What is the value of the first term in the
sequence below?
Rule:
Start at ?
Add 3 then divide by 2 each time
5
3.5-
4 -3.5

Step-by-step explanation:

To find C and D, we can use the given information about the initial position of the person on the ride.

When the person starts the ride, they are 10 feet off the ground. This means that the cosine function has a vertical shift of 10 units, so we have:

f(x) = Acos(Bx - C) + D = 60cos(π/2x - C) + D

At the start of the ride, when x = 0, f(x) = 10. Substituting these values, we get:

10 = 60cos(-C) + D

Simplifying, we get:

D = 10 - 60cos(-C)

We can also use the fact that the minimum height of the ride is 4 feet above the ground. This means that the cosine function has a vertical shift of 4 units, so we have:

f(x) = Acos(Bx - C) + D = 60cos(π/2x - C) + D

At the lowest point of the ride, when x = 1/4, f(x) = 4. Substituting these values, we get:

4 = 60cos(π/8 - C) + D

Substituting D = 10 - 60cos(-C) from the first equation, we get:

4 = 60cos(π/8 - C) + 10 - 60cos(-C)

Simplifying, we get:

cos(-C) = (4 - 10 - 60cos(π/8 - C))/(-60)

cos(-C) = (3cos(π/8 - C) - 1)/2

Using the identity cos(-x) = cos(x), we can rewrite this as:

cos(C) = (3cos(π/8 - C) - 1)/2

Solving for C numerically, we get:

C ≈ 0.438

Substituting this value of C and D = 10 - 60cos(-C) into the equation for f(x), we get:

f(x) = 60cos(π/2x - 0.438) + 10 + 60cos(0.438)

The answer of the given question based on the inequality equation the answer is given below,

An equation is mathematical statement that asserts equality of two expressions. It typically includes of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division

The situation that can be represented by 11+ 6.5p ≤ 89 is:

a) Napoleon is the buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at most $89. What is p,

To solve for p, we can follow these steps:

11 + 6.5p ≤ 89 (subtract 11 from both sides)

6.5p ≤ 78 (divide both sides by 6.5)

p ≤ 12

Therefore, Napoleon can buy at most 12 shirts if he wants to spend at most $89.

b) None of the given situations can be represented by the inequality 11 + 6.5p ≤ 89 when p represents the number of shirts Napoleon can buy. This is because the inequality implies that the total cost of buying p shirts at $11 each and mailing them for $6.50 is no more than $89, which is not consistent with the given information about the cost of the shirts and mailing.

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Answer: [tex]\frac{216}{185} \;\approx 1.1676[/tex]

Given:

   [tex]\displaystyle \frac{\frac{12}{37}}{ \frac{5}{18} }[/tex]

Use the method of "keep, change, flip:"

* keep the first fraction, change to multiplication, flip the second

   [tex]\displaystyle \frac{12}{37}* \frac{18}{5}[/tex]

Multiply across and divide:

   [tex]\displaystyle \frac{216}{185} \;\approx 1.1676[/tex]

Answer:

Step-by-step explanation:

7x+19=0

7x=-19

x=-19/7 ---> This is your final answer!

Plug in the x we found to see if the expression is correct:

7(-19/7)+19=0

-19+19=0

So our x value is correct!

Answer:

5x+120

Step-by-step explanation:

5(x) + 5(24)

5x+120

By making linear equation for the given statement, The salesman sold 40 suits in that week.

What is a linear equation, exactly?

A linear equation is a mathematical equation in which the variables (usually represented by x and y) are raised to the first power and are related to each other by a straight line. In other words, a linear equation represents a straight line on a graph. The general form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

Now,

Let "x" the number of suits the salesman sells in that week.

We know that he sells discounted shirts with 10% of the suits sold, so he sells 0.1x discounted shirts.

The regular price of a suit is $200, so the total revenue from selling x suits is 200x.

The discounted price of a shirt is $20, so the revenue from selling 0.1x discounted shirts is 20(0.1x) = 2x.

Now we can set up an equation based on the total revenue:

200x + 2x = 8080

Simplifying this equation, we get:

202x = 8080

Dividing both sides by 202, we get:

x = 40

Therefore,

               the salesman sold 40 suits in that week.

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The volume of the rectangular prism in cubic feet is solved to be

The volume of a rectangular prism is given by the formula

V = l x w x h,

where

l, w, and h represent the length, width, and height of the prism, respectively.

in the problem, the dimensions are:

Therefore, the volume is:

= 1.5 feet * 3.5 feet * 2 feet

= 10.5 feet³

That is to say the volume of the prism is 10.5 feet³

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Answer:

Multiple of 2

Step-by-step explanation:

There are six possible outcomes when rolling a standard number cube labeled 1 through 6. Out of these six possible outcomes, there are three outcomes that are multiples of 2 (2, 4, and 6) and two outcomes that are multiples of 3 (3 and 6).

Therefore, it is more likely that the cube will show a multiple of 2 than a multiple of 3. The probability of rolling a multiple of 2 is 3/6 or 1/2, while the probability of rolling a multiple of 3 is 2/6 or 1/3.

A radical equation is √(x + 2) = 4 - x and the extraneous solution is x = 7

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

The solution to a radical equation

In step 4 and 5, we have

x = ∛5 * 5 * 5 * 5

x = 5∛5¬ * 5¬ * 5¬ * 5

The above steps are carried out because it would simplify the radical expression to its simplest form

The reason it is done is to have the value of x in its simplest form

Here's an example of a radical equation:

√(x + 2) = 4 - x

Square both sides

x + 2 = 16 - 8x + x^2

Evaluate the like terms

x^2 - 9x + 14 = 0

Factor the quadratic equation

(x - 2)(x - 7) = 0

Solve for x:

x = 2 or x = 7

For x = 2:

√(2 + 2) = 4 - 2

√4 = 2

2 = 2

This is true, so x = 2 is a valid solution.

For x = 7:

√(7 + 2) = 4 - 7

√9 = -3

3 = -3

This is not true, so x = 7 is not a valid solution.

So, there is an extraneous solution

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In  323,400 ways it can be done by using the Combination formula.

The number of ways in which the appetizers, main courses, and desserts can be selected is to be found when a catering service offers 7 appetizers, 5 main courses, and 12 desserts, and a customer is to select 4 appetizers, main 3 courses, and 6 desserts for a banquet.

Let's find the number of ways to choose 4 appetizers from the 7 available:

= ⁷C₄ ⇒ 35 ways (using combinations).

Let's find the number of ways to choose 3 main courses from the 5 available:

= ⁵C₃ ⇒ 10 ways (using combinations).

Let's find the number of ways to choose 6 desserts from the 12 available:

= ¹²C₆ ⇒ 924 ways. (using combinations).

Therefore, the total number of ways in which the customer can select 4 appetizers, 3 main courses, and 6 desserts is:

35 × 10 × 924 ⇒ 323,400 ways.

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The solution to the given problem of speed comes out to be v=21.12m/s.

How quickly something is moving is measured by its speed at a distance. How far an object moves in one unit of time is determined by its speed. Speed is calculated as follows: speed = distance * time. The most widely used speed measurement units are meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) (mph).

Here,

Given :  A 2.0 m long cord is supporting a 3.3 kg lump of clay.

Two swing up to an absolute maximum of 0.080 meters

Ball and clay's subsequent impact velocity

=>√(2*10*0.08)=1.264m/s

To find the velocity of the ball before collision

0.21*v=(3.3+0.21)*1.264

v=21.12m/s

Therefore, the solution to the given problem of speed comes out to be v=21.12m/s.

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Answer: To find the composition g∘f, we first need to find g(f(x)), which means we need to substitute f(x) into g(x) everywhere we see x. So we have:

g(f(x)) = g(2x+5) = (2x+5)^2 - 3

Expanding the square, we get:

g(f(x)) = (4x^2 + 20x + 25) - 3

Simplifying, we get:

g(f(x)) = 4x^2 + 20x + 22

Therefore, the composition g∘f is equal to 4x^2 + 20x + 22.

Step-by-step explanation:

The cup of water reaches a temperature of 173 F after 5 minutes.

Temperature is a measure of the average kinetic energy of particles in a system. It is an important physical quantity used to describe the state of a system, and is widely used in science, engineering, and everyday life. Temperature is a thermodynamic property of a system that indicates how much energy is available to do work. In everyday terms, temperature is a measure of how hot or cold something is.

k = -0.2416
The equation for the cooling rate of the cup of water is:
T(t) = 207 - 0.2416t
After 5 minutes, the temperature of the cup of water can be found by substituting t = 5 into the equation:
T(5) = 207 - 0.2416(5) = 173.08 F
Therefore, the cup of water reaches a temperature of 173 F after 5 minutes.

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The distance between these two streets on Broad St 0.2 miles.

We must apply the idea of comparable triangles to this issue in order to find a solution. Assume that Thomas St. and Denny Way. are separated by x miles on Broad St. Then, we can establish the ratio shown below:

0.2 miles on Aurora Avenue equals x miles on Broad Street

By cross-multiplying and simplifying, we may find the value of x:

Distance on Aurora Ave / (x * 0.2 miles) on Broad St

Broad Street distance is equal to (x * 0.2 miles)/0.2 miles. (since the distance on Aurora Ave is given as 0.2 miles)

Broad Street: distance = x

As a result, Thomas St. and Denny Way are separated by x miles, or 0.2 miles, on Broad St. Thus, the response is:

Distance between Thomas St and Denny Way on Broad St = 0.2 miles (rounded to the nearest tenth of a mile)

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0.68 is a rational number because it can be expressed as a ratio of two integers (17/25).

0.68 is a rational number because it can be expressed as a ratio of two integers.

To see this, we can convert 0.68 to a fraction by placing the decimal value over a denominator of 1 followed by the number of decimal places (two in this case):

0.68 = 68/100

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor,

which is 4:

68/100 = 17/25

Thus, 0.68 can be expressed as the ratio of two integers (17 and 25) and is therefore a rational number.

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Answer:

a)  $324,000

b)  $291,600

c)  $259,200

Step-by-step explanation:

The percentage of the replacement value represents how much of the house will be insured.

a)  100% of 324000 = 1.00 * 324000 = $324,000

b)  90% of 324000 = 0.9 * 324000 = $291,600

c)  80% of 324000 = 0.8 * 324000 = $259,200

The circumference of the circular swimming pool is approximately 245.04 inches.

The circumference of a circle is the distance around it, whereas the diameter is the distance across the circle that passes through its centre. The circumference is equal to (pi) times the diameter, according to the connection between the diameter and circumference. No of the size or proportions of the circle, this connection is true for all circles.

The circumference of the circle is given as:

C = 2πr

We know that, D = 2r = 6 1/2 feet.

6 ½ feet = 6.5 × 12 inches = 78 inches

Substituting the values we have:

C = π × 78 inches = 245.04 inches

Hence, the circumference of the circular swimming pool is approximately 245.04 inches.

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the height VO of the rectangular pyramid VPQRS is 5 cm.

WHAT IS RECTANGULAR PYRAMID?

A rectangular pyramid is a type of pyramid where the base is a rectangle and the lateral faces are triangles with a common vertex (apex) that is not in the plane of the base. It is a polyhedron with a rectangular base and triangular faces that meet at a single vertex. The height of the pyramid is the perpendicular distance from the apex to the base. The volume of a rectangular pyramid can be calculated using the formula:

V = (1/3) * base area * height

where base area is the area of the rectangular base and height is the perpendicular distance from the apex to the base.

To find the height VO of the rectangular pyramid VPQRS, we can use the formula for the volume of a pyramid:

V = (1/3) * base area * height

where base area is the area of the rectangle formed by the base of the pyramid, and height is the height of the pyramid.

We are given that the volume of the pyramid is 100 cm³. We can also find the base area by multiplying the length PQ by the width QR:

base area = PQ * QR = 10 cm * 6 cm = 60 cm²

Substituting these values into the formula for the volume of a pyramid, we get:

100 cm³ = (1/3) * 60 cm² * height

Simplifying, we get:

height = (100 cm³ * 3) / (60 cm²)

height = 5 cm

Therefore, the height VO of the rectangular pyramid VPQRS is 5 cm.

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If Theo takes the loan R9000 that is payable over 48 months monthly installment =R 318,92, the total amount that Theo has to pay back for the loan is R15,307.16.

To calculate the total amount that Theo has to pay back if she takes a loan of R9000 payable over 48 months with a monthly installment of R318.92, we need to multiply the monthly installment by the number of months and add any applicable fees or interest charges.

First, let's calculate the total amount that Theo will pay for the loan over the 48-month period:

Total amount = Monthly installment x Number of months

Total amount = R318.92 x 48

Total amount = R15,307.16

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Complete question is:

Calculate the total amount that Theo has to payback if she takes the loan R9000 that is payable over 48 months monthly installment =R 318,92

There are 6,188 different ways the CEO can choose five employees from a pool of 17 people to take a survey.

To determine how many ways the CEO can select five employees from a pool of 17 people to take a survey, you can use the combination formula. The combination formula is nCr = n!/r!(n-r)! where n is the total number of items to choose from, and r is the number of items to choose.

In this case, n = 17 and r = 5.Using the combination formula: n Cr = 17C5= 17!/5!(17-5)!= 6188 There are 6,188 different ways the CEO can choose five employees from a pool of 17 people to take a survey.

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As per the concept of unitary method, Linda read 5/6 of the book.

In this problem, the quantity we are dealing with is the book that Linda is reading. Let's call the total number of units in the book "x". Since Linda read 1/3 of the book on Friday, we can say that she read (1/3)x units of the book on Friday. Similarly, she read (2/6)x units of the book on Saturday, and (2/12)x units of the book on Sunday.

Now, we need to add up all of these quantities to find the total number of units of the book that Linda read. But before we do that, we need to make sure that all of the fractions have the same denominator. The smallest common multiple of 3, 6, and 12 is 12. So, we will convert all of the fractions to twelfths.

(1/3)x = (4/12)x

(2/6)x = (4/12)x

(2/12)x = (2/12)x

Now, we can add up all of these quantities:

(4/12)x + (4/12)x + (2/12)x = (10/12)x

So, Linda read (10/12)x units of the book in total. But we can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

(10/12)x = (5/6)x

Therefore, the resulting value of x is 5/6

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The two numbers that are multiplied to find out the amount she has after playing her rent is: 2/3 and 1800.

Total income of person: $1800 per month.

Rent amount = 1/3 * income

Remaining amount : 1 - 1/3 = 2/3 of income

So,

Remaining amount = 2/3*1800

Remaining amount = 1200

Thus, the two numbers that are multiplied to find out the amount she has after playing her rent is: 2/3 and 1800.

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The value of length SP for the two given similar triangles is 11.

Similar triangles are triangles that have the same shape but are different in size. In other words, their corresponding angles are equal, and their corresponding sides are proportional.

This means that if you were to take one of the similar triangles and enlarge or shrink it, while keeping the angles the same, it would still be a similar triangle.

The value of length SP is calculated by applying the following method;

|SP| = |ST|

3x + 2 = 5x - 4

3x - 5x = -4 - 2

-2x = - 6

x = 3

Length SP = 3x + 2

                 = 3(3) + 2

                 = 11

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A linear equation to represent the line shown on the graph is given as:

y = 2x - 2.

General point-slope form is:

y = mx + c

(x1, y1) = (3, 2)

y intercept = -2

m = (2 + 2)/(2 - 0)

m = 2

y = 2x + (-2)

y = 2x - 2

Thus,  a linear equation to represent the line shown on the graph is given as: y = 2x - 2.

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The correct question is-

Write a linear equation to represent the line shown on the graphs shown by question 7.

a)  The probability of finding a value greater than $24 is given by:P(X > $24) = P(Z > (24 - 21) / 4) = P(Z > 0.75)Using the standard normal distribution table, we can find that P(Z > 0.75) = 0.2266.Rounding this result to four decimal places, we have:P(X > $24) = 0.2266.

b) The probability of finding a value between $10 and $19 is given by:P($10 < X < $19) = P((10 - 21) / 4 < Z < (19 - 21) / 4) = P(-2.75 < Z < -0.5)Using the standard normal distribution table, we can find that P(-2.75 < Z < -0.5) = P(Z < -0.5) - P(Z < -2.75) = 0.3085 - 0.0030 = 0.3055.Rounding this result to four decimal places, we have:P($10 < X < $19) = 0.3055.

The probability that a randomly selected person spent more than $24One year consumers spend an average of $21 on a meal at a restaurant. The amount spent on a restaurant meat is normally distributed with a standard deviation of $4.The first step to solve this problem is to standardize the normal random variable using the z-score formula, which is:(1)z= (x-μ) / σwhere x is the random variable, μ is the mean, and σ is the standard deviation. The probability of finding a value greater than $24 is given by:P(X > $24) = P(Z > (24 - 21) / 4) = P(Z > 0.75)Using the standard normal distribution table, we can find that P(Z > 0.75) = 0.2266.Rounding this result to four decimal places, we have:P(X > $24) = 0.2266.

The probability that a randomly selected person spent between $10 and $19 The probability of finding a value between $10 and $19 is given by:P($10 < X < $19) = P((10 - 21) / 4 < Z < (19 - 21) / 4) = P(-2.75 < Z < -0.5)Using the standard normal distribution table, we can find that P(-2.75 < Z < -0.5) = P(Z < -0.5) - P(Z < -2.75) = 0.3085 - 0.0030 = 0.3055.Rounding this result to four decimal places, we have:P($10 < X < $19) = 0.3055.

The amount spent by the middle 50% of the customers The middle 50% of the customers is equivalent to the interval that goes from the 25th percentile to the 75th percentile. This interval is also known as the interquartile range (IQR).The 25th percentile can be found by using the standard normal distribution table, which gives us that:P(Z < -0.6745) = 0.25 Solving for Z, we have:Z = -0.6745 Using the z-score formula, we can find the corresponding value of X:$21 + (-0.6745)($4) = $17.30

Therefore, the lower limit of the IQR is $17.30.The 75th percentile can be found by using the standard normal distribution table, which gives us that:P(Z < 0.6745) = 0.75 Solving for Z, we have:Z = 0.6745Using the z-score formula, we can find the corresponding value of X:$21 + (0.6745)($4) = $24.70

Therefore, the upper limit of the IQR is $24.70.The amount spent by the middle 50% of the customers is between $17.30 and $24.70.

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Problem 1:

a) The probability that no customers will be sent to another hotel is 0.039.

b) The probability that exactly 2 guests will be sent to another hotel is 0.228.

c) The probability that 3 or more guests will be sent to another hotel is 0.492.

Problem 2:

a) ( ≤ 20) - Probability of having 20 or fewer customers show up for the reservations.

b) ( = 22) - Probability of exactly 22 customers confirming and showing up for the reservations.

c) ( ≥ 23) - Probability of having 23 or more customers show up for the reservations.

Problem 1:

a. To find the probability that no customers will be sent to another hotel, we need to calculate the probability that all 25 confirmed reservations will show up. Since the hotel manager estimates that 15% of reservations are "no-shows",

Then the probability that a reservation will show up is 1 - 0.15 = 0.85. The probability that all 25 guests will show up is,

P(all 25 show up) = [tex](0.85)^{25}[/tex]

                             = 0.039

So the probability that no customers will be sent to another hotel is 0.039.

b. To find the probability that exactly 2 guests will be sent to another hotel, we have to use the binomial distribution.

The probability of a reservation being a no-show is 0.15, and the probability of a reservation showing up is 0.85. We have 25 confirmed reservations, so the probability of exactly 2 no-shows is,

P(exactly 2 no-shows) = (25 choose 2)[tex](0.15)^2 (0.85)^{23}[/tex]

                                     = 0.228

So the probability that exactly 2 guests will be sent to another hotel is 0.228.

c. To find the probability that 3 or more guests will be sent to another hotel, we need to use the complement rule.

The probability of 0, 1, or 2 guests being sent to another hotel is,

⇒ P(0 guests sent) + P(1 guest sent) + P(2 guests sent)

   = [tex](0.85)^{25}[/tex]+ (25 choose 1)[tex](0.15)^1 (0.85)^{24}[/tex] + (25 choose 2)[tex](0.15)^2 (0.85)^{23}[/tex]

   = 0.039 + 0.168 + 0.301

   = 0.508

The probability of 3 or more guests being sent to another hotel is,

P(3 or more guests sent) = 1 - P(0, 1, or 2 guests sent)

                                         = 1 - 0.508

                                         = 0.492

So the probability that 3 or more guests will be sent to another hotel is 0.492.

Problem 2:

a) To find ( ≤ 20),

We have to add up the probabilities of all the possible values of from 0 to 20. This is because we want to find the probability that 20 or fewer customers confirmed and showed up for the reservations.

We can use the binomial probability formula to calculate each individual probability, or we can use a binomial cumulative distribution table to look up the probability directly.

The reason we want to find this probability is to determine the likelihood of having fewer than 20 customers show up, which could impact staffing and resource allocation for the event.

b) To find ( = 22),

Use the binomial probability formula to calculate the probability of exactly 22 customers confirming and showing up for the reservations. This is because we are interested in a specific outcome, and want to know the likelihood of that outcome occurring. Knowing this probability can help us plan for specific scenarios, such as having to accommodate 22 customers if they all show up.

c) To find ( ≥ 23),

We have to add up the probabilities of all the possible values of from 23 to 25. This is because we want to find the probability that 23 or more customers confirmed and showed up for the reservations.

We can use the binomial probability formula or a binomial cumulative distribution table to find this probability.

The reason we want to find this probability is to assess the risk of having too few resources available if more customers show up than expected, which could lead to a poor customer experience.

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We can say that after answering the offered question Therefore, the equation constant of proportionality in this scenario is 11.25.

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

In this case, we may use the following formula to calculate the proportionality constant:

proportionality constant = output/input

where the output is John's pay and the input is the number of hours he worked.

As a result, the proportionality constant is:

Paycheck/hours worked = proportionality constant

proportionality constant = 450/40

proportionality constant = 11.25

As a result, the proportionality constant in this scenario is 11.25.

In this case, we may use the following formula to calculate the proportionality constant:

proportionality constant = output/input

where the output is John's pay and the input is the number of hours he worked.

As a result, the proportionality constant is:

Paycheck/hours worked = proportionality constant

proportionality constant = 450/40

proportionality constant = 11.25

Therefore, the constant of proportionality in this scenario is 11.25.

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The radii of circle are AB, AC and AE.

The radius of a circle is the distance from the center of the circle to any point on its circumference. To find the radius of a circle, you can use the formula:

radius = diameter / 2

where the diameter is the distance across the circle, passing through its center.

Here, in this figure we need to identify the radii. It means we need to find those lines which starts from centre and touches it's circumference.

Let us first see the option AB, it follows the condition passes through centre and touches the circumference. So, it is radius of circle.

Now, let's look at CE in figure, it passes through centre and touch the two ends of circumference. So, it is diameter not radius.

Now, AC satisfies the condition of radius. So, AC is radius.

FD touches the two ends of circle at circumference not passes through centre. So, it is chord not radius.

AE starts from centre and it's other end touches the circumference of circle. So, it is radius.

So, the radii of circle in given figure are : AB, AC and AE.

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