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The already-investigated geometric case is k = −6. A second value of k also makes the sequence geometric. (i) Show that k2 + 7k + 6 = 0. (ii) Find the first three terms for the second value. (iii) State the sum S2m of its first 2m terms.
State two conditions needed to model a count by a binomial distribution.
Find the expected number who join soldering.
Find (i) P(D = 512); (ii) P(490 ≤ D ≤ 520).
Given 490 ≤ D ≤ 520, find the probability that at most 501 visitors join soldering.
A visitor joins 3D printing with probability 0.68, independently of that visitor’s soldering decision. Find the probability of joining both.
On Sunday there are n visitors, and each joins 3D printing with probability 0.68. The probability that at most 450 join is approximately 0.762. Find n.
(i) Use triangle OCB to show that . (ii) Express h in terms of r and θ.
Hence or otherwise show that .
Show that .