Answer:
58.05% probability that at least 1 of the students is a senior.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the captains are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
Either no seniors are captain, or at least one is. The sum of these probabilities is 100%. The easier way to solve this question is finding the probability of no seniors being captain, and subtratcing 100 from this. So
Probability of no seniors being captain:
Desired outcomes:
Four captains, from a set of 18 + 18 + 15 = 51. So

Total outcomes:
Four captains from a set of 18 + 18 + 15 + 12 = 63. So

Probability:

41.95% probability of no seniors being captains.
Find the probability that at least 1 of the students is a senior.
p + 41.95 = 100
p = 58.05
58.05% probability that at least 1 of the students is a senior.
The greatest common factor of 270 and 360 is 90.
To find this write the factors of each and find the largest one.
270: 1, 270, 2, 135, 3, 90, 5, 54, 6, 45, 9, 30, 10, 27, 15, 18
360: 1, 360, 2, 180, 3, 120, 4, 90, 5, 72, 6, 60, 8, 45, 9, 40, 10, 36, 12, 30, 15, 24, 18, 20
Answer:
Large Box = 15.25KG
Small Box = 13.25KG
Step-by-step explanation:
L = Large Box
S = Small Box
two large boxes and six small boxes has a total weight of 110 kg
2L + 6S = 110
five large boxes and three small boxes has a total weight of 116 kg
5L + 3S = 116
Make one of the coefficents [numbers] the same, in this case S.
2L + 6S = 110
10L + 6S = 232
Subtract the equations.
(10L + 6S = 232) - (2L + 6S = 110)
(10L - 2L) + (6S - 6S) = 232 - 110
8L = 122
L = 15.25
Substitute back into one of the equations to find S
2L + 6S = 110
2(15.25) + 6S = 110
30.5 + 6S = 110
6S = 110 - 30.5
6S = 79.5
S = 13.25
Substitute into the other equation
10L + 6S = 232
10(15.25) + 6(13.25) = 232
For
|a|=b
assume
a=b and a=-b
|x+7|=12
assume
x+7=12 and x+7=-12
minus 7 both sides
x=5 and x=-19
C is answer
Answer:
(-4, 3)
Step-by-step explanation:
There are coordinate rules for reflection that really help me with these:
Reflection over x-axis -- (x, y) -> (x, -y)
Reflection over y-axis -- (x, y) -> (-x, y)
Reflection over y = x -- (x, y) -> (y, x)
Reflection over y = -x -- (x, y) -> (-y, -x)
Hope this helps :]