Astudent is taking a multiple-choice exam in which each question has two choices. assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place two balls (marked upper a and upper b) into a box. she randomly selects one ball for each question and replaces the ball in the box. the marking on the ball will determine her answer to the question. there are four multiple-choice questions on the exam. complete parts (a) through (d) below. a. what is the probability that she will get four questions correct? nothing (round to four decimal places as needed.)

Hi!

So if in the box there are 2 balls and she chose one at random, then she had a 0.5 probability of chose each ball, and then she has a 0.5 probability of choosing the ball that is associated to the correct answer, then she has a 0.5 of getting each answer correct.

Now she has 4 questions, then the probability for getting all of them correct is the product of the probabilities for each one; this is:

0.5*0.5*0.5*0.5 = 0.0625

multiplied by 100%, we get a 6.25% of getting the four answers correct using this method.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

51

step-by-step explanation:

73-22=51 the   mass number minus the amount of protons gives you the amount of neutrons