Line d passes through points (10, 8) and (2, 1). Line e is perpendicular to d. What is the slope of line e? Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer:

Step-by-step explanation:

For the product BA to be defined, the number of columns in matrix A must equal the number of rows in matrix B. Since matrix A has 5 columns, matrix B must have 4 rows. Therefore, the number of columns in matrix B must be 4.

Answer:

Matrix B must also be 5 columns

Step-by-step explanation:

For easy multiplication both matrix should have same number of columns

Answers:

=====================================================

Explanation for part (a)

The table says there are 39 students who do not carry a backpack out of 100 total.

39/100 = 0.39 = 39% of the students do not carry a backpack.

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

Explanation for part (b)

The phrasing "if a junior is chosen" is the same as saying something like "given we know a junior has been chosen". The word "given" is a key term in conditional probability questions.

We focus entirely on the juniors only. Ignore everyone else.

I recommend either using a highlighter to mark the "junior" column, or using two sheets of paper to cover the other columns up.

We have 18 juniors that carry a backpack out of 32 juniors total.

18/32 = 9/16 = 0.5625 is the probability the junior has a backpack. This value is exact and hasn't been rounded.

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

Explanation for part (c)

This is similar to the previous part. The "given" this time is we know 100% the student selected doesn't have a backpack.

Focus solely on the "no backpack" row. There are 14 juniors and 16 seniors in this row. There are 14+16 = 30 juniors or seniors that don't have a backpack. This is out of 39 people who don't have a backpack.

30/39 = 0.7692 which is approximate. Round this value however needed.

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

Explanation for part (d)

Define these events

Then,

If events A and B were independent, then P(A and B) = P(A)*P(B) would be a true equation.

P(A)*P(B) = 0.11*0.61 = 0.0671 exactly without any rounding done to it

This does not match with P(A and B) = 0.08

Therefore, P(A and B) = P(A)*P(B) is false. Events A and B are not independent. They are dependent in some way.

Use this logic to explore the connections between the other grade levels and their status of "backpack" vs "no backpack". You should find that those connections are also dependent.

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

Alternative explanation for part (d)

Once again I'll define these two events:

If the events were independent, then these two equations must be true

The table says P(A) = 0.11 as calculated earlier.

P(A given B) = probability a freshman is chosen, given they have a backpack

P(A given B) = (8 freshmen with backpacks)/(61 people with backpacks)

P(A given B) = 8/61

P(A given B) = 0.1311 approximately

This does not match up with P(A) = 0.11 calculated earlier.

We have shown that P(A given B) = P(A) is false in this case, which must mean the events are dependent somehow. Having prior knowledge of the student having a backpack (or not) changes the probability of P(A).

You should find that P(B given A) = P(B) is false here as well. I'll let you explore this connection, and the other paired connections.

To conclude part (d) in one sentence: Yes there appears to be a connection between grade level and whether the student carries a backpack or not.

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(a) To find the slant height of the cone, we can use the Pythagorean theorem. The slant height (l) of a cone is the hypotenuse of a right triangle formed by the height (h) and the radius (r). In this case, the height (h) of the cone is given as 10 cm and the radius (r) is given as 5 cm.

Using the Pythagorean theorem:

l² = r² + h²

l² = 5² + 10²

l² = 25 + 100

l² = 125

Taking the square root of both sides:

l = √125

l ≈ 11.18 cm

Therefore, the slant height of the cone is approximately 11.18 cm.

(b) The curved surface area (CSA) of a cylinder is given by the formula:

CSA of cylinder = 2πrh

Where r is the radius of the cylinder's base and h is the height of the cylinder.

The curved surface area (CSA) of a cone is given by the formula:

CSA of cone = πrl

Where r is the radius of the cone's base and l is the slant height of the cone.

In this case, the radius (r) for both the cylinder and the cone is 5 cm, and the height (h) for the cylinder is 10 cm.

CSA of cylinder = 2π(5)(10) = 100π cm²

CSA of cone = π(5)(11.18) = 175.93π cm²

To find the ratio of the curved surface area of the cylinder to that of the cone, we divide the CSA of the cylinder by the CSA of the cone:

Ratio = (CSA of cylinder) / (CSA of cone)

Ratio = (100π) / (175.93π)

Ratio ≈ 0.569

Therefore, the ratio of the curved surface area of the cylinder to that of the cone is approximately 0.569.

Answer:

42 cm

:234

Step-by-step explanation:

Answer:

Θ = 23.9°

Step-by-step explanation:

Use inverse tangent in a calculator.

tan Θ = 23/52

tan Θ = 0.4423

tan^-1 0.4423 = 23.9°

The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).

In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:

3(2a^2 - 5a + 2)

Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.

The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:

3(2a - 1)(a - 2)

Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

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Answer: 381 square inches

Step-by-step explanation: The area of a circle with radius r is given by the formula:

A = πr^2

Substituting r = 11 and π = 3.14, we get:

A = 3.14(11)^2

A = 3.14(121)

A = 380.94 (rounded to two decimal places)

Therefore, the area of the circle is approximately 381 square inches.

The length of the longer wire is 82 feet.

Let's denote the length of the longer wire as L. According to the given information, the shorter wire is attached to the ground 16 feet from the base of the pole, and the longer wire is attached to the ground 32 feet from the base of the pole.

We can form two similar right triangles using the wires. The height of each triangle is the height of the pole, and the base of each triangle is the distance from the base of the pole to where the wire is attached to the ground.

In the first triangle, the shorter wire creates an angle with the ground. Let's denote this angle as θ. Since we are given the cosine of this angle, we can use the cosine function to find the height of the pole in terms of θ and the base of the triangle:

cos(θ) = adjacent/hypotenuse = 16/L

Given that cos(θ) = 8/41, we can substitute this value into the equation:

8/41 = 16/L

To solve for L, we can cross-multiply and solve for L:

8L = 41 * 16

L = (41 * 16)/8

L = 82

Therefore, the length of the longer wire is 82 feet.

In summary, the length of the longer wire is 82 feet, as determined by using the cosine of the angle formed by the shorter wire and the ground, and considering the similarity of the triangles formed by the wires and the pole.

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The window is 125 meters high and the distance that the ball lands from the base of the building is 50 meters.

The height of the window can be found by using the formula for the distance travelled under constant acceleration, which in this case is due to gravity.

The formula is: d = ut + 0.5at ²

Since the ball was thrown horizontally, the initial vertical velocity (u) is 0. Substituting these values into the equation gives:

d = 05 + 0.510 * (5 ² )

= 0 + 0.51025

= 125 meters

The horizontal distance the ball travels can be found by multiplying the horizontal speed by the time.

So, the horizontal distance is:

d = vt = 10 x 5

= 50 meters

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The full question is:

Una pelota es lanzada horizontalmente desde una ventana con una velocidad inicial que tiene una magnitud de 10 m/s y cae al suelo después de 5 segundos

¿a que altura se encuentra la ventana?

¿a que distancia cae la pelota de la base del edificio?

Which translates to:

A ball is thrown horizontally from a window with an initial velocity that has a magnitude of 10 m/s and falls to the ground after 5 seconds.

How high is the window?

How far does the ball land from the base of the building?

Answer:

7................

Step-by-step explanation:

36 ÷ 5 = 7 So Yea

Answer:

8

Step-by-step explanation:

after seating 35 guests in 7 tables (5 guests per table), she will have 1 guest left
so she will require 8 tables in total to allow every guest a seat.
any number of tables below 8 is likely to result in guests unable to have a seat

note: if this is NOT a trick question, this answer might be sufficient

hope it helps

The sum is:

7/2x

Work/explanation:

Notice how the problem provides us with two fractions where the denominators are the same. Whenever this happens, we can just add the numerators:

[tex]\sf{\dfrac{1}{2x} +\dfrac{6}{2x}}[/tex]

[tex]\sf{\dfrac{7}{2x}}[/tex]

Hence, the sum is 7/2x.

The answer is 3.99 metric tons.

To calculate the difference in carbon dioxide emissions between a commuter who takes a bus and one who drives a car every day, we need to compare the emissions of each mode of transportation per person.

The car averages 22 miles per gallon, which means it emits 4.3 metric tons of carbon dioxide per year. However, we don't know the number of passengers in the car.

The passenger bus emits 9.2 metric tons of carbon dioxide per year and can carry 30 people at a time. To find the emissions per person, we divide the total emissions by the number of passengers. In this case, each person on the bus emits 9.2 / 30 = 0.3067 metric tons of carbon dioxide per year.

To determine the difference in emissions, we subtract the emissions per person for the bus from the emissions per person for the car. Therefore, the difference is 4.3 - 0.3067 = 3.9933 metric tons of carbon dioxide per year.

Rounding this value to two decimal places, we get 3.99 metric tons.

Therefore, the answer is 3.99 metric tons.

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The areas under the curve of the z-scores are 0.5098, 0.4357 and 0.1254

From the question, we have the following parameters that can be used in our computation:

(a) z = -0.69 to 0.69

This is represented as

Area = P(-069 < z < 069)

Using a graphing calculator, we have

Area = 0.5098

(b) z = -1.52 to 0

This is represented as

Area = P(-1.52 < z < 0)

Using a graphing calculator, we have

Area = 0.4357

(c) z = -0.75 to -0.38

This is represented as

Area = P(-1.52 < z < -0.38)

Using a graphing calculator, we have

Area = 0.1254

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P(x) = 1

P(y) = 1

P(Y > X) = 2/5

P(Y = X) = 1/5

P(XY < 0) = 4/5

To calculate the requested probabilities based on the given probability function PX,Y (x, y), let's evaluate each one:

P(x): To calculate P(x), we need to sum up the probabilities for all y-values associated with each x-value:

P(x = 2) = 1/5

P(x = 3) = 1/5

P(x = -3) = 1/5

P(x = -2) = 1/5

P(x = 17) = 1/5

Therefore, P(x) = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1.

P(y): Similarly, to calculate P(y), we need to sum up the probabilities for all x-values associated with each y-value:

P(y = 3) = 1/5

P(y = 2) = 1/5

P(y = -2) = 1/5

P(y = -3) = 1/5

P(y = 19) = 1/5

Thus, P(y) = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1.

P(Y > X): We need to calculate the probabilities where Y is greater than X. Looking at the given probability function, we can see that there are two cases where Y is greater than X: (x = -3, y = -2) and (x = -2, y = -3), both with a probability of 1/5. Therefore, P(Y > X) = 2/5.

P(Y = X): We need to calculate the probability where Y is equal to X. From the given probability function, there is only one case where Y is equal to X: (x = 17, y = 19) with a probability of 1/5. Therefore, P(Y = X) = 1/5.

P(XY < 0): We need to calculate the probability where the product of X and Y is less than 0. Looking at the given probability function, we can see that there are four cases where the product of X and Y is less than 0: (x = 2, y = -3), (x = 3, y = -2), (x = -3, y = 2), and (x = -2, y = 3), each with a probability of 1/5. Therefore, P(XY < 0) = 4/5.

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The current price of the bond is $402.41 .

To calculate the current price of the bond, we can use the formula for the present value of a bond, taking into account the coupon payments and the final principal repayment.

The coupon payment is the periodic interest payment made by the bond, and it can be calculated as follows:

Coupon Payment = (Coupon Rate × Par Value) / Number of Coupon Payments per Year

In this case, the coupon rate is 4.05% and the par value is $1,000, and since the bond has semi-annual coupon payments, the number of coupon payments per year is 2.

Coupon Payment = (0.0405 × 1000) / 2 = $20.25

Next, we can calculate the total number of coupon payments over the life of the bond. Since the bond has 30 years to maturity with semi-annual coupon payments, the total number of coupon payments is 30 × 2 = 60.

Now, we can calculate the present value of the bond by discounting the future cash flows, including both the coupon payments and the final principal repayment, at the yield to maturity (YTM) rate.

Using the present value formula for a bond:

Bond Price = Coupon Payment × [1 - (1 / (1 + YTM / Number of Coupon Payments per Year))^Number of Coupon Payments] / (YTM / Number of Coupon Payments per Year) + (Par Value / (1 + YTM / Number of Coupon Payments per Year))^Number of Coupon Payments

Bond Price = 20.25 × [1 - (1 / (1 + 0.1584 / 2))^60] / (0.1584 / 2) + (1000 / (1 + 0.1584 / 2))^60

Evaluating this expression, the current price of the bond is approximately $402.41.

Therefore, the current price of the bond is $402.41 (rounded off to two decimal points).

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Answer:

2/9

Step-by-step explanation:

Coin

A coin has 1 side heads and 1 side tails.

total number of possible outcomes = 2

desired outcome: heads

number of desired outcomes = 1

p(event) = (number of desired outcomes)/(total number of possible outcomes)

p(heads) = 1/2

Spinner

The spinner has 9 sections of equal size.

possible outcomes: the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9

total number of possible outcomes = 9

desired outcome: even number

number of desired outcomes = 4

p(event) = (number of desired outcomes)/(total number of possible outcomes)

p(even number) = 4/9

Combined probability

The coin and spinner are independent events. The overall probability of independent events is the product of the individual probabilities.

p(heads then even) = 1/2 × 4/9 = 4/18 = 2/9

Answer: 2/9

The option that shows the missing angles in the triangle is:

Option C: m∠1 < m∠4

We know that the sum of angles in a triangle is 180 degrees.

Therefore looking at the given triangle, we can say that:

m∠1 + m∠2 + m∠3 = 180°

We also know that the sum of angles on a straight line is 180 degrees and as such we can say that:

m∠3 +  m∠4 = 180°

By substitution we can say that:

m∠4 = m∠1 + m∠2

Thus:

m∠1 < m∠4

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The missing options are:

m∠1 > m∠4

m∠2 > m∠4

m∠1 < m∠4

m∠3 = m∠4

Line M and line N are the same line, since they have the same slope and y-intercept. Therefore, there are infinitely many solutions for the pair of equations, since every point on the line satisfies both equations.

After getting the integration  [tex]e^{(1-3x)} dx[/tex] with upper-limit 1 and lower-limit -1, we get [tex]\frac{-1}{3}[e^{-2}-e^{4}][/tex]

We know,

[tex]\int\limits^a_{b} {f(x)} \, dx[/tex] = [tex][F(x)]\limits^a_b[/tex]=F(a)- F(b).

Where,

a⇒Upper limit.

b⇒Lower limit,

f(x)⇒Any function of x.

F(x)⇒ [tex]\int {f(x)}[/tex] gives its antiderivative F(x).

Now here,

a is given as +1, and b is given as -1.

f(x)= [tex]e^{(1-3x)}[/tex].

Suppose, 1-3x =t.

∴ -3dx =dt.[By applying derivative rule]

Now,[tex]\int\limits e^{(1-3x)} dx[/tex]

=[tex]\int e^t.(\frac{-1}{3} ) dt[/tex]

=[tex]-\frac{1}{3} \int {e^t} dt[/tex].

=[tex]-\frac{e^t}{3}dt[/tex]

=[tex]\frac{1}{3}e^{(1-3x)}[/tex]

∴,[tex]\int\limits e^{(1-3x)} dx[/tex]  =[tex]\frac{1}{3}e^{(1-3x)}[/tex].

So,[tex]\int\limits^1_{-1} e^{(1-3x)} \, dx[/tex]

=- [tex][\frac{1}{3}e^{(1-3x)}]^1_{-1}[/tex]

=[tex]\frac{-1}{3}[e^{(1-3)}-e^{(1+3)}][/tex]

=[tex]\frac{-1}{3}[e^{-2}-e^{4}][/tex]

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We can isolate the x term by subtracting  8 from both sides of the equation, giving us 4x=12. dividing by 4 on each side gives us x=3.

So, our answer is x=3.

Step-by-step explanation:

[tex]4x + 8 = 20 \\ 4x = 20 - 8 \\ 4x = 12 \\ x = \frac{12}{4 \\ } \\ x = 3ans [/tex]

hope that it helps

The equation of the line in slope-intercept form is y = (2 / 7)x - 2.

To write the equation of a line in slope-intercept form, we need to determine the slope and the y-intercept of the line using the given points.

The slope of a line can be calculated using the formula:

slope = (y2 - y1) / (x2 - x1),

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Using the given points (-7, -4) and (7, 0), we can calculate the slope:

slope = (0 - (-4)) / (7 - (-7)) = 4 / 14 = 2 / 7.

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1),

where (x1, y1) is a point on the line and m is the slope.

Let's use the point (7, 0):

y - 0 = (2 / 7)(x - 7).

To simplify, we have:

y = (2 / 7)(x - 7).

Therefore, the equation of the line in slope-intercept form is y = (2 / 7)x - 2.

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The equation of the line passing through the given points in slope-intercept form is y = (2/7)x - 2.

To write the equation of a line in slope-intercept form, we need to use the formula y = mx + b, where m is the slope and b is the y-intercept. First, let's calculate the slope using the given points.

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

Slope (m) = (0 - (-4)) / (7 - (-7)) = 4/14 = 2/7

Now that we have the slope, we can choose any of the two given points to find the y-intercept. Using the point (7, 0):

0 = (2/7)(7) + b

b = 0 - 2 = -2

Therefore, the equation of the line in slope-intercept form is y = (2/7)x - 2.

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Carl works at a veterinarian office. The first dog he sees is a Chihuahua who weighs 3 kilograms. The second dog he sees is a Great Dane who weighs 27 times as much as the Chihuahua. The Great Dane weighs 81 kilograms.

Let's denote the weight of the Chihuahua as "x" kilograms. We know that the Great Dane weighs 27 times as much as the Chihuahua. Therefore, the weight of the Great Dane can be expressed as 27x.

Given that the weight of the Chihuahua is 3 kilograms, we can substitute this value into the equation:

27x = 3

To find the weight of the Great Dane, we need to solve for x:

x = 3 / 27

x = 1 / 9

Therefore, the weight of the Chihuahua is 1/9 kilograms.

Now, we can calculate the weight of the Great Dane by multiplying the weight of the Chihuahua by 27:

Weight of the Great Dane = 27 * (1/9) = 27/9 = 3 kilograms

So, the Great Dane weighs 81 kilograms, which is 27 times the weight of the Chihuahua.

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The division by zero is not possible and f/g division is undefined, {20, 6, -4, 39} f /g is undefined (because of division by zero)

The scope and image of a given function and its operations.

f = {(2,4), (5,6), (8,-1), (10,3)}

g = {(2,5), (7,1) , ( 8,4), (10,13), (11,5)}

a) f - g (subtraction):

To find the domain of f - g, find the common element in the domain of f must be considered.

In this case the domains of both f and g are {2, 5, 8, 10}.

Therefore, the domain of f - g is {2, 5, 8, 10}.

Now let's compute the image of f - g using the subtraction operation:

f - g = {(2, 4-5), (5, 6-1), (8, -1-4 ), (10 , 3 -13)}

= {(2, -1), (5, 5), (8, -5), (10, -10)}

Images from f to g are {- 1, 5, -5, -10}.

b) f + g (addition):

As in the previous case, the domain of f + g is {2, 5, 8, 10}.

Now let's compute the image of f + g using the addition operation:

f + g = {(2, 4+5), (5, 6+1), (8, -1+4 ), (10 , 3 +13)}

= {(2, 9), (5, 7), (8, 3), (10, 16)}

f + g image is {9, 7, 3, 16 } .

c) f * g (multiplication):

Again, the domain of f * g is {2, 5, 8, 10}.

Now let's use the multiplication operation to compute the f * g image:

f * g = {(2, 45), (5, 61), (8, -14), (10, 313 )}

= { ( 2, 20), (5, 6), (8, -4), (10, 39)}

The f * g image is {20, 6, -4, 39}.

Division operations must ensure that the denominator is not zero. Looking at the function g, we can see that the x value of 7 has no corresponding y value in g.

Therefore, division by zero is not possible and f/g division is undefined.

region of f - g, f + g, f * g = {2, 5, 8, 10}

region of f / g is undefined (because of division by zero) of f Images - g = {-1, 5, -5, -10} f + g

images in {9, 7, 3, 16} f * g

images in {20, 6, -4, 39} f /g is undefined (because of division by zero).

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The expression equivalent to the given expression 14x^4y^5/7xr^y^2 is 2x^3y^3/r.

This expression can be simplified as follows: Simplifying the expression 14x^4y^5/7xr^y^2First, we can write the given expression as shown below:14 x 4 * y^5 / (7 * x * r * y^2) = 2 * 7 * x^3 * y^3 / 7 * r * x * y^2 = 2x^2y/rr.

Now, the numerator and the denominator have x, y, and r, and we can cancel them out as shown below:2x^2y/rr = 2xy * x * x / rr * y * y / y * y = 2x^3y^3/r.

Therefore, the expression equivalent to the given expression 14x^4y^5/7xr^y^2 is 2x^3y^3/r.

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Answer:  cos∅ = (3√11)/11

Step-by-step explanation:

See image

Answer:

cos∅ = 3/√11

Step-by-step explanation:

If tan ∅ = √(2)/3

We know the relationship:

As given, putting the value to this equation we get:

We know that sec∅ = 1/cos∅

Hence cos ∅ = 1/ sec∅

Putting the value of sec∅, we get:

This is an interesting method by using square relationship!

Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

Answer:

Step-by-step explanation:

To determine how many times smaller 1.2 x 10^6 is than 1.47 x 10^7, we need to divide the larger number by the smaller number:

1.47 x 10^7 / 1.2 x 10^6 = 12.25

Therefore, 1.2 x 10^6 is approximately 12.25 times smaller than 1.47 x 10^7.

To confirm this result, we can also calculate the difference between the two numbers:

1.47 x 10^7 - 1.2 x 10^6 = 1.35 x 10^7

So 1.2 x 10^6 is approximately 1/12.25 = 0.0816 times as large as 1.47 x 10^7.

Answer:

  A) -22j

  B) 4i

Step-by-step explanation:

You want the vector components represented by (a) 22 mph south, and (b) 4 mph east.

Maps are generally oriented with North at the top. When compared to an x-y coordinate plane, this means south is in the -y direction, and east is in the +x direction.

Two-dimensional vector spaces are generally defined with unit vector i pointing to the right, and unit vector j pointing up.

Using these conventions, we can define the vector components of the given speeds.

A unit vector in the direction south could be -j. Then the vector component of cruise ship speed in the direction south will be ...

  -22j

The unit vector in the direction east will be multiplied by the easterly speed to get the vector component for the Gulf Stream:

  +4i

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Additional comment

A vector is often represented using an over-arrow or a bold or italic font.

  [tex]4\vec{i}-22\vec{j}[/tex]

In the answer text above, we have used a different font to indicate the unit vectors. The arrows are generally available only in typeset text.

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Answer:

a. Algeria

b. 5.017 x 10^6

Step-by-step explanation:

a. Algeria

b. (1.13 x 10^6) + (2.38 x 10^6) + (0.924 x 10^6) + (0.583 x 10^6)

= 5.017 x 10^6