If your answer is correct I will give brainliest

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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After answering the provided question, we can conclude that  To circle complete the copied triangle, draw a polygon through points D, E, and F.

A circle appears to be a two-dimensional component that is defined as the collection of all points in a jet that are equidistant from the hub. A circle is typically depicted with a capital "O" for the centre and a lower section "r" for the radius, which is the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant roughly equal to 3.14159. The formula r2 computes the circumference of a circle, which refers to the amount of space inside the circle.

Follow these steps to duplicate the original triangle using only two of its sides and the included angle:

Find the point where the ray and the circle intersect. Place the tip of the compass at point E and draw an arc that intersects the circle twice. Label the point that is on the same side of side AC as point B as point F.

To complete the copied triangle, draw a polygon through points D, E, and F.

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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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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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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 residual of the data for this new baby is 0.7

What is a linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Here, we have

Given: A clinic has recorded the age, x, versus weight, y, of many babies for their first 12 months of life, and claims the line of best fit is ŷ = 0.60x + 3.3, where y is in kg, and x is in months.

ŷ = 0.60x + 3.3

Substitute, x=10

ŷ = 0.60(10) + 3.3   = 9.3

Residual =  y - ŷ  = 10 – 9.3 = 0.7

Hence, the residual of the data for this new baby is 0.7

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Answer:

---------------------------------

See the attached, where the given distance is copied over each option. Since the whole distance is 4 times the 1/4 of the distance, the correct choice is C.

Answer: To find the vertical asymptotes of the given function, we need to find the values of x that make the denominator equal to zero. So, we set each denominator equal to zero and solve for x:

(x-3)(x-1)² = 0

x = 3 or x = 1

Therefore, the vertical asymptotes of the function occur at x = 3 and x = 1.

To find the horizontal asymptotes, we need to look at the degree of the numerator and denominator. Since both the numerator and denominator are degree 2, we can find the horizontal asymptote by dividing the leading coefficient of the numerator by the leading coefficient of the denominator. In this case, the leading coefficient of both the numerator and denominator is 1, so the horizontal asymptote is y = 1/1 = 1.

Therefore, the vertical asymptotes are x = 3 and x = 1, and the horizontal asymptote is y = 1.

Step-by-step explanation:

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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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%

The bias of the estimator is 1/45, so correct option is A.

In mathematics, a proportion is a statement that two ratios are equal. A ratio is a comparison of two quantities, expressed as a fraction or a division of one quantity by another.

For example, the proportion "a/b = c/d" means that the ratio of a to b is equal to the ratio of c to d. This can also be written as "a : b = c : d", where the colon (:) represents the ratio symbol.

Proportions can be used to solve a variety of problems, such as finding unknown quantities in a ratio or comparing quantities that have different units. For instance, if a recipe calls for 2 cups of flour for every 3 cups of water, we can use proportions to determine how much flour and water we need if we want to make a larger or smaller batch.

The estimator for the true proportion of residents in support of the bypass road construction is given by:

p = (X + √2025/2) / 2025

We can see that this estimator involves adding √2025/2 to X, and then dividing the sum by 2025. Since √2025 = 45, we can simplify the estimator as:

p = (X + 45/2) / 2025

Now, we can find the expected value of the estimator:

E[p] = E[(X + 45/2) / 2025]

= (E[X] + 45/2) / 2025

To find the bias of the estimator, we need to compare its expected value to the true value of the parameter being estimated. Since we are estimating the proportion of residents in support of the bypass road construction, the true value of the parameter is the population proportion, denoted by p.

If the estimator is unbiased, then its expected value must equal the true value of the parameter, i.e., E[p] = p. Therefore, we have:

E[p] = (E[X] + 45/2) / 2025 = p

Solving for E[X], we get:

E[X] = 2025p - 45/2

Thus, the bias of the estimator is:

Bias[p] = E[p] - p

= (E[X] + 45/2) / 2025 - p

= [(2025p - 45/2) + 45/2] / 2025 - p

= (2025p - p) / 2025

= 44/2 x 2025

= 1/45

Therefore, the bias of the estimator is 1/45. Answer: A.

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The bias of the estimator is 1/45. The appropriate choise for the posed query is option (a).

In mathematics, a proportion is the assertion that both ratios are equal. A ratio is the division of one quantity by another or the comparison of two quantities given as a fraction.

The ratio "a/b = c/d," for instance, denotes that the ratio of a to b is equivalent to the ratio of c to d. This can also be expressed as "a: b = c: d," where the ratio sign is denoted by the colon (:).

Numerous issues can be resolved using proportions, like comparing amounts with various units or locating unknown values in a ratio. For instance, we may use proportions to calculate the amount of flour and water needed to make a larger or smaller batch of a recipe if it calls for 2 cups of flour and 3 cups of water.

The estimator for the actual percentage of residents in favour of building the bypass route is provided by:

p = (X + √2025/2) / 2025

As we can see, this estimator multiplies X by 2025/2 before dividing the result by 2025.

Since √2025 = 45, The estimator may be distilled down to:

p = (X + 45/2) / 2025

We can now determine the estimator's expected value:

E[p] = E[(X + 45/2) / 2025]

= (E[X] + 45/2) / 2025

We must contrast the estimator's expected value with the actual value of the parameter being estimated in order to determine its bias. The population proportion, given by p, is the genuine value of the parameter because we are calculating the percentage of residents who support the construction of the bypass route.

If the estimator is impartial, then its predicted value must match the parameter's true value, or E[p] = p. As a result, we have:

E[p] = (E[X] + 45/2) / 2025 = p

Solving for E[X], we get:

E[X] = 2025p - 45/2

As a result, the estimator's bias is:

Bias[p] = E[p] - p

= (E[X] + 45/2) / 2025 - p

= [(2025p - 45/2) + 45/2] / 2025 - p

= (2025p - p) / 2025

= 44/2 x 2025

= 1/45

As a result, the estimator's bias is 1/45. Answer: A.

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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:

let l = the length of the rectangle

area of the rectangle (A) = 13 * l

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

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).

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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Answer: p=50 h=2

Step-by-step explanation:

so its 50 x 2=100 is the answer then u add 3

The average amount of money spent for lunch per person in the college cafeteria is $6.45 and the standard deviation is $2.55. Suppose that 44 randomly selected lunch patrons are o

population mean is 6.45

population standard deviation is 2.55.

sample size is 44.

z-score is indicated because you are using population standard deviation and sample size is greater than 30.

The z-score formula is [tex](x - m) / s[/tex]

in this case, x is the sample mean, m is the population mean, s is the standard error.

[tex]standard error = standard deviation / sqrt(sample size0 = 2.55 / sqrt(44) = .3844[/tex] rounded to 4 decimal places.

z-score formula becomes [tex]z = (x - 6.45) / .3844[/tex]

solve for x to get:

[tex]x = .3844 * z + 6.45[/tex]

since you don't have a z-score, you can't find x.

the best you can do is find the critical z-scores, and hence, the critical raw scores.

In order to do that you need to to know the confidence level.

if you know that, you can find the critical z-scores and, from that, the critical x-scores.

we'll compare two confidence levels.

the first is at 99% confidence level.

the second is at 90% confidence level.

with a 99% two-tail confidence level, the critical z-scores are plus or minus 2.5758 rounded to 4 decimal places.

the critical raw scores are found by using the z-score formula.

you get [tex]x = .3844 * 2.5758 + 6.45 = 7.4401[/tex] for the high score.

you get x = [tex].3844 * -2.5758 + 6.45 = 5.4599[/tex] for the low score.

the 99% two-tail confidence level tells you that 99% of your samples of size 44 will have the sample mean between 5.4599 and 7.4401.

that's your 99% confidence interval.

with a 95% two-tail confidence level, the critical z-scores are plus or minus 1.9600 rounded to 4 decimal places.

the critical raw scores are found by using the z-score formula.

you get [tex]x = .3844 * 1.9600 + 6.45 = 7.2034[/tex] for the high score.

you get[tex]x = .3844 * -1.9600 + 6.45 = 5.6966[/tex] for the low score.

the 95% two-tail confidence level tells you that 95% of your samples of size 44 will have the sample mean between 5.6966 and 7.2034.

that's your 95% confidence interval.

the higher the confidence level, the wider the confidence interval when you are dealing with the same population mean and population standard deviation and same sample size.

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Correct and complete question:

The average amount of money spent for lunch per person in the college cafeteria is $6.45 and the standard deviation is $2.55.

Suppose that 44 randomly selected lunch patrons are observed.

Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.

b. What is the distribution of x?

x-N(6.45,_________________)

To solve for the missing value, we need to first find a common denominator for the fractions on the left side of the equation. The common denominator is (m - n)(m + n)(m - 1). Thus, we can write:

[(m - n) - ?]/[(m - n)(m + n)(m - 1)] = 2m/(m^2 - n^2)

Next, we can cross-multiply to eliminate the fractions:

[(m - n) - ?](m^2 - n^2) = 2m[(m - n)(m + n)(m - 1)]

Simplifying the right side of the equation:

2m[(m - n)(m + n)(m - 1)] = 2m(m - n)(m + n)(m - 1)

= 2m(m^2 - n^2)(m - 1)

Expanding the left side of the equation:

[(m - n)(m + n) - ?](m^2 - n^2) = (m - n)(m + n)(m - 1)

Distributing the left side of the equation:

(m - n)(m^2 - n^2 + ?) = (m - n)(m + n)(m - 1)

Canceling out the common factor (m - n):

m^2 - n^2 + ? = (m + n)(m - 1)

Expanding the left side of the equation:

? = (m + n)(m - 1) - (m^2 - n^2)

Simplifying the right side of the equation:

? = m^2 - m + n^2 + n - m^2 + n^2

= 2n^2 - m + n

Therefore, the missing value is ? = 2n^2 - m + n.

The two equations that can be applied to the issue are as follows: A. 5 × 3 Equals 15 (multiplication) (multiplication) . B. 1/5 × 3 Equals 3/5 (multiplication and division) (multiplication and division)

An equation is a claim that two alternatives are equal in mathematics. The equals sign (=) is generally used to denote this claim. It is a mathematics assertion that two expressions are equal. Variables, constant, coefficients, and mathematical operations like addition, subtraction, multiply, and dividing can all be found in an equation. Finding the value(s) of both the variable(s) that render the equation true is the aim of an equation's solution.

given

Each of the five pears Kylie has is divided into thirds. She must therefore distribute the following quantity of pear slices to her teammates:

5 pears cut into 3 slices each equals 15 slices.

The two equations that can be applied to the issue are as follows: A. 5 × 3 Equals 15 (multiplication) (multiplication) . B. 1/5 × 3 Equals 3/5 (multiplication and division) (multiplication and division) .

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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: forgot

Step-by-step explanation:

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

Answer: $4.40 is the cost for the call

The answer of the given question based on the  confidence interval is , it suggests that the drug treatment has significantly reduced the mean wake time , the drug appears to be effective in treating insomnia in the older subjects.

Mean is a statistical measure of central tendency that represents the average of a set of numerical values. It is also referred to as the arithmetic mean or simply "the average." To calculate the mean, we add up all the values in the set and divide the sum by the number of values.

To construct the 99% confidence interval estimate of the mean wake time for a population with the treatment, we can use the following formula:

CI = x⁻ ± tα/2 (s/√n)

where x⁻ is the sample mean (94.9 min), s is the sample standard deviation (24.3 min), n is the sample size (19), and tα/2 is the critical t-value with α = 0.01/2 and degrees of freedom (d f) = n - 1.

The degrees of freedom for this sample is d f = 19 - 1 = 18. Using a t-table or a t-distribution calculator, we find that t0.005,18 = 2.878, where 0.005 is the tail probability for a 99% confidence interval (α/2 = 0.005).

Plugging in the values, we get:

CI = 94.9 ± 2.878 * (24.3/√19) = (80.36, 109.44)

Therefore, we can say with 99% confidence that the mean wake time for a population with the drug treatment falls between 80.36 and 109.44 minutes.

Regarding the mean wake time of 104.0 min before the treatment, we can compare it with the lower bound of the confidence interval (80.36 min). Since the lower bound is much lower than 104.0 min, it suggests that the drug treatment has significantly reduced the mean wake time.

Therefore, based on the confidence interval estimate, the drug appears to be effective in treating insomnia in older subjects.

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a) the initial condition as 0 kg sugar in the tank at time = 0 (pure water)

b) with the net rate of change the amount of sugar after t minutes is S(t) = 236.8 [1 - e (t/740)]

c) time goes to infinity, the amount of sugar in is 236.8 kg.

a) Let A(t) denote the amount of sugar in the tank at time. The tank starts with only pure water, so A(0) = 0 OR you can say that you give the initial condition as 0 kg sugar in the tank at time = 0 (pure water)

b) Sugar flows in at a rate of (0.07 kg/L) * (7 L/min) = 0.49 kg/min = 49/100 kg/min and flows out at a rate of (A(t)/1080 kg/L) * (7 L/min) = 7A(t)/1080 kg/min, so that the net rate of change of is governed by the ODE, multiply both sides by the integrating factor  to condense the left side into the derivative of a product, if t = time and S(t) is the amount of sugar in the tank as a function of time, then the equation that we get is S(t) = 236.8 [1 - e (t/740)]

c) As t---> ∞, the exponential term converges to 0 and we're left with the means when time goes to infinity, the amount of sugar in is 236.8 kg.

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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:

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.