Answers
Answer:
d
Step-by-step explanation:
Related Questions
Each of two vectors, and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?
Answers
Answer:
A lies along the positive x-axis and B lies along negative x - axis .
Step-by-step explanation:
They tell us that we have two vectors, A and B. And they give us a series of conditions for this, now, what would be the correct possibility.
A lies along the positive x-axis and B lies along negative x - axis .
This is because when both vectors will be in x axis but opposite to each other, then the angle between them will be 180 ° and cos180 ° is -1.
Three judges measure the lap times of a runner and each measurement is different from the others by a few hundredths of a second. The most likely reason for this difference is
Answers
Answer:
Systematic error
Step-by-step explanation:
Assuming that none of the judges are biased, the most likely reason for this difference is the occurrence of systematic errors.
Systematic errors are errors introduced by inaccuracy in the experimental design, be it in the observation or measurement process.
In this case, the reaction time from observing the finish and stopping the clock for each judge might be different, which configures a systematic error.
earning a 6% pay increase to current $62,900 annual salary
Answers
Answer:
Step-by-step explanation:
I assume you are asking for the new salary.
To find 1%, divide 62900 by 100.
629
Multiply this by 3.
1887
Add this to the original answer.
64787
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.5 days and a standard deviation of 2.3 days. What is the probability of spending more than 4 days in recovery? (Round your answer to four decimal places.)
Answers
Answer:
[tex]P(X>4)=P(\frac{X-\mu}{\sigma}>\frac{4-\mu}{\sigma})=P(Z>\frac{4-5.5}{2.3})=P(z>-0.652)[/tex]
And we can find this probability with the complement rule and with the normal standard table and we got:
[tex]P(z>-0.652)=1-P(z<-0.652)= 1-0.2572= 0.7428[/tex]
Step-by-step explanation:
Let X the random variable that represent the patient recovery time of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(5.5,2.3)[/tex]
Where [tex]\mu=5.5[/tex] and [tex]\sigma=2.3[/tex]
We are interested on this probability
[tex]P(X>4)[/tex]
And we can solve this problem using the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
And using this formula we got:
[tex]P(X>4)=P(\frac{X-\mu}{\sigma}>\frac{4-\mu}{\sigma})=P(Z>\frac{4-5.5}{2.3})=P(z>-0.652)[/tex]
And we can find this probability with the complement rule and with the normal standard table and we got:
[tex]P(z>-0.652)=1-P(z<-0.652)= 1-0.2572= 0.7428[/tex]
An ecologist wishes to mark off a circular sampling region having radius 10 m. However, the radius of the resulting region is actually a random variable R with the following pdf. f(r) = 3/4 [1 ? (12 ? r)^2] 11 ? r ? 13 0 otherwise
What is the expected area of the resulting circular region? (Round your answer to two decimal places.)
Answers
Answer:
expected area = 453.20 m^2
Step-by-step explanation:
The given data 11 ≤ r ≤ 13
[tex]\left \{ {{3/4(1-(12-r)^2} \atop {0}} \right.[/tex] o / w
Th expected area of the insulating circular region can be calculated using
= E([tex]\pi r^2 )[/tex]
= [tex]\pi E(r^2)[/tex]
we will have to calculate [tex]E(r^2)[/tex]
attached is the remaining part of the solution
The following frequency table summarizes a set of data.
Value Frequency
2 3
3 2
5 1
6 3
7 1
8 2
11 3
For the above data set, you are interested to determine the "spread" of the data.
Would you employ calculations for the sample standard deviation, or population standard deviation for this data set?
You are interested in the heights of students at a particular middle school. Your data set represents the heights of all students in the middle school with 600 students.
Select the correct answer below:
a. Use calculations for sample standard deviation.
b. Use calculations for population standard deviation.
Answers
Answer:
Part A
The population standard deviation is suitable for this dataset as it isnt given whether its a sample or a population distribution and it sure doesn't seem like the findings from such a dataset is to be generalized for some population distribution.
Part B
This is outrightly a population distribution of all the students in the middle school, So, the spread of the height of all students about a mean is best indicated using the population standard deviation.
Step-by-step explanation:
The spread of a dataset is usually the measure of dispersion, a measure of the way the distribution spreads out from a particular mean value.
The problem of which type of standard deviation one should calculate usually arises a lot in Statistics. As the name sounds, population standard deviation usually uses all of the distribution to compute while the sample standard deviation uses the data from the sample distribution
The best advice on when to use the population stamdard deviation formula is that
(1) we have the entire population or
(2) we have a sample of a larger population, but we are only interested in this sample and do not wish to generalize the statistical findings to the population.
The sample standard deviation formula is used when one has a sample of a larger population, one is not only interested in this sample and one wishes to generalize the findings to the population.
The population standard deviation is given as
σ = √[Σ(x - xbar)²/N]
Sample standard deviation
σ = √{[Σ(x - xbar)²]/N-1)}
The only difference is the N and (N-1).
So, for the questions presented,
Part A.
Here, it is evident that the findings for this dataset in the question is just for this dataset, hence,the population standard deviation is suitable for this dataset.
Part B
This is outrightly a population distribution of all the students in the middle school, So, the spread of the height of all students about a mean is best indicated using the population standard deviation.
Hope this Helps!!!
Ujalakhan01! Please help me! ASAP ONLY UJALAKHAN01. What's (x-1)(x-1)?
Answers
Answer:
[tex]x^2-2x+1[/tex]
Step-by-step explanation:
=> (x-1)(x-1)
Using FOIL
=> [tex]x^2-x-x+1[/tex]
=> [tex]x^2-2x+1[/tex]
Answer:
Step-by-step explanation:
simply :
(x-1)(x-1)= (x-1)²= x²-2x=1
One hour is equal to how many seconds? Remember, 1 hour = 60 minutes and 1 minute = 60 seconds.
Answers
Hey there! :)
Answer:
3600 seconds.
Step-by-step explanation:
We can convert from seconds to hours using ratios:
60 seconds = 1 minute
60 minutes = 1 hour
Therefore:
[tex]\frac{60 sec}{1 min} * \frac{60 min}{1 hour} = \frac{3600sec}{1hour}[/tex]
There are 3600 seconds in an hour.
A = P(1 + nr) for r
Answers
Answer:
r = (An−nP)/P
Step-by-step explanation:
A = P(1 + nr)
Divide P on both sides.
A/P = 1 + nr
Subtract 1 on both sides.
A/P - 1 = nr
Divide n on both sides.
A/P/n - 1/n = r
(An−nP)/P = r
The answer is, r = (An−nP)/P
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
here, we have,
given that,
A = P(1 + nr)
Divide P on both sides.
A/P = 1 + nr
Subtract 1 on both sides.
A/P - 1 = nr
Divide n on both sides.
A/P/n - 1/n = r
(An−nP)/P = r
hence, answer is (An−nP)/P = r.
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–24(b − 966) = –768
b = _______
Answers
Answer:
b = 998
Step-by-step explanation:
first distribute the -24
-24b + 23184 = -768
then subtract 23184 on both sides to get
-24b = -23952
then divide -24 on both sides to get
b = 998
then to make sure it is correct you plug it back in
-24(998-966) = -768
Answer:
b = 998
Step-by-step explanation:
[tex]-24(b-966)=-768\\-24b+23184=-768\\-24b=-23,952\\24b=23,952\\b=998[/tex]
Find a function Bold r (t )r(t) for the line passing through the points Upper P (0 comma 0 comma 0 )P(0,0,0) and Upper Q (1 comma 7 comma 6 )Q(1,7,6). Express your answer in terms of Bold ii, Bold jj, and Bold kk.
Answers
Answer:
[tex]r(t)=-ti-7tj-6tk[/tex]
Step-by-step explanation:
Given the points P(0,0,0) and Q(1,7,6).
We are to determine a function r(t) for the line passing through P and Q.
To do this, we express it in the form:
[tex]r(t)=r_0+tD,$ where:\\ r_0$ is the starting point and D is the direction vector.[/tex]
[tex]D=P-D=<0,0,0> -<1,7,6>=<-1,-7,-6)[/tex]
Therefore:
[tex]r(t)=<0,0,0>+t<-1,-7,-6>\\=<-t,-7t,-6t>\\$Therefore, the function for the line passing through P and Q is:$\\r(t)=-ti-7tj-6tk[/tex]
You buy a 33-pound bag of flour for $9 or you can buy a 1- pound bag for $0.39. Compare the per pound cost for the large and small bag. How much is the pounds per dollars
Answers
Answer:
see below
Step-by-step explanation:
9 dollars / 33 lbs = .272727 dollars per lb
.39 / 1 lbs = .39 per lb
The large bag is less expensive
Element X decays radioactively with a half life of 11 minutes. If there are 670 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 26 grams?
Answers
The element X will take 22.10 minutes to decay to 26 grams.
What is radioactive radiation?The radioactive radiations are the radiations that an atom nucleus releases.
What is an arithmetic progression?It is a sequence of numbers which have common difference.
How to find the time?The decaying acts like an arithmetic progression in which a=670,d=-30.45 (per minute decaying) and n we have to find with the an value of 26 gram.
So, the formula of nth term of an arithmetic progression is
nth term=a+(n-1)d
26=670+(n-1)*(-30.45)
-644=-30.45n+30.45
-674.45=-30.45n
n=22.10 (after rounding off)
Hence the element X would take 22.10 minutes to decay to 26 grams.
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Answer:
y=a(.5)^{\frac{t}{h}}
y=a(.5)
h
t
y=30 \hspace{15px} a=670 \hspace{15px} h=11 \hspace{15px} t=?
y=30a=670h=11t=?
30=670(.5)^{\frac{t}{11}}
30=670(.5)
11
t
\frac{30}{670}=\frac{670(.5)^{\frac{t}{11}}}{670}
670
30
=
670
670(.5)
11
t
0.0447761=(.5)^{\frac{t}{11}}
0.0447761=(.5)
11
t
\log(0.0447761)=\log((.5)^{\frac{t}{11}})
log(0.0447761)=log((.5)
11
t
)
\log(0.0447761)=\frac{t}{11}\log(.5)
log(0.0447761)=
11
t
log(.5)
Power Rule.
11\log(0.0447761)=t\log(.5)
11log(0.0447761)=tlog(.5)
Multiply by 11.
\frac{11\log(0.0447761)}{\log(.5)}=\frac{t\log(.5)}{\log(.5)}
log(.5)
11log(0.0447761)
=
log(.5)
tlog(.5)
Divide by log(.5).
t=\frac{-14.838489}{-0.30103}
t=
−0.30103
−14.838489
t=49.29239\approx 49.3 \text{ minutes}
t=49.29239≈49.3 minutes
Step-by-step explanation:
A study was conducted on 64 female college athletes. The researcher collected data on a number of variables including percent body fat, total body weight, lean body mass, and age of athlete. The researcher wondered if total body weight (TBW), lean body mass (LBM), and/or age are significant predictors of % body fat. All conditions have been checked and are met and no transformations were needed. The partial technology output from the multiple regression analysis is given below. How many degrees of freedom does the F-statistic have in this problem?
Answers
Answer:
Hello please your question is in-complete attached is the complete question
degree of freedom = -62.90 ( e )
Step-by-step explanation:
The formula for calculating the F-statistic/test statistic is
test - statistic = Coef ( LBW) / SE Coef ( LBW )
= -0.72399 / 0.01151
= - 62.90
the degree of freedom the F-statistic has = -62.90
F-statistic test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. the value of the test can be gotten from running an ANOVA test or regression analysis on the statistical models
Using the definition of degrees of freedom, it is found that the F-statistic has 63 df.
When a hypothesis is tested, the number of degrees of freedom is one less than the sample size.
In this problem, the sample size is of n = 64.
Hence:
df = n - 1 = 64 - 1 = 63
The F-statistic has 63 df.
A similar problem is given at https://brainly.com/question/16194574
How do I reflect over the x-axis?
Answers
Answer:
Whatever the coordinates are it will be (x,y) all yo have to do is make y negative and thats a refelection
Step-by-step explanation:
Reflection in the x -axis:
The rule for a reflection over the x -axis is (x,y)→(x,−y) .
pls answer quickly!!!
Answers
Answer:
x = 90
y = 100
z = -10
Step-by-step explanation:
To find x and y in the above parallelogram ABCD as shown above, recall that one of the properties of a parallelogram is: the consecutive angles in a parallelogram are supplementary.
This means that the sum of angle A and angle B in the parallelogram ABCD = 180°.
Thus,
(x + 30)° + (x - 30)° = 180°
Solve for x
x + 30 + x - 30 = 180
x + x + 30 - 30 = 180
2x = 180
Divide both sides by 2
2x/2 = 180/2
x = 90
=>Find y:
Also, recall that opposite angles in a parallelogram are congruent.
This means, angle A and angle C in parallelogram ABCD above are equal.
Thus,
(x + 30)° = (y + 20)°
Plug in the value of x to solve for y
90 + 30 = y + 20
120 = y + 20
Subtract 20 from both sides
120 - 20 = y
100 = y
y = 100
=>Find z, if z = x - y
z = 90 - 100
z = -10
Melissa sold 18 raffle tickets for the school fundraiser. Jonah sold half as many tickets as Melissa. Shona sold 1.5 times as many tickets as Melissa. If each ticket cost $6, how much money did the students raise?
Answers
Answer:
Total money raised by the students = $324
Step-by-step explanation:
Raffle tickets sold by Melissa = 18
'Jonah sold half as many tickets as Melissa'
Jonah sold the raffle tickets = [tex]\frac{1}{2}\times 18=9[/tex]
'Shona sold 1.5 times as many as Melissa'
Tickets sold by Shona = 1.5 × 18 = 27
Total number of raffle tickets sold by all of them = 18 + 9 +27 = 54
Since, each ticket cost = $6
Therefore, total money raised by the students = Total number of tickets sold × Cost of each ticket
= 54 × 6
= $324
The volume of a gas in a container varies inversely with the pressure on the gas. A container of helium has a volume of 370in3 under a pressure of 15psi (pounds per square inch). Write the equation that relates the volume, V, to the pressure, P. What would be the volume of this gas if the pressure was increased to 25psi?
Answers
Answer:
Step-by-step explanation:
When two variables vary inversely, it means that an increase in one would lead to a decrease in the other and vice versa. Since the volume of a gas, V in a container varies inversely with the pressure on the gas, P, if we introduce a constant of proportionality, k, the expression would be
V = k/P
If V = 370 in³ and P = 15psi, then
370 = k/15
k = 370 × 15 = 5550
The equation that relates the volume, V, to the pressure, P would be
V = 5550/P
if the pressure was increased to 25psi, the volume would be
V = 5550/25 = 222 in³
Answer:
v=5550/p
222
Step-by-step explanation:
a cat went from a to b a distance of 20 kilometres in one 1/2 hours but return in one hour calculate the average speed for the whole journey
Answers
Answer: 16 kph
Step-by-step explanation:
Average Speed = Total Distance/ Total Time
Distance = Speed x Time
The Distance between A and B is 20 kph
Time(A-B) = 1.5 hrs
Time(B-A) = 1 hour
Total Time = 2.5 hrs
Total Distance = 20 + 20 = 40 km
Average Speed = 40 km / 2.5 hrs = 16 kmph
0.0% complete This is a Numeric Entry Question; skip ahead to question content This question requires a numeric answer Answer here Confirm Q. One of your clients at Wills, Trusts & Estates Law, PLLC passes away. His estate is worth $72,000. He leaves half to charity, and 18 to each of his four children. How much will each child receive? $ _____
Answers
Answer:
$9,000
Step-by-step explanation:
The worth of the estate = $72,000
The client leaves half of his estate to charity, and 1/8 to each of his four children.
Therefore, the amount each of the child will receive
[tex]=\dfrac18 \times \$72,000\\\\=\$9,000[/tex]
Each child will receive $9,000.
Answer:
Step-by-step explanation:
What are the first two steps in solving the radical equation below?
√x - 6 +5 = 12
Look at picture(15 points)
Answers
Answer:
B
Step-by-step explanation:
Given
[tex]\sqrt{x-6}[/tex] + 5 = 12 ( subtract 5 from both sides )
[tex]\sqrt{x-6}[/tex] = 7 ( square both sides )
x - 6 = 49 ( add 6 to both sides )
x = 55
Answer:
B. Subtract 5 from both sides and then square both sides.
Step-by-step explanation:
First, subtract 5 from both sides in order to get [tex]\sqrt{x-6}=7^{2}[/tex]
Second, square both sides in order to get [tex]x-6=49[/tex] (p.s. squaring both sides gets rid of the square root)
Third, add 6 to both sides in order to get x=55
Last, see that the answer is B, as you had to subtract 5 from both sides and then square both sides to get your answer
There you go, and good luck on the other questions!
Roberto wants to buy a $40 gift for his father. He finished one odd job in 4 hours at $3.75 an hour. He is now working at a job which pays $4.00 an hour. How many hours does he need to work to earn the money he needs?
Answers
Step-by-step explanation:
amount left for the money to reach $40
=40-3.75
=36.25
using a method of proportion,
If $4 : 1 hour,then
$36.25 : ?
if more, less divides.
= 36.25 / 4 ×1
=36.25/4
=9.0625 approximately 9 hours
Roberto should work for 6.25 hours to earn the money he needs, solved using linear equations in one variable.
What are linear equations in one variable?Linear equations in one variable are a relation between two algebraic expressions, involving not more than one variable.
The expressions are a combination of terms and terms are combinations of variables and constants. These terms are separated by mathematical operations.
How to solve the question?In the question, we are informed that Roberto wants to buy a $40 gift for his father. He finished one odd job in 4 hours at $3.75 an hour. He is now working at a job that pays $4.00 an hour.
We are asked how many hours he needs to work to earn the money he needs.
First, we calculate how much he earned from working in the first place.
He worked there for 4 hours at $3.75 an hour.
Therefore, his total income = Time * Income per unit time = $ (4 * 3.75) = $ 15.00.
Now, we calculate how much more money he needs.
More money needed = Total money needed - Money already earned,
or, more money needed = $40 - $15 = $25.
Therefore, Roberto works in second place to earn $25.
The rate at which he was working = $4 per hour.
We assume the time he worked for was x hours.
Therefore, his total income = Time * Income per unit time,
or, His total income = $ (x*4) = $4x.
As his total requirement is $25, we equate his earnings to his requirement to get the required linear equation in one variable:
4x = 25.
We find the hours he will work for, by solving this equation, by dividing both sides by 4:
4x/4 = 25/4,
or, x = 6.25.
Therefore, Roberto should work for 6.25 hours to earn the money he needs, solved using linear equations in one variable.
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You may use the unit circle shown below to help you answer this question.
Which of these are true statements about the sine function? Choose all that are correct.
A
For any value of θθ , sin(−θ)=sin(θ)sin(−θ)=sin(θ) .
B
For any value of θθ , sin(−θ)=−sin(θ)sin(−θ)=−sin(θ) .
C
The sine function is an odd function.
D
The sine function is an even function.
E
The sine function has a period of ππ .
F
The sine function has a period of 2π2π .
Answers
Answer:
B, C, F
Step-by-step explanation:
For the first part, this is the negative angle identity of the sine and cosine function. These identities are:
[tex]\cos(-\theta)=\cos(\theta)[/tex]
[tex]\sin(-\theta)=-\sin(\theta)[/tex]
Then (I believe I am reading this right), B is true. I am unsure because of the repeated value in the middle. The next piece is that sine is odd. By definition, an odd function is one such that:
[tex]f(-x)=-f(x)[/tex]
As we just demonstrated with the identities, sine obeys this and therefore is odd. Cosine, on the other hand, is even because it follows:
[tex]f(-x)=f(x)[/tex]
Last, the period of sine, or the distance on the x-axis it takes to complete one full wavelength, and the answer is [tex]2\pi[/tex]. If you look at a graph of the sine function, you will find that the wave repeats itself at the [tex]2\pi[/tex] mark and it does this with cosine as well.
Which of the following is not a quadratic equation?
A. 2x² – 3x + 5 = 0
B. 7x +4= 0
C. 4x - 2 = 0
D. x - 3x = 0
Answers
Answer:
d
Step-by-step explanation:
Translate the following into algebraic expressions: The first class has a kids in it, the second has b kids in it, and the third class has c kids in it. The kids from all three classes are divided equally between two buses. How many kids are in each bus?
Answers
Answer:
(a + b + c)/2
Step-by-step explanation:
Number of kids in first class: a
Number of kids in second class: b
Number of kids in third class: c
The total number of kids in all classes is: a + b + c
The total number of kids is divided equally between 2 buses:
(a + b + c)/2
Answer:
(a + b + c)/2
Step-by-step explanation:
;)
1. The population growth of a small town is modeled by the function P(t) = 6545.52e^0.149t where is the populationand is the number of years since 1980. A. What is the growth rate for P(t)? B. What was the population in 1980? C. Find P(11) and explain what it means in the context of the problem. D. What is the projected population in 2019?
Answers
Answer:
A. Growth rate = r = 0.149
B. P(0) = 6545.52
C. P(11) = 33,709
D. P(39) = 2,185,876
Step-by-step explanation:
The population growth of a small town is modeled by the following function,
[tex]$ P(t) = 6545.52 e^{0.149t} $[/tex]
Where 6545.52 is the initial population, 0.149 is the rate of growth of the population and t is the number of years since 1980.
A. What is the growth rate for P(t)?
The growth rate is
Growth rate = r = 0.149
B. What was the population in 1980?
Since t is the number of years since 1980, therefore, t = 0 for the year 1980.
[tex]P(0) = 6545.52 e^{0.149(0)} \\\\ P(0) = 6545.52 e^{0} \\\\ P(0) = 6545.52 \\\\[/tex]
C. Find P(11) and explain what it means in the context of the problem.
[tex]P(11) = 6545.52 e^{0.149(11)} \\\\P(11) = 6545.52 e^{1.639} \\\\ P(11) = 6545.52 (5.15) \\\\P(11) = 33,709[/tex]
It represents the population of the town after 11 years since 1980.
D. What is the projected population in 2019?
t = 2019 - 1980 = 39 years
[tex]P(39) = 6545.52 e^{0.149(39)} \\\\P(39) = 6545.52 e^{5.811} \\\\ P(39) = 6545.52 (333.95) \\\\P(39) = 2,185,876[/tex]
Therefore, the projected population in 2019 is expected to be 2,185,876.
The graphed line shown below is y = 5 x minus 10. On a coordinate plane, a line goes through (2, 0) and (3, 5). Which equation, when graphed with the given equation, will form a system that has no solution? y = negative 5 x + 10 y = 5 (x + 2) y = 5 (x minus 2) y = negative 5 x minus 10
Answers
Answer:
y = 5 (x + 2)
Step-by-step explanation:
Equations with a different x-coefficient will graph as lines that intersect the given one, so will form a system with one solution.
The equation with the same slope and y-intercept (y = 5(x -2)) will graph as the same line, so will form a system with infinite solutions.
The line with the same slope and a different y-intercept will form a system with no solutions:
y = 5 (x + 2)
Answer:
B
Step-by-step explanation:
got it on edge
help me find the value of c please
Answers
Answer:
8
Step-by-step explanation:
[tex] \because \: p(x) \: is \: divisible \: by (x + 2) \\ \therefore \: x + 2 = 0 \implies \: x = - 2 \\ plug \: x = - 2 \: in \: p(x) \\ p( - 2) = 4 {( - 2)}^{3} + c {( - 2)}^{2} + ( - 2) + 2 \\ p( - 2) = 4 ( - 8) + 4c - 2 + 2 \\ p( - 2) = - 32 + 4c \\ let \: p(x) = 0.. (\because remainder = 0)\\ \therefore \: 0 = - 32 + 4c \\ \therefore \: 32 = 4c \\ \therefore \: c = \frac{32}{4} \\ \huge \red{ \boxed{\therefore \: c = 8}}[/tex]
Please answer this correctly
Answers
Answer:
1/2
Step-by-step explanation:
The numbers that are odd on the spinner are 1, 3, and 5.
3 numbers out of 6.
3/6 = 1/2
P(odd)= 1/2
which of the following is not a perfect cube? 1: 2197 2: 512 3: 2916 4: 343 Which of the following numbers is a perfect cube? * 1: 1525 2: 1728 3: 1458 4: 3993
Answers
Answer:
no 4 is not perfect cube and no 2 is perfect cube
Answer:
3. 2916
2. 1728
Step-by-step explanation:
1: 2197 = 13³
2: 512 = 8³
3: 2916 = 2² × 3² × 61
4: 343= 7³
==============
1: 1525 = 5² × 61
2: 1728 = 12³
3: 1458 = 2 × 9³
4: 3993= 3 × 11³