PART X: Lost at sea

Suddenly, during your race, a powerful thunderstorm strikes. A wave washes over your boat, shorting out your navigation devices. They wouldn't be much use anyhow, because the lightning is interfering with all communications in the area.
When the storm ends and the sea is calm, you're safe, because you observed all safety precautions, but you have no idea how far off course you are. However, you do know:
* The height of a nearby landmark, which you remember from the tourist center you visited yesterday.
> Mykonos: The light in the Armenistis Lighthouse is 604 feet above sea level.
* The length of your thumb - it's about 2 inches long.
* That you can estimate lengths of less than a foot pretty accurately (to the nearest inch).

1. First, you close one eye and hold your thumb up to block your view of the landmark. You move your thumb nearer and farther from your eye until it just covers the landmark.

Make a sketch showing overlapping triangles ΔEBT and ΔELH to illustrate this situation, where your eye is E, the base of your thumb is B, the tip of your thumb is T, the bottom of the landmark is L, and the top of the landmark is H.

2. Explain why ΔEBT~ΔELH

3. When your thumb covers the landmark, you estimate that it is 10 inches from your eye. Label your drawing with the known measurements.

4. Solve for EL, the distance from your eye to the landmark. Show all work and justify each step.

The required equation in terms of 'a' is: a = (ac - by)/x.

The number being calculated is the formula's subject. On one side of the equals symbol, it is identifiable as the letter on its own.

To make 'a' the subject of the equation:

Ax + by = ac

we can start by isolating 'a' on one side of the equation.

Ax = ac - by

Then, we can divide both sides by 'x':

a = (ac - by)/x

Therefore, the equation in terms of 'a' is:

a = (ac - by)/x

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Complete questiion:

Find the subject of the equation ax+by=ac.

Answer:

-1, 2, 5 , 8 , 11   or  2, 5, 8, 11 , 14

Step-by-step explanation:

Assume n starts from 0

a(0) = 3 (0) -1 = -1
a(1) = 3 (1) -1 = 2
a(2) = 3 (2) -1 = 5
a(3) = 3 (3) -1 = 8
a(4) = 3 (4) -1 = 11

notice If we Assume n starts from 1

a(1) = 3 (1) -1 = 2
a(2) = 3 (2) -1 = 5
a(3) = 3 (3) -1 = 8
a(4) = 3 (4) -1 = 11
a(5)= 3 (5) -1 = 14

Notice a sequence can start from any N. But the most common ones are n=0 or n=1

a) The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.

b) The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.

Exponents are mathematical notation used to indicate that a quantity is being multiplied by itself a certain number of times. The exponent is usually written as a superscript to the right of the base number.For example, in the expression 2³, the base number is 2 and the exponent is 3. This means that 2 is being multiplied by itself three times, resulting in a value of 8. Exponents can also be negative or fractional, indicating that the base number is being divided by itself a certain number of times.

In the given question,

a) The value of -42 is different from the value of (-4)². The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.

b) The value of -23 is different from the value of (-2)³. The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.

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Answer:

Step-by-step explanation:

Answer:

y= (5/3)x -4/3

Step-by-step explanation:

Slope obtained from the two points of the graph.

m=5/3

Points:  A(-1,-3).  B(2,2)

m=(y2-y1)/(x2-x1)

m=(2-(-3))/(2-(-1))

m=5/3

Replacing in the equation form: y=mx+b

y=(5/3)x+b

2=(5/3)2+b

2=10/3 +b

2-10/3= b

6/3 - 10/3 = b

b= -4/3

Joining all the terms we obtain:

y= (5/3)x -4/3

Answer: The slope is 5/3

Step-by-step explanation:

the poin at (2,2) is 5 up and 3 right of the point at (

-1,-3)

The proof is completed using two column proof as follows

Statement                               Reason

QT ⊥ PT                                   Given

∠ QRP ≅ ∠ SRT = 90              definition of perpendicularity

∠ QPR ≅ ∠ STR                       Given

Δ PQR is similar to Δ TSR       AA similarity theorem

The AA similarity theorem, also known as the Angle-Angle Similarity Theorem, states that if two triangles have two corresponding angles that are congruent, then the triangles are similar.

In the given triangle, the two angles given to be equal are

Hence the triangles are similar

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Answer:

:)

Hopefully this helps you guys :)

good luck :D

The value of z that should be used when making a 93% confidence interval for p is Z=1.81 that is option D.

The z score is a measure of how many standard deviations a raw score is below or above the population mean. It will be positive if the value is more than the mean and negative if it is less than the mean. It is often referred to as the standard score. It represents the number of standard deviations an entity has from the mean.

To utilise a z-score, both the mean and the population standard deviation must be known. The z score calculates the likelihood of a score occuring within a standard normal distribution. It also allows us to compare scores from various samples. A table for the values of, representing the values of the cumulative distribution function of the normal distribution, is known as a

At 93% confidence, the significance level is,

ɑ= 1-0.93

ɑ= 0.07

Divide alpha by 2,

ɑ/2= 0.07/2= 0.035

Now, from the ‘normal probability’ table, the z value corresponding to the inverse probability of 0.035 is 1.81.

As a result, the z value is 1.81 at 93% confidence level.

z= 1.81

The value for z score is 1.81

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Answer:

I gave a couple solutions as I wasn't sure if you were asking for graphing purposes or substituting y=-x+6 into the second equation 2x-y=-9. So I gave both solutions just in case.

for the first equation y=-x+6, y intercept is (0,6)

for equation two 2x-y=-9, y intercept is (0,9)

In both of the equations the x value is 1.

Solving for y without graphing. Y=9+2x

and x=-1

Step-by-step explanation:substitute i

HOWEVER, if you are saying that the top equation is the value of y, then you substitute it into the bottom equation. 2x--x+6=-9 which would be x=-5

It really depends on what is expected of the question. I wasn't sure which one, so I gave a couple different approaches. If you could give more information, such as, are you graphing, that would be great. I'll keep an eye out for any comments.

The rate of filling water in the tank is 23450t gallons per hour.

Let's assume that the time taken to fill the tank is t hours.

The volume of water filled into the tank at time t is given by the expression V(t) = 23450t.

The tank is originally empty, which means its volume = 0 gallons.

After 5 hours,

t= 5 hours

The volume of water filled in is given by [tex]V(5) = 23450 * 5= 1,17,250[/tex] gallons of water.

Therefore, 1,17,250 gallons of water are filled in the tank after 5 hours.

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In the following question, option B, Juan McDonald is willing to pay $900 for a new iPad. he offers to pay $800 for an iPad at the apple store. it costs apple $700 to produce this iPad. A voluntary economic transaction between "Juan and Apple" will occur because it would be better off due to the transaction.

What is a voluntary economic transaction? Voluntary economic transactions involve willing buyers and willing sellers, and they usually involve the exchange of goods and services in return for money. In a free-market economy, people have the freedom to make voluntary economic transactions, and government intervention is minimal. What are the benefits of voluntary economic transactions? The benefits of voluntary economic transactions include the following: They are beneficial to both parties involved in the transaction.

The buyer obtains what they require, while the seller obtains the money they require. The exchange of goods and services for money encourages individuals to create, produce, and sell more. The economy is stimulated by increased economic activity, which leads to more job creation, more employment opportunities, and more revenue for the government. Juan McDonald is willing to pay $900 for a new iPad. He offers to pay $800 for an iPad at the Apple store. It costs Apple $700 to produce this iPad.A voluntary economic transaction between Juan and Apple will occur because it would be better off due to the transaction. So, the answer is option B: will; both Juan and Apple.

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As we have defined the Matlab function called myta which takes four arguments in the form myta(f,n,a,b).

The purpose of the function is to find the nth Taylor polynomial of the function f(x) at x = a and evaluate it at x = b. Then, it should return the absolute value of the difference between this value and f(b).

Now that we have the nth Taylor polynomial of f(x) at x = a, we can evaluate it at x = b and calculate the absolute difference between this value and f(b).

function result = myta(f,n,a,b)

   syms x; % define x as symbolic variable

   g = f(a); % initialize g as f(a)

   for i=1:n % iterate from 1 to n

       deriv = diff(f,x,i-1); % calculate the ith derivative of f

       term = deriv*(x-a)^(i-1)/factorial(i-1); % calculate the ith term of the Taylor series

       g = g + term; % add the ith term to g

   end

   result = abs(g - f(b)); % calculate the absolute difference between g(b) and f(b)

end

This code calculates the absolute difference between g(b) and f(b) using the "abs" function and assigns it to the output variable "result".

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The Variance Inflation Factor (VIF) measures the degree of correlation or the collinearity of the explanatory variables.

VIF quantifies how much each explanatory variable is correlated with a linear combination of the other variables in a multiple regression model. This can help identify variables that are redundant, irrelevant, or harmful to the model's accuracy. The VIF is calculated for each explanatory variable by dividing the variance of the regression coefficient estimates by the variance of the regression coefficient estimates when that variable is excluded from the model.

If the VIF is greater than 1, it indicates that the variance of the regression coefficient estimate for that variable is inflated by the presence of the other variables, which reduces the model's accuracy. Therefore, a VIF greater than 1 is considered to be an indication of collinearity or multicollinearity in the explanatory variables. The VIF measures the degree of correlation or the collinearity of the explanatory variables, and it can identify variables that are redundant, irrelevant, or harmful to the model's accuracy.

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when we Roll a fair 6 66-sided die. then the probability of P (not 5) is 65/66

     The concept used a die is a tool used for games and gambling. The die is a cube with six faces, each of which has a different number of dots from one to six. The roll of a die is a random event, which means that it is unpredictable, and each roll is independent of any other roll.

 Let's solve the question that is P(not 5)

                 Since the die is fair, we have 66 sides on the die. Each of the sides has a probability of 1/66 of being rolled. P(not 5) means that we need to determine the probability of rolling a number that is not 5.

           We know that a 66-sided die has 65 numbers other than 5.

     Therefore, the probability of rolling a number that is not 5 is 65/66.

            P(not 5) = 65/66

   So, the probability of not rolling a 5 is p(not 5) = 65/66.

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Answer:

x=1.9

Step-by-step explanation:

[tex]\frac{x}{4.6} =\frac{4.6}{11}[/tex]

[tex]11x=21.16[/tex]

[tex]X=1.9[/tex]

Answer: First one (the one you selected in the photo)

Step-by-step explanation:

If you need help draw a number line.

-8 is not equal to 8, as one is negative and the other is positive.

On a number line, -8 is to the left, meaning it is less, so the second one is false.

This means the first one is correct.

On the material was used, the 100-meter flex of 14 AWA wire's entirety would range. If the silver and copper cable are in 0.0013 and 0.0014, aluminum spans 0.002 and 0.004, and iron is between 0.007 and 0.008

A force that works to slow something down or halt its progress: The air/wind drag slowed the vehicle down. the extent to which a material obstructs an electric charge from passing through it: There is little reluctance in copper.

The resistance (R) of a wire is given by the formula:

R = (ρ x L) / A

where:

ρ is the resistivity of the material

L is the length of the wire

A is the wire's cross-sectional size.

The cross-sectional area (A) of a wire with diameter d is given by the formula:

A = π x (d/2)²

where pi is a number in mathematics. (approximately equal to 3.14).

For a 100-meter length of 14 AWA wire with diameter 0.163 cm, we first need to convert the diameter to meters:

d = 0.163 cm = 0.00163 m

The cross-sectional area of the wire is then:

A = π x (0.00163/2)² = 2.087 x 10⁻⁶ m²

Using this value of A and the given resistivities, we can calculate the resistance for each material:

For copper:

R_copper = (1.67 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁻⁶ m²) = 0.00134 Ω

For silver:

R_silver = (1.59 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁻⁶ m²) = 0.00128 Ω

For aluminum:

R_aluminum = (2.65 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁶ m²) = 0.00199 Ω

For iron:

R_iron = (9.71 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁻⁶ m²) = 0.00735 Ω

Therefore, the overall resistance of the 100-meter length of 14 AWA wire made of these materials would depend on which material was used. If copper or silver were used, the resistance would be relatively low, around 0.0013-0.0014 Ω. If aluminum were used, the resistance would be higher, around 0.002 Ω. If iron were used, the resistance would be much higher, around 0.007 Ω.

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The position of C on the number line is 1/8th position.

A number line is a visual representation of the real numbers as points or marks on a straight line. The number line is usually represented horizontally, with zero in the middle and positive numbers to the right of zero and negative numbers to the left of zero.

From the given number line, there are total 8 points between 0 to 1

That means, it's fractions of 8.

Location of point C is on the 1st point,

So, position of C on this number line = (1/8) ÷ (1-0) = 1/8

Therefore, In the number line, C is located in the 1/8th place.

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Answer:

I think it's answer is no.B

Over the range [5, 7], the definite integral of f(x) = 1 / (x² + 10x + 25) is around -1/60.

To find the definite integral of f(x) = 1 / (x² + 10x + 25) over the interval [5, 7], we can use the following formula:

∫[a,b] f(x) dx = F(b) - F(a)

where F(x) is the antiderivative of f(x).

First, we need to find the antiderivative of f(x):

∫ f(x) dx = ∫ 1 / (x² + 10x + 25) dx

To do this, we can use a technique called partial fraction decomposition:

1 / (x² + 10x + 25)

= A / (x + 5) + B / (x + 5)²

Multiplying both sides by the denominator (x² + 10x + 25), we get:

1 = A(x + 5) + B

Setting x = -5, we get:

1 = B

Setting x = 0, we get:

A + B = 1

A + 1 = 1

A = 0

Therefore, the partial fraction decomposition of f(x) is:

1 / (x² + 10x + 25) = 1 / (x + 5)²

Now we can find the antiderivative:

∫ f(x) dx = ∫ 1 / (x² + 10x + 25) dx = ∫ 1 / (x + 5)² dx

Using the substitution u = x + 5, du = dx, we get:

∫ 1 / (x + 5)² dx = -1 / (x + 5) + C

where C is the constant of integration.

Now we can evaluate the definite integral over the interval [5, 7]:

∫[5,7] f(x) dx = F(7) - F(5)

∫[5,7] f(x) dx = [-1 / (7 + 5) + C] - [-1 / (5 + 5) + C]

∫[5,7] f(x) dx = [-1 / 12 + C] - [-1 / 10 + C]

∫[5,7] f(x) dx = -1 / 12 + C + 1 / 10 - C

∫[5,7] f(x) dx = -1 / 60

Therefore, the definite integral of f(x) = 1 / (x² + 10x + 25) over the interval [5, 7] is approximately -1/60.

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Answer:

Point-Slope Form: y - 1 = -1/2(x - 4) or Standard Form: y = -1/2x + 3

Step-by-step explanation:

For a line to be perpendicular, you take the negative inverse of the slope of 2x - y = 4. To do this, rearrange the y to one side and you get y = 2x - 4. The slope of the line is 2. So, taking the negative inverse would be -1/m (with m being slope of the the equation given in the problem. This would give you -1/2.

Using point slope formula, y - y1 = m(x - x1), you can plug in the point given, (4,1) and the slope you found to get y - 1 = -1/2(x - 4). For standard form, isolating the y gets you y = -1/2x + 3.

You can check your answer by using Desmos by putting in the line 2x - y = 4, the point (4,1), and the equation you got as your answer. You will see that the equation is perpendicular to 2x - y = 4 and passes through point (4,1). Your equation of the line is y - 1 = -1/2(x - 4) or y = -1/2x + 3

Answer:

[tex]\textsf{$\boxed{\checkmark}\;\;y$-value\;of\;vertex\;is\;$-1$}[/tex]

[tex]\textsf{$\boxed{\checkmark}$\;\;Minimum\;value\;occurs\;at\;$y = -1$}[/tex]

Step-by-step explanation:

Given equation:

[tex]y=x^2+8x+15[/tex]

As the given equation is quadratic with a positive leading coefficient, it is a parabola that opens upwards. Therefore, its vertex is its minimum point. This means that the minimum value of the range is the y-value of the vertex.

The x-value of the vertex of a parabola in the form y = ax² + bx + c is x = -b/2a. Therefore, the x-value of the vertex of the given equation is:

[tex]\implies x=\dfrac{-8}{2(1)}=-4[/tex]

To find the y-value of the vertex, substitute x = -4 into the equation:

[tex]\begin{aligned}\implies y&=(-4)^2+8(-4)+15\\&=16-32+15\\&=-16+15\\&=-1\end{aligned}[/tex]

Therefore, the minimum y-value of the function is y = -1, so the range is y ≥ -1.

Therefore, the following are true statement about the given equation:

An assignment of probabilities to events in a sample space must obey all of the following: They must obey the addition rule for disjoint events, They must sum to 1 when adding over all events in the sample space, and The probability of any event must be a number between 0 and 1, inclusive. Hence, the correct option is All of the above.

Probability is the branch of mathematics that deals with the likelihood of a random event occurring. Probability is concerned with quantifying the probability of different results in a certain event.

The possibility that a specific event will occur is calculated using probability. Probability is calculated using several methods in mathematics, including axioms, probability spaces, events, random variables, and expectation values.

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The volume of the sphere which is equivalent to the lung capacity is approximately =2,571 cm³

To calculate the volume of a sphere the formula used = V = 4/3 πr³

Radius = 8.5 cm

First cube the radius = 8.5³ = 614.125

The, multiply r³ by π = r³×π = 614.125× 3.14= 1928.3525

Take this answer and multiply it by 4 = 4×1928.3525= 7713.41

Last, divide this answer by 3 = 7713.41/3 = 2571.136666

Therefore the volume of the balloon = 2,571 cm³(approximately)

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The probability that the second child born to the couple will have blood type AB is 1/2.

Blood grouping is the categorization of blood into groups depending on the type of antigen and antibody present on the surface of red blood cells (RBCs).

The ABO blood grouping system, which includes A, B, AB, and O blood types, is the most well-known blood grouping system.

Blood group Rh (Rhesus) grouping system is another well-known blood grouping system that can be determined.

Therefore, the probability that the second child born to the couple will have blood type AB is 1/2.

50 percent of the offspring of this couple will inherit the gene for the ABO blood type A from the mother, while the remaining 50% will inherit the gene for the blood type B from the father.

The probability of inheriting the gene for blood type AB is thus 1/2 for a child born to these parents.

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After 5 hours, the tank will have 50 gallons of water.

To solve this problem, use the following equation:

Gallons = Rate x Time

In this case, the rate is 5 gallons per hour and the time is 5 hours, so the equation becomes:

Gallons = 5 x 5

Therefore, the tank will have 50 gallons of water after 5 hours.

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In summary, when repeated samples of size n are taken from a normal population with an unknown variance, the statistic t follows the t-distribution with n-1 degrees of freedom.

If repeated samples of size n are taken from a normal population with an unknown variance, then the statistic t follows the t distribution with n-1 degrees of freedom. When a sample of size n is taken from a normal population with a known variance and mean, the sample mean follows a normal distribution with a mean of μ and a variance of σ2/n. This distribution is known as the sampling distribution of the mean.

However, when the variance is unknown, the sampling distribution of the mean can no longer be calculated using the normal distribution. In this scenario, the sample mean is calculated using a t-distribution instead of a standard normal distribution.The t-distribution is similar to the standard normal distribution. However, it is more spread out and flatter than the standard normal distribution. As a result, the t-distribution has thicker tails than the standard normal distribution, which makes it more suitable for analyzing small samples of data.

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Answer:

12.

Step-by-step explanation:

Given: 3(x + 2) + 5x

Put in x:

3(2 + 2) + (5 x 2)

(3 x 4) + 10

12 + 10

= 12.

Answer:

[tex]x = 4\sqrt{3}[/tex]

Step-by-step explanation:

The triangle is right-angled

In a right-angled triangle, the following equality holds

[tex]\tan x = \dfrac{\text{Side Opposite x}}{\text{Side adjacent to x}}\\\\\tan 30 = \dfrac{4}{x}\\\\[/tex]

[tex]\tan 30 = \dfrac{1}{\sqrt{3}}\\\\\dfrac{1}{\sqrt{3}} = \dfrac{4}{x}\\\\[/tex]

Cross multiply:
[tex]1 \times x = 4 \times \sqrt{3}\\\\x = 4\sqrt{3}[/tex]

The two remaining angles are 58°, and the length of the third side of the triangle is 6.5 inch.

In order to determine the other two angles of each triangle as well as the length of the third side, we need to use the Cosine Rule. According to the Cosine Rule, for any triangle with sides of length a, b, and c, and angles of A, B, and C, the following equation holds:

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

For the first triangle, we are given that the side of length 5 is adjacent to an angle of 61°. Therefore, a = 5, C = 61°. Using the information provided, we can also determine that b = 4.8. Substituting these values into the Cosine Rule equation, we get:

[tex]c^2 = (5)^2 + (4.8)^2 - 2(5)(4.8) cos(61°)[/tex]

We can solve this equation to get c = 6.5. Therefore, the length of the third side in the first triangle is 6.5. Additionally, we can use the Triangle Angle Sum theorem to determine the other two angles. According to this theorem, the sum of the three angles of a triangle is 180°. Therefore, for the first triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.

For the second triangle, we use the same process, but with the given side lengths reversed. That is, we set a = 4.8, b = 5, and C = 61°. Again, substituting these values into the Cosine Rule equation, we get:

[tex]c^2 = (4.8)^2 + (5)^2 - 2(4.8)(5) cos(61°)[/tex]

We can solve this equation to get c = 6.5. Therefore, the length of the third side in the second triangle is also 6.5. We can use the Triangle Angle Sum theorem again to determine the other two angles. Again, for the second triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.

In conclusion, for each triangle, the two remaining angles are 58°, and the length of the third side is 6.5 inch.

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In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.

The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.

The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.

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