Bosco

One angle of a non-regular quadrilateral is a right angle. The largest angle is 3 times the size of the smallest angle. The fourth angle is 25 degrees greater than the smallest. What is the measure, in degrees, of the largest angle?     

Call the smallest angle "a"     

90 + a + 3a + (a + 25)  =  360     

               90 + 5a + 25  =  360     

                               5a  =  360 – 90 – 25     

                               5a  =  245     

                                 a  =  49     

                 L_argest A_ngle  =  3a     

               L_argest A_ngle  =  147     

check answer     

90 + 49 + (3•49) + (49+25)  =?  360     

            90 + 49 + 147 + 74  =?  360     

                                     360  =  360     

_.     

At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and a muffin, which comes out to $3.50. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15. How many cents does one bagel cost?     

                                  T + B = 315 ¢     ——>      T = 315 – B     

                                  B + M = 350 ¢     ——>     M = 350 – B     

                                   T + 2B + 3M  =  815 ¢     

                                   (315 – B)  +  2B  +  [3 • (350 – B)]  =  815     

                                   315 – B + 2B + 1050 – 3B  =  815     

                                    – 2B + 1365  =  815     

                                    – 2B  =  – 550     

                                         B  =  275 ¢     

_.     

I choose a random integer n between 1 and 10 inclusive. What is the probability that for the n I chose,     

there exist no real solutions to the equation x(x + 8) = -n? Express your answer as a common fraction.     

                                                           x(x + 8)  =  –n     

                                                           x² + 8x  =  –n     

                                                           x² + 8x + n  =  0     

For there to be no real solutions, the discriminant has to be negative.     

                                                           b² – 4ac < 0     

                                                           8² – (4)(1)(n) < 0     

                                                           64 – 4n < 0    

If n is anything larger than 16, there is no real solution.     

If n is anything less than 16, there are two solutions for x.     

So the probability that any number between 1 and 10 will 

result in no real solution is 0 ... that's a zero.     

_.     

     y = mx + b     

                        8 – 6     

     slope  =  –––––––––  =  2 / 10  =  0.2         

                     +5 – (– 5)     

     y-intercept  =  7     

equation is     y = 0.2x + 7     

_.     

Two fair, standard six-sided dice are rolled. What is the probability that one of the two numbers is less than the other number?     

The first die can be anything.                       6 / 6 = 1     

The second die can be anything     

other than what the first die was                  5 / 6     

Probability one is smaller                             5 / 6     

_.     

At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and a muffin, which comes out to $3.50. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15. How many cents does one bagel cost?     

                        T_oast + B_agel  = 315 ¢     ——>>     T = 315 – B     

                        B_agel + M_uffin = 350 ¢     ——>>     M = 350 – B     

                         T + 2B + 3M  =  815 ¢     

                         (315 – B)  +  2B  +  [3 • (350 – B)]  =  815     

                         315 – B + 2B + 1050 – 3B  =  815     

                          – 2B + 1365  =  815     

                          – 2B  =  – 550     

                               B  =  275 ¢     

_.     

In a store window, there was a box of berries having a total weight of 200 kg.  The berries were 99% water, by weight.  After two days in the sun, the water content of the berries was only 90%, by weight.  What was the total weight of the berries after two days, in kg?     

You're starting with 200 kg of berries, and 99% of that is water.     

Since they're 99% water, that means that there's 1% of solid stuff.     

1% of 200 kg means that there are 2 kg of solid stuff.     

Some of the water evaporates in the sun, but the solid stuff doesn't.     

So, after the evaporation, there still remains the same 2 kg of solid stuff.     

Since the new water content is 90%, that means that now the solid stuff is 10%.     

So 2 kg (the solid stuff) is 10% of the total weight.     

That means the new total weight is 20 kg.     

_.