Directions: Work in your small group to complete this worksheet Submit the completed Wor full credit. Canvas by the beginning of the next class. All answers must be justified and work Trigonometric functions are periodic, meaning they repeat the same pattern as x goes toward positive and negative infinity. Hence, trigonometric functions fail to be one to one. Recall, one to one functions must pass BOTH vertical and horizontal line tests. Therefore, to define the trigonometric inverse functions, we must restrict the domain of each trigonometric function to a place where the function IS one to one. 1. Let g(x) be the function whose domain is [0,π] and whose outputs are determined by cos(x) on this interval. Hence, g(x) is the solid line part of the graph pictured to the right. Note: g(x) is defined in terms of cos(x), however g(x)=cos(x) since it has a different domain. a) Does y=cos(x) have an inverse function? Why or why not? b) Explain why g(x) has an inverse function, g−1(x)=cos−1(x). c) State the domain and range of g(x) in interval notation. Domain: Range: d) State the domain and range of g−1(x)=cos−1(x) in interval notation. Domain: Range:

The range of f(x) is {f(x) ∈ ℝ | f(x) ≥ –3}, which means that the possible values of f(x) are all real numbers greater than or equal to –3.

The range of a function is the set of all possible output values.

For the function f(x) = |x| – 3, we can think about the possible values that f(x) can take on.

First, consider the absolute value. For any input x, the absolute value |x| is always non-negative, so |x| – 3 is at least –3.

Next, think about the effect of subtracting 3. This shifts all the values down by 3 units. So the range of f(x) is all the values that can be obtained by subtracting 3 from the absolute value of x.

Therefore, the range of f(x) is {f(x) ∈ ℝ | f(x) ≥ –3}, which means that the possible values of f(x) are all real numbers greater than or equal to –3.

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Answer:

14

Step-by-step explanation:

The formula is

376.8 =

According to the probability distribution, you should rather play the second game than the first one.

a) The probability distribution for your winnings on a single play of this game is given by:

P(X=1) = 1/4

P(X=2) = 1/4

P(X=-1) = 1/2

b) Your expected winnings in this game is 0, since the expected value of X = 1*(1/4) + 2*(1/4) - 1*(1/2) = 0.

c) The probability distribution for your winnings in this game is given by:

P(X=100) = 1/4

P(X=5) = 1/4

P(X=-52) = 1/2

d) Your expected winnings in this game is 22, since the expected value of X = 100*(1/4) + 5*(1/4) - 52*(1/2) = 22.

e) The variance of X for the first game is

Var(X) = (1-0)2*(1/4) + (2-0)2*(1/4) + (-1-0)2*(1/2) = 0.75.

The variance of X for the second game is Var(X) = (100-22)2*(1/4) + (5-22)2*(1/4) + (-52-22)2*(1/2) = 1344.5.

You would rather play the second game, since its variance is much larger, which means there is a greater potential for large gains.  

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Answer:

32 or 24 or 13 or 21

Step-by-step explanation:    

332-240=92

168-118 = 50

86-57 = 29

45-13= 32

or

45-21= 24

A doubling equation in exponential growth can be used to solve the question. The amount after 30 years will be $3911.22

The growth rate is governed by exponential equation. Doubling equation means to the time needed to make the initial amount double. If the number of years and doubling time given, then the doubling equation is,

 P = P₀[tex](2)^{t/d}[/tex]

P is the final amount

P₀ is the initial amount

t is the time in years

d is the doubling time

P₀ = 790  t= 30  d= 13

P = 790 [tex](2)^{30/13}[/tex]

  = 3911.21506157

So the amount after 30 years will be $3911.22

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The slope of the line that contains the points (10, 0) and (-20, -18) is: slope = (change in y)/(change in x) = 3/5.

The slope of a line is the measure of its steepness, and it's found by dividing the change in the y-coordinates by the change in the x-coordinates between two points on the line. In this case, the slope of the line that passes through the points (10, 0) and (-20, -18) can be calculated as follows:

slope = (change in y-coordinates) / (change in x-coordinates)

slope = (-18 - 0) / (-20 - 10)

slope = -18 / -30

slope = 3/5

Therefore, the slope of the line is 3/5.

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The inequality expression (2/3)y - 4 ≥ 2 when evaluated is y ≥ 3

Inequality expressions are those statements in mathematics that use symbols like <, >, ≤, or ≥ to compare two values.

From the question, we have the following inequality expression given as

(2/3)y - 4 ≥ 2

Add 4 to both sides of the inequality

So, we have the following representation

2/3y ≥ 2

Multiply both sides of the inequality expression by 3/2

y ≥ 3

Hence, the solution to the given inequality expression is y ≥ 3

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The side length to the nearest tenth of a centimeter is 5.57

A square is a closed two-dimensional shape (2D shape) with four sides that are equal and parallel to each other.  also, In Euclidean Euclidean geometry, a square is a regular quadrilateral which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles)

The range of the sides is 30 to 31

the area of a square is

A = l² where l = length of side

√30 = l

L= 5.48 or

l = √31 = 5.57

The side length is the mean of the range of numbers

l = (5.48+5.57)/2  = 5.53

My estimate is reasonable because 5.53² = 30.5809 which is a number between 30 and 31

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Due to the fact that a square's area is proportionate to its square of side length, a minor change in the area corresponds to a small change in the side length, making this estimate acceptable.

Let's call the side length of the square "s". We know that the area of the square is between 30 cm² and 31 cm², so we can write:

30 < s² < 31

Taking the square root of all three sides of this inequality, we get:

√30 < s < √31

Using a calculator, we can approximate the square roots to the nearest tenth of a centimeter:

√30 ≈ 5.5

√31 ≈ 5.6

So, we can estimate that the side length of the square is between 5.5 cm and 5.6 cm, to the nearest tenth of a centimeter.

This estimate is reasonable because the area of a square is proportional to the square of its side length, so a small change in the area corresponds to a small change in the side length.

Since the difference between the upper and lower bounds of our estimate is only 0.1 cm, it makes sense that the area of the square is very close to the given range.

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The value of the variable x is 253 degrees

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

Circle and intersecting tangent lines

Using the theorem of angle between intersecting tangents and arcs, we have the following equation

1/2 * (x - 360 + x) = 73

Multiply by 2

(x - 360 + x) = 146

So, we have

2x - 360 = 146

Evaluate the like terms

2x = 506

Divide by 2

x = 253

Hence, the value of x is 253 degrees

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1) The equal expressions are I and III

2) The value of the expression is 3 41/80

An absolute value expression is a mathematical expression that represents the distance of a number from zero, regardless of the sign of the number. The absolute value of a number is always positive, so an absolute value expression represents a positive number or zero.

The absolute value of a number x is denoted by |x| and is defined as follows:

|x| = x, if x is positive or zero

|x| = -x, if x is negative

Since -/x/ = -x then this are the equal expressions.

[tex]a^2/a + 1 + a + 1/a^2[/tex]

Then;

[tex]4^2/4 + 1 + 4 +1/4^2[/tex]

16/5 + 5/16

= 3 41/80

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Answer:

157°

Step-by-step explanation:

We can see that the angle here is an alternate angle, this means it is an opposite angle that has the same value as each other.

Knowing this, we can see that if the angles are alternated the missing angle should be 157 as well.

Hope this helps have a lovely day! :)

The line that goes through the points (0, -2) and (4, -2) can be represented by the equation y = (-1/2)x - 2.

Since both points have the same y-coordinate of 5, the line must be a horizontal line passing through y = 5. Therefore, the equation of the line is y = 5.

Since both points have the same y-coordinate of 0, the line must also be a horizontal line passing through y = 0. Therefore, the equation of the line is y = 0.

The slope of the line passing through the two points can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the given values, we get:

m = (-2 - 0) / (4 - 0) = -1/2

Using the point-slope form of the equation of a line, we can write the equation of the line as:

y - y₁ = m(x - x₁)

Substituting one of the given points, such as (0, -2), we get:

y - (-2) = (-1/2)(x - 0)

Simplifying, we get:

y + 2 = (-1/2)x

Therefore, the equation of the line passing through the points (0, -2) and (4, -2) is y = (-1/2)x - 2.

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The probability that the result is a multiple of five and a multiple of two is 1/3, since there are only three multiples of five and two that can be produced on the spinner: 10, 6, and 2.

The spinner has 12 equal areas, numbered one through 12. The probability of getting a multiple of five and a multiple of two on one spin is 1/3, since there are only three multiples of five and two that can be produced: 10, 6, and 2. To calculate this probability, we need to look at the total number of possible outcomes and divide it by the number of outcomes that are multiples of five and a multiple of two. In this case, the total number of outcomes would be 12, and the number of outcomes that are multiples of five and a multiple of two is three (10, 6, and 2). Dividing 12 by 3 gives us the probability of 1/3.

Total number of outcomes = 12

Number of outcomes that are multiples of five and two = 3 (10, 6, and 2)

Probability = 3/12 = 1/3

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Answer:

x = 18

Step-by-step explanation:

the angle vertically opposite 7x is 7x

making 3x and 7x same- side interior angles summing to 180° , that is

3x + 7x = 180

10x = 180 ( divide both sides by 10 )

x = 18

for A and B to be parallel then x = 18

1. A man with a bachelοr's degree earns apprοximately $25,749 mοre per year than a man with a high schοοl educatiοn.

2. A wοman with a prοfessiοnal degree earns apprοximately $31,610 mοre per year than a wοman with a bachelοr's degree.

3. A man with a bachelοr's degree earns apprοximately 34.8% mοre than a wοman with a bachelοr's degree.

Percentage can be calculated by dividing the value by the tοtal value, and then multiplying the result by 100. Percentage is a number οr ratiο expressed as a fractiοn οf 100. It is οften denοted using the percent sign, "%".

Bachelοr's degree: $66,196

High schοοl educatiοn: $40,447

Difference: $25,749

Therefοre, a man with a bachelοr's degree earns apprοximately $25,749 mοre per year than a man with a high schοοl educatiοn.

Prοfessiοnal degree: $80,718

Bachelοr's degree: $49,108

Difference: $31,610

Therefοre, a wοman with a prοfessiοnal degree earns apprοximately $31,610 mοre per year than a wοman with a bachelοr's degree.

Difference in average earnings fοr men and wοmen with a bachelοr's degree: $66,196 - $49,108 = $17,088

Average earnings fοr wοmen with a bachelοr's degree: $49,108

Percentage difference: ($17,088 / $49,108) x 100 = 34.8%

Therefοre, a man with a bachelοr's degree earns apprοximately 34.8% mοre than a wοman with a bachelοr's degree. Over a 40-year career, this translates tο a difference οf apprοximately $683,520 in earnings ($17,088 x 40).

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Answer:

[tex]x \leq \frac{1}{3}[/tex] or [tex]x \geq \frac{1}{2}[/tex]

Answer:

Below

Step-by-step explanation:

From the graph below you can see that

x < = .33 3   and   x >= .5

combined

  .333  ≥  x  ≥  .5

A Type I error that could have been made in this case would be concluding that there is no difference between the proportions of men and women who intended to vote for Trump when in reality there was a difference.

(a) Yes, there is convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the a = 0. 05 significance level. The p-value of this test is 0.023, which is less than the significance level of 0.05, suggesting that the difference between the proportions of men and women who intended to vote for Trump is statistically significant.

(b) If we had concluded that there was no difference in the proportions of men and women who intended to vote for Trump when there actually was a difference, we would have made a Type I error. This error refers to rejecting the null hypothesis when it is actually true. In this context, a Type I error would mean concluding that there is no difference between the proportions of men and women who intended to vote for Trump when in reality there was a difference.

This answer concludes that there is convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the a = 0.05 significance level.

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Answer:

It's A. x and y are proportional. k=8

Step-by-step explanation:

x and y are proportional since they are related by the equation 8 = xy. To find the constant of proportionality, we can solve for y in terms of x:

y = 8/x

This shows that y is inversely proportional to x, and the constant of proportionality is 8.

Therefore, the correct answer is A. x and y are proportional, and the constant of proportionality is k = 8.

Hope this helped! Sorry if it's wrong. If you need more help, ask me! :]

The weekly allowance of Melanie that she  ended up  is $65 by solving the equation formed according to the question.

An equation is a mathematical statement that shows that two expressions are equal. It typically contains one or more variables and can be written using mathematical symbols such as addition, subtraction, multiplication, division, and exponentiation. An equation can also contain mathematical functions, constants, and other mathematical operations.

In mathematics, a function is a rule that assigns each element in one set, called the domain, to a unique element in another set, called the range or codomain. In other words, a function is a relation between two sets where each element in the domain is mapped to a unique element in the range.

Let's assume that Melanie's weekly allowance is "x".

According to the problem, Melanie spent half of her allowance going to the movies. So, she spent (1/2)x dollars at the movies.

Then, she earned $10 by washing the family car.

Therefore, her total spending is (1/2)x + $10.

Since she ended up with $22.50, we can set up an equation:

x - [(1/2)x + $10] = $22.50

Simplifying this equation, we get:

(1/2)x = $32.50

Multiplying both sides by 2, we get:

x = $65

Therefore, Melanie's weekly allowance is $65.

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We can say that after answering the offered question We may simulate inequality and address numerous issues in disciplines like economics, engineering, and science by employing variables and inequalities.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many simple inequalities can be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.

Choose a scenario where a specific number or quantity must be larger than or equal to 5 for a specific condition to be satisfied in order to write a real-life circumstance for the inequality * 5.

Another illustration might have to do with a fitness objective. The inequality in this case would be " 5," meaning that you must weigh less than or equal to 5 in order to reach your objective.

Inequalities are typically employed to symbolise restrictions or limitations in real-world contexts, such as minimum or maximum demands, financial restraints, or safety standards. We may simulate and address numerous issues in disciplines like economics, engineering, and science by employing variables and inequalities.

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Answer:

x = -3

y = -6

Step-by-step explanation:

We are given the following system of equations:

y = 2x

-3x - 15 = y

We can use the substitution method to solve this system.

Substitute y = 2x from the first equation into the second equation and solve for x:

-3x - 15 = 2x

-5x = 15

x = -3

Now that we have found x, we can use the first equation to find y:

y = 2x = 2(-3) = -6

Therefore, the solution to the system of equations is (x, y) = (-3, -6).

Answer:

A)  Missing Table Values.  See the attached worksheet

B)  The car will be worth less than $8,000 in 9.8 years

Step-by-step explanation:

Part B:  Years until car is less than $8,000

 The new $25,000 car depreciates by 11% each year.  Expressed another way, it retains 89% of its value each year.  The value, y, after x years can be calculated from:

                                 y = ($25,000)*(0.89)^x

This function is graphed on the attached worksheet.  The line intersets the $800 on the y axis at 9.8 years.  The car will be worth less than $8,000 after 9.8 years.

One can also calculate the value of x:

                            $,8000 = ($25,000)*(0.89)^x

        x = 9.77, mathematically

Part A:  Table of values

See the attached worksheet.  The values are not exactly a straight line, but come close to f(x) = 8x+50, from which the missing values may be calculated.  Legally, however, this is a slightly more complex line, for which I'm unclear about the best approach for its derivation.

Answer: 16+4+4

Step-by-step explanation: The answer is 16, 4, and 4.

Square values in 24 are 4,9, and 16.

You can take a look at this and see that a factor of 24 is 4.

You can do 16+4+4.

Hope this helps!

-You Brainly Helper!

Answer:

x=3/8

Step-by-step explanation:

^2×5×3÷5/8=×3/8

Therefore , the solution of the given problem of equation comes out to be he can hire the shoes for three hours with his meagre $11 budget.

Complex algorithms frequently employ a variable term to guarantee congruence with the two opposing assertions. Equations, which are academic expressions, are used to demonstrate the equality of different academic figures. In this instance, the normalise method provides b + 6 rather than merely expression separating 12 into two pieces for using the data from y + 6.

Here,

To begin, we can construct an expression to symbolise the circumstance:

=> y = 2x + 4

where x represents the number of hours that Quentin rents the shoes for and y represents the overall cost of the rental.

We can put y equal to 11 because we know that Quentin only has $11 to spend:

=> 11 = 2x + 4

We can now determine x:

=> 2x = 11 - 4

=> 2x = 7

=> x = 7/2

Quentin can therefore spend $11 to hire the shoes for 3.5 hours (7/2 hours).

He would have to pay either $10 or $12 to hire the shoes for either three or four hours. He can hire the shoes for three hours with his meagre $11 budget.

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The volume of the triangular pyramid is 2 cubic feet.

what is triangle ?

A triangle is a 2-dimensional geometric shape that has three straight sides and three angles. The sum of the angles of a triangle is always 180 degrees.

The first step to solving this problem is to find the area of the base of the pyramid. Since the base is a right triangle, its area can be calculated using the formula for the area of a triangle:

Area of triangle = 1/2 * base * height

In this case, the base is a right triangle with legs of 2 feet, so its area is:

Area of base = 1/2 * 2 * 2 = 2 square feet

Next, we can use the formula for the volume of a pyramid to calculate the volume of the triangular pyramid:

Volume of pyramid = 1/3 * area of base * height

Substituting in the values we have, we get:

Volume of pyramid = 1/3 * 2 * 3 = 2 cubic feet

Therefore, the volume of the triangular pyramid is 2 cubic feet.

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For the given equations, using slope formula option B: Lines 3 and 4 are parallel, is the correct option.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The four different equations are given.

To identify parallel lines, we need to compare their slopes.

If two lines have the same slope, they are parallel.

Line 1 is in slope-intercept form (y = mx + b) where the slope is m = 8.

Line 2 is in point-slope form (y - y1 = m(x - x1)) where the slope is m = 1/8.

Line 3 is in slope-intercept form where the slope is m = 3.

Line 4 is in slope-intercept form where the slope is m = 1/3.

Comparing the slopes, we see that -

Lines 1 and 2 have different slopes, so they are not parallel.

Lines 1 and 3 have different slopes, so they are not parallel.

Lines 1 and 4 have different slopes, so they are not parallel.

Lines 2 and 3 have different slopes, so they are not parallel.

Lines 2 and 4 have different slopes, so they are not parallel.

Lines 3 and 4 have the same slope (m = 3), so they are parallel.

Therefore, lines 3 and 4 are parallel.

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We can see that the signs of the coefficients are different for the terms with x, so the two products are not equal.

What is Algebraic expression ?

In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.

Part a:

To find the product of (3x – 4) and (5[tex]x^{2}[/tex]  – 2x + 6), we need to distribute each term in the first expression to each term in the second expression, and then combine like terms.

(3x – 4) (5[tex]x^{2}[/tex] – 2x + 6)

= 3x(5[tex]x^{2}[/tex] ) – 3x(2x) + 3x(6) – 4(5[tex]x^{2}[/tex] ) + 4(2x) – 4(6)

= 15[tex]x^{3}[/tex]– 6[tex]x^{2}[/tex]  + 18x – 20[tex]x^{2}[/tex]  + 8x – 24

= 15[tex]x^{3}[/tex] – 26[tex]x^{2}[/tex]  + 26x – 24

Therefore, the product of (3x – 4) and (5[tex]x^{2}[/tex]  – 2x + 6) is equal to 15x^3 – 26[tex]x^{2}[/tex]  + 26x – 24 in standard form.

Part b:

No, the product of (3x – 4) and (5[tex]x^{2}[/tex]  – 2x + 6) is not equal to the product of (4 – 3x) and (5[tex]x^{2}[/tex]  – 2x + 6).

(4 – 3x) (5[tex]x^{2}[/tex]  – 2x + 6)

= 4(5[tex]x^{2}[/tex] ) – 4(2x) + 4(6) – 3x(5[tex]x^{2}[/tex] ) + 3x(2x) – 3x(6)

= 20[tex]x^{2}[/tex] – 8x + 24 – 15[tex]x^{3}[/tex] + 6[tex]x^{2}[/tex]  – 18x

= -15[tex]x^{3}[/tex]+ 26[tex]x^{2}[/tex]  - 26x + 24

Therefore, We can see that the signs of the coefficients are different for the terms with x, so the two products are not equal.

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The domain and range for the function f(x) = 2x include the following:

Domain = (-∞, ∞).

Range = (-∞, ∞).

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞} or {x|x ∈ R}.

Range = {-∞, ∞} or {y|y ∈ R}.

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