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?

Guest Sep 20, 2022

#1**0 **

*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**

_{.}

Guest Sep 23, 2022

#2**0 **

*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**.

_{.}

Guest Sep 23, 2022