Write the equation for the line through the given Q-points in slope-intercept form.

8. (5, 21) and (11,3)

9. (4, 8) and (12, 20)

The cost function C is given by\(C = 0.3q^3 - 4q^2 + 80q + F\), where q represents the quantity produced and F represents a fixed cost. The average cost (AC) equation is\(AC = (0.3q^3 - 4q^2 + 80q + F) / q\), and the variable cost (VC) equation is \(VC = 0.3q^3 - 4q^2 + 80q\)

The cost function C represents the total cost of production, which includes both variable costs (costs that change with the level of production) and fixed costs (costs that remain constant regardless of the level of production). In this case, the cost function is a polynomial equation of degree 3.

To calculate the average cost (AC) ,we divide the total cost (C) by the quantity (q) produced. This gives us the average cost per unit of output.

The variable cost (VC) represents the cost associated with producing each unit of output and is obtained by excluding the fixed cost component from the total cost function.

The marginal cost (MC) represents the additional cost incurred by producing one additional unit of output. It is calculated by taking the derivative of the variable cost equation with respect to the quantity (q).

By understanding these equations, we can analyze and make decisions regarding production levels, pricing, and cost optimization in the given scenario.

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Answer:y=25 x 2 -8

Step-by-step explanation:

25 x 2-8

The following equation could be used to represent a function w:

= w(x)=v(x-7)+7

According to the information provided,

The point of discontinuity of rational functions is at x=7.

When a rational function has a point of discontinuity, it generally occurs when,

q(x) = r(x-a), where x = a

In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)

If we know that a=7 and k=7.

The equation which can represent w is as follows,

w(x) = v ( x-7 ) + 7

A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.

Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.

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To determine if a differential form is exact, we need to check if its partial derivatives satisfy the condition of equality. If the differential form is not exact, we can multiply it by an integrating factor to make it exact.

Given a differential form of the form M(x, y)dx + N(x, y)dy, we can determine if it is exact by checking if ∂M/∂y = ∂N/∂x. If this condition is not satisfied, the differential form is not exact. However, we can multiply the differential form by an integrating factor to make it exact.

By multiplying the original differential form by an integrating factor, which is usually a function of either x or y, the resulting form will have equal partial derivatives, satisfying the condition for exactness. The integrating factor effectively "corrects" the form and makes it exact.

By finding the appropriate integrating factor and multiplying it with the given differential form, we can transform it into an exact form. This process is a fundamental technique in solving certain types of differential equations and allows us to find solutions that would otherwise be challenging to obtain.

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There are total 35 students in the class.

Given that,

Vikas ranks 9th in the class,

Assume that there are 'n' number of students in the class  

Therefore,

There are 8 students who have scored better than him.

So, The total number of students with a rank better or equal to Vikas,

= 8 + 1 (Vikas himself)

= 9.

Now, his friend got the 35th rank which is the last rank

This means that there are a total of 35 students in the class.

Also, also given that,

Vikas's rank from the last is 27th,

This means that there are 26 students who have scored lower than Vikas.

So, the total number of students with a rank worse or equal to Vikas,

= 26 + 1 (Vikas himself)

 = 27.

Therefore, The total number of students in the class = 35.

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Answer:

b

Step-by-step explanation:

For each increase of one unit on the x-axis (the horizontal axis), the amount on the y-axis (the vertical axis) increases by the slope of the line.

Slope is the amount of change in the y-axis that occurs as a result of a one-unit change in the x-axis. It is also known as the rise over run.

A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right. If the slope is zero, the line is horizontal.

The slope of a horizontal line is zero, and the slope of a vertical line is undefined because the x or y coordinate does not change as the other changes.

Therefore, the slope of a line represents the amount by which the value on the y-axis increases for every increase of one unit on the x-axis

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The number 100 0011 is a binary number. To convert it to a decimal number, we need to find the value of each digit, which is determined by its position, and then add them up.

The rightmost digit represents 2^0 (1), the next digit to the left represents 2^1 (2), the next represents 2^2 (4), and so on, with each subsequent digit representing a power of 2 that is one more than the previous digit. Therefore, we have:

100 0011 = 1 x 2^6 + 0 x 2^5 + 0 x 2^4 + 0 x 2^3 + 0 x 2^2 + 1 x 2^1 + 1 x 2^0

= 64 + 2 + 1

= 67

So, 100 0011 in binary represents the decimal number 67.

If we need to represent it as a floating-point number, we can use either "float" or "double", depending on the required precision.

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Statements is TRUE

Based on the graph of the general solution to the differential equation dy over dx equals 2 times x - 2 times y = dy/dx=2x-2y.

A differential equation's solution is an expression for the dependent variable in terms of one or more independent variables that satisfy the relationship.

The statement which is true is the slopes are all positive in quadrant I.

Given the differential equation is dy/dx=2x-2y

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

Given dy/dx=2x-2y

now slope=2x-2y

Along x-axis, y=0. So, slope=2x+0.

Since it depends upon x hence the slope along the y-axis are not horizontal.

Along y-axis, x=0. So, slope -2y+0.

The slope along the x-axis are also not horizontal.

In quadrant I:

x,y≥20

So, dy/dx ≥20

Therefore, the slopes are all positive in quadrant I. In quadrant IV,

x≥0,y≤0

so, dy/dx is not always positive.

The slope are not all positive in quadrant IV:

Therefore, the slope are all positive in quadrant I for the differential equation dy/dx=2x-2y.

General solution to the differential equation =

dy/dx=2x-2y.

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Complete Question:

Based on the graph of the general solution to the differential equation dy over dx equals 2 times x plus y comma which of the following statements is true?

The slopes along the y-axis are horizontal.

The slopes along the x-axis are horizontal.

The slopes are all positive in Quadrant 1.

The slopes are all positive in Quadrant 4.

Hope these images helps you...

AnswerEd by Benjemin ☺️

Answer:

x = 50

Step-by-step explanation:

You are correct.

x + m<PQS + m<PSQ = 180

m<PQS = m<QRT = 70

m<QST + m<PSQ = 180

120 + m<PSQ = 180

m<PSQ = 60

x + 70 + 60 = 180

x + 130 = 180

x = 50

Great job!

Fallis has 2000 square centimeters (cm²) tiles, she does not have enough tiles to cover the entire counter.

To find out if Ms. Fallis has enough tiles to cover the counter, we need to calculate how many tiles are required to cover an area of 2 square meters.

Since the tiles have a side length of 3 centimeters, we need to convert the area of the counter to square centimeters.

1 square meter = 10000 square centimeters (cm²)

So, 2 square meters = 20000 square centimeters (cm²)

Now, we need to calculate the area of each tile:

Side length of each tile = 3 centimeters (cm)

Area of each tile = \((side length)^2\) = \((3 cm)^2\) = 9 square centimeters (cm²)

To cover the counter, we need to divide the total area of the counter by the area of each tile:

Number of tiles required = (Total area of counter) / (Area of each tile)

= 20000 cm² / 9 cm²

= 2222.22

Since we cannot have a fraction of a tile, we need to round up to the nearest whole number of tiles. So, Ms. Fallis needs at least 2223 tiles to cover the counter.

Since she has 2000 square centimeters (cm²) tiles, she does not have enough tiles to cover the entire counter.

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Answer:

7) B, C

8) D

Step-by-Step-Explanation:

The first thing you need to solve for is the the parenthesis

the second one simplifies to x ≤ -7

Answer:

18

Step-by-step explanation:

Because -1 q would make it a positive 1q (q) so q=18

Answer:

To find the coordinates of any maximum or minimum and the intervals of increase and decrease for the function f(x) = x^2 + x - 6, we need to analyze its first and second derivatives.

Let's go step by step:

f'(x) = 2x + 1

Set the first derivative equal to zero to find critical points:

critical points: 2x + 1 = 0

critical points: 2x + 1 = 0 2x = -1

critical points: 2x + 1 = 0 2x = -1 x = -1/2

f''(x) = 2

f''(x) = 2Since the second derivative is a constant (2), we can conclude that the function is concave up for all values of x. This means that the critical point we found in step 2 is a minimum.

To find the y-coordinate of the minimum, substitute the x-coordinate (-1/2) into the original function: f(-1/2) = (-1/2)^2 - 1/2 - 6 f(-1/2) = 1/4 - 1/2 - 6 f(-1/2) = -24/4 f(-1/2) = -6

So, the coordinates of the minimum are (-1/2, -6).

Since the function has a minimum, it increases before the minimum and decreases after the minimum.

Interval of Increase:

(-∞, -1/2)

Interval of Decrease:

(-1/2, ∞)

Therefore, in either partial derivatives, we have u = 0 or v = 0.

The given information implies that two vectors u and v satisfy:

u * v = 0, where * denotes the dot product between vectors.

u X v = 0, where X denotes the cross product between vectors.

From the first equation, we know that the angle between u and v is either 90 degrees or 270 degrees. That is, u and v are orthogonal (perpendicular) to each other.

From the second equation, we know that the magnitude of the cross product u X v is equal to the product of the magnitudes of u and v multiplied by the sine of the angle between them. Since u and v are orthogonal, the angle between them is either 90 degrees or 270 degrees, which means that the sine of the angle is either 1 or -1. Therefore, we have:

|u X v| = |u| * |v| * sin(θ)

= 0

Since the magnitudes of u and v are non-negative, it follows that sin(θ) must be zero. This can only happen if the angle between u and v is either 0 degrees (i.e., u and v are parallel) or 180 degrees (i.e., u and v are anti-parallel).

In the case where u and v are parallel, we have:

u * v = |u| * |v| * cos(θ)

= |u|²

= 0

This implies that |u| = 0, which means that u = 0.

In the case where u and v are anti-parallel, we have:

u * v = |u| * |v| * cos(θ)

= -|u|²

= 0

This again implies that |u| = 0, which means that u = 0.

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The argument can be formalized as follows:Premise: Vegetarians don't eat meat.Premise: Bill is a vegetarian.Premise: Pork is a kind of meat.Therefore, Bill does not eat pork.

The argument follows a simple deductive form known as modus tollens. Modus tollens is a valid argument form that states if a conditional statement ("if A, then B") is true and the consequent (B) is false, then the antecedent (A) must also be false.

In this case, the conditional statement is "Vegetarians don't eat meat," and the false consequent is "Bill eats pork." Therefore, the argument concludes that the antecedent must be false, leading to the conclusion that "Bill does not eat pork."

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The given system of equations to have a Unique solution, the value of k must be any real number except 1 (k ≠ 1).

The value of k for which the given system of equations has a unique solution, we can use the concept of determinants. The system of equations is as follows:

kx + 2y = 3   -- (1)

3x + 6y = 10  -- (2)

To have a unique solution, the determinant of the coefficients of x and y must not be zero.

The determinant of the coefficient matrix for the system is:

D = | k   2 |

       | 3   6 |

By calculating the determinant, we have:

D = (k * 6) - (2 * 3)

D = 6k - 6

For the system to have a unique solution, the determinant D must not equal zero.

6k - 6 ≠ 0

Simplifying the inequality:

6k ≠ 6

Dividing both sides by 6:

k ≠ 1

Therefore, for the given system of equations to have a unique solution, the value of k must be any real number except 1 (k ≠ 1).

In other words, if k is not equal to 1, the system of equations will have a unique solution. If k is equal to 1, the system will either have infinitely many solutions or no solution.

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Answer:

B. 70,000

Step-by-step explanation:

The domain of the function is all real numbers and  range is  y ≥ -1.

Since the vertex is at (1,-1), the axis of symmetry is x = 1.

This means that the domain of the function is all real numbers.

To find the range, we need to consider the y-values of the graph. Since the vertex is the lowest point of the graph, the range must be all y-values greater than or equal to -1.

However, since the parabola opens upwards, there is no upper bound on the y-values.

Therefore, the range is given by y ≥ -1.

Hence, the domain of the function is all real numbers and  range is  y ≥ -1.

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When compared to a normal distribution, a t-distribution with a small degrees of freedom has heavier tails, indicating a higher probability of extreme values. As the degrees of freedom increase, the shape of the t-distribution approaches that of a normal distribution.

The shape of a t-distribution with a small degrees of freedom (df) differs from that of a normal distribution. The first paragraph provides a summary of the answer, and the second paragraph explains the details of the comparison.

A t-distribution with a small degrees of freedom has a shape that is similar to a normal distribution, but with heavier tails. As the degrees of freedom decrease, the t-distribution becomes more spread out and has a higher probability of extreme values compared to a normal distribution.

The tails of the t-distribution are fatter or thicker than those of a normal distribution. This means that the t-distribution has a higher probability of extreme values, making it more likely to observe values far away from the mean. In contrast, the normal distribution has thinner tails, indicating a lower probability of extreme values and a higher concentration of data around the mean.

The shape of the t-distribution approaches that of a normal distribution as the degrees of freedom increase. When the degrees of freedom are large (typically above 30), the t-distribution becomes very similar to a normal distribution, and the differences between them become negligible.

The t-distribution is widely used in statistical inference, especially in situations where the sample size is small or when the population standard deviation is unknown. It provides a more appropriate distribution for estimating population parameters when the underlying data exhibit variability.

In summary, compared to a normal distribution, a t-distribution with a small degrees of freedom has heavier tails, indicating a higher probability of extreme values. As the degrees of freedom increase, the shape of the t-distribution approaches that of a normal distribution.

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Answer:

MOnkey mode

Step-by-step explanation:

cause why not

~~~~~~~~~~~~~~~~~~~~~~~~~~~~HITHERE~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

                         ~~~~~~~~~~~~I THINK IT IS 7~~~~~~~~~~~~~~~~~

I THINK IT IS 7 BECAUSE IT CANT BE MORE AND IT CANT BE LESS SO IT        

~~~~~~~~~~      IS A BIG SIDE SO THAT'S WHY I PICKED 7.~~~~~~~~~~~~~

~~~~~~~~~~~~~~TELL ME IF I AM WRONG~~~~~~~~~~~~~~~~~~~

Answer:

x=-2

Step-by-step explanation:

its mcq if u wan full sln i can give

The actual cost to see the game is $150, as that is the amount you paid for the ticket. The cost in this scenario can be considered an opportunity cost. By choosing to attend the game instead of selling the ticket for $400, you forgo the opportunity to earn that additional $400.

In this scenario, the cost of attending the game refers to the actual amount of money you spent on the ticket, which is $150. This is the out-of-pocket expense that directly affects your financial resources.

On the other hand, the opportunity cost is the potential benefit or value that you give up by choosing one option over another. In this case, if you had sold the ticket for $400, you would have received a higher amount of money, which represents the opportunity cost of attending the game. By deciding to go to the game, you forego the opportunity to earn that additional $400.

Opportunity cost is a concept in economics that emphasizes the value of the next best alternative forgone when making a decision. It helps assess the trade-offs involved in different choices and helps in evaluating the true cost of a decision beyond the immediate financial expenses.

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Answer:

Step-by-step explanation:

A function gif g(x)

= f(x + 4) + 8 is a translated version of function f(x) by 4 units in the negative direction of the x-axis (shifted left by 4 units) and the entire graph of function f(x) is shifted 8 units upwards.

The 3 main features of a graph of the function gif g(x)

= f(x + 4) + 8 are: Translation (Shift) in x-axis: The entire graph of f(x) is shifted left or right by a distance of c units. If c is negative, the graph is shifted to the right; if c is positive, it is shifted to the left. Translation (Shift) in y-axis: The entire graph of f(x) is shifted upwards or downwards by a distance of k units. If k is positive, the graph is shifted upwards; if k is negative, it is shifted downwards. Affected Points: Every point on the graph of f(x) is shifted left or right by a distance of c units and up or down by a distance of k units to form the graph of the transformed function g(x).In this particular case, f(x) has been shifted 4 units to the left and then the entire graph has been shifted 8 units up.

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Answer:5.656854

Step-by-step explanation:

The representation of the expression 2x²×3yx²  in terms of A\(x^{m}\)\(y^{n}\)where A is a real number and m and n are integers is 6x⁴y¹.

Index (indices) in Maths is the power or exponent which is raised to a number or a variable.

In another word the mathematics of power or exponent of any number is called indices.

As per the given expression, 2x²3yx²

Rearrange the expression as

2x²3yx² = 2×3×x²x²×y

⇒ 6x²⁺²y

⇒ 6x⁴y¹

Hence"In terms of  A\(x^{m}\)\(y^{n}\) where A is a real number and m and n are integers, statement 2x²×3yx² is represented as 6x4y.x⁴y¹".

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Answer:

Brainliest pls

Step-by-step explanation:

-20

Answer:

The answer is -20.

Step-by-step explanation:

REMEMBER THIS:

Please excuse my dear aunt sally…

PLEASE = PARENTHESIS

EXCUSE= EQUATION

MY = MULTIPLICATION

DEAR = DIVISION

AUNT = ADDITION

SALLY = SUBTRACTION

^In that order^

Remember to use this statement to remember how to simplify the expression. PEMDAS.