The equation A(t) = 900(0.85)t represents the value of a motor scooter t years after it was purchased. Which statements are also true of this situation?
Answers
Answer:
When new, the scooter cost $900
Step-by-step explanation:
The complete question in the attached figure
we have
[tex]A(t)=900(0.85)^t[/tex]
This is a exponential function of the form
[tex]A(t)=a(b)^t[/tex]
where
A(t) ----> represent the value of a motor scooter
t ----> the number of years after it was purchased
a ---> represent the initial value or y-intercept
b is the base of the exponential function
r is the percent rate of change
b=(1+r)
In this problem we have
[tex]a=\$900\\b=0.85[/tex]
The base b is less than 1
That means ----> is a exponential decay function (is a decreasing function)
Find the percent rate of change
[tex]b=(1+r)\\0.85=1+r\\r=0.85-1\\r=-0.15[/tex]
Convert to percentage (multiply by 100)
[tex]r=-15\%[/tex] ---> negative means is a decreasing function
Verify each statements
case A) When new, the scooter cost $765.
The statement is false
Because the original value of the scooter was $900
case B) When new, the scooter cost $900
The statement is true (see the explanation)
case C) The scooter’s value is decreasing at a rate of 85% each year
The statement is false
Because the scooter’s value is decreasing at a rate of 15% each year (see the explanation)
case D) The scooter’s value is decreasing at a rate of 0.15% each year
The statement is false
Because the scooter’s value is decreasing at a rate of 15% each year (see the explanation)
Related Questions
An apartment building currently has rented x apartments with two occupants and 16 apartments with one occupant. The apartment building has 92 total occupants.
2× + 16 =92
How many double-occupancy apartments are currently rented?
Answers
The currently rented double-occupancy apartments are 38 apartments.
Step-by-step explanation:
An apartment has rented x apartments with two occupants and 16 apartments with one occupant and the total occupants were 92, these can be written in the equation as
[tex]2x+16=92[/tex]
To find the number of double occupancy apartments that are rented, we need to solve the equation and find the value of x.
[tex]2x+16=92[/tex]
Subtracting 16 from both sides of the equation,
[tex]\begin{aligned}&2 x=92-16\\&2 x=76\end{aligned}[/tex]
Dividing both sides by 2, we get,
[tex]\begin{aligned}\frac{2 x}{2} &=\frac{76}{2} \\x &=38\end{aligned}[/tex]
Thus, there are 38 double-occupancy apartments are currently rented.
The correct answer is that there are 38 double-occupancy apartments currently rented.
To solve the problem, we start with the given equation that represents the total number of occupants in the apartment building:
[tex]\[ 2x + 16 = 92 \][/tex]
This equation takes into account that each double-occupancy apartment (x) houses two occupants, and there are also 16 single-occupancy apartments. We want to find the value of x, which represents the number of double-occupancy apartments.
First, we subtract 16 from both sides of the equation to isolate the term with x:
[tex]\[ 2x + 16 - 16 = 92 - 16 \][/tex]
[tex]\[ 2x = 76 \][/tex]
Next, we divide both sides of the equation by 2 to solve for x:
[tex]\[ \frac{2x}{2} = \frac{76}{2} \][/tex]
[tex]\[ x = 38 \][/tex]
Therefore, there are 38 double-occupancy apartments currently rented in the building. This matches the correct answer provided at the beginning.
Which statements are true? Check all that apply.
KJ is a chord.
F is point of tangency for FE.
MH is a secant segment.
GN is a secant segment.
C is a point of tangency for DC.
The answer is:
the first, second, and fourth options.
KJ is a chord.
F is point of tangency for FE.
GN is a secant segment.
Answers
Answer:
1,2,4
Step-by-step explanation:
KJ is chord.
F is point of tangency.
GN is secant segment.
Answer:
1, 2, 4
Step-by-step explanation:
one for the team
Consider the solution to the linear equation. 5 (x + 6) = 50. 5 x + 30 = 50. 5 x = 20. x = 4. Which describes the inverse operations used after the distributive property? addition then division subtraction then division multiplication then subtraction division then addition
Answers
Answer:b
Step-by-step explanation:
Answer:
Subtraction then Division
Step-by-step explanation:
Right on Edg
Which is the solution of this system of equations? y=5x−83y=x+18
y+5(3)=15
Answers
Answer:
y=5x−83y=x+18 (the question is wrong; it has 2 equal signs)
y+5(3)=15
y+15=15 (multiply 5*3; you get 15)
y= 15-15
y= 0
Answer:
x=3, y=7
Step-by-step explanation:
angle K and angle L are complementary angels. If the measurement of angle K =(3x+3) and the measurement of angle L =(10x-4).what is the measure of each angle
Answers
The measurement of two angles is 24° and 66°
Step-by-step explanation:
First of all, let us define complementary angles
The angles whose sum is 90° are called complementary angles
Given
∠K = (3x+3)
∠L = (10x-4)
According to the definition,
[tex]K+L = 90\\3x+3 + 10x-4 = 90\\13x -1 = 90\\13x-1+1 = 90+1\\13x = 91[/tex]
Dividing both sides by 13
[tex]\frac{13x}{13} = \frac{91}{13}\\x = 7[/tex]
So,
∠K = 3x + 3 = 3(7) + 3 = 21+3 = 24°
∠L = 10x - 4 = 10(7) -4 =70 -4 = 66°
Hence,
The measurement of two angles is 24° and 66°
Keywords: Complementary angles, Angles
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Nia told Patrick that her new backpack only cost $14 because she used a 30% off coupon when she bought it. Patrick wants to buy a similar backpack. How much will it cost if he does not have a 30% coupon?
Please answer quick, and please show steps on how you did it, tysm.
Answers
i would say if he doesn’t have a coupon it would be roughly $46.6
Nia's backpack after 30% off represents 70% of the original backpack cost. Setting up a ratio of 70/100 = 14/X, we can solve for the original price, X. Patrick will pay $20 if he does not have a 30% off coupon.
Explanation:This problem can be solved using a bit of Percentage Calculations. We know that after a 30% discount, Nia's backpack cost $14. This means that $14 represents 70% of the original backpack cost (100% - 30%). So to find out the 100%, or the full price, we need to determine what number 70% is 14 of. We can set up a ratio to find the original cost (X).
The steps are:
We write the equation 70/100 = 14/X where X is the original price.Then we cross-multiply to solve for X: 70 * X = 100 * 14. Which simplifies to X = (100 * 14) / 70Calculate the value to get X = 20.So, the backpack would cost Patrick $20 without a 30% off coupon.
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What type of function is shown above?
A. Exponential
B. absolute value
C. Polynomial
D. Step
Answers
Answer:
that would be an exponential function
Step-by-step explanation:
in a certain class,10 of 24 students play sports. what is the ratio of students who play sports to those who do not?
Answers
Answer:
Step-by-step explanation:
Student who don't play sports = 24 - 10 = 14
the ratio of students who play sports to those who do not = 10 : 14 = 5:7
Step-by-step explanation:
10:24
5:12
is can be you answer
What is the best estimate for this sum? 1/8+1/6
Answers
The best estimate for the sum of 1/8 and 1/6 is 5/24.
Explanation:The best estimate for the sum of 1/8 and 1/6 is 5/24.
To find the sum of fractions, we need to find a common denominator, which is the least common multiple of the denominators. In this case, the LCM of 8 and 6 is 24.
Thus, we can rewrite 1/8 as 3/24 and 1/6 as 4/24.
Adding 3/24 and 4/24 gives us a total of 7/24, which can be simplified to 5/24.
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The best estimate for the sum of 1/8 and 1/6 is 1/4. Thus, the closest estimate is Option A.
To determine the best estimate for the sum of 1/8 and 1/6, we can use approximate fractions that are easier to work with. 1/8 is approximately equal to 0.125 and 1/6 is approximately equal to 0.167. Adding these decimal values together gives us:
0.125 + 0.167 ≈ 0.292
Given this, we can conclude that the sum will be closer to 1/4 than to 1/2 or 1. So, the best estimate for the given sum is Option A.
Complete question:
What is the best estimate for this sum?
1/8+1/6
A. The sum will be close to 1/4.
B. The sum will be close to 1/2.
C. The sum will be close to 1.
Which expressions are polynomials?
Select each correct answer.
6 + w
2x4−y
z + 1
y2−y√3+4
Answers
Answer:
It is 6+w, z=1, and 2x^4-y
Step-by-step explanation:
The expressions which are polynomials are;
6+ w2x⁴ - yz + 1y² - y√3 + 4What is a polynomial?A polynomial by definition is an expression which is composed of variables, constants and exponents, which are combined using the mathematical operations including addition, subtraction, multiplication and division.
On this note, all of expressions are polynomials.
Read more on polynomials;
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Slope=2; (14,33)
What is the slope
Answers
Step-by-step explanation:
Hi! I am a little confused because in this question they would normally ask for the equation of the line but if you are wondering what the slope is, it says in the information that the slope is 2. I will solve for the line equation anyway though.
A line has this form: y=mx+b.
For this question they will want us to give the answer with x and y as variables (letters) and m and b (the slope and y-intercept respectivly) with numerical values.
First, we can put in the point into the equation. The point given is (14,33) so the x value is 14 and they y value is 33.
y=mx+b
33=m(14)+b
We know the slope is 2 (from the given information) so we can substitute that in for m.
33=(2)(14)+b
Solving for b, the Y-intercept, we get b=5.
Perhaps your question was "what is the Y-intercept" and then this would be the answer.
Finally, the final equation for the line is:
y=2x+5
Hope this helps!
What’s 448+1.75+80.3 step by step
Answers
Answer:
530.05
Step-by-step explanation:
you add 448 and 1.75 together, which is 449.75, then you add 449.75 and 80.3 together, which adds up to 80.3 hope this helps :)
Which ordered pair is a solution to the system of linear equations Negative 4 x + y = 8 and x minus 5 y = 17?
Answers
Answer:
(-3, -4).
Step-by-step explanation:
-4x + y = 8
x - 5y = 17 Multiply this by 4:
4x - 20y = 68 Add this to the first equation:
-19y = 76
y = 76/-19
y = -4.
Plug this into the second equation:
x - 5(-4) = 17
x = 17 - 20
x = -3.
CHECK this result in equation 1:
-4(-3) + -4 = 8
12 - 4 = 8
8 = 8 <------ OK.
The solution of the given system of equations is [tex]y=-4[/tex].
Important information:
[tex]-4x+y=8[/tex] ...(i)[tex]x-5y=17[/tex] ...(ii)System of equations:Multiply both sides by 5 in equation (i).
[tex]-20x+5y=40[/tex] ...(iii)
Add equation (ii) and (iii).
[tex]-19x=57[/tex]
[tex]x=\dfrac{57}{-19}[/tex]
[tex]x=-3[/tex]
Substitute [tex]x=-3[/tex] in (i).
[tex]-4(-3)+y=8[/tex]
[tex]12+y=8[/tex]
[tex]y=8-12[/tex]
[tex]y=-4[/tex]
Thus, the solution of the given system of equations is [tex]y=-4[/tex].
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16 please like I’m dying here
Answers
Answer:
well i need to see the graph
Step-by-step explanation:
Both forms are equivalent, just different ways to write the same thing
==============================================
Explanation:
Use the slope formula first
The points we plug in are (x1,y1) = (-3,4) and (x2,y2) = (6,1)
m = (y2-y1)/(x2-x1)
m = (1-4)/(6-(-3))
m = (1-4)/(6+3)
m = (-3)/(9)
m = -1/3
The slope of the line is -1/3
Use one of the points, say the point (x,y) = (-3,4) and the slope we just found with y = mx+b. The goal is to solve for b
y = mx+b
4 = (-1/3)*(-3) + b
4 = 1 + b
4-1 = b
3 = b
b = 3
We have m = -1/3 as the slope and b = 3 as the y intercept
Therefore, the equation in slope intercept form is y = (-1/3)x + 3
In standard form, Ax+By = C, this is is equivalent to x+3y = 9 after we multiply both sides by 3, then add x to both sides.
Water tank A has a capacity of 250 gallons and is 77% full. Water Tank B is 68% full. The ratio of the capacity of tank A to tank B is 5 : 14. What is the capacity of tank B?
Answers
Answer:
Water tank A has a capacity of 250 gallons and is 77% full. Water Tank B is 68% full. The ratio of the capacity of tank A to tank B is 5 : 14. What is the capacity of tank B?
Step-by-step explanation:
Water tank A has a capacity of 250 gallons and is 77% full. Water Tank B is 68% full. The ratio of the capacity of tank A to tank B is 5 : 14. What is the capacity of tank B?
y=x^2+8x+12 find the y-intercept for the parbola
Answers
Answer:
Y(x+2) (x+6)
Step-by-step explanation:
Enter an algebraic expression that represents the difference between e squared and twenty-one.
Answers
Answer:
e
[tex]d = e {}^{2} - 21 [/tex]
Answer:
e
Step-by-step explanation:
d = e {}^{2} - 21
Find the sum of the whole numbers from 1 to 960
Answers
Step-by-step explanation:
A quick way to do this sort of question:
First add the last number and the first number:
1 + 960 = 961
Then divide the total amount of numbers by 2.
960 ÷2 = 480
Now multiply these two numbers together:
961 × 480 = 461280
The sum of the whole numbers from 1 to 960 can be found using the formula for the sum of an arithmetic series. By substituting the values into the formula, we find that the sum is 461280.
Explanation:The sum of the whole numbers from 1 to 960 can be found using a simple formula for the sum of an arithmetic series. The formula is S = n/2 * (a + l), where 'n' is the number of terms, 'a' is the first term, and 'l' is the last term.
In this case, 'n' is 960 (there are 960 terms from 1 to 960), 'a' is 1 (the first term), and 'l' is 960 (the last term).
Plug these values into the formula to get: S = 960/2 * (1 + 960) = 480 * 961 = 461280. So, the sum of the whole numbers from 1 to 960 is 461280.
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a company pays its salespeople $2,000 a month and a commission of 18% of their total sales (T). which of the following equations represents a salespersons total monthly income (I) ?
Answers
Answer:
2,360
Step-by-step explanation:
18% of 2,000 is 360
(0.18)*(2,000)=360
2,000 + 360 = 2,360
Answer: I=2000 + 0.18 T
Step-by-step explanation:
PLEASE HELP
Using the two-way table, what percentage of the students that do not like to travel out of state like camping? Round to the nearest whole percent.
Likes Traveling Out of State Does Not Like Traveling Out of State Row totals
Likes Camping 52 38 90
Does Not Like Camping 36 74 110
Column totals 88 112 200
32%
34%
38%
42%
Answers
The answer is B. 34%.
The percentage of the students that do not like to travel out of state like camping will be 41%. Then the correct option is D.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol '%' is used to symbolize it.
The two-way table is given below.
Likes Traveling Does Not Like Traveling Totals
Likes Camping 52 38 90
Do Not Like Camping 36 74 110
Column totals 88 112 200
Then the percentage of the students that do not like to travel out of state like camping will be
P = (36 / 88) x 100
P = 0.409090 x 100
P = 40.90%
P ≈ 41%
Thus, the percentage of the students that do not like to travel out of state like camping will be 41%.
Then the correct option is D.
The question was incomplete, but the complete question is attached below.
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A, B, C? No explanation needed.
Answers
Answer: the answer is b
Step-by-step explanation: you said you needed none.
What is a 1 killometers= ?
Answers
Answer:
0.62 miles
Step-by-step explanation:
ask google or siri
What is y = 4 * (0.8) ^ t
Answers
The function y = 4 * (0.8)^t is an exponential decay function, representing the decrease of a quantity over time, with y being the value at time t. To find y at any given t, substitute t into the equation and calculate the result.
Explanation:The given function y = 4 * (0.8)^t is an exponential decay function, where y represents the value of the function at time t, the number 4 is the initial value of the function when t = 0, and 0.8 is the decay factor relevant for each time unit. This type of function is often used in contexts such as radioactive decay, depreciation of value over time, or population decrease in a closed environment, where some quantity decreases by a consistent percentage over equal time intervals.
To solve for y at a given time t, simply substitute the value of t into the function and evaluate the exponential expression. It is important to use a calculator or software tool to evaluate the exponential term accurately when t is not a round number.
Write an equation that represents the sum of b and 5x2
Answers
Answer:
The expression that represents the sum of b and [tex]5x^2[/tex] is [tex]b+5x^2[/tex]
Step-by-step explanation:
Given that the sum of b and [tex]5x^2[/tex]
To find the expression that represents the sum of b and [tex]5x^2[/tex] :
The sum of b and [tex]5x^2[/tex] can be written as [tex]b+5x^2[/tex]
Therefore The sum of b and [tex]5x^2[/tex] is [tex]b+5x^2[/tex]
The expression that represents the sum of b and [tex]5x^2[/tex] is [tex]b+5x^2[/tex]
Steve is driving 440 miles to visit the Grand Canyon he drives at an average rate of 55 mph explain how you could find the amount of time it will take Steve to get to the Grand Canyon
Answers
Answer:
8 hour.
Step-by-step explanation:
because for it takes 1 hour for 55 miles .
so,
here, divide the 440/55 =8 hours.
explanation,
it takes 1 hour to complete the 55 miles and here we have to complete the 440 miles.
so, above we divide the 440 miles by 55 miles for hour. result =8 hour
to verify the answer.
you can multifly by 8 * 55 and result=440miles. because it is directily propotional.
for another to verify the answer.
dived the 440/8 and result comes=55 miles / hour.becauseit is directly propotional.
Therefore, it will take Steve approximately 8 hours to drive to the Grand Canyon.
Explanation:To find the amount of time it will take Steve to get to the Grand Canyon, you can divide the distance he needs to travel (440 miles) by his average rate (55 mph). This will give you the time it takes in hours:
Time = Distance / Rate
So, in this case:
Time = 440 miles / 55 mph = 8 hours
Therefore, it will take Steve approximately 8 hours to drive to the Grand Canyon.
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how do u figure out the area of a rectangle
Answers
Answer:
Step-by-step explanation:
Hey there) We do it like this:
[tex]6\times 3\times 4+3\times 3\times 2=90[/tex]
Hope, this helps. Have a nice day :)
PLEASE ANYONE!!!
The table below shows selected points from a function.
The rate of change for the interval shown in the table is
A. constant
B. not constant
part b
A. linear
B. not linear
Answers
a recipe for lemonade calls for 2 cups of sugar for every 1/2 cup of lemon juice. How many cups of sugar would be needed if you had 3 cups of lemon juice?
Answers
Answer: 12cups of sugar
Step-by-step explanation:
2cups of sugar = 1/2cup of memo
Xcups of sugar =3cups of lemon
X = 6÷ 1/2
= 12
Answer:
12 cups sugar
Step-by-step explanation:
there are a couple ways to do this...by unit rate or a proportion...
2 cups of sugar for every 1/2 cup of lemon juice
2 / (1/2) = 2 * 2 = 4.....the unit rate is 4/1....or 4 cups of sugar for every 1 cup of lemon.
so if u have 3 cups of lemon, and 1 cup of lemon = 4 cups of sugar, then 3 cups of lemon would equal (4 * 3) = 12 cups of sugar
or set it up as a proportion...
2 cups sugar to 1/2 cup lemon = x cups sugar to 3 cups lemon
2 / (1/2) = x / 3....cross multiply
(1/2)(x) = (3)(2)
1/2x = 6
x = 6 * 2
x = 12 cups sugar
either way u choose to do it will result in the same answer.
Peter needs to sell 40 candy bars to raise money for his basketball team. He sold 16 bars last week and 18 bars this week. How many more candy bars does Peter need to sell?
Answers
16+18 = 34
40 - 34 = 6
He needs to sell 6 more candy bars.
Solve the following systems of equations.
2= 2y + 5
| 3y - 3x = -12
Answers
Answer:
x=5/2, y=-3/2. (5/2, -3/2).
Step-by-step explanation:
2=2y+5
3y-3x=-12
--------------
2-5=2y
2y=-3
y=-3/2
3(-3/2)-3x=-12
-9/2-3x=-12
3x=-9/2-(-12)
3x=-9/2+12
3x=-9/2+24/2
3x=15/2
x=(15/2)/3
x=(15/2)(1/3)
x=15/6=5/2
The solution for the system of equations is x = -5/2 and y = -3/2.
To solve the system of equations given, one can use substitution or elimination methods. The first equation 2= 2y + 5 can be rearranged to solve for y:
2y = 2 - 5
2y = -3
y = -3/2
Using the second equation 3y - 3x = -12, we substitute y with -3/2 to solve for x:
3(-3/2) - 3x = -12
-9/2 - 3x = -12
3x = -12 + 9/2
3x = -15/2
x = -15/6
x = -5/2
Therefore, the solution for the system of equations is x = -5/2 and y = -3/2.