Use the table below to calculate the expected value of a mega ball ticket. Remember, the expected value is the expected winnings/loses over many trials. Which means, your solution will be the expected outcome per ticket if you were to buy every possible combination of numbers (all 302,575,350 of them). After calculating the expected value of a ticket, use the information you have calculated to calculate how much the grand prize needs to be in order to break even (have an expected value of $0). When calculating this, don’t forget to deduct the cost of the ticket ($2.00) from any winnings.

Match 5 + Megaball (1/302575350) Prize 40000000
Match 5 (24/302575350) Prize 1000000
Match 4 + Megaball (325/302575350 Prize 10000
Match 4 (7800/302575350) Prize 500
Match 3 + Megaball (20800/302575350) Prize 200
Match 3 (499300/302575350) Prize 10
Match 2 + Megaball (436617/302575350) Prize 10
Match 1 + Megaball (3399723/302575350) Prize 4
Match 0 + Megaball (817712/302575350) Prize 2
Not a Winner (297842418/302575350) Prize 0

Step-by-step explanation:

The 3.5% saltwater means that for every 100 gallons of saltwater, there are 3.5 gallons of salt and 96.5 gallons of purified water. Therefore, to find the number of gallons of salt mix that Julian should add to 30 gallons of purified water, we can set up the following proportion:

3.5 gallons of salt / 100 gallons of saltwater = x gallons of salt / 30 gallons of purified water

Simplifying this proportion, we get:

x = (3.5 gallons / 100 gallons) * 30 gallons / 96.5 gallons

x = 0.01078 gallons of salt mix

To find the number of pints of aquarium salt mix that Julian should use, we can set up another proportion:

1 gallon of salt mix / 8 pints of salt mix = 0.01078 gallons of salt mix / y pints of salt mix

Simplifying this proportion, we get:

y = (0.01078 gallons of salt mix / 1 gallon of salt mix) * (8 pints of salt mix / 1 gallon of salt mix)

y = 0.0862 pints of aquarium salt mix

Rounding to the nearest tenth, Julian should use approximately 0.1 pints of aquarium salt mix for 30 gallons of purified water.

Graph A shows the image of the quadrilateral WXYZ after a reflection over the x-axis and a translation of 2 units.

Option A is the correct answer.

We have,

From the figure,

The coordinates of WXYZ.

W = (5, -3)

X = (-6, 3)

Y = (-3, 1)

Z = (-2, 3)

Now,

After the reflection over the x-axis.

W = (-3, 5) = (-3, 5)

X = (-6, 3) = (-6, -3)

Y = (-3, 1) = (-3, -1)

Z = (-2, 3) = (-2, -3)

Now,

Translation to the right of 2 units.

W = (-3, 5) = (-3, -5) = (-1, 3)

X = (-6, 3) = (-6, -3) = (-4, -3)

Y = (-3, 1) = (-3, -1) = (-1, -1)

Z = (-2, 3) = (-2, -3) = (0, -3)

Thus,

Graph A shows the image of the quadrilateral WXYZ after a reflection over the x-axis and a translation of 2 units.

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The total cost of the item, including the 7.25% sales tax, is $43.54

In Cambridge, Ohio (Guernsey County), the sales tax rate is 7.25%. If you have an item with a pre-tax price of $40.60, you will need to calculate the sales tax amount and the total cost.

First, let's find the sales tax amount. You can do this by multiplying the pre-tax price ($40.60) by the sales tax rate (7.25%).

$40.60 x 0.0725 = $2.9435

Now, round the sales tax amount to two decimal places: $2.94.

Next, add the sales tax amount to the pre-tax price to get the total cost of the item:

$40.60 + $2.94 = $43.54

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Answer:

To find the explicit equation for the nth term of an arithmetic sequence, we use the formula:

an = a1 + (n-1)d

where:

an represents the nth term of the sequence

a1 represents the first term of the sequence

d represents the common difference between consecutive terms in the sequence

In this case, we can see that the first term of the sequence is 7.2, and the common difference between consecutive terms is -3.4 (we subtract 3.4 from each term to get to the next term). Therefore, we have:

an = 7.2 + (n-1)(-3.4)

Simplifying this expression gives:

an = 7.2 - 3.4n + 3.4

which can be further simplified to:

an = 10.6 - 3.4n

So the explicit equation for the nth term of the arithmetic sequence 7.2, 3.8, 0.4, −3, −6.4, ... is an = 10.6 - 3.4n.

Step-by-step explanation:

The calculated value of the cost of the printer ink per ounce is $1.99

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

2300 ounces of printer ink costs $4,577

This means that

Ounces = 2300

Total costs = $4,577

using the above as a guide, we have the following:

Unit rate = Total costs / Ounces

substitute the known values in the above equation, so, we have the following representation

Unit rate = 4577 / 2300

Evaluate

Unit rate = 1.99

Hence, the printer ink costs $1.99 per ounce

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Answer:

So the equation of the line perpendicular to y=-x-7 and passing through (-2, -6) in point-slope form is y = x - 4.

Step-by-step explanation:

To find the equation of a line perpendicular to y=-x-7, we need to find its slope first, which is the coefficient of x, which is -1 in this case. The slope of a line perpendicular to this line will be the negative reciprocal of this slope, so the slope of our line will be 1.

To find the equation of the line in point-slope form, we can use the formula:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line. We are given the point (-2, -6), so we can substitute these values into the formula and get:

y - (-6) = 1(x - (-2))

Simplifying this equation gives:

y + 6 = x + 2

Subtracting 6 from both sides gives:

y = x - 4

So the equation of the line perpendicular to y=-x-7 and passing through (-2, -6) in point-slope form is y = x - 4.

The 30th percentile of the data is 9 and the 75th percentile is 21.

The given data is 1, 3, 5, 6, 9, 10, 11, 13, 14, 15, 16, 18, 18, 24, 27, 31 and 32.

Here, consider 1, 3, 5, 6, 9, 10, 11, 13, 14

30th percentiles is 9.

Consider 15, 16, 18, 18, 24, 27, 31, 32

75th percentiles = (18+24)/2

= 42/2

= 21

Therefore, the 30th percentile of the data is 9 and the 75th percentile is 21.

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As we have proved that points A, C and M lie on a straight line.

To begin with, let's recall what a regular polygon is. A regular polygon is a polygon with all sides of equal length and all angles of equal measure. In this case, we are given a 12-sided regular polygon. That means all the sides of this polygon are of equal length, and all the angles are of equal measure.

Now, let's look at point A. Point A is a vertex of the 12-sided polygon, which means it is one of the points where two sides of the polygon meet. Let's call the vertex adjacent to A as vertex B. Since the polygon is regular, the line segment AB is a side of the polygon, which means it is of equal length to all other sides of the polygon.

Since A and B are vertices of the polygon and AB is a side of the polygon, the line segment AB is a straight line. Since CM is of equal length to all sides of the square CDMN, it is also a straight line.

To show that AB and CM intersect at C, we just need to show that they are not parallel. If they are not parallel, they will intersect at some point, and that point will be C.

Now, let's consider the angle that CM makes with CD. Since CD is a straight line, the angle that CM makes with CD is just the difference between the angles that CM and CD make with AB. We know that the angle between AB and CD is x, and we know that the angle between CM and AB is 90 degrees (because CM is a straight line and AB is a side of the polygon). Therefore, the angle between CM and CD is (90 - x) degrees.

Since x is an angle in a regular 12-sided polygon, we can calculate its value using the formula (12 - 2) * 180 / 12, which simplifies to 150 degrees. Therefore, the angle between CM and CD is (90 - 150) degrees, which is -60 degrees.

Now, let's consider the angle that AB makes with CD. We already know that the angle between AB and CD is x. Since AB is a side of a regular 12-sided polygon, we can also calculate its interior angle using the same formula as before. Therefore, the interior angle of the 12-sided polygon is (12 - 2) * 180 / 12 = 150 degrees, and the angle between AB and CD is 150 degrees.

Therefore, AB and CM must intersect at some point, and that point must be C. This means that A, C, and M lie on the same straight line, which is what we needed to prove.

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Answer: 35

Step-by-step explanation:

The formula is there

a=(41+29)/2= 35

Answer:

the slope is 3,-6. this may not be correct wait for someone else whos really smart

The area of shaded region is = 35[tex]cm^2[/tex]

According to the shaded region:

We use the Area of rectangle.

And, we know that :

Area of rectangle = L × B

where, l is the length of the length and b is the breadth of the rectangle.

We have to find the area of shaded region.

Area of rectangle is = 10 × 5 = [tex]50cm^2[/tex]

Now, From the figure

We have to seen that, there is two triangles

Now, Find the area of the triangle

Area of two triangle = [tex]\frac{1}{2}[/tex] × 3 × 5 +  [tex]\frac{1}{2}[/tex] × 3 × 5 = [tex]15cm^2[/tex]

Hence, The area of shaded region is :

= 50 - 15

= 35[tex]cm^2[/tex]

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The given question is incomplete, so i take similar question.

To see the attachment.

Answer:

Slope: -3/2

Step-by-step explanation:

Use the formula for slope:

[tex]\frac{y_{2} - y_{1}}{x_{2}-x_{1}}\\\frac{-4 - 2}{0-(-2)}\\= \frac{-6}{4} = \frac{-3}{2}[/tex]

The expression that is shown on the number line is 5/6 - 1/6.

Expression is a combination of words and/or symbols that conveys a meaning or an idea. It can take many forms, including verbal, written, and nonverbal communication. Expressions can be used to describe emotions, thoughts, and feelings, and they can be used to explain why something happened or how something works. Expression is a powerful tool that allows people to communicate with each other, build relationships, and understand one another.

The expression that is shown on the number line is C: 5/6 - 1/6. To reach this answer, we must evaluate the points located on the number line. Starting from the left, the first point is 0, followed by -1/6, -2/6, -3/6, -4/6, -5/6, and -1. We can see that the difference between 5/6 and 1/6 is 4/6. Therefore, the expression that is shown on the number line is 5/6 - 1/6.

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A major problem in South Africa since the end of apartheid is B. The failure of government policies to address the race-based wealth gap.

Since the termination of apartheid in South Africa in 1994, the nation has endured numerous social and financial struggles throughout the consecutive decades.

Specifically, a major problem is the long-standing inequity and destitution that putatively affects black South Africans, plausibly due to the lingering impact of past apartheid initiatives. Despite attempts by the government to tackle these problems via Black Economic Empowerment (BEE) policies, the degree of headway achieved appears to be tardy and spotty.

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Both hoses together can fill the kiddie pool in ten minutes.

We'll use the number "t" minutes to represent the amount of time it takes to fill the backyard pool with water. Since it takes 30 minutes to fill the pool using only the backyard hose, we are certain that t = 30.

It takes half that amount of time—i.e., 30/2—to fill the pool with water from the hose in the front yard

Mary can fill the pool at once if she simultaneously utilizes both hoses. Call the period of time it takes for both hoses to simultaneously fill the pool "x" minutes.

With the assumption that the cumulative pace of both hoses filling the pool is the same, we can construct an equation as

1/x = 1/t + 1/15

Substituting in t = 30, we get:

1/x = 1/30 + 1/15

Simplifying this equation, we get:

1/x = 1/10

Multiplying both sides by 10x, we get:

x = 10

Therefore, the kiddie pool will be filled by both hoses simultaneously in ten minutes.

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1) 19.2% is the rate of return for each division.

2) The New South Wales divisional manager seems to be doing a better job.

1) How to compute the rate of return for each division?

To compute the rate of return for each division using the return on investment (ROI) formula stated in terms of margin and turnover, we can use the following formula:

ROI = Margin × Turnover

Where Margin = Net operating income / Sales and Turnover = Sales / Average operating assets.

a. Queensland division:

Margin = -$102,660 / $1,711,000 = -0.06

Turnover = $1,711,000 / -$590,000 = -2.90

ROI = -0.06 × (-2.90) = 0.174 or 17.4%

b. New South Wales division:

Margin = $113,280 / $2,832,000 = 0.04

Turnover = $2,832,000 / $590,000 = 4.80

ROI = 0.04 × 4.80 = 0.192 or 19.2%

2) The New South Wales divisional manager seems to be doing a better job based on given ROI as the ROI of the New South Wales division is higher than which of the Queensl and division.

The New South Wales division generated a 19.2% return on investment.

The Queensland division generated a 17.4% return on investment.

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Answer: C

Step-by-step explanation:

cos ∅ = adj/ hyp = XZ/ZY

the inverse cos is how you find angle

[tex]cos^{-1}\frac{XZ}{YZ}[/tex]  none of these are your choices so try sin

sin∅ = opp/hyp = xy/yz

[tex]sin^{-1}\frac{XY}{YZ}[/tex]

so answer is C

(b) The graph of g(x) is the graph of f(x) horizontally compressed by a factor of 4

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

f(x) = x²

g(x) = (4x)²

The graph of g(x) is the graph of f(x) horizontally compressed by a factor of 4.

To see this, we can rewrite g(x) as g(x) = 4²(x²) = 4²f(x).

This means that g(x) is equal to f(x) horizontally compressed by a factor of 4

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The Area of Patio is 65.12 ft².

We have,

Bases of Trapezoid = 12 feet and 8 feet

Height of Trapezoid= 4 feet

So, the Area of Trapezoid

= 1/2 (Sum of base) x height

= 1/2 (12+8 ) x 4

= 1/2 x 20 x 4

= 10x 4

= 40 square feet

Now, Radius of semi circle = 8/2 = 4 feet

So, Area of semicircle

=  (1/2)πr²

= 1/2 (3.14)(16)

= 25.12 square feet

Thus, Area of patio

= 40 +  25.12

= 65.12 ft²

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Answer:

1. He sold 5 erasers in January

2. He sold 130 erasers.

Step-by-step explanation:

1. ₹1 per eraser = ₹5 for 5 erasers

2. if you add opposites you get 0 So, ₹2 by selling one marker pen, loss of ₹1 per eraser. 65*2 is 130. So 130 erasers.

Answer:

17

Step-by-step explanation:

We can split the expression:

3² + 2³

into two terms:

3²   and   2³

We can evaluate each term individually, then add them at the end.

First, we can evaluate 3²:

3² = 3 × 3 = 9

Remember that an exponent specifies how many times a number should be multiplied by itself.

Next, we can evaluate 2³.

2³ = 2 × 2 × 2 = 8

Finally, we can add these two terms.

9 + 8 = 17

Answer:

Maria earned €600 each week, and she spent 1/4 of her money on food.

So, Maria spent:

(1/4) * €600 = €150 on food each week.

To find how much she earned in 4 weeks, we can simply multiply her weekly earnings by 4:

€600/week * 4 weeks = €2400

Therefore, Maria earned €2400 in 4 weeks.

Answer:

Step-by-step explanation:

8 possible books, you plan to take 7 with you on vacation. How many different collections of 7 books can you take

Answer:

Step-by-step explanation:

a.    30=>33

    increase

  subtract numbers/original

(33-30)/30=.1=10% increase

b.   33 => 30

  decrease

(33-30)/33=.91=9% decrease

c.  It has a difference of 1.  Even though the difference is the same the % increase and decrease is different because the amount you start out with is different.

Expression which represents the distance between point J and point K is d) |-10| + |5|.

The distance between two points is the length of the straight line segment that connects them in Euclidean space.

The distance formula between two points in a coordinate plane is given by:

d = [tex]\sqrt{(x_{2}- x_{1} )^{2} + (y_{2}-y_{1} )^{2} }[/tex]

where ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) are the coordinates of the two points.

Using this formula, the distance between point J(-10,-15) and point K(5,-15) is:

d = [tex]\sqrt{(5-(-10))^{2}+(-15-(15))^{2} }[/tex]

= [tex]\sqrt{(5+10)^{2}+0^{2} }[/tex]

= [tex]\sqrt{15^{2} }[/tex]

= 15

Therefore, the correct expression that represents the distance between point J and point K is:

d) |-10| + |5|

Correct Question :

Which expression represents the distance between point J and point K?​

a) |-10| - |5|

b) |5| + |-15|

c) |-15| - |-10|

d) |-10| + |5|

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If, the cylinder has a radius of x and a height of y. The cone has a radius of 13x. Then, the height of the cone in terms of y is h = (3/169)y.

The volume of a cylinder will be given by the formula V_cylinder = [tex]πr^{2h}[/tex], where r is the radius and h is the height. The volume of a cone is given by the formula V_cone = (1/3)[tex]πr^{2h}[/tex], where r is radius and h is height.

If the cylinder and cone have the same volume, then we can equate their volume formulas;

[tex]πX^{2y}[/tex] = (1/3)[tex](π13X)^{2h}[/tex]

Simplifying, we get;

[tex]πX^{2y}[/tex] = π169[tex]X^{2h/3}[/tex]

Dividing both sides by [tex]πX^{2}[/tex], we get;

y = 169h/3

Therefore, the height of the cone in terms of y is h = (3/169)y.

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Answer:

- 2/5 + 4/5 would give you 2/5

Step-by-step explanation:

think of it as (positive) + 4/5 (subtracted by) - 2/5 then you get 2/5!

An equation of the linear function represented by the table below in slope-intercept form is y = -x + 4.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 - 5)/(2 + 1)

Slope (m) = -3/3

Slope (m) = -1

At data point (2, 2) and a slope of -1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = -1(x - 2)  

y = -x + 2 + 2

y = -x + 4

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