Answer: [tex]\frac{37}{1,101,716,330}\\\\[/tex]
This is the same as writing 37/1101716330
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Explanation:
Let's say the nine winning numbers are: 1,2,3,4,5,6,7,8,9
Let's further say that if we matched everything from 1 to 8, then we'll win second prize. That ninth value can be anything but 9. So we could have something like one of these examples
1,2,3,4,5,6,7,8,101,2,3,4,5,6,7,8,111,2,3,4,5,6,7,8,12As you can see, there are 46-9 = 37 different choices we can have for that last slot. In other words, there are 37 items in the set {10,11,12,...,45,46} we can pick for that last ninth slot. Note that 46-10+1 = 37. This value will form the numerator of the answer.
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Now to calculate how many ways there are to select the nine values regardless if we win or lose.
Since order doesn't matter, we use the nCr combination formula.
[tex]_{n} C _{r} = \frac{n!}{r!*(n-r)!}\\\\_{46} C _{9} = \frac{46!}{9!*(46-9)!}\\\\_{46} C _{9} = \frac{46!}{9!*37!}\\\\_{46} C _{9} = \frac{46*45*44*43*42*41*40*39*38*37!}{9!*37!}\\\\[/tex]
[tex]_{46} C _{9} = \frac{46*45*44*43*42*41*40*39*38}{9!} \ \text{ ... the ``37!'' terms cancel}\\\\_{46} C _{9} = \frac{46*45*44*43*42*41*40*39*38}{9*8*7*6*5*4*3*2*1}\\\\_{46} C _{9} = \frac{399,790,821,830,400}{362,880}\\\\_{46} C _{9} = 1,101,716,330\\\\[/tex]
There are slightly over 1 billion ways to select the nine values.
This large value is the denominator of our answer which is [tex]\frac{37}{1,101,716,330}\\\\[/tex]
The 37 up top represents the number of ways to win the second prize we're after, while the massive number in the denominator represents how many ways there are to play the game.
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Notice that in the jump from step 4 to step 5, shown in the section above, we had the "37!" terms cancel out. What this means is that the prime number 37 is nowhere to be found anywhere in the factorization of 1,101,716,330
Why is this important? Because it tells us that the fraction [tex]\frac{37}{1,101,716,330}\\\\[/tex] cannot be reduced.
Side note: That fraction converts to the decimal form 0.00000003358397 approximately and that converts to the percentage form 0.000003358397%; both of which are very very small numbers. We can see that the odds are definitely stacked against the player.
NO LINKS PLEASE HELP DUE IN 10MINS!While making oatmeal cookies, Angela needs to add cup of milk to her dough. However, she has only a -cup measuring cup. How many times does she need to fill the measuring cup to pour cup of milk?
The number of times Angela needs to fill the -cup measuring cup to pour cup of milk is
Answer:15
Step-by-step explanation:
Given N1 = 6 and Nn+1 = 6(Nn - 4) ). Find N3.
Answer:
48
Step-by-step explanation:
N₁ = 6
N(n+1) = 6*(Nn -4 )
N₍₁₊₁₎= 6* (N₁ - 4)
N₂ = 6 *(6-4) = 6*2
N₂ = 12
N₍₂₊₁₎ = 6*(N₂ - 4)
N₃ = 6*(12 -4) = 6* 8
N₃ = 48
If x is an integer in the first quadrant and sin(x)=3/4 find sin(2x), cos(2x), and tan(2x)
Answer:
[tex] \sin(x) = \frac{ 3}{4} \\ {sin}^{2}(x) + {cos}^{2}(x) = 1 \\ {cos}^{2}(x) + {( \frac{3}{4} )}^{2} = 1 \\ {cos}^{2}(x) = 1 - \frac{9}{16} = \frac{7}{16} \\ cos(x) = \frac{ \sqrt{7} }{4} \\or \\ {4}^{2} - {3}^{2} = {a}^{2} \rightarrow {a}^{2} = 16 - 9 = 7 \\ a = \sqrt{7} \\ cos(x) = \frac{ \sqrt{7}}{4} \\ \tan(x) = \frac{ \sin(x) }{ \cos(x) } = \frac{ \frac{3}{4} }{ \frac{ \sqrt{7} }{4} } = \frac{3}{ \sqrt{7} } \\ \sin(2x) = 2 \sin(x) \cos(x) \\ = 2( \frac{3}{4} . \frac{ \sqrt{7} }{4} ) \\ \sin(2x) = \frac{3 \sqrt{7} }{8} \\ \cos(2x) = { \cos(x) }^{2} - { \sin(x) }^{2} \\ = 1 - 2 { \sin(x) }^{2} \\ \tan(2x) = \frac{ \sin(2x) }{ \cos(2x) } [/tex]
Brainlist for you :)
Answer:BAHAHAHA THATS AWESOME
Step-by-step explanation:
)) Jerry took his extended family out for a dinner that cost $480. Jerry paid 5% sales tax
and left a 20% tip on $480. What was the total cost?
Answer:
$600
Step-by-step explanation:
Katy is older than Alex and Beth. Sarn is
younger than Alex and older than Beth.
Delores is older than Sam but younger than
Katy. Delores is Alex's older sister. If the
ages of these students are 14, 15, 16, 17,
and 18, who is 16 years old?
Can someone help me and explain me how you do this and not only give me the answer?
Answer:
just add the terms -154+8850= 8696 m
Identify the zero(s) of the graph below. A: x = 3 B: x = 1 C: x = {1, 3} D: x= {0, 3}
Answer:
Jan din Ako nahirapan sorry same lang tayo
Snoopy the dog is on a 25-ft long chain that is attached to the back of a barn (see the
picture below). If the chain does not allow him to go past either of the adjacent sides
of the barn, how much space does Snoopy have to roam?
Use pi = 3.14 and round your answer to the nearest tenth.
Answer:
A = 981.3 ft^2
Step-by-step explanation:
Here we're calculating the area of a semicircle of radius 25 ft.
The area of a circle is A = (pi)(r)^2, and that of a semicircle of the same radius is A = (1/2)(pi)(r)^2.
Here pi = 3.14 and r = 25 ft, and so the area/space in question is
A = (1/2)(3.14)(25)^2
A = 981.3 ft^2
The space does Snoopy have to roam is 490.625 square feet.
Given that, Snoopy the dog is on a 25-ft long chain that is attached to the back of a barn.
What is the area of a sector?The area of a sector is the space inside the section of the circle created by two radii and an arc. It is a fraction of the area of the entire circle.
The formula for the area of the sector of a circle is /360° (r²) where r is the radius of the circle and is the angle of the sector.
From the attached image, we see that snoopy is at the edge of a circle with the garage taking up a quarter of that circle.
Now, the area of space Snoopy was roaming
= 90°/360° × (3.14 × 25²)
= 1/4 × (3.14 × 625)
= 0.25 × 1,962.5
= 490.625 square feet
Therefore, the space does Snoopy have to roam is 490.625 square feet.
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Please help me understand
Answer:
C. $30Step-by-step explanation:
According to the first part of the equation, hourly pay is $25, up to 38 hours.
Overtime is paid over 38 hours.
Find the hourly pay for overtime, taking x = 39 and finding the difference with the total at x = 39 and x = 38, then we have the payment for one hour.
30(39 - 38) + 950 - 38*25 = 30 + 950 - 950 = 30Correct choice is C
histogram can be drawn for equal and unequal classes. True/False
Answer:
False
Step-by-step explanation:
Histogram cannot be drawn for equal and unequal classes. Therefore, the statement is false.
Histograms simply means a graphical representation that is used for organizing groups of data. It should be noted that Histogram cannot be drawn for equal and unequal classes. Therefore, the statement is false.Learn more about histograms on:
https://brainly.com/question/2962546
Triangle A, B, C, is shown. Angle C, A, B is 70 degrees. Angle A, B, C is 70 degrees.
Find the missing angle A C B
Answer:
40°
Step-by-step explanation:
<CAB=70°
<ABC=70°
<ACB+ <CAB+ <ABC=180(sum of angles in a triangle)
<ACB +70+70=180
<ACB+140=180
<ACB=180-140
<ACB=40°
100 POINTS!!! & Brainliest
A cat weighing 12.1lb needs insulin at 2.0 international units (IU)/kg. The insulin comes in a concentration of 10 IU/mL. How much insulin do you give the cat? Please show work!
Answer:
[tex]1 \: lb = 0.453 \: kg \: \\ first \: lb \: convert \: to \: kg \\ cat \: weight \: 12.1 \times 0.453 = 5.4813 \: kg \\ how \: much \: iu \: isulincat \: need \\ we \: must \: multiply\: the \: weight \: of \:cat \: to \: 2 \\ \\ 5.4813 \times 2 = 10.9626 \: iu[/tex]
good luck
Is y=-x^3+2x linear or non linear
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Answer:
non-linear
Step-by-step explanation:
The degree of this polynomial equation is the highest power of x: 3. When the degree is not 0 or 1, the relation is non-linear.
please someone solve this too <3
Answer:
<AED = 173 degrees
Step-by-step explanation:
<BEC = 180 - 73-79 = 28 degrees (interior angles of a triangle: 180 degrees)
<CED = 180 - 96 - 37 = 47
<AED = 360 - 28 - 47 - 112 = 173 degrees (circle: 360 degrees)
Is the number zero 0 an integer?
Yep! It is an integer!
Any negative, positive number or 0 is an integer.
Hope it helps!
0 is an integer
an integer is simply any number that does not have a decimal point and is not a fraction.
even of it has a negative sign or positive sign, it is still an integer
it can also be called a whole number
hope this helps,
thank you!!
Jayden needs at least 3 cups of vegetable oil to make chow menu. If Jayden has 20 fluid ounces of vegetable oil , and there are 8 fluid ounces in 1 cup will he be able to make chow mein . Yes or no
Answer: No
Step-by-step explanation:
He need 3 cups which is converted into 24 ounces. There is 8 ounces in a cup and he has three. He has 20 ounces and he needs 24.
You have three pieces of ribbon measuring 16 cm, 24 cm, and 40 cm respectively. You want to cut them into strips of the same length. What is the longest possible length of one strip?
Answer:8
Step-by-step explanation:
(16---->1,2,4,(8),16
24----->1,2,3,4,6,(8),12,24
40----->1,2,4,5,(8),10,20,40
Because 8 is the largest common divisor
In preparation for her math test on Thursday, Emerson studied 1/2 hour on Monday, 1 1/16 hours on Tuesday, and 3/8 hour on Wednesday. What is the total amount of time that Emerson spent studying for her test? (Simplify your answer and state it as a mixed number.)
Answer:
Step-by-step explanation:
1/2 + 1 1/16 + 3/8 = ?
Least common denominator is 16
8/16 + 17/16 + 6/16 = 31/16 = 1 15/16 hours
The path of a skateboarder can be modeled by the equation (x – 3)2 = –4(y – 9), where distance is in feet and air resistance is insignificant. If the skateboarder makes a jump from a ramp at x = 0, what is her maximum height and how far is she horizontally from the end of the ramp when she lands?
Answer:
The correct answer would be: "Maximum height 9 feet; horizontal distance 9 feet".
Step-by-step explanation:
I know this not only because I already took the test, BUT by graphing the equation (you can use graphing apps) it'll give you the answer.
Her maximum height is 9 feet & she is horizontally 9 feet from the end of the ramp when she lands.
What is skateboarders maximum height ?
The path of the skateboarder can be modelled by the equation,
(x-3)² = -4(y-9)
Now, from the equation, solving y,
(x-3)² = -4(y-9)
⇒ y-9 = -[tex]\frac{1}{4}[/tex](x-3)²
⇒ y = -[tex]\frac{1}{4}[/tex](x-3)² + 9
∴ Maximum height is 9 feet.
How far is she horizontally from end of ramp ?We have to take y = 0,
Now, -[tex]\frac{1}{4}[/tex](x-3)² + 9 = 0
⇒ -(x²-6x+9)+36 = 0
⇒ -x²+6x-9+36 = 0
⇒ x²-6x-27 = 0
⇒ x²-9x+3x-27 = 0
⇒ (x-9)(x+3) = 0
⇒ x = 9 or x = -3
Neglecting the negative value we get, x = 9
So, Her horizontal distance from end of the ramp is 9 feet.
Learn more about quadratic problems here :
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You want to buy a shirt that is $11.99 and the store is having a 25% off sale what do u pay for the shirt
It is 25% off so it is 75% of the price. 75/100*11.9 = 8.9925
It rounds to about $8.99
Help help help plz plz
Answer:
6^15
Step-by-step explanation:
please mark me as brainlest
I am thinking of two numbers.
Sum of these two numbers
is 58, and the difference of these two numbers are b.
What are the two numbers?
What is the answer to this problem?
Answer:
Step-by-step explanation:
Let one number=x
Therefore the othernumber=x+b
Since,
x+x+b=58
==>2x+b=58
==>2x=58-b
==>x=(58-b)/2
Therefore the other number is (58-b)/2 + b
Help me on this pls and thank you
Peter increased the amount of crunches he did from 32 to 36. By what percentage did Peter increase the amount of crunches he completed?
A 30%
B 12.5%
C 20%
D 22.5%
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Answer:
B 12.5%
Step-by-step explanation:
The percentage change is calculated as ...
% change = ((new value)/(old value) -1) × 100%
= (36/32 -1) × 100% = 1/8 × 100% = 12.5%
Peter increased his crunches by 12.5%.
can someone help me with this question polynomials:
please help me with this assignment
Answer:
ok but what does p =?
Step-by-step explanation:
Hi, really need help on this last question for the night, heeeeelp pls.
Answer:
Move it 2 places to the right.
Step-by-step explanation:
The magnitude of the exponent of 10 tell you how many places to move
The sign of the exponent of 10 tells you the direction.
Positive, decimal moves right.
Negative, decimal moves left.
Sketch the graphs. - 2x + 3y = -1
Answer:
Step-by-step explanation:
y =2/3x + 1/3
slope 2/3
y-intercept: (0 ,1/ 3)
Answer:
Step-by-step explanation:
- 2x + 3y = -1 is the equation of a line
Pick any values for x then find y or for y and then find x;
if you have two points you can draw a line trough those two points.
For example,
pick x= -1 then find y
- 2*(-1) + 3y = -1
2+ 3y = -1
3y = -1-2
y= -3/3
y= -1
First point has the coordinates (-1, -1)
pick y = 1 then find x
- 2x + 3*1 = -1
-2x +3 = -1
-2x = -1-3
-2x = -4
x= -4/-2
x= 2
Second point has the coordinate (2, 1)
Draw a line trough the points (-1, -1) and (2,1) to sketch the graph of -2x+3y = -1
Which other figure is a part of line CD?
Oliver drove the first 90 miles of his journey in 1.5 hours and the remaining 120 in 3 hours. What was the average speed on the second part of Oliver’s journey?
Answer:
Step-by-step explanation:
90 miles + 120 miles = 210 total miles
1.5 hours + 3 hours = 4.5 total hours.
Average speed = 210 miles / 4.5 hours = 46 2/3 miles per hour
Answer:
40
Step-by-step explanation:
I know meth