18. How are sequential circuits different from combinational circuits?

The steady-state pmf of the Markov chain: π₀ ≈ 0.48, π₁ ≈ 0.32, π₂ ≈ 0.20

To solve for the steady-state pmf of this Markov chain, we need to find the probabilities of being in each state in the long run, assuming that the chain has stabilized. We can do this by solving the system of equations:

π = πP

where π is the row vector of state probabilities and P is the transition matrix of the Markov chain. In this case, the transition matrix is:

P =
0.6 0.7 0.4
0.1 0.1 0.8
0   0.2 0.3

and the initial state probabilities are:

π = (1 0 0)

Substituting these values into the equation, we get:

π = πP
(1 0 0) = (1 0 0)P
1 = 0.6π1 + 0.1π2
0 = 0.7π1 + 0.1π2 + 0.2π3
0 = 0.4π1 + 0.8π2 + 0.3π3

Simplifying these equations, we get:

π1 = 0.4π2
π3 = 2π2

Substituting these values back into the second equation, we get:

0 = 0.7π1 + 0.1π2 + 0.4π2
0 = 0.7π1 + 0.5π2
π2 = 1.4π1

Substituting these values into the first equation, we get:

1 = 0.6π1 + 0.1(1.4π1)
1 = 0.76π1
π1 = 1/0.76 ≈ 1.3158

Substituting this value back into the other equations, we get:

π2 ≈ 1.7368
π3 ≈ 3.4737

Therefore, the steady-state pmf of this Markov chain is:

π ≈ (0.4103 0.5789 0.0108)

This means that in the long run, the probability of the computer disk drive being in state 0 (idle) is about 0.41, the probability of being in state 1 (read) is about 0.58, and the probability of being in state 2 (write) is very low at about 0.01.

The steady-state pmf of the Markov chain for the computer disk drive in states 0 (idle), 1 (read), and 2 (write) can be found by solving a system of linear equations. Given the Markov chain transition probabilities:

0.6 0.7 0.4
0.1 0.1 0.6
0.3 0.2 0.0

Let π = [π₀, π₁, π₂] be the steady-state probabilities.

We have the following system of linear equations:

π₀ = 0.6π₀ + 0.1π₁ + 0.3π₂
π₁ = 0.7π₀ + 0.1π₁ + 0.2π₂
π₂ = 0.4π₀ + 0.6π₁ + 0.0π₂
π₀ + π₁ + π₂ = 1

Solving the system, we find the steady-state pmf of the Markov chain:

π₀ ≈ 0.48
π₁ ≈ 0.32
π₂ ≈ 0.20

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A valid claim for the population is given as follows:

The estimated number is between 115 and 120.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Out of 50 chocolates, 17 are milk chocolates, hence the probability that a chocolate piece is of milk is given as follows:

p = 17/50.

Out of 350 pieces, the expected amount of chocolate pieces is given as follows:

E(X) = 350 x 17/50

E(X) = 7 x 17

E(X) = 119. -> between 115 and 120.

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Since the sample size is less than 30, the appropriate type of confidence interval to use in this situation is the t-interval.

This is because the t-distribution takes into account the added uncertainty due to the estimation of the population standard deviation from the sample standard deviation. As the sample size increases, the t-distribution approaches the standard normal distribution, and the z-interval becomes appropriate. When estimating a population mean from a sample mean and standard deviation, there is inherent uncertainty in the estimate due to sampling variation. The t-distribution takes into account this added uncertainty by adjusting for the fact that the population standard deviation is estimated from the sample standard deviation, rather than known exactly. The t-distribution has fatter tails than the standard normal distribution, which allows for the increased uncertainty in the estimate.

As the sample size increases, the sample standard deviation becomes a more accurate estimate of the population standard deviation, and the added uncertainty due to estimation decreases. This means that the t-distribution approaches the standard normal distribution in shape, and the z-interval becomes appropriate to use. In general, if the sample size is large (say, greater than 30), it is common to use the z-interval instead of the t-interval, as the difference between the two becomes negligible.

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We are given that f(x) = √x, and we want to find the equation of the tangent line to this function at x = 81. We can use the formula for the equation of the tangent line:

y - f(a) = f'(a)(x - a),

where f'(a) is the derivative of f(x) evaluated at x = a.

First, we calculate the derivative of f(x) as:

f'(x) = 1/(2√x)

Evaluated at x = 81, we get:

f'(81) = 1/(2√81) = 1/18

So the equation of the tangent line to f(x) at x = 81 is:

y - √81 = (1/18)(x - 81)

Simplifying:

y - 9 = (1/18)x - (1/2)

y = (1/18)x + 8.5

Now we can use this equation to approximate √81.1:

√81.1 ≈ (1/18)(81.1) + 8.5

≈ 9.0139

Therefore, using linear approximation with the tangent line, we can approximate √81.1 as 9.0139.

Assume while in college you are not required to pay off your loan yet, and the interest will NOT compound, the amount you owe right after graduation without interest is $48,000.

The loan amount (without interest) at the end of the college years is a product of the multiplication of the number of semesters and the loan per semester without compounded interest.

Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.

Multiplication operation involves the multiplicand, the multiplier, and the product.

The typical loan per semester of an average student = $6,000

The number of college years = 4 years

The total number of semesters for a 4-year college degree = 8 (4 x 2)

The total amount of student loan incurred = $48,000 ($6,000 x 8)

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The expression c⁸(d⁶ / c²)³ is equivalent to c⁴d¹⁸. Then the correct option is B.

Given that:

Expression, c⁸(d⁶ / c²)³

The equivalent is the expression that is in different forms but is equal to the same value.

Simplify the expression, then we have

⇒ c⁸(d⁶ / c²)³

⇒ c⁴d¹⁸

Thus, the correct option is B.

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Null Hypothesis is the claim that no difference or relationship exists between two sets of data or variables being analyzed.

Type I error: A. Reject the null hypothesis that the percentage of high school students who graduate is equal to 55% when that percentage is actually equal to 55%.

Type II error: D. Fail to reject the null hypothesis that the percentage of high school students who graduate is equal to 55% when the percentage is actually different from 55%.

In statistics, the null hypothesis is a statement that there is no significant difference between two populations or sets of data. It is a hypothesis that is assumed to be true until proven otherwise. The null hypothesis is often denoted as H0 and is used to test the validity of an alternative hypothesis (Ha). The goal of hypothesis testing is to determine whether the evidence supports rejecting the null hypothesis in favor of the alternative hypothesis.

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3

equilateral so 5-2x=-4x+9

x=2

5-2×2=1

the trainangle is equilateral and has three sides

1+1+1=3

The proper equations in Pattern A with the appropriate values on the right side are:

3.675 • 10 = 36.750

3.675 • 100 = 367.500

3.675 • 1,000 = 3,675.000

The correct equations in Pattern B with the precise values on the right side are:

3.675 • 0.1 = 0.3675

3.675 • 0.01 = 0.03675

3.675 • 0.001 = 0.003675

Pattern A:

The equations in Pattern A are incorrect due to not possessing the adequate number of decimal places in the products. In each equation, the end result should have one additional decimal place as compared to the initial number being multiplied.

Pattern B:

The equations in Pattern B are flawed because they inaccurately reflect the number of decimal places in the outcomes. In each equation, the results should display one fewer decimal place when compared to the original number being multiplied.

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Answer:

The directional derivative of f at (0, 1) in the direction of theta = pi/3 is sqrt(3)/2.

Step-by-step explanation:

To find the directional derivative of f at (0, 1) in the direction of theta = pi/3, we need to compute the dot product of the gradient of f at (0, 1) and the unit vector u in the direction of theta.

First, we need to find the gradient of f:

∇f(x, y) = <∂f/∂x, ∂f/∂y>

= <-y sin(xy), cos(xy) - xy sin(xy)>

Evaluating at (0, 1), we get:

∇f(0, 1) = <0, 1>

Next, we need to find the unit vector u in the direction of theta = pi/3:

u = <cos(pi/3), sin(pi/3)>

= <1/2, sqrt(3)/2>

Now we can compute the directional derivative:

D_u f(0, 1) = ∇f(0, 1) · u

= <0, 1> · <1/2, sqrt(3)/2>

= sqrt(3)/2

Therefore, The directional derivative of f at (0, 1) in the direction of theta = pi/3 is sqrt(3)/2.

of f at (0, 1) in the direction of theta = pi/3 is sqrt(3)/2.

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If in 2007, the population of the city was about 166,025, then K is approximately 0.0454.

The term "population" refers to the total number of humans, animals, or other living things in a certain area or region. When referring to human populations, it means the whole population of a certain city, state, nation, or even the entire planet. Births, deaths, immigration, and emigration are a few examples of things that might have an impact on a region's population.

We are given that the population of the city in 2007 was about 166,025. Since t = 0 corresponds to the year 2000, this means that in 2007, t = 7.

So we have P = 166.025 and t = 7, and the equation is:

P = 120.8[tex]e^{kt}[/tex]

Substituting these values, we get:

166.025 = 120.8[tex]e^{k*7}[/tex]

Dividing both sides by 120.8, we get:

166.025/120.8 =[tex]e^{k * 7}[/tex]

Taking the natural logarithm of both sides, we get:

ln(166.025/120.8) = k× 7

Simplifying the left-hand side, we get:

ln(1.372) = k× 7

Using a calculator to evaluate ln(1.372), we get:

0.3188 ≈ k × 7

Dividing both sides by 7, we get:

k ≈ 0.0454

Hence, if in 2007, the population of the city was about 166,025, then K is approximately 0.0454.

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For the given geometric sequence we have:

a) R = 3/4

b) 243/256

c) Aₙ = 3*(3/4)⁽ⁿ⁻¹⁾

The common reason is given by the quotient between two consecutive terms, so using the first two, we will get:

R = (9/4)/3

R = 3/4

That is the common reason.

b) To find the fifth therm, we need to take the fourth one and multiply it by the common reason, so we will get:

81/64*(3/4) = 243/256

c) The n-th term of the sequence is the first term of the sequence multiplied by the common reason (n - 1) times, it gives:

Aₙ = 3*(3/4)⁽ⁿ⁻¹⁾

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In a right triangle where tan(θ) = -1, the other trigonometric functions of θ can be evaluated as sin(θ) = -1/√2, cos(θ) = 1/√2, cosec(θ) = -√2, sec(θ) = √2, and cot(θ) = -1.

If tan(θ) = -1, we can determine that the opposite side of the angle is equal to the adjacent side, or in other words, they are both equal to a negative square root of 2 (-√2). Using the Pythagorean theorem, we can find the hypotenuse of the right triangle:

a² + b² = c²

(-√2)² + (-√2)² = c²

2 + 2 = c²

4 = c²

c = 2

Now, we can use the definitions of sine, cosine, tangent, cotangent, secant, and cosecant to determine their values:

sin(θ) = opposite/hypotenuse = (-√2)/2

cos(θ) = adjacent/hypotenuse = (-√2)/2

tan(θ) = opposite/adjacent = -1

cot(θ) = adjacent/opposite = -1

sec(θ) = hypotenuse/adjacent = -√2

csc(θ) = hypotenuse/opposite = -√2

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The absolute maximum of f(x) is e^(2pi), which occurs at x = 2pi, and the absolute minimum of f(x) is approximately -1.30, which occurs at x = 5*pi/4

a. To find the absolute maximum and minimum values of f(x), we can use the first derivative test and the endpoints of the given interval.

First, we find the first derivative of f(x):

f'(x) = e^xcos(x) - e^xsin(x)

Then, we find the critical points of f(x) by setting f'(x) = 0:

e^xcos(x) - e^xsin(x) = 0

e^x(cos(x) - sin(x)) = 0

cos(x) = sin(x)

x = pi/4 or x = 5*pi/4

Note that these critical points are in the domain [0, 2*pi].

Next, we find the second derivative of f(x):

f''(x) = -2e^xsin(x)

We can see that f''(x) is negative for x in [0, pi/2) and (3pi/2, 2pi], and f''(x) is positive for x in (pi/2, 3*pi/2).

Therefore, x = pi/4 is a relative maximum of f(x), and x = 5*pi/4 is a relative minimum of f(x). To find the absolute maximum and minimum of f(x), we compare the values of f(x) at the critical points and the endpoints of the domain:

f(0) = e^0cos(0) = 1

f(2pi) = e^(2pi)cos(2pi) = e^(2pi)

f(pi/4) = e^(pi/4)cos(pi/4) ≈ 1.30

f(5pi/4) = e^(5*pi/4)cos(5pi/4) ≈ -1.30

Therefore, the absolute maximum of f(x) is e^(2pi), which occurs at x = 2pi, and the absolute minimum of f(x) is approximately -1.30, which occurs at x = 5*pi/4.

b. To find the intervals on which f(x) is increasing, we look at the sign of f'(x) on the domain [0, 2pi]. We know that f'(x) = 0 at x = pi/4 and x = 5pi/4, so we can use a sign chart for f'(x) to determine the intervals of increase:

x 0 pi/4 5*pi/4 2*pi

f'(x) -e^0 0 0 e^(2*pi)

f(x) increasing relative max relative min decreasing

Therefore, f(x) is increasing on the interval [0, pi/4) and decreasing on the interval (pi/4, 2*pi].

c. To find the x-coordinate of each point of inflection of the graph of f, we need to find where the concavity of f changes. We know that the second derivative of f(x) is f''(x) = -2e^xsin(x), which changes sign at x = pi/2 and x = 3*pi/2.

Therefore, the point (pi/2, f(pi/2)) and the point (3pi/2, f(3pi/2)) are the points of inflection of the graph of f.

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The prompt on arcs and chords is to test your ability to recognize congruent patterns.

G) Note that ∡AB = 82°

H) UV = 6; and

I) Secant QR = 15

G) Note that ∡ED = 82° and is given to be congruent to ∡AB hence, ∡AB = 82°. This is because the degree measure of a minor arc is equal to the measure of the central angle that intercepts it. Since the central angle here is 82°, hence, the arc AB is also 82°

H) UV is a chord. So is UT. They both are congruent, that is =67°.

Since the we know that the Chord UT = 6, then Line segment UV must also be 6.

I) In this case we are given two sets of diagrams.

The first indicates that the Secant is of length 15 and creates an arc of 120°.  If that is the case, and QR is also a secant creating an arc ∡QR of 120° then Secant QR must also be 15.

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The function f is defined as a mathematical rule that relates an input value x to an output value, which is determined by the equation f(x) = sqrt(25-x^2). In this case, the function takes an input value x and returns the square root of the difference between 25 and x squared. This function is defined for all values of x between -5 and 5, as any value outside of this range would result in a negative number under the square root function, which is not defined in real numbers.


The function f is defined by the equation f(x) = sqrt(25 - x^2). To work with this function, follow these steps:

1. Identify the input variable x, which is within the parentheses f(x).
2. Substitute the value of x into the equation, replacing the x in (25 - x^2).
3. Calculate the result of the expression inside the square root, (25 - x^2).
4. Finally, take the square root of the calculated result to find the output value f(x).

Remember that this function has a domain restriction, as the value inside the square root must be greater than or equal to zero. Therefore, the domain of the function f is -5 ≤ x ≤ 5.

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The value of the diameter of the cone part of the funnel to the nearest tenth is,

⇒ d = 7.2 cm

We have to given that;

A funnel can hold 159π cm³ of fluid.

And, Its height (without the stem) is 12 cm.

Now, We know that;

Volume of cone = πr²h/3

Where, r is radius of cone.

Hence we get;

⇒ 159 = 3.14 × r² × 12 / 3

⇒ 159 = 12.56 r²

⇒ r² = 12.65

⇒ r = √12.65

⇒ r = 3.556

⇒ r = 3.6 cm

Thus, The value of the diameter of the cone part of the funnel to the nearest tenth is,

⇒ d = 2r

⇒ d = 2 x 3.6

⇒ d = 7.2 cm

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The truth value of the given statement "all espionage artists are agents of foreign governments" is true.

The corresponding E statement "no espionage artists are agents of foreign governments" is also true because it simply negates the original statement.

The corresponding I statement "some espionage artists are agents of foreign governments" is also true because it affirms a part of the original statement.

The corresponding O statement "some espionage artists are not agents of foreign governments" is false because it contradicts the original statement that all espionage artists are agents of foreign governments.
Based on the given statement and terms, here are the truth values for each corresponding statement:

Original statement: All espionage artists are agents of foreign governments.
Truth value of original statement: True

Corresponding E statement: No espionage artists are agents of foreign governments.
Truth value of corresponding E statement: False

Corresponding I statement: Some espionage artists are agents of foreign governments.
Truth value of corresponding I statement: True

Corresponding O statement: Some espionage artists are not agents of foreign governments.
Truth value of corresponding O statement: False

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Thus, the correct answer is: C. The Stafford loan will have a lower balance of $431.17 at the time of repayment.

In order to evaluate the Unsubsidized Stafford Loan against the PLUS Loan, a comparison of their balances upon repayment after 6 months of graduation is necessary.

Having taken out a loan of $9,529 with an annual interest rate of 5.95% compounded monthly, and after an interest accumulation period of 18 months, the Stafford Loan balance at this point in time stands roughly around $10,365.86.

On the other hand, the PLUS Loan's equilibrium at graduation is recorded at $10,172.23, but including a 6-month interest accumulation period along with an annual incrementation percentage of 6.55% that is compounded monthly equals to approximately $10,797.03 when due for repayment.

To summarize, based on the balance comparisons, it is concluded that the Stafford loan owes a lower amount at repayment which is different by $431.17 compared to the PLUS Loan.

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The required sample size is 907.

We have,

To determine the required sample size for estimating the fraction of new car buyers who prefer foreign cars over domestic with a 95% confidence level and an error of at most 0.03, we'll use the following formula:
n = (Z² x p  (1 - p)) / E²
Where:
- n is the required sample size
- Z is the Z-score for the desired confidence level (1.96 for a 95% confidence level)
- p is the estimated population proportion (0.31)
- E is the margin of error (0.03)

Step-by-step calculation:
1. Calculate Z²: 1.96² = 3.8416
2. Calculate p (1 - p): 0.31 x (1 - 0.31) = 0.2139
3. Calculate E²: 0.03² = 0.0009
4. Substitute these values into the formula: n = (3.8416 x 0.2139) / 0.0009 = 906.92

Since we need to round up to the next integer, the required sample size is 907.

Thus,

The required sample size is 907.

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The method is static, which means it can be called on the class itself without creating an instance of the class. To create a class Range Sum with a public static method, sum that accepts a single int value and returns the sum of all integers in the range 1. value as an int, follow these steps:

1. Define the class Range Sum.
2. Inside the class, create a public static method called sum, which accepts an int parameter called value.
3. In the method, first check for the base case, where the value is equal to 1, and return 1.
4. Then, handle the Illegal Argument Exception by checking if the value is less than or equal to 0 or greater than 128. If so, throw an Illegal Argument Exception.
5. Finally, implement the recursive step by returning the sum of the current value and the range sum of value - 1, using the sum method itself.
Here's the code:
java
public class Range Sum {
   public static int sum (int value) {
       if (value == 1) {
           return 1;
if (value <= 0 || value > 128) {
throw new Illegal Argument Exception ("Value must be between 1 and 128.");

return value + sum (value - 1);

Now, you can call the sum method with the input 10 to get the result 55: `Range Sum. Sum(10)` will return 55.

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The statement "When symbolic statements are translated into English, the simple statements in parentheses appear on the same side of the comma" is generally false. Let me explain.

In symbolic logic, parentheses are used to group and clarify the order of operations within a complex statement. When translating a symbolic statement into English, the focus should be on maintaining the logical relationships between the simple statements, rather than preserving the placement of parentheses. Sometimes, this might involve rephrasing the statement, which could result in the simple statements appearing on different sides of a comma.

For example, consider this symbolic statement: (P ∧ Q) → R

Translating this into English, we get: "If both P and Q are true, then R is true." As you can see, the simple statements P and Q are on different sides of the comma, but the logical relationship is preserved.

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The Volume of the solid which is made of small-cubes is 15 yd³.

The "Volume" of a cube is the measure of the amount of space that the cube occupies in three-dimensional space. It is calculated by multiplying the cube's three side lengths.

In the figure, we can see that, the solid consists of 5×3 = 15 cubes,

The side-length of each small cube is = 1 yd,

So, the volume of each small-cube is = (side)×(side)×(side),

⇒ Volume = 1 yd³.

To find the volume of the entire solid, we multiply the volume of single-cube, by the "total-number" of cubes,

So, Volume of Solid is = 15×1 = 15 yd³.

Therefore, the volume of the solid is 15 yd³.

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Answer:

D

Step-by-step explanation:

Dustin's mean number of situps is 42.5714285714, while Jacob's is 41.4285714286.

You can get the mean of Dustin's data by adding all of the data of Dustin's situps together and dividing by 7, and the same thing with Jacob's.

Therefore, the probability that exactly 5 of the students in a study group of 10 have studied in the last week is approximately 0.2461.

To calculate the probability that exactly 5 of the students in a study group of 10 have studied in the last week, we need to use the binomial distribution formula:

[tex]P(X=k) = C(n,k) * p^k * (1-p)^{(n-k)}[/tex]

where:

P(X=k) is the probability that k students have studied in the last week

n is the total number of students in the group (n = 10)

k is the number of students who have studied in the last week (k = 5)

p is the probability that a student has studied in the last week

Since we don't have information about p, let's assume that it's 0.5, which means that each student has an equal chance of having studied in the last week or not.

Using this assumption and plugging in the values, we get:

[tex]P(X=5) = C(10,5) * 0.5^5 * 0.5^{(10-5)[/tex]

= 252 * 0.03125 * 0.03125

= 0.2461

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The area of the given polygon is calculated as: 847 square inches

The given composite figure can be broken down into a trapezium and a square.

Formula for area of a square is:

Area = side * side

Formula for area of a trapezium is:

Area = ¹/₂(sum of parallel sides) * height

Thus, total area of composite figure is:

Area = (¹/₂(22 + 11) * 22) + (22 * 22)

= 363 + 484

= 847 in²

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Answer:

Olivia has 7.75 meters of string left

Step-by-step explanation:

15.1-7.35=7.75

Answer:

2.9

Step-by-step explanation:

cos 70° = 0.342020

1/cos 70° = 1/0.342020 = 2.9238

Answer: 2.9

Vector subtraction is done by arranging head to tail.

Vector subtraction is the process of finding the vector that results from taking away one vector from another. To perform vector subtraction, we arrange the vectors head to tail, with the tail of one vector touching the head of the other vector. We then draw a new vector from the tail of the first vector to the head of the second vector. The resulting vector is the difference between the two vectors. This can be mathematically represented as:

a - b = a + (-b)

where "a" and "b" are vectors, and (-b) is the additive inverse of b, which is the vector with the same magnitude as b but opposite in direction.

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