Answer:
a) 0.88
b) 0.35
c) 0.0144
d) 0.2084
e) 0.7916
Step-by-step explanation:
a) The probability of a peanut being brown is 12/100 = 0.12. Hence the probability of it not being brown is 1-0.12 = 0.88
b) 12% of peanuts are brown, 23% are blue. So 35% are either blue or brown. The probability of a peanut being blue or brown is, therefore 35/100 = 0.35.
c) 12% of peanuts are red, so the probability of a peanut being red is 12/100 = 0.12. In order to calculate the probability of 2 peanuts being both red, we can assume that the proportion doesnt change dramatically after removing one peanut (because the number of peanuts is absurdly high. We can assume that we are replenishing the peanuts). To calculate the probability of 2 peanuts being both red, we need to power 0.12 by 2, hence the probability is 0.12² = 0.0144.
d) Again, we will assume that the probability doesnt change, because we replenish. The probability of a peanut being blue is 0.23. The probability of it not being blue is 0.77, so the probability of 6 peanuts not being blue is obtained from powering 0.77 by 6, hence it is 0.77⁶ = 0.2084
e) The event 'at least one peanut is blue' is te complementary event of 'none peanuts are blue', so the probability of this event is 1- 0.2084 = 0.7916
Answer: OPTION A
Step-by-step explanation:
It is important to remember the "Angle Addition Postulate" in order to solve this exercise.
You have this larger angle:
According to the "Angle Addition Postulate", if the point "C" is in the interior of , then the measure of this angle can be obtained by adding the angle 
and the angle 
.
You can observe in the figure that:
Then you get that:
Therefore, the correct answer is Option A.
First, we define variables:
x: small hat
y: medium hat
z: large hat
We now write the system of equations:
x + y + z = 47
5.50x + 6y + 7z = 302
-3x + y = 0
We can write the system in matrix form as:
Ax = b
Where,
A = [1 1 1; 5.50 6 7; -3 1 0]
b = [47; 302; 0]
x = [x; y ; z]
Solving the system we have:
x = 6
y = 18
z = 23
Answer:
the coach did purchase 23 large hats
d. 23
If 9 of the sparrows is 45% of the birds in the backyard, 9/x = 45/100.
Cross multiply to get 9 * 100 = 45x; simplified is 900 = 45x or 20.
This means that there are 20 birds in the backyard. You can check this by dividing 9/20 which equals 45%
1. Given the bases a and b of a trapezoid, the length of the median m can be found by the formula
2. MP and NO are the bases so applying the above formula:
x=6
Check the picture for the proof of the theorem m=(a+b)/2
