Answer:
Pieces remaining = 1 - (1/4 + 1/4) - (1/2 x1/5) = 1/2 - (1/2 x1/5) = 1/2 - 1/10 = 4/10
Therefore, 4/10 x 20 = 8 pieces.
Step-by-step explanation:
Sophie ate 1/4 = 5 pieces
Glenn ate 1/4 = 5 pieces
Remaining pieces = 20 - 5 - 5 = 10 pieces
On Monday, Sophie ate = 1/5 x 10 = 2 pieces
Therefore, remaining pieces = 10 - 2 pieces = 8 pieces
Sophie and Glenn consumed half of the pie the first day. This is equal to 10 pieces. The remaining pieces will be 10. If, on Monday, Sophie ate 1/5 of 10 pieces, representing 2 pieces, the number left over is 10 Minus 2, which equals 8 pieces.
Ans=3.77777777...
hope this helps
Answer:
a) P(X = 5) = 0.04397
b) The probability that X exceeds its mean by more than 1 standard deviation = P(z > 1) = 0.159
Step-by-step explanation:
a) This question can be solved using binomial distribution function formula
Using Binomial,
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of refrigerators to be examined before getting 5 refrigerators with defective compressors = 6
x = Number of successes required = 5
p = probability of success = probability of examining a refrigerator with defective compressor out of the total 12 = 5/12 = 0.4167
q = probability of failure = probability of examining a refrigerator without defective compressor out of the total 12 = 1 - (5/12) = 7/12 = 0.5833
P(X = 5) = ⁶C₅ (0.4167)⁵ (0.5833)⁶⁻⁵
P(X = 5) = ⁶C₅ (0.4167)⁵ (0.5833) = 1(0.01256)(0.5833) = 0.04397
P(X = 5) = 0.04397
b) The probability that X exceeds its mean by more than 1 standard deviation represents Z-score of z > 1
Using the normal distribution tables,
P(z > 1) = 1 - P(z ≤ 1) = 1 - 0.841 = 0.159
Answer:
A
Step-by-step explanation:
- 
(x + 3) > x - 3 ( multiply both sides by 2 to clear the fraction )
- (x + 3) > 2x - 6 ← distribute parenthesis on left side by - 1
- x - 3 > 2x - 6 ( subtract 2x from both sides )
- 3x - 3 > - 6 ( add 3 to both sides )
- 3x > - 3
divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity
x < 1
Answer:
We want to rewrite:
q^2 = a*(p^2 - b^2)/p
as a linear equation, in the form:
y = m*x + c
So we start with:
q^2 = a*(p^2 - b^2)/p
we can expand the left side to get:
q^2 = (a/p)*p^2 - (a/p)*b^2
q^2 = a*p - (a/p)*b^2
Now we can ust define:
a*p = c
Then we can replace that to get:
q^2 = -(a/p)*b^2 + c
now we can replace:
q^2 = y
b^2 = x
Replacing these, we get:
y = -(a/p)*x + c
finally, we can replace:
-(a/p) = m
then we got the equation:
y = m*x + c
where:
y = q^2
x = b^2
c = a*p
m = -(a/p)
