geno3141

The probability that the first student chosen is a boy is  1/6.

Now, there are only 5 boys remaining, so the probability that te second student chosen is a boy is  1/5.

Combine these two probabilities by multiplying  (1/6) x (1/5)  =  1/30.

Quadratic equation:  x  =  [ -b  +/-  sqrt( b² - 4 · a · c ) ]  /  ( 2 · a )

In this case:  a = 3     b = 4     c = -12

I think that you forgot something ...

Step 1)  Find the two roots by using the quadratic formula.

Step 2)  Place the answers into the expression:  r² + s².

If you are having difficulty with this, post back with what you have tried and what your results are.

The first term is 3; each succeeding term is 3 times the preceding term.

Using a calculator and writing down only the last two digits:

a₁ = 03     a₅ = 43      a₉ = 83     a₁₃ = 23     a₁₇ = 63     a₂₁ = 03     a₂₅ = 43          .....

a₂ = 09     a₆ = 29     a₁₀ = 49    a₁₄ = 69     a₁₈ = 89     a₂₂ = 09     a₂₆ = 29          .....

a₃ = 27     a₇ = 87     a₁₁ = 47     a₁₅ = 07     s₁₉ = 67     a₂₃ = 27     a₂₇ = 87         .....

a₄ = 81     a₈ = 61     a₁₂ = 41     a₁₆ = 21     a₂₀ = 01     a₂₄ = 81     a₂₈ = 61         .....

Can you figure out where  a₂₀₀₇  belongs in this list?  

The perfect squares below 1,000 are:

 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900 and 961

The answer is ...

Could you have figured out the answer without the list?

Translate  -3 <= a <= 2  into   -3 <= x <= 2  and  -1 <= b <= 4  into  -1 <= y <= 4 

and place this region onto a regular  x-y  plane.

The total region covered is  5 · 5  =  25  square units.

The positive product region is  (2 · 4) +  (-3 · -1)  =  8 + 3  =  11  square units.

The probability of landing on the positive region is  11 / 25.

The area of a parallelogram can be found by multiplying its base (CD) times its height (GE).

CD · GE  =  54 · 18  =  ......

Since  tan = y / x  and both the  x  value and the  y  value are negative in the third quadrant,

                               y = -4  and  x = -7.

Since  r = sqrt( x² + y² )    --->     r = sqrt( (-7)² + (-4)² )     --->     r = sqrt( 65 )

Since  cos = x / r    --->     cos = -7 / sqrt( 65 )