Arlene is showing her work in simplifying −7.9 + 8.2 − 3.4 + 2.1. Identify any errors in her work or in her reasoning. Write feedback to Arlene explaining the mistake she made and how to correct her work. Step Work Reasoning
−7.9 + 8.2 − 3.4 + 2.1 Original problem
1 −7.9 + 8.2 + (−3.4) + 2.1 Additive inverse
2 −7.9 + (−3.4) + 8.2 + 2.1 Associative property
3 (−7.9 + (−3.4)) + (8.2 + 2.1) Commutative property
4 −11.3 + 10.3 Simplify
5 −1 Simplify

She mixed up the commutative and associative properties

Line 3 should be commutative and line 4 should be associative.

Line 3 is commutative because she swapped -3.4 and 8.2

Line 4 is associative because of the parenthesis groupings.

Other than that I don't see any other errors.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560