Right triangle pqr is to be constructed in the xy-plane so that the right angle is at p and pr is parallel to the x-axis. the x- and y-coordinates of p, q, and r are to be integers that satisfy the inequalities -4 < = x < = 5 and 6< = y< = 16. how many different triangles with these properties could be constructed?

(a) 110
(b) 1,100
(c) 9,900
(d) 10,000
(e) 12,100

(C) 9900

Step-by-step explanation:

The right triangle which right angle is at P and PR is parallel to the x-axis can have 4 sets (A,B,C,D as illustrated) of format depends on which direction is the right angle located.

each set have

(1+2+3+4+5+6+7+8+9) x (1+2+3+4+5+6+7+8+9+10) = 45 x 55 = 2475 right triangles

4 sets: 2475 x 4 = 9900

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.  

answer: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.