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Home » f(x) = \frac1\frac14 \sin^2 2x + 1 = \frac4\sin^2 2x + 1 - go-checkin.com

f(x) = \frac1\frac14 \sin^2 2x + 1 = \frac4\sin^2 2x + 1 - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \( (70-74)^2 = 16 \)

📌 \( (82-74)^2 = 64 \)

📌 \( (76-74)^2 = 4 \)

📌 Sum of squared deviations: \( 36 + 0 + 16 + 64 + 4 = 120 \)

📌 Variance (sample): \( \frac{120}{5-1} = 30 \)

📌 Standard deviation: \( \sqrt{30} \approx 5.477 \) → rounds to 5.5

📌 A UX designer is optimizing a form that has 6 input fields. The average time users take to complete the form is 90 seconds, based on a sample of 200 users. If a new prototype reduces the time per field by 15%, and each field contributes equally, what is the new average completion time?

📌 Original average time per field: \( \frac{90}{6} = 15 \) seconds

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We now solve the system:
From (2): $ a = 70 - 4d $
Substitute into (1): $ 2(70 - 4d) + 3d = 60 $ → $ 140 - 8d + 3d = 60 $...
Then $ a = 70 - 4(16) = 70 - 64 = 6 $
So annual retreat sequence:
Year 1: 6
Year 2: 22
Year 3: 38
Year 4: 54
Year 5: 70

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