Answer:
Estimate Tip = $4.50
Step-by-step explanation:
The bill to the nearest $10 is $30.00 : ( $ 30 ($32.43) $40, it is nearer to $30
Estimate Tip = Bill rounded to the nearest $10 × Tip %
Estimate Tip = $30 × 15%
Estimate Tip = $30 × .15 (15% change to a decimal is .15)
Estimate Tip = $4.50
X=-8/3 this is the answer
The formula for determining the apothem of regular hexagon is s/2tan(180/n) , where 's' is any side length of regular hexagon and 'n' is the number of sides of regular hexagon.
So, apothem = 17/2tan(180/n)
= 17/2tan(30)
= 17/1.15
= 14.78 units
Therefore, the measure of apothem of the regular hexagon is 14.7 units.
B is the right answer.
1. This question refers to conditional probability and is asking us to find the probability of Q occurring, given that R occurs. What this means is that we must divide the probability of Q and R occurring by the probability of R occurring (this is because we have the condition that R occurs). This may be written as such:
Pr(Q|R) = Pr(Q ∩ R) / Pr(R)
2. Now, the first step is to find Pr(Q ∩ R). This is given by the value in the centre of the Venn Diagram (ie. in the cross-over between the two circles) divided by the total of all the values:
Pr(Q ∩ R) = 3/(8 + 3 + 4 + 22)
= 3/37
3. The next step is to find Pr(R). This is given by the value in the circle denoted R (including the cross-over with Q) divided by the total of all the values.
Pr(R) = (4 + 3)/(8 + 3 + 4 + 22)
= 7/37
4. Thus, we can now subtitute the probabilities we defined in 2. and 3. into the formula for conditional probability we defined in 1.:
Pr(Q|R) = (3/37) / (7/37)
= 3/7
Thus, the answer is B.
Note that technically there is no need to write out the full probabilities before coming to this answer. The same exact answer could be found by using Pr(Q ∩ R) = 3 and Pr(R) = 7. This works because they are part of the same universal set - in other words, since the total of all the values in the Venn Diagram remains constant, the denominators of the two probabilities would be the same (given that no cancelling is done) and these denominators would be cancelled out when dividing Pr(Q ∩ R) by Pr(R). This can be particularly useful for a multiple choice question such as this one.
2 cups is a pint, 2 pints is a quart,4 quarts is a gallon
