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Home » Point to project: \(\mathbfp = eginpmatrix 5 \ 4 \endpmatrix\) - DNSFLEX

Point to project: \(\mathbfp = eginpmatrix 5 \ 4 \endpmatrix\) - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Thus, the number of positive 4-digit numbers divisible by 11 is $ \boxed{819} $

📌 Question: What is the probability that a randomly selected positive integer less than or equal to 50 is a factor of 50?

📌 Solution: First, we determine all positive integers less than or equal to 50 that are factors of 50.

📌 The positive factors of 50 are: 1, 2, 5, 10, 25, 50. There are 6 such numbers.

📌 There are 50 possible integers to choose from (1 through 50).

📌 \frac{6}{50} = \frac{3}{25}

📌 Therefore, the probability is $ \boxed{\frac{3}{25}} $

📌 Question: Solve for $ x $ in the equation $ 4(x - 3) + 2 = 2(2x + 1) - 6 $

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rac{-3x + 11}{x - 2} < 0.
We analyze the sign of this rational expression by identifying the cri...
Numerator zero: $ -3x + 11 = 0 \Rightarrow x = rac{11}{3} $.
Denominator zero: $ x - 2 = 0 \Rightarrow x = 2 $.
These divide the real line into intervals:
We test the sign of $ rac{-3x + 11}{x - 2} $ in each interval:
For $ x < 2 $, say $ x = 0 $: numerator $ -3(0) + 11 = 11 > 0 $, denom...
For $ 2 < x < rac{11}{3} $, say $ x = 3 $: numerator $ -9 + 11 = 2 >...
For $ x > rac{11}{3} $, say $ x = 4 $: numerator $ -12 + 11 = -1 < 0...
We want where the expression is **less than 0**, so the solution is wh...

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