Answer:
35% chose baseball or soccer
Step-by-step explanation:
baseball or soccer = 20% + 15% = 35%
_____
The categories add to 100%, so are mutually exclusive, as you expect when they are "favorite sport" categories. Hence the union of two of them will be their sum. (Otherwise, you'd have to subtract the amount by which the categories overlap.)
Answer:
Sum of the sequence (Sn) = 33,859
Step-by-step explanation:
Given:
Sequence = 685+678+671+664+...+6
Find:
Sum of the sequence (Sn)
Computation:
a = 685
d = 678 - 985 = -7
an = 6
an = a+(n-1)d
6 = 685+(n-1)(-7)
-679 = (n-1)(-7)
97 = n-1
n = 98
So,
Sum of the sequence (Sn) = (n/2)[a+an]
Sum of the sequence (Sn) = (98/2)[685+6]
Sum of the sequence (Sn) = (49)(691)
Sum of the sequence (Sn) = 33,859
(a) The probability of drawing a blue marble at random from a given box is the number of blue marbles divided by the total number of marbles. We assume that the probability of selecting one of two boxes at random is 1/2 for each box.
... P(blue) = P(blue | box1)·P(box1) + P(blue | box2)·P(box2) = (3/8)·(1/2) + (4/6)·(1/2)
... P(blue) = 25/48 . . . . probability the ball is blue
(b) P(box1 | blue) = P(blue & box1)/P(blue) = (P(blue | box1)·P(box1)/P(blue)
... = ((3/8)·(1/2))/(25/48)
... P(box1 | blue) = 9/25 . . . . probability a blue ball is from box 1
Answer:
3135
Step-by-step explanation:
Givens
a1 = 6
Use t4 - t3 to get d
t4 = 27
t3 = 20
Step One
Find a1 and d
a1 = 6
d = t4 - t3
d = 27 - 20
d = 7
Step Two
Find the 30th Term
tn= a1 + (n -1 )*d
t30 = 6 + (30 - 1) * 7
t30 = 6 + 29*7
t30 = 6 + 203
t30 = 209
Step Three
Find the sum using Sum = (a + t30)*n/2
n = 30 given
a1 = 6 given
t30 = 209 calculated from step 2
Sum = (a1 + t30)*n/2 Substitute
Sum = (6+ 209)*30/2 Combine like terms and divide by 2
sum = 215 * 15 Multiply
Sum = 3135 Answer
