Explanation:Let's find prime numbers between 51 and 90 (excluding 51 and 90 if not prime, but “between” often means exclusive of endpoints unless stated).
Step 1: List numbers between 51 and 90:
52 to 89.
Step 2: Identify primes in that range:
– Check each odd number (even numbers except 2 are not prime):
53 (prime)
55 (divisible by 5, no)
57 (divisible by 3, 5+7=12 divisible by 3, no)
59 (prime)
61 (prime)
63 (divisible by 3, no)
65 (divisible by 5, no)
67 (prime)
69 (divisible by 3, no)
71 (prime)
73 (prime)
75 (divisible by 5, no)
77 (divisible by 7, no)
79 (prime)
81 (divisible by 3, no)
83 (prime)
85 (divisible by 5, no)
87 (divisible by 3, no)
89 (prime)
Step 3: List primes:
53, 59, 61, 67, 71, 73, 79, 83, 89.
Count them: 9 primes.
\( \boxed{9} \)

Explanation:A triangular prism has:
– 3 vertices on top triangle
– 3 vertices on bottom triangle
Total vertices = 6

Explanation:A straight line contains infinitely many points.

Explanation:Prime factorization of 100:
\( 100 = 2^{2} \times 5^{2} \)
Even divisors must include factor 2.
Even divisors are:
2, 4, 10, 20, 50, 100
Total = 6