Bosco

A parking lot in the shape of a trapezoid has an area of 4,750square meters. The length of one base is 82meters, and the length of the other base is 108 meters. What is the width (height)of the parking lot     

Area_trapezoid  =  (the average of the two bases) times (the height)     

                  A  =  (1/2)(a+b) • h     

             4750  =  (1/2)(82 + 108) • h     

             4750  =  (1/2)(190) • h  =  95h     

                   h  =  4750 / 95     

                   h  =  50     

_.     

Find the area of the semicircle. Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal. units^2 2 

raidius=8     

A_circle  =  π r²     so the area of a semicircle would be half as much     

A_semicircle  =  (1/2) • π r²     

                 =  (0.5) • 3.14 • 64 units²     

                 =  100.48 units²     

.     

If 5x - 17 = -x + 7, then x =     

                                         5x – 17          =  –x + 7     

add +x to both sides         5x + x – 17    =  –x + x + 7     

                                         6x       – 17    =  7     

add +17 to both sides       6x – 17 + 17  =  7 + 17     

                                         6x                  =  24     

thus                                                     x  =  4     

_.     

What is the volume of a hemisphere with a diameter of 8.9 cm, rounded to the nearest tenth of a cubic centimeter?     

V_sphere  =  (4 / 3) • π r³       so the volume of a hemisphere would be half of that.     

V_hemisphere  =  (2 / 3) • π r³     

V  =  (2 / 3) • (3.1416) • (4.45 cm)³     

V  =  184.5609 cm³     rounded to a tenth  =  184.6 cm³     

_.     

Andy spins a fair spinner numbered 1 - 5 and rolls a fair dice.     
What is the probability of spinning a multiple of 4 and rolling a factor of 15?     

Between 1 & 5 inclusive, the only multiple of 4 is 4 itself.     

So, there is one chance out of five of landing on it.     

This probability is 1 / 5     

Between 1 & 6 inclusive, the factors of 15 are 1, 3, and 5.     

So, there are three chances out of six of landing on one of them.     

This probability is 3 / 6.     

For the probability of both things happening at the same time,     

multiply the probabilities together.     (1 / 5) • (3 / 6) = 3 / 30  =  1 / 10     

Take notice that I distinguished between a multiple and a factor.     

They are are not the same thing.     

_.     

The area of rectangle ABCD  with vertices A(0, 0), B(0, 4), C(x, 4) and D(x, 0) is 32 square units. If x > 0, what is the value of x?     

Corner A is at the origin.  Corner B is 4 units up, so the height of the rectangle is 4.     

Since the height of the rectangle is 4, then, for the area to be 32, its width must be 8.     

So, x  =  8     Specifically, corner C is at (8,4) and corner D is at (8,0).     

_.     

Dylan has 3 balls. Carlos has 4 more rocks than Dylan. Jake counted his rocks and said, "I have 2 fewer rocks than the two of you have together How many rocks do the boys have altogether?     

D  =  3      

C  =  3 + 4  =  7     

J  =  (3 + 7) – 2  =  8     

D + C + J  =  3 + 7 + 8  =  18     

_.     

Given that the polynomial x^2 - 15x + t = 0 has only positive integer roots, find the average of all distinct possible values of t.      

possible              resulting     

values of x          values of t     

   0   15                     0     

   1   14                   14     

   2   13                   26     

   3   12                   36     

   4   11                   44     

   5   10                   50     

   6     9                   54     

   7     8                   56     

                           ^{–––––}     

total of t's              280     

Avg_t  280 / 8  =  35     

_.     

A ship is traveling in a circle around the outside rim of an island surveying a good place to land. If it is 6 miles from a lighthouse at the center of the island and 120° from due north, how far has the ship traveled from the most northern tip of the island to the nearest tenth?     

(120^o / 360^o) • π d     

(1 / 3) • (3.14 • 12 mi)     

3.14 • 4 mi  =  12.56 mi     

round 12.56 to nearest tenth =  12.6 mi     

_.