Ms. Jones washed most of the laundry and the remaining laundry need to be washed is 7/20.
Converting the fraction to decimal to easily compare the amount of laundry washed.
Laundry washed by Ms. Jones = 2/5
Performing division
Laundry washed by Ms. Jones = 0.4
Laundry washed by her son = 1/4
Performing division
Laundry washed by her son = 0.25
0.4 is greater than 0.25, hence, Ms. Jones washed more laundry.
They washed the laundry in fractions. So, the total laundry can be taken as 1.
Total laundry washed = 0.4 + 0.25
Total laundry washed = 0.65
Remaining laundry = 1 - 0.65
Performing subtraction
Remaining laundry = 0.35
Converting into fraction = 35/100
Remaining laundry in fraction = 7/20
Thus, Ms. Jones washed more laundry and 7/20 is remaining.
Learn more about fractions -
https://brainly.com/question/78672
#SPJ4
The complete question is -
Ms. Jones washed 2/5 of her laundry. Her son washed 1/4 of it. How much of the laundry still needs to be washed?
divie 8x^4-4X^3/2x^2
Answer:
(4x^2) - (2x)
Step-by-step explanation:
Factor the numerator and denominator and cancel the common factors.
The sharks are fed three times a day. During the morning feeding, 2/15 of a ton of fish is fed. During the afternoon feeding the weight of the fish fed will be 1/15 of a ton more than the fish fed during the morning. if the total weight of the fish fed in a day is 1/2 of a ton, how much is fed during the feeding at night?
The shark is fed during the feeding at night is 1/6 tons.
What is a proper fraction?
A proper fraction is one that doesn't contain any whole numbers and has a smaller numerator than a denominator. A fraction that represents a number greater than one and has a larger numerator than the denominator is said to be improper.
Given that during the morning feeding, 2/15 of a ton of fish is fed. During the afternoon feeding the weight of the fish fed will be 1/15 of a ton more than the fish fed during the morning.
The shark fed (2/15 + 1/15) ton during the afternoon.
Assume that the shark fed x tons at night.
Therefore, the total fed is 2/15 + (2/15 + 1/15) + x
The equation is:
2/15 + (2/15 + 1/15) + x = 1/2
Add like terms:
5/15 + x = 1/2
1/3 + x = 1/2
Subtract 1/3 from both sides:
x = 1/2 - 1/3
x = (3-2)/6
x = 1/6
To learn more about improper fraction, click on the below link:
https://brainly.com/question/11708406
#SPJ1
A principal of 2000 is invested at 3.25% interest, compounded annually. How much will the investment be worth after 10 years?
Answer:
$2,753.79
Step-by-step explanation:
Compound Interest Formula
\(\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}\)
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $2,000r = 3.25% = 0.0325n = 1t = 10Substitute the given values into the formula and solve for A:
\(\implies \sf A=2000\left(1+\frac{0.0325}{1}\right)^{(1 \times 10)}\)
\(\implies \sf A=2000(1.0325)^{10}\)
\(\implies \sf A=2753.788608...\)
Therefore, the value of the investment after 10 years will be $2,753.79 to the nearest cent.
batches of a chemical contain random amounts of lead with a mean value of 6.0 mg and a standard deviation of 2.0 mg. if 50 batches are prepared, the probability that their average amount of lead is greater than 6.5 mg is
Therefore, the probability that the average amount of lead in 50 batches is greater than 6.5 mg is approximately 0.038 or 3.8%.
To find the probability that the average amount of lead in 50 batches is greater than 6.5 mg, we can use the Central Limit Theorem (CLT) and the properties of the normal distribution. The Central Limit Theorem states that for a large sample size (in this case, 50 batches), the distribution of sample means will approach a normal distribution regardless of the shape of the original distribution.
Given:
Mean value of lead in a batch (μ) = 6.0 mg
Standard deviation of lead in a batch (σ) = 2.0 mg
Sample size (n) = 50
To apply the CLT, we need to calculate the standard deviation of the sample means, also known as the standard error (SE), which is equal to the population standard deviation divided by the square root of the sample size:
SE = σ / √(n)
SE = 2.0 mg / √(50)
SE ≈ 0.2828 mg
Now, we can standardize the desired average amount of lead (6.5 mg) using the sample mean and the standard error:
Z = (X - μ) / SE
Z = (6.5 mg - 6.0 mg) / 0.2828 mg
Z ≈ 1.7678
We want to find the probability that the average amount of lead is greater than 6.5 mg, which is equivalent to finding the probability that the standardized value (Z) is greater than 1.7678. Using a standard normal distribution table or calculator, we can find the probability corresponding to a Z-value of 1.7678, which is approximately 0.038.
To know more about probability,
https://brainly.com/question/20376325
#SPJ11
DIG DEEPER! A truck produces 22 pounds of carbon dioxide for every gallon of diesel
fuel burned. The fuel economy of the truck is 18 miles per gallon. Write and graph a
function that describes the relationship between carbon dioxide produced y and distance
traveled x.
Answer:
y=22 x=18
Step-by-step explanation:
PLEASEE HELPP I need it asap !!
Answer:
The answer will be 271. check the pic attached with it
Find an angle θ with 0∘<θ<360∘ that has the same:
Sine function value as 230∘θ =_____degrees
Cosine function value as 230∘θ =____ degrees
An angle θ with 0∘<θ<360∘ that has the same:
Sine function value as 230°: θ = 50° degrees
Cosine function value as 230°: θ = 130° degrees
To find an angle θ with 0° < θ < 360° that has the same sine and cosine function values as 230°, you can use the following methods:
For the sine function:
Since sine is positive in the first and second quadrants, you can find the reference angle for 230°, which is in the third quadrant. The reference angle is calculated by subtracting 180° from 230°:
230° - 180° = 50° (reference angle)
Now, to find the angle with the same sine value, we can use the first quadrant angle:
θ = 50° (since sine(50°) = sine(230°))
For the cosine function:
Since cosine is positive in the first and fourth quadrants, you can find the angle in the fourth quadrant that has the same cosine value as 230°. To do this, subtract 230° from 360°:
360° - 230° = 130°
So, the angle with the same cosine value is:
θ = 130° (since cosine(130°) = cosine(230°))
For more such questions on Angle.
https://brainly.com/question/30866190#
#SPJ11
⚠️ BRAIN LIST ⚠️
⚠️ BRAIN-LIST ⚠️
Please HELP. Solve anyone!!!
Answer:
1) x = 36
2) x = 127
3) x = 36
Step-by-step explanation:
1)
x + 144 = 180
x = 36
2)
15 + x + 38 = 180
x + 53 = 180
x = 127
3)
2x + 16 + 92 = 180
2x + 108 = 180
2x = 72
x = 36
a jury pool consists of 30 people, 16 men and 14 women. compute the probability that a randomly selected jury of 12 people is all male.
The probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.
What is the probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
An order does not matter so it is a Combination.
There are 16 men and we are going to choose 12 --> ₁₆C₁₂
There are 30 people and we are going to choose 12 --> ₃₀C₁₂
₁₆C₁₂ / ₃₀C₁₂
\(= \frac{16!}{(16 - 12)!} \div \frac{30!}{(30 - 12)!}\)
= 0.00002104211
= 2.1 × 10⁻⁵
Hence, the probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.
To learn more about the probability visit,
https://brainly.com/question/24756209
#SPJ4
What is the y intercept? 7x+y=10
Answer:
the y intercept is y
Step-by-step explanation:
because we have the variable already/////
The area of a rectangle is 105 sq in and the length of one side is 7 in. What is the length of the perimeter?
Perimeter of Rectangle is 44m
What is Perimeter ?A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape.
According to the given information
Area of Rectangle = l × b
Area of Rectangle = 105 \(m^{2}\)
Length of one side = 7 m
Let the length of the adjacent side = b
Area of Rectangle given = 7 × b
105 = 7 × b
b = \(\frac{105}{7}\)
b = 15 m
Perimeter of Rectangle given = 2( l + b )
= 2 ( 7 + 15 )
= 2 × 22
= 44m
Perimeter of Rectangle is 44m
To know more about Perimeter
https://brainly.com/question/15271274
#SPJ4
use traces to sketch the surface. 9x2 + 4y2 + z2 = 36
Using these traces, we can sketch the surface as an ellipsoid in three dimensions centered at the origin, with semi-major axis of length 6 along the z-axis, semi-major axis of length 3 along the y-axis, and semi-major axis of length 2 along the x-axis.
To sketch the surface 9x^2 + 4y^2 + z^2 = 36 using traces, we can fix values of x, y, and z and plot the resulting curves. When we fix x = 0, we get 4y^2 + z^2 = 36, which is an ellipse in the yz-plane centered at the origin with semi-major axis of length 6 along the z-axis and semi-minor axis of length 3 along the y-axis.
When we fix y = 0, we get 9x^2 + z^2 = 36, which is also an ellipse in the xz-plane centered at the origin with semi-major axis of length 6 along the z-axis and semi-minor axis of length 2 along the x-axis. When we fix z = 0, we get 9x^2 + 4y^2 = 36, which is a horizontal ellipse in the xy-plane centered at the origin with semi-major axis of length 2 along the x-axis and semi-minor axis of length 3 along the y-axis.
To know more about surface,
https://brainly.com/question/31479134
#SPJ11
for research questions about the mean, when is it appropriate to use the t-test if the distribution for the variable upon which the mean was derived is highly skewed to the right?
If the distribution of the variable upon which the mean was derived is highly skewed to the right, it may be appropriate to use the t-test if the sample size is large enough.
When conducting research, the t-test is typically used to compare the means of two groups. One of the key assumptions of the t-test is that the population from which the sample was drawn follows a normal distribution.
However, if the distribution of the variable upon which the mean was derived is highly skewed to the right, it may not meet the normality assumption.
In this case, it is appropriate to use the t-test if the sample size is large enough. The t-test is based on the central limit theorem, which states that the sample mean tends to follow a normal distribution as the sample size increases, even if the population distribution is not normal. For large sample sizes (typically n > 30), the t-test is generally considered to be robust to violations of the normality assumption.
However, if the sample size is small, the t-test may not be appropriate, even if the sample mean follows a normal distribution. In this case, alternative statistical tests may be more appropriate. For example, the Wilcoxon rank-sum test can be used to compare the means of two groups when the normality assumption is not met.
In conclusion, if the sample size is small, alternative statistical tests may be more appropriate.
Learn more about variable at: brainly.com/question/15078630
#SPJ11
respectively Q 1
=160−10P 1
OR r 1
=16−0.1Q 1
aWD 1/P 6
=16 6
−2T −
Q 2
=200−20P 2
ORP 2
=10−0,050,…H1AP 2
=15−0:0% Saga's Total Cost function is: TC =120+4Q With third degree price discrimination, the condition for peofit marimizater is MR 1
=MR 2
=MR=MC Find P 1
,Q 1
,P 2
,Q 1
Total Revenue, Total Cost, and Total proft wit sree discrimination. Find P,Q,TR,TC&π In the absence of price discrimination. Marks: 7
In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.
To find the profit-maximizing conditions with third-degree price discrimination, we need to equate the marginal revenue (MR) to the marginal cost (MC) for each market segment.
Given the demand equations and the total cost function:
Market 1: Q1 = 160 - 10P1 or P1 = 16 - 0.1Q1
Market 2: Q2 = 200 - 20P2 or P2 = 10 - 0.05Q2
Total Cost: TC = 120 + 4Q
To find the profit-maximizing prices and quantities, we equate MR to MC for each market segment:
MR1 = MC:
16 - 0.2Q1 = 4
0.2Q1 = 12
Q1 = 60
MR2 = MC:
10 - 0.1Q2 = 4
0.1Q2 = 6
Q2 = 60
Substituting the quantities back into the demand equations, we find:
P1 = 16 - 0.1(60) = 10
P2 = 10 - 0.05(60) = 7
The total revenue (TR) can be calculated by multiplying the price by the quantity for each market segment:
TR = P1 * Q1 + P2 * Q2
TR = (10 * 60) + (7 * 60)
TR = 600 + 420
TR = 1020
The total cost (TC) is given by the total cost function:
TC = 120 + 4Q
TC = 120 + 4(60 + 60)
TC = 120 + 480
TC = 600
Finally, the profit (π) can be calculated by subtracting total cost from total revenue:
π = TR - TC
π = 1020 - 600
π = 420
In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.
Learn more about absence here:
https://brainly.com/question/30062518
#SPJ11
In anova, by dividing the mean square between groups by the mean square within groups, a(n) _____ statistic is computed.group of answer choices
In anova, by dividing the mean square between groups by the mean square within groups, a(n) Analysis of variance statistic is computed.
What is Analysis of variance ?
With the help of the statistical analysis approach known as ANOVA, apparent aggregate variability within a data set is explained by separating systematic components from random factors. Systematic influences, but not random ones, statistically affect the data set that is being presented.What are some instances where ANOVA has been applied?
An ANOVA demonstrates the link between the dependent variable and the level of the independent variable. For illustration: In order to determine whether there is a difference in the number of hours of sleep each night as your independent variable, you divide the groups into low, medium, and high social media use categories.Learn more about Analysis of variance
brainly.com/question/28274784
#SPJ4
Which pair of variables would most likely have approximately zero correlation?
A. the height of a person and the size shoe a person wears
B. the number of hours studying for a test and the score on a test
c. the height of a student and the day of the month a student was born
D. the number of hours a person exercises and the number of calories a person burns
measure of one interior angle of a regular 16-gon.
The measure of one interior angle of a regular 16-gon is 157.5 degrees. This is obtained by using the formula (n-2) * 180° / n, where "n" represents the number of sides of the polygon. In this case, (16-2) * 180° / 16 = 157.5°..
To find the measure of one interior angle of a regular 16-gon, we can use the formula for the measure of an interior angle of a regular polygon:
Interior Angle = (n-2) * 180° / n
where "n" is the polygon's number of sides.
For a regular 16-gon, substituting the value of "n" into the formula, we get:
Interior Angle = (16 - 2) * 180° / 16
= 14 * 180° / 16
= 2520° / 16
= 157.5°
Therefore, the measure of one interior angle of a regular 16-gon is 157.5 degrees.
To understand the calculation, let's break it down. Equal interior angles and sides define a regular polygon. The sum of the interior angles of any polygon is given by the formula (n-2) * 180°, where "n" is the number of sides. In a regular polygon, all the interior angles are congruent, so to find the measure of one angle, we divide the sum by the number of sides.
In the case of a regular 16-gon, we subtract 2 from 16 to get 14, multiply it by 180°, and then divide by 16 to find that each interior angle measures 157.5°.
Therefore, the measure of one interior angle of a regular 16-gon is 157.5 degrees.
for such more question on interior angle
https://brainly.com/question/24966296
#SPJ8
Antonio has six white socks, two black socks, and four gray socks in a drawer. If he randomly chooses a sock from the drawer, what is the probability he will choose a gray sock?
A.1/12
B.1/4
C.1/3
D.1/2
Answer:
C
Step-by-step explanation:
The probability is 1/3
2a) Determine the unknown angle x.
The unknown angle x in the triangle is 80 degrees
How to determine the unknown angle x.From the question, we have the following parameters that can be used in our computation:
The triangle
The unknown angle x is calculated using the sum of angles in a triangle theorem
So, we have
x + 60 + 40 = 180
Evaluate the like terms
x + 100 = 180
So, we have
x = 80
Hence, the unknown angle x is 80 degrees
Read more about angles at
https://brainly.com/question/31898235
#SPJ1
If i buy a disc which costs $16,30, there's a 10% discount. how much i'm i going to pay?
The price we have to pay for the disc after 10% discount is 1467 dollars.
What is percentage ?Percentage is the value per hundredth.
According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.
10% of 1630 dollars will be
= (10/100) × 1630 dollars.
= 16300/100 dollars.
= 163 dollars.
So, the price we have to pay for the disc after 10% discount is
= (Total amount - Discount amount)
= ( 1630 - 163 ) dollars.
= 1467 dollars.
learn more about percentage here :
https://brainly.com/question/24159063
#SPJ4
How many permutations of the letters abcdefgh contain the strings ab, de, and gh?
5! permutation of the letters abcdefgh contains strings ab, de, and gh.
How to find Permutation?The number of permutations of 'n' objects taken 'r' at a time is determined by the following formula:
P(n,r)=n! / (n−r)!
We can also find permutation using the Selection and Formation Method:
For example:
1. Number of ways to arrange the letter SANOJ:
here number of alphabets are 5, and we have to arrange all the letter so using permutation formula:
P(5, 5 ) = 5! / (5-5)!
P(5, 5 ) = 5! : 0! = 1
without using the formula we can simply write 5! as the answer.
Here, we have given the word, " abcdefgh "
and we have to make those arrangements in which ab, de, and gh come together:
so now, we will count ab, de, and gh as a single word.
now, we will have 5 different words/alphabet:
1 → ab
2 → c
3 → de
4 → f
5 → gh
Number of ways to arrange all the 5 words/alphabet: 5!
Hence,
5! permutation of the letters abcdefgh contains strings ab, de, and gh.
Learn more about " Permutation " from here: https://brainly.com/question/1216161
#SPJ4
3p^2-24+36
factorise with appropriate identity
Answer:
3(p^(2)+4)
Step-by-step explanation:
Suppose that we are interested in dissolved metals in two Montana streams. In Jack Creek the distribution of dissolved metals is believed to be normal with a mean of 1000 and a standard deviation of 40 . For the Cataract Creek the distribution is normal with a mean of 970 and a standard deviation of 20 . Random samples of sizes 30 and 15 are taken from Jack and Cataract Creeks respectively. a) Find the mean and variance of the difference in sample means. b) What is the probability that average amount of dissolved metals at Jack Creek is at least 50 more than the average amount of dissolved metals at Cataract Creek?
a) To find the mean and variance of the difference in sample means, we can use the properties of sampling distributions. The mean of the difference in sample means is equal to the difference in population means:
Mean of the difference in sample means = Mean(Jack Creek) - Mean(Cataract Creek) = 1000 - 970 = 30
The variance of the difference in sample means is calculated by summing the variances of the two samples, divided by their respective sample sizes:
Variance of the difference in sample means = (Variance(Jack Creek) / Sample Size of Jack Creek) + (Variance(Cataract Creek) / Sample Size of Cataract Creek)
Variance of Jack Creek = (standard deviation of Jack Creek)^2 = 40^2 = 1600
Variance of Cataract Creek = (standard deviation of Cataract Creek)^2 = 20^2 = 400
Sample Size of Jack Creek = 30
Sample Size of Cataract Creek = 15
Variance of the difference in sample means = (1600 / 30) + (400 / 15) = 53.33 + 26.67 = 80
Therefore, the mean of the difference in sample means is 30 and the variance of the difference in sample means is 80.
b) To find the probability that the average amount of dissolved metals at Jack Creek is at least 50 more than the average amount at Cataract Creek, we can calculate the probability using the properties of the normal distribution.
Let X be the average amount of dissolved metals at Jack Creek and Y be the average amount at Cataract Creek.
We need to find P(X - Y >= 50). This can be rephrased as P(X >= Y + 50).
Using the properties of normal distributions, we can standardize the random variables X and Y:
Z = (X - Mean(X)) / (Standard Deviation(X)) = (X - 1000) / 40
W = (Y - Mean(Y)) / (Standard Deviation(Y)) = (Y - 970) / 20
Now we can rephrase the probability in terms of Z and W:
P(X >= Y + 50) = P(Z >= (W + 50 - 1000) / 40) = P(Z >= (W - 950) / 40)
To find this probability, we can look up the corresponding value in the standard normal distribution table or use statistical software.
To know more about variance refer here
https://brainly.com/question/31432390#
#SPJ11
a license plates consist of three letters followed by 4 digits. how many different license plates are possible
A total of 175,760,000 different license plates are possible.
A permutation is a count of the different arrangements which can be made from a given set of things. In permutation the details matter, as the order or sequence is important. Permutation and combination are the methods employed in counting how many outcomes are possible in various situations. Permutations are understood as arrangements and combinations are understood as selections. As per the fundamental principle of counting, there are the sum rules and the product rules to employ counting easily.
According to this, if one event can occur in a ways and a second event can occur in b ways, the second event occurring after the first event did, then the two events can occur in a × b ways.
There are 26 letters in an English language.The license plate has 3 digits. There are 10 digits from 0 to 10. The license plate has 4 digits.
The number of different license plate numbers that can be formed:
26 x 26 x 26 x 10 x 10 x 10 x 10 = 175,760,000
Thus, a total of 175,760,000 different license plates are possible.
To learn more about permutations, visit brainly.com/question/1216161
#SPJ4
2. Sally is eating a bag of M&M's. 12 were green, 16 were brown, 8 were
red, and 4 were blue. Sally picked one M&M at random without looking.
What is the probability that the M&M is NOT brown?*
24%
60%
40%
34%
Answer:
60%
Step-by-step explanation: 12+16+8+4 is equal to 40. 40 minus the number of brown m&ms is 24 .24/40 as a percentage is 60%. Hope this helps!!!
me ajudem fiquei doente e voltei agora pra fazer as provas alguem pode me explicar essa formula pfv
log3 x=4
the solution to the equation log3 x=4 is x = 81.The equation "log3 x=4" is a logarithmic equation with a base of 3.
It means that 3 raised to the power of 4 is equal to x. In other words, x is the value that satisfies the equation 3^4 = x.
To solve this equation, we need to isolate the variable x. We can do this by taking the exponential of both sides of the equation with a base of 3. This will cancel out the logarithm on the left side of the equation, leaving us with:
3^(log3 x) = 3^4
The base of the exponential function and the logarithmic function cancel each other out, and we're left with:
x = 81
Therefore, the solution to the equation log3 x=4 is x = 81.
to learn more about log click here: brainly.com/question/15673235
#SPJ11
Question 5 of 22
Select the action you would use to solve x - 4 = 16. Then select the property
that justifies that action.
O A. Action: Divide both sides by 4.
B. Property: Multiplication property of equality.
C. Property: Addition property of equality.
D. Action: Add 4 to both sides.
O E. Action: Multiply both sides by 4.
O F. Property: Division property of equality.
SUBMIT
What is the missing side length in this right triangle?
ANSWER :
PLEASE HELP
what is there value of y?
what is the value of x?
Answer:
x=14
y=30
Step-by-step explanation:
5x+25=3x+53
5x=3x+28
2x=28
x=14
2y+35=95
2y=60
y=30
(I assumed all of the angles are equal, correct me if I'm wrong.)
Answer:x=14
Step-by-step explanation:
Let's first understand what we need to do. We need to solve for two variables, x and y. We do these by setting two systems of equations equal to each other. This is easily done for x, but for y the other equation is missing. Keep this in mind for later.
So, we will first start off by solving for x. We do this by using inverse operations.
5x+25=3x+53 We will subtract
5x=3x+28
2x=28 Divide
x=14
You can plug 14 into both the xs and they will be similar, and both will have the similar results once you solve for y and plug it into the equation along with x.
We know that the 5x+25 on the left is adjacent to 2y+35, and so is the second x. Adjacent angles add up to 180 total, and so to solve for y we need to plug 12 in the first x.
5(14)+25=95
180-95=85
85 is the value of 2y+35
We will solve for y just like any other alegrbaic problem
85=2y+35
50=2y
y=25
We know know that y is 25 and x is 14
Plug both values into 2 adjacent angles and they will add up to 180.
Let A and B be square matrices. Show that even though AB and BA may not be equal, it is always true that det AB = det BA.
det(MBA) = det(diag(det A, det A, ..., det A)BA) = det(diag(det A, det A, ..., det A)) * det(BA) = det A * det(BA)
Bet AB = det BA, as required.
what is square matrix?
A square matrix is a matrix that has the same number of rows and columns. That is, a matrix A is square if A has dimensions n x n, where n is a positive integer.
To show that det AB = det BA, we can use the fact that for any invertible matrix M, we have det(MAB) = det(MBA) = det(M) * det(AB) = det(M) * det(BA). Therefore, it is sufficient to show that there exists an invertible matrix M such that det(MAB) = det(MBA).
Let M be the diagonal matrix with diagonal entries given by the determinant of A, i.e., M = diag(det A, det A, ..., det A). Then, we have:
det(MAB) = det(diag(det A, det A, ..., det A)AB) = det(diag(det A, det A, ..., det A)) * det(AB)
= det A * det(AB)
Similarly, we have:
det(MBA) = det(diag(det A, det A, ..., det A)BA) = det(diag(det A, det A, ..., det A)) * det(BA)
= det A * det(BA)
Therefore, det AB = det BA, as required.
To learn more about square matrix from the given link:
https://brainly.com/question/4017205
#SPJ1