You are painting all four walls of a shed. Each wall is a rectangle with a length of 12 feet and a height of 12 feet. A gallon o
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Factor the following:
4 p (4 p - 1) - 3 (4 p - 1)^2
Factor 4 p - 1 from 4 p (4 p - 1) - 3 (4 p - 1)^2:
(4 p - 1) (4 p - 3 (4 p - 1))
-3 (4 p - 1) = 3 - 12 p:
(4 p - 1) (4 p + 3 - 12 p)
Grouping like terms, 4 p - 12 p + 3 = 3 + (4 p - 12 p):
(4 p - 1) (3 + (4 p - 12 p))
4 p - 12 p = -8 p:
Answer: (4 p - 1) (-8 p + 3)
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Factor the following:
m (m + n) - 3 m (m + n)^2
Factor m + n out of m (m + n) - 3 m (m + n)^2, resulting in (m + n) (m - 3 m (m + n)^(2 - 1)):
(m + n) (m - 3 m (m + n)^(2 - 1))
2 - 1 = 1:
(m + n) (m - 3 m (m + n))
Factor m out of m - 3 m (m + n), resulting in m (1 - 3 (m + n)):
m (1 - 3 (m + n)) (m + n)
-3 (m + n) = -3 m - 3 n:
Answer: m (m + n) (-3 m - 3 n + 1)
___________________________________________________________Answer : -(-6 + p^2) (-1 - 6 q + p^2 q)
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Factor the following:
6 u^2 (2 u - 5)^2 - 12 u^2 (2 u - 5) (u + 5)
Factor u^2 out of 6 u^2 (2 u - 5)^2 - 12 u^2 (2 u - 5) (u + 5), resulting in u^2 (6 (2 u - 5)^2 - 12 (2 u - 5) (u + 5)):
u^2 (6 (2 u - 5)^2 - 12 (2 u - 5) (u + 5))
(2 u - 5) (2 u - 5) = (2 u) (2 u) + (2 u) (-5) + (-5) (2 u) + (-5) (-5) = 4 u^2 - 10 u - 10 u + 25 = 4 u^2 - 20 u + 25:
u^2 (6 4 u^2 - 20 u + 25 - 12 (2 u - 5) (u + 5))
6 (4 u^2 - 20 u + 25) = 24 u^2 - 120 u + 150:
u^2 (24 u^2 - 120 u + 150 - 12 (2 u - 5) (u + 5))
(u + 5) (2 u - 5) = (u) (2 u) + (u) (-5) + (5) (2 u) + (5) (-5) = 2 u^2 - 5 u + 10 u - 25 = 2 u^2 + 5 u - 25:u^2 (150 - 120 u + 24 u^2 - 122 u^2 + 5 u - 25)
-12 (2 u^2 + 5 u - 25) = -24 u^2 - 60 u + 300:
u^2 (-24 u^2 - 60 u + 300 + 24 u^2 - 120 u + 150)
Grouping like terms, 24 u^2 - 24 u^2 - 60 u - 120 u + 150 + 300 = (-120 u - 60 u) + (24 u^2 - 24 u^2) + (150 + 300):
u^2 ((-120 u - 60 u) + (24 u^2 - 24 u^2) + (150 + 300))
-120 u - 60 u = -180 u:
u^2 (-180 u + (24 u^2 - 24 u^2) + (150 + 300))
150 + 300 = 450:
u^2 (-180 u + (24 u^2 - 24 u^2) + 450)
24 u^2 - 24 u^2 = 0:
u^2 (450 - 180 u)
Factor 90 out of 450 - 180 u:
Answer: u^2×90 (5 - 2 u)
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4 p (4 p - 1) - 3 (4 p - 1)^2
Factor 4 p - 1 from 4 p (4 p - 1) - 3 (4 p - 1)^2:
(4 p - 1) (4 p - 3 (4 p - 1))
-3 (4 p - 1) = 3 - 12 p:
(4 p - 1) (4 p + 3 - 12 p)
Grouping like terms, 4 p - 12 p + 3 = 3 + (4 p - 12 p):
(4 p - 1) (3 + (4 p - 12 p))
4 p - 12 p = -8 p:
Answer: (4 p - 1) (-8 p + 3)
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Factor the following:
m (m + n) - 3 m (m + n)^2
Factor m + n out of m (m + n) - 3 m (m + n)^2, resulting in (m + n) (m - 3 m (m + n)^(2 - 1)):
(m + n) (m - 3 m (m + n)^(2 - 1))
2 - 1 = 1:
(m + n) (m - 3 m (m + n))
Factor m out of m - 3 m (m + n), resulting in m (1 - 3 (m + n)):
m (1 - 3 (m + n)) (m + n)
-3 (m + n) = -3 m - 3 n:
Answer: m (m + n) (-3 m - 3 n + 1)
___________________________________________________________Answer : -(-6 + p^2) (-1 - 6 q + p^2 q)
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Factor the following:
6 u^2 (2 u - 5)^2 - 12 u^2 (2 u - 5) (u + 5)
Factor u^2 out of 6 u^2 (2 u - 5)^2 - 12 u^2 (2 u - 5) (u + 5), resulting in u^2 (6 (2 u - 5)^2 - 12 (2 u - 5) (u + 5)):
u^2 (6 (2 u - 5)^2 - 12 (2 u - 5) (u + 5))
(2 u - 5) (2 u - 5) = (2 u) (2 u) + (2 u) (-5) + (-5) (2 u) + (-5) (-5) = 4 u^2 - 10 u - 10 u + 25 = 4 u^2 - 20 u + 25:
u^2 (6 4 u^2 - 20 u + 25 - 12 (2 u - 5) (u + 5))
6 (4 u^2 - 20 u + 25) = 24 u^2 - 120 u + 150:
u^2 (24 u^2 - 120 u + 150 - 12 (2 u - 5) (u + 5))
(u + 5) (2 u - 5) = (u) (2 u) + (u) (-5) + (5) (2 u) + (5) (-5) = 2 u^2 - 5 u + 10 u - 25 = 2 u^2 + 5 u - 25:u^2 (150 - 120 u + 24 u^2 - 122 u^2 + 5 u - 25)
-12 (2 u^2 + 5 u - 25) = -24 u^2 - 60 u + 300:
u^2 (-24 u^2 - 60 u + 300 + 24 u^2 - 120 u + 150)
Grouping like terms, 24 u^2 - 24 u^2 - 60 u - 120 u + 150 + 300 = (-120 u - 60 u) + (24 u^2 - 24 u^2) + (150 + 300):
u^2 ((-120 u - 60 u) + (24 u^2 - 24 u^2) + (150 + 300))
-120 u - 60 u = -180 u:
u^2 (-180 u + (24 u^2 - 24 u^2) + (150 + 300))
150 + 300 = 450:
u^2 (-180 u + (24 u^2 - 24 u^2) + 450)
24 u^2 - 24 u^2 = 0:
u^2 (450 - 180 u)
Factor 90 out of 450 - 180 u:
Answer: u^2×90 (5 - 2 u)
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Answer:
The probability that you get zero questions correct is 0.4096
The probability that you get one questions correct is 0.4096
The probability that you get three questions correct is 0.0256
Step-by-step explanation:
These probability can be describe with a Binomial Distribution. These distribution can be used when we have n identical and independent situations in which there is a probability p or probability of success and a probability q or probability of fail. Additionally q is equal to 1 - p. The probability of x for a situation in which we can apply binomial distribution is:
Where x is the variable that says the number of success in the n situations
And nCx is calculate as:
From the question we can identify that:
- n is equal to 4 multiple choice question
- p is 1/5 or 0.2, the probability of get one question correct
- q is 4/5 or 0.8, the probability of get one question incorrect
Then the probability of get zero questions correct of 4 questions is:
The probability of get one question correct of 4 questions is:
The probability of get three questions correct of 4 questions is: