Can someone help me with 12 & 13.

Directions: Find the volume of each figure. Round to the nearest hundredth when necessary.

The solution of  f(x)/g(x) is the function x ^5/2 + 6x^3/2 + 1

option C is correct.

Here, we have,

given that,

the functions are:

f(x) = x^3+6x^2+x^1/2

g(x) = x^1/2

so, we have,

f(x)/g(x)

= x^3+6x^2+x^1/2 / x^1/2

= x^3/ x^1/2  +6x^2/ x^1/2  +x^1/2/ x^1/2

=x ^5/2 + 6x^3/2 + 1

Hence, The solution of  f(x)/g(x) is the function x ^5/2 + 6x^3/2 + 1

option C is correct.

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The area of the shaded region is (133π/9) square feet.

Given that the radius (r) is 4 ft, the area of the entire circle is:

A = π(4)² = 16π ft²

To find the area of the sector, we need to calculate the fraction of the circle that the central angle represents.

The fraction is determined by dividing the measure of the central angle (110°) by the total angle in a circle (360°).

Fraction of the circle represented by the sector = 110° / 360° = 11/36

To find the area of the sector, we multiply the fraction by the area of the entire circle:

Area of the sector = (11/36) × (16π)

= (11π/9) ft²

Finally, to find the area of the shaded region, we subtract the area of the sector from the area of the entire circle:

Area of shaded region = Area of entire circle - Area of sector

Area of shaded region = 16π - (11π/9)

= (144π - 11π)/9

= (133π/9) ft²

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Two reports that could be used to verify the accuracy of retirement contributions for the most recent payroll period are the Payroll Summary Report and the Retirement Contribution Report.

Two reports that could be used to verify the accuracy of retirement contributions for the most recent payroll period are:

Payroll Summary Report: This report provides a summary of the payroll transactions for the period, including details of employee wages, deductions, and employer contributions.

It should include a specific section or breakdown for retirement contributions, showing the individual employee contributions and the corresponding employer contributions.

By reviewing this report, one can ensure that the retirement contributions have been accurately calculated and remitted.

Retirement Contribution Report: This report specifically focuses on the retirement contributions made by both employees and the employer.

It should provide a detailed breakdown of the contributions for each employee, including the employee's contribution amount, the employer's matching or non-elective contribution amount, and any additional details related to the retirement plan.

This report allows for a comprehensive review of the retirement contributions to verify if they match the expected amounts based on employee records and plan guidelines.

By comparing the information in these reports with the employees' individual contribution records and the retirement plan requirements, it is possible to verify that the retirement contributions were accurately remitted for the most recent payroll period.

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The total surface area of the square pyramid is 28 m²

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

Given the square pyramid net:

Area of square base = 2 m * 2 m = 4 m²

Area of each triangle face = (1/2) * 2 m * 6 m = 6 m²

Area of the four triangle face = 4 * 6 m² = 24 m²

Total surface area = 24 m² + 4 m² = 28 m²

The total surface area is 28 m²

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Answer:

x=12.124

simplified would be x=12

Step-by-step explanation:

Here is your answer!

Answer:

[tex](x - 5)^2 + (y + 2)^2 = 5[/tex]

Step-by-step explanation:

The equation of a circle with a center at (h, k) and radius r is given by:

[tex]\bold{(x - h)^2 + (y - k)^2 = r^2}[/tex]

In this case, the center is at (5, -2) and the point that the circle passes through is (4, 0).

The distance between the center and the point is:

[tex]\sqrt{(5 - 4)^2 + ((-2) - 0)^2} = \sqrt{1 + 4} = \sqrt{5}[/tex]

Therefore, the equation of the circle is:

[tex](x - 5)^2 + (y + 2)^2 = \sqrt{5}^2[/tex]

Simplifying the equation, we get:

[tex]\bold{(x - 5)^2 + (y + 2)^2 = 5}[/tex] is a required equation

The additional information is needed to prove the triangles are congruent by the SAS Postulate is <ACB = <ACD.

We have, CB = CD

As, The SAS Congruence Theorem states that if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the two triangles are congruent.

In triangle ACB and ACD

AC = AC (common)

CB=  CD (given)

Now, to prove using SAS rule we need only one angle which is in between the two congruent sides then

<ACB = <ACD

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As the degrees of freedom increase, the Chi-square distribution becomes less skewed.

Option C is the correct answer.

We have,

The Chi-square distribution is a probability distribution that is commonly used in statistics.

It is often used in hypothesis testing and in constructing confidence intervals for population variances.

The shape of the Chi-square distribution depends on the degrees of freedom (df). The degrees of freedom represent the number of independent pieces of information used to estimate a parameter or make an inference.

When the degrees of freedom are small, such as 1 or 2, the Chi-square distribution is highly skewed to the right.

This means that the distribution has a long tail on the right side and is concentrated toward the lower values.

However, as the degrees of freedom increase, the Chi-square distribution becomes less skewed.

The distribution becomes more symmetrical and approaches a bell shape, similar to the shape of a normal distribution. This means that the values are more evenly spread out and there is less concentration towards the lower values.

Therefore,

As the degrees of freedom increase, the Chi-square distribution becomes less skewed.

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Answer:

-8 and 4

Step-by-step explanation:

P= -2

-2+6 = 4

-2-8= -8

The dimensions of the smaller prism are each multiplied by the factor of 1/3 for length, 1/4 for width, and 1/4 for height to produce the corresponding dimensions of the larger prism.

To determine the factor by which the dimensions of the smaller prism are multiplied to produce the corresponding dimensions of the larger prism, let's consider the relationship between the two prisms.

A prism is a three-dimensional shape with two parallel, congruent bases connected by rectangular faces. Since the problem specifies that the dimensions of the smaller prism are being multiplied to obtain the dimensions of the larger prism, we can infer that the prisms are similar, meaning they have the same shape but possibly different sizes.

Let's denote the dimensions of the smaller prism as length, width, and height, and the corresponding dimensions of the larger prism as L, W, and H.

To find the factor by which the dimensions are multiplied, we need to compare the corresponding sides of the two prisms. Based on the information provided, we can establish the following relationships:

L = 3 × length

W = 4 × width

H = 4 × height

We can rewrite these relationships as:

length = L/3

width = W/4

height = H/4

Now, let's compare the ratios of corresponding sides:

length/L = (L/3)/L = 1/3

width/W = (W/4)/W = 1/4

height/H = (H/4)/H = 1/4

From these ratios, we can observe that each dimension of the smaller prism is one-third (1/3) the size of the corresponding dimension of the larger prism in terms of length, one-fourth (1/4) in terms of width, and one-fourth (1/4) in terms of height.

Therefore, the dimensions of the smaller prism are each multiplied by the factor of 1/3 for length, 1/4 for width, and 1/4 for height to produce the corresponding dimensions of the larger prism.

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Answer:

65/100 that is the answer to this question

Answer:

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

In the given right triangle we have an angle of 37° and adjacent leg of 11 units given.

Missing is the length of hypotenuse, x.

Use cosine function:

Plug in known values and solve for x:

An additional information that is needed to prove the triangles are congruent by the SAS Postulate is: D. ∠BAC ≅ ∠DAC.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce that ∆BAC is congruent to ∆DAC when the angles A (∠A) are congruent by the reflexive property.

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Answer:

391 cm²

Step-by-step explanation:

area of the parallelogram,

A = base * height

= 23 * 17

= 391 cm²

Step-by-step explanation:

To multiply the polynomials (8v - 5)(v + 7), we can use the distributive property:

(8v - 5)(v + 7) = 8v(v + 7) - 5(v + 7)

Now we can simplify by multiplying each term:

8v(v + 7) - 5(v + 7) = 8v^2 + 56v - 5v - 35

Finally, we can combine like terms to get the simplified expression:

8v^2 + 51v - 35

Therefore, (8v - 5)(v + 7) = 8v^2 + 51v - 35.

The equation of the circle is (x - 2)² + (y - 3)² = 36

From the question, we have the following parameters that can be used in our computation:

The circle

Where, we have

Center = (a, b) = (2, 3)

Radius, r = 6 units

The equation of the circle is represented as

(x - a)² + (y - b)² = r²

So, we have

(x - 2)² + (y - 3)² = 6²

Evaluate

(x - 2)² + (y - 3)² = 36

Hence, the equation is (x - 2)² + (y - 3)² = 36

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Answer:

length=12ft

width=6ft

Step-by-step explanation:

The volume formula is V=lwh.

Plug the values into the equation like this: 432=(x+6)(x)(6)

Divide both sides of the equation by 6: 72=(x+6)(x)

Distribute the x:  [tex]72=x^{2} +6x[/tex]

Subtract the 72:  [tex]0=x^{2} +6x-72[/tex]

Factor: 0=(x+12)(x-6)

x=-12

x=6

Now, plug in x into the original length and width equations.

length: (6+6)

length=12

width=6

Answer:
147 floors

Explanation:

To determine the number of floors in the Burj Khalifa, we can use the information provided. We know that Andre stood 1000 meters away from the building and looked up at a 39.62-degree angle using a laser rangefinder. Let's calculate the height of the Burj Khalifa using basic trigonometry.

First, we can find the height of the building using the tangent function:

tan(angle) = height / distance

tan(39.62 degrees) = height / 1000 meters

height = tan(39.62 degrees) * 1000 meters

height ≈ 747.97 meters

Now, let's calculate the number of floors in the Burj Khalifa. We are given that each floor is 5.079 meters tall.

Number of floors = height / height of each floor

Number of floors = 747.97 meters / 5.079 meters

Number of floors ≈ 147.23 floors

Since we cannot have fractional floors, we can round the number down to the nearest whole number.

Therefore, there are approximately 147 floors in the Burj Khalifa.

Answer:

-4

Step-by-step explanation:

i jus did this question

The graph of the solution of the inequality is attached

From the question, we have the following parameters that can be used in our computation:

x - 4 < 5

Add 4 to both sides of the inequality

So, we have

x - 4 + 4 < 5 + 4

Evaluate the like terms

So, we have

x < 9

This means that the solution of the inequality is x < 9

See attachment for the graph

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Answer:

A. mBC = 71

B. mAB = 142

C. AD = 30

D. BD = 30

E. YD = 16

F. DC = 18

Step-by-step explanation:

A. mBC = mAC = 71

B. mAB = mBC + mAC = 71 + 71 = 142

C. AD = AB/2 = 60/2 = 30

D. BD = AD = 30

E. YA^2 = YD^2 + AD^2

YD^2 = YA^2 - AD^2 = 34^2 - 30^2 = 1156 - 900 = 256

YD = √256 = 16

F. DC + YD = YC

DC = YC - YD = 34 - 16 = 18

Below are the right probabilities for each scenario;

8. P(red, then green) [tex]\frac{1}{32}[/tex]; P(yellow, then blue) = [tex]\frac{1}{16}[/tex] and P(blue both times) [tex]\frac{1}{4}[/tex]

9. The probability of choosing a boy then rolling a number that is at most 4 is [tex]\frac{5}{14}[/tex]

10. The probability that both flights will be delayed is [tex]\frac{2}{7}[/tex].

11. P(nickel, then quarter) [tex]\frac{1}{20}[/tex];  P(penny, then not a dime) [tex]\frac{1}{10}[/tex]; P(both dimes)[tex]\frac{3}{20}[/tex]; P(both nickels) [tex]\frac{1}{20}[/tex]

For the compounded probability, we can solve them the following way;

8. a) P(red, then green) = P(red) × P(green) = (2/8) × (1/8) = 1/32

b) P(yellow, then blue) = P(yellow) × P(blue) = (1/8) ×(4/8) = 1/16

c) P(blue both times) = P(blue) × P(blue) = (4/8) ×(4/8) = 1/4

9. There are 28 total students and 6 total outcomes on a standard die.

P(boy, then a number at most 4) = (15/28) × (4/6) = 5/14

10. The probability of the first flight being delayed is 6/14, and the probability of the second flight being delayed is 8/12.

P(both flights delayed) = 6/14 × 8/12 = 2/7

11. There are 25 total coins: 4 pennies, 6 nickels, 10 dimes, and 5 quarters.

a) P(nickel, then quarter)  = (6/25) × (5/24) = 1/20

b) P(penny, then not a dime)  = (4/25) × (15/24) = 1/10

c) P(both dimes) = (10/25) × (9/24) = 3/20

d) P(both nickels) = (6/25) × (5/24) = 1/20

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Answer: 1080

Step-by-step explanation:

12x10x9=1080

Hoped this helped?!

Answer: C-Cylinder

Step-by-step explanation:

In this problem, you are rotating the rectangle on the x axis. If you rotate it along this side, the rectangle makes it a cylinder.

Para aquellos que necesitas este respuesta en español: En este problema, estás girando el rectángulo sobre el eje x. Si lo giras a lo largo de este lado, el rectángulo lo convierte en un cilindro.

I hope this helps!

Answer:

The correct answer is (C), cylinder.

Explanation:

When the rectangle is rotated around the axis shown, it will create a three-dimensional shape with two parallel bases that are connected by a curved surface. This shape is called a cylinder.

The area of the right triangle is 18.02 cm².

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sum of angles in a triangle is 180 degrees.

Therefore, let's find the area of the right angle triangle as follows;

let's find the height and base of the triangle.

using trigonometric ratios,

cos 75 = adjacent / hypotenuse

cos 75 = base / 12

base = 3.10582854123

Therefore,

sin 75 = opposite / hypotenuse

sin 75 = h / 12

height = 11.5911099155

height = 11.59

Therefore,

area of the triangle = 1 / 2 × 3.11 × 11.59

area of the triangle = 36.0483518371 / 2

area of the triangle = 18.0241759186

area of the triangle = 18.02 cm²

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The expression -2(5 + 7x) + 5(x + 5) is equivalent to the expression -9x + 15. So, the answer is option B: 15 - 9x.

To simplify the expression -2(5 + 7x) + 5(x + 5), we can distribute the coefficients and simplify further.

Starting with the expression -2(5 + 7x):

-2(5 + 7x) = -2 × 5 - 2 × 7x

= -10 - 14x

= -14x - 10

Now let's simplify the expression 5(x + 5):

5(x + 5) = 5 × x + 5× 5

= 5x + 25

Finally, combining the two simplified expressions:

-14x - 10 + 5x + 25

Combining like terms:

(-14x + 5x) + (-10 + 25)

-9x + 15

Therefore, the expression -2(5 + 7x) + 5(x + 5) is equivalent to the expression -9x + 15.

So, the answer is option B: 15 - 9x.

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