Prove that any number n of the form abcabc, where a, b, and c are decimal digits, is divisible by 7, 11 and 13.

We can factorize abcabc as

abcabc = abc000 + abc

abcabc = abc (1000 + 1)

abcabc = abc × 1001

abcabc = abc × 7 × 11 × 13

so naturally each of 7, 11, and 13 must divide abcabc.

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

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