Answer:
Option B
Step-by-step explanation:
we know that
The sum of an arithmetic series is equal to
S=n(a1+an)/2
where
a1 is the first term
an is the last term
n is the number of terms
In this problem we have
n=20
a1=102
an=159
substitute the values in the formula
S=20(102+159)/2
Answer:
Shaded area is 55 units²
Step-by-step explanation:
Ignoring the white cutout, we have a rectangle of length 10 and width 7 (count the squares in each direction). The area of this larger rectangle is
(10 units)(7 units) = 70 units². The white area that we previously ignored has dimensions 3 by 5 units, and thus an area of 15 units²
Subtract the latter from the former, obtaining the net area
70 units² - 15 units² = 55 units²
This is a case of joint probability: you want to know what the odds are of this event AND that event occurring. For a joint probability, the formula is usually given as:
P(A and B)=P(A)*P(B)
where P(A) is the probability of event A happening, P(B) is the probability of event B happening, and P(A and B) is the probability of both happening.
For this problem, let's say that event A is the probability that the spinner stops at the green color. Since the spinner has 3 colors and they have equal area (sector) occupied in the circle, each color has the same chance, 1/3 chance of being picked. Thus, there's a 1/3 chance of the spinner stopping at the green color so P(A)=1/3.
Event B is the probability of Jordan picking up the yellow card. There are six possible colors to pick and since Jordan picked up the card without peeking, each color has an equal chance to be picked. Thus, there's a 1/6 chance that the yellow card will be selected so P(B)=1/6.
Using the formula, we can then calculate P(A and B), the probability that the spinner stops at green and a yellow card is selected:
P(A and B)=P(A)*P(B)=1/3*1/6=1/18
