for the sample space s of problem 3a (number of each ball), indicate the following events as subsets of s. a. obtaining the same number on both draws. b. obtaining a sum of numbers equal to seven. c. obtaining at least one three. d. obtaining exactly one red ball. e. obtaining same color on both draws.

The features of the circle in this problem are given as follows:

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The center for this circle has the coordinates given as follows:

(2,-1).

The radius is the distance of any point on the circumference of the circle from the center, hence, tracing a horizontal line at y = -1, we have that:

r = 7 - 2

r = 5.

Hence the equation is given as follows:

(x - 2)² + (y + 1)² = 25.

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   ( 0, 7 ) and ( 0,4 ) are  two points of the equation .

What Is an Equation, exactly?

An equation is a mathematical expression with two equal sides and an equal sign in between.

                                  An equation is, for instance, 4 + 6 = 10. 4 + 6 is visible on the equal sign's left side, and 4 + 6 is visible on the equal sign's right side.

    ( 4,0) & ( 0,7 )

Given constraint  is

        7x₁ + 4x₂ ≤ 28

  IF  x₁ = 0

         4x₂  =  28  

          x₂ = 7

        ( 0, 7 )

If x₂  = 0

    7x₁ = = 28

     x₁  = 4

       ( 4 ,0 )

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The volume of the round metal washer is  94.25 cm cube.

As inferred from the question, the shape of the round metal washer is that of a hollow cylinder with:

outer radius=  8 cm

inner radius =2 cm

thickness = 0.5 cm

we know that the formula for calculating the volume of a hollow  cylinder is as follows:

V = π ( [tex]R^{2}[/tex]-[tex]r^{2}[/tex])h cubic units

[ where R = outer radius, r= inner radius]

Putting the values in the above formula gives:

V=  π ( 8 - 2) X 0.5

-> V=  π (64-4) X 0.5 = 94.25 cm cube

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Answer:

II and III only

Step-by-step explanation:

The required equation of the line is y = 5x + 3.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

From the given table we have slope(m) = (3 + 2)/(0 + 1) = 5/1 = 5.

Now, - 2 = 5(-1) + b.

- 2 = - 5 + b.

b = 3.

Therefore, y = 5x + 3 is the required equation of the line.

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Answer:

16 19/50

Step-by-step explanation:

first make improper fractions of both 3 9/10 and 4 1/5

mutltiply the denomiator (the number on the bottom) by the whole number, add the numerator (the number on the top) and put that number over the denomiator. 3 9/10 = 39/10 and 4 1/5 = 21/5. Multiply the improper fractions. numerator x numerator and write that on the top with a line under it. Multiply the denomiators and write that on the bottom. 39*21= 819. 10*5=50. your number would be 819/50. Then divide 819 by 50. You get 16 19/50

Answer: function A is linear

Step-by-step explanation:

The central angle corresponds to an arc length of 2 yd and a radius of 7 yd is 0.09 pi

Central angle is the angle subtended by an arc of a circle at the center of a circle. The radius vectors form the arms of the central angle. In other words, it is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle. When these two points are joined they form an arc. Central angle is the angle subtended by this arc at the center of the circle

The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. A circle can be divided into sectors by using the central angle. An excellent illustration of a central angle is a pizza slice. A pie chart is made up of several sectors and is useful for representing various amounts.

Central angle =(s*360)/(2pir)

=we have s=2 yd

radius = 7 yd

angle = 16.5 degree = 0.09 pi

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Answer:

yes

Step-by-step explanation:

because everytime you add 2 for x you add 1.8 for y

that means the difference is constant and the function is linear

Answer:

I Don.t really know the answer

The correct justification of the equation from 2(y - 5) + 4 = 4 to 2y - 10 + 4 = 4 using distributive property of addition.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

2(y - 5) + 4 = 4

Apply distributive property of addition. Then the equation is written as,

2(y - 5) + 4 = 4

2y - 10 + 4 = 4

Simplify the equation further, then we have

2y - 10 + 4 = 4

2y - 6 = 4

2y = 10

y = 5

The correct justification of the equation from 2(y - 5) + 4 = 4 to 2y - 10 + 4 = 4 using distributive property of addition.

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Answer:

The amount budgeted for Auto expenses is $100,000 * 14% = $14,000.

Step-by-step explanation:

Answer:

To write equivalent fractions with a common denominator, we need to find the least common multiple (LCM) of the denominators of the fractions and then write each fraction with the LCM as the denominator. Here's a step by step guide:

1. To find the LCM of 3 and 6, we list the multiples of each number and find the smallest one that is common to both:

Multiples of 3: 3, 6, 9, 12, 15, 18, ...

Multiples of 6: 6, 12, 18, 24, 30, 36, ...

The LCM of 3 and 6 is 6, so we write 2/3 and 3/6 with 6 as the denominator:

2/3 = 4/6 and 3/6 = 1/2

2. To find the LCM of 4 and 12, we list the multiples of each number and find the smallest one that is common to both:

Multiples of 4: 4, 8, 12, 16, 20, 24, ...

Multiples of 12: 12, 24, 36, 48, 60, 72, ...

The LCM of 4 and 12 is 12, so we write 3/4 and 5/12 with 12 as the denominator:

3/4 = 9/12 and 5/12 = 5/12

3. To find the LCM of 5 and 10, we list the multiples of each number and find the smallest one that is common to both:

Multiples of 5: 5, 10, 15, 20, 25, 30, ...

Multiples of 10: 10, 20, 30, 40, 50, 60, ...

The LCM of 5 and 10 is 10, so we write 3/5 and 7/10 with 10 as the denominator:

3/5 = 6/10 and 7/10 = 7/10

You can use this process to find the LCM and write equivalent fractions with a common denominator for the rest of the problems.

The point that creates a right triangle with the points (3, 6) and (8, -2), which Christopher could place on the graph to create a right triangle is the point (8, 7.25)

A right triangle is a triangle with one ninety degrees (90°) interior angle.

The points on the right triangle Christopher already graphed (3, 6), and (8, -2)

The property of a right triangle is one of the interior angles is 90°, therefore, the legs or two of the sides of a right triangle are perpendicular.

The slope of the line joining the specified two points is found as follows;

Slope = (-2 - 6)/(8 - 3) = -8/5

The slope of the line perpendicular to the line segment Christopher used to join the points (3, 6), and (8, -6) is 5/8

The equation of the perpendicular line is therefore;

y - 6 = (5/8)·(x - 6)

y = (5/8)·(x - 6) + 6 = 5·x/8 + 18/8

y = 5·x/8 + 18/8

When x = 8, we get; y = 5 × 8/8 + 18/8 = 7.25

Therefore, the point (8, 7.25), forms a right triangle with the points (3, 6) and (8, -2)

A point Christopher can place on the graph to create a right triangle is (8, 7.25)

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Answer:

Below

Step-by-step explanation:

y = 1/2 x + 1

y = 3/2x + 4        Use first equation to sub in for y

1/2 x + 1  = 3/2 x + 4

-3 = x       then use this value in one of the equations to calc  y

y = 1/2 x + 1

y = 1/2 (-3) + 1 =  - 1/2

The correct answer is option (C). The answer is round function.

Given that,

Instead of just altering what is presented, Excel changes the amount of decimal places it really keeps.

To find : Something alters the real number of decimal places?

Number is rounded using ROUND function to a given number of digits. You can use the following formula, for instance, to round the value 23.7825 in cell A1 to two decimal places: =ROUND(A1,2) (A1,2) is 23.78 is the output of the function

Therefore, option is the right response (C). Round function is the solution.

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A regular hexagon can be divided into six equilateral triangles by drawing lines from the center of the hexagon to each of its vertices.

Each of these equilateral triangles has an area that is one-sixth of the total area of the regular hexagon.

When the midpoints of the sides of the regular hexagon are joined to form a smaller regular hexagon, it can be seen that the smaller hexagon is made up of six equilateral triangles, each of which has half the area of the equilateral triangles in the larger hexagon. This is because the sides of the smaller hexagon are half the length of the sides of the larger hexagon.

Therefore, the fraction of the area of the larger hexagon that is enclosed by the smaller hexagon is:

[tex]6 * (1/2)^2 = 6 * 1/4 = 3/2[/tex]

This means that the smaller hexagon encloses 3/2 of the area of the larger hexagon.

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Line segment is a a measurable part of a line that consists of two points, called endpoints.

a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Given that measurable part of a line that consists of two points, called endpoints is a line segment.

A line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints.

Hence, line segment is a a measurable part of a line that consists of two points, called endpoints.

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Assume a stick of length 1 is randomly broken into two portions. The smaller piece's estimated length is 0.25.

The random variable L (the length for the shorter stick) has a uniform distribution.

Thus the probability density function for L is as follows:

This means 2 for all length in the range 0 - 0.5

Now, we calculate the expected value for random variable L as seen on the attachment. Based on the calculation, 0.25 is the smaller piece's estimated length for the randomly broken stick.

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The first four terms are 35, 50, 65, 80.

And the recursive formula:

aₙ = aₙ₋₁ + 15

A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

The sequence defined by the explicit formula g(n)=15n + 35

The first term,

g(0) = 0 + 35 = 35.

g(1) = 15 + 35 = 50

g(2) = 30 + 35 = 65

g(3) = 45 + 35 = 80.

The common difference is 15.

The recursive formula:

aₙ = aₙ₋₁ + 15

Therefore, the formula is aₙ = aₙ₋₁ + 15.

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The student's answer is incorrect; they should have distributed the negative sign to the terms in the second parentheses, then combine like terms: 6b 4r - 2b r = 4b + 3r.

The student's answer is incorrect; they should have distributed the negative sign to the terms in the second parentheses. To correctly simplify the expression, first distribute the negative sign, then combine like terms. Start by distributing the negative sign: 6b 4r - 2b r = 6b 4r + (-2b) (-r). Then, combine like terms: 6b 4r + (-2b) (-r) = 6b + (-2b) + 4r + (-r) = 4b + 3r. This is the correct answer.  It is important to note that when subtracting within parentheses, you must distribute the negative sign to each term. Once the negative sign has been distributed, you can then combine like terms. This method can be used to simplify any expression with parentheses and subtractions.

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Answer:

#9       (x, y) = (6, 32)

#10      The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same and is $32

Step-by-step explanation:

The legend is missing so by looking at the graph alone we are unable to determine which color line corresponds to which kind of kite(Kites-R-Fun or Windy Kites)

However the associated table will help us determine this

The linear equation for a line is expressed as

y = mx + c

where m = slope of the line and b = y-intercept which is the y-value for the point where the line crosses the y-axis(at x = 0)

Slope m = rise/run = Δy/Δx = (y2 - y1)/(x2 - x1) for any two points (x1, y1) and (x2, y2) on the line

Let's take the two  x values as x1=0 and x2=1 and use the table

For Kites-R Fun
x1 = 0 ==> y1 = 8. This is also the y-intercept, b
We see that the red line corresponds to x = 0, y = 8

x2 = 1 ==> y2 = 12

y2 - y1 = rise = Δy =12 - 8 = 4

x2 -   x1 = Δx = 1 - 0 =1

Slope m = 4/1 = 4

Equation of Kites-R Fun is 4x + 8

For Windy Kites

x1 = 0 ==> y1 = 20
y-intercept = 20 or b = 20

x2 = 1 ==> y2 = 22

Rise = Δy =22 - 20 = 2
Run = Δx = 1 - 0 = 1
Slope = m, b = 20

Equation of blue line is
y = 2x + 20

The two equations are:
y = 4x + 8
y = 2x + 20

Equating right sides:
4x + 8 = 2x + 20

Move 2x to the left side and 8 to the right side:

4x + 2x + 8 - 8 = 2x - 2x + 20 -8

2x = 12

x = 6

For x = 6 the costs are the same

Plugging x = 6into equation y = 4x + 8:
y = 4(6) + 8 = 24 + 8 = 32

So the solution set is
(6, 32)

Looking at the graph we see the two lines intersect at this point
(Heck, we could have avoided all this work and just looked at the graph but I don't expect that was what they intended. You can add this as a side note)

On the second part

For Kites-R-US, each kite costs $4
The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same.

The solution is,  Rectangle A has the largest area.

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

from the given figure we get,

Each square is 1 square unit.

now, Rectangle A has 18 square

Rectangle C has 10 squares

Rectangle B has 8 squares

So, area of Rectangle A is 18 sq. unit

Rectangle C is 10 sq. unit

Rectangle B is 8 sq. unit

i.e. 18>10>8

Hence, Rectangle A has the largest area.

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If Logan has given out a total of 6.65 in nickels and dimes , then the number of dimes he has given out is  38 .

Let the number of nickels that Logan gave out be = n , and

the number of dimes that Logan gave out be =  d ;

From the information , we know that Logan gave out 50% more nickels than dimes,

that means ; n = d + 0.5d = 1.5d   ...equation(1) ;

We also know that the total amount given out in nickels and dimes is $6.65, and each nickel is worth of  $0.05 and each dime is worth of  $0.10,

So ,  n×0.05 + d×0.10 = 6.65 ;

Substituting the expression for n from the first equation into the second:

⇒ (1.5d)×0.05 + d×0.10 = 6.65 ;

Expanding and solving for d ;

we get ;

⇒ 0.075d + 0.10d = 6.65 ;

⇒ 0.175d = 6.65 ;

⇒ d = 6.65/0.175 = 38 ;

Therefore ,  Logan gave out 38 dimes.

The given question is incomplete , the complete question is

Logan works as a cashier. Today, he has given out 50% more nickels than dimes. if he has given out a total of 6.65 in nickels and dimes, How many dimes has he given out ?

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The volume of the solid is approximately 807.08 cubic units.

To determine the volume of the solid, we can use the method of cylindrical shells.

Imagine taking a slice of the solid parallel to the base, with the cross-sectional area being a square of side length x (where x is a function of the height). The volume of this slice is the product of the square area and the height. The height of the slice is equal to the difference in the radii of two consecutive circular cross sections.

The radius of the larger circular cross-section can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the radius) is equal to the sum of the squares of the other two sides (the height and half the side length of the square). Thus, we have:

r² = x² + (15-x)²

Solving for x, we get:

x = 15 * √(1 - (r/15)²)

The volume of the slice is then given by:

V = x² * (15 - x)

To find the total volume of the solid, we integrate this expression with respect to r from 0 to 15. The result is approximately 807.08 cubic units.

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The statistical procedure that researchers use to identify underlying components that may exist in test without first proposing a formal model is exploratory factor analysis.

In order to carry out a statistical analysis, we need to collect and review a sample of the data available in the research results for analysis.

While there is no single way to perform interpretive analysis, there are practices that can be replicated in any research if done in a way that is appropriate to the information provided.

These tips will allow us to carry out useful statistical analysis.

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Answer:

3rd quadrant

since the x and the y co-ordinates are negative ,it can only fit in the third since

1st=positive, positive

2nd=negative, positive

3rd=negative, negative

4th=positve, negative

A rectangular board is 1300 millimeters long and 800 millimeters wide. Then, the area of the board in square meters is 104 m².

These are the specified parameters:

Length of the board (l) = 1300 mm

Breadth of the board (b) = 800 mm

The area of a rectangular board

A = l × b

  = 1300 mm × 800 mm

  = 1040000 mm²

The area of the board in square meters

To convert mm² to m², divide mm² by 10000.

Therefore

A = 1040000 mm²

  = 1040000 : 10000 m²

  = 104 m²

So, the area of the board in square meters is 104 m².

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Sigma notation for the sum is  ∑5ⁿ⁻⁴ (where n = 1 to 5)

Sigma notation is the most easiest way of writing a very large sum of elements of a sequence in a simple manner.

∑ is the symbol that is pronounced as "sigma".

"i" or "n" is called the index of summation

Given sum,

1/125 + 1/25 + 1/5 + 1 + 5

First term a is 1/125

Common ratio r = 1/25/1/125 = 5

Sequence can be written as

aⁿ = a.rⁿ⁻¹

aⁿ = 1/125 . 5ⁿ⁻¹

aⁿ = 5⁻³. 5ⁿ⁻¹

aⁿ = 5ⁿ⁻⁴

Sigma notation can be written as

∑5ⁿ⁻⁴ where n = 1 to 5.

Hence, Sum expressed as Sigma notation ∑5ⁿ⁻⁴ (where n = 1 to 5).

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