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kari74 [83]
3 years ago
11

In the california state lottery, you must select six numbers from fifty-two numbers to win the big prize. the numbers do not hav

e to be in a particular order. what is the probability that you will win the big prize if you buy one ticket?
Mathematics
1 answer:
Stolb23 [73]3 years ago
3 0

C(n,r) = [n!/((n-r)!*r!)]  
.  
n is the number of possibilities and it is 52 in question and r is the number of  
things to be taken at a time which is 6  
.  
if we substitiue  
.  
C(n,r) = [52!/((52-6)!*6!)= 52!/((46)!*6!)]  
.  
52! = 52*51*49*48*47*46*45*44*43*42*..... and 46! = 46*45*44*43*42*....  
.
  
you divide 52! by 46! the result after canceling all the   
common terms is just 52*51*50*49*48*47. The question is reduced to    
.  
C(n,r) = (52*51*50*49*48*47)/6!  
.  
and 6! = 6*5*4*3*2*1  
.  
If you want you can divide the numbers from 6! into the numbers in the numerator to simplify  
things a little or you can just take your calculator and multiply out the numerator and  
then divide that answer by 720 which is what 6! equals.  
.  
If you just multiply out the numerator your calculator should tell you that the answer is   
1.46581344*10^10 and when you divide that by 720 you get 20,358,520. This means that for  
every 20,358,520 lottery tickets sold there is likely to be 1 winner among them. Pretty slim  
odds of your ticket being that one.  
.  

If you have a cheap scientific calculator you might examine it carefully to see if it has  
a key function labeled nCr. If you do it will calculate this combination automatically.  
.  
Just enter 52, then press the nCr function, then enter 2, and press the equal sign.
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zmey [24]

Answer:

Part 1) The inequality that represent this situation is 5(x+7)^{2} \geq1,050  or  5x^{2}+70x+245 \geq1,050

Part 2) Yes, 8 inches is a reasonable width for his tablet

Step-by-step explanation:

Part 1)

Let

L -----> the length of the screen television

W ----> the width of the screen television

x ---->  the width of Andrew's tablet

we know that

L=5W ------> equation A

W=x+7 ----> equation B

The area of the television is

A=LW -----> equation C

Substitute equation A and equation B in equation C

A=5(x+7)(x+7)

A=5(x+7)^{2}

5(x+7)^{2} \geq1,050

5(x^{2}+14x+49) \geq1,050

5x^{2}+70x+245 \geq1,050 ------> inequality that represent this situation

Part 2) Determine if 8 inches is a reasonable width for his tablet

For x=8 in

Substitute in the inequality

5(8+7)^{2} \geq1,050

5(15)^{2} \geq1,050

1,125 \geq1,050 -----> is true

therefore

Yes, 8 inches is a reasonable width for his tablet

3 0
3 years ago
5. Michael is going to buy a new pair of shoes. The shoes cost $44.20. He has to pay 15% tax on the
solniwko [45]

Answer:

$50.83

Step-by-step explanation:

44.20 x .15 = 6.63

44.20 + 6.63= 50.83

8 0
3 years ago
Read 2 more answers
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