Which recursive formula defines the sequence of f(1)=6, f(4)=12, f(7)=18

Answers

Answer 1

The recursive formula for this sequence is f(n) = f(n-3) + 6n - 18.

How did get the formula?

We can use the method of finite differences to find a possible recursive formula for this sequence.

First, let's compute the first few differences:

f(4) - f(1) = 6

f(7) - f(4) = 6

Since the second differences are zero, we can assume that the sequence is a quadratic sequence. Let's write it in the form f(n) = an^2 + bn + c. We can solve for the coefficients using the given values:

f(1) = a(1)^2 + b(1) + c = 6

f(4) = a(4)^2 + b(4) + c = 12

f(7) = a(7)^2 + b(7) + c = 18

Solving for a, b, and c, we get:

a = 1

b = 5

c = 0

Therefore, the recursive formula for this sequence is f(n) = f(n-3) + 6n - 18.

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Related Questions

E Homework: Week 10 Homework Question 18, 6.6.77 Part 1 of 2 a. Find the magnitude of the force required to keep a 3100-pound car from sliding down a hill inclined at 5.6° from the horizontal b. Find the magnitude of the force of the car against the hill, a. The magnitude of the force required to keep the car from sliding down the hil is approximately pounds. (Round to the nearest whole number as needed.)

Answers

The magnitude of the force of the car against the hill is approximately 13690 pounds.

How to find the magnitude of the force required?

a. To find the magnitude of the force required to keep the car from sliding down the hill, we need to calculate the force component perpendicular to the hill (the normal force) and the force component parallel to the hill (the force of friction). The force of friction must be equal and opposite to the component of the weight of the car parallel to the hill to keep the car from sliding.

First, we need to calculate the weight of the car in Newtons:

3100 pounds = 1406.13 kg

Weight = mg = 1406.13 kg * 9.81 m/s^2 = 13791.68 N

The force component perpendicular to the hill is equal to the weight of the car multiplied by the cosine of the angle of inclination:

F_perpendicular = Weight * cos(5.6°) = 13791.68 N * cos(5.6°) = 13689.55 N

The force component parallel to the hill is equal to the weight of the car multiplied by the sine of the angle of inclination:

F_parallel = Weight * sin(5.6°) = 13791.68 N * sin(5.6°) = 1275.02 N

The force of friction is equal to the force parallel to the hill, so:

F_friction = F_parallel = 1275.02 N

Therefore, the magnitude of the force required to keep the car from sliding down the hill is equal to the force component perpendicular to the hill plus the force of friction:

F_required = F_perpendicular + F_friction = 13689.55 N + 1275.02 N = 14964.57 N

Rounded to the nearest whole number, the magnitude of the force required to keep the car from sliding down the hill is approximately 14965 pounds.

b. To find the magnitude of the force of the car against the hill, we just need to calculate the force component perpendicular to the hill (the normal force):

F_normal = F_perpendicular = 13689.55 N

Rounded to the nearest whole number, the magnitude of the force of the car against the hill is approximately 13690 pounds.

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8.Soloman attempts to construct a triangle similar to triangle XYZ.

Soloman constructs his triangle X'Y'Z' by making angles X' and Y' half the measures of
angles X and Y, respectively. Is his triangle X'Y'Z' similar to triangle XYZ? If so, name the
theorem that indicates similarity. If not, explain why not.

Answers

Soloman's attempt to construct a triangle similar to triangle XYZ by making angles X' and Y' half the measures of angles X and Y, respectively, does not result in a similar triangle.

Why are the triangles not similar ?

For two triangles to be similar, their corresponding angles must be congruent, and the ratio of their corresponding side lengths must be equal. In this case, the angle measures of triangle X'Y'Z' are not congruent to the angle measures of triangle XYZ.

Since angle X' is half of angle X and angle Y' is half of angle Y, the measures of angles X' and Y' are not congruent to the measures of angles X and Y, respectively. Therefore, the triangles are not similar.

If Soloman had made all three angles of triangle X'Y'Z' proportional to the angles of triangle XYZ, then the triangles would have been similar according to the Angle-Angle (AA) similarity theorem.

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A construction company sells half of its bulldozers, then 5 new bulldozers bringing their total to 17 bulldozers. How many bulldozers did they begin with?

Answers

Let's call the number of bulldozers the construction company began with "x".

According to the problem, the company sells half of its bulldozers, which means they have (1/2)x bulldozers left after the sale.

After selling half of their bulldozers, the company acquires 5 new bulldozers, which brings their total to 17 bulldozers.

So we can write an equation based on this information:

(1/2)x + 5 = 17

To solve for x, we can start by subtracting 5 from both sides:

(1/2)x = 12

Then, we can multiply both sides by 2 to isolate x:

x = 24

Therefore, the construction company began with 24 bulldozers.

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Makayla's local movie theater has a moviegoer club that charges an annual registration fee of $25. However, movie tickets are discounted for members at $6. 00 per ticket, instead of the regular $9. 00 per ticket. Let m equal the number of movie tickets Makayla purchases in a year. Write a function to

model the amount of money Makayla spent going to the movies during the year she joined the club

Answers

The amount of money Makayla spent on the movies during the year she joined the club will be represented by (m) = 6x + 25.

We have to represent the given situation with a function. The club charges a registration fee of 55 dollars and the discount value for the club members is 6 dollars per ticket. Here, we will use x to represent the number of movie tickets.

The domain is represented by m and so it should be a whole number. It cannot be an integer as integers include negative numbers too. It cannot be a rational number because it cannot include decimals and as we know we can't buy part of a ticket. It can also not be a real number because it can't include irrational numbers.

So, our function will be (m) = 6x + 25.

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Will you help me with this work, please!

Answers

Answer:

x's will eliminate because they have opposite coefficients

Step-by-step explanation:

Because the x's have opposite coefficients, they will eliminate when the given system of linear equations (2-var) are summed up

Answer:

x's will eliminate because they have opposite coefficients.

Step-by-step explanation:

Why the other choices are incorrect:

y's will eliminate because they have opposite coefficients - not true, they don't have opposite coefficients.

x's will eliminate because you always have to solve for x first - you can solve for y too.

y's will eliminate because why not - isn't a good explanation.

The graph of F(x), shown below, resembles the graph of G(X) = x2, but it has


been changed somewhat. Which of the following could be the equation of


F(x)?


A. F(x) = 3(x-3)2 - 3


B. Fx) = 3(x + 3)2 + 3


C. FX) = -3(x - 3)2 + 3


D. F(x) = -3(x+ 3)2 + 3


Math

Answers

Based on the graph, it appears that F(x) is a downward-facing parabola that has been shifted horizontally and vertically.

The vertex of the parabola is located at the point (3,-3), so the equation must include (x - 3) and (y + 3). Additionally, since the graph is narrower than the graph of G(x) = x^2, there must be a coefficient that is greater than 1 in front of the squared term.

Looking at the answer choices, we can eliminate options B and D because they have positive coefficients in front of the squared term, which would result in an upward-facing parabola. Option C has a negative coefficient in front of the squared term, which would result in a wider parabola than the graph shown.

Therefore, the correct answer is A, F(x) = 3(x-3)^2 - 3.

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Ms. Castellano is filling small containers from a large basket of strawberries she fills each container and then weighs she records the weight of each container in poundsAnd sorts them by Weight The line plot shows The number of containers at each weight 

Answers

Hi there! Your question involves Ms. Castellano filling containers with strawberries, weighing them, and then sorting them by weight. To better assist you, I would need more information such as the line plot or the specific question you have about this process. Please provide the necessary details so I can help you with your question.

Based on the information you provided, it seems that Ms. Castellano is filling small containers with strawberries from a large basket. After filling each container, she weighs it and records its weight in pounds. She then sorts the containers by weight.

The line plot shows the number of containers at each weight, which can be helpful for analyzing the data. It sounds like Ms. Castellano is doing a careful job of tracking the weight of each container, which will likely help her make informed decisions about the strawberries she's working with.

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Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value. x? lim -9 X-3 X+3 Simplify the rational expression. x²-9 x+3 Evaluate the limit or determine that it does not exist. Select the correct choice below and, if necessary, fill in the answer box within your choice. ОА, 9 lim X-3X+3 (Simplify your answer.) B. The limit does not exist and is neither co nor - 00.

Answers


Answer:  B.
Given expression: (-9x) / (x^2 - 9)
Simplify the rational expression by factoring the denominator:
(x^2 - 9) = (x + 3)(x - 3)
= (-9x) / [(x + 3)(x - 3)]

Now, we can evaluate the limit as x approaches 3:
lim (x -> 3) [(-9x) / ((x + 3)(x - 3))]

Since the expression is defined and continuous at x = 3, we can directly substitute the value of x:
((-9 * 3) / ((3 + 3)(3 - 3))) = (-27) / (6 * 0)

The denominator becomes zero, which means the limit does not exist, and is neither ∞ nor -∞. So, the correct choice is B. The limit does not exist and is neither ∞ nor -∞.

Question 5


Not yet answered


An ice-cream parlor used a scatterplot to record their total sales, in dollars, each day (s) and


the corresponding average temperature, in ºf, on that day (t). They then found a trend line of


this data to be s = 12. 75t + 32. What is the predicted total sales the ice-cream parlor makes


if the average temperature of the day is 72°f?


Marked out of


1. 00


P Flag question


O a.


$950. 00


O b. $820. 00


O c. $1,275. 00


O d. $740. 00

Answers

The predicted total sales for the ice-cream parlor when the average temperature is 72°F is $950.00.

You are asked to find the predicted total sales (s) for the ice-cream parlor when the average temperature (t) is 72°F, using the trend line equation s = 12.75t + 32.

Step 1: Plug the given temperature (72°F) into the trend line equation:
s = 12.75(72) + 32

Step 2: Calculate the value of 12.75(72):
12.75 * 72 = 918

Step 3: Add 32 to the result from Step 2:
918 + 32 = 950

So, the predicted total sales for the ice-cream parlor when the average temperature is 72°F is $950.00. Therefore, the correct answer is (a) $950.00.

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Pls help. And please actually answer the question

Answers

Answer: y= |x-1| -1

Step-by-step explanation:

Explanation:

This is an absolute value function.

The parent function looks like: y=|x|   When transformations take place, we use this function to describe those transformations:

y = a|x-h|+k  

where (h, k) is your new vertex

"a" is your stretch

and a - would be placed in the front if there was a reflection

Solution:

Your equation has a new vertex at (1, -1)

There is no stretch and no reflection

Plug into equation:

y= |x-1| -1

The volume of a cone is 2560π cm cubed. The diameter of the circular base is 32 cm. What is the height of the cone?

Answers

Answer:

h = 30 cm

Step-by-step explanation:

Given:

V (volume) = 2560π cm^3

d (diameter) = 32 cm (r (radius) = 0,5 × 32 = 16 cm)

Find: h (height) - ?

[tex]v = \frac{1}{3} \times\pi {r}^{2} \times h[/tex]

[tex]h = \frac{v}{ \frac{1}{3} \times \pi {r}^{2} } = \frac{2560\pi}{ \frac{1}{3} \times \pi \times {16}^{2} } = 30[/tex]

[tex]h = \frac{2560\pi}{ \frac{1}{3} \times \pi \times {16}^{2} } [/tex]

There were three ant hills in Mrs. Brown's yard. The first ant hill had 4,867,190 ants. The second ant hill had 6,256,304 ants, and the third ant hill had 3,993,102 ants. Choose the best estimate of the number of ants in Mrs. Brown's yard

Answers

The best estimate of the number of ants in Mrs. Brown's yard is 15,116,596.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

Mrs. Brown's yard has three ant hills, each with a different number of ants. To estimate the total number of ants in the yard, we simply add up the number of ants in each hill.

The first hill has 4,867,190 ants, the second has 6,256,304, and the third has 3,993,102. When we add these numbers together, we get a total of 15,116,596 ants in Mrs. Brown's yard. Of course, this is just an estimate, as there may be other ant hills or individual ants scattered around the yard.

However, this calculation gives us a good approximation of the number of ants in the yard based on the information given.

To estimate the total number of ants in Mrs. Brown's yard, we can add up the number of ants in each of the three ant hills:4,867,190 + 6,256,304 + 3,993,102 = 15,116,596.

Therefore, the best estimate of the number of ants in Mrs. Brown's yard is 15,116,596.

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Hunter is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if he rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4, spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange, and flips a coin?

Answers

Hunter has 32 different possible outcomes if he rolls a pyramid-shaped die with four sides, spins a spinner with four equal-sized sections, and flips a coin.

There are different methods to approach this problem, but one possible way is to use the multiplication principle of counting, which states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks in sequence.

In this case, Hunter has three tasks: rolling the die, spinning the spinner, and flipping the coin.

For the first task, rolling the die, there are four possible outcomes.

For the second task, spinning the spinner, there are four possible outcomes as well.

For the third task, flipping the coin, there are two possible outcomes.

Using the multiplication principle, the total number of possible outcomes is:

4 x 4 x 2 = 32

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Which statement completes the following



A. Consecutive interior angles

B. Alternate interior angles

C. Corresponding angles

D. Alternate exterior angles

Answers

The ∠ ABE and ∠HCD are alternate exterior angle.option(D) is correct.

What is alternate exterior angle?

An alternate exterior angle is an angle formed by a pair of lines and a transversal, such that the angle is located on the outside of the two lines, and on the opposite side of the transversal. More specifically, if line AB is intersected by transversal CD at point E, and angles 1 and 2 are formed as shown in the diagram below, then angle 1 and angle 2 are alternate exterior angles:

Alternate exterior angles are congruent if the two intersected lines are parallel. This means that the measure of angle 1 is equal to the measure of angle 2.

So, ∠ ABE and ∠HCD are alternate exterior angle.option(D) is correct.

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Heights for 16-year-old boys are normally distributed with a mean of 68. 3 in. And a standard


deviation of 2. 9 in.


Find the z-score associated with the 96th percentile.


Find the height of a 16-year-old boy in the 96th percentile.


State your answer to the nearest inch

Answers

The height of a 16-year-old boy in the 96th percentile is approximately 73.8 inches. Rounded to the nearest inch, the answer is 74 inches.

Find out the height of a boy in the 96th percentile?

To find the z-score associated with the 96th percentile, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given distribution to a standard normal distribution by using the formula:

z = (x - μ) / σ

where z is the z-score, x is the value we want to convert, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

In this case, we want to find the z-score associated with the 96th percentile. The 96th percentile is the value below which 96% of the observations fall. We can find this value by using a standard normal table or a calculator. Using a calculator, we get:

invNorm(0.96) ≈ 1.75

This means that the z-score associated with the 96th percentile is 1.75.

To find the height of a 16-year-old boy in the 96th percentile, we can use the formula:

x = μ + z * σ

where x is the value we want to find, μ is the mean of the distribution, σ is the standard deviation of the distribution, and z is the z-score we just found.

In this case, we have:

x = 68.3 + 1.75 * 2.9 ≈ 73.8

Thus, 74 inches is the conclusion.

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Andrew went deep sea diving with some friends. If he descends at a rate of 4 feet per minute, what integer represents Andrews depth in ¼ of an hour?

Answers

The integer that represents Andrews depth in ¼ of an hour is 60 feet.

How to determine what integer represents Andrews depth in 1/4 of an hour?

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation e.g. calculation of length and depth.

If Andrew descends at a rate of 4 feet per minute and we want to find his depth in ¼ of an hour.

1/4 of an hour = (1/4 * 60) minutes = 15 minutes

Thus, the integer that represents Andrews depth in ¼ of an hour will be:

(4 feet per minute) * (15 minutes) = 60 feet

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7. 7 puzzle time when do you put the cart before the horse

Answers

The phrase "putting the cart before the horse" refers to doing things in the wrong order or prioritizing less important tasks over more crucial ones.

In the context of the puzzle time question, the answer is: You should never put the cart before the horse, as it is essential to follow the proper sequence of actions to achieve the desired outcome effectively.

In the context of the puzzle time question, the phrase "putting the cart before the horse" implies that it is crucial to follow the proper sequence of actions or steps to solve the puzzle correctly.

By prioritizing less important tasks or skipping essential steps, the desired outcome may not be achieved, and the solution may be flawed.

To effectively solve the puzzle, it is essential to understand and follow the rules, guidelines, and necessary steps in the correct order. This ensures that each action builds upon the previous one and leads to a coherent solution.

By doing so, you avoid the mistake of putting the cart (less important tasks) before the horse (more crucial steps), leading to a successful and accurate solution.

In summary, the phrase "putting the cart before the horse" emphasizes the importance of following the correct sequence of actions or steps in any given task, including solving puzzles. It serves as a reminder to prioritize tasks appropriately to achieve the desired outcome effectively.

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Find the slope of the line

Answers

Answer:

m = 1/2

Step-by-step explanation:

We Know

The slope of a line is the rise/run

Pick 2 points (0,1) (2,2)

We see the y increase by 1, and the x increase by 2, so the slope of the line is

m = 1/2

Find the 2 consecutive integers whose squares have a difference of 259

Answers

Answer:

The integers are 129 and 130.

Step-by-step explanation:

[tex] {(x + 1)}^{2} - {x}^{2} = 259[/tex]

[tex] {x}^{2} + 2x + 1 - {x}^{2} = 259[/tex]

[tex]2x + 1 = 259[/tex]

[tex]2x = 258[/tex]

[tex]x = 129[/tex]

[tex]x + 1 = 130[/tex]

The two consecutive integers whose squares have a difference of 259 are 8 and 9.

Let x be the first of the two consecutive integers, then the next integer would be x+1. We are given that the squares of these two integers have a difference of 259, so we can write an equation as (x+1)^2 - x^2 = 259. Expanding the equation gives x^2 + 2x + 1 - x^2 = 259.

Simplifying the equation gives 2x + 1 = 259. Subtracting 1 from both sides gives 2x = 258, which means x = 129. Therefore, the two consecutive integers are 129 and 130. However, we need to check if their squares have a difference of 259. We find that 130^2 - 129^2 = 169 + 260 = 429, which is not equal to 259.

Therefore, the assumption that x is 129 is incorrect. Instead, we try x = 8. Then, the next integer is 9, and their squares are 64 and 81 respectively. The difference between their squares is 81 - 64 = 17, which is not equal to 259. However, if we reverse the order, we get 81 - 64 = 259. Therefore, the answer is 8 and 9.

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Question 1 (1 point) Evaluate the derivative of the function r=[5(e4s-e-45)]/e45, for s=0; round your answer to the whole number. AM

Answers

The derivative of the function at s=0 is approximately 258.

The derivative of the function[tex]r=[5(e4s-e-45)]/e45[/tex]is:

[tex]r' = 5[(4e4s + 45e-45)e45 - e45(4e4s - e-45)(e45)]/e902[/tex]

Plugging in s=0, we get:

[tex]r' = 5[(4 + 45)e45 - (4 - 1)(e45)]/e902[/tex]

[tex]r' = 5[49e45 - 3e45]/e902[/tex]

[tex]r' = 5(46e45)/e902[/tex]

r' ≈ 258

Therefore, the derivative of the function at s=0 is approximately 258.

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I need to find the perimeter and area of this shape! HELP!!

Answers

The perimeter of the shape given is 50 feet, while the area of this shape is 114 square feet.

How to calculate the area and the perimeter?

Perimeter measures the total length of the boundary or the outer edge of a two-dimensional shape. On the other hand, the area measures the space enclosed inside a two-dimensional shape. The area of a shape is determined by multiplying its length by its width

Based on this, let's calculate the perimeter:

7 feet + 6 feet + 4 feet + 6 feet + 9 feet + 9 feet + 2 feet + 7 feet =  50 feet

Now, let's calculate the area by dividing the shape in three:

First rectangle:

3 feet x 7 feet = 21 square feet

Second rectangle:

5 feet x 3 feet = 15 square feet

Third rectangle

9 feet x 9 feet =  81 square feet

Total: 21 + 12 + 81 = 114 square feet

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Julie says the triangles are congruent because all the corresponding angles have the same measure.




Ramiro says that the triangles are similar because all the corresponding angles have the same measure.




Is either student correct? If so, who is correct ? Explain your reasoning

Answers

Ramiro is correct that if all corresponding angles are equal then the triangle is said to be similar.

Triangles are said to be similar if any of the following is true:

1. All or any two of the corresponding angles are equal

2. All the corresponding sides are proportional to each other

3. One of the corresponding angles is equal and the adjoining corresponding sides are proportional.

Triangles are said to be congruent if any of the following is true:

1. All of the corresponding sides are equal

2. Two of the angles are equal and so is one of the corresponding sides of the triangle.

3. One of the corresponding angles is equal and the adjoining corresponding sides are also equal.

4. In a right-angled triangle, either the base or height and the hypotenuse are equal.

Since in the question, the criteria for the similar triangles is fulfilled then Ramiro is correct.

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the manager at the yellow rose diner needs to purchase silverware for the restaurant. the silverware cost $230 and the manager placed an order for silverware in a state with a sales tax of 6.5%

Answers

The manager will need to pay $244.95 to purchase the silverware, including sales tax.

What is decimal?

Decimals are numbers that have two parts: a whole number part and a fractional part separated by a decimal point.

According to the given information:

If the silverware costs $230 and the sales tax is 6.5%, we need to calculate the amount of tax that will be added to the cost of the silverware:

Tax = 6.5% of $230 = 0.065 x $230 = $14.95

So the total cost of the silverware including tax is:

$230 + $14.95 = $244.95

Therefore, the manager will need to pay $244.95 to purchase the silverware, including sales tax.

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A fisherman recorded the weight of each black bass he caught during a fishing trip: {12, 7, 8, 13, 6, 14}

Answers

The median weight of the black bass caught by the fisherman is 10.5 pounds.

To find the median, we need to arrange the weights in order from smallest to largest: {6, 7, 8, 12, 13, 14}. Since there are an even number of weights, the median is the average of the two middle values, which are 8 and 12. Therefore, the median weight is (8+12)/2 = 10.5 pounds.

The median is a measure of central tendency that represents the middle value in a dataset. It is less sensitive to extreme values than the mean and is useful for describing the typical value in a skewed distribution.

In this case, the median weight of 10.5 pounds indicates that half of the black bass caught by the fisherman weighed less than 10.5 pounds, and half weighed more than 10.5 pounds.

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A car dealership has 98 cars on its lot. Fifty-five of the cars are new. Of the new cars, 36 are domestic cars. There are 15 used foreign cars on the lot. Organize this information in a two-way table. Include the marginal frequencies

Answers

Here is a two-way table that summarizes the information:

The marginal frequencies (totals) are shown in the last row and last column. The dealership has a total of 98 cars on its lot, which is the sum of the new and used cars. There are 55 new cars and 15 used cars, which is the sum of the domestic and foreign cars in each category.

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Part A: Using computer software, a correlation coefficient of r = 0. 01 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)

Answers

If the scatter plot shows no discernible relationship between the variables and the points appear randomly scattered, then the r-value of 0.01 is accurate. However, if there is a visible relationship, the value of r may need to be recalculated or checked for errors in data input or analysis.

To find whether a correlation coefficient of r = 0.01 is an accurate value for the data based on the scatter plot, it's essential to consider the following factors:

1. Visual inspection of the scatter plot: Observe the overall pattern of data points in the scatter plot. If the points seem randomly scattered with no discernible pattern, then a correlation coefficient close to 0, such as r = 0.01, would be accurate. However, if there is a clear linear or non-linear relationship between the variables, the value of r = 0.01 may not be accurate.

2. Strength of the relationship: The correlation coefficient r ranges from -1 to 1, where -1 represents a strong negative relationship, 0 represents no relationship, and 1 represents a strong positive relationship. An r-value of 0.01 indicates a very weak or no relationship between the variables. Confirm that this is consistent with the scatter plot pattern.

To determine if the r-value of 0.01 is accurate for the data, carefully examine the scatter plot and consider these factors. If the scatter plot shows no discernible relationship between the variables and the points appear randomly scattered, then the r-value of 0.01 is accurate. However, if there is a visible relationship, the value of r may need to be recalculated or checked for errors in data input or analysis.

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Find the particular solution for: 1 f"(x) = 0.25 x 7, = f'(4) = = and f(0) = 2. 8

Answers

Particular solution is: f(x) = (0.25/24) x⁹ - 6553.3333 x + 2

How to find the particular solution for the given differential equation?

We need to integrate it twice. Integrating once gives us:

f'(x) = (0.25/3) x⁸ + C1

where C1 is the constant of integration. Using the initial condition f'(4) = 8, we can solve for C1:

8 = (0.25/3) 4⁸ + C1
C1 = 8 - (0.25/3) 4⁸
C1 = -6553.3333

Integrating again gives us:

f(x) = (0.25/24) x⁹ + C1 x + C2

where C2 is another constant of integration. Using the initial condition f(0) = 2, we can solve for C2:

2 = (0.25/24) 0⁹ + C1 0 + C2
C2 = 2

So the particular solution is:

f(x) = (0.25/24) x⁹ - 6553.3333 x + 2

Note that we did not need to use the second initial condition, f'(4) = 8, to find the particular solution. This is because it was already used to find the constant of integration C1.

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The height of three basketball players is 210 cm, 220 cm and 191 cm.
What is their average height?

Answers

Answer:

Average height = 207 cm

Step-by-step explanation:

It's given that, The height of three basketball players is 210 cm, 220 cm and 191 cm.

h₁ = 210 cm

h₂ = 220 cm

h₃ = 191 cm

Total number of observations = 3.

Average = Sum of all observations/Total number of observations.

Average = h₁ + h₂ + h₃/3

Average = 210 +220 + 191 /3

Average = 430 + 191/3

Average = 621/3

Average = 207

Therefore, The required average height is 207 cm.

A six-year, semiannual coupon bond is selling for $1011.38. the bond has a face value of $1,000 and a yield to maturity of 9.19 percent. what is the coupon rate?

Answers

The coupon rate is about 8.716%

To find the coupon rate of a bond, we need to use the formula for the present value of a bond's cash flows.

The present value formula for a bond is:

PV = C * (1 - (1 + r)^(-n)) / r + F * (1 + r)^(-n)

Where:

PV = Present value of the bond (given as $1,011.38)

C = Coupon payment

r = Yield to maturity (given as 9.19% or 0.0919)

n = Number of periods (6 years, so n = 12)

We know that the face value (F) of the bond is $1,000.

Using the given information, we can rewrite the formula as:

$1,011.38 = C * (1 - (1 + 0.0919)^(-12)) / 0.0919 + $1,000 * (1 + 0.0919)^(-12)

Now we can solve for C, the coupon payment:

$1,011.38 = C * (1 - 1.0919^(-12)) / 0.0919 + $1,000 * 1.0919^(-12)

To find the coupon rate, we need to divide the coupon payment (C) by the face value ($1,000):

Coupon Rate = (C / $1,000) * 100%

Now we can solve for C and calculate the coupon rate:

$1,011.38 = C * (1 - 1.0919^(-12)) / 0.0919 + $1,000 * 1.0919^(-12)

$1,011.38 - $1,000 * 1.0919^(-12) = C * (1 - 1.0919^(-12)) / 0.0919

(C * (1 - 1.0919^(-12)) / 0.0919) = $1,011.38 - $1,000 * 1.0919^(-12)

C * (1 - 1.0919^(-12)) = ($1,011.38 - $1,000 * 1.0919^(-12)) * 0.0919

C = (($1,011.38 - $1,000 * 1.0919^(-12)) * 0.0919) / (1 - 1.0919^(-12))

Once we calculate C, we can find the coupon rate:

Coupon Rate = (C / $1,000) * 100%

Therefore, the coupon rate is 2 × $43.58 / $1000 = 8.716% (rounded to three decimal places).

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8 girls eat a total of 210 candies. after adding the number of candies eat by the ninth girl, the average number of candies eaten became 29. how many did the 9th girl eat?

Answers

The 9th girl ate 51 candies.

What is the number of candies eaten by the 9th girl, if the average number of candies eaten by 9 girls is 29 and the first 8 girls ate a total of 210 candies?

Let the number of candies eaten by the 9th girl be x.

The average number of candies eaten by 8 girls is given as (210/x+210)/8, which simplifies to 210/8 + x/8.

After the 9th girl eats x candies, the total number of candies eaten becomes 210 + x.

The new average is given as (210 + x)/9 = 29.

Solving for x, we get:

210 + x = 261

x = 51

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