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one number is chosen from the first three prime numbers, and a second number is chosen from the first three positive composite numbers. what is the probability that their sum is greater than or equal to 9? express your answer as a common fraction

 

two numbers, x and y, each between 0 and 1, are multiplied. if the tenths digit of x is 1 and the tenghts digit of y is 2, what is the greatest possible value of the hundredths digit of the product?

 Sep 20, 2022
 #1
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one number is chosen from the first three prime numbers, and a second number is chosen from the first three positive composite numbers. what is the probability that their sum is greater than or equal to 9? express your answer as a common fraction  

 

The first three prime numbers are 2, 3, & 5 

The first three composite numbers are 4, 6, & 8  

 

Make a grid – the numbers inside are the sums     

 

            4     6      8  

     2     6     8     10 

     3     7     9     11 

     5     9    11    13 

 

As you can see, there are 9 totals and 6 of them are greater than or equal to 9. 

 

Therefore the probability is 6/9 which reduces to 2/3  

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 Sep 23, 2022
 #2
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two numbers, x and y, each between 0 and 1, are multiplied. if the tenths digit of x is 1 and the tenghts digit of y is 2, what is the greatest possible value of the hundredths digit of the product?  

 

Not sure I understand the question, but I'll try. 

 

x = 0.1 and then some more 

y = 0.2 and then some more 

 

Let's try some numbers and see if we can see a pattern. 

 

0.11 • 0.21 = 0.0231  hundredths is 2 

0.12 • 0.22 = 0.0264  hundredths is 2 

0.13 • 0.23 = 0.0299  hundredths is 2 

0.14 • 0.24 = 0.0336  hundredths is 3 

 

Let's skip ahead and see what happens. 

 

0.18 • 0.28 = 0.0502  hundredths is 5  

0.19 • 0.29 = 0.0551  hundredths is 5 

 

0.1999999999999 • 0.2999999999999 = 0.5999999999995

 

I don't think it's going to break over to 6 unless you round it to fewer significant digits. 

 

So I'm going out on a limb here and say the largest number that can be in the hundredths place is 5

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 Sep 23, 2022

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