Answer:
a) rate of depreciation is 11.24%
b) original price of car = $18605.33
Step-by-step explanation:
The formula to apply is;
current price= original price *(1-r)^n where r is the rate of depreciation as a decimal and n is the time period
a) Find the rate of depreciation given that ;
The car was bought at $10,250 when it was 5 years old
After 2 years, the value was $8,075
Apply the formula ;
current price= original price *(1-r)^n
8,075=10,250* (1-r)²
8,075/10250 = (1-r)²
0.78780487804 =(1-r)²
√0.78780487804 =(1-r)
0.88758373016 = 1-r
r=1-0.88758373016
r=0.11241626983 ⇒ 11.24%
b) When the car was first bought, the price was;
Apply the formula;
current price= original price *(1-r)^n
10,250 =original price * (1-0.1124)⁵
10,250=O.P *(0.5509)
10,250/0.5509 = original price
$18605.33= original price
which answer is correct
Answer:
B and D
Step-by-step explanation:
they are irrational numbers and fall between the two numbers...
Simplify: -4 1/5- (-13 1/10)
Answer:
.
Step-by-step explanation:
Guilherme observed the number of minutes his dormmates spent on social media sites while they were at the library. He reported his data in the following table.
Dormmate Number of minutes on social media
Vera 13
Timothy 0
Manueala 14
Khaled 36
Yash 18
Fernanda 12
Find the mean number of minutes on social media.
The mean number of minutes his dormmates spent on social media is: 15.5 minutes.
What is the Mean of a Data?Mean of a data set is the average of the data values in that data set.
Given the data, 13, 0, 14, 36, 18, 12
Mean number of minutes = (13 + 0 + 14 + 36 + 18 + 12)/6
Mean number of minutes = 93/6
Mean number of minutes = 15.5
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What is the end behavior of f(x) = 5x 3 - 2x + 5?
A)
It rises to the left and rises to
the right.
C) It falls to the left and rises to the right.
B)
It rises to the left and falls to
the right.
D) It falls to the left and falls to the right.
Answer:
It falls to the left and falls to the right. You can use Geogebra. There you just type the formula and it makes graph from which you can see the directions
in a class of 32 students
the mean height of the 14 boys is 1.56 m
the mean height of the 32 students is 1.515 m
work out the mean height of the girls
Answer:
14(1.56) + 18h = 32(1.515)
21.84 + 18h = 48.48
18h = 26.64
h = 1.48 meters
The mean height of the girls in the class is 1.48 meters.
Explanation:To calculate the mean height of the girls in the class, we will use the information provided about the mean heights of the boys and the entire class. Since we know the mean height of the 14 boys is 1.56 meters, we can find the total height of all boys by multiplying 1.56 by 14, which equals 21.84 meters. For the entire class of 32 students, the mean height is 1.515 meters. Multiplying 1.515 by 32 gives us the total height for the entire class, which is 48.48 meters. To find the total height of the girls, we subtract the total height of the boys from the total height of the class: 48.48 meters - 21.84 meters = 26.64 meters. Since there are 32 students in total and 14 boys, there must be 18 girls. To find the mean height of the girls, divide the total height of the girls by the number of girls: 26.64 meters / 18 girls = 1.48 meters.
A car is purchased for $23,500. After each year, the resale value decreases by 25%. What will the resale value be after 3 years?
Use the calculator provided and round your answer to the nearest dollar.
Answer:
$5,875
Step-by-step explanation:
Answer:
After 3 years it will be $9,400
Step-by-step explanation:
First multiply 23,500 by .20 and get 4700. Now multiply by 3 which is 3 years and it equals 14,100. Now subtract from 23,500-14,100 and get 9,400.
Find the missing dimension of the solid. Round your answer to the nearest 10th
Answer:
the answer is 9.9997 ft
Step-by-step explanation:
the equation to find the radius is
r = √(3v / πh)
^ ^
| THE CHART |
A company makes yellow golf balls and white golf balls. The table below shows the company’s sales of white golf balls for the last three years. The company expects sales of white golf balls to continue to increase by the same amount in year 4 as it did in previous years. The company also expects the ratio of white golf balls sold to yellow golf balls sold to be 5 to 1. All golf balls are sold in boxes of 12. How many total boxes of golf balls should this company expect to sell in year 4?
ANSWER CHOICES:
A: 22,140
B: 26,568
C: 265,680
D: 318,816
Answer:
B. 26568
Step-by-step explanation:
As per table, white golf balls sold at an increasing rate of:
224 640 - 204 120= 245 160 - 224 640 = 20520 per yearExpected white golf ball to be sold in the year 4:
245160 + 20520 = 265680Expected yellow golf ball to be sold:
265680/5= 53136Expected total golf balls to be sold in the year 4:
265680 + 53136= 318816Expected total boxes of golf balls:
318816/12= 26568Correct answer choice:
B. 26568idk what to do i need help asap please & thank you
Answer:
[tex]170(1.3)^{t}[/tex]
Step-by-step explanation:
For this formula it would be exponential growth. The formula for exponential growth is: [tex]y = a(1+r)^{t}[/tex]
a is the initial value
r is the growth rate
t is the number of time intervals that have passed in the given situation
In this problem, you would substitute the r for the given percent (0.3) and substitute the a for 170 as the initial value. The equation would then be:
[tex]170(1.3)^{t}[/tex]
i hope this explanation is helpful
There are 800 bags of beans. Each bag contains 20,000 beans. How many beans are there in all?
Answer: 16,000,000
Step-by-step explanation:
Answer:
16,000,000 beans total.
Step-by-step explanation:
Start with what you're given. Each bag has 20,000 beans, right?
There are, for some unknown, ungodly reason, 800 bags. Okay, great. It's a lot of bags of beans and I don't understand why there needs to be so much, but this is math. Most "related to real-world" problems in math don't make logical sense.
So we've established how many bags there are, and how many beans each bag has. You'll need to multiply those two together to get how many beans there are total. However, 20,000 times 800 is a very ridiculously large number and takes a lot of time. So, how do we make it easier to understand?
We focus on the most important parts.
800 and 20,000 are large numbers, but simple as well. The only digits are 8 and 2, followed by zeroes. Just multiply 8 times 2, and you get 16. Now add the number of zeroes from 800, and the number of zeroes from 20,000, and you'll end up with 6 zeroes.
So your answer should be 16 followed by 6 zeroes, or 16,000,000.
That's a lot of beans.
An 18-inch cylindrical cake roll with a radius of 4 inches has been cut
into 8 identical pieces. What is the volume of each piece of cake?
Select one:
O 28872
O 36tin
O 12tuin
O 14411n
The value of a computer is decreasing at a rate that is proportional at any time to the value of the computer
at that time.
The computer is worth $850 initially, and it is worth $306 after 2 years.
How much will the computer be worth after 5 years?
A. $0
B. $66
C. $79
Step-by-step explanation:
The price of computer = 850
The price of computer after 2 years = 306
By compound depreciation,
[tex]Pn = P (1 - \frac{R}{100} ) ^ T[/tex] ... (i)
where Pn = 306
P = 850
R = rate of interest to be calculated
T = 2( number of years)
substituting the values in equation (1), we get
[tex]306 = 850 (1 - \frac{R}{100} ) ^ 2[/tex]
0.6 = 1 - [tex]\frac{R}{100}[/tex]
R = 40%
The worth after 5 years =
[tex]Pn = 850 (1 - \frac{40}{100} ) ^ 5[/tex]
Pn = 850 (0.077)
= $66.096 = $ 66
The computer be worth after 5 years = $ 66 (option B)
After 5 years, the computer will be worth is $66 (B).
To solve this problem, we'll use the formula for exponential decay, where the rate of decrease is proportional to the value of the computer at that time.
Step 1 :The formula for exponential decay is:
[tex]\[ V(t) = V_0 \times e^{-kt} \][/tex]
Where:
- [tex]\( V(t) \)[/tex] is the value of the computer at time [tex]\( t \)[/tex],
- [tex]\( V_0 \)[/tex] is the initial value of the computer,
- [tex]\( k \)[/tex] is the decay constant, and
- [tex]\( t \)[/tex] is the time in years.
Given:
- [tex]\( V_0 = $850 \)[/tex]
- [tex]\( V(2) = $306 \)[/tex]
We need to find the value of [tex]\( k \)[/tex] using the given information.
[tex]\[ 306 = 850 \times e^{-2k} \][/tex]
Divide both sides by 850:
[tex]\[ \frac{306}{850} = e^{-2k} \][/tex]
Taking the natural logarithm of both sides:
[tex]\[ \ln\left(\frac{306}{850}\right) = -2k \][/tex]
Solve for [tex]\( k \)[/tex]:
[tex]\[ k = -\frac{\ln\left(\frac{306}{850}\right)}{2} \][/tex]
Step 2 :Now that we have [tex]\( k \)[/tex], we can find [tex]\( V(5) \)[/tex]:
[tex]\[ V(5) = 850 \times e^{-5k} \][/tex]
Substitute the value of [tex]\( k \)[/tex] and compute:
[tex]\[ V(5) = 850 \times e^{-5 \times \left(-\frac{\ln\left(\frac{306}{850}\right)}{2}\right)} \][/tex]
[tex]\[ V(5) = 850 \times e^{\frac{5\ln\left(\frac{306}{850}\right)}{2}} \][/tex]
[tex]\[ V(5) = 850 \times \left(\frac{306}{850}\right)^{\frac{5}{2}} \][/tex]
V(5) = 66.61
Therefore, after 5 years, the computer will be worth is $66.
1. Two pair of jeans and three shirts cost $133. The cost of
three pair of jeans and six shirts is $231. Find the cost of each
pair of jeans and each shirt.
Answer:
1 Pair of Jeans cost $35
1 Shirt costs $21
Step-by-step explanation:
$231 - $133= $98
$133 - $98 = $35 --- Pair of Jeans
$35 × 2 = $70
$133 - $70 = $63
$63/3 = $21 --- Shirt
The cost of each pair of jeans and each shirt can be found by setting up and solving simultaneous equations. The cost of each pair of jeans is $27, and the cost of each shirt is $25.
Explanation:This problem can be solved using the method of simultaneous equations. We'll first form two equations based on the given information. Let's assume the cost of a pair of jeans is 'x' dollars and the cost of a shirt is 'y' dollars.
The cost of two pairs of jeans and three shirts is $133. Hence, the first equation would be 2x + 3y = 133.The cost of three pairs of jeans and six shirts is $231. The second equation would therefore be 3x + 6y = 231.Let's simplify the second equation by dividing it by 3, which makes it x + 2y = 77. Subtract this from the first equation to eliminate 'x'. You're left with y = 25. Substitute y = 25 into the simplified second equation to get x = 27. So each pair of jeans costs $27 and each shirt costs $25.
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A summer camp has 32 campers. A total of 22 of them
swim, 20 play softball, and 5 do not swim or play
softball. Which values complete the table?
O
a= 15, b = 10, c=7, d=5, e = 12
a = 15, b = 7, c=5, d = 10, e = 12
a=14, b = 7, c=5, d = 12, e = 10
a=14, b = 12,c=7, d =5, e = 10
Answer:
B. a = 15, b = 7, c = 5, d = 10, e = 12
Step-by-step explanation:
The values that complete the table are a = 15, b = 7, c = 5, d = 10, and e = 12. Therefore, option B is correct.
What the solution of the given question?Given that there are 32 campers in total, and 22 of them can swim, and 20 of them play softball. We also know that 5 campers do not play softball or swim.
We are asked to complete the table, which consists of rows and columns, with the third row and third column showing the totals.
Let's start with the third row. According to the table, the total number of campers who can swim and play softball is a + b. And since we know that 20 campers play softball, we can write:
a + b = 20
Moving on to the third column, the total number of campers who can swim is a + c. We also know that 22 campers can swim, so we can write:
a + c = 22
Now we have two equations and two unknowns, namely a and c. We can solve for a by subtracting the second equation from the first equation:
(a + b) - (a + c) = 20 - 22
Simplifying this expression, we get:
b - c = -2
We also know that 5 campers do not play softball or swim. So the total number of campers who do not play softball is:
32 - 20 = 12
And since 5 campers do not play softball or swim, the remaining 7 campers do not play softball but can swim. Therefore, we can write:
c + d = 7
Substituting the value of d from equation (1), we get:
c + 10 = 7
Solving for c, we get:
c = 5
Now that we know the value of c, we can solve for a using equation (2):
a + c = 22
Substituting the value of c, we get:
a + 5 = 22
Solving for a, we get:
a = 15
Using the value of a, we can solve for b using equation (3):
a + b = 20
Substituting the value of a, we get:
15 + b = 20
Solving for b, we get:
b = 5
Finally, we can solve for e using equation (4):
20 + e = 32
Solving for e, we get:
e = 12
Therefore, the values that complete the table are a = 15, b = 7, c = 5, d = 10, and e = 12.
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evaluate 5log5 63. A. 58 B. 315 C. log5 63 D. 63
To evaluate 5log5 63, use the property of logarithms that states loga b = logc b / logc a. Using a calculator, we find that 5log5 63 ≈ 2.57.
Explanation:To evaluate 5log5 63, we use the property of logarithms which states that loga b = logc b / logc a. In this case, a = 5 and b = 63. So, 5log5 63 = log10 63 / log10 5. Using a calculator, we find that log10 63 ≈ 1.798 and log10 5 ≈ 0.699. Therefore, 5log5 63 ≈ 1.798 / 0.699 ≈ 2.57. So the correct answer is not listed among the options provided.
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Simply 3/4 - (6 - 3/4s)
Answer:
-21/4 + 3s/4
Step-by-step explanation:
Answer:
− 21/ 4 + 3 s/ 4
Step-by-step explanation:
Plot A shows the number of hours ten girls watched television over a one-week period. Plot B shows the number of hours ten boys watched television over the same period of time.
Television Viewing Hours for a One-Week Period
Sorry im asking a lot i forgot to study! Which statement correctly compares the measures of center in the two sets of data?
Both the mean and median are greater for Plot A than for Plot B.
Both the mean and median are greater for Plot B than for Plot A.
Plot A has a greater median than Plot B, but Plot B has a greater mean.
Plot B has a greater median than Plot A, but Plot A has a greater mean.
Answer:
Both the mean and median are greater for Plot A than for Plot B.
Step-by-step explanation:
Plot A data set is : 4,4,5,5,6,6,7,7,10
mean(Plot A) = 5.7
median(Plot A) = 5.5
Plot B data set is : 4,4,5,5,5,6,6,6,7
mean(Plot B) = 5.1
median(Plot B) = 5
Both the mean and median are greater for plot A than for plot B.
Answer:
A. Both the mean and median are greater for Plot A than for Plot B.
Correct statement, question and plots:
Plot A shows the number of hours ten girls watched television over a one-week period. Plot B shows the number of hours ten boys watched television over the same period of time.
Television Viewing Hours for a One-Week Period
Which statement correctly compares the measures of center in the two sets of data?
A. Both the mean and median are greater for Plot A than for Plot B.
B. Both the mean and median are greater for Plot B than for Plot A.
C. Plot A has a greater median than Plot B, but Plot B has a greater mean.
D. Plot B has a greater median than Plot A, but Plot A has a greater mean.
Plots are available below
Source:
Previous question that can be found at brainly
Step-by-step explanation:
As we can see, the number of hours in plot A goes from 3 to 10 with a gap in 8 and 9, while in plot B, goes from 3 to 7, with no gaps.
Let's calculate the mean and media for both plots:
Plot A:
Mean = (3 + 2 * 4 + 2 * 5 + 2 * 6 + 2 * 7 + 10)/10
Mean = 57/10 = 5.7
Median = 5 + 6/2 = 11/2 = 5.5
Plot B:
Mean = (3 + 2 * 4 + 3 * 5 + 3 * 6 + 7)/10
Mean = 51/10 = 5.1
Median = 5 + 5/2 = 10/2 = 5
Mean comparison: 5.7 > 5.1
Median comparison: 5.5 > 5
In consequence, the correct answer is A. Both the mean and median are greater for Plot A than for Plot B.
Juanita is shopping for a new shirt, and she has narrowed her decision down to two. Both shirts are $35, and both are on sale. Shirt A is 25% off. Shirt B is $10 off. Which shirt is the better deal?
I'm pretty sure the better deal would be shirt a
if I'm wrong don't get mad
Juan gives 8 cookies to his friends. If that represents 40% of the cookies in the package, what is the total number of cookies in the package? (I NEED THIS PLS ASAP)
Answer:
20 Cookies
Step-by-step explanation:
If Juan has 8 cookies and 8 cookies = 40%, multiply by 2. 16 = 80%. Now we only need 20% more and that will identify how much there are. To do this is just simply divide 8 by 2. 4 is our answer. It's half of 8 meaning half of 40%. So add 16 and 4, you get 20.
P.S
Have a Amazing Day!
Faker/Tosrel
The first three terms of an arithmetic sequence are as follows.
39, 32, 25
Find the next two terms of this sequence.
Answer:
18,11
Step-by-step explanation:
seven is reduce in all terms
Answer:
18, 11
Step-by-step explanation:
just took a test
Hi! Can someone help me with this?
Answer:
The answer is 4.3
1.8 + 2.5 = 4.3
Hope it helped :)
Step-by-step explanation:
Please mark brainliest :)
simplify a⁵ × (a³)²
Answer:
[tex]a^{11}[/tex]
Step-by-step explanation:
In solving for a⁵ × (a³)², we need to follow the rules of PEMDAS
Therefore, your equation would look like this:
a⁵ × (a³)² = a⁵ × [tex]a^{6\\[/tex]
When two variables are the same, we add their exponents when multiplying and we would subtract them if we divided.
With that information, your final answer would be
[tex]a^{11}[/tex] as 5+6 = 11
Hope this Helps!
In mathematics, the expression a⁵ × (a³)² simplifies to a¹¹ by following rules of exponents. Simplify within parentheses first to get a⁶, then combine to get a¹¹.
Explanation:The term a⁵ × (a³)² represents the product of a number 'a' raised to the power of 5 and 'a' raised to the power of 3, squared. To simplify an expression like this, use the rule of exponents that states: aⁿ * aᵐ = aⁿ+ᵐ and for (a^n)^m, this equates as a^(n*m).
Start by simplifying the exponent in the parentheses first: (a³)² = a^(3*2) = a⁶. Then you're left with a⁵ × a⁶. Using the rules of exponents again, you add the powers together: a^(5+6) which simplifies to a¹¹.
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What are the possible outcomes?
A=
Jerry can buy a school shirt in a certain size and color
shown in the lists below. He started the table to find the
combinations.
Size: X-large, Large, Medium, or Small
Color: Blue, Gray or White
B =
C =
The total number of combinations is
X-large
Large
Medium
Small
Blue
A
Gray
White
Answer:
A= X,B
B= L,G
C= M,W
The total number of combinations is 12
Answer:
look at pic
Step-by-step explanation:
To kick off the summer, Ted is planning a "School's Out!" party for all his friends. He and his
mom pick up a giant sub and a vat of root beer from Subs & Suds. When they get to the
park, they cut the sub into 12 equal sections. Each section is 7 of a foot long.
there’s no question?
Find 26th term in the arithmetic sequence: -15,-35,-55,-75,...
Answer:
-515
Step-by-step explanation:
In this example the first value is −15 and every value afterwards is 20 less.
After substituting these values to above formula, we obtain:
All we have to do is add 25 twenties or 25 x 20 = 500 and -15 - 500 = -515
The required 28 th term of the given arithmetic sequence is given as -555.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values that are equal.
What is geometric progression?Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
Here,
Given sequence,
-15,-35,-55,-75,...
From the above sequence,
The first term, a = -15
Common difference d = -35 +15 = -20
nth term is given as,
nth = a + (n - 1)d
nth = -15 -20 (n - 1)
Now put n = 28
28th = -15 -20(28 - 1)
= -15 - 540
= -555
Thus, the required 28 th term of the given arithmetic sequence is given as -555.
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tp he Pew Research Center and Smithsonian magazine recently quizzed a random sample of 1006 U.S. adults on their knowledge of science. One of the questions asked, "Which gas makes up most of the Earth's atmosphere: hydrogen, nitrogen, carbon dioxide, or oxygen?" A 95% confidence interval for the proportion who would correctly answer nitrogen 0.175 to 0.225. Interpret this confidence interval.
Answer:
This interval (0.175, 0.225) represents the range of values that the true proportion of U.S. adults that can answer the question of 'which gas makes up the most of the atmosphere?' correctly, can take on, with a confidence level of 95%.
Step-by-step explanation:
Confidence Interval is an interval obtaimed from sample data, for the population proportion. It is an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean (sample proportion).
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the sample proportion)
Critical value is obtained from the z-tables or the t-tables depending on which information is available. For distributions where information on the population standard deviation is known or it isn't know but the sample size is large enough for the sample standard deviation can approximate the population standard deviation, the z-tables is used and for those distributions whose population standard deviation information is not known, and sample size isn't large enough, the critical value is read off the t-tables.
The critical value depends on the confidence level for both the z-tables and the t-tables critical value.
The interval obtained now represents the region of values where the true population proportion can exist within, at a certain level.of confidence.
Hope this Helps!!!
Which descriptions from the list below accurately describe the relationship
between AQRS and ATUV?
The answer is either D or B but it's most likely D sorry if u get this wrong
A circle has a circumference of 11,304 units.
What is the diameter of the circle?
Answer:
3,600 units
Step-by-step explanation:
divide 11,304 by 3.14 and you get,
3,600.
(basically reversed way of trying to find the circumference)
Answer:
d=3600
Step-by-step explanation:
C=πd
11,304=3.14d
divide:11,304÷3.14=3600
C=11,304=3.14*3600
On a coordinate plane, which BEST describes where the point (0, 11) lies?
A) in Quadrant I
B) on the x-axis
C) on the y-axis
D) in Quadrant II
Answer:
The y- axis
Step-by-step explanation:
If it was (0,0) then the x and y would not matter but in this cause the answer is the y axis because it has a point to it but not the x. It is not Quadrant 2 or 1 because it does not matter what box it is in all that matters is where the points are located
oops I mest upStep-by-step explanation:
A music store bought a CD set at a cost of $20. When the store sold the CD set, the percent markup was 40%. Find the selling price.
Answer:
Selling price = $28
Step-by-step explanation:
Cost price = $20
Selling price = ?
Percent markup = 40%.
Percentage markup is the difference between a products selling price and cost as a percentage to the cost.
% mark up = (selling price - cost price) / (cost price) * 100
[(Selling price - 20) / 20 ] * 100 = 40
40 / 100 = (selling price - 20) / 20
0.4 * 20 = selling price - 20
8 = selling price - 20
Selling price = $(8 + 20)
Selling price = $28.
The selling price was $28
Answer: The selling price is $28
Step-by-step explanation: If the CD set was bought at the cost of $20 and sold at a selling price of $20 plus 40% (or 0.4), then we should start by calculating the value of 40% of the cost price, which would then be added to the cost price to arrive at the selling price.
The calculation is as follows;
Mark up = 20 x 0.4
Mark up = 8
Selling price = Cost price + Mark up
Selling price = 20 + 8
Selling price = 28
Therefore the selling price is $28