Given that 'n' is a natural number. Prove the following text with mathematical induction:
2n^3-3n^2+n+6 is a multiple of 6.
Please show your work too. Thanks!

Answer: 50 degrees

Step-by-step explanation:

To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

Answer:

c

Step-by-step explanation:

Which ordered pair would form a proportional relationship with the point graphed below?

HOPE IT WILL HELP YOU

The equation of the parabola that has its focus at (0, -2) and directrix at y = 4 is presented as follows;

\(y = 1 - \frac{ x² }{12}\)

The focus of the parabola, obtained from a similar question posted online is (0, -2)

The given directrix is y = 4

From the definition of the directrix, we have;

(x - 0)² + (y - (-2))² = (y - 4)²

Which gives;

x² + (y + 2)² = (y - 4)²

4•y = y² - 8•y + 16 - (x² + y² - 4)

12•y = 12 - x²

The equation of the parabola is therefore;

\(y = 1 - \frac{ x² }{12}\)

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Answer:

73 Centimeters

Step-by-step explanation:

I hope this helps!

Answer:

(-2, -3)

Step-by-step explanation:

Sorry if im wrong but I looked it up and the person who wrote it got 131 thanks' so im guessing its this.

Consider giving brainlist :D

Answer:

d

Step-by-step explanation:

Answer:

The second answer is correct.

Step-by-step explanation:

Answer:

DAB

look at the first two letters MO which has the same amount of lines as DA on the triangle

next look at the last two letters OP which has the same amount of lines as AB on the triangle

Answer:

82 is the median

Step-by-step explanation:

Answer:

i also guess 2+2=4 not 5 ╮(╯▽╰)╭

Answer: 7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.

An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.

Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.

Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.

In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.

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So, the inputs for which the output of function f(x) is 2 are x = 3√2 or x = -3√2.

an equation is a mathematical statement that asserts the equality of two expressions. it typically consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=). the expressions on both sides can contain variables, constants, operations, and functions, and the equation is usually solved by finding the values of the variables that make both sides of the equation equal to each other. equations can be used to model real-world phenomena, analyze data, and solve problems in various fields such as physics, engineering, finance, and statistics.

To solve for x when \(y = f(x) = 1/2 x^2 - 7\), we can set y to 2 and solve for x:

\(2 = 1/2 x^2 - 7\)

Adding 7 to both sides, we get:

\(9 = 1/2 x^2\)

Multiplying both sides by 2, we get:

\(18 = x^2\)

Taking the square root of both sides (remembering to consider both the positive and negative roots), we get:

x = ±√18 = ±3√2

So, the inputs for which the output of f(x) is 2 are x = 3√2 or x = -3√2.

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Answer:

You can use symbolab for problems such as these, they'll provide step-by-step guides on how to do it. Symbolab is a math calculator that shows you how to solve each problem.

Answer:

Step-by-step explanation:

Perimeter means the distance around the outside of your shape. So you need to add up all the sides.

The radical sides might look scary but when you are adding or subtracting you can basically treat them like variables. See image.

rad(8) + 3rad(8) + 5rad(8)

=9rad(8)

This is an answer. But you always have to simplify. And rad8 is not completely simplified. see image.

rad8 = rad4×rad2

The square root of 4 is 2.

rad8 = 2rad2

See image.

The original question answer is 9rad8

=9×2rad2

=18rad2

The probability that an observation taken from a standard normal population is less than 1.59, P(Z < 1.59), is approximately 0.0559, which corresponds to option e. 0.0560 in the answer choices.

The Z-table, also known as the standard normal distribution table, is a useful tool for finding probabilities associated with the standard normal distribution. It provides the cumulative probabilities for different values of Z. By looking up -1.59 in the Z-table, we can find the probability of Z being greater than -1.59, which is the same as the probability of Z being less than 1.59.

When we look up -1.59 in the Z-table, we find that the corresponding probability is approximately 0.0559. Since the standard normal distribution is symmetric, the probability of Z being less than 1.59 is the same as the probability of Z being greater than -1.59. Therefore, the probability P(Z < 1.59) is also approximately 0.0560

Hence the correct option is (e).

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The area of the given shape is 78.5 unit²

Given,

The shape is 1/4th part of circle.

The radius is given as 10 units

We have to find the area of the shape.

Here,

The area of a circle is pi times the radius squared (A = π r²).

Area of circle = π × r²

Then

Area of 1/4th part of circle = π × r² / 4

That is,

Area of 1/4th part of circle = 3.14 × 10² / 4

Area of 1/4th part of circle  = 314 / 4

Area of 1/4th part of circle = 78.5 unit²

That is,

The area of the given shape is 78.5 unit²

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Answer:

correct

Step-by-step explanation:

you got it right

Answer:

Its

Step-by-step explanation:

not it's because it's is the same thing as it is

Answer:

Step-by-step explanation:

15 divded by 3 is 5 one 5 is 2 second 6 third 7

Question:

In three days Tina sold 15 boxes. On the second day, she sold 1 more than on the first. On the third day, she sold 5 more than on the first. How many boxes did she sell on the third day?

Answer:

8. Tina sold eight boxes on the third day.

Step-by-step explanation:

Three days, 15 boxes.

On the first day, Tina sold 3 boxes.

On the second, she sold one more than on the first. (4)

On the third day, she sold five more than on the first. (8)

 3 + 4 = 7

7 + 8 = 15

So your answer would be:

Tina sold eight boxes on the third day.

The presence of a negative externality causes the MSC to be higher than the MSB, which leads to the market over-producing the good. This is because producers are only taking their private costs and benefits into account, not the costs and benefits to society as a whole. The difference between the private and social optima is known as the deadweight loss. In this case, the deadweight loss is equal to the shaded triangle in the attached image.

1. This is a negative externality. We can see this by the MSC being higher than the MSB. This means that the cost to society of producing the good is higher than the benefit to society, resulting in the market over-producing the good.2. See the attached image. 3. At private decision making, we set the MSB equal to the MPC: 12-0.5Q = 2+0.5Q. Solving for Q gives Q = 8. 4. To find the socially optimal quantity, we need to set MSB equal to MSC: 12-0.5Q = 2+1.5Q. Solving for Q gives Q = 4. 5. The private and social optima are different because of the negative externality.

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the equation of the horizontal line passing through (-3, 4) is y = 4.

The equation of a horizontal line is of the form y = c, where c represents the y-coordinate of any point on the line. In this case, we are given that the line passes through the point (-3, 4). Since the line is horizontal, the y-coordinate remains constant for all points on the line.

Therefore, the equation of the horizontal line passing through (-3, 4) is y = 4. This means that no matter what x-value we choose, the y-value will always be 4.

In other words, all the points on this line will have a y-coordinate of 4.

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Complete question is below

Write the equation of the horizontal line that passes through (-3, 4).

The equation for the horizontal line that passes through a given point is y = b.

A horizontal line is a straight line that is parallel to the x-axis. The equation of a horizontal line is of the form y = c, where c is a constant. Since the line is horizontal, the value of y remains constant for all values of x. Therefore, the equation of a horizontal line passing through a given point (a, b) is y = b.

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For the given function f(x) = 5x² + 2x - 3,

Part A: The x-intercepts of the graph f(x) are: (-1, 0) and (3/5, 0).

Part B: The vertex of the graph of f(X) is going to be a minimum and its coordinates are (-0.2, -3.2).

Part C: The values obtained in the part A and Part B are used for graphing the given function. Since the vertex is minimum, the parabola opens upwards.

The x-intercepts of a function or equation are obtained at y = 0.

Then, on substituting y = 0 in the function gives the x-coordinate i.e., the x-intercept.

To calculate the x coordinate of vertex(h, k), use the formula mentioned below:

h = -b/2a

When the function is in the form of ax² + bx + c.

Then, to calculate the y-coordinate of the vertex, substitute obtained h value in the place of x in the function.

Thus, the required coordinates of the vertex are obtained as (h, k).

It is given that,

f(x) = 5x² + 2x - 3

Part A: Finding the x-intercepts:

Substituting y = 0 i.e., f(x) = 0;

⇒ 5x² + 2x - 3 = 0

On simplifying/factorizing,

⇒ 5x² + 5x - 3x - 3 = 0

⇒ 5x(x + 1) - 3(x +1) = 0

⇒ (5x - 3)(x + 1) =0

∴ x = 3/5 or x = -1

Thus, the x-intercepts are (3/5, 0) and (-1, 0).

Part B: Finding the vertex of the given function:

We have h = -b/2a

From the given function 5x² + 2x - 3; a = 5, b = 2 and c = -3

So, h = -2/2(5) = -1/5 = -0.2

Then, on substituting h = x = -0.2 in the function we get

k = 5(-0.2)² + 2(-0.2) - 3

k = -3.2

Thus, the coordinates of the vertex are (h, k) = (-0.2, -3.2).

Since a > 0 i.e., 5 > 0, the vertex of the graph is going to be minimum and the graph of f(x) opens upwards.

Part C: Steps to graph f(X):

Step 1: Plot the x-intercepts in the coordinate plane

Step 2: Plot the vertex of the function

Step 3: draw a curve line passing through them, opening towards up.

Thus, the graph of the given function is plotted as shown below.

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The statement is not true in general. The correct formula relating the second differential equations of y with respect to x and t is:

(d²y)/(dx²) = [(d²y)/(dt²)] / [(d²x)/(dt²)]

This formula is known as the Chain Rule for Second Derivatives, and it relates the rate of change of the slope of a curve with respect to x to the rate of change of the slope of the curve with respect to t. However, it is important to note that this formula only holds under certain conditions, such as when x is a function of t that is invertible and has a continuous derivative.

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Answer:

x = 2

Step-by-step explanation:

The side is split by the midpoint, so each section is the same length.

4x = 8 | Given

x = 2 | Divide sides by 4

The required difference will be;

⇒ 6

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The difference between a two-digit number and the number obtained by interchanging the digits is 54.

And, The ratio between the digits of the number is 1 : 3.

Now,

Since, The number is greater than the number obtained in reversing the digits and the ten's digit is greater than the unit digit.

Let the unit and ten's place are x and 3x.

Hence, We get;

⇒ (10 × 3x + x) - (10x + 3x) = 54

⇒ 31x - 13x = 54

⇒ 18x = 54

⇒ x = 3

Thus, The required difference,

⇒ (3x + x) - (3x - x)

⇒ 4x - 2x

⇒ 2x

⇒ 2 × 3

⇒ 6

Therefore, The required difference will be;

⇒ 6

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