Find a formula for the nth partial sum of this Telescoping series and use it to determine whether the series converges or diverges. (pn)-² Σ 2 3 2+2+1 n=1n² n

Answer:

The total cost is 519

Step-by-step explanation:

22x12=264 and 22-5=17 so 17x15=255

264+255= 519

Answer:

y = 3 x − 29

Step-by-step explanation:

First, let's find the slope of the line  

y = 3 x + 2

As the equation is already in slope-intercept form  

y = m x + c

Slope =  3

Let a point  ( x , y )  be on the new line.

By finding the slope again,

y − 1 x − 10 = 3

y − 1 = 3 ( x − 10 )

y − 1 = 3 x − 30

Which can then be converted to different forms:

Standard form:  

3 x − y = 29

Equation form:  

3 x − y−29 = 0

Slope-intercept form:  

y = 3 x − 29

graph{3x-y=29 [-32.3, 47.7, -34.1, 5.9]}

Answer:

Could u give us more info in ur question pls?

Answer:

Pretty sure it's B. 1

Step-by-step explanation:

y = mx + b is y-intercept form and B is usually where you put the first dot on the y axis, and that is positive 1, as you can see on the graph.

Hope you get a good grade! :)

Answer:

   \(\frac{2}{6}\) or \(\frac{1}{3}\)

Step-by-step explanation:

To find a fraction of a fraction simply multiply the numerators and denominators into another fraction:

\(\frac{1}{2}*\frac{2}{3} = \frac{2}{6} = \frac{1}{3}\)

Answer:

1/3.

Step-by-step explanation:

'of' means multiply. so

1/2 of 2/3

= 1/2 * 2/3

= 1*2  /  2*3

= 2/6

= 1/3.

Answer:

16.1, 16, 16

Step-by-step explanation:

1) we are going to do the mean :)

you add all the number together and divide by the same number

you should get 354/22 which is 16.0909....... since its round to tenth place, we place it at 16.1.

2)  median, for this one, you have to lay out the numbers and see which one is in the middle, in 14,15,16,17,19, 16 is the median.

3)  the number that appear the most is the mode, so right now we have

three 17s and six 16s, don't worry about the others because its not in the answer choice, so its 16.

Hope this helps :D

=13.62

- We are given the interarrival time (a = 15 min), service time (p = 20 min), number of servers (m = 3 people), standard deviation of interarrival time (15 min) and standard deviation of service time (60 min). - Therefore, the coefficient of variation of arrival times is 15 / 15 = 1 and the coefficient of variation of service times is 60 / 20 = 3. Moreover, the utilization is 20 / (15 x 3) = 0.4444. Therefore, the average time in the queue is 6.6667 x 0.4086 x 5.0 = 13.6211 minutes, or 13.62 minutes rounded to two decimals

- We are given the interarrival time (a = 15 min), service time (p = 20 min), number of servers (m = 3 people), standard deviation of interarrival time (15 min) and standard deviation of service time (60 min). - Therefore, the coefficient of variation of arrival times is 15 / 15 = 1 and the coefficient of variation of service times is 60 / 20 = 3. Moreover, the utilization is 20 / (15 x 3) = 0.4444. Therefore, the average time in the queue is 6.6667 x 0.4086 x 5.0 = 13.6211 minutes, or 13.62 minutes rounded to two decim

Emma's luggage may be lost with probability p = 0.1. The luggage and its content are estimated to be worth 316.05. Emma's utility insures against the loss of the luggage. What is the maximum insurance premium I that Emma would be willing to pay?

Solution:To calculate Emma's maximum insurance premium, let's start by calculating her expected utility if she doesn't insure her luggage.U (no insurance) = 0.9 x U (316.05) + 0.1 x U (0)where U (316.05) is Emma's utility function for 316.05 value, and U (0) is Emma's utility function for a loss of the luggage. Emma has not insured her luggage, hence, if it gets lost, she will get 0 value for it.A sum of 316.05 is worth more than 0, Emma will still get a certain amount of utility, which will be larger than 0.

Therefore, Emma's utility function is likely to be positive, so let us assume that U (0) = 0.If we plug this information into the above equation, we will have:U (no insurance) = 0.9U (316.05) + 0.1 × 0 = 0.9U (316.05)Hence, Emma's expected utility, if she doesn't insure her luggage, will be 0.9U (316.05).However, if Emma chooses to insure her luggage, she will pay the insurance premium I. If the luggage gets lost, she will get reimbursed by the insurance company for 316.05. Her expected utility function, if she insures her luggage, will be:

U (insurance) = 0.9U (316.05 – I) + 0.1U (316.05)Where U (316.05 – I) is Emma's utility function for 316.05 – I value. Emma will get this amount if the luggage is not lost, but she has to pay the premium I.If we compare Emma's expected utility when she insures her luggage and when she doesn't insure her luggage, we will have the following inequality:

U (insurance) ≥ U (no insurance)0.9U (316.05 – I) + 0.1U (316.05) ≥ 0.9U (316.05)Let us solve this inequality:0.9U (316.05 – I) + 0.1U (316.05) ≥ 0.9U (316.05)0.9U (316.05 – I) ≥ 0.8U (316.05)U (316.05 – I) ≥ 0.89U (316.05)Since U (316.05 – I) is a decreasing function, it will get smaller as I gets larger.

Hence, to maximize Emma's expected utility, we need to minimize the insurance premium I that she pays to the insurance company.If Emma doesn't insure her luggage, her expected utility will be 0.9U (316.05)Emma will choose to insure her luggage if her expected utility is larger if she insures her luggage.U (insurance) = 0.9U (316.05 – I) + 0.1U (316.05)0.9U (316.05 – I) ≥ 0.8U (316.05)U (316.05 – I) ≥ 0.89U (316.05)Emma will choose to insure her luggage if her expected utility is larger if she insures her luggage. Hence,Emma's maximum insurance premium I that Emma would be willing to pay is $31.35.

If Emma chooses to insure her luggage, she will pay the insurance premium I. Her expected utility function, if she insures her luggage, will be U (insurance) = 0.9U (316.05 – I) + 0.1U (316.05). Emma will choose to insure her luggage if her expected utility is larger if she insures her luggage. Therefore, Emma's maximum insurance premium I that Emma would be willing to pay is $31.35. The utility function is considered decreasing as Emma has to pay more premium.

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Answer:

144 pages read

Step-by-step explanation:

80% = 0.8

0.8 * 180 = 144

Answer: To find how much Godwin owes Aidan, we first need to calculate the total cost of the items Aidan purchased:

10 cans of soup for $8.69, so the cost per can of soup is $8.69/10 = $0.869 per can.

1 case of chili for $19.20, so the cost per can of chili is $19.20/24 = $0.80 per can.

Godwin takes 4 cans of soup at $0.869 per can, which is a total of 4 x $0.869 = $3.476 for the soup.

Godwin takes 12 cans of chili at $0.80 per can, which is a total of 12 x $0.80 = $9.60 for the chili.

Therefore, Godwin owes Aidan $3.476 + $9.60 = $13.076.

The unit rate of the soup is $0.869 per can.

The unit rate of the chili is $0.80 per can.

Step-by-step explanation:

The perimeter of the polygon will be 20 units and the area will be 21 square units.

From the given vertices a rectangle will be formed. A rectangle is a closed figure in which each interior angle is a right angle. The Perimeter of the rectangle can be given by formula 2(l + b) and the area is given by l×b where l is the length and b is breadth of rectangle. Now from the given points the dimensions of rectangle will follow the order W (5, -1), X (5, 6), Z (2, 6) and Y (2, -1).

The length of the rectangle is given by l = √ (6 + 1) ² + (5 - 5) ²

l = √49

l = 7 units

The breadth of the rectangle is given by b = √ (6 - 6) ² + (2 - 5) ²

b = √9

b = 3 units

Now, the perimeter of rectangle = 2 (l + b)

P = 2(7 + 3)

P = 20 units

Area of the rectangle = l×b

A = 7×3

A = 21 square units.

Thus, the perimeter and area are 20 units and 21 square units respectively.

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population at 1992 = 3590

Population after Seven years (1999) = 4500

Given two points (t1, P1) and (t2, P2), the slope of the line m can be found.

p1 = (1992, 3590) and p2 = (1999, 4500)

m= ΔP/Δt

m= ((4500-3590))/((1999-1992))

m = 910/7

m=130 is the slope

The linear population function P(t) is

P(t)=130t + P0

Find the Y-Intercept P0

The population function P(t) is measured since the year 1990, year zero. The first moose population was measured in 1992, one year later. This provides an initial condition P (1) = 4500.

P (1) =130 (1) + P0 = 4500

P0 = 4370

P(t)=20t+4630

The moose population P(t) changes linearly year after year. The population function P(t) is measured in terms of t years since 1990.

t= 1990, P (0) =4370

t =1992, P (1) =130 (1) + 4370 = 4500 matches data

t=1999, P (2) = 130(2) + 4370 = 4630

t=2006, P (3) = 130(3) + 4370 = 4760

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The absolute value of inequality representing the range of John's weight is | x - 156 | ≤ 8.

An absolute value inequality is an inequality that contains an absolute value expression. The absolute value of a number represents the distance between that number and zero on a number line.

An absolute value expression is a mathematical expression that contains an absolute value function, denoted by vertical bars around a number or expression. The absolute value of a number is its distance from zero on a number line, so an absolute value expression represents a positive number, regardless of whether the original number was positive or negative.

As per the given question,

If John weighed 156 pounds give or take 8 pounds ten years ago, then his weight could have been anywhere from 156 - 8 = 148 pounds to 156 + 8 = 164 pounds.

To write this as an absolute value inequality, we can let x represent John's weight, and use the absolute value to represent the distance from the mean weight of 156 pounds. The inequality would be:

| x - 156 | ≤ 8

This inequality says that the distance between John's weight (x) and the mean weight of 156 pounds must be less than or equal to 8 pounds. In other words, John's weight must be within 8 pounds of 156, which represents the range of possible weights he could have had ten years ago.

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Answer:

Step-by-step explanation:

I'm just going to go out on a limb here and assume that those are a set of poorly made parenthesis. This, then, would be your equation:

\(x+\frac{x}{7}+\frac{1}{11}(x+\frac{x}{7})=60\)

The first thing to do is distribute through the parenthesis to get:

\(x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60\)

Next is to get rid of the denominators by multiplying by the LCM of 77:

\(77(x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60)\) which gives you:

77x + 11x + 7x + x = 4620 and

96x = 4620 so

\(x=\frac{385}{8}\)

using standard z value, 20% of sandwiches are less than 10.58 inches.

In the given question,

Subway sells foot long sandwiches that have a mean of 11 inches and a standard deviation of 0.5 inches.

20% of sandwiches are less than...............inches.

The cumulative standardized normal distribution table indicates a z value of -0.84 for 20%.

From the question we know that

Mean(μ) = 11 inches

Standard Deviation(σ) = 0.5 inches

We have to find less than of 20% of sandwiches for z value of -0.84

P(ƶ<z) = 20%

We can write it as

P(ƶ<-0.84) = 20/100

P(ƶ<-0.84) = 0.20

Since z = -0.84

X-μ/σ = -0.84

Now putting the value

X-11/0.5 = -0.84

Multiply by 0.5 on both side

X-11/0.5 *0.5= -0.84*0.5

X-11= -0.42

Add 11 on both side

X-11+11= -0.42+11

X = 10.58

Hence, 20% of sandwiches are less than 10.58 inches.

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Right question is here

Subway sells foot long sandwiches that have a mean of 11 inches and a standard deviation of 0.5 inches. 20% of sandwiches are less than ................. inches. (The cumulative standardized normal distribution table indicates a z value of -.84 for 20%)

(a) 11.500

(b) 11.42

(c) 10.58

(d) cannot be determined from the information given

A. The work done is 300 ft-lbs when a 100 lb rock is lifted to a height of 3 ft.

To calculate the work done, we can use the formula: Work = force x distance x cos(Ф).In this case, the force is the force of gravity acting on the rock, which can be calculated using the formula:

force = m * g

where m is the mass of the rock and g is the acceleration due to gravity (32.17 ft/s^2).

force = 100 lb * 32.17 ft/s^2 = 3,217 ft-lbs

The distance is the height to which the rock is lifted, which is 3 ft.

The angle of the rock to the vertical is 90 degrees, so cos(90) = 0.

So,

Work = force x distance x cos(theta) = 3,217 ft-lbs * 3 ft * 0 = 300 ft-lbs

So, the work done is 300 ft-lbs.

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The answer to this arithmetic expression is approximately 9.9998 x 10¹⁸

A combination of numbers, variables, and operators that represents a quantity or mathematical relationship is called an expression.

First, divide sextillion (10²¹) by nonmillion (10⁶) to get 10¹⁵.

Next, multiply 10¹⁵ by 10,000 to get 10¹⁹.

Subtract 200 million (2 x 10⁸) from 10¹⁹ to get 9.9998 x 10¹⁸.

Finally, add 5,000 to get the result of approximately 9.9998 x 10¹⁸ + 5,000 = 9.9998 x 10¹⁸ + 0.0005 x 10¹⁸ = 9.9998 x 10¹⁸.

Therefore, the answer to this arithmetic expression is approximately 9.9998 x 10¹⁸

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Answer:

x = 9/2

Step-by-step explanation:

4x = 18

divide the 4 on both sides so it equals

x = 18/4

then simplify it to

x = 9/2

Sample size and the confidence level width have an inverse relationship. As the sample size increases, the confidence level width decreases.

When determining a confidence interval for a population parameter, such as the mean or proportion, a larger sample size provides more information about the population. This increased information leads to a narrower confidence interval.

The confidence level width is influenced by two factors: the sample standard deviation (or the variability of the data) and the critical value associated with the desired confidence level. As the sample size increases, the sample standard deviation becomes a more accurate estimate of the population standard deviation. This reduces the variability and leads to a narrower confidence interval.

A larger sample size leads to a decrease in the confidence level width, providing a more precise estimate of the population parameter with a higher level of confidence.

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There can be several possibilities and causes

y>2x-1

y<2x-1

y≤2x-1

y≥2x-1

y=2x-1

Credit: Mister Brainly

There can be several possibilities and causes:

y>2x-1

Then line will be dashed and solution region to be shaded.

y<2x-1

Same like before

y≤2x-1

Solid line should be done and shading the solution region

y≥2x-1

Same like before

y=2x-1

A straight line and no shading

The power of 2 is called a square due to the definition of the area of a square.

What are a square and Power?

A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.

The base number is the factor that is multiplied by itself, and the exponent is the number of times the same base number has been multiplied. Power is defined as a base number raised to the exponent.

The power of two is called a square.

The square function's name derives from the fact that a square with sides of length \(l\) equals \(l^2\) has a significant role to play in the definition of area.

The area is inversely proportional to size: the area of a form that is \(n\) times larger is \(n^2\) times larger.

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Answer:

  a) h(t) = -16t^2 +41t +37

  b) see attached (3.270 seconds)

  c) (41+√4049)/32 seconds

  d) 1.28125 seconds; 63.265625 feet

  e) [1.5, 2]: -15; [2, 2.5]: -31; [2.5, 3]: -47

Step-by-step explanation:

a) The formula and initial values are given. Putting those values into the formula, we get ...

  h(t) = -16t^2 +41t +37

__

b) The graph is attached. It shows the t-intercept to be about 3.270 seconds.

__

c) Using the quadratic formula, we can find the landing time as ...

  \(t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-41\pm\sqrt{41^2-4(-16)(37)}}{2(-16)}\\\\=\dfrac{41\pm\sqrt{4049}}{32}\qquad\text{only $t>0$ is useful}\)

The exact landing time is (41+√4049)/32 seconds.

__

d) The highest point is at t=-b/(2a) = -41/(2(-16)) = 41/32 seconds.

The value of the function at that point is ...

  h(41/32) = (-16(41/32) +41)(41/32) +37 = 41^2/64 +37 = 4049/64

The maximum height is 4049/64 = 63.265625 feet.

__

e) For a quadratic function, that average rate of change on an interval is the derivative at the midpoint of the interval. Here, the derivative is ...

  h'(t) = -32t +41 . . . in feet per second

Then the average rates of change are ...

  arc[1.5, 2] = h'(1.75) = -32·1.75 +41 = -15 ft/s

  arc[2, 2.5] = h'(2.25) = -32(2.25) +41 = -31 ft/s

  arc[2.5, 3] = h'(2.75) = -32(2.75) +41 = -47 ft/s

These are the average velocity of the water balloon over the given interval(s) in ft/s. Negative indicates downward.

Answer:

(a) h(t) = -16t² + 41t + 37

(b) About 3.3 s

\(\large \boxed{\text{(c) }\dfrac{41+ \sqrt{4049}}{32}\text{ s}}\)

(d) -15 ft/s; -31 ft/s; -47 ft/s

Step-by-step explanation:

(a) The function

h(t) = -16t² + v₀t + s₀

 v₀ = 41 ft·s⁻¹

 s₀ = 37 ft

The function is

h(t) = -16t² + 41t + 37

(b) The graph

See Fig. 1.

It looks like the water balloon lands after about 3.3 s.

(c) Time of landing

h = -16t² + 41t + 37

a = -16; b = 41; c = 37

We can use the quadratic formula to solve the equation:

\(h = \dfrac{-b\pm\sqrt{b^2 - 4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}\)

(i) Evaluate the discriminant D

D = b² - 4ac = 41² - 4(-16) × 37 = 1681 + 2368  = 4049

(ii) Solve for t

\(\begin{array}{rcl}h& = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-41\pm\sqrt{4049}}{2(-16)}\\\\ & = & \dfrac{41\pm\sqrt{4049}}{32}\\\\t = \dfrac{41- \sqrt{4049}}{32}&\qquad& t = \dfrac{41+ \sqrt{4049}}{32}\\\\\end{array}\\\)

\(\text{The water balloon will land after $\large \boxed{\mathbf{\dfrac{41+ \sqrt{4049}}{32}}\textbf{ s}} $}\)

(d) Time and maximum height

(i) Time

The axis of symmetry (time of maximum height) is at t = -b/(2a)

\(t = \dfrac{-41}{2(-16)} = \dfrac{41}{32} = \textbf{1.281 s}\)

(ii) Maximum height

The vertex is at y = h(1.281) = h(t) = -16(1.281)² + 41(1.281) + 37  = 63.27 ft

(e) Average rate of change

(i) Arc{1.5,2}

h(1.5) = 62.5

  h(2) = 55

m = (h₂ - h₁)/(t₂ - t₁) = (55 - 62.5)/(2 - 1.5) = -7.5/0.5 = -15 ft/s

The water balloon has started to fall after it has reached peak height, so it is not going very fast

(ii) Arc{2,2.5}

h(2.5) =39.5

m = (39.5 - 55)/(2 - 1.5) = -15.5/0.5 = -31 ft/s

The balloon is in mid-fall, so gravity has caused it to speed up.

(iii) Arc{2.5,3}

h(3) = 16

m = (16 - 39.5)/(2 - 1.5) = -23.5/0.5 = -47 ft/s

The balloon is about to hit the ground, so it is falling at almost its maximum velocity.

Fig. 2 shows the height of the balloon at the above times.

The cost of the dinner without tax or tip is  $22.              

Given,

The sales tax on meals = 10%

Tip she leaved before sales tax is added = 15%

The total amount for dinner = $27.50

We have to find the cost of dinner without adding tax or tip;

Let cost of meals be x.

Then,

She pays 10% of x as a sales tax

So that brings the total up to 100% + 10% = 110%

Before paying, she pays 15% on x as her tip. The tax does not touch the tip.

So that brings the total up to 100% + 10% + 15% = 125% of this is based on x, the cost of the meal.

So 125% of x = 27.50                        

125/100 * x = 27.50                          

125/100 * 100/125x = 100/125 * 27.50

x = 100/125 * 27.50                    

x = 2750 / 125 = 22

That is, the cost of the dinner without tax or tip is  $22.              

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In this question, we are asked to determine the truth-values of two statements involving sets A and B. For each statement, we need to determine if it is true or false. If it is false, we need to provide specific counterexamples by choosing appropriate sets A and B.

a. (A\B) ⊆ A

The statement (A\B) ⊆ A is true for any sets A and B. This is because the set difference (A\B) contains elements that are in A but not in B. Therefore, by definition, every element in (A\B) is also an element of A. There are no counterexamples to this statement.

b. A^c ⊆ (AUB)

The statement\(A^c\) ⊆ (AUB) is true for any sets A and B. This is because the complement of A, denoted as \(A^c\), contains all elements that are not in A.

On the other hand, the union of A and B, denoted as (AUB), contains all elements that are in A or in B or in both.

Since the complement of A contains all elements not in A, it includes all elements in B that are not in A as well.

Therefore, \(A^c\) ⊆ (AUB) holds true for any sets A and B. There are no counterexamples to this statement.

In conclusion, both statements are true for any sets A and B, and there are no counterexamples.

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the surface area of the regular pyramid is approximately  \(40sqrt(14) + 43.3 mm^2.\)To find the surface area of a regular pyramid, we need to find the area of each triangular face and add them together, then add the area of the base.

Let's start with finding the area of each triangular face. Since the pyramid is regular, all the triangular faces will be congruent, so we just need to find the area of one.

We know that the base of the triangle is 10 mm, and the height of the triangle is half the distance between the apex (the point at the top of the pyramid) and the base. Since the pyramid is regular, the apex is directly above the center of the base.

The height of the pyramid can be found using the Pythagorean theorem, where the height of the pyramid (h) is the hypotenuse of a right triangle with the base (b) and half the slant height (s) as the legs.

\(s^2 = hr^2 - (b/2)^2\)

We know the base is 10 mm and the height of the big triangle is 9 mm, so the half slant height is:

\(s = sqrt(h^2 - (b/2)^2) = sqrt(9^2 - (10/2)^2) = sqrt(81 - 25) = sqrt(56) = 2sqrt(14)\)

Now we can find the area of one triangular face using the formula:

Area = 1/2 x base x height

Area = 1/2 x 10 mm x 2sqrt(14) mm = \(10sqrt(14) mm^2\)

Since there are four triangular faces, the total area of the triangular faces is:

4 x 10sqrt(14) mm{power}2 = \(40sqrt(14) mm^2\)

Finally, we need to add the area of the base, which we know is 43.3 \(mm^2.\)

So the total surface area of the pyramid is:

\(Surface Area = 40sqrt(14) mm^2 + 43.3 mm^2 = 40sqrt(14) mm^2 + 43.3 mm^2 = 40sqrt(14) + 43.3 mm^2\)

Therefore, the surface area of the regular pyramid is approximately \(40sqrt(14) + 43.3 mm^2.\)

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Answer:

nose porque está en una idioma que no se

Answer:

see explanation

Step-by-step explanation:

To show the points are collinear, that is lie on the same line.

Then the slope between A and B, B and C must be equal

Calculate slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = A(- 3, - 1) and (x₂, y₂ ) = B(6, 5)

\(m_{AB}\) = \(\frac{5+1}{6+3}\) = \(\frac{6}{9}\) = \(\frac{2}{3}\)

Repeat with (x₁, y₁ ) = B(6, 5) and (x₂, y₂ ) = C(3, 3)

\(m_{BC}\) = \(\frac{3-5}{3-6}\) = \(\frac{-2}{-3}\) = \(\frac{2}{3}\)

Since the slope between the 2 segments are equal and there is a common point B.

Then the points A, B and C are collinear

The coin is flipped at least 52 times in order to obtain a 99% confidence interval of width of at most . 18 for the probability of flipping a head.

Hence, Option F is correct answer.

In a sample with a number n of people surveyed with a probability of a success of π , and a confidence level of (1-α), we have the following confidence interval of proportions.

\(\pi\) ± z\(\sqrt{\frac{\pi \p(1-\pi )}{n} }\)

z is the z-score that has a pvalue of \(1-\frac{\alpha }{2}\)

Since, the coin is fair, so \(\pi =0.5\).

The margin of error is:

\(M=z\sqrt{(\frac{\pi (1-\pi )}{n} )}\)

99% confidence level:

So \(\alpha =0.01\) ,z is the value of Z that has a p value of 1-\(\frac{0.01}{2}\)=0.995,

so Z= 2.575

We have to flip the coin in order to obtain a 99% confidence interval of width of at most 18 for the probability of flipping a head at least n times.

n is found when M=0.18 .

So

M=\(z\sqrt{\frac{\pi (1-\pi )}{n} }\)

\(0.18=2.575\sqrt{\frac{0.5*0.5}{n} }\)

\(0.18\sqrt{n} =2.575*0.5\)

\(\sqrt{n}=\frac{2.575*0.5}{0.18}\)

\(\sqrt{n} ^{2} =(\frac{2.575*0.5}{0.18} )^{2}\)

n = 51.16

Thus, we have to flip the coin at least 52 times.

Learn more about the Probability here: https://brainly.com/question/24756209

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Answer:

\(5x = - 1 - 1 = 5x \div 5 = - 2 \div 5 = 2 \div 5\)