Below is a graph of the murphys' annual expenses. how much will the murphys' pay in state/local taxes if their gross annual
household income is $85,420?
murphys' annual expenses
federal taxes
other 24%
state/local
clothing s
taxes
10%
9%
5%
recreation
transportation
housing and
household
27%
food
medical care
7%
a.
b.
c.
d.
$3,559.17
$8542.00
$20,500.80
$29,897.00

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

()1. how do you find range? 2.the following set of data is to be organized into a histogram. if there are to be five intervals on the graph, what should the length of each interval be? 30, 34, 23, 21, 27, 25, 29, 29, 25, 23, 32, 31

Astudy was interested in determining if eating milk chocolate lowered someone's cholesterol levels. ten people's cholesterol was measured. then, each of these individuals were told to eat 100g of milk chocolate every day and to eat as they normally did. after two weeks, their cholesterol levels were measured again. is there evidence to support that their cholesterol levels went down? how should we write the alternative hypothesis? (mud = the population mean difference= before - after)a. ha: mud = 0b. ha: mud > 0c. ha: mud < 0d. ha: mud does not equal 0