Income for x hours =30+15x
Since he only accepts jobs if he will earn at least $90 the job.
[tex]\text{Total Income}\geq 90[/tex]
[tex]30+15x\geq 90[/tex]
We then solve the inequality for x
[tex]30+15x\geq 90\\$Subtract 30 from both sides\\30-30+15x\geq 90-30\\15x\geq 60\\$Divide both sides by 15\\15x\div 15\geq 60 \div 15\\x\geq 4[/tex]
We therefore conclude that Deepak only accepts jobs that last 4 or more hours.
The correct option is A.
Answer:
A) He only accepts jobs that last 4 or more hours.
Step-by-step explanation:
Correct me if i'm wrong sorry if i am :)
What are the coordinates of the pre-image of B'?
O (2, -8)
O (-8, -2)
O (-2, 8)
O (8,2)
Answer:
b. (-8, -2)
Step-by-step explanation:
Reflection across the x-axis
(x, y) ---> (x, -y)
B'(- 8, 2) ---> B( - 8, -2)
The coordinates of the pre image of B is (-8,-2) by studying the given graph.
How to find reflected coordinates of B'The given figure ABCD is reflected across the x-axis to create the figure A'B'C'D'.
By referring the graph we can say that the coordinate of B' is (-8,2)
The reflected point will have y coordinate's sign changed as the figure is reflected across x-axis.
Thus the pre image of B' will be (-8,-2)
Hence the coordinates of the pre image of B' is (-8,-2)
Learn more about coordinate system here:
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A car is traveling at a speed of 63 kilometers per hour. What is the car's speed in kilometers per minute? How many kilometers will travel in 5 minutes?
Answer:
5.25 kilometers
Step-by-step explanation:
63k/60 = 1.05k
1.05k x 5 = 5.25k
Data on a sample of 100 customers of Alibaba, a direct marketing company, for the current year. The variables are defined as follows: Customer = a code for the customer Own Home = 1 if customer owns home, o if renting Close = 1 if lives close to stores (with similar merchandise), O if not Salary = annual household salary in $ Catalogs = number of catalogs this customer was sent this year Amount Spent = Amount spent total on purchases this year You are given the result of the multiple regression with dependent variable = Amount Spent. Use this output to answer the questions
(a) - (g) below the output. SUMMARY OUTPUT Regression Statistics Multiple R 0.8366 R Square 0.6999 Adjusted R Squ 0.6873 Standard Error 512.72 Observations 100 ANOVA df f ignificance F 55.39 0 .000 Regression Residual Total 4 95 99 SS 58241400.88 24974011.87 83215412.75 M S 14560350.22 262884.34 Intercept Own Home Close Salary Catalogs Coefficients Standard Error -91.67 185.917 -229.47 121.800 -604.90 114.229 0.02216 0.002 42.62 8.451 t Stat -0.493 -1.884 -5.295 9.836 5.043 P-value Lower 95% Upper 95% 0.623 -460.76 277.42 0.063 -471.27 12.34 0.000 -831.67 -378.12 0.000 0.02 0.03 0.000 25.84 59.40
(b) Using the regression model in (a), predict the mean amount spent by Amy, a customer who has the following characteristics: does not own a home, but lives close to stores that have similar merchandise, salary is $60,000 and is sent 12 catalogs this year. Give the value rounded to the nearest cent.
(c) Suppose Brenda has the same characteristics as Amy but does not live close to store with similar merchandise. How much would you expect Brenda to spend? Give the value rounded to the nearest cent.
Answer:
a. [tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* ownhome)-(604.90 * close) +(0.02216 * salary) + (42.62 * catalogs)[/tex]
b. the expected amount spent by Amy is $1144.47
c. the expected amount that Brenda is going to spend is $1749.37
Step-by-step explanation:
(a)
From the regression output; the equation for the regression model can be written as:
[tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* ownhome)-(604.90 * close) +(0.02216 * salary) + (42.62 * catalogs)[/tex]
From the information given in the question;
(b)
Amy does not own a home but rent; the variables given also stated that ;
Own Home = 1 if customer owns home, 0 if renting
So for Amy ; Own Home = 0 (since it is rented)
Close = Yes(1)
Salary = $60,000
Catalogs = 12
Therefore;
the mean amount spent by Amy is by using the regression model is ;
[tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* 0)-(604.90 * 1) +(0.02216 * 60000) + (42.62 * 12)[/tex]
[tex]\hat{amount} \ \hat{ spent} = -91.67 -0-604.90 +1329.6 + 511.44[/tex]
[tex]\hat{amount} \ \hat{ spent} =1144.47[/tex]
Thus; the expected amount spent by Amy is $1144.47
(c)
If Brenda has the same characteristics as Amy but does not live close to store with similar merchandise.
Then the Close for Brenda will be = No (0)
Thus; the amount spent by Brenda will be:
[tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* 0)-(604.90 * 0) +(0.02216 * 60000) + (42.62 * 12)[/tex]
[tex]\hat{amount} \ \hat{ spent} = -91.67 -0-0 +1329.6 + 511.44[/tex]
[tex]\hat{amount} \ \hat{ spent} = 1749.37[/tex]
Thus, the expected amount that Brenda is going to spend is $1749.37
The profit a company makes from producing x tabletops is modeled by the equation p(x) = 480x minus 2x squared. For what number of tabletops does the company need to make a profit of zero dollars?
Answer:
240 table tops or none
Step-by-step explanation:
p(x) = 480x- 2x^2
For profit to be 0, it means;
p(x)= 0
Therefore 480x- 2x^2 = 0
Dividing through by 2 we have ;
240x - x^2 = 0
By factorisation of x we have ;
(240-x) x = 0
x = 0 or 240-x= 0; x= 240( by moving x to the right of the expression:240-x= 0; we have 240=x => x=240).
So the company needs to produce 240 table tops or none in order not to make a profit.
The company need to make a profit of zero dollars will be 240.
What is a profit?A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running or creating anything.
The profit a company makes from producing x tabletops is modeled by the equation is given as,
p(x) = 480x – 2x²
Then the company need to make a profit of zero dollars will be
p(x) = 0
480x – 2x² = 0
2x(240 – x) = 0
x = 0, 240
More about the profit is given below.
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In a study, 43% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 13 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 13 adults are randomly selected, at most 3 are in excellent health.
Answer:
13.44% probabilith that at most 3 are in excellent health.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they are in excellent health, or they are not. The probability of an adult being in excellent health is independent of other adults. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
43% of adults questioned reported that their health was excellent.
This means that [tex]p = 0.43[/tex]
13 adults randomly selected
This means that [tex]n = 13[/tex]
Find the probability that when 13 adults are randomly selected, at most 3 are in excellent health.
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{13,0}.(0.42)^{0}.(0.58)^{13} = 0.0008[/tex]
[tex]P(X = 1) = C_{13,1}.(0.42)^{1}.(0.58)^{12} = 0.0079[/tex]
[tex]P(X = 2) = C_{13,2}.(0.42)^{2}.(0.58)^{11} = 0.0344[/tex]
[tex]P(X = 3) = C_{13,3}.(0.42)^{3}.(0.58)^{10} = 0.0913[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0008 + 0.0079 + 0.0344 + 0.0913 = 0.1344[/tex]
13.44% probabilith that at most 3 are in excellent health.
Find the distance between the points (1,7) and ( 5, 10).
Answer:
Step-by-step explanation:
[tex]\sqrt{(5-1)^{2} +(10-7)^{2}\\\\\sqrt{4^{2} + 3^{2} \\\\\sqrt{16+9} = \sqrt{25} = 5[/tex]
Find the surface area of the triangular prism shown below .
Answer:
the surface area should be 544 (whatever the unit is)
Step-by-step explanation:
You start by taking the rectangles on the side and finding their area.
1. (10×14)×2 ←Because there are two rectanglular sides.
2. find the area of the triangles on the side. 1/2bh = area of triangle.
(.5×8×6)×4 ← in order to find the area for all of the triangles.
3. lastly take the base of the prism and find the area then add the previously found values together.
(12×14)+(.5×8×6)×4+ (10×14)×2 = 544
Answer:
544
Step-by-step explanation:
It is right on Khan academy so I hope this helps!!!
Can someone please help me :)
Answer:
90 degree
Step-by-step explanation:
Three points A, B, and C are added and shown in attached picture.
As the property of inscribed angle in circle:
angle BAC = (1/2) x 88 = 44 deg
As the property of complement angle:
angle ABC = 180 - 89 = 91 deg
As the property of sum of three angles in a triangle:
angle ACB + angle ABC + angle BAC = 180 deg
=> angle ACB = 180 - angle ABC - angle BAC = 180 - 44 - 91 = 45 deg
One more time, we use the property of inscribed angle in circle:
x = 2 x angle ACB = 2 x 45 = 90 deg
Hope this helps!
Ana purchased a gallon of milk for $2.22, bagels for $2.97, and a box of
cereal for $2.42. How much money did Ana spend in all? Do not include s in
your answer.
Answer:
7.61
Step-by-step explanation:
Sum all of the values
2.22+2.97+2.42=7.61
Answer:
761
Step-by-step explanation:
Statistical Process Control (SPC) is often described as an applied side of the Binomial, Poisson, and Normal distributions. Many have said that an X-bar control chart is simply a Normal distribution turned on its side. Some argue that our statistics course shouldn't try to cover these applications because they represent an analytical skill rather thana statistical technique. Discuss, first whether or not you agree with the notion that SPC is an application of what we're learning in this class, and second, whether coverage of the topic is helpful in this class. How might your outcomes after this class be affected - positively or negatively - by whether or not we cover Chapter 16 in the text?
Answer: The answer is provided below
Step-by-step explanation:
Statistical Process Control (SPC) is described as the applied side of binomial, poisson, and the normal distributions. It has been often said that an X-bar control chart is a normal distribution that is turned on its side. Some people argue that statistics shouldn’t cover these applications because it represent an analytical skill rather than statistical technique. It's an application of what is learnt on statistics.
Statistical Process Control(SPC) is very useful in our lives. As a statistics student, one should be thorough with every mathematical concepts and its applications.
What is the value of x in the equation- x - y = 30, when y= 15?
4
8
80
200
Answer:
x - 15 = 30
x = 45
Step-by-step explanation:
Answer:
D: 200
Step-by-step explanation:
1/5x-2/3 times 15=30
Simplify each term
x/5 -10=30
Move all terms not containing x to the right side of the equation
x/5=40
Multiply both sides of the equation by 5
5 times x/5=5 times 40
Simplify both sides of the equation
x=200
Hope this helped!
The function g(x) = x^3 has the point(-3, -27) on its graph. Determine g(3) without using substitution. What is the output based on the eve/odd nature of the function?
-27
27
not enough information
Answer:
27
Step-by-step explanation:
Any positive integer to 3rd power will have positive answer.
Odd functions with number next to x^3 that is positive are increasing from left to right and thay also have a rotational symmetry with respect to the origin.Whe you put this together it's clear that the answer is 27
A new car is purchased for 15100 dollars. The value of the car depreciates at 12.25% per year. To the nearest year, how long will it be until the value of the car is 2300 dollars?
Answer: 14
Step-by-step explanation:
need asap to get the points plz
the problaty of getting Gray tile is 6 time