Find the inverse of the function below and sketch by hand a graph of both the function and it’s inverse on the same coordinate plane. Share all steps as described in the lesson to earn full credit. Images of your hand written work can be uploaded. F(x)=x^2+2 with the domain x>0

However, if we assume that the election cycle follows the typical pattern, where one-third of the Senate is up for reelection, then the probability would be approximately 1/3 or 0.333 as a fraction.

The probability that a randomly selected senator is up for reelection in November 2014 depends on the specific year and election cycle in question. In general, the term length for a U.S. senator is six years, and approximately one-third of the Senate is up for reelection every two years.

Therefore, the probability that a randomly selected senator is up for reelection in November 2014 would depend on the number of senators whose terms expire in that election cycle. Without additional information, it is not possible to determine this probability.

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Answer:

B. Radius

The line from the center of a circle to the edge is called a radius. The radius can be used in pi and a lot of other things

The equivalent expression for 2(n+2) is 2n +4.

Equivalent expressions are expressions that have the same effect even though they look different. If two algebraic expressions are equivalent, then both expressions have the same value when we insert the same value for the variable.

Problems with equivalent expressions often have simple and complex expressions. Check which complex expression is equivalent to a simple expression:

(1) Divide any coefficient: a(bx±c) = abx± aca, open parenthesis, b, x, addition and subtraction, c, close parenthesis, equals , a , b, x, plus or minus, a, c.

(2) Combine all like terms on both sides of the equation: the x term and the constant.

(3) Arrange the terms in the same order, usually the term x precedes the constant.

(4) Two expressions are equivalent if all their terms are identical.

The given expression is : 2(n+2)

Multiplying the expression by 2 : 2n+4

Here, 2n + 4 is the equivalent expression.

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At exactly 2:00, the distance between the tips of the two hands is changing at the rate of 4 cm/min.Therefore, at exactly 2:00, the distance between the tips of the two hands is changing at the rate of [tex]2\sqrt{13}[/tex] cm/min.

The phrase "at exactly 2:00" means that at 2:00:00, the hour hand and the minute hand overlap. Both hands are together pointing upwards in the vertical direction. At this moment, the angle between the minute hand and the hour hand is 0 degrees.How do we determine the rate of change of the distance between the tips of the two hands?We start by calculating the angle between the two hands. The angle is given by:

θ(t) = 30h - 11/2m

where h is the number of hours past midnight and m is the number of minutes past the most recent hour. At exactly 2:00, h = 2 and m = 0. Thus:

θ(t) = 30(2) - 11/2(0) = 60 degrees

Next, we use the formula for the distance between two points (the tips of the two hands). Let the hour hand be at the point (0,0) and let the minute hand be at the point (x,y).

The distance between the two points is given by:

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

To find x and y, we use the formulas:

x(t) = r cos θ(t)y(t) = r sin θ(t)

where r is the length of each hand. At exactly 2:00:

[tex]r = 4 cmx(t) = 4 cos 60 = 2 my(t) = 4 sin 60 = 2\sqrt{(3) m}[/tex]

Therefore: [tex]d(t) = \sqrt{(x^2 + y^2)}  = \sqrt{(2 m)^2 + (2sqrt(3) m)^2)}  = 2\sqrt{(13) m}[/tex]

Finally, we differentiate with respect to time t to find the rate of change of [tex]d(t):d'(t) = 2\sqrt{13}[/tex] cm/min

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Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is [tex]12-0=12[/tex].

[tex]\bold{12}[/tex]

The smallest two-digit prime number that is not an emirp is 11.

An emirp is a prime number that, when its digits are written in reverse order, becomes another prime number. In this way, 73 is an emirp because when its digits are reversed, we get 37, which is also a prime number.

To answer this question, we must examine each of the two-digit prime numbers and verify whether or not they are emirps.

Let's begin by listing all of the two-digit prime numbers:

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

We must now test each of the above prime numbers to see whether they are emirps by reversing their digits and then testing if the new number is also prime.

We do not need to examine the primes in reverse order since, if a number is a two-digit prime, its reverse will also be a two-digit number.

Let's start by checking whether 11 is an emirp or not by reversing its digits.11 reversed becomes 11, which is the same number. Since 11 is a prime number, it is not an emirp.

Therefore, 11 is the smallest two-digit prime number that is not an emirp.

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We can claim that after answering the above question, the  This function would simulate the car's resale value if it depreciated at a rate of 15% each year.

In mathematics, a function is a relationship between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, while outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.

1.1) Both Kala and Remy are incorrect. The given function, [tex]p(x) = 30,000(0.68)^x[/tex], models the resale value of an automobile after x years, with a starting value of $30,000. The function's exponent x reflects the number of years since the car was purchased, and the base 0.68 is the percentage of the original value that remains after each year.

1.2) If the car's value fell by 15% per year, the function would be[tex]p(x) = 30,000(1 - 0.15)^x[/tex]. This means that the car loses 15% of its worth each year, leaving 85% of the value. This function would simulate the car's resale value if it depreciated at a rate of 15% each year.

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On average, you would expect to select approximately 1.90

Americans in order to find your first married respondent. This is because according to the U.S. Census Bureau, the national marriage rate in 2018 was 6.9 per 1,000 individuals, which is equivalent to 0.69% of the population being married.

Therefore, if we assume the population of Americans is uniformly distributed, the probability of randomly selecting a married American is 0.69%. Consequently, the expected number of trials necessary to select a married respondent is 1/0.0069 = 1.90.

To calculate this, we used the probability formula for a single trial: P(X) = N/S, where P(X) is the probability of success, N is the number of successes, and S is the number of trials.

Therefore, by substituting the number of successes (1) and the probability of success (0.0069) into the formula, we can determine the expected number of trials necessary to select a married respondent (1/0.0069 = 1.90).

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If an automobile manufacturer of a certain model of car wants to estimate the mileage this model car gets in highway driving. The manufacturer needs to sample at least 39 cars.

We can use the formula for the margin of error in a confidence interval for a mean:

Margin of Error = z* (σ/√n)

Where:

z* is the critical value of the standard normal distribution for the desired level of confidence, which is 90% in this case.

σ is the known population standard deviation, which is 5.7 mpg.

n is the sample size we want to determine.

We want the margin of error to be 1.5 mpg, so we can set up the equation:

1.5 = 1.645 * (5.7 / √n)

where 1.645 is the z-score for 90% confidence level.

Simplifying this equation, we get:

√n = 1.645 * (5.7 / 1.5)

√n = 6.251

Squaring both sides, we get:

n = 39.07

Rounding up to the nearest integer, we get:

n = 39

Therefore, the manufacturer needs to sample at least 39 cars to estimate the highway mileage with a 90% confidence interval and a margin of error of 1.5 mpg.

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Answer: We can solve the given inequality as follows:

|2x + 2| > 4

There are two cases to consider, depending on whether the expression inside the absolute value is positive or negative:

Case 1: 2x + 2 > 4

2x > 2

x > 1

Case 2: 2x + 2 < -4

2x < -6

x < -3

Therefore, the solution to the inequality is x < -3 or x > 1.

To graph the solution, we can plot the two critical points x = -3 and x = 1 on a number line, and shade the regions to the left of -3 and to the right of 1. This gives us the following graph:

<==================o-----------------o===================>

    x < -3       x > 1

The open circles indicate that the points -3 and 1 are not included in the solution, since the inequality is strict (|2x + 2| > 4).

Step-by-step explanation:

The probability that the first question she gets right is question number 4, is 0.1054.

Number of options there are for a single query = 4

P(guessing correct answer for a single question) = 1/4

P(guessing correct answer for a single question) = 0.25

Probability of getting correct answer P(correct) = 0.25

Probability of getting wrong answer P(wrong) = 1 - Probability of getting correct answer

Probability of getting wrong answer P(wrong) = 1 - 0.25

Probability of getting wrong answer P(wrong) = 0.75

So, the probability that the first question she gets right is question number 4 = Probability of getting 1st question wrong × Probability of getting 2nd question wrong × Probability of getting 3rd question wrong × Probability of getting 4th question right

The probability that the first question she gets right is question number 4 = 0.75 × 0.75 × 0.75 × 0.25

The probability that the first question she gets right is question number 4 = 0.1055

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The complete question is:

In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. (Round your answers to four decimal places.)

What is the probability that the first question she gets right is question number 4?

The shaded region of the provided number is 214.5 yards, according to the given statement.

A rectangular shape is an illustration of a trapezoid with proportionate and matched opposite sides. It has four sides, four 90-degree borders, and is shaped like a rectangular. Any shape with only two sides is said to be rectangular.

Calculating Area by Subtracting Area from Two as well as More Regions: To determine the area for combined figures consisting of basic forms that overlap, deduct the area of the unshaded figure from the total area to obtain the area of the shaded region.

For illustration, let's calculate the size of the shaded section in the provided picture.

It is clear from the provided picture that a triangular and a rectangle have overlapped. We must deduct the triangular area from the size of the parallelogram in order to determine the area about the shaded figure. Area of the shaded figure =

Area of the rectangle −

Area of triangle

=l×b−12×b×h

=22×11−12×11×5

=214.5yd2

Hence, the area of the shaded figure is 214.5yd2

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The type of transformation that occurred in each object are:

1) Rotation

2) Translation

3) Reflection

4) Translation

There are different types of transformations of objects such as:

Translation: Translation is said to occur when we slide a figure in any direction.

Reflection: Reflection is said to occur when we flip a figure over a line.

Rotation: Rotation is said to occur when we rotate a figure a certain degree around a point.

Dilation: Dilation is said to occur when we enlarge or reduce a figure.

1) The given transformation is rotation because the original object was clearly rotated.

2) The given transformation is said to be translation because the object just changed position.

3) The transformation that occurred is said to be a reflection because it is a mirror image.

4)  The given transformation is said to be translation because the object just changed position.

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The expression 2(10+12) can be rewritten as 44 using the distributive property of multiplication over addition.

The distributive property is a fundamental property of arithmetic that relates multiplication to addition and subtraction. The distributive property of multiplication over addition states that for any numbers a, b, and c

a( b + c ) = ab + ac

Using this property, we can rewrite the expression 2(10+12) as

2( 10 + 12 ) = 2(10) + 2(12)

Here, we have distributed the factor of 2 over the terms inside the parentheses, using the distributive property. This gives us:

2(10+12) = 20 + 24

Simplifying further, we get

2(10+12) = 44

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The probability that 2 red balls and 2 blue balls are taken from the box is 3/7. This can be expressed mathematically as [tex](8C2 * 8C2) / (16C4) = 3/7[/tex].

To better understand this probability, let's look at an example. Say there are 8 red balls and 8 blue balls in the box. This can be represented as:

R = 8, B = 8

We want to determine the probability of taking 2 red balls and 2 blue balls out of the box. To do this, we need to calculate the total number of ways of selecting 4 balls from the box (16 balls in total) and then calculate the total number of ways of selecting 2 red and 2 blue balls out of the box.

The total number of ways of selecting 4 balls from the box can be expressed as (16C4). This is calculated by dividing the number of ways of selecting 4 balls out of 16 (16!) by the number of ways of arranging those 4 balls in any order (4!):

[tex](16C4) = 16! / 4! = 1820[/tex]

The total number of ways of selecting 2 red and 2 blue balls out of the box can be expressed as (8C2 * 8C2). This is calculated by multiplying the number of ways of selecting 2 red balls out of 8 (8C2) by the number of ways of selecting 2 blue balls out of 8 (8C2):

[tex](8C2 * 8C2) = 8C2 * 8C2 = 28[/tex]

The probability of taking 2 red balls and 2 blue balls out of the box is then the ratio of the number of ways of selecting 2 red and 2 blue balls out of the box (28) to the total number of ways of selecting 4 balls from the box (1820):

P(2 red balls, 2 blue balls) = 28 / 1820 = 3/7

In conclusion, the probability of taking 2 red balls and 2 blue balls out of a box containing 8 red balls and 8 blue balls is 3/7.

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Answer: Proper fraction

Step-by-step explanation:

A proper fraction is a fraction that has its numerator value less than the denominator.

For example, ⅔, 6/7, 8/9, etc. are proper fractions.

Answer:1 and 0

Step-by-step explanation:

If x=0 and y=0

?=0

if x=1 and y=1

?=1

if  x=2 and y=2

?=1

if x=3 and y=3

?=1

if x=4 and y=4

?=1

if x=5 and y=5

?=1

In the context of lean tools and approaches, one of the components of the 5s principles refers to a clean work area. The component that is being referred to here is "shine".

The 5s principles are a set of lean tools and approaches that are used to promote workplace organization, efficiency, and safety. These principles include:

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The magnitude of the resultant force is given by:

|F| = [tex]sqrt((-7)^2 + 0^2) N|F| = 7 N[/tex]The direction of the resultant force is given by:

[tex]θ = tan^-1(0/-7)θ = tan^-1(0) = 0[/tex]

Therefore, the magnitude of the resultant force is 7 N, and its direction is along the negative x-axis.

1. Cartesian vector expression for five forcesThe five forces acting along the edges of a pentagon plate ABC are shown below:Force acting on AB = (6i + 6j) NForce acting on BC = (8i + 4j) NForce acting on CD = (-5i + 10j) NForce acting on DE = (-10i - 8j) NForce acting on EA = (4i - 12j) N2.

Cartesian vector expression of the resultant force of these five forcesThe resultant force acting on the pentagon plate ABC can be determined by finding the vector sum of the five forces. The cartesian vector expression of the resultant force can be found as follows:[tex]F = F1 + F2 + F3 + F4 + F5F = (6i + 6j) N + (8i + 4j) N + (-5i + 10j) N + (-10i - 8j) N + (4i - 12j) N= (-7i + 0j) N[/tex]

Therefore, the cartesian vector expression of the resultant force is (-7i + 0j) N.3. Magnitude and direction of the resultant forceThe magnitude and direction of the resultant force can be determined by using the cartesian vector expression of the resultant force obtained in the previous step.

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From the given information provided, Susan's percentile rank in class is approximately 6.9%.

To find the percentile rank for Susan who is 5th in a class of 58 students, we need to use the following formula:

Percentile rank = (Number of students below Susan / Total number of students) x 100

Since Susan is the 5th student in the class, there are 4 students with higher ranks than her. Therefore, the number of students below Susan is 4.

Using the formula, we can calculate the percentile rank as:

Percentile rank = (4 / 58) x 100

Percentile rank = 6.9 (rounded to one decimal place)

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The equation of the line y = 3x + 10 in standard form is 3x - y = -10.

Given the equation of line in the question:

y = 3x + 10

To write the equation of the line in standard form, we need to rearrange the equation so that the x and y terms are on the left side and the constant term is on the right side of the equation.

It is expressed as;

Ax + Bx = C

y = 3x + 10

Subtracting 3x from both sides, we get:

y - 3x = 3x - 3x + 10

y - 3x = 10

Reorder

-3x + y = 10

Multiply each term by -1

-3x(-1) + y(-1) = 10(-1)

3x - y = -10

Therefore, the equation in standard form is 3x - y = -10.

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Answer: BC, AC, AB

Step-by-step explanation: I think I'm wrong but tell me if I'm right.

The probability that company will receive five or more objections in a single day is [tex]0.9951[/tex].

Probability is simply the possibility that something will happen. We may talk about the possibility with one result, or the probability of numerous outcomes, if we don't understand how such an occurrence will turn out. Statistical is the study of events that follow a probabilistic model.

Probability is typically considered as one of the most difficult mathematical concepts because probabilistic arguments can occasionally give results that seem inconsistent or nonsensical. The Monty Hill paradox and the anniversary problem are two examples.

Let [tex]X[/tex] be the random variable denoting the number of complaints received in a day. We need to find P(X ≥ 5).

Using the Poisson probability mass function,

P(X ≥ 5) = 1 - P(X < 5)

[tex]= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4)[/tex]

[tex]= 1 - e^{(-7)(1 + 7 + 24.5 + 57.33 + 100.18)}[/tex]

[tex]= 1 - 0.0049[/tex]

[tex]= 0.9951[/tex]

Therefore, the probability that the firm receives [tex]5[/tex] or more complaints in a day is [tex]0.9951[/tex].

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The volume of the tank can be found using the given information as:[tex]Volume=\int\limits^b_a {\pi f(x)^2} \, dx[/tex]

Assuming that the area bounded is given by a function f(x), the volume of the oil storage tank can be calculated using the formula for the volume of a solid of revolution:

[tex]Volume=\int\limits^b_a {\pi f(x)^2} \, dx[/tex]

where a and b are the limits of integration. In this case, the axis of revolution is the x-axis, so we are revolving the area about the x-axis.

Therefore, the volume of the tank can be found using the given information as:

[tex]Volume=\int\limits^b_a {\pi f(x)^2} \, dx[/tex]

We need more information about the function f(x) or a curve that bounds the area in order to find the limits of integration and calculate the volume.

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A causal study is a study that seeks to determine whether one variable causes another variable.

The independent variable is the variable that is believed to cause the change in the dependent variable, while the dependent variable is the variable that is believed to be influenced by the independent variable.

In a causal study of the effect of shelf placement on sales of a brand of cereal, the independent variable is where the cereal was placed on the shelf. The dependent variable is sales of the cereal.

This is because the sales of the cereal are influenced by where it is placed on the shelf.The answer to the question is sales of the cereal.

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The repair costs $90 for parts, plus $70 per hour for labor describes the situation. The solution has been obtained by using the equation.

What is an equation?

An equation is an assertion that two expressions containing variables and/or numbers are equivalent. The basic driving factors behind the growth of mathematics have been the attempts to rationally answer equations, which are essentially questions.

We are given an equation of the function as C(x) = 90 + 70x.

This depicts that $90 is fixed cost whereas $70 is variable cost and is dependent on the value of x.

So, the statement that describes the given situation is that the he repair costs $90 for parts, plus $70 per hour for labor.

Hence, the fourth option is the correct option.

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Answer:

The ring-shaped region has an inner radius of 10m and a width of 3m. To find the area of the shaded region, we need to subtract the area of the inner circle from the area of the outer circle. The area of a circle is given by A = πr^2, where r is the radius. Therefore, the area of the outer circle is A1 = π(10+3)^2 = 169π m^2 and the area of the inner circle is A2 = π(10)^2 = 100π m^2. Subtracting these two areas gives us: A1 - A2 = (169π - 100π) m^2 = 69π m^2. Therefore, the area of the shaded region is approximately 216.27 m^2 (69π ≈ 216.27) .

The Probability of that Lila selects a black ribbon and Jessica selects a green ribbon = 6/35. What is Probability? Probability is possibility that deals with "occurrence of random event. It values varies from 0 to 1". According to the question,

Number of black ribbon = 3

Number of green ribbon = 12

Total number of ribbon  = 3+12 =15

Formula for Probability of an event P(E) = (Number of favorable outcomes) /(Total number of outcomes)

Probability of Lila selecting black ribbon =3/15

Jessica selects a ribbon at random from the remaining ribbons, therefore total number of ribbons is reduced to 14.

Probability of Jessica selecting Green ribbon = 12/14

The Probability of that Lila selects a black ribbon and Jessica selects a green ribbon =(3/15)(12/14)=6/35.Hence, the Probability of that Lila selects a black ribbon and Jessica selects a green ribbon is 6/35.

The required  cost of each shirt is $21.28.

A mathematical statement known as an equation is made up of two expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the quantity x is 7.

The total cost of 3 identical shirts, including shipping, is $71.83. So we can write the equation as:

3s + 7.99 = 71.83

To solve for the cost of each shirt, we need to isolate the variable "s" on one side of the equation. We can start by subtracting 7.99 from both sides:

3s = 63.84

Then, we can divide both sides by 3:

s = 21.28

Therefore, the cost of each shirt is $21.28.

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Answer: -4

Step-by-step explanation:

If homogenous equation ax^2+2hxy+by^2=0---------------(a)

represent two perpendicular lines then, a+b=0

Calculation :

Given 3x² - 8xy + my² = 0

on comparing with equation (a) we get, a=3 and b=k

given lines are mutually perpendicular then

m+3= 0

m=-3