The diameter of the mirror with the frame is 17
inches. To the nearest hundredth, what is the area of only the frame? Use 3.14
for π

Finding the area of the circle of spilled juice as a function of time is: j(t) = πr(t)²

An equation is mathematical statement that asserts  equality of two expressions. It contains one or more variables, and typically consists of terms on either side of equals sign.

Part A:

Let the radius of the circular pattern be r at time t. Then, we have:

j = πr²

Taking the derivative of both sides with respect to time, we get:

dj/dt = 2πr(dr/dt)

Since the rate of change of the radius is unknown, we can express it in terms of the rate of change of j:

dr/dt = (1/2πr)(dj/dt)

Substituting this expression for dr/dt back into our original equation, we get:

j = πr²

dj/dt = π(2r)(dr/dt)

dj/dt = 2πr(dr/dt)

dj/dt = 2πr(1/2πr)(dj/dt)

dj/dt = dj/dt

Therefore, the area of the spilled juice as a function of time is:

j(t) = πr(t)²

Part B:

If we assume that the rate of change of the radius is constant over the first 2 minutes, we can use the formula for the area of a circle to find the area of the spilled juice after 2 minutes:

j(2) = πr(2)²

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The final message would be "ABCE"

It prompts the user to enter the number of people (N), the letters assigned to each person (S), and the forwarding indices (A).

It initializes a message array with the first letter (S[0]).

It follows the forwarding chain until it reaches the 0th person. For each person K in the chain, it appends the corresponding letter (S[A[K]]) to the message.

It terminates the message with a null character (\0) and prints the final message.

The C program will be:

#include <stdio.h>

#include <stdlib.h>

#define MAX_N 100

int main() {

   char S[MAX_N];

   int A[MAX_N];

   int N, K;

   printf("Enter the number of people (N): ");

   scanf("%d", &N);

   printf("Enter the letter assigned to each person:\n");

   for (K = 0; K < N; K++) {

       printf("S[%d]: ", K);

       scanf(" %c", &S[K]);

   }

   printf("Enter the forwarding indices:\n");

   for (K = 0; K < N; K++) {

       printf("A[%d]: ", K);

       scanf("%d", &A[K]);

   }

   char message[MAX_N];

   message[0] = S[0];

   K = 0;

   while (A[K] != 0) {

       message[K+1] = S[A[K]];

       K = A[K];

   }

   message[K+1] = '\0';

   printf("Final message: %s\n", message);

   return 0;

}

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For the function (g o f)(x/2) the value is obtained as 2x + 11.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The function g(x) is given as g(x) = 4x - 1.

The function f(x) is given as f(x) = x + 3.

To find (g o f)(x/2), we need to first find f(x/2) and then substitute this value into g(x) in place of x.

f(x) = x + 3

So, f(x/2) = (x/2) + 3

Now, substitute this into the equation of g(x) in place of x -

g(x) = 4x - 1

g(f(x/2)) = 4(f(x/2)) - 1

= 4((x/2) + 3) - 1 (substituting f(x/2))

= (4x/2 + 12) - 1

= 2x + 11

Therefore, the value is (g o f)(x/2) = 2x + 11.

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Answer:

Step-by-step explanation:

Answer:

They need 8 vans.

Step-by-step explanation:

8 × 9 is 72. If you have 8 vans that carry 9 students each, you will have room for 72 students. Then you have enough room for 70 students.

If you only have 7 vans you can only transport 7 × 9, or 63 students. That is not enough. They need 8 vans.

Answer:

[tex]\boxed{\mbox{\large{\quad 54\quad }}} \quad\text{ 25\% of last year's attendance}\\\\\boxed{\mbox{\large{\quad 216\quad }}}\quad\text{100\% of last year's attendance}\\\\[/tex]  

Step-by-step explanation:

If we let x be the number of attendees last year then since this year's attendees 270 is 125% of x we get

125% of x = 270

125% as a decimal = 125/100 = 1.25

So we get the equation
1.25x = 270

Divide by 1.25 to get

1.25x/1.25 = 270/1.25

x = 216

So there were a total of 216 attendees last year

25% of last year attendees = 0.25 x 216 = 54

By looking at the logistic model of US population, it can be said that the population will exceed 600 million by the year 2148.

(a) The logistic model for the US population is given by P(t) = (C/1 + Ae^(-kt)), where C is the carrying capacity, A is a constant, k is a constant, and t is time. Given that the carrying capacity for the US population is 800 million and the population was 282 million in 2000, we can formulate the logistic model as follows:

P(t) = (800/1 + Ae^(-kt))

To find the value of A, we can plug in the initial conditions. Let t = 0 correspond to the year 2000 and P(0) = 282:

282 = (800/1 + Ae^(0))
282 = (800/A + 1)
A = (800/282) - 1
A = 1.84

Therefore, the logistic model for the US population is:

P(t) = (800/1 + 1.84e^(-kt))

(b) To determine the value of k in the model, we can use the fact that the population in 2010 was 309 million. Let t = 10 correspond to the year 2010 and P(10) = 309:

309 = (800/1 + 1.84e^(-10k))
1.84e^(-10k) = (800/309) - 1
e^(-10k) = 0.593/1.84
-10k = ln(0.593/1.84)
k = -0.076

Therefore, the value of k in the model is k = -0.076.

(c) To predict the US population in the years 2100 and 2300, we can plug in the values of t = 100 and t = 300 into the model:

P(100) = (800/1 + 1.84e^(-100(-0.076))) = 535.7 million
P(300) = (800/1 + 1.84e^(-300(-0.076))) = 762.2 million

Therefore, the predicted US population in the year 2100 is 535.7 million and in the year 2300 is 762.2 million.

(d) To predict the year in which the US population will exceed 600 million, we can set P(t) > 600 and solve for t:

(800/1 + 1.84e^(-kt)) > 600
1.84e^(-kt) < (800/600) - 1
e^(-kt) < 0.333/1.84
-kt < ln(0.333/1.84)
t > -ln(0.333/1.84)/k

Using the value of k from part (b), we get:

t > -ln(0.333/1.84)/(-0.076) = 147.7

Therefore, the population of US will exceed 600 million by the year 2148.

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Answer:8%

Step-by-step explanation:Since the cards are put back after each pick, the two picks are independent events.

The probability of picking a 4 on the first pick is 1/5, as there is one card with a value of 4 out of five cards in total.

The probability of picking a number greater than 4 on the second pick is 2/5, as there are two cards with values greater than 4 (5 and 6) out of five cards in total.

The probability of both events occurring (picking a 4 and then a number greater than 4) is the product of the probabilities of each event:

1/5 x 2/5 = 2/25

So the probability of picking a 4 and then picking a number greater than 4 is 2/25.

To express this as a percentage, we can multiply by 100:

2/25 x 100 = 8%

Therefore, the probability of picking a 4 and then picking a number greater than 4 is 8%.

The correct way to name the image is Southwest Vector BA, indicating the direction of the vector from B to A.

Vector BA : This notation indicates that the vector starts at point B and ends at point A, and it is read as "vector B-A" or "B-A vector". The order of the letters reflects the direction of the arrow, from B to A.

Arrow SW or SW arrow: This notation indicates the direction of the vector, which is towards the southwest, and it is read as "arrow southwest" or "southwest arrow". The order of the letters reflects the direction of the vector, from the northwest to the southeast.

Southwest Vector BA : This notation combines both the direction and the points of the arrow, and it is read as "southwest vector B-A" or "B-A southwest vector". The order of the words reflects the direction of the vector, from the northwest to the southeast, and the order of the letters reflects the starting and ending points of the arrow.

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The value of x in its simplest form is x = 67√2 = 94.75.

The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilise the sine function. The ratio between the side perpendicular to the angle and the hypotenuse is known as the sine of an angle in a right-angled triangle.

The relation between the opposite side and the hypotenuse is given by the sine function.

Thus,

sin (45) = opposite side / hypotenuse = 67 / x

1 / √2 = 67/x

x = 67√2 = 94.75

Hence, the value of x in its simplest form is x = 67√2 = 94.75.

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The shape of the histogram will remain the same but will stretch horizontally.

1. Histograms Suppose that the line of code data.hist('x') generated Histogram A and the line of code data.hist('y') generated Histogram B. This is because Histogram A shows the distribution of the x values and Histogram B shows the distribution of the y values.

The x-axis of Histogram A corresponds to the x values and the y-axis corresponds to the frequency of those values. Similarly, the x-axis of Histogram B corresponds to the y values and the y-axis corresponds to the frequency of those values.

2. The new histogram generated by running new_data.hist('x') will look similar to Histogram A, but the x values will be multiplied by 5. This means that the x-axis will have larger values and the bars will be shifted to the right. The y-axis, which corresponds to the frequency of the x values, will remain the same.

The overall shape of the histogram will also remain the same, but it will be stretched horizontally.

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The probability that ht/th occurs before hh, given that the first coin toss is H or T, is 1/4.

To find the probability that ht/th occurs before hh, by conditioning on the first coin toss is as follows: The sample space can be represented as T or H. 1) If the first toss is a T, then the following toss should be an H to obtain the sequence ht, which is what we want. The probability of this event is 1/2. If the second toss is T, we get the sequence tt, and the process repeats.

2) If the first toss is an H, then we need to obtain the sequence th. The probability of this event is 1/2. If we obtain the sequence hh, the process repeats. We now have two cases that must be considered: case 1: If the first toss is a tail, then the probability that ht occurs before hh can be calculated as follows:

P(ht occurs before hh|first toss is a T) = P(ht occurs before hh|TT)P(TT)+ P(ht occurs before hh|HT)P(HT)= 0 * 1/4 + (1/2) * 1/2= 1/4Therefore, the probability of ht occurring before hh, given that the first toss is a T, is 1/4. case 2: If the first toss is an H, then the probability that ht occurs before hh can be calculated as follows:

P(ht occurs before hh|first toss is an H) = P(ht occurs before hh|TH)P(TH)+ P(ht occurs before hh|HH)P(HH)= (1/2) * 1/2 + 0 * 1/2= 1/4Therefore, the probability of ht occurring before hh, given that the first toss is an H, is 1/4. Therefore, the probability that ht occurs before hh, given that the first coin toss is H or T, is 1/4.

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Answer:

Shirley's water bottle holds 4 quarts when it is half full.

Step-by-Step-Explanation

If the second bottle is one-third full and holds 2 quarts, then it means that it can hold a total of 2 / (1/3) = 6 quarts when completely full.

Let's call the amount of water in Shirley's bottle "x" quarts. We know that when she pours it into the second bottle, it becomes completely full with 6 quarts. So we can set up the equation:

x + 2 = 6

Solving for x, we get:

x = 6 - 2

x = 4

Answer:

I think its (C) - 2/3

By handing the survey to every third person, Kyle used a: 1. nonrandom sampling.

Each student in his class had an unequal chance of being selected to receive the survey.

A statement that best explain why Kyle's survey may be biased is: 3. Two out of every three students entering Kyle's class didn't receive the survey.

In Mathematics and Statistics, there are different types of sampling used by researchers and these include the following;

Based on the information provided about the survey conducted by Kyle, we can reasonably infer and logically deduce that a systematic sampling method (nonrandom sampling) was adopted.

Consequently, the survey may be considered as being biased because each student in Kyle's class had an unequal chance of being selected to receive the survey.

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The population of salmonella enterica after 75 hours is 80 grams, which is equivalent to 8 cells. That is, the population of salmonella enterica has increased from 1 cell to 8 cells after 75 hours.

Exponential growth is a pattern of growth that is rapid and often exponential. It occurs when the rate of change in a variable is proportional to the variable's current value. This means that a small change in the variable can result in a large increase or decrease in its value over a short period of time.

The population of salmonella enterica bacteria doubles every 25 hours. This means that each hour, the population of the bacteria increases by a factor of two. To calculate the number of bacteria after 75 hours, we need to apply the concept of exponential growth. Exponential growth is a process by which the value of a variable increases exponentially, or multiplicatively, over time.

Assuming that the population of salmonella enterica was initially 10 grams, the population after 75 hours can be calculated using the equation:

Population = 10 * 2⁽⁷⁵÷²⁵⁾

The population after 75 hours is thus 10 * 2³ = 80 grams. This means that the population of salmonella enterica has increased from 10 grams to 80 grams after 75 hours.

Since each cell of salmonella enterica has a mass of 10 grams, the population after 75 hours can also be calculated in terms of cells. The population of salmonella enterica after 75 hours is 80 grams, which is equivalent to 8 cells. That is, the population of salmonella enterica has increased from 1 cell to 8 cells after 75 hours.

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An African elephant weighs 88,000 ounces. To convert pounds to ounces, we need to know the conversion factor between the two units.

There are 16 ounces in one pound, which means we can convert pounds to ounces by multiplying the weight in pounds by 16. A pound is equal to 28 grams. A one-quarter ounce contains seven grams. A half-ounce has 14 grams in it. One-eighth of an ounce has 3.5 grams.

In this case, the African elephant weighs 5,500 pounds. To find out how many ounces that is, we can multiply 5,500 by 16:

Therefore, the African elephant weighs 88,000 ounces.

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Answer: y=3/2x+4

Step-by-step explanation: The equation for the line below is [tex]y=\frac{3}{2}x +4[/tex]

This equation is correct because the formula is y=mx+b. m is the slope and you can see the slope is [tex]\frac{3}{2}[/tex] and x is to represent that the number is the slope. The b, or +4 represents where the line crosses over the x-axis.

The equation is [tex]y=\frac{3}{2}x +4[/tex]

Let me know if you have any other questions about this problem.

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The surface area of the cylinder is 420 in^2. The base area of the cylinder is 67.02 in².

Given that the surface area of the cylinder is 420 in², we have to find its base area.

To find the base area of the cylinder, we have to use the formula for the surface area of the cylinder.

The formula is:

Surface area of the cylinder = 2πr(r + h)

Here, π = 3.14,

r is the radius of the base of the cylinder, and h is the height of the cylinder.

Since the base is a circle, the area of the base is given by the formula:

A = πr²We can calculate the radius of the cylinder using the given surface area.

420 = 2πr(r + h)420

      = 2 × 3.14 × r(r + h)420

      = 6.28 r² + 6.28 rh

Now we need to assume some value of h. For example, if we take h = 7, then we have:

420 = 6.28 r² + 6.28 r (7)

420 = 6.28 r² + 43.96 or

6.28 r² + 43.96 r - 420 = 0

Now we can solve this quadratic equation to find the value of r. Using the quadratic formula:

r = [-b ± sqrt(b² - 4ac)] / 2a

Putting a = 6.28, b = 43.96, and c = -420, we get:

r = [-43.96 ± sqrt(43.96² + 4(6.28)(420))] / 2(6.28)

r = [-43.96 ± sqrt(3291.84)] / 12.56r = (-43.96 + 57.40) / 12.56 or

r = (-43.96 - 57.40) / 12.56r = 1.10 or r = -1.82

We can discard the negative value of r, so we have:r = 1.10

Now we can calculate the base area of the cylinder using the formula for the area of a circle.A = πr²A = 3.14 × (1.10)²A = 3.14 × 1.21A = 3.80 (rounded to the nearest hundredth)

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Answer:

1

Step-by-step explanation:

17 is a prime number, so only 1 and 17 are its factors. 17 is not a factor of either 22 or 46, but 1 is.

Using the system of equations, we found that :

plane speed = 267.00 mph; wind speed = 27.00 mph

What is meant by an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

The distance travelled =  1176.00 miles

Time taken = 4 hours and 54 minutes = 4*60 + 54 = 294 minutes

The times taken for return flight = 4 hours = 240 minutes

Let,

x = speed of the plane

y = speed of the wind

In a headwind the speed reduces.

So the relative speed of the plane is (x-y)

distance = speed * time

1176 = (x-y) * 294

x-y = 4

Now for the return flight, the wind is tailwind and the speed increases.

So the relative speed of the plane is (x+y).

1176 = (x+y) * 240

x + y = 4.9

Now we have a system of equations.

x - y = 4

x + y = 4.9

Adding,

2x = 8.9

x  = 4.45 miles/min = 4.45 * 60 miles/hour = 267 miles/hour

and

y = 4.9 - x = 4.9 - 4.45 = 0.45 miles/min = 0.45*60 = 27 miles/hour

Therefore using the system of equations, we found that :

plane speed = 267.00 mph; wind speed = 27.00 mph

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Answer:

We can start by simplifying both sides of the equation:

5x² + 18x = 25x + 15 + 3x²

2x² - 7x - 15 = 0

Now we need to factor this quadratic equation:

2x² - 7x - 15 = (2x + 3)(x - 5)

Setting each factor equal to zero gives us the solutions:

2x + 3 = 0 or x - 5 = 0

Solving for x, we get:

x = -3/2 or x = 5

Therefore, the solutions to the quadratic equation are x = -3/2 and x = 5.

So, the correct answer is (x - 5)(2x+3).

Answer:

Step-by-step explanation:

If Y+2.91=11, simply subtract 2.91 from 11. 11-2.91 is 8.09. Y is 8.09.

Answer:

B) 8.09

Equation:

y + 2.91 = 11

To solve for the value of y, we need to isolate y on one side of the equation by performing the same operation on both sides.

Start by subtracting 2.91 from both sides:

y + 2.91 - 2.91 = 11 - 2.91

Finally, all we need to do is simplify:

y = 8.09

Therefore, the value of y that makes the equation true is 8.09.

Step-by-step explanation:

284.8 = 282.2 ( b)^1             1 is the number of years....looking for 'b'

284.8 / 282.2 = b = ~ 1.009

P(t) = 282.2 ( 1.009)^t         where P(t) is in millions and :

The variable t represents the number of years since July of 2000. Round your value of b to the nearest thousandth.

The anticipated break-even number of barrels for the following year is 254.40 million per barrel.

a) To compute the break-even number of barrels for the current year, we need to first calculate the total fixed costs and the total variable costs for the year.

Total Fixed Costs = Selling, general, and administrative expenses - Variable Selling, general, and administrative expenses + Operating Income before special items

Total Fixed Costs = 14,439 - (0.5 * 14,439) + 13,275

Total Fixed Costs = $20,494.5 million

Total Variable Costs = Cost of goods sold - Variable Cost of goods sold

Total Variable Costs = 17,803 - (0.75 * 17,803)

Total Variable Costs = $4,450.75 million

Now, we can calculate the contribution margin per barrel as follows:

Contribution Margin per Barrel = (Sales - Variable Costs) / Number of Barrels

Contribution Margin per Barrel = ($45,517 - $4,451) / 500

Contribution Margin per Barrel = $82.132 million / barrel

To find the break-even number of barrels, we can use the following formula:

Break-even Number of Barrels = Total Fixed Costs / Contribution Margin per Barrel

Break-even Number of Barrels = $20,494.5 million / $82.132 million per barrel

Break-even Number of Barrels = 249.53 million barrels

Therefore, the break-even number of barrels for the current year is 249.53 million.

To compute the anticipated break-even number of barrels for the following year, we need to consider the increase in fixed costs due to the new distribution and general office facilities. Assuming all other costs and per-barrel amounts remain constant, the new total fixed costs would be:

New Total Fixed Costs = Total Fixed Costs + Increase in Fixed Costs

New Total Fixed Costs = $20,494.5 million + $400 million

New Total Fixed Costs = $20,894.5 million

Using the same contribution margin per barrel as in the current year, we can calculate the anticipated break-even number of barrels for the following year:

b) Anticipated Break-even Number of Barrels = New Total Fixed Costs / Contribution Margin per Barrel

Anticipated Break-even Number of Barrels = $20,894.5 million / $82.132 million per barrel

Anticipated Break-even Number of Barrels = 254.40 million barrels

Therefore, the anticipated break-even number of barrels for the following year is 254.40 million.

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The correct question would be:

Break-Even Sales Anheuser-Busch InBev SA/NV (BUD) reported the following operating information for a recent year (in millions): $45,517 Sales Cost of goods sold Selling, general, and administrative expenses $17,803 14,439 (32,242) Operating income $13,275 *Before special items In addition, assume that Anheuser-Busch InBev sold 500 million barrels of beer during the year. Assume that variable costs were 75% of the cost of goods sold and 50% of selling, general, and administrative expenses. Assume that the remaining costs are faced. For the following year, assume that Anheuser-Busch InBev expects pricing variable costs per barrel and fixed costs to remain constant, except that new distribution and general office facilities are expected to increase fixed costs by $400 million

a. Compute the break-even number of barrels for the current year. In computing variable and fixed costs and per-barrel amounts, round to two decimal places. Round the break-even number of barrels to one decimal place. million barrels

b. Compute the anticipated break-even number of barbels for the following year Round to one decimal place in millions of barrels million barrels.

The coordinate plane of curve crosses the y-axis at (0, 5), it increases to (2, 8), and then decreases to (6, 2). The graph of the equation, shown below.

The term "graph" can refer to a visual representation of data or information, typically in the form of a diagram or chart. Graphs can be used to show relationships or patterns between different sets of data.

For the given equation,

[tex]h=3Sin [\frac{\pi }{2} (t+2)] +5[/tex]

Follow the steps for drawing the graph,

         [tex]h = 3 Sin [\frac{\pi }{2} (0 + 2)] + 5 = 3 Sin [\pi] + 5 = 5[/tex]

This means that when the ball is at the midpoint of its oscillation                  (i.e., at time t = 0), its height is 5 feet above the equilibrium position.

Using these steps, we can create the graph of the equation, which looks like the below diagram.

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Answer:

64cm³

Step-by-step explanation:

Surface area of a cube is 6a²

6a² = 96

Divide both sides by 6

a² = 16

Square root of both sides

a = 4cm

Volume of a cube is a³

Volume =4³

Volume 64cm³

The slope and the y-intercept of the line that is perpendicular to y = 5x - 2 and passes through the origin are given as follows:

The line for this problem is given as follows:

y = 5x - 2.

Meaning that the slope and the intercept are given as follows:

When two lines are perpendicular, the multiplication of their slopes is of -1, hence the slope of the line perpendicular to y = 5x - 2 is given as follows:

5m = -1

m = -1/5.

The line also passes through the origin, meaning that when x = 0, y = 0, hence the intercept is of zero.

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Answer:

the distance between the two points (-8,-3) and (-1,4) is 7sqrt(2) units.

Step-by-step explanation:

We can use the distance formula to find the distance between the two points:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's substitute the given coordinates:

d = sqrt((-1 - (-8))^2 + (4 - (-3))^2)

d = sqrt(7^2 + 7^2)

d = sqrt(2 x 7^2)

d = 7sqrt(2)

Therefore, the distance between the two points (-8,-3) and (-1,4) is 7sqrt(2) units.

The sum of the first 8 terms of the sequence is 720.

A sequence is a set of numbers that are arranged in a specific order, according to some rule or pattern. Each number in the sequence is called a term, and the position of the term in the sequence is called its index or subscript. Sequences can be either finite or infinite.

We can see that this is an arithmetic sequence with a first term a = 27 and a common difference d = 18. To find the sum of the first 8 terms of the sequence, we can use the formula for the sum of an arithmetic sequence:

Sn = n/2[2a + (n-1)d]

where Sn is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.

Plugging in the values we know, we get:

S8 = 8/2[2(27) + (8-1)(18)]

= 4[54 + 126]

= 4(180)

= 720

Therefore, the sum of the first 8 terms of the sequence is 720.

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