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Home » Why Every Gamer is Screaming at $X—Switch 2 Price Is Insanely High! - Carbonext

Why Every Gamer is Screaming at $X—Switch 2 Price Is Insanely High! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question: A mechanical engineer tests 6 nanoscale sensors, each with 3 calibration settings. What is the probability that exactly 4 sensors are set to "precision mode" if each setting is chosen uniformly and independently?

📌 Solution: The total number of possible calibration configurations is $3^6$. To count favorable cases, choose 4 sensors to be in "precision mode" in $\binom{6}{4}$ ways, and the remaining 2 sensors can be in either of the other 2 settings, giving $2^2$ possibilities. The probability is $\frac{\binom{6}{4} \cdot 2^2}{3^6} = \frac{15 \cdot 4}{729} = \frac{60}{729} = \frac{20}{243}$. Thus, the final answer is $\boxed{\dfrac{20}{243}}$.Question: A tech startup founder wants to align two project timelines with cycles of 10 and 15 months. What is the least number of months after which both projects will synchronize?

📌 Solution: To find when both projects synchronize, compute the least common multiple (LCM) of 10 and 15. Factorize: $10 = 2 \times 5$ and $15 = 3 \times 5$. The LCM is $2 \times 3 \times 5 = 30$. Thus, the projects will align after $\boxed{30}$ months.

📌 Question: A palynologist observes two pollen dispersal patterns repeating every 9 and 12 days. What is the smallest day number when both patterns coincide?

📌 Solution: The smallest day both patterns coincide is the LCM of 9 and 12. Factorize: $9 = 3^2$ and $12 = 2^2 \times 3$. The LCM is $2^2 \times 3^2 = 36$. The patterns coincide on day $\boxed{36}$.

📌 Question: How many lattice points lie on the ellipse $x^2 + 4y^2 = 16$?

📌 Solution: Rewrite the equation as $\frac{x^2}{16} + \frac{y^2}{4} = 1$. Possible integer values for $y$ are $-2, -1, 0, 1, 2$. For each $y$, solve for $x$:

📌 $y = 0$: $x^2 = 16 \Rightarrow x = \pm4$ (2 points).

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