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Thus, $ 33 $ measurements are taken before exceeding.

This is an arithmetic sequence with first term $ a = 100,000 $, common difference $ d = 200,000 $, and last term $ l = 900,000 $.

How many positive 4-digit numbers are divisible by both 9 and 11?

A number divisible by both 9 and 11 is divisible by their least common multiple. Since 9 and 11 are coprime:

We need to count the number of 4-digit numbers divisible by 99.

The smallest 4-digit number is 1000, the largest is 9999.

Find the smallest 4-digit multiple of 99:

Number of terms: $ 101 - 11 + 1 = 91 $.

The average of $ 3v - 4 $, $ 5v + 7 $, and $ v + 10 $ is 24. What is the value of $ v $?

Solution: To compute the total profit after 3 years, we evaluate both profit functions at $ x = 3 $ and sum the results.

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