A dodecahedral die (one with 12 sides numbered from 1 to 12) is tossed once.

A dodecahedral die. Only the front half, which is composed of 6 sides, is visible. In the center, a pentagonal side labeled 12 connects along its 5 edges to 5 other pentagonal sides, labeled 3, 8, 7, 9, and 11, respectively. Find the following probability. (Enter your probability as a fraction.)
The number on the upward face is not 1.

The range of the function is y = {11, 13, 17, 25}.

In mathematics, the range of a function refers to the set of all possible output values that the function can produce when given a set of input values. It is also known as the image of the function. The range of a function can be found by evaluating the function for all possible input values, or by analyzing the properties of the function.

To find the range of the function, we need to substitute each value of the domain into the function and record the corresponding output values.

For x = 2, f(2) = 2(2) + 7 = 11.

For x = 3, f(3) = 2(3) + 7 = 13.

For x = 5, f(5) = 2(5) + 7 = 17.

For x = 9, f(9) = 2(9) + 7 = 25.

Therefore, the range of the function is y = {11, 13, 17, 25}.

The answer is A. y = {9, 10, 12, 16} is not the correct range for this function with the given domain.

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the partial fraction decomposition of x^3-x/x^4+2x^2+1 is (x^3 - x)/(x^4 + 2x^2 + 1) = -1/4/(x^2 + 1)

To find the partial fraction decomposition of x^3-x/x^4+2x^2+1, we first factor the denominator:

x^4 + 2x^2 + 1 = (x^2 + 1)^2

So we can write:

(x^3 - x)/(x^4 + 2x^2 + 1) = A/(x^2 + 1) + B/(x^2 + 1)^2

Multiplying both sides by the denominator, we get:

x^3 - x = A(x^2 + 1) + B

Now we can solve for A and B by choosing appropriate values for x. Let's choose x = 0 first:

0 - 0 = A(0^2 + 1) + B

B = 0

Now let's choose x = 1:

1 - 1 = A(1^2 + 1) + 0

A = -1/4

So the partial fraction decomposition of x^3-x/x^4+2x^2+1 is:

(x^3 - x)/(x^4 + 2x^2 + 1) = -1/4/(x^2 + 1) + 0/(x^2 + 1)^2

or

(x^3 - x)/(x^4 + 2x^2 + 1) = -1/4/(x^2 + 1)

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Answer:

The total cost, C (in dollars), for driving x miles is given by:

C = 0.06x + 10.75

where x is the number of miles driven.

To find the total cost for driving a certain number of miles, simply substitute that value for x in the equation and solve for C.

Answer:

To find the distance between a point and a line in a plane, we can use the formula:

distance = |Ax + By + C| / √(A^2 + B^2)

where A, B, and C are the coefficients of the general form of the line equation (Ax + By + C = 0), and (x,y) are the coordinates of the point.

First, we need to rewrite the given line equation in the standard form (y = mx + b):

2x - 3y = -2

-3y = -2x - 2

y = (2/3)x + 2/3

Now we can identify the slope (m) and y-intercept (b) of the line:

m = 2/3

b = 2/3

Next, we can find the equation of the perpendicular line that passes through the point (1,2), since the distance between the point and the line will be the length of the segment connecting the point to the intersection of these two lines. The slope of a line perpendicular to a line with slope m is -1/m, so the equation of the perpendicular line passing through (1,2) is:

y - 2 = (-3/2)(x - 1)

y = (-3/2)x + (7/2)

Now we need to find the intersection of the two lines by solving the system of equations:

y = (2/3)x + 2/3

y = (-3/2)x + (7/2)

(-3/2)x + (7/2) = (2/3)x + 2/3

(-13/6)x = -5/6

x = 5/13

y = (2/3)(5/13) + 2/3

y = 11/13

So the intersection point of the two lines is (5/13, 11/13). Now we can use the distance formula to find the distance between this point and the given point (1,2):

distance = √[(5/13 - 1)^2 + (11/13 - 2)^2]

distance = √[(36/169) + (25/169)]

distance = √(61/169)

distance = √61/13

The closest answer choice is (A) √13, but the simplified expression is actually √61/13. Therefore, none of the answer choices provided are completely accurate.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The domain of a function refers to the set of all possible input values (independent variable) for which the function is defined. In this case, the graph has points (6,80) and (11,40), which means that the function is defined for the values of g (the independent variable) between 6 and 11. Therefore, the domain of the function is:

D. 6≤g≤11

The domain of the function in the given graph is 6≤h≤11, as it includes all possible values of h between and including 6 and 11 on the horizontal (h) axis. So the correct option is D.

The domain of a function refers to the set of all possible input values for the function. In the given graph, which is plotted on the h-g axis and includes points (6, 80) and (11, 40), we are interested in determining the valid range for the independent variable, h.

The lowest h-value on the graph is 6, corresponding to the point (6, 80), and the highest h-value is 11, corresponding to the point (11, 40). These are the boundaries that define the domain of the function. Any value of h that falls within this range is a valid input for the function, and any value outside this range is not represented on the graph.

Therefore, the domain of the function is 6≤h≤11, as it includes all values of h between and including 6 and 11. This range encompasses all possible inputs for this function as depicted in the graph.

In summary, the domain represents the valid input values, and in this case, it is limited to the interval from 6 to 11 on the h-axis.

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Answer:

9/5x+7

Step-by-step explanation:

You can keep the slope the same, because it is parallel, but the y-intercept must change to plus seven in order to go through (-5, -2)

Juan traveled approximately 288.24 miles.

The direct road would be approximately 288 miles long.

Juan's trip would be approximately 0.24 miles shorter if he was able to take the direct route.

We have,

a.

Here is a diagram illustrating Juan's trip:

    Grand Canyon

         |

         |

         |

Juan's    |       x

house --------->

         y

b.

To find the total distance Juan traveled, we can use the Pythagorean theorem:

distance² = x² + y²

Juan drove 280 miles south (y direction) and 64 miles east (x direction), so we have:

distance² = 280² + 64²

distance² = 78,976 + 4,096

distance² = 83,072

Taking the square root of both sides, we get:

distance ≈ 288.24 miles

c.

To find the length of the direct road, we can use the Pythagorean theorem again:

distance² = x² + y²

The direct road forms a right triangle with legs of 280 miles and 64 miles, so we have:

distance² = 280² + 64²

distance² = 78,976 + 4,096

distance² = 83,072

Taking the square root of both sides, we get:

distance ≈ 288.24 miles

d.

To find how much shorter Juan's trip would be if he took the direct route, we can subtract the distance he traveled from the direct road distance:

288 - 288.24 ≈ -0.24

Thus,

Juan traveled approximately 288.24 miles.

The direct road would be approximately 288 miles long.

Juan's trip would be approximately 0.24 miles shorter if he was able to take the direct route.

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Plotting the graph of the function h(x) = [tex](x^2 - 3x - 4) / (x - 4)[/tex], we get y- intercept = 1, vertical asymptotes at x=4 and  horizontal asymptotes at y=1.

The connection between a function's input values (usually written as x) and output values (often indicated as y) is represented by the function's graph. It gives insights on the function's characteristics, including its domain, range, intercepts, asymptotes, and general form, as well as a visual representation of how the function acts.

Steps to plot the graph of the give function h(x) =[tex](x^2 - 3x - 4) / (x - 4)[/tex]:

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Answer:

Step-by-step explanation:

26/7

Answer:

Use Formula nPr, to solve the following question

6P4 = 360

The p-value associated with the test statistic of z = 2.566 is 0.0045, accurate to four decimal places.

Based on the given information, we can conduct a one-tailed right-sided test using a normal distribution calculator to find the p-value associated with the test statistic of z = 2.566.

In hypothesis testing, a one-tailed right-sided test is a statistical test where the alternative hypothesis (H1) is specified to detect a change typically towards larger values.

Using a normal distribution calculator, we can find the cumulative distribution function (CDF) of the standard normal distribution at z = 2.566.

The CDF gives us the probability that a randomly selected value from a standard normal distribution is less than or equal to a given value.

Using a normal distribution calculator:

CDF at z = 2.566 = 0.9955 (rounded to four decimal places)

Since we are conducting a one-tailed right-sided test, we are interested in the probability of getting a value greater than the test statistic. Therefore, the p-value for the given test statistic is:

p-value = 1 - CDF at z = 2.566 = 1 - 0.9955 = 0.0045 (rounded to four decimal places)

Thus, the p-value associated with the test statistic of z = 2.566 is 0.0045, accurate to four decimal places.

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Answer:

m∠A = 50°

Step-by-step explanation:

The ∑ of all interior angles of any given triangle is 180°. Set all angle measurements equal to 180:

[tex](x + 30) + (2x - 10) + 70 = 180[/tex]

First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:

[tex](x + 2x) + (30 - 10 + 70) = 180\\(3x) + (90) = 180[/tex]

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, subtract 90 from both sides of the equation:

[tex]3x + 90 = 180\\3x + 90 (-90) = 180 (-90)\\3x = 180 - 90\\3x = 90[/tex]

Next, divide 3 from both sides of the equation:

[tex]3x = 90\\\frac{(3x)}{3} = \frac{(90)}{3}\\ x = \frac{90}{3}\\ x = 30[/tex]

Plug in 30 for x in the given angle measurement of A and simplify:

[tex]m\angle{A} = 2x - 10\\m\angle{A} = 2(30) - 10\\m\angle{A} = (60) - 10\\m\angle{A} = 50[/tex]

50° is your answer for m∠A.

~

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Answer:

m∠A = 50°

Step-by-step explanation:

The ∑ of all interior angles of any given triangle is 180°. Set all angle measurements equal to 180:

[tex](x + 30) + (2x - 10) + 70 = 180[/tex]

First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:

[tex](x + 2x) + (30 - 10 + 70) = 180\\(3x) + (90) = 180[/tex]

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, subtract 90 from both sides of the equation:

[tex]3x + 90 = 180\\3x + 90 (-90) = 180 (-90)\\3x = 180 - 90\\3x = 90[/tex]

Next, divide 3 from both sides of the equation:

[tex]3x = 90\\\frac{(3x)}{3} = \frac{(90)}{3}\\ x = \frac{90}{3}\\ x = 30[/tex]

Plug in 30 for x in the given angle measurement of A and simplify:

[tex]m\angle{A} = 2x - 10\\m\angle{A} = 2(30) - 10\\m\angle{A} = (60) - 10\\m\angle{A} = 50[/tex]

50° is your answer for m∠A.

~

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Answer:

Step-by-step explanation:

There is no correlation between the two.

The graph provided is a scatter plot and the dots are to spread out to have any time of coloration

if 1 2 3 = 2

then 3 5 4 = 5

hope it helps:)

The empirical rule to determine the interval middle 99.7% of Caroline's finishing times in the 400 meter race is 63.5 seconds to 72.5 seconds

Given data ,

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Since the middle 99.7% of data falls within three standard deviations of the mean, we can calculate the upper and lower limits of this interval as follows:

Lower limit = Mean - (3 x Standard Deviation)

Upper limit = Mean + (3 x Standard Deviation)

Plugging in the values for mean and standard deviation:

Lower limit = 68 - (3 x 1.5) = 68 - 4.5 = 63.5 seconds

Upper limit = 68 + (3 x 1.5) = 68 + 4.5 = 72.5 seconds

Hence , the interval of times that represents the middle 99.7% of Caroline's finishing times in the 400 meter race is 63.5 seconds to 72.5 seconds

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The length of the garden containing the soil is L = 24 feet

Given data ,

Volume = Length x Width x Height

Width = 4 1/2 feet

Height = 1/2 foot

Total volume of topsoil used = 18 bags x 3 cubic feet/bag = 54 cubic feet

So , the length of the garden is

54 = Length x 4 1/2 x 1/2

On simplifying , we get

54 = Length x 9/2 x 1/2

Now, let's simplify the right-hand side by multiplying the numerator and denominator by 2

54 / (9/2 x 1/2) = The length of the garden

The length of the garden = 54 /9 x 4

The length of the garden = 6 x 4

The length of the garden = 24 feet

Hence , the length of the garden bed is 24 feet

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Answer:

C is correct

Step-by-step explanation:

Answer:

Your calculator should be in radian mode.

a)

[tex]f(x) = 56 \sin( \frac{2t\pi}{12} + \frac{\pi}{2} ) + 4[/tex]

b)

[tex]f(x) = 56 \cos( \frac{2t\pi}{12} - \frac{\pi}{2} ) + 4[/tex]

c)

The height of the wheel's central axle is 32 meters.

f(x) = 56sin((2(x + 4)π/12) - (π/2)) + 4

The total number of different ways that the student can be assigned during a 4-day work week is 81 different ways.

A student is a person who is enrolled in an educational institution, such as a college, university, or trade school. Students are typically required to attend classes and complete assignments to gain knowledge and develop skills related to their field of study. Depending on their level of education, students may also be required to participate in research or internships in order to gain practical experience.

There are 3 possible floors that the student can be assigned to, so for each day of the 4-day week, there are 3 possible assignments.
Therefore, the total number of different ways that the student can be assigned during a 4-day work week is 3 x 3 x 3 x 3
= 81 different ways.

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Answer:

171.76 Pounds

Step-By-Step Explanation:

So the explanation to how I got the answer is in the link below.

To calculate the expected value of playing this game, we need to multiply the probability of winning each amount by the corresponding payout and then sum them up.

Let's start by calculating the probability of selecting each type of marble:

   Probability of selecting a gold marble: 3/34

   Probability of selecting a silver marble: 8/34

   Probability of selecting a black marble: 23/34

Now, let's calculate the expected value of playing the game:

E(x) = (3/34) * $3 + (8/34) * $2 + (23/34) * (-$1)

E(x) = $0.26

So the expected value of playing this game is $0.26. This means that over many plays of the game, we would expect to win an average of $0.26 per play. However, it's important to remember that this is just an average, and in any individual play of the game, you could win more or less than this amount.

The function graphed on the axis above should be expressed as a piecewise function as follows;

f(x) = x + 1       {x < -5}

     = 5x - 10   {x > 1}

In order to determine the piecewise function, we would determine an equation that represent each of line shown on the graph. Therefore, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-7 + 4)/(-8 + 5)

Slope (m) = -3/-3

Slope (m) = 1.

At data point (-5, -4) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 4 = 1(x + 5)  

y = x + 1

1, -5 2 0

For the second line, we have:

Slope (m) = (0 + 5)/(2 - 1)

Slope (m) = 5/1

Slope (m) = 5.

At data point (2, 0) and a slope of 5, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 5(x - 2)  

y = 5x - 10

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Answer:

The same, Congruent

Step-by-step explanation:

The measures of alternate exterior angles are equal when two parallel lines are intersected by a transversal line. That is, if we have two parallel lines l and m intersected by a transversal line t, then the alternate exterior angles are congruent, which means that they have the same measure. More formally, if angle 1 and angle 2 are alternate exterior angles, then:

angle 1 = angle 2

The reason for this is that when the parallel lines are intersected by the transversal line, they form a Z-shape pattern, and the alternate exterior angles are located on opposite sides of the transversal line, but outside of the two parallel lines. The angles are congruent because they are formed by a pair of corresponding angles and a pair of vertical angles.

-

The limiting value or horizontal asymptote of the function y = 2x/4x-5 is y = 0.5

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

y = 2x/4x-5

The limiting value or horizontal asymptote can be calculated by graph

So, we start by plotting the graph of y = 2x/4x-5

See attachment for the graph

From the graph, we can see that

The function does not have a defined value at y = 0.5

This means that the limiting value or horizontal asymptote is y = 0.5

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The canoe traveled approximately a distance of 21.9ft.

let the distance the canoe travels be "d".

Initial position = 65 ft

After  7s,

The Final position is 40ft away

From the given information the canoe moves =(65-40)=25ft closer

Let x=25ft

Using the tangent function

we know that, tan(50degree)=x/d

therefore, d=25/tan(50 degree)

d=21.9ft

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A number with eight tens and one one is  = 81.

A  number with five tens and five ones is  = 55.

A number with eight tens and nine ones is 89.

A number with five tens and eight ones = 58.

A number with one ten and seven ones is 17.

A number with five tens and two ones is 52.

A  number with six tens and two ones is 62.

A number with three tens and zero ones  is 30.

A number with four tens and five ones is 45.

The phrase "eight tens and one one" denotes a numerical value featuring the digit 8 in the tens position and 1 in the ones position. This is equal to the sum of 80 and 1, resulting in a total value of 81.

Therefore "a numerical figure composed of 5 tens and 5 units" indicates a number where 5 is in the tens position while 5 is in the ones position, resulting in a total of 50 + 5, which equals 55.

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The values of x, y and  z of the given parallelogram are: x = 12, y = -20 and z = -32

A quadrilateral has two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle, and then the quadrilateral is called a parallelogram. Also, the opposite sides are equal in length.

The key properties of angles of a parallelogram are:

- If one angle of a parallelogram is a right angle, then all the angles are right angles

- Opposite angles of a parallelogram are equal (or congruent)

- Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees)

Consecutive angles are supplementary and as such:

85 + 8x - 1 = 180

8x = 181 - 85

8x = 96

x = 96/8

x = 12

Opposite angles are equal and as such:

85 = -4y + 5

-4y = 80

y = -20

Similarly:

85 - 3z - 4 = 180

3z = -96

z = -96/3

z = -32

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the three friends spent L.120.00, L.240.00, and L.360.00, respectively.

How to solve the problem?

Let's denote the amount that Alicia spends as "x". According to the problem statement, we know that Juan spends twice as much as Alicia, which means he spends 2x. Similarly, we know that Ana spends three times as much as Alicia, which means she spends 3x.

We also know that the three friends together have spent L.720.00. So, we can set up an equation to represent this:

x + 2x + 3x = 720

Simplifying this equation, we get:

6x = 720

Dividing both sides by 6, we get:

x = 120

So, Alicia spent L.120.00, Juan spent twice as much as Alicia, which is L.240.00, and Ana spent three times as much as Alicia, which is L.360.00.

Therefore, the three friends spent L.120.00, L.240.00, and L.360.00, respectively.

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The table is completed as below

                             Interested in            NOT Interested in      Total

                             Athletics                   Athletics

Interested in

Academic Clubs        26                              58                          84

Not Interested in

Academic Clubs        118                              38                          156

Total                         144                               96                         240

To fill in the table, we start with the total number of students, which is 240.

We know that 35% of students are interested in athletics, so we can find the number of students interested in athletics as:

0.35 x 240 = 84

Similarly, we know that 3/5 of students are interested in academic clubs, so we can find the number of students interested in academic clubs as:

(3/5) x 240 = 144

We also know that 26 students are interested in both athletics and academic clubs, so we can fill in that cell as 26.

To fill in the remaining cells, we can use the fact that the row and column totals must add up correctly. For example, in the "Interested in athletics" row, we know that there are a total of 84 students interested in athletics. We also know that 26 of these students are interested in both athletics and academic clubs. Therefore, the number of students interested in athletics but not academic clubs is:

84 - 26 = 58

We can use similar reasoning to fill in the remaining cells. For example, in the "Not interested in athletics" column, we know that there are a total of 214 students who are not interested in athletics. We also know that 144 students are interested in academic clubs. Therefore, the number of students who are not interested in athletics but are interested in academic clubs is:

144 - 26 = 118

Let x represent "not interested in academics club" and "not interested in athletic". Using the total in the horizontal (bottom row) we have:

144 + 58 + x = 240

x = 240 - 202

x = 38

Hence 58 + 38 = 96 and 118 + 38 = 156

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