Answers
Step-by-step explanation:
this is the answer of given question
Related Questions
Tammy is driving a racecar. The table below gives the distance Dt (in meters) she has driven at a few times t (in seconds) after she starts.
Answers
The average rate of change for the distance driven from 0 seconds to 4 seconds is 36.9 meters per second and the average rate of change for the distance driven from 6 seconds to 9 seconds is 33.9 meters per second
How to determine the average rates of change?The average rate of change for the distance driven from 0 seconds to 4 seconds
The average rate of change is calculated as:
Rate = [f(b) - f(a)]/[b - a]
Where
a and b are the bounds of the intervals
So, we have:
a = 0 and b = 4
This gives
Rate = [f(4) - f(0)]/[4 - 0]
Using the table of values, we have:
Rate = [147.6 - 0]/[4 - 0]
Evaluate
Rate = 36.9
Hence, the average rate of change for the distance driven from 0 seconds to 4 seconds is 36.9 meters per second
The average rate of change for the distance driven from 6 seconds to 9 seconds
The average rate of change is calculated as:
Rate = [f(b) - f(a)]/[b - a]
Where
a and b are the bounds of the intervals
So, we have:
a = 6 and b = 9
This gives
Rate = [f(9) - f(6)]/[9 - 6]
Using the table of values, we have:
Rate = [287.1 - 185.4]/[9 - 6]
Evaluate
Rate = 33.9
Hence, the average rate of change for the distance driven from 6 seconds to 9 seconds is 33.9 meters per second
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True or false
-y = -112 + 4; (0, -4)
Answers
Answer:
False
Step-by-step explanation:
A 78.0 kg sprinter starts a race with an acceleration of 1.64 m/s2. If the sprinter accelerates at that rate for 25 m, and then maintains that velocity for the remainder of the 100 m dash, what will be his time (in s) for the race?
Answers
The sprinter will complete the race in approximately 17.07 seconds.
To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.
Acceleration Phase:
The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:
v = u + at
Here:
v = final velocity (which is the velocity at the end of the acceleration phase)
u = initial velocity (which is 0 since the sprinter starts from rest)
a = acceleration
t = time
Rearranging the equation, we have:
t = (v - u) / a
Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:
t = v / a
Plugging in the values, we get:
t = 25 m / 1.64 m/s²
Constant Velocity Phase:
Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:
t = d / v
Here:
d = distance
v = velocity
Plugging in the values, we get:
t = 75 m / (v)
Since the velocity remains constant, we can use the final velocity from the acceleration phase.
Now, let's calculate the time for each phase and sum them up to get the total race time:
Acceleration Phase:
t1 = 25 m / 1.64 m/s²
Constant Velocity Phase:
t2 = 75 m / v
Total race time:
Total time = t1 + t2
Let's calculate the values:
t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)
Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:
v = u + at
Here:
u = initial velocity (0 m/s)
a = acceleration (1.64 m/s²)
t = time (25 m)
Plugging in the values, we get:
v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s
Now, let's calculate the time for the constant velocity phase:
t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)
Finally, let's calculate the total race time:
Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)
Therefore, the sprinter will complete the race in approximately 17.07 seconds.
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BRAINLIEST TO CORRECT
Answers
Answer:
.
Step-by-step explanation:
Determine the domain and range of the quadratic function. \(f(x)=2x^{2}-4x+2\)
Answers
The domain of a quadratic function is (-∞, +∞), and the range depends on the coefficient a and can be [c, +∞) or (-∞, c] depending on the direction of the parabola.
To determine the domain and range of a quadratic function, we consider the characteristics of the function and its graph.
The domain of a quadratic function, represented by the variable x, is the set of all possible input values for which the function is defined. Since quadratic functions are defined for all real numbers, the domain of a quadratic function is (-∞, +∞) or the set of all real numbers.
The range of a quadratic function, represented by the variable y or f(x), is the set of all possible output values that the function can take. For a quadratic function in the form f(x) = ax^2 + bx + c, where a ≠ 0, the range depends on the coefficient a. If a > 0, the parabola opens upward, and the range is [c, +∞). If a < 0, the parabola opens downward, and the range is (-∞, c].
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Consider the following table:
X: 5 , -1 , 0 , -3 , 4
Y: 0 , 6 , 5 , 8 , 1
Which graph corresponds to this table?
Answers
the equation of straight line y=-x+5
Define straight lineA straight line is a geometric object that extends infinitely in both directions and has a constant slope or gradient. It is the shortest path between two points in Euclidean space and is characterized by the equation y = mx + b, where m is the slope or gradient of the line and b is the y-intercept, which is the point where the line intersects the y-axis.
Let the equation of straight line be y=mx+c
Putting the values;
x=5
y=0
5m+c=0…..Equation 1
Putting the values;
x=0
y=5
5=c
Putting value of c in equation1, we get
5m+5=0
m=-1
Hence, the equation of straight line y=-x+5
Image of graph is attached below
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10 Ten Atlas batteries were tested to find their average life. The times, in hours, that the batteries lasted were as follows: 10.8, 10.6, 11.4, 8.9, 10.1, 10.6, 9.9, 12.6, 10.5, 11.9. a Find, to the nearest tenth of an hour, the average life of the ten batteries. b Which of the following advertisements is more accurate? i Atlas batteries are guaranteed to last 10 hours. ii Atlas batteries have an average life of over 10 hours.
Answers
a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2
Number of values = 10
Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63
Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.
b) Comparing the two advertisements:
i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum
ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.
Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.
In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.
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Question 14 (Essay Worth 12 points)
(Comparing Data HC)
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Sky View School
9, 7, 2,0
8, 7, 6, 5, 5, 5, 4, 3, 1, 0
0
1
South Lake School
5,8
0, 1, 2, 6, 6, 8
2
0 3
Key: 2|1|0 means 12 for Sky View and 10 for South Lake
5, 5, 6, 7, 8
0,6
Part A: Calculate the measures of center. Show all work. (5 points)
Part B: Calculate the measures of variability. Show all work. (5 points)
Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (2 points)
7
Answers
To find the measures of center, we need to determine the median for each school.
For Sky View School:
Arrange the data in order: 0, 0, 1, 2, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9
The median is the middle value, which is 5.
For South Lake School:
Arrange the data in order: 0, 0, 1, 2, 2, 5, 6, 6, 8
The median is the middle value, which is also 5.
Therefore, the median class size for both schools is 5.
Part B: Measures of variability
To find the measures of variability, we need to determine the range and interquartile range (IQR) for each school.
For Sky View School:
The smallest value is 0 and the largest value is 9, so the range is 9 - 0 = 9.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 1 + 2 + 3 + 4)/5 = 2. The third quartile is the median of the upper half, which is (6 + 7 + 8 +9)/4 = 7.25 (rounded to two decimal places).
Therefore, the IQR is 7.25 - 2 = 5.25.
For South Lake School:
The smallest value is 0 and the largest value is 8, so the range is 8 - 0 = 8.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 0 + 1 + 2)/4 = 0.75 (rounded to two decimal places). The third quartile is the median of the upper half, which is (6 + 6 + 8)/3 = 6.67 (rounded to two decimal places).
Therefore, the IQR is 6.67 - 0.75 = 5.92 (rounded to two decimal places).
Part C: Choosing a school based on class size
If you are interested in a smaller class size, South Lake School is the better choice. This is because the range and IQR for South Lake School are smaller than those for Sky View School, indicating that the class sizes at South Lake School are more consistent and less variable. Additionally, the largest class size at South Lake School is 8, while the largest class size at Sky View School is 9, further indicating that South Lake School may have smaller class sizes overall.
Measures of center for Sky View School:
Mean = (0+1+2+3+4+5+5+5+6+7+7+8+9)/13
Mean = 4.8
Median = 5
Measures of center for South Lake School:
Mean = (0+1+2+2+3+5+6+6+8+8)/10
Mean = 4.1
Median = 5
Part B:
Measures of variability for Sky View School:
Range = 9 - 0 = 9
Interquartile Range (IQR) = Q3 - Q1 = 7 - 2 = 5
Variance = [(0-4.8)^2 + (1-4.8)^2 + (2-4.8)^2 + (3-4.8)^2 + (4-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (6-4.8)^2 + (7-4.8)^2 + (7-4.8)^2 + (8-4.8)^2 + (9-4.8)^2]/12
Variance = 7.6
Standard Deviation = √7.6
Standard Deviation = 2.76
Measures of variability for South Lake School:
Range = 8 - 0 = 8
Interquartile Range (IQR) = Q3 - Q1 = 6 - 1 = 5
Variance = [(0-4.1)^2 + (1-4.1)^2 + (2-4.1)^2 + (2-4.1)^2 + (3-4.1)^2 + (5-4.1)^2 + (6-4.1)^2 + (6-4.1)^2 + (8-4.1)^2 + (8-4.1)^2]/9
Variance = 6.45
Standard Deviation = √6.45
Standard Deviation = 2.54
Part C:
If you are interested in a smaller class size, South Lake School is a better choice for you. This is because the measures of center and variability for South Lake School are both smaller than those for Sky View School.
Brooklyn is going to invest in an account paying an interest rate of 3.5% compounded continuously. How much would Brooklyn need to invest, to the nearest ten dollars, for the value of the account to reach $64o in 9 years?
Answers
Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.
To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:
A = \(Pe^(^r^t^)\)
where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.
In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:
640 = \(Pe^(^0^.^0^3^5^*^9^)\)
640 = Pe^0.315
P =\(640/e^0^.^3^1^5\)
P = 432.43
Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.
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Is (7,-6) a solution to this system of equations?
y = 1/7x+ 7
X = 7
yes
no
Answers
If you want to get is
Y=mx+b
Y=1/7x+7
Y=1/7*7+7 Since x=7
Y=1+7 Compute 1/7*7
Y=8
Juan's Bagel Shop has a variety of bagels for sale.
pumpernickel bagels 12
poppy seed bagels 14
raisin bagels 1
onion bagels 3
sesame seed bagels 4
What is the probability that a randomly selected bagel will be a sesame seed bagel?
Write your answer as a fraction or whole number.
P(sesame seed bagel) =
Answers
Answer:
340%
Step-by-step explanation:
I dont know I just guessed but I did
12+14+1+3+4 = 34
then I multiplied by 10 so yea.
Question 2 (2 points)
Subtract.
A) -18 - (-12) =
on &
5
Answers
Answer:
-6
(I don’t understand what you mean by on & 5 but..)
Step-by-step explanation:
The two negatives (the -(- ) cancel each other out and make a postive, so
-18 + 12 = -6
Answer:
-6
Step-by-step explanation:
-18 - (-12)=-18+12
-18+12=-6
For the following vectors, (a) find the dot product v•w ; (b) find the angle between v and w , (c) state whether the vectors are parallel, octagonal, or neither. V=-3i-4j, w=6i+8j
A- v•w
B-the angle between v and w is theta ^•?
C- the vectors v and w are?
Answers
B) The angle between vectors v and w can be found using the formula: cos(theta) = (v • w) / (||v|| ||w||), where ||v|| and ||w|| are the magnitudes of vectors v and w respectively.
First, we need to find ||v|| and ||w||:
||v|| = sqrt((-3)^2 + (-4)^2) = 5
||w|| = sqrt((6)^2 + (8)^2) = 10
Now, we can substitute in the values to get:
cos(theta) = (-50) / (5 * 10) = -1
theta = arccos(-1) = pi radians or 180 degrees.
Therefore, the angle between vectors v and w is 180 degrees.
C) Two vectors are parallel if their directions are the same, which can be determined by comparing their unit vectors.
The unit vector of v is:
v_hat = v / ||v|| = (-3/5)i + (-4/5)j
The unit vector of w is:
w_hat = w / ||w|| = (6/10)i + (8/10)j = (3/5)i + (4/5)j
We can see that the unit vectors are in opposite directions, which means that the vectors are anti-parallel or opposite. Therefore, the vectors v and w are neither parallel nor orthogonal.
7. The Taylor Rule states that the central bank should set the short-term nominal interest rate (i)
based on the inflation gap [the difference between inflation (3.14) and desired inflation (3.14*)] and the
output gap (the percentage difference between real GDP (Y) and potential GDP (Y*) An
example of a Taylor Rule would be the formula
i - 3.14 = 1.5 +0.5(3.14-3.14*) +0.5 (Y-Y*/Y*)
The term on the left-hand side is the real interest rate. Consider the following table
Inflation rate (3.14), %
Target inflation rate (3.14*), %
Output gap, %
Real interest rate
Nominal interest rate
Base Scenario Scenario B Scenario C
4.0
20
2.0
20
0.0
20
20
20
00
a. Fill in the real and nominal interest rates chosen by the policy maker in the base scenano
b. How does scenario B differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move the inflation rate toward its target?
c. How does scenario C differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move output toward the potential level?
d. Suppose a new chair of the central bank is appointed and she switches to a new policy rule of
the form given in the next equation. Recalculate the real and nominal interest rates for the
three scenarios. What has been the effect of the change in weights?
i-3.14=1.5 +0.75(3.14-3.14*) +0.25(Y-Y*/Y*)
Answers
The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%
a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.
b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).
Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).
Now, let's calculate the real interest rate.
Real interest rate in base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)
= 19.22%.
The real interest rate has moved in the direction to move inflation rate towards its target.
c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.
Inflation gap is 0% in both the scenarios
Inflation rate is 3.14% and in scenario C, inflation rate is 2%.
Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)
= 20.15%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.
The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.
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Write this number in standard form 3 thousands, 16 tens,7 ones
Answers
An algebra question does anyone know the answer?
Answers
Answer:
inverse of the function = {{2, 0), (3, 2), ( 2, 4), (0, -1)}
yes, the function is one to one.
A quarterback completes 44% of his passes. Show all work.
a. Construct a probability distribution table (out to n = 6) for the number of passes attempted before the quarterback has a completion?
b. What is the probability that the quarterback throws 3 incomplete passes before he has a completion?
c. How many passes can the quarterback expect to throw before he completes a pass?
d. Determine the probability that it takes more than 5 attempts before he completes a pass.
e. If he throws 8 passes on the opening drive, what is the probability that he made at least half of them?
Answers
a.The probability distribution table for the first six attempts is shown below:
X P(X=k)
1 0.44
2 0.56 ×0.44
3 0.56²×0.44
4 0.56³ × 0.44
5 0.56⁴ ×0.44
6 0.56⁵×0.44
b. the probability is 0.1399.
c. the quarterback can expect to throw about 2.27 passes before completing one.
d. the probability is 0.1865.
e. the probability is 0.7349.
what is probability?The possibility or chance of an event occurring is measured by probability. The expression is given as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. Compared to occurrences with a probability closer to 0, those with a probability closer to 1 are more likely to occur.
a. To construct a probability distribution table for the number of passes attempted before the quarterback has a completion, we can use the geometric probability distribution, which is given by:
P(X=k) = \((1-p)^{k-1}\)×p
where X is the number of attempts before the completion, p is the probability of completion on each attempt, and k is the number of attempts.
The probability distribution table for the first six attempts is shown below:
X P(X=k)
1 0.44
2 0.56 ×0.44
3 0.56²×0.44
4 0.56³ × 0.44
5 0.56⁴ ×0.44
6 0.56⁵×0.44
b. The probability that the quarterback throws 3 incomplete passes before he has a completion is given by:
P(X=3) = (1-0.44)³⁻¹× 0.44 × (1-0.44)⁰
= 0.56²×0.44
= 0.1399
Therefore, the probability is 0.1399.
c. The expected number of passes that the quarterback can throw before he completes a pass is given by the formula:
E(X) = 1/p
where p is the probability of completion on each attempt.
In this case, p = 0.44, so the expected number of passes is:
E(X) = 1/0.44
= 2.27
Therefore, the quarterback can expect to throw about 2.27 passes before completing one.
d. The probability that it takes more than 5 attempts before the quarterback completes a pass is given by:
P(X > 5) = 1 - P(X <= 5)
= 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]
= 1 - [0.44 + (0.56 × 0.44) + (0.56² ×0.44) + (0.56³ × 0.44) + (0.56⁴×0.44)]
= 0.1865
Therefore, the probability is 0.1865.
e. If the quarterback throws 8 passes on the opening drive, the probability that he completes at least half of them is given by the binomial probability distribution, which is given by:
P(X ≥ 4) = 1 - P(X < 4)
where X is the number of completed passes and the probability of completion on each attempt is p = 0.44.
Using the binomial probability distribution table or calculator, we can find:
P(X≥4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]
= 1 - [0.56⁸ + (8× 0.56⁷×0.44) + (28 × 0.56⁶ × 0.44²) + (56× 0.56⁵×0.44³)]
= 0.7349
Therefore, the probability is 0.7349.
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what does 3 - (-8) equal????
Answers
Answer:
11
Step-by-step explanation:
3-(-8) = 3+8
= 11
avier is considering two options for college. Option A: Complete the first two years of schooling at a community college and then transfer to a university. Option B: Complete all four years of schooling at the university.
Answers
Answer:
kok
Step-by-step explanation:
Please answer immediately I beg.
A pyramid and a cone have the same base area and height. The volume
of the pyramid is 175m³. What is the volume of the one? Explain your answer.
Answers
The volume of cone is 175 m³
Firstly,
Volume of Pyramid.
The volume (V) of a pyramid is
V = ⅓Ah
Data:
V = 175m³
Calculation:
175 = ⅓× A× h
Ah = 175*3
Ah = 525m³
Secondly,
The volume (V) of a cone is
V = ⅓Ah
Data:
Ah = 525 m³
Calculation:
V = ⅓ A× h
V = 175 m³
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If the ratio y/x is the same for all related pairs of x and y, what does that mean about the relationship between x and y?
Answers
Answer:
The the relationship is linear
Step-by-step explanation:
If y/x is same for all pairs of x and y, slope is a constant value that is not changed by value of x or y. Hence, it is linear function.
If f(x)=x^(2)+3x-2, find f(-2)
Answers
Answer:
hello
Step-by-step explanation:
Choose the table that represents g(x) = 3⋅f(x) when f(x) = x − 1
Answers
What is the length of BC?
Answers
Answer:
18
Step-by-step explanation:
AC=AB
BC^2=AB^2+AC^2
162+162=324
Square root of 324 is 18.
Write the
degree of (x²+1) (x3 + 1)²
Answers
Answer:
The polynomial degree is 8
Step-by-step explanation:
A line that includes the point (4, 7) has a slope of 3. What is its equation in slope-intercept form?
Answers
Answer: slope intercept is solve for y
Step-by-step explanation:
point slope
y-y1=m(x1,y1) and the slope is m
given
slope=3
a point i (4,7)
y-7=3(x-4)
solve for y
y-7=3x-12
add 7 both sides
y=3x-5 is slope intercept form
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 8. If there were 9854 total votes, how many no votes were there?
Answers
There were approximately 6056 no votes.
Let's assume the number of yes votes is represented by the variable "5x," where x is a positive constant.
Similarly, the number of no votes can be represented by "8x" since the ratio of yes votes to no votes is 5 to 8.
The total number of votes is given as 9854, so we can set up the following equation:
\(5x + 8x = 9854\)
Combining like terms, we have:
\(13x = 9854\)
To solve for x, we divide both sides of the equation by 13:
\(x = \frac{9854 }{13}\)
\(x \approx 757.23\)
Since x represents a positive constant, we round it to the nearest whole number, giving us x = 757.
Now, we can find the number of no votes by multiplying x by the ratio of no votes:
No votes \(= 8x\)
\(= 8 \times 757\)
\(= 6056\)
Therefore, there were approximately 6056 no votes.
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I’m confused with this question
Answers
9514 1404 393
Answer:
(a) max: None; min: -5
(b) max: 5; min: None
Step-by-step explanation:
a) The upward pointing arrow on the end of the graphed curve tells you that the graph extends upward indefinitely. There is no absolute maximum value.
The solid dot at (-4, -5) is the lowest point on the graph. That tells you the absolute minimum is -5.
__
b) The solid dot at (-4, 5) is the highest point on the graph. That tells you the absolute maximum is 5.
The open dot at (3, -5) is the lowest point on the graph. This means values of the function can be arbitrarily close to -5, but -5 is not one of them. There is no absolute minimum value.
Simplify (a÷b)³×(b÷c)×(c÷a)³ when a=3,b=a²,c=a³
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Answer:
To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.
Substituting the values of a, b, and c:
a = 3
b = a² = 3² = 9
c = a³ = 3³ = 27
Now let's simplify the expression:
(a÷b)³×(b÷c)×(c÷a)³
(3÷9)³×(9÷27)×(27÷3)³
Simplifying each term:
(3÷9) = 1/3
(9÷27) = 1/3
(27÷3) = 9
Now we can substitute the simplified values back into the expression:
(1/3)³×(1/3)×9
Simplifying further:
(1/27)×(1/3)×9
1/9
Therefore, the simplified expression is 1/9.
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Answer:
A
Step-by-step explanation: