HELP ASAP, 65 POINTS NEED ANSWERS ​

The sum of the rational expression as required to be determined in the task content is; (7x² + 11) / (x² + 6x + 5).

It follows from the task content that the rational expression whose sum is to be determined is;

x / x+1 + 6x / x+5

Therefore, by using the LCM; (x + 1) (x + 5).

Therefore, the sum is as follows;

{x(x + 5) + 6x (x + 1)} / (x + 1) (x + 5).

= (7x² + 11) / (x² + 6x + 5)

Ultimately, the sum as required is; (7x² + 11) / (x² + 6x + 5).

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Answer:

[tex] \frac{x(7x + 11)}{(x + 1)(x + 5)} [/tex]

Step-by-step explanation:

[tex]1. \: \frac{x(x + 5) +6x(x + 1)}{(x + 1)(x + 5)} \\ 2. \: \frac{x(x + 5 + 6(x + 1))}{(x + 1)(x + 5)} \\ 3. \: \frac{x(x + 5 + 6x + 6)}{(x + 1)(x + 5)} \\ 4. \: \frac{x((x + 6x) + (5 + 6))}{(x + 1)(x + 5)} \\ 5. \: \frac{x(7x + 11)}{(x + 1)(x + 5)} [/tex]

The slope of the line that best suits the data is -0.1463.

slope = [tex]\sum (( x -\bar x )( y - \bar y )) / \sum ( x - \bar x ) ^2[/tex]

where x is the number of ice cream treats sold, y is the number of coffee drinks sold, x bar is the mean of the number of ice cream treats sold, and ȳ is the mean of the number of coffee drinks sold.

Using the given data, we find that:

[tex]\bar x =[/tex] (16 + 19 + 28 + 27 + 28 + 36 + 38 + 41 + 41 + 48) / 10 = 32.2

[tex]\bar y =[/tex] (55 + 43 + 51 + 46 + 32 + 36 + 43 + 25 + 10 + 33) / 10 = 36.4

Next, we calculate the terms needed for the formula:

[tex]\sum (( x - \bar x )( y - \bar y ))[/tex] = (16 - 32.2)(55 - 36.4) + (19 - 32.2)(43 - 36.4) + ... + (48 - 32.2)(33 - 36.4) = -686.6

[tex]\sum ( x - \bar x )^2[/tex] = (16 - 32.2)² + (19 - 32.2)² + ... + (48 - 32.2)² = 4690.6

Plugging these values into the formula, we get:

slope = [tex]\sum (( x - \bar x )( y - \bar y )) / \sum ( x - \bar x )^2[/tex] = -686.6 / 4690.6 = -0.1463

Therefore, the slope of the line that best fits the data is -0.1463.

Interpreting the slope in terms of the situation, we can say that for every additional ice cream treat sold, the number of coffee drinks sold decreases by an average of 0.1463.

To write the equation of the line that best fits the data, we use the slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept. We already know the value of m, so we just need to find b. To do this, we can use the mean values of x and y:

y = mx + b

36.4 = (-0.1463)(32.2) + b

b = 41.9

Therefore, the equation of the line that best fits the data is:

y = -0.1463x + 41.9

To estimate the number of coffee drinks sold on a day that 32 ice cream treats were sold using the equation of the line of best fit, we simply substitute x = 32 into the equation and solve for y:

y = -0.1463(32) + 41.9

y ≈ 36.9

So we can estimate that approximately 36.9 coffee drinks were sold on a day that 32 ice cream treats were sold. This conclusion is justified because we used the equation of the line that best fits the data to make the estimate, which takes into account the overall trend of the data and the relationship between the number of ice cream treats sold and the number of coffee drinks sold. However, it's important to note that this is only an estimate and there may be other factors that could affect the actual number of coffee drinks sold on a particular day.

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Answer:

1:3

Step-by-step explanation:

We Know

Arturo earns 1,800 per month.

He pays 600 a month on rent.

What is the ratio of his rent to his monthly income?

The ratio is

600:1800

Simplify by 600; we get the ratio

1:3

So, the ratio of his rent to his monthly income is 1:3

Replacing x with x + 2 means that the graph of f(x) = |x - 4| will be translated 2 units left.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The change from x to x + 2 means that we calculated f(x + 2), thus the graph is translated 2 units left.

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Answer:

Step-by-step explanation:

The distance that the plane can travel in 2x + 1 hours can be found by multiplying the plane's rate (x + 150 miles per hour) by the time (2x + 1 hours):

Distance = Rate × Time

Distance = (x + 150)(2x + 1)

Simplifying this expression, we can use the distributive property of multiplication:

Distance = 2x(x) + 2x(1) + 150(x) + 150(1)

Distance = 2x^2 + 2x + 150x + 150

Finally, we can combine like terms:

Distance = 2x^2 + 152x + 150

Therefore, the expression that represents the distance that the plane can travel in 2x + 1 hours is 2x^2 + 152x + 150.

0 + (-66) Plus 18 = -48 is indeed the common sum for every one of these pairings. Hence, -48 is the solution.

The total of the first n terms in the arithmetic sequence is equal to the sum (addition) of the n terms in AP. It is equal to n split by 2 times total sum of thrice the first term, "a," and the product of difference between the second and first term, "d," also; known as the common difference, plus (n-1), where n is the number of terms to be added.

The following step is to add -62 to all of the three remaining integers to create three new ones: -62 + (-4) (= -66, -62 Plus (-2) = -64, & -62 plus 80 = 18. From these three numbers, we now need to select two pairs that sum up to the same number.

We are able to observe that -66 plus -64 is -130, therefore the answer is 18. We obtain 148 when we multiply 130 by 18. As a result, the following three sets of numbers add up to a single total:

-80 and -80, -62 and - 4, and -148

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Parents Card = 1/6 cards Glen has. 1/6=0.1666667, as a percet 16.6667%

Sister Card = 1/6 cards Glen has. 1/6=0.1666667, as a percet 16.6667%

After answering the provided question, we can conclude that  the oil industry and related sectors were the primary direct beneficiaries.

An expression in mathematics is a collection of representations, octal, and huge corporations that resemble a clear association or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include inclusion, subtraction, rapid spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

Option 2 is the correct response. Texas benefited from OPEC's oil production restrictions in 1973 because it resulted in a significant increase in oil prices, which brought wealth to the state. At the time, Texas was the largest oil-producing state in the United States.

Option 1, 3, and 4 are incorrect. While OPEC's restrictions did increase competition from other countries, which could have affected employment in the oil industry, there is no evidence that it resulted in fewer jobs in Texas overall. Finally, while transportation industries may have benefited indirectly from the increase in oil prices, the oil industry and related sectors were the primary direct beneficiaries.

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Respuesta (Español/Spanish):

20 lapices

Explicación paso-a-paso (Español/Spanish):

Multiplica 28 por 5/7.

Answer (English/Inglés):

20 pencils

Step-by-step explanation (English/Inglés):

Multiply 28 by 5/7

the total number of seats available is 45,000. just by using graph percentage and given information we are able to get answer

what is percentage?

A percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol % (per cent), which means "per hundred".For example, if we say that a student scored 80% on a test, it means that they got 80 out of 100 possible points.

In the given question,

We know that the number of box seats available is 12,600 and the number of club seats available is 5,400.

Let's use the information about the percentages of grandstand and bleacher seats to find their actual numbers.

If grandstand seats make up 42% of the total seats, then we can write:

Grandstand seats = 0.42 x Total seats

Similarly, if bleacher seats make up 18% of the total seats, we can write:

Bleacher seats = 0.18 x Total seats

We can now add up the number of seats in each category to find the total number of seats:

Total seats = Box seats + Club seats + Grandstand seats + Bleacher seats

Total seats = 12,600 + 5,400 + 0.42 x Total seats + 0.18 x Total seats

Simplifying the equation, we get:

Total seats = 18,000 + 0.6 x Total seats

0.4 x Total seats = 18,000

Total seats = 45,000

Therefore, the total number of seats available is 45,000..

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Answer: $4.40 is the cost for the call

For the given functions of x Table 2 is a one to one function. Table 2 is not a one to one function. Table 3 is not a one to one function.

A one-to-one function is one in which every distinct input (or x-value) corresponds to a distinct output (or y-value). To put it another way, no two distinct inputs may result in the same outcome. Also, the same input cannot result in more than one output.

Injective functions are another name for one-to-one operations. They are crucial in many branches of mathematics, such as geometry, algebra, and calculus. A function's inverse, or new function that "undoes" the previous function by flipping the input and output variables, is defined in particular using one-to-one functions.

Table 1:

Because each x-value corresponds to a distinct y-value and each y-value to a unique x-value, Table 1 depicts y as a function of x and is one-to-one.

Table 2:

Because there are two separate y-values associated with the x-value of 10, Table 2 does not show y as a function of x. (8 and 12).

Table 3:

Because the y-value of 8 has two separate x-values, Table 3 does not show y as a function of x. (10 and 13).

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The answers of the given question are (12) the maximum angle at which the ball can be hit and land within the court is approximately 9.56° degrees. (14) the length of the ramp is approximately 35.5 inches.

an angle is a measure of the difference in direction between two lines or surfaces that meet at a point. It is defined as the ratio of the length of the arc that separates two intersecting lines or planes to the radius of the circle or sphere that the arc belongs to.

Angles are typically measured in degrees or radians, with a full circle consisting of 360° degrees or 2π radians. Angles can be acute (less than 90° degrees), right (exactly 90° degrees), obtuse (greater than 90° degrees but less than 180° degrees), or straight (exactly 180° degrees).

(12). To determine the maximum angle at which the ball can be hit and land within the court, We can use the following formula to solve the problem:

d = v² * sin(2θ) / g

Where:

d = the horizontal distance the ball will travel

v = the initial velocity of the ball

θ = the launch angle

g = the acceleration due to gravity

We can assume that the initial velocity of the ball is constant and equal to the velocity at which the ball was hit. Also, we know that the height at which the ball was hit is 2.44m, so we can use the following formula to find the initial velocity of the ball:

v² = 2gh

Putting in given values, we will get:

v² = 2 * 9.81 m/s² * 2.44m = 47.9424

v = √(47.9424) = 6.92 m/s (rounded to two decimal places)

we can plug in the given values and solve for θ:

9.4 = (6.92)² * sin(2θ) / 9.81

sin(2θ) = 9.4 * 9.81 / (6.92)² = 0.3209

2θ = sin^-1(0.3209) = 19.12

θ = 9.56° degrees (rounded to the nearest degree)

Therefore, the maximum angle at which the ball can be hit and land within the court is approximately 9.56° degrees.

(14). To find the length of the ramp, we can use the following formula:

length = height / sin(θ)

Where:

height = 12 inches

θ = 17° degrees

Plugging in the given values, we get:

length = 12 / sin(17) = 35.5 inches (rounded to one decimal place)

Therefore, the length of the ramp is approximately 35.5 inches.

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Answer:

A'(2, 3)

Step-by-step explanation:

When a point is reflected across the x-axis, its y-coordinate is negated while its x-coordinate remains unchanged.

Therefore, reflecting point A(2,-3) across the x-axis results in a new point with the same x-coordinate but a negated y-coordinate:

A'(2, 3)

So the coordinates of the reflected point A' are (2, 3).

Plane A 4 hours to travel 2300 miles.

Plane takeoff angle.

Angel

During take off, a plane leaves the ground and travels in a straight line until it reaches a height of 10 km. The distance the plane flies during take off should be in the range 57 km to 62 km. What is the smallest possible angle that the path of the plane could make with the ground? Give your answer in degrees to 1 d. p.

Let's assume that the plane travels a distance of x km during take off and reaches a height of 10 km. Then, using trigonometry, we can find the angle θ between the ground and the path of the plane:

tan(θ) = 10/x

We want to find the smallest possible angle θ, which means we need to maximize x. From the given information, we know that x must be in the range 57 km to 62 km. Therefore, to maximize x, we choose x = 62 km.

Plugging this into the equation above, we get:

tan(θ) = 10/62

θ = arctan(10/62) ≈ 8.8°

Therefore, the smallest possible angle that the path of the plane could make with the ground is approximately 8.8 degrees.

Angel

Xochitl spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7425 feet. Xochitl initially measures an angle of elevation of 19° to the plane at point A. At some later time, she measures an angle of elevation of 37° to the plane at point B.

Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary

Let's assume that the distance from Xochitl to point A is d1 and the distance from Xochitl to point B is d2. We want to find the distance the plane traveled from point A to point B, which is the difference between d1 and d2.

From the given information, we can set up the following two equations:

tan(19°) = 7425/d1

tan(37°) = 7425/d2

Solving for d1 and d2, we get:

d1 = 7425/tan(19°) ≈ 22977.6 feet

d2 = 7425/tan(37°) ≈ 13060.2 feet

Therefore, the distance the plane traveled from point A to point B is:

d1 - d2 ≈ 9917.4 feet ≈ 3021 meters

Rounding to the nearest foot, we get that the distance the plane traveled from point A to point B is approximately 9917 feet.

Angel

Plane B is flying 75mph 75 ⁢ mph faster than Plane A. Find the time it takes for Plane A to travel 2300 2300 miles if it takes Plane B the same amount of time to travel 2600 2600 miles.

Let's start by using the formula for distance, rate, and time:

distance = rate x time

Let's assume that Plane A's speed is r mph. Then we know that Plane B's speed is r + 75 mph.

We also know that Plane A travels 2300 miles and Plane B travels 2600 miles. Since they take the same amount of time to travel their respective distances, we can set up the following equation:

2300/r = 2600/(r + 75)

To solve for r, we can cross-multiply and simplify:

2300(r + 75) = 2600r

2300r + 172500 = 2600r

300r = 172500

r = 575 mph

Now that we know Plane A's speed, we can use the formula for distance, rate, and time to find the time it takes for Plane A to travel 2300 miles:

distance = rate x time

2300 = 575 x time

time = 4 hours

The lost annual income from savings on those refunds would be $43,032,000.

o calculate the lost annual income from savings on those refunds, we need to first calculate the total amount of money refunded, and then calculate the lost income from that amount.

The total amount refunded would be:

421,000 people x $3,400 per person = $1,434,400,000

Next, we can calculate the lost income from that amount at an interest rate of 3 percent. To do this, we can use the simple interest formula:

I = P x R x T

Where:

I = interest

P = principal (the amount refunded)

R = interest rate (as a decimal)

T = time (in years)

Substituting the values we have:

I = $1,434,400,000 x 0.03 x 1

I = $43,032,000

Therefore, the lost annual income from savings on those refunds would be $43,032,000.

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y=3

Step-by-step explanation:

3×5=15

2×3=6

15-6=9

The five-number summary for data and construct a box plot is: 59, 62, 65, 70, 77
The IQR for the data is 8.

What is median ?

The median is a measure of central tendency in statistics. It is the value separating the higher half from the lower half of a data sample. To find the median of a data set, the data is first arranged in ascending or descending order, and then the middle value is identified. If the data set has an odd number of values, the middle value is the median. If the data set has an even number of values, the median is the average of the two middle values. The median is a useful measure of central tendency when the data contains outliers or extreme values that may affect the mean.

According to the question:
a. The five-number summary consists of the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum. To find these values:

Minimum: 59

Q1: the median of the lower half of the data, which is the median of the first 20 values (when ordered from smallest to largest): (62 + 62) / 2 = 62

Median (Q2): the middle value when the data is ordered from smallest to largest: (65 + 65) / 2 = 65

Q3: the median of the upper half of the data, which is the median of the last 20 values: (70 + 70) / 2 = 70

Maximum: 77

Therefore, the five-number summary is: 59, 62, 65, 70, 77

To construct a box plot, we can draw a number line and mark the five-number summary points. We then draw a box from Q1 to Q3, with a line at the median (Q2) inside the box. Finally, we draw whiskers from the box to the minimum and maximum values, unless there are outliers that are more than 1.5 times the interquartile range (IQR) away from the box.

b. The interquartile range (IQR) is the difference between the upper and lower quartiles, or Q3 - Q1. From part (a), we have Q1 = 62 and Q3 = 70, so:

IQR = Q3 - Q1 = 70 - 62 = 8

Therefore, the IQR for the data is 8.

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4,110 cm³ of beverage needs to be added to fill the dispenser completely.

The beverage dispenser is a rectangular prism, so we need to use the formula of volume of a rectangle prism to find the total amount of beverage in the dispenser. Now subtract the amount of beverage initially the dispenser have from the total amount of beverage dispenser.

Here we have

A beverage dispenser at a party measured 14 cm x 13 cm x 60 cm.

Before it was filled the beverage dispenser was only 5/8 full.

The total volume of the beverage dispenser can be calculated by multiplying its dimensions:

V_total = 14 cm x 13 cm x 60 cm = 10,920 cm³

If the dispenser was only 5/8 full, then the remaining volume that needs to be filled will be equal to 3/8  

V_remaining = (3/8) x V_total = (3/8) x 10,920 cm³ = 4,110 cm³

Therefore,

4,110 cm³ of beverage needs to be added to fill the dispenser completely.

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The probability of exactly 2 nurses preferring the night shift in a random sample of 10 nurses is approximately 0.302 or 30.2%.

A sort of probability distribution known as a binomial probability defines the likelihood of a certain number of successes (or "positive outcomes") in a predetermined number of independent trials with just two potential outcomes (often referred to as "success" and "failure").

According to the given information:

This is a binomial probability problem since we have a fixed number of trials (sampling 10 nurses) and two possible outcomes (nurses preferring or not preferring the night shift) with a known probability of success (20% or 0.2).

The probability of getting exactly 2 nurses who prefer the night shift can be calculated using the following formula:

P(X = k) = (n choose k) *[tex]p^{k} *(1-p)^{n-k}[/tex]

where:

P(X = k) is the probability of getting k successes (2 nurses who prefer the night shift)

n is the total number of trials (10 nurses)

k is the number of successes we want (2 nurses who prefer the night shift)

p is the probability of success (0.2, or 20%)

(n choose k) is the number of ways to choose k items from a set of n items, which can be calculated using the binomial coefficient formula: (n choose k) = n! / (k! * (n-k)!)

Substituting the values into the formula, we get:

P(X = 2) = (10 choose 2) * [tex]0.2^2 * 0.8^8[/tex]

= 45 * 0.04 * 0.16777216

= 0.301989888

Therefore, the probability of exactly 2 nurses preferring the night shift in a random sample of 10 nurses is approximately 0.302 or 30.2%.

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Therefore option c is the best answer:

Define  weight?

Weight is a measure of the force exerted on an object due to gravity. It is proportional to the mass of the object and the acceleration due to gravity. The standard unit of weight is the Newton (N) in the International System of Units (SI).

What exactly is MASS?

Mass is a measure of the amount of matter in an object. It is a scalar quantity and is usually measured in kilograms (kg) in the International System of Units (SI).

A box had 6pencils each pencil wt. x gram.

The 6pencil wt. a combined total is 54 gram.

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Answer:

Step-by-step explanation:

You want the different ways sides of similar triangles can be shown as proportional.

From shorter to longer, the corresponding sides in the similar triangles are ...

Smaller ... Larger

  b . . . . . . . e

  a . . . . . . . d

  c . . . . . . . f

The proportions are written by choosing two letters and their corresponding letters. The two chosen can be from different columns (part 1) or from the same column (part 2). The corresponding letters are written in the same place in the proportion fraction

  [tex]\dfrac{a}{d}=\dfrac{b}{\boxed{e}}=\dfrac{\boxed{c}}{f}[/tex]

  [tex]\dfrac{a}{b}=\dfrac{d}{e}\qquad\dfrac{b}{\boxed{c}}=\dfrac{e}{f}\qquad\dfrac{c}{a}=\dfrac{f}{\boxed{d}}[/tex]

__

Additional comment

Any proportion can be written "sideways" or "upside down." Corresponding parts have the same relationship in any case.

  [tex]\dfrac{a}{b}=\dfrac{d}{e}\ \Leftrightarrow\ \dfrac{a}{d}=\dfrac{b}{e}\ \Leftrightarrow\ \dfrac{b}{a}=\dfrac{e}{d}\ \Leftrightarrow\ \dfrac{d}{a}=\dfrac{e}{b}[/tex]

Answer: 85% or 17/20

Step-by-step explanation: Ok, so 17 being what percent of 20 is 17/20. Then, simply divide from there to get 0.85, also known as 85%.

Answer: forgot

Step-by-step explanation:

1. Mark is late. Do you think he forgot about the dinner?

The lengths of the variables are 17. x = 14√2, 18. x = 22.5√2, 19. x = 22√2, 20. x = 105√2 and other solutions are listed below

Question 17 - 22

In a 45-45-90 triangle, also known as an isosceles right triangle, the two legs (the sides opposite to the two 45-degree angles) are congruent and the hypotenuse (the side opposite to the 90-degree angle) is equal to the √2 times the length of either leg.

Using the above, we have the following values

17. x = 14√2

18. x = 22.5√2

19. x = 22√2

20. x = 105√2

21. x = 88√2

22. x = 10

Question 23

Here, we have

sin(30) = 9/x

x = 18

y² = 18² - 9²

y² = 9√3

Question 24

Here, we have

cos(60) = y/4√3

y = 2√3

x² = (4√3)² - (2√3)²

x = 6

Question 25

Here, we have

sin(30) = 20/y

y = 40

x² = (40)² - (20)²

x = 20√3

Question 26

Here, we have

cos(60) = x/98

x = 49

y² = (98)² - (49)²

y = 49√3

Question 27

Using the definition above, we have

Leg = 38/√2

Leg = 19√2

Question 28

Using the definition above, we have

Hypotenuse = 77√2

Question 29

For the equilateral triangle, we have

Triangle length = x

This gives

tan(60) = 33/(x/2)

So, we have

x/2 = 33/tan(60)

x/2 = 33/√3

x = 22√3

So, the side lengths are 22√3 feet long

Question 30

Here, we have

Side length = 150 ml

So, the hypotenuse is

Hypotenuse = 150√2

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The scatterplot of the Median Value of Used Car Sales (in billions of pounds) to the Median Volume of Used Cars Sold (in millions) indicates;

(a) Independent variable; Median Volume of Used Cars Sold

Dependent variable; Median Value of Used Car Sales

(b) The median is less sensitive to outliers in the data than the mean

(c) The estimate of the median value is 20 billion pounds

(d) The predicted median value is about £28.185

(e) The other factors includes; The age, condition and location of the car, and the availability of financing.

A scatterplot is a mathematical diagram or plot on Cartesian coordinates to display values of data points containing two variables in a dataset.

(a) The vertical axis of the scatter plot is the median value of used car sales in billions of pounds. The horizontal axis is the median volume of used cars sold in millions. Therefore;

(b) The variability of the values in the scatter plot indicates that the possibility for outliers in the data.

The median value and median volume are used instead of the mean because of the lower sensitivity of the median to the outliers than the mean. The median is defined as the middle value in a set of data while the mean is the average of all the values in a dataset. Whereby the dataset consists of outliers, the outliers can skew the mean, while the outliers do not affect the median.

(c) The median value of the data point on the graph that corresponds to the 2.3 million median volume of used car sold is about 20 billion pounds. Therefore;

(d) The equation for the median value of used car sales, value = 30.97 - 1.211 × Volume, indicates that if the volume of used cars sold is 2.3 million, we get;

Value = 30.97 - 1.211 × 2.3 ≈ 28.185

Therefore, using the equation, 30.97 - 1.211 × Volume;

(e) The other factors beside the price of the used cars that influence the volume of used cars sold includes the following factors,

The age of the car

The car's condition

The car's location

The availability of financing

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Therefore, nine rabbits will need 7.5 sacks of food for one week.

The unitary method is a mathematical technique that involves finding the value of a single unit to determine the value of a given number of units. It is a method of solving mathematical problems that involve proportional relationships between quantities. The unitary method is commonly used in various areas of mathematics, such as algebra, arithmetic, and geometry. It is also used in everyday life to solve problems related to money, time, distance, and other quantities.

Here,

To solve this problem, we can use proportionality. We know that the number of sacks of food needed is directly proportional to the number of rabbits.

Let x be the number of sacks needed for 9 rabbits. Then, we can set up the following proportion:

6/10 = 9/x

Cross-multiplying, we get:

6x = 90

Dividing both sides by 6, we get:

x = 15/2 or 7.5

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Complete question:

If six rabbits need 10 sacks of food per week, how many sacks will nine rabbits need to eat for one week?

Answer:

The given statement is False. When the interest is compounded half yearly the number of conversion periods will be two because a year comprises 12 months and has two periods of six months each.

Step-by-step explanation:

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Both angles on the parallel lines are related as ∠1=180°-∠7

Vertical angles, also known as vertically opposed angles, are generated when two lines intersect. Angles that are vertically opposite one another are always equal to one another. Moreover, a vertical angle and the angle to which it is next are supplementary angles, meaning their sum is 180 degrees.

To find: measure ∠1 through ∠7

∠7=∠5 ( vertically opposite angle)

∠5=∠2( co-exterior angle)

∠1+∠2=180°

( A straight line has a maximum angle of 180°.)

∠1=180°-∠2

∠1=180°-∠5

∠1=180°-∠7

Hence, both angles on the parallel lines are related as ∠1=180°-∠7

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