Crml Stock Price Alert: You Wont Believe How Quickly Its Climbing!

Crml Stock Price Alert: You Wont Believe How Quickly Its Climbing!

**Crml Stock Price Alert: You Wont Believe How Quickly Its Climb

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Solution: Using the binomial formula:\binom{6}{2} (0.20)^2 (0.80)^4 = 15 \cdot 0.04 \cdot 0.4096 = 0.24576The probability is $\boxed{0.2458}$.Question: What is the remainder when the sum of the first 5 terms of the sequence $ a_n = 3n + 2 $ is divided by 7?Solution: The first 5 terms are $ a_1 = 5 $, $ a_2 = 8 $, $ a_3 = 11 $, $ a_4 = 14 $, and $ a_5 = 17 $. Their sum is $ 5 + 8 + 11 + 14 + 17 = 55 $. Dividing 55 by 7 gives a quotient of 7 and a remainder of $ 55 - 7 \times 7 = 55 - 49 = 6 $.Question: What is the least common multiple of the number of eggs laid by three different snake species, which are 12, 18, and 30?Solution: Factorize each number: $ 12 = 2^2 \times 3 $, $ 18 = 2 \times 3^2 $, and $ 30 = 2 \times 3 \times 5 $. The LCM is the product of the highest powers of all primes: $ 2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 180 $.\boxed{180}Question: What two-digit number is one more than a multiple of 9 and also one more than a multiple of 11?Solution: Let $ x \equiv 1 \pmod{9} $ and $ x \equiv 1 \pmod{11} $. This implies $ x \equiv 1 \pmod{99} $, since 9 and 11 are coprime. The two-digit numbers satisfying this are $ 99 + 1 = 100 $ (not two-digit) and $ 1 $. However, the next smaller solution is $ 1 $, which is not two-digit. Thus, no two-digit number satisfies both conditions.\boxed{1} (Note: The question may require reevaluation for valid constraints.)