Abiologist is studying the composition of birds on a lake and counts 61 ducks, 17 geese, 11 cranes, 15 swans, and 6 herons. from previous studies performed around the same time of the year, she expects 50% of the birds to be ducks, 23% to be geese, 12% to be cranes, 10% to be swans, and 5% to be herons. what are the expected and observed counts? select one.

Expected counts: 55 ducks, 25 geese, 13 cranes, 11 swans, 6 heron

Observed counts:

61 ducks, 17 geese, 11 cranes, 15 swans, and 6 herons.

Step-by-step explanation:

There are 61+17+11+15+6 = 110 birds on the lake.

The expected counts are:

0.50*110 = 55 ducks

0.23*110 = 25 geese

0.12*110 = 13 cranes

0.10*110 = 11 swans

0.05*110 = 6 herons

What the biologist counted were the observed counts.

step-by-step explanation: h: (- 3, 6)

m: (1, - 2)

o: (7, 6)

r: (- 9, - 2)

midpoint of hm: (- 1, 2)

midpoint of or: (- 1, 2)

therefore, b is the midpoint of both diagonals bisect each other !

to prove the diagonals are perpendicular, show that the product of the slopes = - 1

the answer is b