Since 1/49 can be expressed as 7^(-2), we have 7^x = 7^(-2), thus x = -2.

The percentage of people who like only sports is 80% - 30% = 50%.

Using inclusion-exclusion, the percentage liking at least one is 80% + 60% - 30% = 110%, which is capped at 100%.

Dividing both sides by 4 gives 2x ≡ 1 (mod 3). The solution is x = 2.

Substituting the values gives 2(2) + 3(3) = 4 + 9 = 13.

Calculating, a^b = 2^3 = 8 and b^a = 3^2 = 9, thus a^b + b^a = 8 + 9 = 17.

Substituting gives 2(2^2) + 3(3) = 8 + 9 = 17.

Calculating 3^2 = 9 and 2^3 = 8, thus 9 + 8 = 17.

The total number of games is calculated as 10 teams * 9 opponents * 2 games = 90.

The discount is 20% of $15, which is 0.2 × 15 = $3. Therefore, the sale price is $15 - $3 = $12.

Total balls = 3 + 2 = 5. Probability of selecting a red ball = Number of red balls / Total balls = 3/5.

The probability of selecting a non-defective item is 16/(4+16) = 16/20 = 4/5.

Speed = Distance/Time = 150 km / 3 h = 50 km/h.

Time for first part = 120/60 = 2 hours; Time for second part = 180/90 = 2 hours. Total time = 2 + 2 = 4 hours.

Speed = Distance / Time = 120 km / 2 hours = 60 km/h.

Speed = Distance / Time = 150 km / 2 hours = 75 km/h.

Average speed = Total distance / Total time = 150 km / 3 hours = 50 km/h.

The total time taken is 1.5 hours. Average speed = total distance / total time = 60 km / 1.5 h = 40 km/h.

After 1 year: $20,000 * 0.9 = $18,000; After 2 years: $18,000 * 0.9 = $16,200; After 3 years: $16,200 * 0.9 = $14,580.

Using the formula C = πd, we find d = C/π = 62.8/3.14 = 20 cm.

The length of an arc is given by L = (θ/360) * 2πr. Here, L = (90/360) * 2π(10) = 17.5 cm.

The area of a circle is calculated using A = πr². Thus, A = π(7)² = 49π ≈ 154 cm².

The equation of the circle is x² + y² = 25. The point (6, 0) gives 6² + 0² = 36, which is greater than 25, hence it lies outside.

Wednesday is the only day where a student cannot attend without missing a class.

The number of ways to choose 3 people from 5 is given by 5C3 = 10.

The number of ways to choose 3 members from 5 is given by 5C3 = 10.

Focusing on marketing at the expense of R&D can lead to neglecting innovation, which is a long-term risk, making option 2 the correct choice.

While the change may benefit some employees, it does not guarantee that all will find it advantageous.

Reallocating budget from R&D to marketing is likely to decrease innovation due to reduced funding for research, making option 1 correct.

While the new strategy may have contributed to the profit increase, it cannot be concluded that it is the sole reason without further evidence.