Hi there, first we change the mixed numbers into improper fractions, 9 5/9=86/9 and 6 5/6=41/6. Second, we solve the problem now. 86*6-41*9÷9*6, 516-369/54=147/54. Third, we simplify 147/54 into 49/18. Fourth, we make 147/54 into a mixed number. 147/54 as a mixed number is 2 13/18
This relates to behavioral economics because when you’re short on supplies or ideas, you become stressed and you try <span>to figure out how you come up with what you need.</span>
Answer:
107.86 to 2 d.p.
Step-by-step explanation:
makes a triangle. 120 feet is the hypotenuse.
we want to find the opposite so we will use sine.
sin(x) = opp/hyp which means opp = sin(x)hyp.
opp = sin(64)120
opp = 107.86 to 2d.p.
60*0.08 Multiply the price of the sweater by 0.08, or 8%
4.8 solution
60-4.8 Subtract discount from original price
55.2 solution
7/100=a/55.2 construct formula to find sales tax
a=3.864 solution
55.2+3.864 add solution to discounted price
59.064 solution
$59.06 round down to 59.06
It will be less than 60 dollars because, according to the work shown, 59.06<60.
The probability of an event A occurring given that B has occurred is
P(A | B) = P(A and B) / P(B)
a. By the definition above,
P(spade | black) = P(spade and black) / P(black)
- P(black) = 26/52 = 1/2 because 26 of the 52 cards have a black suit
- All spade cards are black, so P(spade and black) = P(spade) = 13/52 = 1/4
Then P(spade | black) = (1/4) / (1/2) = 1/8.
b. We can do the same breakdown as in (a), or we can make use of the definition of conditional probability
P(A | B) = P(A and B) / P(B) = (P(B | A) * P(A)) / P(B)
Then
P(black | spade) = (P(spade | black) * P(black)) / P(spade)
- P(black) = 1/2
- P(spade) = 1/4
- P(spade | black) = 1/8
Then P(black | spade) = (1/8 * 1/2) / (1/4) = 1/64.
c. By definition,
P(7 | black) = P(7 and black) / P(black)
- P(7 and black) = 1/52 because this is a unique card
- P(black) = 1/2
Then P(7 | black) = (1/52) / (1/2) = 1/104.
d. By definition,
P(king | face) = P(king and face) / P(face)
- All kings are face cards, so P(king and face) = P(king) = 4/52 = 1/13
- P(face) = 12/52 = 3/13
Then P(king | face) = (1/13) / (3/13) = 1/3.