9.166 Consider the set of bitstrings x ∈ {0, 1} n+k with n zeros and k ones with the additional condition that no ones are adjacent. (For n = 3 and k = 2, for example, the legal bitstrings are 00101, 01001, 01010, 10001, 10010, and 10100.) Prove by induction on n that the number of such bitstrings is n+1 k .

Step-by-step explanation:

find attached the prove  

a right triangle. and in the future use this desmos.com to you

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.