Answer:
see below
Step-by-step explanation:
(ab)^n=a^n * b^n
We need to show that it is true for n=1
assuming that it is true for n = k;
(ab)^n=a^n * b^n
( ab) ^1 = a^1 * b^1
ab = a * b
ab = ab
Then we need to show that it is true for n = ( k+1)
or (ab)^(k+1)=a^( k+1) * b^( k+1)
Starting with
(ab)^k=a^k * b^k given
Multiply each side by ab
ab * (ab)^k= ab *a^k * b^k
( ab) ^ ( k+1) = a^ ( k+1) b^ (k+1)
Therefore, the rule is true for every natural number n
Hello, n being an integer, we need to prove that one statement depending on n is true, let's note it S(n).
The mathematical induction involves two steps:
Step 1 - We need to prove S(1), meaning that the statement is true for n = 1
Step 2 - for k integer > 1, we assume S(k) and we need to prove that S(k+1) is true.
Imagine that you are a painter and you need to paint all the trees on one side of a road. You have several colours that you can use but you are asked to follow two rules:
Rule 1 - You need to paint the first tree in white.
Rule 2 - If one tree is white you have to paint the next one in white too.
What colour do you think all the trees will be painted?
Do you see why this is very important to prove the two steps as well ?
Let's do it in this example.
Step 1 - for n = 1, let's prove that S(1) is true, meaning [tex](ab)^1=a\cdot b =a^1\cdot b^1[/tex]
So the statement is true for n = 1
Step 2 - Let's assume that this is true for k, and we have to prove that this is true for k+1
So we assume S(k), meaning that [tex](ab)^k=a^k\cdot b^k[/tex]
and what about S(k+1), meaning [tex](ab)^{k+1}=a^{k+1}\cdot b^{k+1}[/tex] ?
We will use the fact that this is true for k,
[tex](ab)^{k+1}=(ab)\cdot (ab)^k =(ab) \cdot a^k \cdot b^k[/tex]
We can write it because the statement at k is true and then we can conclude.
[tex](ab)^{k+1}=(ab)\cdot (ab)^k =(ab) \cdot a^k \cdot b^k=a^{k+1}\cdot b^{k+1}[/tex]
In conclusion, we have just proved that S(n) is true for any n integer greater or equal to 1, meaning [tex](ab)^{n}=a^{n}\cdot b^{n}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A right circular cone has a volume of 30π m. If the height of the cone is multiplied by 6 but the radius remains fixed, which expression represents the resulting volume of the larger cone?
A. 6 + 30π m
B. 6 x 30π m
C. 6 x 30π m
D. 6 x (30π) m
PLZ HURRY IM TIMED
Answer:
Below
Step-by-step explanation:
The formula of the volule of a cone is:
● V= (1/3) × Pi × r^2 × h
h is the height and r is the radius.
■■■■■■■■■■■■■■■■■■■■■■■■■■
We are given that the volume is 30 Pi m^3
● V = 30 Pi
● 1/3 × Pi × r^2 × h = 30 Pi
If we multiply h by 6 we should do the same for 30 Pi since it's an equation
● 1/3 × Pi × r^2 × h = 30 × Pi × 6
Answer:
REVIEW: B is Correct Exit
A right circular cone has a volume of 30π m. If the height of the cone is multiplied by 6 but the radius remains fixed, which expression represents the resulting volume of the larger cone?
A. 6 + 30π m
B. 6 x 30π m
C. 6 x 30π m
D. 6 x (30π) m
Step-by-step explanation:
The answer is be all i did was dig into what the other person was saying and got b it is correct:)
The mean number of days to observe rain in a particular city is 20 days with a standard deviation of 2 days. Suppose that the rain pattern is Normally distributed. what is the probability of raining if the number of days are more than 23?
Answer:
The probability of raining if the number of days is more than 23 is 0.0668.
Step-by-step explanation:
We are given that the mean number of days to observe rain in a particular city is 20 days with a standard deviation of 2 days.
Let X = Number of days of observing rain in a particular city.
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean number of days = 20 days
[tex]\sigma[/tex] = standard deviation = 2 days
So, X ~ Normal([tex]\mu=20, \sigma^{2} = 2^{2}[/tex])
Now, the probability of raining if the number of days is more than 23 is given by = P(X > 23 days)
P(X > 23 days) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{23-20}{2}[/tex] ) = P(Z > 1.50) = 1 - P(Z [tex]\leq[/tex] 1.50)
= 1 - 0.9332 = 0.0668
The above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.
Alpha (a) is used to measure the error for decisions concerning true null hypotheses. What is beta (ß) error used to measure?
Answer:
Alpha (α) is used to measure the error for decisions concerning true null hypotheses, while beta (ß) is used to measure error for decisions concerning false null hypotheses.
Step-by-step explanation:
Suppose we have events X and Y.
1. If it is said that X equals Y, when X is actually not equal to Y, α is used in this case, the null hypotheses.
2. If X is said to not be equal to Y, when X is actually equal to Y, β is used in this case, the false null hypotheses.
6 people consists of 3 married couples. Each couple wants to sit with older partner on the left.
Required:
a. How many ways can they be seated together in the row?
b. Suppose one of the six is a doctor who must sit on the aisle in case she is paged. How many ways can the people be seated together in the row with the doctor in an aisle seat?
c. Suppose the six people consist of three married couples and each couple wants to sit together with the husband on the left. How many ways can the six be seated together in the row?
a. The first part asks for how many ways they can be seated together in a row. Therefore we want the permutations of the set of 6 people, or 6 factorial,
6! = 6 [tex]*[/tex] 5
= 30 [tex]*[/tex] 4
= 360 [tex]*[/tex] 2 = 720 possible ways to order 6 people in a row
b. There are two cases to consider here. If the doctor were to sit in the left - most seat, or the right - most seat. In either case there would be 5 people remaining, and hence 5! possible ways to arrange themselves.
5! = 5 [tex]*[/tex] 4
= 20 [tex]*[/tex] 3
= 120 [tex]*[/tex] 1 = 120 possible ways to arrange themselves if the doctor were to sit in either the left - most or right - most seat.
In either case there are 120 ways, so 120 + 120 = Total of 240 arrangements among the 6 people if the doctor sits in the aisle seat ( leftmost or rightmost seat )
c. With each husband on the left, there are 3 people left, all women, that we have to consider here.
3! = 3 [tex]*[/tex] 2 6 ways to arrange 3 couples in a row, the husband always to the left
A city council consists of seven Democrats and six Republicans. If a committee of five people is selected, find the probability of selecting two Democrats and three Republicans.
Answer:
solution,
let d and r denote democrats and republicans respectively.
given,
no. of total sample space n(s) =7+6=13
no. of total democrats n(d)=7
no. of total republicans n(r)=6
no. of democrats events n(D1)=2
no. of republicans events n(R1)=3
it is a mutually exclusive event. so the probability of selecting two democrats and three republicans= {n(D1)/n(s)} * {n(r1)/n(s)}
=(2/13)*(3/13)
=6/169
Answer:
6/169
Step-by-step explanation:
Find the first three nonzero terms in the power series expansion for the product f(x)g(x).
f(x) = e^2x = [infinity]∑n=0 1/n! (2x)^n
g(x) = sin 5x = [infinity]∑k=0 (-1)^k/(2k+1)! (5x)^2k+1
The power series approximation of fx)g(x) to three nonzero terms is __________
(Type an expression that includes all terms up to order 3.)
Answer:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 1 to 3.
= -196.5
Step-by-step explanation:
Given
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to infinity
The expression that includes all terms up to order 3 is:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to 3.
= 0 + (-1/2 × 5³) + (1/6 × 10^5) + (-1/5040 × 15^5)
= -125/2 + 100000/6 - 759375/5040
= -62.5 + 16.67 - 150.67
= - 196.5
A classroom has 35 students. If the ratio of boys to girls was 5:2, , how many girls were in the class
Answer:
35/14
Step-by-step explanation: 35/14
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
Answer:
10 girls.
Step-by-step explanation:
Boys: 5x
Girls: 2x
next... 5x + 2x = 35
7x= 35
x=5
Answer. 10 girls.
Calculate the nominal rate of interest convertible once every four years that is equivalent to a nominal rate of discount convertible quarterly. Let d^(4) be the nominal rate of discount convertible quarterly.
Answer:
i am having issues using the math editor and my time is almost running out. i added an attachment.
Step-by-step explanation:
Christina's time for a race was 22.3 seconds. Another runner's time was 4.41 seconds faster. Write and evaluate an equation with a variable to find the difference between Christina's time and the other runner's time.
Answer:
[tex]Difference = 4.41[/tex]
Step-by-step explanation:
Given
Represent Christina's time with C and the other runner's time with R
C = 22.3
R = 4.41 + C
Required
Determine the difference using an equation
The difference between both runner's time is as follows;
[tex]Difference = R - C[/tex]
Substitute 4.41 + C for R
[tex]Difference = 4.41 + C - C[/tex]
[tex]Difference = 4.41[/tex]
Hence, the difference is 4.41 seconds
group the like term together
Answer:
Step-by-step explanation:
[tex]xy^{2}[/tex], [tex]5y^{2}x[/tex], [tex]\frac{-3}{5}[/tex][tex]xy^{2}[/tex]
[tex]-3x^{2}y[/tex], [tex]\frac{2}{3}[/tex][tex]yx^{2}[/tex]
Hope this helps
plz mark it as brainliest!!!!!
Can someone explain to me what a “derivative” means? How do you find the derivative of f(x)=x^3+1?
if 2500 amounted to 3500 in 4 years at simple interest. Find the rate at which interest was charged
Answer:
35%
Step-by-step explanation:
[tex]Principal = 2500\\\\Simple\:Interest = 3500\\\\Time = 4 \:years\\\\Rate = ?\\\\Rate = \frac{100 \times Simple \: Interest }{Principal \times Time}\\\\Rate = \frac{100 \times 3500}{2500 \times 4} \\\\Rate = \frac{350000}{10000}\\\\ Rate = 35 \%[/tex]
[tex]S.I = \frac{PRT}{100}\\\\ 100S.I = PRT\\\\\frac{100S.I}{PT} = \frac{PRT}{PT} \\\\\frac{100S.I}{PT} = R[/tex]
Answer:
35%
Step-by-step explanation:
I REALLY HOPE I HELPED
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
How to convert 2cm to feet?
Answer:
Divide by 30.48: It would be 0.0656168 feet.
Step-by-step explanation:
Answer:
0.0656
Step-by-step explanation:
2.54 cm = 1 in
12 in = 1 ft
2.54 * 12 = 30.48
2/30.48 = 0.0656167979
A farmer decides to try out a new fertilizer on a test plot containing 10 stalks of corn. Before applying the fertilizer, he measures the height of each stalk. Two weeks later, after applying the fertilizer, he measures the stalks again. He compares the heights of these stalks to 10 stalks that did not receive fertilizer. Did the fertilizer help? Use a significance level of 0.10 to test whether the height of the stalks increased.
The differences are calculated and the mean difference is found to be -3.36 inches with a standard deviation of 1.05 inches. Set up the appropriate hypothesis test and find the standardized test statistic.
t* = -14.31
t* = 3.2
t* = -3.2
t* = -10.12
Answer:
d) t = -10.12
Step-by-step explanation:
Explanation:-
Given sample size 'n'=10
Given the differences of mean x⁻ -μ = -3.36
Standard deviation of the sample 'S' =1.05 inches
We will use t-statistic
[tex]t = \frac{x^{-}-Mean }{\frac{S}{\sqrt{n} } }[/tex]
[tex]t= \frac{-3.36}{\frac{1.05}{\sqrt{10} } }[/tex]
t = -10.12
Answer: D
Step-by-step explanation:
10 points plssssss!!!
Answer:
A. rectangle
B. any of triangle, quadrilateral, pentagon, hexagon
Step-by-step explanation:
A. A plane perpendicular to the base will intersect 2 adjacent or 2 opposite lateral faces, as well as the two bases. Each plane intersected will result in an edge of the cross sectional figure. The figure will have two pairs of parallel edges, so is a rectangle.
__
B. If the intersecting plane is not constrained to be perpendicular to the base(s), it can intersect 3, 4, 5, or all 6 faces of the prism. Hence, the shape of the cross section can be any of ...
trianglequadrilateralpentagonhexagonAn Uber driver provides service in city A and city B only dropping off passengers and immediately picking up a new one at the same spot. He finds the following Markov dependence. For each trip, if the driver is in city A, the probability that he has to drive passengers to city B is 0.25. If he is in city B, the probability that he has to drive passengers to city A is 0.45. Required:a. What is the 1-step transition matrix? b. Suppose he is in city B, what is the probability he will be in city A after two trips? c. After many trips between the two cities, what is the probability he will be in city B?
Answer:
a. 1-step transition matrix is be expressed as:
[tex]P= \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right][/tex]
b. The probability that he will be in City A after two trips given that he is in City B = 0.585
c. After many trips, the probability that he will be in city B = 0.3571
Step-by-step explanation:
Given that:
For each trip, if the driver is in city A, the probability that he has to drive passengers to city B is 0.25
If he is in city B, the probability that he has to drive passengers to city A is 0.45.
The objectives are to calculate the following :
a. What is the 1-step transition matrix?
To determine the 1 -step transition matrix
Let the State ∝ and State β denotes the Uber Driver providing service in City A and City B respectively.
∴ The transition probability from state ∝ to state β is 0.25.
The transition probability from state ∝ to state ∝ is 1- 0.25 = 0.75
The transition probability from state β to state ∝ is 0.45. The transition probability from state β to state β is 1 - 0.45 = 0.55
Hence; 1-step transition matrix is be expressed as:
[tex]P= \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right][/tex]
b. Suppose he is in city B, what is the probability he will be in city A after two trips?
Consider [tex]Y_n[/tex] = ∝ or β to represent the Uber driver is in City A or City B respectively.
∴ The probability that he will be in City A after two trips given that he is in City B
=[tex]P(Y_0 = 2, Y_2 = 1 , Y_3 = 1) + P(Y_0 = 2, Y_2 = 2 , Y_3 = 1)[/tex]
= 0.45 × 0.75 + 0.55 × 0.45
= 0.3375 + 0.2475
= 0.585
c. After many trips between the two cities, what is the probability he will be in city B?
Assuming that Ф = [ p q ] to represent the long run proportion of time that Uber driver is in City A or City B respectively.
Then, ФP = Ф , also p+q = 1 , q = 1 - p and p = 1 - q
∴
[tex][ p\ \ \ q ] = \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right] [ p\ \ \ q ][/tex]
0.75p + 0.45q = q
-0.25p + 0.45q = 0
since p = 1- q
-0.25(1 - q) + 0.45q = 0
-0.25 + 0.25 q + 0.45q = 0
0.7q = 0.25
q = [tex]\dfrac{0.25} {0.7 }[/tex]
q = 0.3571
After many trips, the probability that he will be in city B = 0.3571
Classify the following random variable according as either discrete or continuous. The temperature in degrees Celsius on January 1st in a certain city
A continuous
B discrete
Answer:
continuous
Step-by-step explanation:
A quantity like temperature is a continuous random variable. A continuous random variable is different from a discrete random variable because it can take on many values infinitely.
From the question, measuring the Temperature in degrees can take on many different values because there are an uncountable number of possible temperatures that could be taken.
GIVING OUT BRAINLIEST TO THE FIRST PERSON TO ANSWER!!
One circle has a diameter of 6 inches. A second, larger circle has a diameter that is four times the diameter of the first circle. What is the ratio of the area of the smaller circle to the larger circle?
A. 2:3
B. 1:6:4
C. 1:16
D. 1:64
Please include ALL work! <3
Answer:
The answer is option CStep-by-step explanation:
To find the ratio first find the diameter of the larger circle
Diameter of first circle = 6 inches
Diameter of second circle = 4 × diameter of the first circle
Which is
Diameter of second circle
= 4 × 6 = 24 inches
Area of a circle = πr²
r is the radius
Area of smaller circle
Diameter = 6 inches
Radius = 6 / 2 = 3 inches
Area = (3)² π = 9π in²
Area of larger circle
Diameter = 24 inches
Radius = 24 / 2 = 12 inches
Area = (12)²π = 144π in²
The ratio of the smaller circle to the larger circle is
[tex] \frac{9\pi}{144\pi} [/tex]
Reduce the fraction by 9π
That's
[tex] \frac{1}{16} [/tex]
We have the final answer as
1 : 16Hope this helps you
Answer:
C. 1:16
Step-by-step explanation:
Area of a circle is:
[tex]\pi \times {r}^{2} [/tex]
Small circle Area:
radius = diameter/2
radius = 6/2 = 3
[tex]area \: of \: a \: circle \: = \pi {3}^{2} [/tex]
a = 28.27
Large circle 4 times larger diameter
6*4 = 24
diameter = 24
r = 24/2
r = 12
[tex]a \: = \pi {12}^{2} [/tex]
a = 452.39
area of large circle/ area of small circle
452.39/28.27 = 16.00
ratio is 1:16
The area of the triangle is 5.88 square centimeters.what is the length of the base.the heights is 2.1
Answer:
base = 5.6 cm
Step-by-step explanation:
area of a triangle = 1/2 * base * height
area = 5.88 cm²
height = 2.1 cm
5.88 = 1/2 * base * 2.1
5.88 = 1.05 base
5.88 / 1.05 = base
base = 5.6 cm
the area of triangle is 5.25 sq cm what is length of base
The Masim family’s monthly budget is shown in the circle graph provided in the image. The family has a current monthly income of $5,000. How much money do they spend on food each month? A. $250 B. $500 C. $750 D. 1,100 Please show ALL work! <3
Answer:
C. $750
Step-by-step explanation:
The amount of money to be spent monthly on food = percentage covered by food in the circle ÷ 100% × total monthly income
= [tex] \frac{15}{100}*5000 [/tex]
[tex] = \frac{15}{1}*50 [/tex]
[tex] 15*50 = 750 [/tex]
Amount of money spent each month by the Masims is $750.
The local bowling alley pays you
$7.25 per hour to manage the desk.
Last week you worked 16 hours.
What is your straight-time pay?
Answer:
my straight time payment will be $116 for last week
Step-by-step explanation:
The local bowling alley pays
$7.25 per hour to manage the desk.
If worked 16 hours, my straight time payment will be
Rate= $7.25 per hour
Hour worked= 16 hours
my straight time payment = rate*hour worked
my straight time payment = 7.25*16
my straight time payment = 166.00
my straight time payment will be $116
what is the magnitude of the vector?
Answer:
[tex]\boxed{\sqrt{65}}[/tex]
Step-by-step explanation:
Magnitude is solved with the following equation: [tex]\sqrt{x^{2}+y^{2}}[/tex]
Therefore, just plug in your x and y-values and solve.
[tex]\sqrt{4^{2}+7{^{2}}[/tex]
[tex]\sqrt{16 + 49}[/tex]
[tex]\sqrt{65}[/tex]
Because [tex]\bold{\sqrt{65}}[/tex] cannot be simplified further, this is the magnitude of the vector.
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = - x
B.
y = -2x
C.
y = 2x
D.
y = x
E.
y = -4x
F.
y = - x
Answer:
The answer is option FStep-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To calculate the equation of the line first find the slope
Slope of the line using points
(0 , 0) and (4 , -2) is
[tex]m = \frac{ - 2 - 0}{4 - 0} = \frac{ - 2}{4} = - \frac{1}{2} [/tex]
Now use the formula
y - y1 = m(x - x1) to find the equation of the line using any of the points
Using point (0,0)
That's
[tex]y - 0 = - \frac{ 1}{2} (x - 0)[/tex]
The final answer is
[tex]y = - \frac{1}{2} x[/tex]
Hope this helps you
Answer:
F
Step-by-step explanation:
Please helppp meee I don’t know the answer
Answer:
First use the protractor then round the number to the nearest 10
Answer:
Round to the nearest tenth
Step-by-step explanation:
determine x in the following equation 2x - 4 = 10
Answer:
7
Step-by-step explanation:
10+4 = 14
14/2 = 7
x = 7
The amount of rainfall in January in a certain city is normally distributed with a mean of 3.1 inches and a standard deviation of 0.4 inches. Find the value of the quartile Q 1.
Answer:
2.83
Step-by-step explanation:
For a normally distributed data :
Mean = 3.1 inches
Standard deviation = 0.4 inches
Find the value of the quartile Q1:
The quartile Q1 represents the first quartile which is the Lower 25% of the distribution
25% = 0.25
Using the z-table :
0.25 = - 0.68
The z- score formula
Z-score = ( x - mean / standard deviation)
-0.68 = ((x - 3.1) / 0.4)
x - 3.1 = (-0.68 * 0.4)
x - 3.1 = - 0.272
x = - 0.272 + 3.1
x = 2.828
x = 2.83
Mathematical induction is:
Answer:
The third option.
Step-by-step explanation:
Mathematical induction is a 2 step mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number.
Step 1 (Base step) - It proves that a statement is true for the initial value.
Step 2 (Inductive step) - It proves that if the statement is true for the nth iteration (or number n), then it is also true for (n + 1)th iteration (or number n + 1)
Hope this helps.
Please mark Brainliest.
Answer:
A method of improving statments
Step-by-step explanation:
"Mathematical Induction is a mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number."
Help Quick Please. Will give brainliest.
Answer:
72[tex]\sqrt{3}[/tex] units²
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = ST = a = 12 and h = RS
To calculate RS use the tangent ratio in the right triangle and the exact value
tan60° = [tex]\sqrt{3}[/tex] , thus
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{RS}{ST}[/tex] = [tex]\frac{RS}{12}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 12 )
RS = 12[tex]\sqrt{3}[/tex]
Thus
A = [tex]\frac{1}{2}[/tex] × 12 × 12[tex]\sqrt{3}[/tex] = 6 × 12[tex]\sqrt{3}[/tex] = 72[tex]\sqrt{3}[/tex] units²
What is the volume of a cube with a side length of
of a unit?
A cube has an edge of 2 feet. The edge is increasing at the rate of 5 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed.
Answer:
[tex]V(m) = (2 + 5m)^3[/tex]
Step-by-step explanation:
Given
Solid Shape = Cube
Edge = 2 feet
Increment = 5 feet per minute
Required
Determine volume as a function of minute
From the question, we have that the edge of the cube increases in a minute by 5 feet
This implies that,the edge will increase by 5m feet in m minutes;
Hence,
[tex]New\ Edge = 2 + 5m[/tex]
Volume of a cube is calculated as thus;
[tex]Volume = Edge^3[/tex]
Substitute 2 + 5m for Edge
[tex]Volume = (2 + 5m)^3[/tex]
Represent Volume as a function of m
[tex]V(m) = (2 + 5m)^3[/tex]
