Math Question of the week (5)

The originator of a chain letter writes 5 letters instructing each recipient to write 5 similar letters to additional people.  Then these people each send 5 similar letters to other people.  Determine the number of people who should receive letters if the chain continues unbroken for 12 steps.                      

Answer Key for Math question of the week (4)

a.    d = 3

       u_n = a + n − d

       u₁₀₁ = 2 +100—3

       u₁₀₁ = 302 

b.   152 = 2 + (n −1)(3)

      150 = (n −1)(3),

      50 = n −1,

      152 = −1+ 3n

       n = 51

Math Question of the week (4)

Consider the arithmetic sequence 2, 5, 8, 11, .......

a. Find U<sub>101

b. Find the value of n so that</sub> U_{n = 152.}

Answer Key for Math question of the week (3)

a.  6C4 (0.4)^4 (0.6)^2 = 0.13824


b. (0.6)(0.6)(0.4) = 0.144

Math question of the week (3)

When John throws a stone at a target, the probability that he hits the target is 0.4 He throws a stone 6 times. 

(a) Find the probability that he hits the target exactly 4 times. 

(b) Find the probability that he hits the target for the first time on his third throw.

Answer key for Math question (2)

a) 7C4 [ (0.9)^4 * (1 - 0.9)^(7 - 4) ] 
     = 7!/(4!*3!) [(0.9)^4 * (0.1)^3] 
     = 35(0.0006561) 
        =0.023

b) 7C4 [p^4 * (1 - p)^3] 
     = 35p^4(1 - 3p + 3p^2 - p^3) 
     = 35p^4 - 105p^5 + 105p^6 - 35p^7

c) 0.15 = 35p^4 - 105p^5 + 105p^6 - 35p^7
    p = 0.356 or

    p = 0.770

Math question of the week (2)

Evan likes to play two games of chance, A and B.

For game A, the probability that Evan wins is 0.9. He plays game A seven times.

(a) Find the probability that he wins exactly four games. 

     For game B, the probability that Evan wins is p . He plays game B seven times.

(b) Write down an expression, in terms of p , for the probability that he wins exactly

     four games. 

(c) Hence, find the values of p such that the probability that he wins exactly four

     games is 0.15. 

Answer key for math question (1)

(a)

     (i) sin140⁰ = p

     (ii) cos70⁰ = −q

(b)

      Using sin²θ + cos²θ =1

      cos140⁰ = ±√1− p²

      cos140⁰ = − √1− p²

(c)

       tan140 ⁰ = sin140⁰/ cos140⁰

                         = -p / (√1− p²)

Math question of the week (1)

Let p=sin40⁰ and q=cos110⁰. Give your answers to the following in terms of p and/or q

(a) Write down an expression for 

      1. sin140⁰ 

      2. cos110⁰

(b) Find an expression for cos140⁰.

(c) Find an expression for tan140⁰.