Two dice are tossed. Let X be the absolute difference in the number of dots facing up. (a) Find and plot the PMF of X. (b) Find the probability that X lessthanorequalto 2. (c) Find E[X] and Var[X].

Answer:

a) The rotational speed of the clay: 3.45 rad/s.

b) The value of A in the equation of motion: 0.15 m.

c) The value of ϕi: 90° or π/2 rad.

Given that;

Revolution per minute( rpm) is = 33( 1/3) =  100/3

The frequency ( f) is= 100 / 3(60) = 0.55 Hz

a) Rotational speed W = 2πf

we substitute

W = 2π × 0.55

W = 3.45 rad/s

So, the rotational speed of the clay is  3.45 rad/s.

b) given equation; y(t)=Asin(ωt+ϕi)

given that radius = 0.15 m

y(t)=(0.2)sin(ωt+ϕi)

So, the value of A in the equation of motion is 0.15 m.

c) since y(t) has the maximum value at t =0

so at t=0

y(0) = (0.15)sin(ω(0)+ϕi)

= 0.15sin(ϕi)

this gives maximum value when ϕi = 90°

so,

y(0) = (0.15)sin(ω(0)+ϕi)

= 0.15sin(90°)

= 0.15

So, the value of ϕi is 90° or π/2 rad.

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The complete question is:

You are standing next to a table and looking down at a record player sitting on the table. Take the spindle (axis of rotation) to be the center of your coordinate system and the y-axis to be perpendicular to the side of the player you are standing next to. Long-playing records revolve 33(1/3) times per minute. You put a small blob of clay at the edge of a record that has a radius of 0.15 m, positioning the clay such that it is at its greatest value of y at t = 0.

Equation of motion for the y component of the clay's position: y(t)=Asin(ωt+ϕi)

Required:

a. What is the rotational speed of the clay?

b. Determine the value of A in the equation of motion.

c. Determine the value of ϕi in the equation of motion. Suppose that −π<ϕi≤π

The graph which represents the linear equation; y = (1/4)x + 1 as required in the task content is; the graph of a line passing through the points 0 comma 1 and negative 4 comma 0.

It follows from the task content that the graph which represents the given linear equation be determined.

Since the given linear equation is; y = (1/4)x + 1.

By comparison of the given equation to the slope-intercept form equation of a straight line, the y-intercept is; ( 0, 1).

Additionally, by checking (-4, 0); we have that;

0 = { (1/4) × -4 } + 1

0 = -1 + 1

0 = 0.

On this note, the graph which represents the linear equation is the; graph of a line passing through the ( 0, 1 ) and (-4, 0).

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The graph which represents the linear equation; y = (1/4)x + 1 as required in the task content is; the graph of a line passing through the points 0 comma 1 and negative 4 comma 0.

Which graph best represents the given linear equation?

It follows from the task content that the graph which represents the given linear equation be determined.

Since the given linear equation is; y = (1/4)x + 1.

By comparison of the given equation to the slope-intercept form equation of a straight line, the y-intercept is; ( 0, 1).

Additionally, by checking (-4, 0); we have that;

0 = { (1/4) × -4 } + 1

0 = -1 + 1

0 = 0.

On this note, the graph which represents the linear equation is the; graph of a line passing through the ( 0, 1 ) and (-4, 0).

84 math students are not from England

Given that

In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.

The term "percent" is derived from the Latin per centum, meaning "hundred" or "by the hundred". The sign for "percent" evolved by gradual contraction of the Italian term per cento, meaning "for a hundred". The "per" was often abbreviated as "p."—eventually disappeared entirely. The "cento" was contracted to two circles separated by a horizontal line, from which the modern "%" symbol is derived.

At a Cambridge College,65% of the math student are from England

If there are 240 math student

now we need to find how many are not from England

= (100 - 65)% = 35% percentage

= [tex]\frac{35}{100}[/tex] * 240

= 84

84 math students are not from England

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The equation of the line passing through the points P(2, -3) & Q(-5, -3) is y = -3

An equation is a expression that shows the relationship between numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

The equation of the line passing through P(2, -3) & Q(-5, -3) is:

y - (-3) = [(-3-(-3))/(-5-2)](x-2)

y + 3 = 0(x - 2)

y = -3

The equation of the line is y = -3

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The simplest way to solve the system of equations 7x + 5y = 19 and -7x - 2y = -16 would be using the method of c i.e Elimination.

Elimination, also known as the method of adding or subtracting equations. This method involves adding or subtracting the equations in such a way that one of the variables is eliminated, making it easier to solve for the other variable.

Here is one way to solve the system of equations 7x + 5y = 19 and -7x - 2y = -16 using the elimination method:

Add the two equations together:

(7x + 5y) + (-7x - 2y) = 19 + (-16)

This eliminates the x variable and gives you:

3y = 3

Divide both sides of the equation by 3 to get:

y = 1

Substitute this value of y back into one of the original equations (either 7x + 5y = 19 or -7x - 2y = -16) to find the value of x. For example, using the first equation:

7x + 5(1) = 19

7x + 5 = 19

7x = 14

x = 2

So the solution to the system of equations is x = 2 and y = 1.

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The  equation of the line is y =  x + 6.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

here, we have,

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4x + y = 7 ( subtract 4x from both sides )

y = - 4x + 7 ← in slope- intercept form

with slope m = - 4

given a line with slope m then the slope of a line perpendicular to it is

= 1/-m  =1/ 4  

then,

y =  x/4 + c ← is the partial equation of the perpendicular line

to find c substitute )- 4, 5 ) into the partial equation

5 = - 1 + c ⇒ c = 5 + 1 = 6

hence, y =  x/4 + 6 ← equation of perpendicular line.

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The formula to find the position of an image is x = (width of the canvas - width of the image)/2 and y = (height of the canvas - height of the image)/2.

1. First, calculate the width of the canvas by subtracting the x-coordinate of the right side of the canvas from the x-coordinate of the left side.

2. Then, calculate the height of the canvas by subtracting the y-coordinate of the top side of the canvas from the y-coordinate of the bottom side.

3. Next, calculate the width of the image by subtracting the x-coordinate of the right side of the image from the x-coordinate of the left side.

4. Then, calculate the height of the image by subtracting the y-coordinate of the top side of the image from the y-coordinate of the bottom side.

5. Finally, calculate the x-coordinate of the position of the image by dividing the width of the canvas by two and subtracting the width of the image from that result.

6. Calculate the y-coordinate of the position of the image by dividing the height of the canvas by two and subtracting the height of the image from that result.

Therefore, the formula for finding the position of an image is x = (width of the canvas - width of the image)/2 and y = (height of the canvas - height of the image)/2.

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Answer: Area: (100+75π/2)cm^2 Perimeter: (10+75π/2)cm

Step-by-step explanation:

Area of total shape

= square+3 semi-circles

=100cm^2 + 5*5πcm^2*3/2 = 100cm^2+75/2*πcm^2

= (100+75π/2)cm^2

Perimeter of shape

= 10cm + 25/2π*3cm

= (10+75π/2)cm

Step-by-step explanation:

in this figure you can observe 1 cube and 3 half cirles

the flield of the square would by using a formula a(lenght) * b(height)

in this case it would be 10m * 10m = 100m

and the formula for a cirle would be

A = pir^2

knowing that we can connect two of the halfs and make a cirle with a radius of 5

A= pi 5^2

A= pi 25

25pi approximatly equals to 78.53982m

knowing that information we can devide that value by 2 and get the value of the 3rd half cirlce

which is 39.26991m

than we add all the values we collected

39.26991m + 78.53982m + 100m = 217.80973 m

The two numbers are either 0 and 1 or 1 and 0. This is a method of solving a system of equations called substitution method

To solve this problem you can use a mathematical one, called a system of equations. A system of equations is a set of two or more equations that contain multiple variables. In this case, we have two equations with two variables, x and y.

We know that when you add the two numbers, the result is 1. We also know that when you multiply the two numbers, the result is 0.

Given these two equations:

x + y = 1 and x*y = 0

We know that one of the numbers is 0, because when we multiply any number by 0 the result is 0.

So x=0 or y=0

Now we can use the first equation, x + y = 1, and substitute in one of the values we know:

x = 0 and y = 1

or

y = 0 and x = 1

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Answer: We can start solving this problem by using the information given in the equation 6b + 2r = 60. This equation represents the total cost of the bread and rolls sold, with 6b representing the cost of the bread (6 dollars per loaf) and 2r representing the cost of the rolls (2 dollars each). The goal is to find the value of b, the number of loaves of bread sold.

We can use the information that the baker sold 24 rolls. If we substitute this value into the equation, we get:

6b + 2(24) = 60

Next, we can simplify the equation by substituting in the value of 24 for r:

6b + 48 = 60

Now we can subtract 48 from both sides of the equation to find the value of b:

6b = 12

Finally, we can divide both sides of the equation by 6 to find the value of b:

b = 12/6 = 2

So the graph suggests that the baker must sell approximately 2 loaves of bread if 24 rolls are sold.

We can check this by substituting this value in the equation to make sure that it works and total cost of the bread and rolls sold is $60

6(2) + 2(24) = 60, which is true

It is important to note that this is an approximation based on the information given, and it is possible that the baker may have sold a different number of loaves of bread while selling 24 rolls.

Step-by-step explanation:

Answer:

85

Step-by-step explanation:

First, take your 400 and minus the 60 on the floor.
Then take your 340 and divide it by 4.
Which then leads to your final answer of 85 per box.

Answer:

C) DF

Step-by-step explanation:

since the HF is the diameter of the top circle because the line is formed from the centre of the circle (c)

therefore,

the line made from the centre of (b), DF is the diameter

both DF and HF are congruent aswell as HD but thats not the option available in this question.

Sine function relates side lengths of a right triangle to an acute angle.

In a right triangle, the side lengths are related to the acute angles through the trigonometric functions. The side opposite the acute angle is related to the angle through the sine function, the side adjacent to the acute angle is related to the angle through the cosine function, and the hypotenuse is related to the angle through the tangent function.

More specifically, if θ is an acute angle in a right triangle and a and b are the lengths of the side opposite and adjacent to the angle respectively, and c is the length of the hypotenuse, we have:

sin(θ) = a/c

cos(θ) = b/c

tan(θ) = a/b

Thus, we can use these functions to find the length of any side of the right triangle if we know the measure of one of the acute angles and the length of one of the other sides.

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It is possible to construct a triangle whose sides are 4 cm, 7 cm and 8 cm because the sum of two sides are greater than third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 4 cm, 7 cm and 8 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.

To check this we firstly add the 4 and 7

4 + 7 > 8

11 > 8

Now we add 7 and 8

7 + 8 > 4

15 > 4

Now we add 4 and 8

4 + 8 > 7

12 > 7

It is possible to construct a triangle whose sides are 4 cm, 7 cm and 8 cm because the sum of two sides are greater than third sides.

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Answer: 2 17/77

Step-by-step explanation:

I assume that simplify means convert to a fraction because it is a fraction

Hope this helps !

The next four terms in the geometric sequence are 500, 100, 20 and 4

Sequence is a set or series of related items or events in a particular order. It can refer to a number of different things, such as a set of numbers, a set of events, or a set of objects. In mathematics, a sequence is a series of numbers or other mathematical objects that follow a particular pattern.

In the given problem, the sequence is;

312,500, 62,500, 12,500, 2,500

This is most likely a geometric sequence and we have to find the common ratio.

r = 62500 / 312500 = 0.2 or 2500 / 12500 = 0.2

The common ratio is 0.2

The next term will be the 5th term

Tₙ = arⁿ⁻¹

T₅ = ar⁴

a = first term = 312500

T₅ = 312500(0.2)⁴

T₅ = 500

The next term is 6th term

T₆ = ar⁵

T₆ = 312500(0.2)⁵

T₆ = 100

T₇ = ar⁶

T₇ = 312500(0.2)⁶

T₇ = 20

T₈ = 312500(0.2)⁷

T₈ = 4

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Considering the graph the scale factor of the dilation is calculated to be

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

In solving to get the scale factor of an image reference point is chosen and the proportion of the dimensions are taken

Let the reference point be TV and T'V'

TV = 6 units

T'V' = 2 units

scale factor = T'V' / TV

= 2 / 6

= 1 / 3

the scale factor is 1/3

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A statement which is true about the given ratios include the following: C. 12/14 > 22/28.

In order to determine the statement that is true, we would evaluate each of the given ratios as follows by converting the fractions into a decimal number as follows;

9/14 is greater than 5/7 i.e 9/14 > 5/7;

Dividing both denominators by 7, we have the following:

9/2 > 5/1 = 4.5 > 5 (False).

9/14 > 5/7 = 0.64 > 0.71 (False).

5/7 is greater than 22/28 i.e 5/7 > 22/28;

Dividing both denominators by 7, we have the following:

5/1 > 22/4 = 5 > 5.5 (False).

5/7 > 22/28 = 0.71 > 0.79 (False).

12/14 is greater than 22/28 i.e 12/14 > 22/28;

Dividing both denominators by 14, we have the following:

12/14 > 22/28 = 12 > 22/2

12 > 22/2 = 12 > 11 (True).

9/14 is greater than 12/14 i.e 9/14 > 12/14;

Dividing both denominators by 14, we have the following:

9/14 > 12/14 = 9 > 12

9 > 12 (False).

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Complete Question:

Which is a true statement about the given ratios?

9/14, 22/28, 5/7, 12,14

A. 9/14>5/7

B. 5/7>22/28

C. 12/14 > 22/28

D. 9/14>12/14

variable X represent the number of colors in T-shirt. The equation of the

Total cost = 75 ( $3+$50 X)

It is a mathematical statement that shows the equality between two or more expressions. There are various types of equation such as linear, polynomial, quadratic, exponential and so on. By using equation, the value of unknown variable is determined.

Here,

What will be the equation that representing the given relationship?

given, number of T-shirt = number of members = 75

charges of each T-shirt = $ 3

$50 fee for each color printed in the shirt.

let, X be the number of colors on the T-shirt.

The equation that represents the total cost of the order.

75($3 + $50 X) = total cost

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Answer:

The slope is -2/3 and the y-intercept is 5

The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure

Scale factors in geometry are defined as a conversion factor for distances in similar shapes, so the scale factor is the factor you would have to multiply all of the dimensions of one shape by in order for it to have the same dimensions as the other, so a scale factor of 4 means that if you multiplied all of the dimensions of one shape by 4, they would be the same dimensions as the dimensions of the other.

Alternatively, if this is not involving another shape, a scale factor of 4 is merely a factor for dilation, the transformation that makes a shape larger, therefore a scale factor of 4 would simply need you to multiply all of the original’s dimensions.

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The expression for the quarters you take is (1 - 0.50) x 28

The money you have left is $3.50.

The expression that is used to represent the total number of quarters is:

Total number of quarters = number of quarters you have x ( 1 + percent you find/100)

Total number of quarters = 20 x (1 + 40/100)

Total number of quarters = 20 x 1.40 = 28 quarters

Number of quarters you have left = (1 - percentage spent/100) x number of quarters

= (1 - 50%/100) x 28

(1 - 0.50) x 28

0.50 x 28 = 14 quarters

Value of 14 quarters in dollars = 14 x 0.25 = $3.50

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q = 84

q = 4 + 0.8p  (where "p" = 100)

q = 4 + 0.8 × 100

q = 4 + 80

q = 84

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q = 84 for the equation q = 4 + 0.8p to be true, when `p` is 100.

q=4+0.8p (given)

If 'p' is equal to 100

Putting p = 100 into the above equation,

q = 4 + 0.8p

q = 4 + 0.8 × 100

q = 4 + 80

q = 84

Hence, when 'p' is 100, q would be 84 to make the equation true.

Therefore , the solution of the given problem of coordinate plane is we can translate an image on a coordinate plane .

The term "coordinate plane" refers to a two-dimensional region that consists of two number lines. It emerges when the X-axis & Y-axis intersect at a location known as the origin. Using the numbers on a coordinate grid, one can locate points.

Here,

If we are aware of the direction and magnitude of the figure's movement, we may draw the translation in the coordinate plane.

Use P'(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up.

So, translating an image onto a coordinate plane is the answer to the provided coordinate plane problem.

Therefore , the solution of the given problem of coordinate plane is we can translate an image on a coordinate plane .

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The y + 9 is the variable expression represents the phrase below.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

y is the number of yellow cars.

And the expression,

"the sum of yellow cars and 9 red cars."

The expression,

= the number of yellow cars + the number of red cars

= y + 9

Therefore, y + 9 is the required expression.

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The missing number to be added to the polynomial is 16. 2x³ − 3x² − 8x + 16 leaves a remainder of 12 when divided by 2x.

The polynomial 2x³ − 3x² − 8x + ? leaves a remainder of 12 when divided by 2x. We can solve this by using the Remainder Theorem. The Remainder Theorem states that if a polynomial p(x) is divided by (x-a), the remainder is p(a).

We can use this theorem to solve the problem by setting x=2 and p(x)=2x³ − 3x² − 8x + ?. We can then solve for ? to find the missing number.

p(2) = 2(2³) − 3(2²) − 8(2) + ? = 16 - 12 - 16 + ? = ?

Therefore, the missing number to be added to the polynomial is 16. 2x³ − 3x² − 8x + 16 leaves a remainder of 12 when divided by 2x.

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Answer:

Yes, you are correct!

Step-by-step explanation:

When you see a number after the decimal is larger than 5 you will round up; when you see a number after the decimal is smaller than 5, you will round down.

In this case

3.045

The number after the decimal is 0, which is smaller than 5, so we round down and get the answer 3.

Answer:

Inverse most likely

Step-by-step explanation:

The numbers in a function table follow a pattern and have inputs and outputs. By constructing an equation using variables .

A collection of numbers, or "terms," is referred to as a sequence. Examples of terms include 2, 5, and 8. Some sequences can be made endlessly long by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the series. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it has pieces (also called elements or terms). the act of placing two or more items in a logical order. Chronological.

given

The numbers in a function table follow a pattern and have inputs and outputs.

By constructing an equation using variables, you may determine the rule. Make sure your rule is applicable to all possible combinations of inputs and outputs .

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Answer:

To find the length of the third side of a triangle for class 7, you can use the Pythagorean theorem. The Pythagorean theorem 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.

The theorem can be written as: c^2 = a^2 + b^2, where c is the hypotenuse and a,b are the other two sides.

So, if you know the lengths of the other two sides, you can use this theorem to find the length of the third side. For example, if you know the lengths of sides a and b, you can use the following formula to find the length of side c: c = √(a^2 + b^2)

You can also use the converse of the Pythagorean theorem, which states that if the square of the length of one side is equal to the sum of the squares of the other two sides, the triangle is a right triangle.

It is always a good idea to draw a diagram to help you understand the problem and to double check the answer.

Step-by-step explanation: