The goal of the exercise is to find the year in which cigarette consumption reach

Step-by-step explanation:

let the smallest angle = x

tan x = 5/8

x = arctan 5/8

x = 32°

Answer: The smallest angle of the triangle is 32°

Step-by-step explanation:

Given: 

one side of the triangle= 8 cm

The other side of the triangle = 5 cm

Angle between AB and BC = 90°

⇒ ∠ABC = 90°

ΔABC is a right angled triangle

Use trigonometric function: For X

tanx= AB/CB

tanx= 8/5

x=tan-1 (8/5)

x= 58°

Use trigonometric function: For Y

tany= BC/AB

tany=5/8

y=tan-1 (5/8)

y = 32°

Making 32° be the smallest angle of the triangle

Step-by-step explanation:

we simply use the definitions in the main expression.

f(x) = -3x²

therefore,

f(x + h) = -3(x + h)² = -3(x² + 2hx + h²) = -3x² - 6hx - 3h²

so, we have

((-3x² - 6xh - 3h²) - -3x²)/h

(-3x² - 6xh - 3h² + 3x²)/h

(-6xh - 3h²)/h

this is then

-6x - 3h

and for the limit of h going to 0 this is -6x.

Answer:

A=[tex]\pi[/tex]r(r+h2+r2)=[tex]\pi[/tex]·7·(7+122+72)≈459.44884

rounded off to 500 square millimetres

Step-by-step explanation:

The total surface area of a cone is the combination of the curved surface as well as the base area of a cone. The formula to calculate the total surface area of the cone is:

TSA of cone = [tex]\pi[/tex]r^2 + [tex]\pi[/tex]r l = r (l + r) square units.

The value of the given product or expression is =1,

An algebraic equation is said to have an algebraic identity if it is true regardless of the values of its variables. An equality that remains constant when the values of the variables change are known as an algebraic identity, to put it simply. Algebraic identities are routinely used to factor polynomials more rapidly and efficiently.

Using letters or alphabets to represent numbers without giving their exact quantities is the idea behind algebraic expressions. The principles of algebra taught us how to express an unknown value using letters like x, y, and z. These letters are referred to here as variables. In an algebraic expression, both constants and variables can be employed. Any amount that is added before a variable and then multiplied by is a coefficient.

The given product can be solved by the algebraic identity,

[tex]a^2+2ab+b^2=(a+b)^2\\a^2-2ab+b^2=(a-b)^2[/tex]

[tex]899^2-2*899*898+898^2\\=(899-898)^2\\=1[/tex]

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Based on the above, the 7 melons together will weigh about 21,000 grams.

We know that 2 melons of the same size together weigh 6 kg, therefore each melon weighs:

6kg / 2 = 3kg

To know how many grams the 7 melons weigh, we first need to know how many grams a kilogram weighs:

1kg = 1000g

So each melon weighs 3 kg * 1000 g/kg = 3000 g.

Therefore, 7 melons equal to the ones Alberto bought will weigh:

7 * 3000g = 21,000g

Therefore, the 7 melons together will weigh 21,000 grams.

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See text below

Alberto bought 2 melons of the same size and together they weigh 6 kg. How many grams will 7 melons equal to the ones Alberto bought weigh?

The constant of proportionality between the plant's height and time in weeks is 2 inches/week. So,correct answer is (D) 2.

The constant of proportionality is a factor that relates two variables that are directly proportional, indicating the ratio of change between them.

We can use the given information to determine the constant of proportionality between the plant's height and time in weeks.

The plant's height increased by 6 - 0 = 6 inches in the first three weeks (from week 0 to week 3). Therefore, the rate of growth during this period was 6 inches / 3 weeks = 2 inches/week.

Similarly, the plant's height increased by 10 - 6 = 4 inches during the next two weeks (from week 3 to week 5), so the rate of growth during this period was 4 inches / 2 weeks = 2 inches/week.

Finally, the plant's height increased by 14 - 10 = 4 inches during the last two weeks (from week 5 to week 7), so the rate of growth during this period was also 4 inches / 2 weeks = 2 inches/week.

Since the plant grows at a constant rate, we can assume that the rate of growth was 2 inches/week throughout the entire period from week 0 to week 7.

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The probability that you choose a 7 out of the deck of cards is P(A)= 1/13.

There are 52 cards in a standard deck of cards, with four of each type of card: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. Let event A be choosing a 7 out of a deck of cards. Identify the numbers of each of the following:

There are cards in the sample space. There are cards in event A. There are cards in the sample space. There are cards in event A. Probability that you choose a 7 out of the deck of cards is P(A)= 1/13. There are 52 cards in a standard deck of cards, with four of each type of card: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

We have to find out the probability of choosing 7 out of a deck of cards. The sample space is the total number of possible outcomes. Here, a standard deck of cards has 52 cards, so there are 52 possible outcomes. There are four 7s in the deck. So, there are 4 possible successful outcomes. Event A is defined as choosing a 7 out of a deck of cards.

Since there are four 7s, there are 4 possible outcomes in event A. Therefore, There are 52 cards in the sample space. There are 4 cards in event A. P(A) is the probability of choosing a 7 out of a deck of cards.

P(A) = number of successful outcomes/number of possible outcomes= 4/52= 1/13

Therefore, the probability that you choose a 7 out of the deck of cards is P(A)= 1/13.

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The statement is True. According to the Central Limit Theorem, in a sufficiently large random sample, the distribution of a random variable X, with mean μ and standard deviation σ, is a normal distribution with mean μ and standard deviation σ/sqrt(n).

1. The Central Limit Theorem states that the distribution of the sample means of a large sample size will approach a normal distribution, regardless of the original distribution of the population from which the sample is drawn.
2. For a sufficiently large sample size, the mean of the sample means will approach the population mean (μ) and the standard deviation of the sample means will approach the population standard deviation divided by the square root of the sample size (σ/sqrt(n)).
3. Therefore, in a sufficiently large random sample, the distribution of a random variable X, with mean μ and standard deviation σ, is a normal distribution with mean μ and standard deviation σ/sqrt(n).

This is the case because the Central Limit Theorem states that the distribution of sample means is approximately normal, regardless of the original distribution of the population from which the sample is drawn.

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Answer ! :)

If Jazmin spent  $38.75 on all

Then it would 15miles ( 15m ) to get home.

As your adding the extra $5 which starts the process.

Basically a equation could be:

(5 + 2.25 = 7.25) + ( 2.25 x 14 )

Extra info if needed more explanation: ( 2.25 x 14 = 31.5 ) Which 31.5 + 7.25 = 38.75

Info on counting:

7.25, 9.50, 11.75, 14, 16.25, 18.50, 20.75, 23, 25.25, 27.50, 29.75, 32, 34.25, 36.50, 38.75

Kiran is correct in saying that a solution to the equation x + 4 = 20 must also be a solution to the equation 5(x + 4) = 100. This is because the second equation is simply the first equation multiplied by 5. To see this, we can distribute the 5 on the left side of the second equation to get 5x + 20 = 100. We can then subtract 20 from both sides to get 5x = 80, and finally divide both sides by 5 to get x = 16.

Since x = 16 satisfies the first equation, it must also satisfy the second equation. This is because if we substitute x = 16 into the first equation, we get 16 + 4 = 20, which is true. If we substitute x = 16 into the second equation, we get 5(16 + 4) = 100, which is also true. Therefore, any solution to the first equation will also be a solution to the second equation when the second equation is just the first equation multiplied by a constant factor.

Answer:

Kiran is correct. To see why, let's first simplify the second equation, 5(x + 4) = 100, by multiplying both sides by 1/5:

5(x + 4) = 100

⇒ (1/5) * 5(x + 4) = (1/5) * 100

⇒ x + 4 = 20

Now we can see that the second equation simplifies to the first equation, x + 4 = 20. This means that any solution that satisfies the first equation (x + 4 = 20) will also satisfy the second equation (5(x + 4) = 100).

In other words, if we find a value of x that makes x + 4 = 20 true, then substituting that value of x into 5(x + 4) = 100 will also make it true. Therefore, any solution to the equation x + 4 = 20 will also be a solution to the equation 5(x + 4) = 100.

Step-by-step explanation:

Jethro must get a mark of 92 out of 100 for the last test to have a mean mark of at least 77 for all 6 tests.

To work out the least mark that Jethro needs to get for the last test, we can use the Mean formula: Mean = (Sum of all scores) / (Number of scores).

We know that the Mean of the 5 tests that Jethro has already sat is 74, so we can calculate the sum of the 5 test scores by multiplying the mean by the number of tests (74 x 5 = 370). We also know that Jethro wants his mean mark for all 6 tests to be at least 77, so the sum of all 6 test scores must be higher than (77 x 6 = 462).

To calculate the least mark Jethro needs to get for the last test, we can combine these two facts. We know the sum of the 5 test scores is 370, so the sum of all 6 test scores must be 462 or higher. This means the least mark Jethro needs to get for the last test must be (462 – 370) = 92. This means that Jethro must get a mark of at least 92 out of 100 for the last test to have a mean mark of at least 77 for all 6 tests.

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Answer:

h(t) = 40 cos(π/22.5 t) + 10.

Step-by-step explanation:

The function that models Amelia's height, h, at time t can be written as:

h(t) = r cos(ωt) + a

where:

r is the radius of the ferris wheel (40 m)

a is the initial height of the cart above the ground (10 m)

ω is the angular velocity of the ferris wheel, which is equal to 2π divided by the time for one complete rotation (T)

T is the time for one complete rotation, which is given as 45 seconds

To find ω, we can use the formula:

ω = 2π/T

ω = 2π/45

ω = π/22.5

Substituting the values into the function, we get:

h(t) = 40 cos(π/22.5 t) + 10

Therefore, the function that models Amelia's height, h, at time t since she got on the ride is h(t) = 40 cos(π/22.5 t) + 10.

Therefore, the two possible values for AC are approximately 13.266 cm and 16.734 cm.

An assortment of similarly spaced out points in a plane make up a circle. The center is where the point is located, but the radius is the distance from the center. Two times the radius equals the diameter.

We can see that triangle ADC is a right triangle since it's inscribed in a semi-circle (the smaller circle). So we can use the Pythagorean theorem to find AC:

AC² = AD² - CD²

Since AD is the radius of the larger circle (15 cm) and CD is the radius of the smaller circle (7 cm), we have:

AC² = 15² - 7²

AC² = 176

AC = √(176)

AC ≈ 13.266 cm

So one possible value for AC is approximately 13.266 cm.

Now let's consider the other intersection point, D. We can see that triangle BDC is also a right triangle since it's inscribed in a semi-circle (the smaller circle). So we can use the Pythagorean theorem again to find BD:

BD² = BC² + CD²

Since BC is the radius of the larger circle (15 cm) and CD is the radius of the smaller circle (7 cm), we have:

BD² = 15² - 7²

BD² = 176

BD = √(176)

BD ≈ 13.266 cm

Since BD is a diameter of the larger circle, we have:

AC + BD = 2 * 15 = 30

So the other possible value for AC is:

AC = 30 - BD

AC ≈ 16.734 cm

Therefore, the two possible values for AC are approximately 13.266 cm and 16.734 cm.

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a. Probability of candidate being forecast as the winner ≈ 17.78%

b. Probability of candidate being forecast as the winner ≈ 99.65%

c. Probability of candidate being incorrectly forecast as the winner ≈ 1.58%

d. 95% confidence interval for the true percentage of the candidate's vote ≈ (0.449, 0.651)

e. No, there is not sufficient evidence at 90% level of confidence that she has won the election.

a. If the population percentage of the candidate's vote is 50%, then the probability of her receiving at least 55% of the vote in a sample of 100 voters can be calculated using the binomial distribution with n=100 and p=0.50:

P(X ≥ 55) = 1 - P(X < 55) = 1 - binomial distribution (54, 100, 0.50, true)

≈ 0.1778

b. If the true percentage of the candidate's vote is 60%, then the probability of her receiving at least 55% of the vote in a sample of 100 voters can be calculated using the binomial distribution with n=100 and p=0.60:

P(X ≥ 55) = 1 - P(X < 55) = 1 - binomial distribution (54, 100, 0.60, true)

≈ 0.9965

c. If the true percentage of the candidate's vote is 49%, then the probability of her receiving at least 55% of the vote in a sample of 100 voters can be calculated using the binomial distribution with n=100 and p=0.49:

P(X ≥ 55) = 1 - P(X < 55) = 1 - binomdist(54, 100, 0.49, true) ≈ 0.0158

d. The 95% confidence interval for the true percentage of the candidate's vote can be calculated using the following formula:

CI = p ± zα/2 × √(p×(1-p)/n)

where p is the sample proportion (55/100=0.55), zα/2 is the critical value for a 95% confidence interval (1.96), and n is the sample size (100).

Substituting the values, we get:

CI = 0.55 ± 1.96 × √(0.55×(1-0.55)/100) ≈ (0.449, 0.651)

e. If 55% of a sample of 300 indicated that they have voted for her, the sample proportion is p=0.55 and the sample size is n=300. We can calculate the standard error of the sample proportion using the following formula:

SE = √(p×(1-p)/n) ≈ √(0.55×(1-0.55)/300) ≈ 0.0316

The margin of error for a 90% confidence interval can be calculated by multiplying the standard error by the critical value for a 90% confidence interval, which is approximately 1.645:

ME = 1.645 × SE ≈ 0.052

The 90% confidence interval for the true proportion can be calculated as:

CI = p ± ME ≈ 0.55 ± 0.052 ≈ (0.498, 0.602)

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Answer:

8pi

Step-by-step explanation:

Since the triangle is a 30-60-90 triangle, the hypotenuse is 2 times the shortest side and the second longest side is sqrt3 times the shortest side. Since it is given that the second longest side is 4sqrt3, this means that the shortest side is 4, so the hypotenuse is 8.

Because of this, the diameter is 8, which means the radius is half of the diameter, which is 4.

The formula for circumference is 2*pi*r, and since r is 4, we can plug this in to get 2*pi*4, which is 8pi.

Answer:

[tex]\huge\boxed{\sf 48.3 \ miles}[/tex]

Step-by-step explanation:

Given that,

1 day = 6.9 miles

1 × 7 days = 6.9 × 7 miles

[tex]\rule[225]{225}{2}[/tex]

Answer:

7 days = 48.3 miles

Step-by-step explanation:

Given information,

→ Ronald bikes 6.9 miles every day.

Now we have to,

→ Find the distance travelled in 7 days.

General formula we use,

→ Distance travelled × Number of days

Then the distance travelled will be,

→ Miles × Days

→ 6.9 × 7

→ 48.3 miles

Hence, the answer is 48.3 miles.

According to the given information, the terminal side of an angle of 7 radians is in the second quadrant.

What is the terminal angle?

The terminal angle is the angle formed by the terminal side of an angle in standard position (i.e., with its initial side along the positive x-axis) and the nearest x-axis. It is typically measured in a counterclockwise direction from the positive x-axis.

An angle of 7 radians is greater than 2π radians (which is approximately 6.28 radians), so it corresponds to more than one full revolution around the unit circle.

To find the terminal side of an angle of 7 radians, we can subtract 2π radians (or 360 degrees) from 7 radians until the result is between 0 and 2π radians. We have:

[tex]$$7 \text{ radians} - 2\pi \text{ radians} \approx 1.716 \text{ radians}$$[/tex]

Since 1.716 radians is less than π radians (which is approximately 3.14 radians), the terminal side of an angle of 7 radians is in the second quadrant.

The terminal side of an angle of 7 radians is in the second quadrant.

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The area of the given figure is 94.29 [tex]in^{2}[/tex].

An object of area is how much space it takes up in 2-D. It is the measurement of object is unit squares than , completely cover the surface of a closed figure. The square unit, is frequently expressed as square inches, square feet,square meter,etc. is the accepted unit of area.

A shape is created by combining multiple  shapes is known as a composite figure. We add up all of outside sides of shape to find the perimeter. We  calculate the areas of each independently, and then add the resulting areas to determine the area.

First of all ,we will find the area of, the triangle.

The formula for area of a triangle =[tex]\frac{1}{2} *base* height[/tex].

According to question ,

base of triangle = 10 in.

Height of triangle =11 in.

value of base and height  substitute in formula than we get,

area of a triangle =[tex]\frac{1}{2} * 10 * 11[/tex]

area of a triangle= 1* 5*11

area of a triangle= 55 [tex]in^{2}[/tex].

Now,we will find the area of semi circle,

The formula for area of semi circle  =[tex]\frac{1}{2} \pi r^{2}[/tex]

According to question ,

[tex]r=\frac{10}{2} =5 in.[/tex] and use [tex]\pi =\frac{22}{7}[/tex]

area of semi circle=

[tex]=\frac{1}{2} *\frac{22}{7}*5^{2} \\\\=\frac{1}{2} *\frac{22}{7}*25\\\\=\frac{11}{7}*25}\\\\=1.57*25\\\\=39.29 in^{2}[/tex]

Now,area of given shape =

[tex]55 in^{2}+39.29 in^{2}\\\\=94.29 in^{2}[/tex]

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The regular price of one baseball bat is $80.40.

A discount is a drop in a product's or service's price. It is often provided by the vendor as an inducement to lure customers into making a purchase. Often, the discount is indicated as a percentage or a dollar amount off the list price.

The standard price and the discount rate must be known in order to determine a discount. Often, the discount rate is expressed as a percentage. We multiply the usual price by the discount rate to determine the discount amount.

Given that, coach buys 5 identical baseball bats for a total of $327.45.

Thus,

5P = 327.45

P = 65.49

So one bat cost him 65.90.

Now, the regular cost of the bat will be:

Price = 65.90 + 14.50

Price = 80.40

Hence, the regular price of one baseball bat is $80.40.

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Answer:

Step-by-step explanation:

If the value of the car has decreased by 44%, it still retains 56% of its value. Thus, the solution for the depreciation is 63,765(.56) = $35,708.40

a. The surface area of the outer square pyramid is 11.25 square centimeters. b. The side length of the inner square pyramid is 2.25 centimeters.

a. To find the surface area of the outer square pyramid, we need to calculate the area of each of its faces and add them together. The outer square pyramid has four triangular faces and a square base.

Area of a triangular face = (1/2) x base x height

Area of a triangular face = (1/2) x 1.5 cm x 3 cm = 2.25 cm²

The area of the square base can be found using the formula for the area of a square:

Area of square base = side length²

Area of square base = 1.5 cm x 1.5 cm = 2.25 cm²

Therefore, the total surface area of the outer square pyramid is:

Surface area = 4 x area of triangular face + area of square base

Surface area = 4 x 2.25 cm² + 2.25 cm²

Surface area = 11.25 cm²

Therefore, the surface area of the outer square pyramid is 11.25 square centimeters.

b. The dimensions of the inner square pyramid have a ratio of 2:3 to the dimensions of the outer square pyramid. Let's call the side length of the inner square pyramid "x". Since the ratio of the dimensions is 2:3, we know that the side length of the outer square pyramid is (3/2)x.

The volume of a square pyramid can be calculated using the formula:

Volume = (1/3) x base area x height

Since the two pyramids are similar, the ratio of their volumes is the cube of the ratio of their corresponding side lengths:

Volume of inner pyramid / Volume of outer pyramid = (x / (3/2)x)³ = (2/3)³

We also know that the volume of the outer pyramid is:

Volume of outer pyramid = (1/3) x base area x height

The height of the two pyramids is the same, since they are stacked on top of each other, so we can write:

Volume of inner pyramid / Volume of outer pyramid = (1/3) x base area of inner pyramid / (1/3) x base area of outer pyramid

Simplifying this expression, we get:

(x / (3/2)x)³ = (1/3) x² / (1/3) (3/2x)²

Solving for x, we get:

x = (3/2)²

x = 2.25

Therefore, the side length of the inner square pyramid is 2.25 centimeters.

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The complete question is :

a. For the outer square pyramid, the side length of the base is 1.5 centimeters and the height of one of the triangular faces is 3 centimeters. What is the surface area of the outer square pyramid?

b. The dimensions of the inner square pyramid have a ratio of 2:3 to the dimensions of the outer square pyramid. What are the dimensions of the inner square pyramid?

Answer:

-51 would be the answer for this equation.

Step-by-step explanation:

The hypotenuse measures 3 cm in length. (Using the Pythagorean theorem: c2 = a2 + b2 where c is the hypotenuse and a and b are the other two sides.)

According to the Pythagorean theorem, the square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the legs. This formula may be used to get the hypotenuse length of a right triangle with sides that are 4 and 5 cm long.

With the Pythagorean theorem in use, we have:

2 hypotenuse Equals 4 + 5

(2)Hypotenuse = (16 + 25)

Hypotenuse 2 equals 41

When we square the two sides, we obtain:

41 cm is the hypotenuse.

Hence, the right triangle's hypotenuse measures around 6.4 cm in length (rounded to one decimal place).

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We can conclude after answering the provided question that We can see from the diagram that the sides of triangle XYZ are of varying lengths. As a result, XYZ is a scalene triangle.

A triangle is a closed, double-symmetrical object made up of three line segments called sides that meet at three points called vertices. Triangles can be identified by their sides and angles. Based on their sides, triangles can be equilateral (equal factions), isosceles, or scalene. Triangles can be acute (all angles less than 90 degrees), okay (one angle equal to 90 degrees), or orbicular (all angles greater than 90 degrees) (all angles greater than 90 degrees). A triangle's region can be calculated using the formula A = (1/2)bh, where a represents the neighborhood, b represents the triangle's base, and h represents the triangle's height.

We can see from the diagram that the sides of triangle XYZ are of varying lengths. As a result, XYZ is a scalene triangle.

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Answer:

x = 18

Step-by-step explanation:

[tex]\frac{6}{7}=\frac{x}{21} \\\\6*21=7*x\\\\126=7x\\\\x=18[/tex]

As a result, the answer to the following question, As a result, the length triangle of side JS is 18.

A triangle is a polygon because it contains four or more parts. It features a simple rectangular shape. A triangle ABC is a rectangle with the edges A, B, and C. When the sides are not collinear, Euclidean geometry produces a single plane and cube. If a triangle contains three components and three angles, it is a polygon. The corners are the points where the three edges of a triangle meet. The sides of a triangle sum up to 180 degrees.  

We must apply the Pythagorean theorem to answer question 19. We know that JN is the hypotenuse of a right triangle with legs of 6 and 8 lengths. As a result, we may apply the formula:

[tex]JN^2 = 6^2 + 8^2\\JN^2 = 36 + 64\\JN^2 = 100\\JN = square root (100)\\JN = 10\\[/tex]

As a result, the length of side JN is 10.

JS/NS = JM/JN

When we substitute the provided values, we get:

12/10 = JS/NS

When we simplify the left side, we get:

6/5 = JS/NS

When we multiply both sides by NS, we get:

JS = (6/5)NS

We also know that NS is 15, therefore we may substitute that number for:

[tex]JS = (6/5) * 15\sJS = 18[/tex]

As a result, the length of side JS is 18.

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Answer:

Step-by-step explanation:

2a = -b - d + c

     = c - b - d

x = c/2 - b/2 - d/2

The vector a in terms of other vectors for the given vectors in the image is  c/2 - b/2 - d/2.

A vector is a quantity that determines both an object, its magnitude, and its direction.

The resultant vector is obtained when the tail of one vector is attached to the head of another vector such the resultant vector is formed from the sum of the two vectors.

Let a be the total vector of the given figure.

The vectors are written as:

2a = -b - d + c

a = c - b - d

a = c/2 - b/2 - d/2

Hence, the vector a in terms of other vectors is  c/2 - b/2 - d/2.

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