Answer:
The proportion of jugs which receive more than 65 ounces of detergent is 0.0062 or 0.62%
Step-by-step explanation:
Mean amount of detergent = u = 64
Standard deviation = 
= 0.4
We need to find the proportion of jugs with over 65 ounces of detergent. Since the population is Normally Distributed and we have the value of population standard deviation, we will use the concept of z-score to solve this problem.
First we will convert 65 to its equivalent z-score, then using the z-table we will desired proportion. The formula to calculate the z-score is:
x = 65 converted to z score will be:
Therefore, the probability of detergent being more than 65 ounces is equivalent to probability of z-score being over 2.5
i.e.
P(X > 65) = P(z > 2.5)
From the z-table and using the property of symmetry:
P(z > 2.5) = 1 - P(z < 2.5)
= 1 - 0.9938
= 0.0062
Therefore,
P(X > 65) = P(z > 2.5) = 0.0062
So, the proportion of jugs which receive more than 65 ounces of detergent is 0.0062 or 0.62%
Multiplying the whole function by -1 reflects the function across the x axis
so f(x) to -f(x) would be a reflection across the x axis
multiplying the whole function by a fraction is a vertical transformation, if you multiply by a value x, such that 0<x<1, then it is a vertical shrink, if x>1, then it is a vertical stretch
so like f(x) to 2f(x) is a vertical stretch by a factor of 2
adding a value to the whole function moves it up by that number
ok
so
we have multiplied the whole thing by -1 and 1/2 and then added 2 to the whole function
that is a reflection across the x axis, a vertical shrink by a factor of 1/2, and translated up by 2 units in that order
The continent which has 59% of the total population will have more than 5.31 billion people by 2050.
<u>Step-by-step explanation:</u>
It is given that,
- The total number of people is 9 billion.
- The estimated number of people in 2050 year is 5.31 billion.
Therefore, you need to find out which continent has the estimated number by finding the percentage value.
<u>To find what percent 5.31 is of billion is of 9 billion :</u>
Let x be the percentage to be calculated.
⇒ x percent of 9 billion is 5.31 billion.
⇒ (x/100) × 9 = 5.31
⇒ x = (5.31 × 100) / 9
⇒ x = 531 / 9
⇒ x = 59 %
∴ The continent which has 59% of the total population will have more than 5.31 billion people by 2050.
Answer:
The answer is below
Step-by-step explanation:
Let S denote syntax errors and L denote logic errors.
Given that P(S) = 36% = 0.36, P(L) = 47% = 0.47, P(S ∪ L) = 56% = 0.56
a) The probability a program contains both error types = P(S ∩ L)
The probability that the programs contains only syntax error = P(S ∩ L') = P(S ∪ L) - P(L) = 56% - 47% = 9%
The probability that the programs contains only logic error = P(S' ∩ L) = P(S ∪ L) - P(S) = 56% - 36% = 20%
P(S ∩ L) = P(S ∪ L) - [P(S ∩ L') + P(S' ∩ L)] =56% - (9% + 20%) = 56% - 29% = 27%
b) Probability a program contains neither error type= P(S ∪ L)' = 1 - P(S ∪ L) = 1 - 0.56 = 0.44
c) The probability a program has logic errors, but not syntax errors = P(S' ∩ L) = P(S ∪ L) - P(S) = 56% - 36% = 20%
d) The probability a program either has no syntax errors or has no logic errors = P(S ∪ L)' = 1 - P(S ∪ L) = 1 - 0.56 = 0.44
