Consider an upright cone that has a base radius of r and height h that has been obtained by revolving a triangular plane region (pictured below) about the y-axis. Apply the cylindrical shells method to con- Ty firm that the volume of the cone is V = arh. h + 0 r

True. Marginal cost refers to the additional cost incurred by producing one more unit of output.

Since the production of one more unit requires the use of additional variable factors of production (such as labor or raw materials), marginal cost always reflects the cost of those variable factors. Fixed costs, on the other hand, do not change with changes in output and are not included in marginal cost calculations. Therefore, marginal cost only reflects the change in cost associated with variable factors of production.

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Answer:

\(( c / 10 ) * 4\)

Step-by-step explanation:

\(\displaystyle\bf \underbrace{19}_910{\underbrace{1}_9} \Longrightarrow This\: is \:an \:\:arithmetic\:\: progression\)

the volume of the solid generated by revolving the plane region about the x-axis is 486π/5 cubic units.

To use the shell method to find the volume of the solid generated by revolving the plane region about the x-axis, we need to integrate the circumference of a cylindrical shell from x = 0 to x = 3 (where y = 27 corresponds to x^3 = 27, or x = 3).

Consider a cylindrical shell of thickness dx, with radius x and height y = \(x^3\). The circumference of the shell is 2πx, and its volume is given by the product of the circumference and the height of the shell, which is y =\(x^3\):

\(dV = 2πx * x^3 dx\)

Integrating from x = 0 to x = 3, we have:

V = ∫[0,3] 2πx *\(x^3\) dx

= 2π ∫[0,3] \(x^4\) dx

= 2π [\(x^5/5\)] [0,3]

= 2π * (\(3^5\)/5)

= 2π * 243/5

= 486π/5

Therefore, the volume of the solid generated by revolving the plane region about the x-axis is 486π/5 cubic units.

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Answer:

uh I don't even know what this is

Answer: x = 500

Step-by-step explanation:

Use the Pythagorean Theorem

a²+b²=c²

300² + 400² = x²

90000 + 160000 = x²

250000 = x²

√250000 = √x²

500 = x

hope i explained it :)

The population in 2020 is given as follows:

255,323.

The population is obtained applying the proportions in the context of the problem.

From 2010 to 2015, the population grew by 7%, hence the population in 2015 is obtained as follows:

246000 x 1.07 = 263220.

From 2015 to 2020, the population fell by 3%, hence the population in 2020 is obtained as follows:

0.97 x 263220 = 255,323.

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Find parametric equations for the line that is tangent to the given curve at the given parameter value. This statement is False.

In order to find parametric equations for a line tangent to a curve at a given parameter value, we need to know the equation of the curve. The terms "parametric equations" and "tangent to the given curve" indicate that we are dealing with a parametric curve. Therefore, we cannot determine if the statement is true or false without additional information.

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The solution to the initial value problem is:

y(t) = (-3/4) * e^(-4t+4) + (3/8) * e^(2t+8)

To solve a second-order linear homogeneous differential equation the equation is y′′ 2y′-8y = 0.

Given initial conditions: y(102) = 3 and y′(102) = -12.

To solve this differential equation, we can use the characteristic equation: r^2 + 2r - 8 = 0

Factoring this equation, we get: (r + 4)(r - 2) = 0

So the roots of the characteristic equation are r = -4 and r = 2.

The general solution to the differential equation is:

y(t) = c1 * e^-4t + c2 * e^2t

To find the values of c1 and c2, we can use the initial conditions.

We know that y(102) = 3, so we can substitute t = 2 into the general solution:

3 = c1 * e^-8 + c2 * e^4

We also know that y′(102) = -12, so we can take the derivative of the general solution and substitute t = 2:

y′(t) = -4c1 * e^-4t + 2c2 * e^2t

y′(102) = -4c1 * e^-8 + 2c2 * e^4 = -12

Solving for c1, we get:

c1 = (-3/4) * e^4 + (3/4) * e^-8

Solving for c2, we get:

c2 = (3/8) * e^8 - (3/8) * e^-4

Therefore, the solution to the initial value problem is:

y(t) = (-3/4) * e^(-4t+4) + (3/8) * e^(2t+8)

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To make 40 liters of a 35%  insecticide solution, the botanist should take 28 liters from the 20% solution and 12 liters from 70% solution.

The concentration of a solution indicates the fraction of solute in the solution. Concentration can be expressed in volume per volume or weight per volume. For example 20% v/v means in 100 ml solution there is 20 ml solute.

In the given problem:

solution A = 20%

solution B = 70%

New solution = 35%, volume 40 liters

Let p be the volume taken from the solution A, then the volume taken from the solution B = 40 - p.

Hence,

The amount of solute in the new solution:

20% p + 70% (40 - p) = 35% x 40

0.2 p + 0.7(40 - p) = 0.35 x 40

0.7 p - 0.2 p = 0.7 x 40 - 0.35 x 40

0.5 p = 0.35 x 40

p = 2 x 0.35 x 40 = 28

Hence, the volume taken from solution A = p = 28 liters and from solution B is (40 -28) = 12 liters.

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Answer:

$2520

Step-by-step explanation:

would it be 42$ or 42000$? if its 42000$ it would be $2520

42000/100*6

Answer:

m = -5/3

Y-intercept: (0, 64/3)

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (14, -2) and (5,13)​

We see the y increase by 15 and the x decrease by 9, so the slope is

m = -15/9 = -5/3
The y-intercept is located at ( 0, 64/3)

Step-by-step explanation:

For a right triangle such as this

Cos Φ = adjacent leg / hypotenuse

For this question      cos (37 ) = 11/x

                                x =   11 / cos (37) =   8.8    units

Answer:

Gross Domestic Product (GDP) includes all final goods and services produced within a country, in a specific period and doesn't necessarily include all the transactions that are going in the economy.

For example: Used domestic car buying or selling won't be counted for the GDP of current year, as it was manufactured and sold in 2000.\]Step-by-step explanation:

Let's check one by one

#1

False

#2

True

#3

True

#4

False

Answer:

A sphere

Step-by-step explanation:

A cross section of a three dimensional figure is the surface or intersection of the three dimensional figure and a plane, it is the shape obtained by cutting straight through the three dimensional figure

The shape of an inclined cross section of a cube can be a triangle however, he shape of a horizontal and inclined cross section of a sphere is a circle.

Answer:

12

Step-by-step explanation:

\(\frac{25.2}{2.1}=\frac{252}{21} =\frac{84}{7}=12\)

Answer:

Karina is correct

Step-by-step explanation:

See attached

Area that Karina cleaned up:

Area that Petty cleaned up:

As we see Karina cleaned up more area than Petty, so she is correct

The chi-square value for a one-tailed (upper tail) hypothesis test at a 5% level of significance and a sample size of n=25 is c. 36.415

What is chi-square?

Chi-square (χ²) is a statistical test that measures the relationship between categorical variables. It is used to determine if there is a significant association or independence between two variables based on observed frequencies compared to expected frequencies. The chi-square test is a statistical method used to determine if there is a significant association or independence between categorical variables based on observed and expected frequencies in a contingency table.

Degrees of freedom = n - 1

= 25 - 1

= 24

and alpha = 0.05

χ²⁽⁰°⁰⁵,²⁴⁾ =  36.415      …using chi-square table for right tail.

Therefore, the chi-square value for a one-tailed (upper tail) hypothesis test at a 5% level of significance and a sample size of n=25 is c. 36.415.

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The skewness of the annual salary column is -1.35, indicating that the data is slightly skewed to the left, and the kurtosis of the annual salary column is 0.46, indicating that the data is slightly platykurtic.

a. Age: Numeric

Gender: Categorical

Department: Categorical

Job Title: Categorical

Annual Salary: Numeric

Experience: Numeric

b. Number of Males: 40

Number of Females: 60

Proportion of Males: 40/100 = 0.40

Proportion of Females: 60/100 = 0.60

Annual Salary Frequency 0 - 9,999 10 10,000 - 19,999 15 20,000 - 29,999 10 30,000 - 39,999 13 40,000 - 49,999 8 50,000 - 59,999 6 60,000 - 69,999 6 70,000 - 79,999 5 80,000 - 89,999 4 90,000 - 99,999 3 100,000 - 109,999 2 110,000 - 119,999 1 120,000 - 129,999 4 130,000 - 139,999 0 140,000 - 149,999 1 150,000 - 159,999 1 160,000 - 169,999 0

Annual Salary Frequency Relative Frequency 0 - 9,999 10 0.1 10,000 - 19,999 15 0.15 20,000 - 29,999 10 0.1 30,000 - 39,999 13 0.13 40,000 - 49,999 8 0.08 50,000 - 59,999 6 0.06 60,000 - 69,999 6 0.06 70,000 - 79,999 5 0.05 80,000 - 89,999 4 0.04 90,000 - 99,999 3 0.03 100,000 - 109,999 2 0.02 110,000 - 119,999 1 0.01 120,000 - 129,999 4 0.04 130,000 - 139,999 0 0 140,000 - 149,999 1 0.01 150,000 - 159,999 1 0.01 160,000 - 169,999 0 0

Annual Salary Frequency Relative Frequency Cumulative Frequency 0 - 9,999 10 0.1 10 10,000 - 19,999 15 0.15 25 20,000 - 29,999 10 0.1 35 30,000 - 39,999 13 0.13 48 40,000 - 49,999 8 0.08 56 50,000 - 59,999 6 0.06 62 60,000 - 69,999 6 0.

The six variables are Age (Numeric), Gender (Categorical), Department (Categorical), Job Title (Categorical), Annual Salary (Numeric), and Experience (Numeric). The number of males and females are 40 and 60 respectively, with proportions of 0.40 and 0.60 respectively. The skewness of the annual salary column is -1.35, indicating that the data is slightly skewed to the left, and the kurtosis of the annual salary column is 0.46, indicating that the data is slightly platykurtic.

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To determine which functions are solutions of the given differential equation y'' + y = 3 sin(x), we need to check if plugging each function into the differential equation satisfies the equation. We will examine each option and identify the functions that satisfy the equation.

The differential equation y'' + y = 3 sin(x) represents a second-order linear homogeneous differential equation with a particular non-homogeneous term.
(a) Plugging y = 3 sin(x) into the differential equation gives 0 + 3 sin(x) ≠ 3 sin(x). Therefore, y = 3 sin(x) is not a solution.
(b) Plugging y = (3/2)x sin(x) into the differential equation gives (3/2) sin(x) + (3/2)x sin(x) = (3/2)(1 + x) sin(x), which is not equal to 3 sin(x). Therefore, y = (3/2)x sin(x) is not a solution.
c) Plugging y = 3x sin(x) - 4x cos(x) into the differential equation gives 6 cos(x) - 4 sin(x) + 3x sin(x) - 3x cos(x) = 3 sin(x), which satisfies the equation. Therefore, y = 3x sin(x) - 4x cos(x) is a solution.
(d) Plugging y = 3 cos(x) into  the differential equation gives -3 sin(x) + 3 cos(x) = 3 sin(x), which is not equal to 3 sin(x). Therefore, y = 3 cos(x) is not a solution.
(e) Plugging y = (-3/2)x cos(x) into the differential equation gives (3/2) sin(x) - (3/2)x cos(x) = (-3/2)(x cos(x) - sin(x)), which is not equal to 3 sin(x). Therefore, y = (-3/2)x cos(x) is not a solution.
Based on the analysis, the only function that is a solution to the given differential equation is y = 3x sin(x) - 4x cos(x) (option c).

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The equation of the plane passing through the point (1, -1, 0) and containing the line with symmetric equations x = y = 2z is x + y - 4z = -4. The equation of the plane passing through the line of intersection of the planes x - 2y + 3z = 6 and 2x + y - z = 4 is 5x - 4y + 7z = 18.

To find the equation of the plane passing through the point (1, -1, 0) and containing the line with symmetric equations x = y = 2z, we can use the point-normal form of the equation. Since the line is parallel to the plane, its direction ratios (1, 1, 2) become the normal vector of the plane. Substituting the point (1, -1, 0) into the equation form, we get x + y - 4z = -4.

To determine the equation of the plane passing through the line of intersection of the planes x - 2y + 3z = 6 and 2x + y - z = 4, we need to find a vector that is perpendicular to both planes. The cross product of the normal vectors of the given planes will give us the direction vector of the line of intersection. Taking the cross product, we obtain (5, -4, 7). Using this direction vector and a point on the line of intersection, we can form the equation of the plane as 5x - 4y + 7z = 18.

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This question is about rotations of polygons.

To rotate a polygon onto itself, we need to know the exact rotation we have to do. This rotation depends on the type of polygons, specifically, the number of sides.

To know the exact angle rotation to map the polygon onto itself, we just have to divide 360° by the number of sides.

Answer:

This question is about rotations of polygons.

To rotate a polygon onto itself, we need to know the exact rotation we have to do. This rotation depends on the type of polygons, specifically, the number of sides.

To know the exact angle rotation to map the polygon onto itself, we have to divide 360° by the number of sides.

Therefore, the right answer is the third choice.

Step-by-step explanation:

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The final expression is (28 + 45x²)/63x

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

4/9x + 5x/7

Find LCM of 9x and 7

The LCM of 9x and 7 is 63x

Now,

(28 + 45x²)/63x

Thus,

The final expression is (28 + 45x²)/63x

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Answer:

6.26 yards

Step-by-step explanation:

Answer:

6.25 would be the answer :)

Step-by-step explanation:

Rounded to the nearest hundredths place, the value of x in the equation is approximately 3.15.

To find the value of x in the equation 0.45(x * 1.6) + 5x = 18, we need to solve the equation for x. Let's go step by step:

0.45(x * 1.6) + 5x = 18

First, simplify the expression inside the parentheses:

0.45(1.6x) + 5x = 18

Multiply 0.45 by 1.6:

0.72x + 5x = 18

Combine like terms:

0.72x + 5x = 18

5.72x = 18

Now, divide both sides of the equation by 5.72 to solve for x:

x = 18 / 5.72

x ≈ 3.15

Rounded to the nearest hundredths place, the value of x in the equation is approximately 3.15.

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Answer:

A

Step-by-step explanation:

In a parallelogram the opposite angles are congruent, thus

∠ JHF = ∠ JEF = 142°

∠ JHF and ∠ FHG are adjacent angles and are supplementary, thus

∠ FHG = 180° - 142° = 38°

The sum of the 3 angles in a triangle = 180° , thus

∠ HFG = 180° - (90 + 38)° = 180° - 128° = 52° → A

Answer:

Area of cube = 6l²

= 6×2²

= 24 ft²

2 feet.

how many square feet of wood he used to build the box.

each side measures 2ft.

A=L²=(2 ft)²=4 ft²

A cube has 6 sides so the total quantity of wood is:

Wood=6×A

=6×4 ft²

=24 ft²

he used 24 ft² of wood to build the box.

Step-by-step explanation:

Here is a linear program that would decide how James should invest his money to maximize the total amount of money he would have at year 10:

Let x[i][j] represent the amount of money invested in bond type j in year i, where j = A, B, C. Let s[i] represent the amount of money in the savings account at the end of year i.

Maximize: s[10]

Subject to:

s[0] = M

s[i] = s[i-1]*1.025 + n + 1.045*x[i-2][A] + 1.07*x[i-3][B] + 1.4641*x[i-4][C] + 0.045*x[i-1][A] + 0.07*x[i-2][B] for 2 < i < 9

s[9] = s[8]*1.025 + n + 1.045*x[7][A] + 1.07*x[6][B] + 1.4641*x[5][C] + 0.045*x[8][A]

s[10] = s[9]*1.025 + 1.045*x[8][A] + 1.07*x[7][B] + 1.4641*x[6][C]

x[i][j] >= 0 for all i and j

The objective function maximizes the amount of money in the savings account at the end of year 10.

The first constraint sets the initial amount of money in the savings account to M.

The second constraint calculates the amount of money in the savings account at the end of each year for years 2 to 8, taking into account the interest earned on the savings account, additional investment n, and any matured bonds or interest payments.

The third constraint calculates the amount of money in the savings account at the end of year 9, taking into account the interest earned on the savings account, additional investment n, and any matured bonds or interest payments.

The fourth constraint calculates the amount of money in the savings account at the end of year 10, taking into account any matured bonds.

The last constraint ensures that all investments are non-negative.

This linear program can be solved using a linear programming solver to determine how James should invest his money to maximize his total amount at year 10.

To maximize the total amount of money James would have at year 10, we can formulate a linear program considering James's investments in bonds A, B, and C, as well as his savings account.

Let's define the decision variables as follows:

xA: The amount invested in Bond A in each year.

xB: The amount invested in Bond B in each year.

xC: The amount invested in Bond C in each year.

xS: The amount placed in the savings account in each year.

The objective function to maximize would be:

Maximize Z = 1.045^2 * xA + 1.07^3 * xB + 1.1^4 * xC + 1.025^10 * xS

Subject to the following constraints:

xA, xB, xC, xS ≥ 0 (non-negativity constraint)

xA + xB + xC + xS ≤ M + (n * 7) (total investment limit each year)

xA ≤ M (investing limit in Bond A)

xB ≤ M + n (investing limit in Bond B)

xC ≤ M + (n * 3) (investing limit in Bond C)

The sum of the investments in each year (xA + xB + xC + xS) should be less than or equal to the amount available in the previous year plus the additional amount (n) available for the current year.

These constraints ensure that James invests within the given limits and distributes his investments appropriately each year. By solving this linear program, we can determine the optimal investment strategy for James to maximize his total amount of money at year 10, considering the interest rates and maturity periods of the bonds as well as the savings account interest rate.

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The arithmetic average return is probably too high for longer periods and the geometric average is probably too low for shorter periods.

When we look at historical returns, the difference between the geometric and arithmetic average returns isn't too hard to understand.

To put it slightly differently, the geometric average tells you what you actually earned per year on average, compounded annually. The arithmetic average tells you what you earned in a typical year. You should use whichever one answers the question you want answered. A somewhat trickier question concerns forecasting the future, and there's a lot of confusion about this point among analysts and financial planners.

Now, If we have estimates of both the arithmetic and geometric average returns, then the arithmetic average is probably too high for longer periods and the geometric average is probably too low for shorter periods.

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\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)