A certain lottery consists of selecting five different numbered balls from numbered 1 to 13 white balls and one from 1 to 12 gold Mega balls. A player wins the jackpot by matching all five numbers drawn from white balls (1 through 13) and matching the number on the gold Mega Ball (1 through 12). What is the probability of winning the jackpot?
Answers
The probability of winning the jackpot is 0.000065
The number of successful outcomes is 1 because there is only one winning combination.
The total number of possible outcomes can be calculated by multiplying the number of possibilities for each event:
Number of possibilities for selecting 5 white balls out of 13:
This can be calculated using the combination formula (nCr).
In this case, it is 13C5.
Number of possibilities for selecting 1 gold Mega Ball out of 12 is simply 12.
Therefore, the total number of possible outcomes is (13C5) × 12.
To calculate (13C5), we can use the combination formula: nCr = n! / (r! (n - r)!)
(13C5) = 13! / (5! × (13 - 5)!)
= 13! / (5! × 8!)
= (13 × 12 × 11 × 10 × 9) / (5 × 4 × 3 × 2 × 1)
= 1287
Now, we can calculate the total number of possible outcomes:
Total number of possible outcomes = (13C5) × 12
= 1287 × 12
= 15444
The probability of winning the jackpot by dividing the number of successful outcomes by the total number of possible outcomes:
Probability of winning the jackpot = 1 / 15444
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Related Questions
Suppose a system of 2 linear equations has one solution. What must be true about the graph of the 2 equations
Answers
Answer:
They are intersecting lines.
Step-by-step explanation:
Parallel lines do not intersect and have no common solution. The same line has infinite solutions with itself. Anything else must be intersecting lines.
Evaluate 8 ÷ -2 · 42 + 9. -100 -55 73 -23
Answers
Steps to solve:
8 / -2 * 42 + 9
~Divide
-4 * 42 + 9
~Multiply
-168 + 9
~Add
177
Best of Luck!
The simplified expression is equivalent to -159.
Given is an expression 8 ÷ -2 · 42 + 9, we need to simplify it,
To evaluate the expression 8 ÷ -2 · 42 + 9, we need to follow the order of operations, which is typically remembered using the acronym PEMDAS.
In this case, we should first perform the multiplication and division, and then the addition.
Starting with the multiplication and division:
8 ÷ -2 = -4
-4 · 42 = -168
Now we can add the result to 9:
-168 + 9 = -159
Therefore, the evaluation of 8 ÷ -2 · 42 + 9 is -159.
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What is the square root of -1
Answers
Answer:
The square root of ( -1 ) is i
Answer:
the square root of -1 is i
Have a nice day! :D
Step-by-step explanation:
select the spreadsheet formula that would correctly calculate the average (mean) of the following values: 25, 50, and 75.
Answers
The spreadsheet formula that would correctly calculate the average (mean) of the given values is: (25 + 50 + 75) / 3 = 50.
What is an average?An average is a single number taken as representative of a list of numbers, generally the sum of the numbers divided by how many numbers are in the list (the arithmetic mean).
What is the formula to calculate the average?The formula to calculate the average of given numbers is equal to the sum of all the values divided by the total number of values. Average = Sum of Values / Number of Values.
So, in this case:
Values: 25, 50, 75
Number of Values: 3
Thus, the average:
Sum of Values / Number of Values = (25 + 50 + 75) / 3 = 50
Hence, the spreadsheet formula that would correctly calculate the average (mean) of the given values is: (25 + 50 + 75) / 3 = 50.
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9. Use the graph of the function f(x) = x³ – 7x² + 10x to
x`
identify its relative maximum and minimum.
da
-4
8
8
2
K
T
2
da
y
8
+w
8
maximum = 4.1, minimum = -8.2
maximum = 0.9, minimum = 3.8
Answers
The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:
Relative maximum: (0.88, 4.061).Relative minimum: (3.786, -8.209).What are the relative minimums and the relative maximums of a function?The relative minimums of a function are given by the points in which the function's behavior changes from decreasing to increasing, that is, where the function curves down.The relative maximums of a function, meanwhile, are given by the points in which the function's behavior changes from increasing to decreasing, that is, where the function curves up.More can be learned about extremas of a function at https://brainly.com/question/9839310
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Six 2-foot tall pine tress were planted during the school's observation of Earth Awareness Week in 1990. The trees have grown at an average rate of 3/4 foot per year. What Linear equation in y=mx+b y=mx+b form gives the height of the tree in terms of number of years since they were planted?
Answers
Answer:
The linear equation that gives the height of the tree in terms of number of years since they were planted is y = 3/4x + 2 OR y = 0.75x + 2
Step-by-step explanation:
In the linear equation, y =mx + b
This is the equation of a straight line where m is the gradient and b is the intercept on the y-axis.
In the equation, y represents the height of the trees after x years.
m is the gradient, that is, the rate at which the trees are growing.
and b is the height at the time they were planted, that is, at time x = 0.
From the question,
Six 2-foot tall pine trees were planted during the school's observation of Earth Awareness Week in 1990, that is,
b = 2
Also, from the question,
The trees have grown at an average rate of 3/4 foot per year, that is,
m = 3/4
Hence, the equation becomes
y = 3/4x + 2 (\(y = \frac{3}{4}x + 2\))
OR
y = 0.75x + 2
Hence, the linear equation that gives the height of the tree in terms of number of years since they were planted is y = 3/4x + 2 OR y = 0.75x + 2.
Equation that represents the height of the tree in terms of number of years since they were planted
\(y=\frac{3}{4}x+2\)
Given :
Six 2-foot tall pine tress were planted.
The trees have grown at an average rate of 3/4 foot per year.
We need to frame linear equation that represents the height of the tree in terms of number of years.
Linear equation is y=mx+b
where b is the initial height of the tree
m is the rate of growth of the tree
y is the final height of the tree
and x represents the number of years
Initial height of the tree is 2 foot
rate of growth is 3/4 foot per year
x is the number of years
Replace all the values inside y=mx+b formula
\(y=\frac{3}{4}x+2\)
Equation that represents the height of the tree in terms of number of years since they were planted
\(y=\frac{3}{4}x+2\)
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Only help if you know please
Answers
The sum of slip is 9 small coffee order, then sum is 11 medium coffee order, and when the sum is 6 or 14 large coffee is ordered.
What is arrangement?Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.
A hat contains 4 slips of paper labeled as 3,3,6 and 8. One slip is selected randomly and without replacing, another one is selected. The number on the slips are added together.
The probability of getting a sum of 6 (3+3) is,
\(P_(3,3)=\dfrac{1}{4}\times\dfrac{1}{3}+\dfrac{1}{3}\times\dfrac{1}{4}\\P_(3,3)=\dfrac{1}{12}+\dfrac{1}{12}\\P_(3,3)=\dfrac{2}{12}\\P_(3,3)=\dfrac{1}{6}\)
The probability of getting the sum of 9 (6+3) or (3+6) is,
\(P_(3,6)=\dfrac{1}{4}\times\dfrac{2}{3}+\dfrac{2}{4}\times\dfrac{1}{3}\\P_(3,6)=\dfrac{2}{12}+\dfrac{2}{12}\\P_(3,6)=\dfrac{4}{12}\\P_(3,6)=\dfrac{1}{3}\)
The probability of getting the sum of 9 (6+3) or (3+6) is,
\(P_(3,8)=\dfrac{1}{4}\times\dfrac{2}{3}+\dfrac{2}{4}\times\dfrac{1}{3}\\P_(3,8)=\dfrac{2}{12}+\dfrac{2}{12}\\P_(3,8)=\dfrac{4}{12}\\P_(3,8)=\dfrac{1}{3}\)
The probability of getting a sum of 6 (3+3) is,
\(P_(6,8)=\dfrac{1}{4}\times\dfrac{1}{3}+\dfrac{1}{3}\times\dfrac{1}{4}\\P_(6,8)=\dfrac{1}{12}+\dfrac{1}{12}\\P_(6,8)=\dfrac{2}{12}\\P_(6,8)=\dfrac{1}{6}\)
There are three size of coffee to order:
Small sizeMedium sizeLarge SizeThus, when the sum of slip is 9 small coffee order, if sum is 11 medium coffee order, and when the sum is 6 or 14 large coffee is ordered.
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Helpppppppppppppppppppppppp
Answers
and its pretty easy tbh
Solving absolute inequalities
the meteorologist predicted that the temperature would be within 3 of 25F
solve the absolute value inequality. Write the solution using set-building notation.
Answers
Answer:
I'm not sure what you're getting at.
Step-by-step explanation:
Please explain further so I can give an answer.
suface area of cuboid 9 5 4
Answers
The cuboid in question has a surface area of 202 square units.
We must sum together the areas of all six faces to determine a cuboid's surface area.
The dimensions of the given cuboid are:
length (l) = 9 units
width (w) = 5 units
height (h) = 4 units
The area of each face is given by:
Top and bottom faces:\(lw = 9 * 5 = 45\) square units each
Front and back faces: \(lh = 9 *4 = 36\) square units each
Left and right faces: \(wh = 5 * 4 = 20\) square units each
Therefore, the total surface area of the cuboid is:
\(2(lw + lh + wh) = 2(45 + 36 + 20)\\ = 2(101) \\= 202 \ square \ units\)
Hence, the surface area of the given cuboid is 202 square units.
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The functions f and g are shown below.
50 POINTS TO HELP ME!!
Which of the following statements is true?
A.
Over the interval [0, 2], the average rate of change of f is the same as that of g. The y-intercept of f is greater than the y-intercept of g.
B.
Over the interval [0, 2], the average rate of change of f is greater than that of g. The y-intercept of f is the same as the y-intercept of g.
C.
Over the interval [0, 2], the average rate of change of f is the same as that of g. The y-intercept of f is less than the y-intercept of g.
D.
Over the interval [0, 2], the average rate of change of f is less than that of g. The y-intercept of f is the same as the y-intercept of g.
Answers
Answer:
A ................................
What is the standard form of the following equation?
y= -3x+2
3x+y=2
y-2=-3x
y-3x=2
3x-y=2
Answers
Answer:
(a) 3x +y = 2
Step-by-step explanation:
You want the equation y = -3x +2 written in standard form.
Standard formThe standard form of a linear equation is ...
ax +by = c
where a, b, c are mutually prime integers with a ≥ 0. If a=0, then b > 0.
To put the given equation into that form, we can add 3x to both sides:
3x +y = 3x -3x +2
3x +y = 2
the exact derivative of f(x)=x^3 at x=5
Answers
Answer:
\(75\)
Step-by-step explanation:
\(\frac{d}{dx}\left(x^3\right)\)
\(=3x^{3-1}\)
\(=3x^2\)
\(3\left(5\right)^2\)
\(=3\cdot \:25\)
\(=75\)
Solve the inequality below. Use the drop-down menus to describe the solution and its graph. 7 13 11 Click the arrows to choose an answer from each menu. The solution to the inequality is Choose.... Choose... A graph of the solution should have Choose.... and be shaded to the
Answers
Answer:
\(x \leq -4\)
There will be a filled-in hole at -4.
Step-by-step explanation:
We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)
\(-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4\)
The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.
For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.
In another example, \(x \leq -4\), -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.
A filled-in hole means the number is included in the inequality, while an empty one means it isn't.
In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.
a factory produce 1188440 bulbs in one year (365 days) how many bulbs did it produce in the month of August
Answers
BULBS PRODUCED PER DAY:-
\(\\ \sf\longmapsto \dfrac{1188440}{365}\)
\(\\ \sf\longmapsto 3256\)
Total days in August=31Total bulbs
\(\\ \sf\longmapsto 31(3256)\)
\(\\ \sf\longmapsto 100936\)
Sally bought 1.4 kilograms of bananas for AED 7.35 $ a kilo. How many kilograms
of apples sold at 10.20 $ per kilogram should you buy so that the kilogram of fruit
costs 8.15 $
Answers
You should buy approximately 1.067 kilograms of apples at $10.20 per kilogram in order to have the kilogram of fruit cost $8.15.
Let's assume that Sally bought x kilograms of apples at $10.20 per kilogram.
The total cost of bananas is given as AED 7.35 per kilogram, and Sally bought 1.4 kilograms of bananas. So, the cost of the bananas is:
Cost of bananas = AED 7.35 * 1.4 = AED 10.29
The total cost of apples is given by the equation:
Cost of apples = $10.20 * x
The total cost of the fruits combined should be AED 8.15 per kilogram. So, the equation becomes:
Total cost of fruits = (Cost of bananas + Cost of apples) / (1.4 + x) = AED 8.15
Substituting the known values, we have:
(10.29 + 10.20 * x) / (1.4 + x) = 8.15
Cross-multiplying and simplifying, we get:
10.29 + 10.20 * x = 8.15 * (1.4 + x)
Expanding the equation, we have:
10.29 + 10.20 * x = 11.41 + 8.15 * x
Rearranging the equation, we get:
10.20 * x - 8.15 * x = 11.41 - 10.29
1.05 * x = 1.12
Dividing both sides by 1.05, we find:
x = 1.12 / 1.05
x ≈ 1.067
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What is the slope of the graph shown below?
Answers
Answer:
Option 3: -2
Step-by-step explanation:
The slope of the graph is negative, and the only option with a negative term for the slope is -2.
So the slope of the graph is -2.
Create an expression that has the same value as (6x-4) + (x + 5).
Write the correct numbers from the list in the blank boxes. Each number
may be used once, more than once, or not at all.
Answers
Answer: 7x + 1
Step-by-step explanation:
(6x-4)+(x+5)
Step 1: Remove Parentheses:
6x-4+x+5
Step 2: Combine Like Terms:
7x +1
which choice correctly expresses the number below in scientific notation?
0.000611
Answers
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
6.11/104
Find the point on the y-axis that is 7 units from the point (−7, −5).
Answers
The point which is on the y-axis and is the y axis and is 7 units from the point (-7, -5) is;
What is the point on the y-axis that is 7 units from the point (−7, −5)?Since the point is on the y-axis, it follows that it's x-coordinate is zero and hence; the point is; (0, y).
The distance is therefore 7 units and hence;
7² = (-7-0)² + (y - (-5))²
49 -49 = (y +5)²
0 = y +5
y = -5
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Classify the following triangle as acute, obtuse, or right.
A. Obtuse
B. Acute
C. Right
D. None of these
Answers
Answer:
Acute Triangle.
Explanation:
The figure shows an equilateral triangle which has all the angles equal.
Acute Triangles are those who has angles less than 90°
Hence, an equilateral triangle is always an acute triangle.
Additional,
A right angle triangle has 90° angle.
An obtuse triangle has greater than 90° angle.
At Silver Gym, membership is $35 per month, and personal training sessions are $30 each. At Fit Factor,
membership is $85 per month, and personal training sessions are $20 each. In one month, how many
personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Sarah would have to buy
equal.
personal training sessions to make the total cost at the two gyms
Answers
Answer:
5 sessions each
Step-by-step explanation:
Let the personal training sessions be x.
Then at Silver Gym Sarah would spend:
35 + 30xAnd at Fit Factor she would spend:
85 + 20xSince total costs are same, the amounts will be equal:
35+30x = 85 + 20x30x - 20x = 85 - 3510 x = 50x= 50/10x= 5So Sarah would buy 5 training sessions for each of the gyms.
And she would spend $185 at each.
PLEASE HELP HELP
Referring to the Fig. in Question #31, the spinner is divided
into equal parts. What is the probability of
stopping on a multiple of 3?
Answers
Answer:75 ithink
Step-by-step explanation:
he roots of the function f(x) = x2 – 2x – 3 are shown. What is the missing number?
x = –1 and x =
Answers
Your school needs to set up chairs for the band concert. They can fit 17 rows with 36 chairs in each row. How many chairs will be needed for the concert?
Answers
Explanation multiply 17x36 giving you 612
Classify the following triangle as acute, obtuse, or right.
132⁰
36⁰
12⁰
O A. Acute
OB. Right
O C. Obtuse
OD. None of these
Answers
The given triangle is an obtuse triangle. Option C is correct.
What is angle measurement?An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry.
Angle less ess than 90-degree angles is considered acute. The right angle is 90 degrees. Angles that are obtuse are more than 90 degrees.
The acute, obtuse angles are 36⁰,132⁰ and none of the angles is the right angle.
The given triangle is an obtuse triangle.
Hence, option C is correct.
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Solve the system of equations
x+y=14
2x+2y=28
Answers
If you look at both equations of the system, you’ll notice that the second equation is just the doubles version of the first equation, showing that both lines have infinitely many solutions when on a graph.
Find equation of the line shown
Answers
The equation of the line is y = x + 6
How to detemrine the equatiin of the lineFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following highlights
The graph intersect the y-axis at y = 6
This means that the intercept c is 6
Also, as x changes by 1, the y values changes by 1
This mean sthat the slope is 1
So, we have
y = mx + c
This gives
y = x + 6
Hence, the equation is y = x + 6
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The linear equation on the graph can be written as:
y = (3/2)*x + 6
How to find the equation in the graph?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁), then the slope will be:
a = (y₂ - y₁)/(x₂ - x₁)
In this case we can see the points (0, 6) (so the y-intercept is b = 6) and (4, 10)
Then the slope will be:
a = (10 - 6)/(4 - 0) = 6/4 = 3/2
Then the linaer equation is:
y = (3/2)*x + 6
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is (3 + 5) + 4 = 3 + (5 + 4) a Multiplicative Identity
Answers
What is the y-coordinate of point T? Write a decimal coordinate.
Answers
Answer:
-4.5
Step-by-step explanation:
look at the y-axis and line it up with the point
Answer:
-4.5
Step-by-step explanation:
thick brain