1. Sketch the solid of rotation formed by rotating the given two-dimensional figure
using the horizontal line shown as an axis of rotation.

Nominal variables are calculated in current year prices and real variables are measured in base year dollars to adjust for the effect of inflation by the price index.

Nominal Variable:

Nominal variables as well as dichotomous and ordinal variables constitute the three types of categorical variables. Dichotomous variables are a subtype of dummy variables that can only have two levels or categories. On the other hand, ordinal variables can have two or more categories, but they can be ordered or ordered. In addition to categorical variables, other types of variables are used, such as interval and ratio variables. An example of a dummy variable is hair color. Indeed, the hair can be of different colors like blond, black, brown, red, etc. These categories cannot be sorted and no operations can be performed.

Real Variable:

A real variable is one that does not take into account the effects of price and/or inflation. Conversely, nominal variables are variables that do not take into account the effect of inflation. As a result, changes in prices and inflation affect nominal rather than real variables. Real changes in private equity, real disposable income, real government spending, real private fixed investment, etc. The same concept of calculating real wages applies to all of these variables.

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The composite function has its value to be 25

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

f(x) = x^2 - 4

g(x) = 2x - 1

Given the composite function [f x g] (3)., we have

[f x g] (3) = f(3) * g(3)

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

[f x g] (3) = (3^2 - 4) * (2 * 3 - 1)

Evaluate

[f x g] (3) = 25

Hence, the solution is 25

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The conversion of 71 inches is equal to 5.9166666667 feet.

The US customary measuring unit is the foot,

It is denoted by the letter "ft."

To convert 5 meters (m) to feet,

The imperial and American customary systems of measuring both use the symbol "in" to represent 1 inch as a unit of length.

It was decided that one inch was exactly equal to 25.4 millimetres.

12 inches make up a foot, and 36 inches make up a yard.

We know that,

1 in = 0.0833333333 ft

1 ft = 12 in

1 in = 2.54 cm and 1 cm equals 0.3937007874 in

To convert inches to feet,

We need to divide the number of inches by 12,

Since there are 12 inches in a foot.

Therefore,

71 inches divided by 12 gives us:

71 inches ÷ 12 = 5.9166666667 feet

(rounded to ten decimal places)

So 71 inches is equal to approximately 5.9166666667 feet.

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There are a total of 2π Radians in a circle that is equal to 360°.

A circle is the locus of all those points which are at the same distance from a particular point called center in any plane. A radian is basically another unit of measuring the angle, it is equivalent to the standard degrees measures that we use commonly to find an angle.

When we make a circle, the angle it makes is equal to 360°. This is a characteristics property of a circle.

Now, we know,

π Radians = 180°

2 x 180° = 2xπ Radians

360° = 2π Radians

So, the circle will have a total of 2π Radian in it.

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A total of 23800 cubes can fit inside the box of the given dimensions.

The volume of a cube is given by -

Volume = a x a x a = a³

Given is that a box has a length of 10 inches, a width of 8[tex]\frac{3}{4}[/tex] inches, and a height of 4[tex]\frac{1}{4}[/tex] inches.

The volume of the box would be -

V = 10 x 8[tex]\frac{3}{4}[/tex] x 4[tex]\frac{1}{4}[/tex]

V = 10 x 35/4 x 17/4

V = 371.875 inches³

The volume of cube -

v = 1/4 x 1/4 x 1/4

v = 0.015625 inches³

Number of cubes that will fill the box would be -

n = V/v

n = 371.875/0.015625

n = 23800

Therefore, a total of 23800 cubes can fit inside the box of the given dimensions.

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The value of 105 lbs into kilogram can be converted by multiplying pounds by 0.453592 so the answer is 47.627 kilograms.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

The SI unit of mass is the kilogramme (kg). It has the same mass as the international kilogramme prototype. The International Bureau of Weights and Measures maintains a platinum-iridium international prototype similar to this one. A kilogramme is about equivalent to 2.20462262184878 pounds.

The legal definition of a pound, or the international avoirdupois pound, is 0.45359237 kilogrammes.

105 x 0.45359237 = 47.62719885

105 lbs ≈ 47.63 kg

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As per measurement, 30 inches is equivalent to 2.5 feet.

Measurement is an essential aspect of our daily life, and it helps us to quantify things precisely. The measuring units are used to determine the size, weight, or any physical quantity of an object. It is essential to know the conversions between the measuring units to make the necessary calculations accurately.

In this context, let's discuss the conversion of inches to feet.

Inches and feet are two common units of measurement used for length or distance. Inches are the smaller unit, and feet are the larger unit. One foot is equivalent to 12 inches. Therefore, to convert inches to feet, we divide the given number of inches by 12.

Let's consider we need to convert 30 inches to feet.

30 inches / 12 inches per foot = 2.5 feet

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To convert between pounds and kilogrammes, multiply the number of pounds by 0.45359237, and to do the opposite, multiply the number of kilogrammes by 2.20462.

65 kg is equal to 143.3003 lbs.

The fundamental mass unit in the metric system is the kilogramme (kg). A kilogramme and 1,000 cubic centimetres of water have fairly similar masses.

One pound is approximately equal to 454 grams. One kilogram is the same as 2.20462 lbs.

One pound is equal to 0.45359237 kilograms.

To convert kilograms (kg) to pounds (lbs), you can use the following formula:

To convert kilograms to pounds, multiply your figure by 2.20462

To convert 65 kg to lbs, you can multiply 65 by 2.20462:

65 kg X 2.20462 lbs/kg

= 143.3003 lbs

Therefore, 65 kg is approximately equal to 143.3003 lbs.

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The probability that a student took both music and dance classes is 0.1.

Probability in mathematics is the possibility of an event in time. In simple words how many times does that incident is happening in any given time interval?

From the information given, we know that:

35 students took music classes, which includes x and y.

45 students took dance classes, which includes y and z.

30 students did not take either music or dance classes, which includes the area outside the circles.

We can also see that the total number of students is 100, so the sum of all the areas in the Venn diagram must be 100.

Therefore, we can set up the equation:

x + y + z + 30 = 100

Simplifying, we get:

x + y + z = 70

We want to find the probability that a student took both music and dance classes, which is the area of the overlap between the music and dance circles (represented by y) divided by the total number of students (100).

So, the probability is:

y/100

To find y, we can use the formula:

y = (total in music) + (total in dance) - (total in both)

y = 35 + 45 - (x + y + z)

Substituting x + y + z = 70, we get:

y = 35 + 45 - 70 = 10

Therefore, the probability that a student took both music and dance classes is:

y/100 = 10/100 = 0.1

Therefore, the probability is 0.1 or 10%.

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Answer: To determine which expressions are equivalent to the given expression, we need to simplify the given expression first:

2/3 (3a + 3b + 8) = 2a + 2b + 16/3

Now we can check which expressions are equivalent to this simplified expression:

A. 3a + 3b + (8 + 4) − 4 = 3a + 3b + 8, not equivalent

B. −(−¾a + ½¾⁄b + 8) = 3/4 a - 3/2 b - 8, not equivalent

C. (a + b + 8) (3a + 3b + 8) × ²1/1 = (3a^2 + 9ab + 24a + 3b^2 + 24b + 64)/1, not equivalent

D. 6x = 6x, not equivalent

E. a + b + 0 × c + 8 = a + b + 8, not equivalent

None of the expressions is equivalent to the given expression 2/3 (3a + 3b + 8).

Step-by-step explanation:

Answer:

  A) Only for 180° rotations

Step-by-step explanation:

You want to know if a quadrilateral can be rotated so that each side is parallel to the corresponding side of its image.

In general, a line segment's image will be parallel to the original if it is rotated 180°. Hence the line segments that make up a quadrilateral's image will be parallel to corresponding sides if the quadrilateral is rotated 180°.

The attachment shows a quadrilateral rotated 180°.

__

Additional comment

We assume that the "corresponding side" of AB is A'B' in the image.

If square ABCD is rotated 90°, then side AB will be parallel to side B'C', and the same will be true for 3 other pairs of sides. For the purpose of this question, we don't consider AB and B'C' to be "corresponding" sides.

Answer:

Where is the angle so I can help you?

The value 0.75 inches to mm is 19.05

in one inch = 25.4  millimeters

so in 0.75 inch is 0.75* 25.4 = 19.05 mm

customs (character: in or ″) is the unit of length in the British Imperial and US systems of measurement.1/36yard or1/12

one leg. A word derived from the Roman uncia ("twelfth"), the inch is sometimes used to convert similar units in other measurement systems that are usually understood to be derived from the width of the human thumb. .

The standard for the exact length of one inch has historically varied, but since its adoption by international shipyards in the 1950s and his 1960s, the inch has been based on the metric system and defined exactly as 25.4 mm. increase.

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To draw the different views of this figure we must simulate its rotation to see it from different angles. In the attached image are the different views.

To draw the different views of this figure we must take into account its shape. In this case we have a figure made up of four squares. Three of them are aligned and one of them is in the middle zone.

According to the above, to draw the views we must simulate rotations of this figure to establish its views. In the attached image are the views. In the top view you would only see two squares, in the front view you would see three squares and in the side view you would see all four squares.

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Answer:

Step-by-step explanation:

m

=

1

;  

n

=

−

2

Explanation:

Given:

4

m

+

n

=

2

-------------------------------Equation (1)

m

−

4

n

=

9

..........................................Equation (2)

Determine the value of n

Showing every step in the first part to demonstrate method

Consider Equation (2)

Add 4n to both sides

m

−

4

n

+

4

n

=

9

+

4

n

But

4

n

−

4

n

=

0

m

=

9

+

4

n

.....................................(3)

Substitute for m in (1) using (3)

4

m

+

n

=

2

→

4

(

9

+

4

n

)

+

n

=

2

Multiply out the bracket

⇒

36

+

16

n

+

n

=

2

36

+

17

n

=

2

Subtract 36 from both sides

17

n

=

−

34

Divide both sides by 17

n

=

−

34

17

=

−

2

'.........................................................

Determine the value of m

Substitute

n

=

−

2

into (2)

m

−

4

n

=

9

→

m

−

4

(

−

2

)

=

9

m

+

8

=

9

m

=

9

−

8

m

=

1

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Check

4

m

+

n

=

2

→

4

(

1

)

+

(

−

2

)

=

2

m

−

4

n

=

9

→

1

−

4

(

−

2

)

=

9

The given set of points {(-7, 20), (3, 5), (0, 5), (-2, 0), (6, -4), (-6, -9), (4, 4)} is a function since each x-value has a unique y-value.

To determine whether the given set of points is a function or not, we need to check if each input (x-value) corresponds to exactly one output (y-value).

Let's first list the x-values in the set: -7, 3, 0, -2, 6, and -6.

Now, we need to check if each of these x-values has a unique y-value. We can see that:

The point (-7, 20) has an x-value of -7 and a y-value of 20.

The point (3, 5) has an x-value of 3 and a y-value of 5.

The point (0, 5) has an x-value of 0 and a y-value of 5.

The point (-2, 0) has an x-value of -2 and a y-value of 0.

The point (6, -4) has an x-value of 6 and a y-value of -4.

The point (-6, -9) has an x-value of -6 and a y-value of -9.

The point (4, 4) has an x-value of 4 and a y-value of 4.

We can see that each of the x-values has a unique y-value. Therefore, this set of points is a function.

In fact, we can even represent this function using set-builder notation as:

{ (x, y) | x ∈ {-7, 3, 0, -2, 6, -6, 4}, y is the corresponding y-value for x }

or using a mapping notation as:

f = { (-7, 20), (3, 5), (0, 5), (-2, 0), (6, -4), (-6, -9), (4, 4) }

where f(x) is the corresponding y-value for x.

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The sum of the algebraic expressions 8x - 2 and -3x² - 7 is given as follows:

-3x² + 8x - 9.

The algebraic expressions for this problem are defined as follows:

To add them, we must combine the like terms, that is, add the terms that have the same variable and exponent, which are given as follows:

Hence the sum has the result given as follows:

-3x² + 8x - 9.

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The percentages of executives receiving bonuses are given as follows:

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for the percentage of executives receiving bonuses in t years after 1998 is given as follows:

B(t) = 4.816(1.338)^t.

2002 is 2002 - 1998 = 4 years after 1998, hence the percentage is given as follows:

B(4) = 4.816(1.338)^4 = 15.44%.

The percentage for 2003 is then given as follows:

B(5) = 4.816(1.338)^5 = 20.65%.

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Answer:

122.5 feet

Step-by-step explanation:

[tex]\frac{4}{35}[/tex] = [tex]\frac{14}{x}[/tex]  cross multiply and solve for x

4x = 490  Divide both sides by 4

x = 122.5

The solution for each parts is shown below.

Where two lines intersect, there are two vertical angles.

Given:

1. Two adjacent angles

<1 + <2 = 135

2x + 2x+ 7 = 135

4x + 7 = 135

4x = 128

x= 32

2. If one of the angles has a measure of 39° then other angle is

= 90 - 39

= 51 degree.

3. The angles are complementary.

2x + 3 + 2x = 90

4. Two complementary angles are expressed as 2x and 3x.

2x + 3x= 90

5x = 90

x = 18

So, 2x = 36 and 3x = 54 degree.

5. Angles j and k are supplementary angles.

<j + <k = 180

<j + 117 = 180

<j = 63

6. Two supplementary angles are ∠ABC=105° and ∠CBD=(3x−24)°.

105 + 3x -24 = 180

3x + 81 = 180

7. Two angles are supplementary. ∠ACB=4x° and ∠BCD=6x+50°.

<ACB + <BCD = 180

4x + 6x + 50 = 180

10x = 130

x= 13

8. For two vertical angles where ∠1=2x+26° and ∠3=3x−32°

<1 = < 3

2x + 26 = 3x -32

2x - 3x = -32 - 26

-x =-58

x= 58

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First, we need to perform the calculation within the parentheses:

698347 + 2834619 = 3532966

Then, we can multiply the result by 3:

3532966 x 3 = 10598898

Therefore, 698347+2834619 times 3 is equal to 10598898.

Answer:

i have no clue whats going on sorry i cant help

Step-by-step explanation:

(a) The additional equation that will complete the system of equations with no solution is -2x + 3y = 7 and 4x - 6y = -16.

(b) The additional equation that will complete the system of equations with  one solution is 2x + y = 8 and 3x - 2y = 7

(b) The additional equation that will complete the system of equations with infinitely many solutions is 4x - 6y = 12 and 2x - 3y = 6

Some additional equations that can complete systems with no solution, one solution, and infinitely many solutions:

No solution:

-2x + 3y = 7

4x - 6y = -16

One solution:

2x + y = 8

3x - 2y = 7

Infinitely many solutions:

4x - 6y = 12

2x - 3y = 6

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The compound interest of average family's health premiums will be approximately $12,593.25 in 2 years.

What is compound interest?

Compound interest is interest that is calculated not only on the initial principal but also on the accumulated interest of previous periods. This means that the interest earned each period is added to the principal, and then the interest is calculated on the new, higher principal for the next period. In other words, it is interest on interest. Compound interest can be contrasted with simple interest, which is calculated only on the principal amount. Compound interest can lead to significant growth in investment or debt over time, depending on the interest rate and the length of time.

Given by the question:
To solve the problem, we need to use the formula for compound interest:

[tex]A = P(1 + r)^n[/tex]

where A is the final amount, P is the initial amount, r is the annual interest rate as a decimal, and n is the number of years.

In this case, the initial amount is $11,430, the annual interest rate is 5% or 0.05, and we want to find the final amount in 2 years. So we have:

[tex]A = 11,430(1 + 0.05)^2[/tex]

[tex]A = 11,430(1.1025)[/tex]

[tex]A = 12,593.25[/tex]

Therefore, the average family's health premiums will be approximately $12,593.25 in 2 years.

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The base of the triangle is 9 inches and the height is 2 inches.

Let's denote the height of the triangle as h, and the base as b.

We know that the area of a triangle is given by the formula:

Area = (1/2) * base * height

Substituting the values we have:

9 = (1/2) * b * h

Multiplying both sides by 2 gives:

18 = b * h

We also know that the base is 5 inches more than 2 times the height:

b = 2h + 5

Substituting this expression for b in terms of h in the area equation, we get:

18 = (2h + 5) * h

Expanding the right-hand side, we get:

18 = 2h^2 + 5h

Rearranging this equation, we get:

2h² + 5h - 18 = 0

We can solve for h by using the quadratic formula:

h = [-b ± [tex]\sqrt{b² - 4ac}[/tex]] / 2a

where a = 2, b = 5, and c = -18.

Plugging these values into the formula, we get:

h = [-5 ± [tex]\sqrt{5^{2} - 4(2)(-18) }[/tex]] / (2 * 2)

Simplifying:

h = [-5 ± [tex]\sqrt{169}[/tex]] / 4

Taking the positive solution:

h = [-5 + 13] / 4

h = 2

Now that we know the height is 2 inches, we can use the equation b = 2h + 5 to find the base:

b = 2(2) + 5 = 9

Therefore, the base of the triangle is 9 inches and the height is 2 inches.

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The relationship between the lines is (a) parallel

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

y =-5/6x - 4

-10x - 12y = -18

To determine if the two lines are parallel or not we need to compare their slopes.

Make y the subject

y = -5/6x - 4

y = -5/6x  + 3/2

A linear equation represented as

y = mx + c

...has its slope to be m

Using the above as a guide, we have the following:

Since the slopes are equal, the two lines are parallel.

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Answer:

1/8 = 12.5%

first, you can convert your fraction into a decimal by 1 divided by 8, which is 0.125. To change a decimal to percent, I can use DP, so D meaning decimal, and P meaning percent so we are going from the decimalcto percent by moving two places to the right, starting at your point. So 0.125 is 12.5%

The volume of the composite solid is 320.7 cubic inches.

A composite solid is a three-dimensional object that is created by combining or "composing" two or simpler three-dimensional shapes, such as prisms, cylinders, pyramids, cones, or spheres. The combined shape may be more complicated or asymmetrical than the sum of its parts, yet it may still be measured and examined using the same geometrical rules and formulas. Cones with a frustum or truncated bases, pyramids with rectangular or triangular bases, and structures created by fusing together cylinders, prisms, or spheres are a few examples of composite solids. In order to build and create complicated structures and objects, composite solids are frequently utilized in architecture, engineering, and manufacturing.

To find the volume of the composite solid, we need to find the volumes of each of its components and add them together.

The volume of a hemisphere with a radius of 5 inches is given by:

V_hemisphere = [tex]\frac{2}{3}\pi r^{3}[/tex] = [tex]\frac{2}{3}\pi 5^{3}[/tex] = 523.6 cubic inches

Since there are two hemispheres, the total volume of the hemispheres is:

V_total_hemispheres = 2V_hemisphere = 2(523.6) = 1047.2 cubic inches

The cylinder has a radius of 5 inches and a length of 13 inches. The volume of a cylinder is given by:

V_cylinder = [tex]\pi r^2h[/tex] = [tex]\pi 5^2(13)[/tex] = 1025.0 cubic inches

The total volume of the composite solid is:

V_total = V_total_hemispheres + V_cylinder = 1047.2 + 1025.0 = 2072.2 cubic inches

Rounding to the nearest tenth, we get:

V_total ≈ 320.7 cubic inches

Therefore, the answer is option (c) 320.7 cubic inches.

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Yes, the ordered pair [1,-5] is a solution of 3x-2y=13. Because when evaluating the ordered pair in the equation it is true.

To determine if an ordered pair is a solution to an equation, we can plug in the values of the ordered pair into the equation and see if the equation is true.

In this case, the ordered pair is [1,-5], which means x=1 and y=-5. We can plug these values into the equation 3x-2y=13 and see if it is true:

3(1) - 2(-5) = 13

3 + 10 = 13

13 = 13

Since the equation is true, the ordered pair [1,-5] is a solution of 3x-2y=13.

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