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Computing expected value in a game of chance
QUESTION
Scott is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a numbered slice at random.
This game is this: Scott spins the spinner once. He wins $1 if the spinner stops on the number 1, $3 if the spinner stops on the number 2, $5 if the spinner
stops on the number 3, and $7 if the spinner stops on the number 4. He loses $1.25 if the spinner stops on 5 or 6.
(a) Find the expected value of playing the game.
dollars
(b) What can Scott expect in the long run, after playing the game many times?
Scott can expect to gain money.
He can expect to win dollars per spin.
Start
Scott can expect to lose money.
He can expect to lose dollars per spin.
Scott can expect to break even (neither gain nor lose money).
00 EXPLANATION
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The solution to the problem at hand i.e. to draw a horizontal line segment, OM, of any length, the longer the better using ruler, protractor, compass and coloured pencils

are as follows:

Step 1: Take a ruler and align it with a sheet of paper and draw a line. This line can be of any length, although longer lines are preferred.

Step 2: The line is now OM; we must now label its endpoints. Label the leftmost point O, and the rightmost point M.

Step 3: The coloured pencils are used to add decorations to the line. To add decorations, use coloured pencils to make patterns and stripes along the length of the line. This is entirely optional and based on personal preference.

Step 4: To ensure that the line is perfectly horizontal, the protractor should be used. Place the protractor on the line and make sure the zero-degree angle is at O. The line will be horizontal if it is parallel to the baseline of the paper.

Step 5: Using a compass, measure the length of OM to ensure that it is of the desired length.

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An equation to represent this situation is y = 60x

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we can logically deduce that the cheetah was clocked running 60 miles per hour over a 50-yard distance. This ultimately implies that, an equation that models this situation is given by:

y = 60x

Where:

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y = 3x - 1: consistent, independent

2y - 6x = 4: consistent, independent

2y = -x + 6: consistent, independent

4y + 2x = 12: consistent, independent

y = 2x + 3: consistent, independent

x + y = -9: consistent, dependent

y = 3x - 1 and 2y = -x + 6: inconsistent

Let's match each system on the left with the appropriate words that describe the system on the right:

y = 3x - 1: consistent, independent

This system represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

2y - 6x = 4: consistent, independent

Similar to the first system, this represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

2y = -x + 6: consistent, independent

This system also represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

4y + 2x = 12: consistent, independent

Like the previous systems, this represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

y = 2x + 3: consistent, independent

This system represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

x + y = -9: consistent, dependent

This system represents a linear equation with infinitely many solutions. The equations are multiples of each other, meaning they represent the same line. Therefore, any point on the line satisfies both equations.

y = 3x - 1 and 2y = -x + 6: inconsistent

This system represents inconsistent equations that do not have a common solution. The lines represented by the equations are parallel and do not intersect.

To summarize the matches:

y = 3x - 1: consistent, independent

2y - 6x = 4: consistent, independent

2y = -x + 6: consistent, independent

4y + 2x = 12: consistent, independent

y = 2x + 3: consistent, independent

x + y = -9: consistent, dependent

y = 3x - 1 and 2y = -x + 6: inconsistent

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Let's denote crew A's work per week as A and crew B's work per week as B.

We are given that A = 58 ft per week and B = 59 ft per week.

We have to calculate how many weeks it will take both crews to complete the tunnel.

585 feet have already been dug from the south end. So, the total tunnel length that needs to be dug is 7605 - 585 = 7020.

Now, let's assume that both the crews continue to work at their respective rate of A = 58 ft/week and B = 59 ft/week.

Therefore, total tunnel length that needs to be dug in weeks = (7020 ft) / (A + B)

                       =  (7020 ft) / (58 ft/week + 59 ft/week)

                       =  120.20 weeks

Hence, it will take a total of 120.20 weeks for both crews to complete the tunnel.

Answer:

alternate interior angles are congruent

The reason that is NOT typically used in a proof is two angles being congruent. Option C.

Among the options A, B, C, and D, the reason that is NOT typically used in a proof is option C: two angles being congruent.

Congruence is a fundamental concept in geometry that refers to the equality of shape and size. When two angles are congruent, it means they have the same measure. While congruence is an important concept used in geometric proofs, it is typically not used as a standalone reason in a proof.

In geometric proofs, various properties, theorems, and postulates are used to establish relationships and make deductions. Let's briefly discuss the other options:

A. Definition of supplementary angles: This is a valid reason that is commonly used in proofs involving supplementary angles. The definition states that if the sum of two angles is 180 degrees, they are considered supplementary.

B. Substitution property: The substitution property is a logical property used in algebraic proofs. It allows us to replace one expression with another expression that is equal to it. This property is often employed when simplifying equations or substituting known values.

D. Parallel lines: The concept of parallel lines is frequently utilized in geometric proofs, particularly in proving angles and angle relationships. Properties such as alternate interior angles, corresponding angles, and vertical angles are established based on the parallel lines. Option C is correct.

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Answer:

[A'] = {c,d,f,g,h,i,j,k,m,n,p,q,u,w,x,z}

Step-by-step explanation:

[A'] is read as the set of A complement, which is all the elements from the universal set that are not contained in set A.

Therefore, [A'] = {c,d,f,g,h,i,j,k,m,n,p,q,u,w,x,z}

The cumulative frequency to be used in solving the 28th percentile is 16.

Cumulative frequency is described as  the total of a frequency and all frequencies in a frequency distribution until a certain defined class interval.

we add up the frequencies until we reach or exceed 28% of the total data set in order to find the cumulative frequency for the 28th percentile.

Total frequency = 4 + 9 + 16 + 10 + 9 + 2 = 50

28th percentile = (28/100) * Total frequency

28th percentile = (28/100) * 50 = 14

We start from the beginning of the distribution and add up the frequencies until we reach or exceed 14 so as to find the cumulative frequency.

In conclusion, and with reference to the given data set we notice that the cumulative frequency exceeds 14 at the 91-120 minute interval = 16.

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Answer:

b) graph pass through origin for both.

c) mario would take 5minutes to have more balloons filled than tanesha

The instantaneous rate of change of y = √x at x = 2 is √2 / 2.

To find the instantaneous rate of change of y = √x at x = 2, we need to calculate the derivative of the function with respect to x and evaluate it at x = 2.

Taking the derivative of y = √x using the power rule for differentiation, we have:

dy/dx = (1/2) × x^(-1/2)

Now, substituting x = 2 into the derivative expression:

dy/dx = (1/2) × 2^(-1/2)

= (1/2) × √2

= √2 / 2

Therefore, the instantaneous rate of change of y = √x at x = 2 is √2 / 2.

None of the provided options (-1/2, -1/4, -1) are the correct instantaneous rate of change at x = 2.

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For an item with a marked price of Rs. 26,600 and a 10% discount, the discount price is Rs. 2,660. Therefore, the customer will pay Rs. 23,940 after applying the discount.

To calculate the amount of discount on an item with a marked price of Rs. 26,600 and a discount percentage of 10%, we can follow a simple formula.

First, let's calculate the discount amount. The discount percentage is 10%, which means we can find the discount amount by multiplying the marked price by the discount percentage:

Discount amount = Marked price × Discount percentage

= Rs. 26,600 × 10/100

= Rs. 2,660

So, the discount amount for the item is Rs. 2,660.

Now, let's understand what this means. A discount is a reduction in the original price of an item. In this case, the discount amount of Rs. 2,660 is the amount by which the price of the item is reduced. Therefore, after applying the discount, the customer would only need to pay Rs. 26,600 - Rs. 2,660 = Rs. 23,940.

It's important to note that the discount amount is not the final price the customer pays. The final price is the marked price minus the discount amount. So, in this scenario, the customer will receive a discount of Rs. 2,660, and they will pay Rs. 23,940 for the item.

Understanding how discounts work can be helpful when making purchasing decisions or comparing prices. It allows customers to evaluate the value they are receiving and make informed choices based on their budget and preferences.

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Probable question:

What is the amount of the discount if the marked price of an item is Rs. 26,600 and the discount percentage is 10%?

Answer:

42 = 23 + j

Step-by-step explanation:

The equation representing the given sentence would be:

42 = 23 + j

Here, the variable "j" represents Janelle's age.

Length of gz = 12 units

Length of ot = 14.4 units

Given,

Triangle EGD with centroid at Z .

Now,

As we know that centroid divides the line segment in the ratio 2:1 .

Firstly calculate the length of gz,

gu = 18 unit

gz:zu = 2:1

gz = 2/3  * 18

gz = 12 units .

Secondly calculate the length of ot,

zt = 4.8 units

oz:zt = 2:1

oz = 4.8 * 2

oz = 9.6 units

ot = 9.6+ 4.8

ot = 14.4 units

Hence with the centroid length of ot and gz can be found out .

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The total volume of the 21 bowling balls is 6048π cubic inches.

We have,

To find the total volume of the 21 bowling balls, we first need to calculate the volume of a single ball and then multiply it by the number of balls.

The volume of a sphere can be calculated using the formula:

V = (4/3) x π x r³

where V is the volume and r is the radius of the sphere.

Given that the diameter of the bowling ball is 12 inches, the radius can be calculated as half of the diameter:

r = 12/2 = 6 inches

Now we can calculate the volume of a single ball:

V_ball = (4/3) x π x (6³) = (4/3) x π x 216 = 288π cubic inches

Since there are 21 balls, we can calculate the total volume by multiplying the volume of a single ball by the number of balls:

Total volume = 21 x 288π = 6048π cubic inches

Thus,

The total volume of the 21 bowling balls is 6048π cubic inches.

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Answer:

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x = 5/7,−3,3

Step-by-step explanation:

Answer: each base angle in an isosceles right triangle measures 45 degrees.

Step-by-step explanation:

In an isosceles right triangle, two sides have equal lengths, and one angle is a right angle (90 degrees).

Since it is an isosceles triangle, the two base angles (the angles opposite the equal sides) must be congruent, meaning they have the same measure.

To find the measure of each base angle, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Let's denote the measure of each base angle as "x". Then, the sum of the three angles in the triangle can be expressed as:

x + x + 90 = 180

Simplifying the equation:

2x + 90 = 180

Subtracting 90 from both sides:

2x = 90

Dividing both sides by 2:

x = 45

The value of x in the given figure is 8.

In the given figure there are two lines which are parallel.

We have to find the value of x.

In the straight line the sum of angles is 180 degrees.

8x+1+115=180

8x+116=180

Subtract 116 from both sides:

8x=180-116

8x=64

Divide both sides by 8:

x=64/8

x=8

Hence, the value of x in the given figure is 8.

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Step-by-step explanation:

you just have to put that value in place of x in the function.

don't be so lazy you a hole do it yourself

The distance of Satellite B from the Earth is approximately 4915.71 kilometers.

To determine the distance of Satellite B from the Earth, we can use the concept of similar triangles.

Let's break down the problem step by step:

We have a triangle formed by Satellite A, Satellite B, and the center of the Earth.

Let's call the center of the Earth point O, Satellite A point A, and Satellite B point B.

Since Satellite A orbits closer to the Earth, its distance from the center of the Earth is equal to the radius of the Earth plus the distance from Satellite A to Satellite B.

Let's call this distance OA.

OA = Radius of the Earth + Distance from Satellite A to Satellite B

OA = 6371 km + 21185.5 km

OA = 27556.5 km

Now, we need to find the distance of Satellite B from the Earth. Let's call this distance OB.

We know that OA and OB form a triangle, and they are parallel to the side AB.

Since the triangle formed by OA, OB, and AB is similar to the triangle formed by OA, AB, and the radius of the Earth, we can set up a proportion to find OB.

OA / AB = Radius of the Earth / OB

OB = (Radius of the Earth x AB) / OA

OB = (6371 km x 21185.5 km) / 27556.5 km

OB ≈ 4915.71 km

Therefore, the distance of Satellite B from the Earth is approximately 4915.71 kilometers.

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Answer:        -0.7

Step-by-step explanation:

Given statement solution is :- The area (A) of the base of the cylinder, you need to use the formula for the area of a circle, which is A = [tex]πr^2[/tex], where π is approximately 3.14 and r is the radius of the base.

To calculate the area (A) of the base of the cylinder, you need to use the formula for the area of a circle, which is A = [tex]πr^2[/tex], where π is approximately 3.14 and r is the radius of the base.

Given that the radius (r) is 10 cm, the area of the base (ABase) can be calculated as follows:

ABase =[tex]πr^2[/tex]

ABase = 3.14 * [tex](10 cm)^2[/tex]

ABase = 3.14 * [tex]100 cm^2[/tex]

ABase = 314 [tex]cm^2[/tex]

The area of the base is [tex]314 cm^2.[/tex]

To calculate the volume (V) of the cylinder, you need to multiply the area of the base (ABase) by the height (h):

V = ABase * h

V = 314 [tex]cm^2[/tex] * 30 cm

V = 9420 [tex]cm^3[/tex]

The volume of the cylinder is 9420 [tex]cm^3.[/tex]

However, there seems to be some confusion in the provided information. The given values for the area of the base (ABase) and the volume (V) are not clear. The values "- 20 gm" and "cm cm?" are not meaningful units for area or volume.

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The description of the image is one that has a four-horned star. The description is as follows:

It comprises of four equilateral triangles and One Square.

Next,

The image or shape has twelve (12) symmetrical lines.

Next,

It must be rotated 90° (clockwise or anticlockwise) in order for the image to match itself.

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Answer:

Step-by-step explanation:

The value of the expression 226²⁸ ● (25)⁶ is approximately [tex]4.1406562 \times 10^{119.[/tex]

To evaluate the expression 226²⁸ ● (25)⁶, we can follow the order of operations (also known as PEMDAS/BODMAS) which states that we should perform any calculations inside parentheses, then evaluate any exponents, and finally perform any multiplications or divisions from left to right.

Let's break down the expression :

Evaluate the exponent (25)⁶

[tex](25)^{6} = 25^{(6\times 1)} = 25^6 = 244,140,625[/tex]

Substitute the value into the expression:

226²⁸ ● 244,140,25.

Evaluate the exponent 226²⁸

[tex]226^{28} = 226^{(2\times28) = 226^{56 \\[/tex]

Now, calculating [tex]226^{56}[/tex] might not be feasible manually due to the large exponent.

However, we can use a calculator or a computer program to obtain the result.

[tex]226^{56} \approx 1.6951718 \times 10^{112[/tex]

Substitute the value back into the expression:

[tex]1.6951718 \times 10^{112[/tex] ● 244,140,625

Perform the multiplication:

[tex]1.6951718 \times 10^{112}\times 244,140,625 \approx 4.1406562 \times 10^{119[/tex] .

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y intercept will be 0,-6 .

Given,

Amplitude = 6

Time period = pi

Phase shift = pi/4

In trigonometry, the sine function can be defined as the ratio of the length of the opposite side(perpendicular) to that of the hypotenuse in a right-angled triangle.

The sine function is used to find the unknown angle or sides of a right angled triangle.

Mathematically,

sinФ = p/h

Now ,

Let us assume the phase shift to be on right side.

So the graph will be at negative y axis.

Thus the points will be 0 , -6 .

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Answer:

The three costs that contribute to the total cost of a mortgage are the down payment, mortgage tax and monthly interest.

Step-by-step explanation:

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Hence the surface area of the given figure 168 km².

In the given prism contains

3 rectangular surface,

For rectangular surface 1:

Length = 6 km

Width = 7 km

Surface area = 6x7

                      = 42 km²

For rectangular surface 2:

Length = 8 km

Width = 7 km

Surface area = 8x7

                      = 56 km²

For rectangular surface 3:

Length = 10 km

Width = 7 km

Surface area = 10x7

                      = 70 km²

Hence total surface area of the given figure is,

⇒ 42 + 56 + 70

⇒ 168 km²

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The restriction of a function f is when the domain of f is limited to a subset of its original domain.

The restriction of a function f can be demonstrated by considering a function f: R -> R, where R represents the set of real numbers.

Let u say f(x) = x^2. Now, if we restrict the domain of f to the interval [0, 5], the new function becomes f restricted: [0, 5] -> R and its expression would be f restricted(x) = x^2 for x in the interval [0, 5].

This means that the function f restricted only takes inputs from the interval [0, 5] and behaves the same way as the original function within that interval.

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Collecting the like terms in the expression 5z - 7 - 13z + 35 gives -8z + 28

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

5z - 7 - 13z + 35

Consider an expression given as

Ax + Bx

Where A and B are constants and x is a variable

The terms Ax and Bx are like terms

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

5z - 7 - 13z + 35 = 5z - 13z - 7 + 35

Evaluate the like terms

5z - 7 - 13z + 35 = -8z + 28

Hence, collecting the like terms gives -8z + 28

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The volume of the prisms are:

1. 432 yd³

2. 36in³

3. 252 m³

4. 240 ft³

5. 576 mm³

6. 144 cm³

7. 343 m³

8. 120 yd³

9. 150 in³

The formula for calculating the volume of a rectangular prism is expressed as;

V = lwh

such that;

Now, substitute the value for each of the prisms, we have;

1. Volume = 6 × 6 ×12

Multiply

Volume = 432 yd³

2. Volume = 2 ×9 × 2

Multiply

Volume = 36in³

3. Volume = 9 × 4 × 7

Multiply

Volume = 252 m³

4. Volume = 10 × 8 × 3

Multiply

Volume = 240 ft³

5. Volume = 4 × 12 × 12

Multiply the values

Volume = 576 mm³

6. Volume = 6 × 8 × 3

Volume = 144 cm³

7. Volume = 7 × 7 ×7

Volume = 343 m³

8. Volume = 8 × 3 × 5

Volume = 120 yd³

9. Volume = 5 × 6 × 5

Volume = 150 in³

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