Answer:
Equation: 
Solve for n: n = 112
Step-by-step explanation:
To first set up the equation, you need to look at the verbal description and translate into numbers and operations:
'three fourths a number' = 
'plus 8' = + 8
'is' =
'20 less' = - 20
'the number' = n
Put the expressions together:
'three fourths a number plus 8': 
'20 less than the number': n - 20
Set them equal to each other and solve:
Add 20 to both sides: 
Subtract 
from both sides: 
Multiply both sides by 
: 
Solve for n: n = 112
Sides of first rectangle are 12 inches and 6 inches
and sides of second rectangle are 10 inches and 5 inches
So to find the ration of sides we can do
Ratio of bases = 12/10 = 6/5
Ratio of altitudes = 6/5
Area of first rectangle = base * altitude = 12 *6 = 72 square inches
Answer:
P(A) = 44.44%
P(B) = 50%
P(B|A) = 37.5%
P(B|A) different from P(B).
A and B are independent.
Step-by-step explanation:
If we have a total of 180 students, and 80 of them have a Playstation, we have that P(A) = 80/180 = 0.4444 = 44.44%
If we have 90 students that have a Xbox, we have that P(B) = 90/180 = 0.5 = 50%
If we have 30 students that have both consoles, we have that P(A and B) = 30/180 = 0.1667 = 16.67%
To find P(B|A), we will find for a student that has an Xbox inside the group of students that has a Playstation, that is, we have 30 students in a total of 80 students, so P(B|A) = 30/80 = 0.375 = 37.5%
P(B|A) is different from P(B), the first is 37.5% and the second is 50%, so events A and B are independent events.
Answer:
60
Step-by-step explanation:
Cot is the same as 1/tan so:
By rearranging the equation, we get:
By taking the inverse tan, we get:
