A player tosses a fair coin n times. Each time, if the coin lands on Head, the player
win a dollar, otherwise, the player loses a dollar. What is the expected earning of the
player? What is the variance of the earning of the player? Now the player apply a
new strategy: the player will play the game until he gets a head. What is the expected
earning of the new strategy? Does the result depend on n?

a. The length is (3b) meters

b. length of hall is 36m.

We have given,

a. Breadth of the rectangle = b meters,

Since, length of a rectangular hall is 3 times the breadth of the hall,

⇒ Length = 3 × Breadth

⇒ Length = 3b

Hence, the length of the rectangle is (3 b) meters.

b. if the breadth is 12 m

Then, the length of the hall = [tex]3\times 12[/tex]

                                           = 36m.

Length is a measure of distance. In the International System of Quantities, length is a quantity that has a measured distance. In most  measurement systems, a base unit of length is chosen from which all other units are derived. In the International System of Units, the basic unit of length is the meter.  Length generally refers to  the widest dimension of a fixed object. However, this does not always happen and may depend on the location of the object.

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ANSWER

637.5π mm³

EXPLANATION

The volume of a cylinder is the product of its base area and its height. In this problem, the radius of the base of the cylinder is 5 mm, and its height is 25.5 mm. The volume is,

Hence, the volume is 637.5π mm³.

The probability of event A is 0.0012 and the probability of event B is 0.0288

There are 7 people and 4 prices.

A) The probability that Ann wins the first prize is 1/7, assuming that all 7 people have the same probability of winnig.

Then Jim is second, now the probability is 1/6 (because we don't count Ann anymore).

Soo wins the third one, with a probability 1/5.

Kira wins the last one, with a probability of 1/4.

The joint probability is the product of all the individual ones:

P(A) = 1/7*1/6*1/5*1/4  = 0.0012

B) Now we just want that Soo, Ann, Ravi, and Hans win, but the order does not matter.

So we have the same probability than above, but now we need to include the permutations of the 4 elements, so we add a factor 4!.

P(B) = 4!*0.0012 = 4*3*2*1*0.0012 = 0.0288

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SNSWER

. x = 2

F. x = -1

EXPLANATION

e can rewrite this equation as a quadratic frunction equal to zero.

First apply the binomial squared on the left side:

This is to write it in standard form. Now we have the equation:

We can add 3x on both sides of the equation:

And subtract 6 from both sides:

Now we can use the quadratic formula to solve this for x:

In our equation a = 1, b = -1 and c = -2:

Therefore the solutions to the given equation are x = 2 and x = -1

To know if a graph represents a function, we have to use the vertical line test, which consists in drawing a vertical across the curve.

If the vertical line intercepts twice the curve, then it's not a function.

Then, the graph has no function symmetry because the graph is not that of a function.

Based on the statement about Thomas's income rising along with his stress income, the correlation and cause is C. Positive correlation; common underlying cause.

Positive correlation between two variables means that they move in the same direction. When one of the variables increases, the other variable increases as well. When one variable decreases, the other variable decreases too.

The income level of Thomas is increasing at the same time the stress is increasing so this is a positive correlation.

A higher Income level might lead to more work and responsibilities which is most likely the common underlying cause for the positive correlation.

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The value of x is 10 .

In the question ;

from the given figure , we can see that MS=SL   and KR=RL which means

that R and S are the mid points of sides ML and KL respectively .

The Mid Point Theorem states that

If the line segment adjoining the mid points of any of the sides of the triangle then the line segment is said to be parallel to the third  side and is half of the length of the third side .

which means RS parallel  to KM   and KM/2=RS  ( ... by mid point theorem)

Substituting the values of RS=2x-10 and KM=2x, we get

2x/2=2x-10

2x = 2(2x-10)

2x = 4x -20

4x-2x=20

2x=20

x=10

Therefore , the value of x is 10 .

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The x and y coordinates of the line are utilized to compute the steepness of the line using the slope formula.We are aware that one of a line's most crucial qualities is its slope because it aids in determining the pace of change.

What is the point-slope form of the equation of the line?

A line's steepness can be determined by looking at its slope.Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

Using the formula

m=y2y1/2x1,

which is the change of y over the change of x, determine the slope of the line between (3,5) and (9,1).

Slope is equal to the change in y over the change in x

, or rise over run.

m=change in y /change in x

The change in x is equal to the difference in x-coordinates (also called run), and the change in y

is equal to the difference in y-coordinates (also called rise).

m=y2−y1/x2−x1

To determine the slope, enter the values of x and y into the equation.

m=1−(5)/9−(−3)

m=-4/12

m=12/4

m=3

To replace x1 and y1 in the point-slope form yy1=m(xx1), which is derived from the slope equation

m=y2y1/x2x1,

use the slope 3 and the specified point (3,5).

y−(5)=3(x+3)

Keep the equation in point-slope form and make it simpler.

y−5=3(x+3)

Do the y math.

To continue, tap...

y=x+8

List the equation in all its variations.

Form of a slope-intercept:

y=x+8

Forming a point-slope: y=5=1(x+3)

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As The triangles are congruent the value of y = 1 and x = 4

The basic polygonal shape of a triangle has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol. It has three connected vertices. Triangles can be divided into a variety of categories according on their sides and angles.

AS the triangles are congruent

15x-8y = 52.....(i)

6x +14y +142=180

6x +14y = 38

3x +7y =19 ....(ii)

x=[tex]\frac{19-17y}{3}[/tex]

15([tex]\frac{19-17y}{3}[/tex])-8y = 52

5(19-17y)-8y=52

95-85y-8y =52

93y =93

y = 1

x =4

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Answer: 33/10

Step-by-step explanation:

=3.3 X 10/10

= 33/10

Answer done. 33/10 #

The function g in terms of f so that the statement is true is g(x) = 4f(x)

The point (x, y) on the graph of f (x) is changed to the point (x, ky) on the graph of g (x), where k 1. This is known as a vertical stretch. If k is equal to 1, the graph remains the same; otherwise, it shrinks vertically.

There is a 4-inch vertical stretch in our query. As a result, the points on the new graph would be (x.y/4) rather than f(x)=y.

g(x) = 4f as a result of transformation (x)

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The statement is true g(x) = 4 +f(x).

The point (x, y) on the graph of f (x) is changed to the point (x, k y) on the graph of g (x), where k=1. This is known as a vertical stretch. If k is equal to 1, the graph remains the same otherwise, it shrinks vertically.

There is a 4-inch vertical stretch in our query. As a result, the points on the new graph would be (x. y/4) rather than f(x)=y.

g(x) = 4 +f(x) as a result of transformation of x.

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L = 2w - 5

Plug this in for perimeter equation:

2l + 2w = 56

4w - 10 + 2w = 56

6w = 66

W=11

now find length

L = 22 - 5

L = 17

If the amount of money is even, then the item that costs an odd number of money has to be bought an even number of times. Some possible combinations could be 2 lb potato salad and 7 lb Mac salad, or 4 lb potato salad and and 4 lb mac salad, or 6 lb potato salad and 1 lb mac salad.

Answer:

A. 366-249=125

B. 13386-9608=4788

Answer and Explanation:

1B: {x | -7 ≤ x ≤ 8}

2A: [-4, 3]

2B: {y | -4 ≤ y ≤ 3}

The range of a function is its set of y-values.

Set builder notation (roster method) is a way to define the values within a set.

Answer:

the least common denometer for 5/12, 7/16 would be 48.

Step-by-step explanation:

Based on given diagram we can conclude that d || e.

As per the diagram given there are some lines and angles which are defined and some of them are to be find so that we can conclude answer from the given options.

The attached image shows the Angles which are solved for the solution of the question as follows;

For line 'a' makes an angle of 110° with line 'd' and as total angle made by a line is always 180° Therefor another angle made by line 'a' with line 'd' will be 180° - 110° = 70° a shown in the attached figure.

For line 'c' makes an angle of 115° with line 'd' and as total angle made by a line is always 180° Therefor another angle made by line 'c' with line 'd' will be 180° - 115° = 65° a shown in the attached figure.

For line 'b' makes an angle of 60° with line 'd' and as total angle made by a line is always 180° Therefor another angle made by line 'b' with line 'd' will be 180° - 60° = 120° a shown in the attached figure.

By Comparing All the angles we can conclude that line a ∦ b, a ∦ c, b ∦ c.

∴ Line 'd' is parallel to line 'e'.  => d || e.  

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In the picture there is a parallel line with the intersection line. ∠5=91° and ∠2=(8x+1)°and x value is 11.

Given that,

In the picture there is a parallel line with the intersection line.

We have to find the x value.

Given ∠5=91° and ∠2=(8x+1)°

We know that if there are 2 parallel line and 1 line is intersecting to the parallel line then the corresponding angles are equal.

∠1=∠5

So, ∠1=91°

Now,

We can write as ∠1+∠2=180° because the ∠1 and ∠2 are on 1 line.

91+8x+1=180

8x+92=180

8x=180-92

8x=88

x=88/8

x=11

Therefore, x value is 11.

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Answer:

C. 1/36

Explanation:

The probability of rolling a 2 in a six-sided die is 1/6 because there are 6 possible outcomes and 1 of them is 2. In the same way, the probability of rolling a 6 is also 1/6 because there are 6 possible outcomes and 1 of them is 6.

Then, the probability of rolling a 2 and then a 6 can be calculated as:

Because they are independent events and each one has a probability of 1/6.

Therefore, the answer is:

C. 1/36

well, one uses 75% and that other uses 76%,  so hmmmm those values aren't equal however the statements are talking about the same type of group.

let's reword them

a)

75% of the HCLT will be paid by folks making < 120K

b)

HCLT is paid in 76% by folks making < 120k

a) we know that 75% of the HCLT is paid by those folks

b) we only know that many folks pay for the HCLT, but 76% of it is paid by folks making < 120k, namely 76% of the HCLT is paid by them.

pretty much the same group is referred on both statements.

∠1 and ∠8 are alternate exterior angle.

∠2 and ∠4 are corresponding angle.

∠3 and ∠6 are alternate interior angle.

∠6 and ∠7 are consecutive interior angle.

When a transversal intersects two or more lines, alternate exterior angles are produced. These angles are created on the various transversal sides' outer sides.Any two parallel lines that cross a transversal produce a few pairs of angles with the transversal. In the area inside the parallel lines, interior angles are generated, whilst alternate external angles are created in the area outside the parallel lines.

Corresponding angles are those that are created when two parallel lines are intersected by another line, whether it be a transversal or a matching corner (i.e. the transversal). Angle p and angle w, for instance, are the matching angles in the illustration below.

The pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles. All of these angles are equal. There is another way to look at this. The alternative interior angles can establish the parallelism or non-parallelism of the given lines. The supplied lines that are crossed by a transversal are said to be parallel if these angles are equal.

The pair of interior angles that are not contiguous to one another and are on the same side of the transversal are referred to as consecutive interior angles. Things that follow one another are referred described as being "consecutive." On a transversal's internal side, adjacent interior angles are found next to one another.

∠1 and ∠8 are alternate exterior angle.

∠2 and ∠4 are corresponding angle.

∠3 and ∠6 are alternate interior angle.

∠6 and ∠7 are consecutive interior angle.

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The ending balance Statement of Changes in Owner's Equity for this data is given by: $222,000.

The ending balance is given by the difference between all the amounts that were on the account, and were added, by all amounts that were removed from the account.

The amounts that were added to the balance are given as follows:

The amounts that were removed from the balance are given as follows:

Hence the ending balance is calculated as follows:

6,000 + 200,000 + 15,000 + 10,000 + 56,000 - 5,000 - 60,000 = $222,000.

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1. Length of rectangular area = 120 yards

Width of rectangular area = 120 yards

2. Maximum area = 14,400 square yards.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Total fencing Peter has = 480 yards

Now,

We can say that the total fencing he has in terms of length L and width W of the rectangle will be;

⇒ L + L + W + W = 480

⇒ 2(L+W) =480

Divide both sides by 2 to get

⇒ L+W = 240

Subtract W from both sides so we get L in terms of W;

⇒ L= 240 - W

Since, The area of a rectangle is Length times width.

So, Area = (L × W)

⇒ Area  = (240-W) W

⇒ Area  = 240W - W²

Now, By comparing the equation with an quadratic equation

ax² + bx + c , we get;

⇒ a = -1 and b = 240

Since, Area is maximum when;

W = -b/2a

W = - 240/-2

W = 120

So, for W = 120 yards area is maximum.

Hence, Length of yards = 240 - 120 = 120 yards.

(b) Maximum area of the rectangle can be found by substitute this

W = 120 in the Area equation;

So, the maximum area ,

A = 240 (120) - 120²

A = 28800 - 14400

A = 14400

Hence, Maximum area = 14,400 square yards.

Thus,

1. Length of rectangular area = 120 yards

Width of rectangular area = 120 yards

2. Maximum area = 14,400 square yards.

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The set of irrational numbers is the union of the set of rational numbers Q in the real numbers R. Therefore, the correct answer option is C. union.

An irrational number is a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11.

A rational number simply refers to a type of number which comprises fractions, integers, terminating or repeating decimals such as 4.

In Mathematics, the union of the set of all irrational numbers (Q') and the set of all rational numbers (Q) are generally referred to as a set of real numbers (R).

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Complete Question:

The set of irrational numbers is the ______ of the set of rational numbers Q in the real numbers R

Select one:

A. complement

B. ratio

C. union

D. Intersection

If the side length of the cube is x⁻² inches then the volume of the cube will be x⁻⁶ .

The volume of  the cube with side length "a" can be calculated using the formula

Volume = a³ ,

For Example : if the side length of the cube is 2m , then the volume of the cube will be

Volume = 2³  = 8m³ .

In the question ,

it is given that ,

the  side length of the cube is x⁻² inches ,

So, substituting the value of side length in the Volume formula , we get

volume = (x⁻²)³

= x⁻⁶         ....(as (xᵃ)ᵇ = (x)ᵃˣᵇ = xᵃᵇ )

Therefore , If the side length of the cube is x⁻² inches then the volume of the cube will be x⁻⁶ inches³ .

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Space available for the art show is 2/3 or 66.6%.

A number that represents a rational number is called a common fraction. Additionally, that same quantity can be expressed as a decimal, a percent, or a negative exponent.

The art room is divided into a total of three divisions, as can be seen from the information given. There is 2/3 of the total amount of space available for the art section because the artwork will only be presented on 2 of the 3 available parts. With 33.3% of the art room currently filled and unavailable, only 66.6% of the space is available for the art to be displayed on.

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The radius of the hole to the nearest hundredth of a foot will be 0.20 feet.

The problem we are dealing with here is related to volume, which is referred to as may be a degree of involved three-dimensional space. It is regularly measured numerically utilizing SI-inferred units (such as the cubic meter and liter) or by different majestic units (such as the quart, gallon, and cubic inch) and the volume formula we are referring to is of the cylinder which is,

Volume = πr²h

Where r is the radius of the cylinder, π is the constant which is equal to  3.14 and h is the height of the cylinder.

From the information given to us, the volume of the hole ( cylindrical in  this case ) is  3500 cubic feet and the height is   4.8 miles

So First we Converting  the 4.8 miles to feet,

Since we know 1 mile = 5280 feet

therefore, 4.8 miles = 4.7 × 5280 = 25344 feet

Now putting the desired in the formula,

=>3500 = 3.14 × r² × 25344

=> 79580.16r² = 3500

=>r² = 3500/79580.16

=>r²= 0.04398

=>r = √0.04398

     = 0.2097 feet

    = 0.20 feet

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In order to simplify the expression, start by solving the subtraction of fractions in the form

then,

Answer:

-868

Step-by-step explanation:

-Absolute change is simply defined as the number by which a change has occurred.

-We therefore determine the difference between the two years by subtracting the new value from the old or reference value

Answer: True

Step-by-step explanation: