Please help solving this
Quite urgent, thanks :)

The closest answer is 3xLn3 which is (B).

If k(x) = 3x, then f(x) can be expressed as the integral of k(x) with respect to x:

f(x) = ∫ k(x) dx = ∫ 3x dx = (3/2)x² + C

where C is the constant of integration.

To find f'(x), the derivative of f(x) with respect to x, we simply differentiate the expression for f(x):

f'(x) = d/dx [(3/2)x² + C] = 3x

A differential equation is a mathematical equation that relates a function and its derivatives. Specifically, a differential equation describes how a quantity changes as a function of its own rate of change.

Differential equations are commonly used in physics, engineering, and other sciences to model and analyze natural phenomena.

For example, the motion of a simple pendulum can be described using a differential equation that relates the position and velocity of the pendulum to its acceleration and the forces acting upon it.

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Answer:

3246

Step-by-step explanation:

To calculate this equation, we need to follow the order of operations, also known as PEMDAS. First, we evaluate anything inside parentheses, which in this case is (82-33), giving us 49. Next, we perform division, so we have 6 ÷ 49. Then, we multiply 49 and 66, resulting in 3234. Finally, we add 12 to 3234, leading to the final answer of 3246. Therefore, the value of the expression 12+6÷(82-33)x66 is 3246.

Answer:

3246

Step-by-step explanation:

The solution to the given composite function is; C: 4x² - 4x - 2

From the question, we are given the individual functions as;

f(x) = x² - 3

g(x) = 2x - 1

Now when it comes to composite functions, we know that;

(f ° g)(x) = f[g(x)]

Substitute the known values in the above equation, so, we have the following representation

(f ° g)(x) = f(2x - 1) = (2x - 1)² - 3 = 4x² - 2x - 2x + 1 - 3 = 4x² - 4x - 2

This is the final solution of the composite function expression.

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The solution to the given composite function is; Option D: 2x² - 7

Composite functions are defined as functions where the output of one function is used as the input of another. Wheb we have a function f and another function g, then the function fg(x), said as “ f of g of x”, is the composition of the two functions.

The given functions are:

f(x) = x² - 3

g(x) = 2x - 1

We want to find (g ° f)(x) . We know that:

(g ° f)(x) = g[f(x)]

Thus:

(g ° f)(x) = g(x² - 3)

= 2(x² - 3) - 1

= 2x² - 6 - 1

= 2x² - 7

This is the final result of the composite function expression.

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George sold 18, 22, 26, 12, 25, 20, and 19 cars per month over the past seven months.

George's first mistake was in Step 1 where he tried to find the total number of cars he needs to sell in the next month to have a mean number of sales per month of 24. To find this value, George should have multiplied the desired mean number of sales per month (24) by the total number of months (7) to get the total number of cars needed to have a mean of 24 over 7 months. However, it seems that George skipped this step and directly assumed that the total number of cars needed for a mean of 24 in the next month is simply 24.

Let's go through each step to explain

Step 1 Find the total cars needed to have a mean of 24

To find the total number of cars George needs to sell over the next 7 months to have a mean of 24 cars sold per month, he should multiply the desired mean (24) by the number of months (7)

Total cars needed = 24 * 7 = 168

Step 2  Find the total cars sold

To find the total number of cars George sold over the past 7 months, he should add up the individual sales for each month:

Total cars sold = 18 + 22 + 26 + 12 + 25 + 20 + 19 = 142

Step 3 Subtract the total cars sold from the total cars needed

To find the number of cars George needs to sell in the next month to meet his target mean of 24 cars sold per month over the past 8 months, he should subtract the total number of cars sold from the total cars needed

Cars needed in the next month = Total cars needed - Total cars sold

Cars needed in the next month = 168 - 142 = 26

Step 4 State the answer

George needs to sell 26 cars next month to have a mean of 24 cars sold per month over the past 8 months.

Therefore, George's mistake was in Step 1 where he did not correctly calculate the total number of cars he needs to sell over the next 7 months to have a mean of 24 cars sold per month.

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Answer:you need to include the expression

Step-by-step explanation:

once you have the expression, substitute the numbers given for each variable and use order of operations to

The confidence interval can be expressed as a trilinear inequality: 82.9% < p < 95.7%.

The confidence interval in interval form is (0.1864, 0.3026).

The given confidence interval, 89.3% ± 6.4%, means that we are 89.3% confident that the true value of the population parameter lies within a range of 6.4% above and below the sample estimate.

To express this in the form of a trilinear inequality, first find the upper and lower bounds of the interval.

Upper bound = 89.3% + 6.4% = 95.7%

Lower bound = 89.3% - 6.4% = 82.9%

Therefore, the confidence interval 89.3% ± 6.4% can be expressed in the form of a trilinear inequality as:

82.9% < p < 95.7%

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The volume of the cone is 288π m³. Hence, the answer is option C, 288π m³.

A cone is a shape created by connecting all the points of a circular base (which does not contain the apex) to a common point known as the apex or vertex using a series of line segments or lines. The height of the cone is determined by measuring the distance between its vertex and base.

The formula for the volume of a cone is given by V = (1/3)πr²h, where r is the radius and h is the height.

Substituting the given values, we get:

V = (1/3)π(6²)(24)

V = (1/3)π(36)(24)

V = (1/3)(864π)

V = 288π

Therefore, the volume of the cone is 288π m³.

Hence, the answer is option C, 288π m³.

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Answer:

a) The common difference between consecutive terms is 9. Thus, the nth term can be expressed as:

n(9)+(-3)

b) To find the 10th term, we substitute n=10 in the expression we just found:

10(9) + (-3) = 87

Therefore, the 10th term of the sequence is 87.

the mean absolute deviation for the high temperatures in Julia's town for the week is 4.9 degrees.

How to solve the question?

To find the mean absolute deviation (MAD) for the high temperatures in Julia's town, we first need to find the mean temperature for the week.

To do this, we add up all the temperatures and divide by the number of temperatures:

(49 + 55 + 42 + 46 + 47 + 42 + 38) ÷ 7 = 43.3

The mean temperature for the week is 43.3 degrees.

Next, we need to find the distance of each temperature from the mean. To do this, we subtract the mean from each temperature:

|49 - 43.3| = 5.7

|55 - 43.3| = 11.7

|42 - 43.3| = 1.3

|46 - 43.3| = 2.7

|47 - 43.3| = 3.7

|42 - 43.3| = 1.3

|38 - 43.3| = 5.3

We take the absolute value of each difference to ensure that the distances are positive.

Now, we find the mean of the distances by adding up all the distances and dividing by the number of temperatures:

(5.7 + 11.7 + 1.3 + 2.7 + 3.7 + 1.3 + 5.3) ÷ 7 = 4.9

Therefore, the mean absolute deviation for the high temperatures in Julia's town for the week is 4.9 degrees.

In conclusion, the mean absolute deviation is a measure of the variability of a set of data. It is calculated by finding the mean of the absolute distances of each data point from the mean. In this case, the MAD is 4.9 degrees, indicating that the temperatures for the week were relatively close to the mean.

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2nd and 3rd scatterplot do not suggest a linear relationship between x and y.

What is scatterplot?

A scatter plot is a particular type of plot or mathematical diagram by using Cartesian coordinates to display values for typically two variables for a set of values. It represents the correlation between two sets of data which may be linear or non linear sometimes strongly positive linear sometimes it may be curvilinear sometimes it may be null.

In the first plot it visibly showing a graph for straight line that is strong positive linear scatter plot. Same for the last but there is a little difference that it is negative linear scatter plot.

For the second one there is a null scatter plot. So there is no correlation.

For the 3rd graph there is a curvilinear relation in the scatterplot.

Hence, 2nd and 3rd scatterplot do not suggest a linear relationship between x and y.

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according to the question 77% population use a cell phone that is less than 1 year old.

Probability theory, a subfield of mathematics, quantifies the likelihood that an event is going to happen or that a statement is true. The probability for an event is a number between 0 and 1, where 0 roughly denotes how probable the event is to occur and 1 denotes certainty. A probability is a numerical representation of the likelihood that a certain event will occur. In addition to numbers from 0 to 1, probability values can also be stated as percentages between 0% and 100%. the fraction of an entire set of equally likely possibilities that result in a certain occurrence out of all possible outcomes, expressed as a ratio.

given,

The probability distribution for the age of a randomly selected young adult's cell phone can be represented using a probability mass function (PMF) as follows:

P(X = 3) = 0.01 (1% use a cell phone that is 3 years or older)

P(2 ≤ X ≤ 3) = 0.02 (2% use a cell phone that is 2-3 years old)

P(1 ≤ X ≤ 2) = 0.20 (20% use a cell phone that is 1-2 years old)

P(X < 1) = 0.77 (77% use a cell phone that is less than 1 year old)

Note that the values of the PMF correspond to the probabilities of the different age categories for the cell phones of young adults. The PMF satisfies the two main properties of a probability distribution: 1) the probabilities are non-negative, and 2) the sum of the probabilities is equal to 1.

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Two quadratic functions that contains the points (5, 3) and (8, 0) are

In this problem we must find two possible quadratic functions that contains two points: (x, y) = (5, 3), (x, y) = (8, 0). The factor form of the quadratic function is now introduced:

y = a · (x - r₁) · (x - r₂)

Where:

If we know that (x₁, y₁) = (5, 3) and (x₂, y₂) = (8, 0), then the two possible quadratic functions are:

3 = a · (5 - r₁) · (5 - r₂)

3 = a · [25 - 5 · (r₁ + r₂) + r₁ · r₂]

0 = a · (8 - r₁) · (8 - r₂)

0 = 64 - 8 · (r₁ + r₂) + r₁ · r₂

0 = 64 - 8 · r₁ - 8 · r₂ + r₁ · r₂

0 = 64 - 8 · r₁ + (r₁ - 8) · r₂

Now we clear r₂:

r₂ = (8 · r₁ - 64) / (r₁ - 8)

And we eliminate r₂ in the first equation:

3 = a · [25 - 5 · [r₁ + (8 · r₁ - 64) / (r₁ - 8)] + r₁ · [(8 · r₁ - 64) / (r₁ - 8)]]

And variable a is now cleared:

a = 3 / [25 - 5 · [r₁ + (8 · r₁ - 64) / (r₁ - 8)] + r₁ · [(8 · r₁ - 64) / (r₁ - 8)]]

The function is graphed and two possible solutions are introduced below:

(r₁, a) = (6, 1), (r₁, a) = (10, 0.2)

And the values of r₂ are, respectively:

(r₁, a) = (6, 1):

r₂ = (8 · 6 - 64) / (6 - 8)

r₂ = - 16 / (- 2)

r₂ = 8

(r₁, a) = (10, 0.2):

r₂ = (8 · 10 - 64) / (10 - 8)

r₂ = 16 / 2

r₂ = 8

Finally, we complete and graph the resulting quadratic functions.

Case 1:

y = (x - 6) · (x - 8)

y = x² - 14 · x + 48

Case 2:

y = 0.2 · (x - 10) · (x - 8)

y = 0.2 · (x² - 18 · x + 80)

y = 0.2 · x² - 3.6 · x + 16

The graphs of the two quadratic functions are shown in the second image.

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Answer:two lines are parallel if their slopes are equal and they have different y-intercepts

Step-by-step explanation:

Using the given zero . The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.

If 1 + i is a zero of the polynomial function P(x), then its conjugate, 1 - i, must also be a zero of the polynomial, since complex zeros of polynomial functions with real coefficients always come in conjugate pairs.

To find the remaining zero, we can use polynomial division or synthetic division to divide P(x) by (x - 1 - i)(x - 1 + i), which is the quadratic factor corresponding to the two known zeros:

      2x^2 - 3x + 2

P(x) = --------------

       (x - 1 - i)(x - 1 + i)

Now we need to solve for the roots of the quadratic factor 2x^2 - 3x + 2. We can use the quadratic formula:

x = [3 ± sqrt(9 - 4*2*2)] / (2*2)

 = [3 ± sqrt(1)] / 4

 = 1/2 or 2

Therefore, the remaining zeros of P(x) are 1/2 and 2. The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.

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Answer:

Sure. Here are the steps on how to find an equivalent expression to 2-4(x+1)-18:

1. Expand the parentheses:

```

2-4(x+1)-18 = 2-4x-4-18

```

2. Combine like terms:

```

2-4x-4-18 = -4x-14

```

Therefore, the equivalent expression to 2-4(x+1)-18 is -4x-14.

2 - 4(x + 1) - 18 can be simplified as follows:

= 2 - 4x - 4 - 18 [distribute -4]

= -20 - 4x [combine like terms]

Therefore, an equivalent expression to 2-4(x+1)-18 is -20 - 4x.

The inequality that represents the sentence that the absolute value of x is greater than 6 is given as follows:

|x| > 6.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The absolute value of x is represented as follows:

|x|.

The inequality that represents the absolute value being greater than six is gjven as follows:

|x| > 6.

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Answer:

|x| > 6

Step-by-step explanation:

The correct statement is: |x| > 6.

This means that the distance between x and 0 on the number line is greater than 6 units, so x can be any number greater than 6 or less than -6.

The options given are:

Therefore, the correct statement is |x| > 6.

here's how to express the statement |x| > 6 as an inequality part 10a^2

| x | > 6

x^2 > 6^2

x^2 > 36

10x^2 > 360

10x^2 - 360 > 0

10x^2 - 360 > 0

Note that this inequality does not directly involve "a," as it is not mentioned in the original statement.

Hence ,the basketball team  scored 83 points in  the first game.

Basketball is a team sport in which two teams,  most commonly of five players each,  opposing one another on a rectangular court,  compete with the primary objective of shooting a basketball through the defender's hoop,  while preventing the opposing team from shooting through their own hoop.

A team is a group of individuals (human or non-human) working together to achieve their goal.As defined by Professor Leigh Thompson of the Kellogg School of Management, team is a group of people who are interdependent with respect to information, resources, knowledge and skills and who seek to combine their efforts to achieve a common goal

Let x be  the number of points  scored in the first game.

According  to the  question,

747 = 9 x

now  9 divided by both sides,

x = [tex]\frac{747}{9}[/tex]

than we get:

x = 83

Therefore,  the basketball team  scored 83 points in  the first game.

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Complete question is:

A basketball scored 747 points for the season.This was 9 times the number of points they scored in the first game.How many points were scored in the first game.

The volume and surface area of a triangular prism is 1,848 cubic meters and 1,694 square meters.

What is surface area?

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.

the volume and surface area of a right triangular prism with base dimensions of 24 m and 7 m height and a length of 22 m.

The volume of a right triangular prism is given by the formula:

V = (1/2) * b * h * l

where b is the base width, h is the height, and l is the length. Plugging in the given values, we get:

V = (1/2) * 24 m * 7 m * 22 m = 1,848 m³

Therefore, the volume of the right triangular prism is 1,848 cubic meters.

The surface area of a right triangular prism is given by the formula:

SA = 2 * (b * h + l * h + b * l)

Plugging in the given values, we get:

SA = 2 * (24 m * 7 m + 22 m * 7 m + 24 m * 22 m) = 1,694 m²

Therefore, the surface area of the right triangular prism is 1,694 square meters.

Hence, the volume and surface area of a triangular prism are 1,848 cubic meters and 1,694 square meters.

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The evaluation of the expression consisting of surds indicates that we get;

(9·x + 42 - 69·√x)/(x - 49)

A surd is a value under a square root sign, which can not be further simplified into fractions or whole numbers.

The expression (9·√x - 6)/(√x + 7), can be simplified by using the rationalization of surds technique as follows;

(9·√x - 6)/(√x + 7) = ((9·√x - 6)/(√x + 7)) × ((√x - 7)/(√x - 7))

(√x + 7) × (√x - 7) = ((√x)² - 7²) = (x - 49)

(9·√x - 6) × (√x + 7) = 9·x + 42 - 69·√x

Therefore; (9·√x - 6)/(√x + 7) = (9·x + 42 - 69·√x)/(x - 49)

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Answer:

To solve the expression 2 + 7 • (-3)^2, we follow the order of operations, also known as PEMDAS/BODMAS, which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, we evaluate the exponent: (-3)^2 = 9 (because squaring a number means multiplying it by itself).

Next, we perform multiplication: 7 • 9 = 63.

Finally, we perform addition: 2 + 63 = 65.

So, the value of the expression 2 + 7 • (-3)^2 is 65.

The width of the rectangle is 5.

The area of a rectangle is given by the formula:

Area = Length x Width

where Length and Width are the measurements of the two adjacent sides of the rectangle.

For example, if a rectangle has a length of 6 units and a width of 4 units, then its area would be:

Area = Length x Width

Let's start by using the formula for the area of a rectangle:

Area = Length x Width

We are given that the area of the rectangle is 30xF²y and that one of its sides (length) is 6xy. Substituting these values into the formula, we get:

30x²y = (6xy) x Width

Simplifying the right-hand side by multiplying 6xy by Width, we get:

30x²y = 6x²y x Width

Dividing both sides by 6x²y, we get:

Width = 30x²y / 6x²y

Simplifying the right-hand side by canceling out the common factors of 6, x², and y, we get:

Width = 5

Therefore, the width of the rectangle is 5.

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The value for the trigonometric expression cos(A+B) is (5√7 - 288)/325

Explain trigonometry.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It includes the study of trigonometric functions such as sine, cosine, and tangent, which are used to calculate unknown angles or sides of a triangle. Trigonometry has many practical applications in fields such as engineering, physics, and navigation.

According to the given information

We can use the trigonometric identity cos(A + B) = cos(A)cos(B) - sin(A)sin(B) to find cos(A + B).

Since cos(A) = -5/13 and A is in Quadrant II, we can use the Pythagorean identity sin²A + cos²A = 1 to find sin(A). Solving for sin(A), we get sin²A = 1 - cos²A = 1 - (-5/13)² = 144/169. Since A is in Quadrant II, sin(A) is positive, so sin(A) = √(144/169) = 12/13.

Similarly, since sin(B) = 24/25 and B is in Quadrant II, we can use the Pythagorean identity to find cos(B). Solving for cos(B), we get cos²B = 1 - sin²B = 1 - (24/25)² = 7/625. Since B is in Quadrant II, cos(B) is negative, so cos(B) = -√(7/625) = -√7/25.

Substituting these values into the identity for cos(A + B), we get:

cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

          = (-5/13)(-√7/25) - (12/13)(24/25)

          = (5√7)/(13*25) - (12*24)/(13*25)

          = (5√7 - 288)/(13*25)

          = (5√7 - 288)/325

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Answer:

To find the greatest common factor (GCF) of 8a^3b^2 and 12ab^4, we need to factor each term into its prime factors and then find the common factors.

8a^3b^2 can be written as:

8a^3b^2 = 2^3 * 2 * a * a * a * b * b

12ab^4 can be written as:

12ab^4 = 2^2 * 3 * a * b * b * b * b

The common factors are 2, a, and b^2.

Therefore, the GCF of 8a^3b^2 and 12ab^4 is:

2 * a * b^2 = 2ab^2

Dev's velocity is [tex]\sqrt{5}[/tex]. Thus option B.

Kinetic energy is a amount of energy possessed when an object is in motion. Such that;

KE = 1/2 m v^2

Where m = mass, v = velocity

It is measured in Joules.

From the given question, we have;

KE = 1/2 m v^2

2KE = m v^2

v^2 = 2KE/ m

      = (2*150)/ 60

      = 300/ 60

      = 5

V = (5)^1/2

The velocity of Dev is B. [tex]\sqrt{5}[/tex].

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Answer:3-7=5

Step-by-step explanation: 3-7=5