A tank contains 12 litres of water in which is dissolved 24 grams of chemical A solution containing 4 grams per litre of the chemical flows into the tank at a rate of 4 litres per minute, and the well-stirred mixture flows out at a rate of 2 litres per minute. Determine the amount of chemical in the tank after 15 minutes.

The inverse of the given matrix [1 -1 0 -4 2 -1 4 3 3] is:

[0  -2  4/3]
[4/3  -1  -4/3]
[-4/3  4/3  2/3]

The inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix. To find the inverse of the given matrix [1 -1 0 -4 2 -1 4 3 3], we need to use the following steps:

Step 1: Find the determinant of the matrix. The determinant of a 3x3 matrix is given by:

|A| = a(ei - fh) - b(di - fg) + c(dh - eg)

where a, b, c, d, e, f, g, h, and i are the elements of the matrix. Plugging in the values from the given matrix, we get:

|A| = (1)(2*3 - (-1)*3) - (-1)(-4*3 - 0*4) + (0)(-4*(-1) - 2*4)

|A| = (1)(6 + 3) - (-1)(-12) + (0)(4 - 8)

|A| = 9 - 12 + 0

|A| = -3

Step 2: Find the matrix of minors. The matrix of minors is found by taking the determinant of each 2x2 matrix that can be formed by removing one row and one column from the original matrix. The matrix of minors for the given matrix is:

[(-1)(3) - (-1)(3)  (0)(3) - (-1)(4)  (0)(3) - (-1)(-4)]
[(-4)(3) - (2)(3)   (1)(3) - (0)(4)   (1)(-4) - (0)(2) ]
[(-4)(-1) - (2)(0)  (1)(0) - (-1)(-4) (1)(2) - (-1)(-4)]

= [0  4  4]
 [-6 3 -4]
 [4 -4 -2]

Step 3: Find the matrix of cofactors. The matrix of cofactors is found by multiplying each element of the matrix of minors by -1 raised to the power of the sum of its row and column indices. The matrix of cofactors for the given matrix is:

[0  -4  4]
[6  3  -4]
[-4 4  -2]

Step 4: Find the adjugate matrix. The adjugate matrix is found by taking the transpose of the matrix of cofactors. The adjugate matrix for the given matrix is:

[0  6  -4]
[-4 3  4]
[4  -4  -2]

Step 5: Find the inverse matrix. The inverse matrix is found by dividing each element of the adjugate matrix by the determinant of the original matrix. The inverse matrix for the given matrix is:

[0/(-3)  6/(-3)  -4/(-3)]
[-4/(-3) 3/(-3)  4/(-3)]
[4/(-3)  -4/(-3)  -2/(-3)]

= [0  -2  4/3]
 [4/3  -1  -4/3]
 [-4/3  4/3  2/3]

Therefore, the inverse of the given matrix [1 -1 0 -4 2 -1 4 3 3] is:

[0  -2  4/3]
[4/3  -1  -4/3]
[-4/3  4/3  2/3]

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The effective annual IRR (internal rate of return) is 8%. If the dollars invested and withdrawn and the inflation rate for the 19-year time span of the investment is 9% per year the inflation-free IRR is -0.92%.

To calculate this, we need to use the IRR formula: IRR = [Sum of cash flows / (-initial investment)]1/n - 1, where n is the number of periods.

a. To find the effective annual IRR earned on this investment, we can use the following formula:

0 = -10,000/(1+IRR) - 10,000/(1+IRR)^2 - 10,000/(1+IRR)^3 - 10,000/(1+IRR)^4 + 10,000/(1+IRR)^5 + 10,000(1-0.05)/(1+IRR)^6       + 10,000(1-0.05)^2/(1+IRR)^7 + ... + 10,000(1-0.05)^14/(1+IRR)^18

The effective annual IRR earned on this investment to the nearest percent is 8%.

b. To find the inflation-free IRR earned on this investment, we can use the following formula:

Inflation-free IRR = (1 + IRR)/(1 + inflation rate) - 1

Plugging in the values we found in part (a), we get:

Inflation-free IRR = (1 + 0.08)/(1 + 0.09) - 1 = -0.0092

So the inflation-free IRR earned on this investment is approximately -0.92%.

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Answer:

To find the volume of the container in cubic centimeters, we multiply its length, width, and height:

Volume = 60 cm x 20 cm x 45 cm = 54,000 cubic centimeters

To convert cubic centimeters to liters, we divide by 1,000:

54,000 cubic centimeters ÷ 1,000 = 54 liters

Therefore, the container can hold 54 liters of water before it overflows.

Step-by-step explanation:

The cost of a cylindrical pole is $3462

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, a solid cylinder has a density of 6.1 g/cm³, the dimension is a diameter of 41.2 cm and a height of 710 cm, this metal can be purchased for $0.60 per kilogram.

we need to find the cost of the cylinder,

Finding the volume first,

Cylinder's volume = π × radius² × height

= 3.14 × 20.6² × 710

= 946,068 cm³

∵ density = mass / volume

mass = density × volume

= 6.1 × 946,068

= 5771014.8 grams

= 5771 kg

Now, the cost of the cylinder = 5771 × 0.60 = 3462

Hence, the cost of a cylindrical pole is $3462

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Answer: Explanation below

Step-by-step explanation:

R4000 is the money to be split

5:3:2 is the ratio

We can add the ratios together.

5+3+2=10

The first winner = 5/10 x 4000

                           = R2000

The second winner = 3/10 x 4000

                                 = R1200

The third winner = 2/10 x 4000

                             = R800

Hope this helped :)

The equation of the circle that has center (-1,2) and passes through(-6,6) is (x + 1)^2 + (y - 2)^2 = 41.

The equation of a circle with center (h,k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2. In this case, the center of the circle is (-1,2) so h = -1 and k = 2. We can use the given point (-6,6) to find the radius of the circle.

The distance between the center and the given point is the radius of the circle, and we can use the distance formula to find it:
r = √((-6 - (-1))^2 + (6 - 2)^2)
r = √((-5)^2 + (4)^2)
r = √(25 + 16)
r = √41

So the equation of the circle is:
(x - (-1))^2 + (y - 2)^2 = (√41)^2
(x + 1)^2 + (y - 2)^2 = 41

Therefore, the equation of the circle that has center(-1,2) and passes through(-6,6) is (x + 1)^2 + (y - 2)^2 = 41.

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The hypotenuse of the right triangle is 25.5 inches.

A right triangle is a triangle that has one angle as 90 degrees. The sum of angles in a triangle is 180 degrees.

The right right triangle has the legs as 19 inches and 17 inches. Let's find the hypotenuse.

Using Pythagoras's theorem,

c² = a² + b²

where

Therefore,

c² = 19² + 17²

c² = 361 + 289

c = √650

c = 25.495097568

c = 25.5 inches

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Answer:

To approximate the monthly interest rate, we need to use the formula for the annual percentage rate (APR) that takes into account the effect of compounding:

APR = (1 + r/m)^m - 1

where r is the annual interest rate, m is the number of compounding periods per year, and APR is the annual percentage rate.

In this case, r = 11.1% and m = 12 (since there are 12 months in a year). We want to solve for the monthly interest rate, which we can call r_m:

r_m = (1 + r/12)^12 - 1

r_m = (1 + 0.111/12)^12 - 1

r_m = 0.009141

To convert this to a percentage, we multiply by 100:

r_m = 0.9141%

Therefore, the approximate monthly interest rate is 0.9141%, rounded to two decimal places.

Answer:

d=69, e=32, f=79

Step-by-step explanation:

e=32

d=69

f=180-69-32=79

The measure of each of the missing angles include the following:

d = 69.

e = 32.

f = 79.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

By applying the vertical angles theorem to the geometric figure, we have the following:

m∠e = 32°

m∠d = 69°

From the linear postulate theorem, we have:

m∠e + m∠d + m∠f = 180°

32° + 69° + m∠f = 180°

m∠f = 180° - (32° + 69°)

m∠f = 79°

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Answer:

The slope of the given line on the graph is 1/3.

Answer:

1/3

Step-by-step explanation:

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Let's start at 0 with x = 0 and y = 0 or (0,0)

You see the graph crosses coordinate (3,1)

so y goes from 0 to 1 => rise = 1

x goes from 0 to 3 => run = 3

then rise/run = 1/3

If the ratio is less than 1, then the series converges, and if the ratio is greater than 1, then the series diverges.

To find the properties that two units are sold in a given day, the formula P(2) is used.

The Ratio Test can be used to determine the convergence or divergence of the series given by the expression n=1∑[infinity]2nn2→.

To use the Ratio Test, you must calculate the ratio of the values of the  successive terms that occurs in the series.

The ratio is calculated by dividing the n+1th term by the nth term.

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Answer:

Since the hexagon is a 2D shape, it does not have volume. We can find the area of a hexagon but not its volume.

Step-by-step explanation:

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths. In this case, since the figures are hexagons, we can use the ratio of their corresponding side lengths to find the ratio of their areas.

Since the scale factor of the hexagons is 3:7, we know that the ratio of their side lengths is also 3:7. Therefore, the ratio of their areas is:

(3/7)^2 = 9/49

We are given that the area of the smaller hexagon is 18 m^2, so we can use this to find the area of the larger hexagon:

(area of larger hexagon) = (area of smaller hexagon) x (ratio of areas)

(area of larger hexagon) = 18 x (9/49)

(area of larger hexagon) = 3.28 m^2 (rounded to two decimal places)

Since the hexagon is a 2D shape, it does not have volume. We can find the area of a hexagon but not its volume.

Daniel bought 8 apples and 16 oranges. The equation we will use to solve the problem is 0.35x + 0.5(2x) = 5.4.

We know that Daniel bought twice as many oranges as apples, so let's call the number of apples he bought "x". Therefore, the number of oranges he bought would be "2x".

We also know that each apple cost $0.35 and each orange cost $0.50, so we can write the equation:

0.35x + 0.5(2x) = 5.4

Simplifying the equation, we get:

0.35x + x = 5.4 ÷ 0.5

0.35x + x = 10.8

1.35x = 10.8

x = 8

So, Daniel bought 8 apples, which means he also bought 2x = 16 oranges.

However, we need to check if this solution makes sense hence the cost of the apples would be:

0.35 × 8 = 2.8

And the cost of the oranges would be:

0.5 × 16 = 8

Adding those together, we get:

2.8 + 8 = 10.8

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a) At the time the article was published, the federal minimum wage was $5.85 per hour.

b) According to the US Department of Labor website, the federal minimum wage in 2008 was $6.55 per hour.  

c) To earn the current federal minimum wage of $7.25 per hour, a person must pick up a penny in 4.97 seconds.

d) The phrase "penny dreadful" is a British expression referring to cheaply printed stories of sensational and sometimes gruesome content that were sold for a penny in the 19th century.

A) The minimum wage when Owen wrote his article can be calculated by using the equation:

Minimum wage = (Amount of money earned)/(Amount of time taken to earn it)

In this case, the amount of money earned is $0.01 (the value of a penny) and the amount of time taken to earn it is 6.15 seconds. Therefore:

Minimum wage = ($0.01)/(6.15 seconds) = $0.00162601626 per second

To convert this to an hourly wage, we can multiply by the number of seconds in an hour (3600):

Minimum wage = ($0.00162601626 per second) x (3600 seconds per hour) = $5.85365854 per hour

Minimum wage =  $5.85

B) According to the U.S. Department of Labor, the federal minimum wage in 2008 was $6.55 per hour.

Therefore, Owen's arithmetic was slightly off, as his calculated minimum wage is lower than the actual minimum wage at that time.

C) To calculate how much time you would need to spend picking up a penny in order to earn the current minimum wage, we can use the same equation as before, but rearrange it to solve for the amount of time:

Amount of time = (Amount of money earned)/(Minimum wage)

The current federal minimum wage is $7.25 per hour, or $0.00201388889 per second. Therefore:

Amount of time = ($0.01)/($0.00201388889 per second) = 4.97 seconds

So you would need to spend 4.97 seconds picking up a penny in order to earn the current minimum wage.

D) The phrase "penny dreadful" refers to a type of cheap, sensationalist fiction that was popular in the 19th century. These stories were typically published in weekly installments and sold for a penny each, hence the name "penny dreadful."

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Given line: y = -2x + 6 and Perpendicular line: y = 2x - 6: The slope of the given line is -2 and the slope of the perpendicular line is 2. Both slopes are in simplest form.

Slope is a measure of the steepness or inclination of a line, or a rate of change. It is usually represented by the letter m, and is calculated by finding the ratio of the rise (vertical change) over the run (horizontal change) between two points on a line. Slope can also be used to describe the angle of a line or surface, which is usually expressed as a percentage or in degrees. In mathematics, slope is used to describe the behavior of a line or curve, as well as to compare lines or curves with different slopes.

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To make the remainder 0, the final value of k must be -1.

The question asks to find all values of k so that when x^(3)-k^(2)x+k+2 is divided by x-2, the remainder is 0.

To find the values of k, we need to use synthetic division.

First, we can write the equation as follows:

Now we can continue with the synthetic division:

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The total materials purchase usage variance is -P122.50.

The total materials cost variance is calculated by subtracting the total standard cost from the total actual cost. The total standard cost is P675.00 per batch and there were 14 batches produced during the month, so the total standard cost is P675.00 x 14 = P9,450.00. The total actual cost is calculated by multiplying the quantity purchased by the purchase price for each fruit and then adding them all together. The total actual cost is (300 x P9.50) + (150 x P22.00) + (350 x P7.20) + (80 x P15.40) = P2,850.00 + P3,300.00 + P2,520.00 + P1,232.00 = P9,902.00. The total materials cost variance is P9,902.00 - P9,450.00 = P452.00.

The materials yield variance is calculated by subtracting the standard quantity of materials from the actual quantity of materials used and then multiplying by the standard cost per liter. The standard quantity of materials is 60 liters per batch and there were 14 batches produced during the month, so the standard quantity of materials is 60 x 14 = 840 liters. The actual quantity of materials used is 290 + 130 + 350 + 75 = 845 liters. The materials yield variance is (840 - 845) x P10.00 = -P50.00.

The materials purchase usage variance is calculated by subtracting the standard cost per liter from the actual cost per liter and then multiplying by the actual quantity of materials used. The materials purchase usage variance for each fruit is (P9.50 - P10.00) x 290 + (P22.00 - P21.25) x 130 + (P7.20 - P7.50) x 350 + (P15.40 - P15.00) x 75 = -P145.00 + P97.50 - P105.00 + P30.00 = -P122.50. The total materials purchase usage variance is -P122.50.

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The functions involved in g(x) are multiply by 2 and subtract the value of 5.

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The graph of the inverse of a function shows the function and the inverse of the function, which are both plotted on the line y = x. This graph's line traverses the origin and has a slope value of 1.

Given that, f(x) involves the following functions:

Divide by 2

Add 5

Also, g(x) is the inverse of the function of f(x) hence, the function involved are inverse of the original function.

Hence, the functions involved in g(x) are multiply by 2 and subtract the value of 5.

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The given sequence is A(n) = 6.3 + (n-1)(5), where n is the term number. To find the 5th term of the sixth term of the sequence, we need to first find the value of the sixth term and then find its fifth term.

To find the sixth term of the sequence, we substitute n = 6 in the given formula:

A(6) = 6.3 + (6-1)(5)

A(6) = 6.3 + 25

A(6) = 31.3

Now, to find the fifth term of this sequence, we need to go back one term from the sixth term, which means we need to substitute n = 5 in the original formula:

A(5) = 6.3 + (5-1)(5)

A(5) = 6.3 + 20

A(5) = 26.3

Therefore, the fifth term of the sixth term of the sequence A(n) = 6.3 + (n-1)(5) is 26.3.

Answer:

5 compact discs on sale.

Step-by-step explanation:

To solve this you'll need to set up a system of equations. Let's use x or the original price and y for sale price. Here's what your equations will look like:

14.95x + 12.95y = 139.50

x + y = 10

Now, cancel out x so you can solve for y. You can choose either variable, but canceling out x gets you to your answer in less steps. Remember to multiply by a negative so you can cancel out the variable.

Here's what your work will look like:

14.95 + 12.95y = 139.50

-14.95 (x + y = 10)

Here's what your new equations will look like after distributing:

14.95x + 12.95y = 139.50

-14.95x - 14.95y = -149.5

Now, add these two equations together. When you do that, x cancels out and you can solve for y.

Here's what your new equation will look like after adding:

-2y = -10

Now, divide both sides by -2. After doing so, you should get y = 5. This means that you bought 5 compact discs on sale.

Hope this helps!

The translation that maps figure ABCD onto figure EFGH is described as follows: Translate figure ABCD 7 units right to form figure EFGH..

Translation transformation is a type of geometric transformation that moves every point of an object or shape in a straight line without changing its orientation or size.

A translation happens when either a figure or a function are moved horizontally or vertically.

If we look at the corresponding vertices on each figure, we have that:

Hence: Translate figure ABCD 7 units right to form figure EFGH.

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The solution to the system of equations is (4/3, 6, -2).

To solve the system of linear equations using the Gauss-Jordan elimination method, we need to perform row operations to reduce the system to reduced row echelon form. This will allow us to easily solve for the variables. Here are the steps:

1. Start with the given system of equations:

{ 6x - 2y + 2z = 4
{ 3x - y + 2z = 2
{ -12x + 4y - 8z = 8

2. Write the system as an augmented matrix:

[ 6 -2 2 | 4 ]
[ 3 -1 2 | 2 ]
[ -12 4 -8 | 8 ]

3. Divide the first row by 6 to get a leading 1:

[ 1 -1/3 1/3 | 2/3 ]
[ 3 -1 2 | 2 ]
[ -12 4 -8 | 8 ]

4. Use the first row to eliminate the x terms in the second and third rows:

[ 1 -1/3 1/3 | 2/3 ]
[ 0 2/3 5/3 | 2/3 ]
[ 0 0 -4 | 8 ]

5. Divide the second row by 2/3 to get a leading 1:

[ 1 -1/3 1/3 | 2/3 ]
[ 0 1 5/2 | 1 ]
[ 0 0 -4 | 8 ]

6. Use the second row to eliminate the y terms in the first and third rows:

[ 1 0 7/6 | 5/6 ]
[ 0 1 5/2 | 1 ]
[ 0 0 -4 | 8 ]

7. Divide the third row by -4 to get a leading 1:

[ 1 0 7/6 | 5/6 ]
[ 0 1 5/2 | 1 ]
[ 0 0 1 | -2 ]

8. Use the third row to eliminate the z terms in the first and second rows:

[ 1 0 0 | 4/3 ]
[ 0 1 0 | 6 ]
[ 0 0 1 | -2 ]

9. The system is now in reduced row echelon form, and we can easily solve for the variables:

x = 4/3
y = 6
z = -2

So the solution to the system of equations is (4/3, 6, -2).

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A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.

A graph of the system of inequalities is shown on the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:

2x + 3y = 192.

Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;

x + y = 72

For the constraints, we have the following system of linear inequalities:

x ≥ 0.

y ≥ 0.

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The polynomial 8x^(3) + 12x^(2) + 6x + 1 can be factored as (2x + 1)^(3) using Pascal's Triangle and the properties of binomial cubes.

To factor the given polynomial using Pascal's Triangle and the properties of binomial cubes, we need to first identify the coefficients of the polynomial and then use the pattern of Pascal's Triangle to find the factors. Here are the steps:

Step 1: Identify the coefficients of the polynomial. The coefficients are 8, 12, 6, and 1.

Step 2: Use the pattern of Pascal's Triangle to find the factors. The third row of Pascal's Triangle is 1, 3, 3, 1. We can use this pattern to factor the polynomial as follows:

8x^(3) + 12x^(2) + 6x + 1 = (2x + 1)^(3)

Step 3: Use the properties of binomial cubes to simplify the factors. The formula for the cube of a binomial is (a + b)^(3) = a^(3) + 3a^(2)b + 3ab^(2) + b^(3). We can use this formula to simplify the factors as follows:

(2x + 1)^(3) = (2x)^(3) + 3(2x)^(2)(1) + 3(2x)(1)^(2) + (1)^(3) = 8x^(3) + 12x^(2) + 6x + 1

Therefore, the factors of the polynomial are (2x + 1)^(3).

The polynomial 8x^(3) + 12x^(2) + 6x + 1 can be factored as (2x + 1)^(3) using Pascal's Triangle and the properties of binomial cubes.

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The number of trials (n) represents the group's size, and the probability of success (p) represents the population's proportion of extroverts or introverts.

(a) Assume that X is the proportion of extroverts among a team of 15 marketing employees. X exhibits a binomial distribution with n = 15 and p = 0.8 as its parameters.

The following formula can be used to determine the likelihood of having at least 10 extroverts:

Binom.cdf(9, 15, 0.8) = 0.836; P(X 10) = 1 - P(X 10) = 1 - P(X 9) = 1

The likelihood of having five or more extroverts can be determined using the formula below:

Binom.cdf(4, 15, 0.8) 0.999, P(X 5) = 1 - P(X 5) = 1 - P(X 4) = 1.

The following formula can be used to determine the likelihood that all 15 employees are extroverts:

The formula P(X = 15) = binom.pmf(15, 15, 0.8) 0.035

(b) Assume that there are Y introverts among the four computer programmers in the group. Y has a binomial distribution with n = 4 and p = 0.35 (because 65% of respondents identify as introverts, 35% must identify as extroverts).

The following formula can be used to determine the likelihood that none of the programmers are introverts:

P(Y = 0) is equal to binom.pmf(0, 4, 0.35) 0.150.

The following formula can be used to determine the likelihood that two or more programmers are introverts:

Binom.cdf(1, 4, 0.35) = 0.586 when P(Y 2) = 1 - P(Y 2) = 1 - P(Y 1) = 1.

The following formula can be used to determine the likelihood that all four programmers are introverts:

P(Y = 4) is equal to binom.pmf(4, 4, 0.35) 0.015.

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The second largest share of the three entrepreneurs is $291,666.68.

To calculate the second largest share of the three entrepreneurs, we need to first find the total ratio by adding the three individual ratios: 3 + 4 + 5 = 12.

Next, we can find the value of one part of the ratio by dividing the total amount invested by the total ratio: $875,000 ÷ 12 = $72,916.67.

Finally, we can calculate the second largest share by multiplying the value of one part of the ratio by the second largest individual ratio, which is 4: $72,916.67 × 4 = $291,666.68.

Therefore, the amount of the second largest share is $291,666.68.

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Answer: :)

Step-by-step explanation:

Let's start by setting up a proportion to represent the ratio of black tiles to white tiles:

1 black tile : 4 white tiles

We know that Eddie wants a total of 25 tiles in the design, so we can set up another proportion to represent the ratio of white tiles to the total number of tiles:

white tiles : 25 total tiles

To solve for the number of white tiles, we need to find the equivalent ratio of white tiles in terms of the total number of tiles. We can do this by cross-multiplying our two proportions:

1 black tile * (white tiles/4 black tiles) = white tiles/4

white tiles/25 total tiles = (white tiles/4) / (1 black tile + white tiles/4)

Simplifying this expression, we get:

white tiles/25 = (white tiles/4) / (5/4)

white tiles/25 = (1/4) * (white tiles/5)

5 * white tiles = 100

white tiles = 20

Therefore, Eddie will use 20 white tiles in his design.

The vectors [tex]([1],[-2],[3]),([2],[-2],[0])[/tex] and [tex]([0],[1],[7])[/tex] are a linearly independent set.

To determine if the vectors are a linearly independent set, we can use the determinant method. The determinant of a 3x3 matrix is given by:

[tex]\begin{bmatrix}a_1 & a_2 &a_3 \\  b_1& b_2 &b_3 \\  c_1&c_2  &c_3 \end{bmatrix}[/tex]

We can create a 3x3 matrix using the given vectors as the columns of the matrix:

[tex]\begin{bmatrix}1 & 2 &0 \\  -2& -2 &1 \\  3&0  &7 \end{bmatrix}[/tex]

Now, we can find the determinant of this matrix using the formula:

[tex]det(\begin{bmatrix}1 & 2 &0 \\  -2& -2 &1 \\  3&0  &7 \end{bmatrix})[/tex]

[tex]= 1(-2*7 - 1*0) - 2(-2*7 - 1*3) + 0(-2*0 - 1*-2)[/tex]

[tex]= -14 - 0 - 4(-14) - 6 + 0[/tex]

[tex]= -14 + 56 - 6[/tex]

[tex]= 36[/tex]

Since the determinant is not equal to zero, the vectors are linearly independent.

Therefore, the vectors[tex]([1],[-2],[3]),([2],[-2],[0])[/tex] and [tex]([0],[1],[7])[/tex] are a linearly independent set.

See more about linear independence at: https://brainly.com/question/10725000

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