A "Pick 2" lottery game involves drawing 2 numbered balls from separate bins each containing balls labeled from 0 to 9. So there are 100 possible selections in total: 00, 01, 02, ..., 98, 99. Players can choose to play a "straight" bet, where the player wins if they choose both digits in the correct order. Since there are 100 possible selections, the probability a player wins a straight bet is 1/100. The lottery pays $50 on a successful $1 straight bet, so a player's net gain if they win this bet is $49. Let X represent a player's net gain on a $1 straight bet. Calculate the expected net gain E(X). Hint: The expected net gain can be negative. E(X) = dollars

Use the table in the book to find the P-value rounded to at least 4 decimal places.

It is not possible to find the exact P-value rounded to at least 4 decimal places by using tables, as the P-value is a continuous variable and tables only give a range of values containing the P-value.

The probability that you would have discovered a specific collection of observations if the null hypothesis were true is expressed as a number called the p value, which is determined from a statistical test.

In order to determine whether to reject the null hypothesis, P values are utilised in hypothesis testing. You are more inclined to reject the null hypothesis the smaller the p value.

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The volume of air present in the room is 27410.7075 lt .

The space occupied inside an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied inside an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to imagine in any shape, yet it may be compared amongst shapes. For instance, a compass box has a larger volume than an eraser placed inside of it. We split the area into equal square units to get the area of any two-dimensional form. Similar to this, we shall split the volume of solid objects into equal cubical units while calculating it. In the part after this one, let's examine how to determine the volume of various solid forms.

The dimension of the room is 11*11*8 in feet.

so, 11 ft = 11 *2.54*12 = 335.28 cm

And, 8 ft = 8 *2.54*12 = 243.84 cm

Volume of the room is = 335.28 * 335.28 * 243.84 = 27410707.5 [tex]cm\x^{3}[/tex]

In litre,

27410707.5 [tex]cm\x^{3}[/tex] = 27410707.5/1000 = 27410.7075 lt.

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The constant of variation for the given data is 1/4.

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Given that the data in the table is,

x        f(x)

-8       -2

-4       -1

0        0

4         1

8        2

The constant of proportionality will be calculated as,

F(x) = kx

-2 = k x -8

k = -2 / -8

k = 1 / 4

Here, the proportionality constant will be 1/4.

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We determined that the probability of lunch cost is between the above-mentioned value is P (0.2011 < Z < 0.2748)

Probability is the possibility of happening an event. It is expressed as the ratio of the number of favorable outcomes to the total possible outcome.

We can find probability from a statistical data based on the mean value and standard deviation.

given, average cost for lunch per person = mean value = $5.97

standard deviation of cost = $2.25

number of samples = 46

assume distribution of money spent is normal.

the probability of a single lunch patron that has a cost between $6.4225 and $6.5884 can be calculated by the following way.

Z-score = (actual price - mean price) / standard deviation

Z-score when actual price is $6.4225.

                    Z = ($6.4225 - $5.97) / $2.25

    Z = 0.2011

Now, Z-score when actual value is $ 6.5884.

 Z = ($6.5884 - $5.97) / $2.25

Z = 0.2748

If actual value is denoted by X than the probability is shown as

P (6.4225< X< 6.5884) and P (0.2011< Z< 0.2748)

For the group of 46 patrons the above probability is also the same.

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The interest rate is 2.5 %.

Simple interest is the form of interest used for short term loans, such as one receives at pawnshops or from loan sharks. It is governed by the formula:

I = Prt

where I is the amount of interest, P is the principal (amount of money borrowed), r is the interest rate (per year), and t is the time (expressed in years).

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

I = $25, P = $500, r = ?, t = 2 years

∴ I = Prt

∴ r = I / Pt

∴ r = 25 / ( 500 * 2)

∴ r = 25 / 1000

∴ r = 0.025

∴ r = 0.025 * 100 %

∴ r = 2.5 %

Therefore, the interest rate is 2.5 %.

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18 m²

The area is the size of a 2-dimensional shape.

Area of a Triangle

The formula for the area of a triangle is [tex]\frac{1}{2}bh[/tex], where b is the base and h is the height.

This formula comes from the fact that a triangle is half of a rectangle. Remember that the area of a rectangle is the base times the height, so a triangle would be half of this.

Solving for Area

The base of the triangle is 9 meters. Then, the height is 4 meters. So, we can plug these values into the formula.

So, A = 18. Then, since meters are being multiplied by each other, the units are meters squared. The final answer is 18 m².

m = the unknown value

4m = four times that unknown value

4m = 4/3

m = (4/3)*(1/4)

m = 4/12

m = 1/3

Therefore, we multiply 4 with 1/3 to end up with 4/3.

Answer: 0.640

Step-by-step explanation:

Multiply in your calculator

Answer:

Step-by-step explanation:

y - 5 = -1/7(x - 4)

y - 5 = -1/7x + 4/7

y - 35/7 = -1/7x + 4/7

y = -1/7x + 39/7

The answer of 2/7 + 3/5 is a fraction. The answer is 31/ 35.

To add two fractions, the denominators must be the same, in this case, the denominators are different, so we need to find a common denominator to add these two fractions.

A common denominator for 2/7 and 3/5 is 35.

So we can convert both fractions to have 35 as the denominator,

2/7 becomes (2×5)/(7×5) = 10/35

3/5 becomes (3×7)/(5×7) = 21/35

then we can add the numerators:

10/35 + 21/35 = 31/35

so the final answer is 31/35

This is also the simplest form of this fraction which would be 31/35.

--The question is not clear, answering to the question below--

"What is the answer of 2/7 + 3/5?"

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Answer:

C.  The y-intercept is (0,24).  Jamie has 24 tickets before going on any rides.

Step-by-step explanation:

Rides  Tickets Left

  0           24

  1            18

  2           12

  3             6

  4             0

Let x be the number of rides taken and y be the number of tickets remaining.  We can write the equation for this linear function as:

  y = -6x + 24

The y-intercept, 24, tells us how many tickets Jamie has before taking any rides (x = 0).  He has 24 tickets.  His first ride reduces that amount by 6, so the slope of this line is -6 (Jamie uses 6 tickets per ride).

The y-intercept is written as (0,24):  Jamie has 24 tickets before any ride is taken.  This is option C.

Answer:

110° and 215°

Step-by-step explanation:

to measure the bearing from one point to another

the bearing is measured clockwise from a north line.

(a)

clockwise from the north line N at C to D is 110°

(b)

clockwise from the north line N at C to D is 215°

The graph is increasing when the graph has positive slope and the graph is decreasing when the graph have a negative slope .

What is Slope ?

The slope of any line can be calculated by using any two distinct points on the line. The slope of a line formula calculates the ratio of the vertical change to horizontal change between two distinct points of the line.

that means , let the two points on the line be [tex](a,b)[/tex] , [tex](c,d)[/tex] . So , the slope will be calculated as : Slope(m) = [tex]\frac{d-b}{c-a}[/tex] .

(i) When the slope of the graph is positive , it indicates that the graph rises when moving from left to right , Hence , the graph is increasing .

(ii) When the slope of the graph is negative , it indicates that the graph falls when moving from left to right , Hence , the graph is decreasing .

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The degree of the given polynomial is 4.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.

The given polynomial is y=3x²-7x⁴+5-9x.

a) The polynomial in standard form is -7x⁴+3x²-9x+5.

b) The degree of the polynomial is 4.

c) The number of terms in the polynomial are 4.

d) Use the degree and the leading coefficient to determine the behavior.

Falls to the left and falls to the right

e) Use the derivative to find the maximum and minimum.

(−0.78859507, 11.25584002) is a local maxima

f) Here the y-intercept is (0, 5)

g) 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. x≈−1.33755842,0.5797309.

h) Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.

Domain: (−∞,∞),{x|x∈R}

i) Range: (−∞,11.25584002],{y|y≤11.25584002}

Therefore, the degree of the given polynomial is 4.

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The Third side of a triangle if the two sides are given and one angle is given can be found by using the Cosine Law .

What is Cosine Law ?

The Cosine Law states that the square of any one side of the triangle is equal to difference between  sum of squares of the other two sides and double of product of other sides and cosine of the angle included between them.

In mathematical terms it  means that ;

let a , b be the the know sides and "c" be the unknown side of the triangle ABC , and the known angle be = angle C ;

So , the side c will be ⇒ [tex]c^{2}= a^{2} +b^{2} - 2ab\times Cos(C)[/tex] ;

Therefore , the Cosine Law helps in finding the missing third side .

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The cost of a pack of gum bought by Lionel is $2.1.

Let the variable g represent the cost of a pack of gum.

Let the variable c represent the cost of a candy bar.

Since Lionel bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80, a linear equation that models this situation is;

4c + 2g = 9.80    ......equation (1)

Additionally, two packs of gum cost the same as three candy bars:

2g = 3c     ......equation (2)

c = 2g/3     ......equation (3)

Substituting equation (3) in equation (1), we get:

4(2g/3) + 2g = 9.80

8g/3 + 2g = 9.80

14g/3 = 9.80

14g = 29.4

= 29.4/14

= $2.1

The cost of a pack of gum is $2.1.

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The complete question is -

Lionel bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80. Two packs of gum cost the same as three candy bars. Let g represent the cost of a pack of gum and c represent the cost of a candy bar. What is the cost of a pack of gum?

Answer:

Step-by-step explanation:

original equation equivalent to 7x+5-3x-2 = 7x-3x+5-2=4x+3

the answer is 4x+3

Answer:

The answer is 4x+3

In Python, __main__ is the name of the environment where top-level code is run.

We know that in Python, the main function acts as the starting point of execution for any software program.

As we know the program executes only when it runs directly, and if it is imported as a module, then it will not run, the execution of the program starts only when the main function is defined in Python.

__main__ is the name of the top-level scope in which top-level code executes.

Also, all the functions and modules will be executed in the top-level scope __main___ in the interpreter shell.

Using the top-level scope __main__ increases the reusability.

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1. The best geometric model for the rail road is C. Line

2. Two straight lines cannot go through any two points. It is false.

3. The length of the cake is A. 5.5 inches.

4. The vertical angles are AHC and GHE.

The best geometric model for a set of railroad tracks would likely be a line, as it represents the linear path that the tracks follow. A point would not be appropriate as it does not represent the length or direction of the tracks, and a plane would not be necessary as the tracks are linear and exist in a three-dimensional space.

It should be noted that two straight lines cannot go through any two points. Only one line can. The length of the cake will be:

= 6.0 - 0.5

= 5.5

It should be noted that vertical angles are equal. This was Illustrated as AHC and GHE.

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the main three types of trigonometry are ,

1- sine angle (sin Q)

2- cosine angle (cos Q)

3- tangent angle (tan Q)

all the other types of trigonometry are related to these three types only.

sine angle

we can find out the sine angle by taking perpendicular of the triangle divided by hypotenuse of the triangle. sine angle is a acute angle.

cosine angle

we can find out the cosine angle by taking base of the triangle divided by hypotenuse of the triangle. cosine angle is a acute angle.

tangent angle

we can find out the sine angle by taking perpendicular of the triangle divided by base of the triangle.

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Answer:

Step-by-step explanation:

x + 4 + 2x - 6 + 10 > 50

4 - 6 + 10 = 8

x + 2x = 3x

3x + 8 > 50

Subtract 8 from both sides

3x > 50 - 8

3x > 42

Divide 3 from both sides

42/3 = 14

x > 14

The perimeter of the sign is 22 inches.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A rectangular school banner has a length of 21 inches and a perimeter of 66 inches.

Let the perimeter of the sign for the length of 7 inches of the banner = x

So, By definition of proportion, we get;

⇒ 21 / 66 = 7 / x

Solve for x;

⇒ x = 7 × 66 / 21

⇒ x = 22

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Answer:

x=16/3

Step-by-step explanation:

4=3/4x+0

4=3x/4

4=3x/2square

4times4=16

3x/3=16/3

x=16/3

The expression that represents the total price plus tax that Julian paid during shopping is 1.0575pp

How to write the expression of the total price Julian paid

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

5.75%

= 5.75 percent

= 5.75 / 100

= 0.0575

The factor 0.0575 of the price  (pp dollars and cents) gives the total price paid

when the price paid is pp dollars and cents

= 0.0575 * pp + pp

= 1.0575pp

The total price paid is 1.0575pp

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The four types of problem solving can be named as Trial and Error , Algorithms , Inductive Reasoning and Deductive Reasoning .

What is Problem Solving ?

The Problem solving can be defined as the act of defining a problem , finding cause of problem, identifying, prioritizing and selecting the alternatives for solution and implementing it .

The four types of problem solving are :

(i) Trial and Error : It is defined as trying the different ways of doing something until we find the best solution .

(ii) Algorithms : The algorithm can be defined as a  set of step by step procedures which provides correct answer to a particular problem.

(iii) Inductive Reasoning : It is defined as a process where we come to a conclusion where a general statement is reached from specific result.

(iv) Deductive Reasoning : It is defined as a process where we get specific results from general statements .

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Answer:

You do length time width

log with base 10 is mainly used to simplify manual computation and it is also related to the decimal system. if we calculate the log of any variable with base 10, then an integer just greater than that calculated value gives the number of digits in that number.

likewise, log with base 2 is used in digital and computer applications where binary system prevails.

The worth of log e is around equal to 0.4342944819 where log e has a base value equal to 10.

1. The value of log e base 10 is around equal to 0.4342944819.

2. The value of log e with base e, that is, ln the e value is equal to 1.

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