Question 2
Which of the following best describes the process to find the product of rational
expressions?
O Multiply the numerators and then add the denominators.
O Multiply the numerators and then multiply the denominators.
O Multiply the numerators and then subtract the denominators.
O Add the numerators and then multiply the denominators.

Answer: It is not possible to use only translations and dilations to map one circle to another unless the two circles are identical in size and shape.

A translation is a transformation that moves an object without changing its size, shape, or orientation. It involves moving every point on the object the same distance in the same direction. Since a circle is defined by all the points that are equidistant from its center, a translation will simply move the entire circle in the same direction, but will not change its size or shape.

A dilation is a transformation that changes the size of an object, but not its shape or orientation. It involves multiplying the distance of every point on the object from a fixed center point by a scale factor. While a dilation can change the size of a circle, it will also change the distance between points on the circle, and thus change its shape.

Therefore, if the two circles are not identical in size and shape, it would be necessary to use other transformations, such as rotations or reflections, to map one circle to the other.

Step-by-step explanation:

Using angle theorems the value of x = 67.5°

Angle theorems are rules that govern the properties of angles.

Given that we have the figure and we desire to find angle x, we proceed as folllows.

Now, we notice that one angle is a right angle and it is equal to 90°.

Also, we notice that all the angles meet at the same point.

So, we have that

x + 3x + 90° = 360° (sum of angles at a point)

Solving for x, we have that

x + 3x + 90° = 360°

4x + 90° = 360°

4x = 360° - 90°

4x = 270°

x = 270°/4

x = 67.5°

So, the value of x = 67.5°

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The measure of the two angles is x = 69 degrees and y = 70 degrees.

In every triangle, the total of the angles is 180 degrees. The Triangle Sum Theorem.

For triangle ABC it is given as follows:

Angle A + Angle B + Angle C = 180.

Let us suppose the measure of two angles as x and y.

According to the ratio we can write as follows:

x = 6k and y = 7k

The sum of the angles in a triangle is 180°, so we can write:

50° + 6k + 7k = 180°

13k + 50° = 180°

13k = 130°

k = 10°

Substituting the value of k in x and y we have:

x = 6k = 6(10°) = 60°

y = 7k = 7(10°) = 70°

Hence, the measure of the two angles is x = 69 degrees and y = 70 degrees.

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Answer:

1.7 × .5 = .85

15% smaller than the original

F(prime) = 30

Given the information in the question, we can calculate \(F^{\prime}(2)\) using the chain rule. The chain rule states that \(F^{\prime}(x) = f^{\prime}(g(x))\cdot g^{\prime}(x)\). Thus, \(F^{\prime}(2) = f^{\prime}(-5)\cdot g^{\prime}(2)\). Plugging in the given values, we get \(F^{\prime}(2) = 6 \cdot 5 = 30\). Therefore, \(F^{\prime}(2) = 30\).

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The solution to the system of equations is (5.56, -4.73).

To solve the system of equations by the addition method, we need to follow these steps:

Step 1: Multiply one or both of the equations by a constant to make the coefficients of one of the variables the same in both equations.
Step 2: Add the two equations together to eliminate one of the variables.
Step 3: Solve for the remaining variable.
Step 4: Substitute the value of the variable back into one of the original equations to find the value of the other variable.

Let's apply these steps to the given system:

-2x - 7y = 22
7x - 4y = -20

Step 1: Multiply the first equation by 7 and the second equation by -2 to make the coefficients of x the same:

-14x - 49y = 154
-14x + 8y = 40

Step 2: Add the two equations together to eliminate x:

-41y = 194

Step 3: Solve for y:

y = 194/(-41)
y = -4.73

Step 4: Substitute the value of y back into one of the original equations to find the value of x:

-2x - 7(-4.73) = 22
-2x + 33.11 = 22
-2x = -11.11
x = 5.56

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Answer:

こんにちは

Step-by-step explanation:

2. 答えは2.5

次の番号 3 の場合は 6.9 次の番号は 4 の場合は 5.6

Therefore , the solution of the given problem of probability comes out to be roughly 0.2667, or 26.67%.

The primary goal of the schemes within a technique known as criteria is the evaluation of the likelihood that a claim is accurate or that a specific event will occur. Any figure between 0 and 1, with 0 typically signifying probability and 1 typically signifying a degree of certainty, can represent chance. A probability diagram shows the chance that a specific event will occur.

Here,

We can use combinations and probability to fix this issue.

First, we can determine how many different methods there are to choose 2 individuals from a group of 15:

=>  C(15,2) = 105 is the total number of options.

Next, we can determine how many options there are to choose two women from a group of eight women:

There are 28 different methods to choose 2 women, or

=>  C(8,2).

The likelihood that the two selected to respond to queries will both be women is as follows:

P(both women) equals the variety of methods to choose two women (total number of ways)

=>  P(all females) = 28/105

=> P(all females) = 0.2667

The likelihood that both of the two people selected to respond to questions are women is therefore roughly 0.2667, or 26.67%.

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The probability distribution function of Y = |X| is given by:
P(Y ≤ y) = P(|X| ≤ y) = P(-y ≤ X ≤ y) = P(X ≤ y) - P(X < -y)

Since X ~ N(0, 2), we can use the standard normal distribution to find the probabilities:
P(X ≤ y) = Φ(y/√2)
P(X < -y) = Φ(-y/√2)

Therefore, the probability distribution function of Y is:
P(Y ≤ y) = Φ(y/√2) - Φ(-y/√2)

To find E(|X|) and Var(|X|), we can use the properties of the absolute value function:
E(|X|) = ∫_(-∞)^(∞) |x| f(x) dx = 2 ∫_(0)^(∞) x f(x) dx
Var(|X|) = E(|X|^2) - (E(|X|))^2 = 2 ∫_(0)^(∞) x^2 f(x) dx - (2 ∫_(0)^(∞) x f(x) dx)^2

Since f(x) is the probability density function of X, we can substitute it with the standard normal distribution:
f(x) = (1/√(2π)) e^(-(x^2)/4)

Therefore, E(|X|) and Var(|X|) can be found by evaluating the integrals:
E(|X|) = 2 ∫_(0)^(∞) x (1/√(2π)) e^(-(x^2)/4) dx = √(2/π)
Var(|X|) = 2 ∫_(0)^(∞) x^2 (1/√(2π)) e^(-(x^2)/4) dx - (√(2/π))^2 = 2 - (2/π)

So the final answers are:
1. E(|X|) = √(2/π)
2. Var(|X|) = 2 - (2/π)

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To find the exact value of s in the given interval that has the given circular function value, we can use the properties of the tangent function and the unit circle.

The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle. In the unit circle, the opposite side is the y-coordinate and the adjacent side is the x-coordinate. Therefore, we can write:

tan s = y/x

Given that tan s = √3, we can write:

√3 = y/x

Cross-multiplying and simplifying, we get:

y = √3x

Now, we can use the Pythagorean theorem to find the value of x:

x^2 + y^2 = 1

Substituting y = √3x, we get:

x^2 + ( √3x)^2 = 1

Simplifying, we get:

4x^2 = 1

Dividing by 4, we get:

x^2 = 1/4

Taking the square root of both sides, we get:

x = ±1/2

Since we are looking for the value of s in the interval [????, 3????/2], we need to find the corresponding value of y for x = 1/2. Substituting x = 1/2 into y = √3x, we get:

y = √3(1/2)

Simplifying, we get:

y = √3/2

Therefore, the point on the unit circle that corresponds to the given value of the tangent function is (1/2, √3/2).

Now, we can use the properties of the unit circle to find the value of s. The angle s is the angle between the positive x-axis and the line connecting the origin and the point (1/2, √3/2). Since the point (1/2, √3/2) is in the first quadrant and the angle is measured counterclockwise, the value of s is:

s = π/3

Therefore, the exact value of s in the given interval that has the given circular function value is π/3.

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The surface area of the cylinder would be SA = 2π(1.6)² + 3.2π(3.8) square feet.

Option (A) is correct.

What is the surface area of the cylinder?

The surface area of a cylinder can be calculated using the following formula:

SA = 2πr² + 2πrh

where r is the radius of the circular base of the cylinder, h is the height of the cylinder, and π is the mathematical constant pi, approximately equal to 3.14159.

The surface area of a cylinder is the sum of the areas of its top and bottom circles, plus the area of its lateral surface (the curved surface that connects the two circles). The lateral surface area of a cylinder is found by multiplying the height of the cylinder by the circumference of one of its circular bases. Therefore, the correct method to calculate the surface area of the cylinder with diameter labeled 3.2 feet and height labeled 3.8 feet is:

SA = 2π(1.6)² + 3.2π(3.8)

So, the correct answer is:

SA = 2π(1.6)² + 3.2π(3.8) square feet

Hence, the surface area of the cylinder would be SA = 2π(1.6)² + 3.2π(3.8) square feet.

Option (A) is correct.

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The area of a trapezoidal region is 1/2h(a+b), where a and b are the lengths of the two parallel sides, and h is the height.

The area of a trapezoidal region is given by the formula A = 1/2h(a+b), where a and b are the lengths of the two parallel sides, and h is the height. This formula can be derived by dividing the trapezoid into two right triangles and a rectangle, and finding the area of each of these shapes.

First, let's consider the two right triangles. The height of each of these triangles is h, and the lengths of their bases are (a-b)/2 and (b-a)/2, respectively. The area of each of these triangles is therefore 1/2h(a-b)/2 = 1/4h(a-b).

Next, let's consider the rectangle. The length of this rectangle is b, and the height is h. The area of this rectangle is therefore bh.

The area of the trapezoidal region is the sum of the areas of the two right triangles and the rectangle. This gives us:

A = 1/4h(a-b) + 1/4h(b-a) + bh

Simplifying this equation gives us:

A = 1/2h(a+b)

Therefore, the area of a trapezoidal region is 1/2h(a+b), where a and b are the lengths of the two parallel sides, and h is the height.

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Using a graphing calculator or algebraic methods, we can find that x ≈ 71.6. Therefore, the model projects the civilian labor force to be 152 million in the year 1950 + 71.6 = 2021.6, or approximately in the year 2022.

According to the given model, the size of the civilian labor force (in millions) for selected years from 1950 and projected to 2050 can be modeled by y = - 0.0001 x^3 + 0.0058 x^2 + 1.43x + 56.7, where x is the number of years after 1950.

To find the projected civilian labor force in 2013, we need to plug in the value of x as 2013-1950 = 63 into the given model:

y = - 0.0001 (63)^3 + 0.0058 (63)^2 + 1.43(63) + 56.7
y = - 0.0001 (250047) + 0.0058 (3969) + 90.09 + 56.7
y = - 25.0047 + 23.0002 + 90.09 + 56.7
y = 144.7855

Therefore, the model projects the civilian labor force to be approximately 144.7855 million in 2013.

To find the year when the model projects the civilian labor force to be 152 million, we need to set y = 152 and solve for x:

152 = - 0.0001 x^3 + 0.0058 x^2 + 1.43x + 56.7
0 = - 0.0001 x^3 + 0.0058 x^2 + 1.43x - 95.3

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The probability that the first sister wins the first prize, the second sister wins the second prize, and the third sister wins the third prize is given as follows:

1/1320.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The probabilities for each sister are given as follows:

Hence the probability is given as follows:

1/12 x 1/11 x 1/10 = 1/(12 x 11 x 10) = 1/1320.

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well, for the cosine of G we'll need the hypotenuse GH, so let's get it, Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{GH}\\ a=\stackrel{adjacent}{\sqrt{6}}\\ o=\stackrel{opposite}{1} \end{cases} \\\\\\ GH=\sqrt{ (\sqrt{6})^2 + 1^2}\implies GH=\sqrt{ 6 + 1 } \implies GH=\sqrt{ 7 } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cos(G )=\cfrac{\stackrel{adjacent}{\sqrt{6}}}{\underset{hypotenuse}{\sqrt{7}}}\implies \cos(G )=\cfrac{\sqrt{6}}{\sqrt{7}}\cdot \cfrac{\sqrt{7}}{\sqrt{7}}\implies \cos(G )=\cfrac{\sqrt{42}}{7}[/tex]

Answer:

Step-by-step explanation:

The altitude of an equilateral triangle is basically the height of the triangle. We can find this using trigonometry, even though I'm sure there's a beautiful little formula that can find this.

If you cut an equilateral triangle in half, you get two special 30-60-90 triangles. The base of each triangle is 3.5 cm in length, and the height (not the hypotenuse!) is equal to:

[tex]base*\sqrt{3}[/tex]

So basically we have 3.5(sqrt(3)), or our altitude! Wow, how easy!

[tex]3.5(\sqrt{3})=6.06[/tex]

Hope this helps!

The given statement in the problem (f/g)(-2) = -6/5 is true.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

f(x) = 3x²

g(x) x - 8 ; (f/g)(-2) = -6/5

Now,

To evaluate (f/g)(-2), we need to divide f(-2) by g(-2).

We have f(x) = 3x², so f(-2) = 3(-2)² = 12.

We also have g(x) = x - 8, so g(-2) = (-2) - 8 = -10.

(f/g)(-2) = f(-2) / g(-2) = 12 / (-10) = -6/5.

So the statement (f/g)(-2) = -6/5

Therefore, the answer according to the given equation will be true.

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Answer:

9

Step-by-step explanation:

5'4 to 6'0 is 8

6'0 to 6'1 is 9

i think im right i dont use inches tho

The height difference between 5’4 and 6’1 is 9 inches.

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is essential to determine the quantity of any object.

There are two heights given.

5’4 and 6’1.

5'4 means that 5 feet and 4 inches.

1 feet = 12 inches

5 feet = 60 inches

5'4 = 60 inches + 4 inches = 64 inches

Similarly,

6'1 = 6 feet + 1 inch

    = (6 × 12) inches + 1 inch

    = 73 inches

Height difference = 73 inches - 64 inches = 9 inches

Hence the height difference is 9 inches.

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If the two rates remain the same, the number of hours needed for the values of the two stocks to be equal is 2.17 hours.

The slope, rate of change, or change in throughout the change in of a line determines its rate of change. A graph's slope triangle or 2 points in a column can be used to compute the slope.

Let 'x' be the time taken by each stock to reach at same value.

Then,

13.45 + 0.07x = 13.95 - 0.16x

13.45 - 13.95 = -0.16x - 0.07x

x = 0.5/0.23

x = 2.17 hours

If the two rates remain the same, the number of hours needed for the values of the two stocks to be equal is 2.17 hours.

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78 ft is the value of x in Triangles.

What is a triangle and what are its types?

Triangles are three-sided shapes. The various triangle varieties go under various names. The size of the angles and side lengths determine what kind of triangle it is (corners).

                         According on how long their sides are, triangles can be classified as equilateral, isosceles, or scalene.

Sin45° = x/110

  1/√2 = x/110

  √2 x  = 110

       x = 110/√2

       x = 77.78

        x = 78 ft

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The height of the plane is modeled by the linear equation:

height = 3000ft - 2000ft*t

If the rate at which the plane descends is constant, then the height is modeled by a linear equation.

We can write:

height = initial height - rate*time

We know that the initial height is 3000ft, and that the plane descends at ar ate of 2,000ft per minute, then we can write the linear equation:

height = 3000ft - 2000ft*t

Where t is the time in minutes.

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Complete question:

"an airplane 3,000 ft above the ground begin descending at a rate of 2,000 ft per minute​, which will be the height of the plane after t minutes?"

To find the quotient of x^2 + 4x - 32 when divided by x + 8, we can use polynomial long division or synthetic division. Here's how to do it using polynomial long division:

    x - 4

____________

To find the quotient of x^2 + 4x - 32 when divided by x + 8, we can use polynomial long division or synthetic division. Here's how to do it using polynomial long division:

markdown

Copy code

    x - 4

____________

x + 8 | x^2 + 4x - 32

- (x^2 + 8x)

____________

-4x - 32

- ( -4x - 32 )

____________

0

Therefore, the quotient is x - 4.

In order to answer these questions, we need to have data on Mr. Reede's laptimes. Without this information, it is impossible to accurately calculate the proportions and laptime necessary for Mr. Reede to be in the fastest 3% of all his laps. Please provide the data so that we can accurately answer the questions.

Once we have the data, we can use the following steps to answer the questions:

1. To find the proportion of laptimes between 1.75 and 1.85 minutes, we can count the number of laptimes in this range and divide it by the total number of laptimes.
2. To find the proportion of laptimes that took more than 2 minutes, we can count the number of laptimes that took more than 2 minutes and divide it by the total number of laptimes.
3. To find the laptime necessary for Mr. Reede to be in the fastest 3% of all his laps, we can first calculate the 97th percentile of the data (since the fastest 3% of laptimes would be in the top 3% of the data). Then, we can find the laptime that corresponds to this percentile.
4. To redo the problems using the Applet, we can input the data into the Applet and use the built-in functions to calculate the proportions and percentile.

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Step-by-step explanation:

5% Tip = $4.80

1% = $4.80/ 5

Cost of procedure = $4.80/5 x 100% (Equation)

b = $4.80 x 20.0 or 20($4.80)

b =$96

Step-by-step explanation:

a=55 because

75+50+a=180 (Sum of angle in a stratight line)

or, 125+a=180

or, a=180-125

a=55

b=75 because they are alternate angles

c=50 because they are alternate angles

d=50 Because d=c(vertically opposite angle) and c=50

The multiplication expression will be (9*3+1)/3.

What exactly are expressions?

In mathematics, an expression is a combination of one or more numbers, variables, and/or mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and logarithms) that can be evaluated to produce a single numerical or algebraic value.

Expressions can be very simple, such as a single number or variable, or they can be more complex, involving multiple variables and operations. They can also include mathematical functions and constants, such as pi or the square root of a number.

Here are some examples of expressions in mathematics:

Now,

We have expression 9 1/3

and to change it to simple fraction

we do this 9*3+1/3

=27+1/3

=28/3

Hence,

           The multiplication expression will be (9*3+1)/3.

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Answer:

12(a) 4(x+19)=752 (b) 169

Step-by-step explanation:

12(a) 4(x+19)=752

   (b) 4(x+19)=752

        4x+76=752

               4x=676

                 x=169

a. The equation representing the situation is 4(x+19)=752

b. The price of one ticket is $169

It is important to note that algebraic expressions are defined as expressions consisting of terms, coefficients, constants, factors and variables

They are also made up of mathematical operations are;

From the information given, we have that;

Let x be the price ticket

This is then represented as;

4(x+19)=752

expand

4x + 76 = 752

collect the like terms

4x = 676

Divide by the coefficient

x = $169

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In given graph, Points that meet the condition X>-2 are A, B, C, and D. and Points that are below the line y=1 are points A, B, C, and E.  and also None of the other students correctly plotted the point 4 units away from A.

What is graph?

A set of vertices or nodes connected by edges or arcs is known as a graph. Graphs are used to represent various mathematical concepts, relationships, and structures, such as networks, functions, sets, and data. Graphs can be visualized and analyzed to draw conclusions and make predictions about the underlying phenomena they represent.

For question 17:

a. Points that meet the condition X>-2 are A, B, C, and D.

b. Points that are below the line y=1 are points A, B, C, and E.

c. The point located three units to the right of the origin and two units above the x-axis is point F.

For question 18:

a. The labeled points are:

A: (3,0)

B: (4,3)

C: (-4,-2)

D: (1/12, 1/12)

E: (-3/2, 2/12)

F: (-4,-2)

b. The student who correctly plotted the point 4 units away from point A is Cassandra, who plotted the point (7,0). None of the other students correctly plotted the point 4 units away from A.

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