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#### 10 cm by 20 cmQuestion: A GIS analyst is mapping urban heat zones and records temperature data at 7 different locations, each labeled either H for high heat or L for low heat. How many such 7-character sequences contain at least one instance of two consecutive Hs?
$ a_n $: number of valid sequences of length $ n $ with no two consecutive Hs.
$ a_2 = 3 $: sequences are LL, LH, HL (excluding HH)
= $1,157.63 (rounded to two decimals)
#### 36Question: How many 6-digit binary numbers contain exactly one occurrence of two consecutive 1s?
#### Area of Circle: 50.24 square units
$ p = 2 $: $ 16 + 8 + 4 + 2 + 1 = 31
$ p = 3 $: $ 81 + 27 + 9 + 3 + 1 = 121
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