Solve the system of linear equation using Gauss-Seidel Method. Limit your answer to 5 decimals places and stop the iteration when the previous is equal to the present iteration.


Use these initial values x = 0 ; y = 0; z = 0 w 2x - y = 2 x - 3y + z = -2 , -x + y - 3z = -6

Answer:

s= 100

r= 130

x= 38

y= 30

Step-by-step explanation:

Answer:

15 is the answer

Step-by-step explanation:

We know that x = -4, so substitute x for -4 in the problem

11 - (-4)

2 negative signs make a positive sign

11 + 4

=15

Answer:

Hi! The answer to your question is [tex]15[/tex]

How to solve is whenever there is an x, replace it with a -4 so the problem would be set up like this 11-(-4) and at that point you can just solve it in a calculator

Step-by-step explanation:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

☁Brainliest is greatly appreciated!!☁

Hope this helps!!

- Brooklynn Deka

Answer:

njbrdjbbgdbjbfjfj

Step-by-step explanation:

The statement "Linear programming can be used to find the optimal solution for profit, but cannot be used for nonprofit organizations" is False.

Linear programming can be used to find the optimal solution for profit as well as for non-profit organizations. Linear programming is a method of optimization that aids in determining the best outcome in a mathematical model where the model's requirements can be expressed as linear relationships. Linear programming can be used to solve optimization problems that require maximizing or minimizing a linear objective function, subject to a set of linear constraints.

Linear programming can be used in a variety of applications, including finance, engineering, manufacturing, transportation, and resource allocation. Linear programming is concerned with determining the values of decision variables that will maximize or minimize the objective function while meeting all of the constraints. It is used to find the optimal solution that maximizes profits for for-profit organizations or minimizes costs for non-profit organizations.

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Answer:

Area of a rectangle is length multiplied by the width. In this case, length is equal to width. So, Area is 8 ft * 8 ft which is 64 ft2.

Answer:

18.

Step-by-step explanation:

The mean is ≈ 8.793. The variance is approximately 9.641. The standard deviation is approximately 2.964

Given frequency table:

Value: 2 3 6 9 12

Frequency: 3 6 9 7 4

a) Mean:

[tex]\[\text{{Mean}} = \frac{{\text{{Sum of (Value * Frequency)}}}}{{\text{{Total number of observations}}}}\]\[\text{{Mean}} = \frac{{(2 \times 3) + (3 \times 6) + (6 \times 9) + (9 \times 7) + (12 \times 4)}}{{3 + 6 + 9 + 7 + 4}}\]\[\text{{Mean}} = \frac{{189}}{{29}}\][/tex]

≈ 8.793

b) Variance:[tex]\[\text{{Variance}} = \frac{{(3 \times (2 - \text{{Mean}})^2) + (6 \times (3 - \text{{Mean}})^2) + (9 \times (6 - \text{{Mean}})^2) + (7 \times (9 - \text{{Mean}})^2) + (4 \times (12 - \text{{Mean}})^2)}}{{29}}\][/tex]

 ≈ 8.793

c) Standard Deviation:

[tex]\[\text{{Standard Deviation}} = \sqrt{{\text{{Variance}}}}\][/tex]

Therefore, the standard deviation is approximately [tex]\sqrt{8.793} \approx 2.964[/tex]

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Answer:

x+Y =x68 i thinkStep-by-step explanation:

Answer:

86

Step-by-step explanation:

Example 1

Make a graph for the table in the Opening Exercise.

Example 2

Use the graph to determine which variable is the independent variable and which is the dependent variable. Then state the relationship between the quantities represented by the variables

The solution to the system of equations is: x1 = 1/2,  x2 = 9/4,  x3 = 1,  x4 = 0

a) Solving the system of equations using inverse matrix:

Let's write the system of equations in matrix form: AX = B

The coefficient matrix A is:

A = [[y, 2, 2], [1, -2, 2], [3, -1, 5]]

The variable matrix X is:

X = [[x], [y], [z]]

The constant matrix B is:

B = [[1], [-3], [7]]

To solve for X, we need to find the inverse of matrix A (if it exists):

Calculate the determinant of matrix A: |A|

|A| = y((-2)(5) - (-1)(2)) - 2((1)(5) - (3)(2)) + 2((1)(-1) - (3)(-2))

= -9y + 4

Check if |A| is non-zero. If |A| ≠ 0, then the inverse of A exists.

Since |A| = -9y + 4, it can only be zero if y = 4/9.

If y ≠ 4/9, then |A| ≠ 0, and we can proceed to find the inverse of A.

Calculate the matrix of minors of A: Minors(A)

Minors(A) = [[(-2)(5) - (-1)(2), (1)(5) - (3)(2), (1)(-1) - (3)(-2)],

[(2)(5) - (2)(2), (3)(5) - (3)(2), (3)(-1) - (3)(-2)],

[(2)(-1) - (2)(-2), (3)(-1) - (1)(2), (3)(-2) - (1)(-1)]]

= [[-8, -1, -1],

[6, 9, -3],

[2, -1, -5]]

Calculate the matrix of cofactors of A: Cofactors(A)

Cofactors(A) = [[(-1)^1(-8), (-1)^2(-1), (-1)^3(-1)],

[(-1)^2(6), (-1)^3(9), (-1)^4(-3)],

[(-1)^3(2), (-1)^4(-1), (-1)^5(-5)]]

= [[-8, 1, -1],

[6, -9, 3],

[-2, 1, -5]]

Calculate the adjugate of A: Adj(A) = Transpose(Cofactors(A))

Adj(A) = [[-8, 6, -2],

[1, -9, 1],

[-1, 3, -5]]

Calculate the inverse of A: A^(-1) = Adj(A)/|A|

A^(-1) = [[(-8)/(9y - 4), 6/(9y - 4), (-2)/(9y - 4)],

[1/(9y - 4), (-9)/(9y - 4), 1/(9y - 4)],

[(-1)/(9y - 4), 3/(9y - 4), (-5)/(9y - 4)]]

Multiply A^(-1) by B to find X:

X = A^(-1) * B

= [[(-8)/(9y - 4), 6/(9y - 4), (-2)/(9y - 4)],

[1/(9y - 4), (-9)/(9y - 4), 1/(9y - 4)],

[(-1)/(9y - 4), 3/(9y - 4), (-5)/(9y - 4)]] * [[1], [-3], [7]]

Simplifying the multiplication will give the solution for X in terms of y.

b) Solving the system of equations using reduced row echelon form:

Let's write the system of equations in augmented matrix form [A | B]:

The augmented matrix [A | B] is:

[1, 2, 2, 5 | 0]

[1, -2, 2, -4 | 0]

[3, -1, 5, 2 | 0]

[3, -2, 6, -3 | 0]

Using Gaussian elimination and row operations, we can transform the augmented matrix to reduced row echelon form.

Performing row operations:

R2 = R2 - R1

[1, 2, 2, 5 | 0]

[0, -4, 0, -9 | 0]

[3, -1, 5, 2 | 0]

[3, -2, 6, -3 | 0]

R3 = R3 - 3R1

[1, 2, 2, 5 | 0]

[0, -4, 0, -9 | 0]

[0, -7, -1, -13 | 0]

[3, -2, 6, -3 | 0]

R4 = R4 - 3R1

[1, 2, 2, 5 | 0]

[0, -4, 0, -9 | 0]

[0, -7, -1, -13 | 0]

[0, -8, 0, -18 | 0]

R2 = (-1/4)R2

[1, 2, 2, 5 | 0]

[0, 1, 0, 9/4 | 0]

[0, -7, -1, -13 | 0]

[0, -8, 0, -18 | 0]

R3 = R3 + 7R2

[1, 2, 2, 5 | 0]

[0, 1, 0, 9/4 | 0]

[0, 0, -1, -1 | 0]

[0, -8, 0, -18 | 0]

R4 = R4 + 8R2

[1, 2, 2, 5 | 0]

[0, 1, 0, 9/4 | 0]

[0, 0, -1, -1 | 0]

[0, 0, 0, -6 | 0]

R4 = (-1/6)R4

[1, 2, 2, 5 | 0]

[0, 1, 0, 9/4 | 0]

[0, 0, -1, -1 | 0]

[0, 0, 0, 1 | 0]

R1 = R1 - 2R2 - 2R3

[1, 0, 0, 1/2 | 0]

[0, 1, 0, 9/4 | 0]

[0, 0, -1, -1 | 0]

[0, 0, 0, 1 | 0]

R3 = -R3

[1, 0, 0, 1/2 | 0]

[0, 1, 0, 9/4 | 0]

[0, 0, 1, 1 | 0]

[0, 0, 0, 1 | 0]

The reduced row echelon form of the augmented matrix is obtained.

From the reduced row echelon form, we can write the system of equations:

x1 = 1/2

x2 = 9/4

x3 = 1

x4 = 0

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Answer:

159.25 ft²

I hope this helps! :)

Step-by-step explanation:

Formulas:

For the Rectangle... bh = a

For the Semicircle... 1/2 × πr²

Step 1:

Solve the area for the rectangle:

bh = a

10 × 12 = 120

a = 120 ft²

Step 2:

Solve the Area for the Semicircle:

1/2 × πr²

1/2 × 3.14 = 1.57

Radius = Diameter ÷ 2

10 ÷ 2 = 5

Radius = 5

1.57 × 5²

1.57 × 5 × 5

= 39.25 ft²

Step 3:

Add the two areas together:

120 + 39.25 = 159.25 ft²

Answer:

zero

Step-by-step explanation:

If today is Wednesday, the probability of tomorrow being Saturday is zero.

To compute the moment generating function (MGF) for the random variable X, we need to use the formula:

[tex]My(t) = E(e^(tx))[/tex]

Given that the density function for X is fx(x) = e^(-x), x < 0, and 0 otherwise, we can write the MGF as follows:

[tex]My(t) = ∫[from -∞ to ∞] e^(tx) * fx(x) dx[/tex]

Since the density function fx(x) is non-zero only for x < 0, we can rewrite the integral accordingly:

[tex]My(t) = ∫[from -∞ to 0] e^(tx) * e^x dx + ∫[from 0 to ∞] e^(tx) * 0 dx[/tex]

The second integral is zero because the density function is zero for x ≥ 0. We can simplify the expression:

[tex]My(t) = ∫[from -∞ to 0] e^(x(1+t)) dx[/tex]

Using the properties of exponents, we can simplify further:

[tex]My(t) = ∫[from -∞ to 0] e^((1+t)x) dx[/tex]

Now we can evaluate this integral:

[tex]My(t) = [1 / (1+t)] * e^((1+t)x) | [from -∞ to 0)[/tex]

= [tex][1 / (1+t)] * (e^((1+t)(0)) - e^((1+t)(-∞)))[/tex]

= [tex][1 / (1+t)] * (1 - 0)[/tex]

= [tex]1 / (1+t)[/tex]

The moment generating function My(t) simplifies to 1 / (1+t).

To compute the expected value (E(X)) and variance (Var(X)), we can differentiate the MGF with respect to t:

E(X) = My'(t) evaluated at t=0

Var(X) = My''(t) evaluated at t=0

Taking the derivative of My(t) = 1 / (1+t) with respect to t, we get:

[tex]My'(t) = -1 / (1+t)^2[/tex]

Evaluating My'(t) at t=0:

E(X) = [tex]My'(0) = -1 / (1+0)^2 = -1[/tex]

Thus, the expected value of X is -1.

To compute the second derivative, we differentiate My'(t) =[tex]-1 / (1+t)^2[/tex]again:

[tex]My''(t) = 2 / (1+t)^3[/tex]

Evaluating My''(t) at t=0:

Var(X) =[tex]My''(0) = 2 / (1+0)^3 = 2[/tex]

Thus, the variance of X is 2.

Now, let's compute the MGF for the random variable Y = X - 2:

[tex]My_Y(t) = E(e^(t(Y)))= E(e^(t(X - 2)))= E(e^(tX - 2t))[/tex]

Using the properties of the MGF, we know that if X is a random variable with MGF My(t), then e^(cX) has MGF My(ct), where c is a constant. Therefore, we can rewrite the MGF for Y as:

[tex]My_Y(t) = e^(-2t) * My(t)[/tex]

Substituting My(t) = 1 / (1+t) from the previous calculation, we get:

[tex]My_Y(t) = e^(-2t) * (1 / (1+t))[/tex]

Simplifying further:

[tex]My_Y(t) = e^(-2t) / (1+t)[/tex]

Thus, the MGF for Y = X

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Answer:

Step-by-step explanation:

yes

The ∠3 is an alternate angle of ∠4 so it is 35° while ∠3 is a complimentary angle of ∠4 so it will be 55°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

Since we lack a measurement for angular rotation, the angle is a valuable tool for measuring angular distance. For instance, a meter or an inch is a unit of measurement for linear motion.

Given that AB and CD are parallel and AC is perpendicular to both.

So,

∠ACD = 90°

∠3 + ∠4 = 90°

∠3 = 90 - 35 = 55°.

Now,

Since ∠4 and ∠2 are alternative angles so both will be the same.

So,

∠2 = 35°

Hence "The ∠3 is an alternate angle of ∠4 so it is 35° while ∠3 is a complimentary angle of ∠4 so it will be 55°".

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(a) fz (z) and fw (w) in terms of cumulative distribution functions (CDFs) are:

   fz(z) = Fx(z) * (1 - Fy(z)) + Fy(z) * (1 - Fx(z))

   fw(w) = 1 - fz(w)

(b) If X and Y are independent exponential random variables with parameter λ, then fw(w) = [tex]1 - e^{-2\lambda w}[/tex] for w ≥ 0.

To determine fz(z) and fw(w) in terms of the marginal cumulative distribution functions (CDFs) of X and Y random variables, we need to consider the region of interest on the X-Y plane.

(a) Drawing the region of interest on the X-Y plane:

The region of interest can be visualized as the area where Z = max(X, Y) and W = min(X, Y) take specific values. This region is bounded by the line y = x (diagonal line) and the lines x = z (vertical line) and y = w (horizontal line).

Determining fz(z):

To find fz(z), we need to consider the cumulative probability that Z takes a value less than or equal to z. This can be expressed as:

fz(z) = P(Z ≤ z) = P(max(X, Y) ≤ z)

Since X and Y are independent random variables, the probability can be calculated using the joint CDF of X and Y:

fz(z) = P(max(X, Y) ≤ z) = P(X ≤ z, Y ≤ z)

Using the marginal CDFs of X and Y, denoted as FX(x) and FY(y), respectively, we can express fz(z) as:

fz(z) = P(X ≤ z, Y ≤ z) = P(X ≤ z) * P(Y ≤ z) = FX(z) * FY(z)

Determining fw(w):

To find fw(w), we need to consider the cumulative probability that W takes a value less than or equal to w. This can be expressed as:

fw(w) = P(W ≤ w) = P(min(X, Y) ≤ w)

Since X and Y are independent random variables, the probability can be calculated using the joint CDF of X and Y:

fw(w) = P(min(X, Y) ≤ w) = 1 - P(X > w, Y > w)

Using the marginal CDFs of X and Y, denoted as FX(x) and FY(y), respectively, we can express fw(w) as:

fw(w) = 1 - P(X > w, Y > w) = 1 - [1 - FX(w)][1 - FY(w)]

Special case when X and Y are independent exponential random variables with parameter A:

If X and Y are independent exponential random variables with a common parameter A, their marginal CDFs can be expressed as:

[tex]FX(x) = 1 - e^{-Ax}\\FY(y) = 1 - e^{-Ay}[/tex]

Using these marginal CDFs, we can substitute them into the formulas for fz(z) and fw(w) to obtain the specific expressions for the random variables Z and W.

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Experiment to verify the result of the study:A study at the University of Illinois found that young men who drank two pints of beer first were better able to solve certain word puzzles than sober men. An experiment to verify this result should be designed with the following steps:

Population: The population in this experiment would be young men who are eligible to consume beer legally.

Sampling: The sampling method will be convenient sampling. In this type of sampling, participants will be selected based on their availability to participate. Any participant that is within the age range of eligibility and is willing to participate can be considered for the study.

The participants will be divided into two groups, one group will drink two pints of beer while the other group will not drink any beer.

Executing the experiment: Both groups will be given word puzzles to solve after the beer is consumed by the test group and given to the control group directly.

The participants will not be given any hints on how to solve the puzzle to keep it fair. Data Collection: Both groups will be timed to solve the puzzle.

The group that solves the puzzle faster will be regarded as the winner. The number of people in each group that solve the puzzle will be recorded.

A correlation test would be performed to determine if the solution time is related to the consumption of beer.

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Data will be collected and analyzed using statistical tools such as the t-test to determine if there is a significant difference in performance between the two groups.

The experiment is designed to verify whether young men who drank two pints of beer first were better able to solve certain word puzzles than sober men. This question requires a well-planned experimental design. The experiment requires a hypothesis and a null hypothesis.

Hypothesis

Drinking two pints of beer can improve the performance of young men in word puzzles than sober men.

Null Hypothesis

Drinking two pints of beer cannot improve the performance of young men in word puzzles than sober men.

Population

The target population of the study is young men aged between 18 to 30 years.

Sample collection

To collect the sample, we will identify potential participants based on the age range of 18-30 years. The study will recruit volunteers who drink alcohol regularly and those who don't. Participants who have consumed alcohol before the study will be required to take a breathalyzer test to ensure they are within the recommended limits. Only those with a blood alcohol concentration of 0.08% and below will be included in the study. Participants will also be required to sign informed consent to participate in the study.

Execute the experiment

Participants will be randomly assigned into two groups: the control group and the experimental group. The control group will be given water to drink while the experimental group will be given two pints of beer. Participants will then be given a set of word puzzles to solve, and their performance will be recorded. Each group will be given an equal time limit to solve the word puzzles.

Data Collection

The data collected will include the number of word puzzles solved by each group, the time taken to solve the word puzzles, and the number of incorrect answers. The data collected will be analyzed using statistical tools such as the t-test to determine if the difference in performance between the two groups is statistically significant. ConclusionThe experiment is designed to verify if drinking two pints of beer can improve the performance of young men in solving certain word puzzles than sober men. The experiment involves a sample size of young men aged 18-30 years who will be randomly assigned to two groups; the experimental group and the control group. Data will be collected and analyzed using statistical tools such as the t-test to determine if there is a significant difference in performance between the two groups.

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Answer:

Step-by-step explanation:

Answer:

x = 15[tex]\sqrt{3}[/tex] , y = 15

Step-by-step explanation:

Using the sine and cosine ratios in the right triangle and the exact values

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos60° = [tex]\frac{1}{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{30}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 30[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 15[tex]\sqrt{3}[/tex]

---------------------------------------------------------

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{30}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2y = 30 ( divide both sides by 2 )

y = 15

The correct answer is: c. 8:9 and 64:81. The ratio of the areas of the first figure to the second figure is 64:81. This means that the area of the second figure is larger by a factor of 81/64 compared to the first figure.

When two figures are similar, their corresponding sides are proportional. This means that the ratio of the perimeters is equal to the ratio of the corresponding side lengths. Additionally, 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, the ratio of the perimeters of the first figure to the second figure is 8:9. This means that the perimeter of the second figure is larger by a factor of 9/8 compared to the first figure.

The ratio of the areas of the first figure to the second figure is 64:81. This means that the area of the second figure is larger by a factor of 81/64 compared to the first figure.

Therefore, the correct answer is c. 8:9 and 64:81.

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Answer:

a = 6, b = 5

Step-by-step explanation:

Assuming you require to find the values of a and b

Given

(a - 1) + (b + 3)i = 5 + 8i

Equate the real and imaginary parts on both sides , that is

a - 1 = 5 ( add 1 to both sides )

a = 6

and

b + 3 = 8 ( subtract 3 from both sides )

b = 5

There are 54 different ways of obtaining a tray from the automatic storage and retrieval rack.

To find the number of different ways of obtaining a tray from an automatic storage and retrieval rack, we can use the concept of the multiplication principle.

The multiplication principle states that if there are m ways to do one thing and n ways to do another thing, then there are m × n ways to do both things together.

In this case, we have two steps involved in obtaining a tray:

Selecting a storage rack: There are 9 different storage racks available. We can choose any one of them.

Selecting a tray within the chosen storage rack: Once we have chosen a storage rack, there are 6 different trays in each rack. We can select any one of these trays.

According to the multiplication principle, the total number of ways to perform both steps is the product of the number of options for each step.

Number of ways = Number of options for Step 1 × Number of options for Step 2

= 9 × 6

= 54

Therefore, there are 54 different ways of obtaining a tray from the automatic storage and retrieval rack.

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Answer:

x=8

Step-by-step explanation:

Because you are solving for x, you want to cancel out the y terms. You can do this by multiplying the entire equations by numbers that will make the y terms have equal numbers but opposite signs.

2(2x-5y=1)

5(-3x+2y=-18)

This turns into

4x-10y=2

-15x+10y=-90

The y terms cancel out, and the other terms can be added together.

-11x=-88

x=8

In a dataset with a bell-shaped distribution, approximately 99.7% of the values lie within three standard deviations of the mean. Given a mean score of 64 and a standard deviation of 4 on a competency test, we can determine the range within which about 99.7% of the values will fall. The correct range is between 56 and 72.

To calculate the range, we need to consider three standard deviations above and below the mean. Three standard deviations from the mean account for approximately 99.7% of the data in a bell-shaped distribution.

Lower limit: Mean - (3 * Standard Deviation)

           = 64 - (3 * 4)

           = 64 - 12

           = 52

Upper limit: Mean + (3 * Standard Deviation)

           = 64 + (3 * 4)

           = 64 + 12

           = 76

Therefore, about 99.7% of the values lie between 52 and 76.

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Answer:

a.) 25, b.)10, c.)9

Step-by-step explanation:

a.) 25x25=625

b.)10x10=100

c.) 9x9=81

Answer:

Base angles of an isosceles triangle are always congruent.

Answer:

1. A

2. C

Step-by-step explanation:

1.8 turns must an ideal solenoid should have if it is to generate a magnetic field of 1.5 mT when a current of 1.0 A passes through it

To calculate the number of turns required for an ideal solenoid, we can use the formula for the magnetic field inside a solenoid: B = μ₀ * n * I, where B is the magnetic field, μ₀ is the permeability of free space (constant), n is the number of turns per unit length, and I is the current.

Rearranging the formula, we have n = B / (μ₀ * I).

Given B = 1.5 mT (or 1.5 x 10⁻³ T) and I = 1.0 A, and knowing that μ₀ is a constant, we can substitute these values into the formula to find n.

n = (1.5 x 10⁻³) / (4π x 10⁻⁷ * 1.0) ≈ 1.19 x 10⁴ turns/m.

Since the solenoid is 10 cm (0.1 m) long, we can multiply n by the length to find the total number of turns:

Total turns = (1.19 x 10⁴ turns/m) * 0.1 m ≈ 1.19 x 10³ turns.

Rounding to the nearest whole number, the closest option is (b) 1.8.

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Answer: A,B, and E for sure. I'm not sure about C though.

Step-by-step explanation:

Answer:

$150

Step-by-step explanation:

200/4=50

200-50=150

Answer:

1/324

Step-by-step explanation: