Suppose you model a game of chance with a discrete probability distribution. Let X be the net amount of money won or lost by the player. Let P ( X ) be the probability of the corresponding outcome. The three events are as follows: There is a 23% chance the player wins 5 dollars. There is a 29% chance the player breaks even. There is a 48% chance the player loses 3 dollars. Complete the table below to model the scenario

The 999th digit to the right of the decimal point is 9.

Decimal expansion is the representation of a number in decimal form. In decimal expansion, a number is represented using the base-ten positional notation system, where each digit represents a multiple of a power of ten.

For example, the decimal expansion of the number 1234.5678 is:

which simplifies to:

1000 + 200 + 30 + 4 + 0.5 + 0.06 + 0.007 + 0.0008 = 1234.5678

The decimal expansion of a number can be finite or infinite, and it may or may not be a repeating decimal. A repeating decimal is a decimal that has a repeating pattern of digits after the decimal point. For example, the decimal expansion of 1/3 is 0.3333..., with the digit 3 repeating infinitely.

To find the 999th digit to the right of the decimal point, we need to determine the repeating block of digits in the decimal expansion of 9/23.

The remainder when 9 is divided by 23 is 9, so we can start the long division as follows:

         0.3913043478260869565217...

         --------------------------------

23 |    9.00000000000000000000

           - 6

          --------

                30

               -23

               -----

                   7

                    ...

We can see that the decimal expansion of 9/23 repeats after 22 digits, since the remainder becomes 7, which is the same as the remainder we obtained after dividing 9 by 23.

Therefore, the 999th digit to the right of the decimal point is the same as the (999 mod 22)th digit, which is the 9th digit in the repeating block of digits:

0.3913043478260869565217...

9

So the 999th digit to the right of the decimal point is 9.

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Answer:

The total volume, in cubic feet, of the three boxes is 144 cubic feet.

Chain of thought:

1. Volume = base x height

2. Box 1: Volume = 16 sq feet x 3 feet = 48 cubic feet

3. Box 2: Volume = 16 sq feet x 3 feet = 48 cubic feet

4. Box 3: Volume = 16 sq feet x 5 feet = 80 cubic feet

5. Total Volume of three boxes = 48 + 48 + 80 = 144 cubic feet

After looking at the provided number lines, it is clear that the number line (B) accurately reflects 1/4 + 1 < 5.

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics.

It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

A number on the left of a number line is always smaller than a number on the right.

A number to the right is always greater than a number to the left, too.

So, the inequality we have is:

1/4 + 1 < 5

Now, after observing the given lines, we can easily tell that the number line (B) represents 1/4 + 1 < 5 perfectly.

Therefore, after looking at the provided number lines, it is clear that the number line (B) accurately reflects 1/4 + 1 < 5.

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Complete question:

Which number line shows the solution to 1/4 + 1 < 5

Answer: 22

Step-by-step explanation:

The first one is 10.

The other 2 has 6, because 10-4=6

So

10+(6x2)=22

Using area formula,

a. Area of the trapezium = 47.5m².

b. Area of parallelogram = 54inches².

The area of a thing is the amount of space it occupies in two dimensions. It is a way to count how many unit squares completely round the surface of a closed figure. The standard unit of area is the square unit, which is usually expressed as square inches, square feet, etc.

a. Sides of the trapezium are, a = 5m and b = 14m.

Height, h = 5m.

Area of the trapezium = (a+b)/2 × h

= (5 + 14)/2 × 5

= (19× 5)/2

= 95/2

= 47.5m².

b. Height of parallelogram = 6inches.

Base of parallelogram = 9inches.

Area = b × h

= 6 × 9

= 54inches².

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Answer:

The angles are congruent, the two that are touching, m<s

Step-by-step explanation:

The probability of there being no defects in the entire shipment is 0.2075.

What is probability?

Probability can be used to calculate an event's probability. It can only be used to assess the possibility that an event will occur. A scale from 0 to 1, where 0 is impossible and 1 is a particular occurrence.

We are given that out of the 400 components, 68 are defective and 332 are non-defective computer components.

A random sample of 25 is taken.

So,

⇒ Probability (Defects in the shipment) =  [tex]\frac{68}{400}[/tex]

⇒ Probability (Defects in the shipment) = 0.17

Thus,

⇒ Probability (No Defects in the shipment) =25 * (1 - 0.17)

⇒ Probability ( No Defects in the shipment) = 25 * (0.83)

⇒ Probability ( No Defects in the shipment) = 0.2075

Hence, the probability of there being no defects in the entire shipment is 0.2075.

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The next three terms are:

Answer:

367

Step-by-step explanation:

Places in the alphabet:
T=20, H=8, E=5, R=18, E=5. 20+8+5+18+5=56. THERE=56
A=1, R=18, E=5. 1+18+5=24. ARE=24
S=19, O=15, M=13, E=5. 19+15+13+5=52. SOME=52
S=19, A=1, N=14, D=4, W=23, I=9, C=3, H=8, E=5, S=19. 19+1+14+4+23+9+3+8+5+19=105. SANDWICHES=105
O=15, N=14. 15+14=29. ON=29
T=20, H=8, E=5. 20+8+5=33. THE=33
S=19, H=8, E=5, L=12, F=6. 19+8+5+12+6=49. SHELF=49
56+24+52+19+105+29+33+49=367

sin60=√3/2 = x/12

x=√3×12/2

x=√3×6

x=6√3

The approximate diameter of the garden is 12.82 feet.

What is circumference?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.

Here, we have

Given: A circular garden has a circumference of 40.25 feet.

We have to find the diameter of the garden.

The formula for the circumference of a circle is given as 2πr.

We have to find the radius of the circular garden

Hence: 2πr = 40.25m

π = 3.14

To find the radius, the formula would be given as

r = C/2π

Where C = Circumference of the circle

r = (40.25/2)x 3.14

r = 63.195

d =  C/π

d = 40.25/3.14

d = 12.82

Hence, the approximate diameter of the garden is 12.82 feet.

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The future value of Ted's investment after 30 years would be approximately $13,711.86.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

Ted can use the formula for the future value of an annuity to calculate the future value of his investment:

FV = Pmt x (([tex](1 + r)^{n}[/tex]) - 1) / r

Where:

FV = Future Value

Pmt = Payment per period (monthly in this case)

r = Interest rate per period (monthly in this case)

n = Number of periods (in this case, 30 x 12 = 360 months)

Substituting the given values, we get:

FV = $250 x (([tex](1 + 0.062/12)^{360}[/tex] - 1) / (0.062/12)

FV = $250 x (283.8576) / 0.0051667

FV = $13,711.86

Therefore, the future value of Ted's investment after 30 years would be approximately $13,711.86.

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The value of the expression is 9y⁵z³/x⁶

Note that index forms are described as mathematical forms of writing numbers that are large or too small in more convenient forms.

The rules of index forms are;

From the information given, we have that;

(y³z⁻¹) (3x⁻³y/z⁻²)²

expand the bracket, we get;

(y³z⁻¹) 9x⁻⁶y²/z⁻⁴

Take the inverse exponent of the denominator

(y³z⁻¹) 9x⁻⁶y²z⁴

Now, add the exponents

9x⁻⁶y³⁺²z⁻¹⁺⁴

9x⁻⁶y⁵z³

Then, we have;

9y⁵z³/x⁶

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Number of math textbooks is 110 and number of history textbooks is 330 were sold when a textbook store sold a combined total of 440 math and history textbooks in a week.

There are two categories of textbooks. Let "x" stand for the quantity of math textbooks and "y" for the quantity of history textbooks.

A textbook store sold a combined total of 440 math and history textbooks in a week.

Equation,

x + y = 440

The number of math textbooks sold was three times the number of history textbooks sold.

x = 3y

Substituting the values in equation x + y = 440,

3y + y = 440

4y = 440

y = [tex]\frac{440}{4}[/tex]

y = 110

Number of math textbooks = 110

Number of history textbooks:

3y

3 × 110

330

Number of math textbooks is 110 and number of history textbooks is 330 were sold when a textbook store sold a combined total of 440 math and history textbooks in a week.

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Answer:

215.95

Step-by-step explanation:

68.4+49.6+97.95

The interest on $58,254.26 was calculated to be $146.38, the payment to principal was calculated to be $182.62, and the new principal was calculated to be $58,071.64.

Payment is the transfer of funds from one party to another in exchange for goods, services, or to fulfill a legal obligation. Payment can take various forms, including cash, check, credit card, money order, or electronic transfer. Payment can be made in person, over the phone, or online. The most important aspect of payment is that it is a legally binding contract between two parties. Payment is an important part of the economic system that facilitates the exchange of goods and services and helps to ensure that all parties involved receive what they expect from the transaction.

The interest on $58,254.26:
To calculate the interest on $58,254.26, we first need to determine the interest rate. Assuming that the interest rate is 3%, we can calculate the interest owed as follows:

Interest = Principal x Interest Rate x Time

Interest = $58,254.26 x 0.03 x 1/12

Interest = $146.38

b) The payment to principal:
To calculate the payment to principal, we need to subtract the interest from the total payment amount.

Payment to Principal = Total Payment – Interest

Payment to Principal = $329 - $146.38

Payment to Principal = $182.62

c) The new principal:
To calculate the new principal, we need to subtract the payment to principal from the original principal.

New Principal = Original Principal – Payment to Principal

New Principal = $58,254.26 - $182.62

New Principal = $58,071.64

In conclusion, the interest on $58,254.26 was calculated to be $146.38, the payment to principal was calculated to be $182.62, and the new principal was calculated to be $58,071.64.

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Answer:

150 men and 252 women

Step-by-step explanation:

            Men : Women = 5 : 9

Number of men = 5x

Number of women = 9x

42 women left the museum.

Number of remaining women = 9x - 42

              New ratio = 2 : 3

                      [tex]\dfrac{5x}{9x -42}=\dfrac{2}{3}\\\\\\\bf Cross \ multiply,[/tex]

                          3*5x  = 2*(9x - 42)

                          15x     = 2*9x - 2*42

                              15x = 18x - 84

                  18x - 84 = 15x

Add 84 to both the sides,

                         18x = 15x + 84

Subtract 15x from both sides,

                18x - 15x = 84

                         3x = 84

Divide both sides by 3,

                            x = 84 ÷ 3

                            x =  28

Number of men = 5 * 28 = 140

Number of women = 9*28 = 252

Answer:

308 yards^2

Step-by-step explanation:

Area = length * width

Length = 20

Width = 15.4

20 * 15.4 = 308

Answer: 308 yards

Step-by-step explanation:

The argument to symbols of the logic expression is shown below

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

The argument in symbols can be expressed as:

p -> q

~p

Therefore, ~q

Where:

p = "It rains."

q = "I will watch the Real World marathon."

"->" denotes "implies".

"~" denotes "not".

So the argument can be read as "If it rains, then I will watch the Real World marathon. It did not rain.

Therefore, I did not watch the Real World marathon."

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The 5-digit number that can be formed is 100,000.

5-digit numbers using 0,1,,2,3,4,5,6,7,8,9,

 We can use any of the 10 numbers to form a 5-digit number

The first place, there can be any of the 10 numbers

       In the second place, there can be any of the 10 numbers

       In the third place, also there can be any of the 10 numbers and so on.

       Therefore we have:

   10×10×10×10×10 = 100,000 digits

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Rule 1: The output is the square of the input. For example, if the input is 3, then the output would be 9 (3 squared).

Rule 2: The output is 90 greater than the input. For example, if the input is 3, then the output would be 93 (3 + 90).

These are the two rules you've provided, and they describe how to calculate the output (y) based on the input (x).
Rule 1: The output is the square of the input.
In this rule, when you have an input value (let's call it x), you square it (multiply it by itself) to get the output value (y). Mathematically, this can be written as:
[tex]y = x^2[/tex]
Rule 2: The output is 90 greater than the input.
In this rule, when you have an input value (x), you add 90 to it to get the output value (y).

Mathematically, this can be written as:
y = x + 90.

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The value of y for the inverse variation when x = -12 is derived to be equal to 1.

Inverse variation is a mathematical relationship between two variables, in which an increase in one variable leads to a proportional decrease in the other variable. Mathematically, inverse variation can be expressed as y = k/x, where y and x are the two variables, k is a constant of proportionality, and the product of y and x is always equal to k.

when x = 6 and y = -2, then k is derived as:

-2 = k/6

k = -12 {cross multiplication}

when x = -12, y is derived as:

y = -12/-12

y = 1

Therefore, the value of y for the inverse variation when x = -12 is derived to be equal to 1.

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Answer:

y = 150x + 3000

Step-by-step explanation:

We can express the cost (y) as a linear function of heater quantity (x) by writing the equation in the slope-intercept form (y = mx + b), where m is the slope (in this case change in cost / change in heater quantity) and b is the y-intercept (when x = 0).

To find the slope (m), we can use the slope formula, which is

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x1 and y1 are one point and x2 and y2 are the other point.

If we allow (30, 7500) to represent x1 and y1 and (40, 9000) to represent x2 and y2, our slope is:

[tex]m=\frac{9000-7500}{40-30}\\ \\m=\frac{1500}{10}\\ \\m=150[/tex]

Now, we can find the y-intercept by plugging in the slope and one of the points and solving for b:

[tex]7500=150(30)+b\\7500=4500+b\\3000=b[/tex]

Thus, our equation where y (cost) is a function of x (heater quantity) is y = 150x + 3000

Given triangle is not a right angle triangle.

What is Pythagoras theorem?

For any right angle triangle,

Hypotenuse ²= Base²+Height ²

To determine whether the any triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's denote the sides of the triangle as follows,

a = 14

b = 10

c = 4√19

Then we can check whether the Pythagorean theorem holds for these values:

c² = (4√19)² = 16×19 = 304

a²+ b² = 14²+ 10² = 196 + 100 = 296

Since c² is not equal to a² + b², the triangle is not a right triangle. Therefore, the answer is no, the given triangle is not a right angle triangle.

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To find the value of tan(-284°24'), we can use the fact that the tangent function has period π, which means that:

tan(x) = tan(x + nπ)

where n is any integer. We can use this fact to convert the angle -284°24' to an equivalent angle between 0° and 360°:

-284°24' = -360° + 75°36' = 75°36'

Now, we need to find the reference angle, which is the acute angle between the terminal side of the angle and the x-axis. Since 75°36' is in the second quadrant (where the tangent function is positive), the reference angle is:

75°36' - 180° = -104°24'

Finally, we can use the identity:

tan(-θ) = -tan(θ)

to find the value of tan(-104°24'):

tan(-104°24') = -tan(104°24')

We can use a calculator to find that:

tan(104°24') ≈ 2.3835

Therefore:

tan(-284°24') ≈ -2.3835 (rounded to the nearest ten-thousandth)

So, the value of tan(-284°24') to the nearest ten-thousandth is -2.3835.

Using the method of conversion,

The patient will take 6 teaspoons of the elixir and 2 tablespoons of the elixir as prescribed by the physician.

Conversion means changing a particular unit of measurement into another so that the values or the measurements are in a single unit which then allows us to solve the problem or the sum easily. Both the base units compared should be same.

This helps to reduce the complications that are created in a question.

Now here in the question,

We have 1 ounce of elixir.

Now to convert 1 ounce in 1 teaspoon we need to multiply the value by 6.

Similarly in order to convert 1 ounce into tablespoon, we need to multiply it by 2.

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Using the area formula, the length of the sides of the two squares are 22 cm and 25 cm respectively.

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.

It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.

The square's four sides are equal to one another or congruent.

The square's opposing sides run parallel to one another.

The square's diagonals form a 90° angle with one another.

The square's two diagonals are equal to one another.

Area: s²

s² + (s+3)² = 1017

s² + s² + 9 = 1017

2s² = 1017 - 9

2s² = 1,008

s² = 1008/2

s² = 504

s = ²504

s = 22.44

Round off: 22 cm

Then, (s+3) = 22 + 3 = 25 cm

Therefore using the area formula, the length of the sides of the two squares are 22 cm and 25 cm respectively.

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Answer:

Step-by-step explanation:

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Answer:

D. 4 units

Step-by-step explanation:

Similar figures have corresponding lengths in proportion.

[tex]\frac{4x}{2x}=\frac{x+1}{x} \\ \\ 2=1+\frac{1}{x} \\ \\ 1=\frac{1}{x} \\ \\ x=1[/tex]

Therefore, the height of Figure 1 is 4.