From the information given,
x represents number of small boxes while y represents number of large boxes.
If each small box can hold 6 books and each large box can hold 10 books, it means that the expression for the number of books that x small boxes and y large boxes can hold is
6x + 10y
If James can pack up to 110 books, it means that the number of books that he can pack is less than or equal to 110. The inequality representing this scenario is
6x + 10y ≤ 110
10y ≤ - 6x + 110
Dividing both sides of the equation by 10, we have
y ≤ - 6x/10 + 110/10
y ≤ - 3x/5 + 11
The graph is shown below
The inequality that represents this sitaution is 6x + 10y ≤ 110
The graph of the inequality wil have solid boundary at y = - 3x/5 + 11
and will be shaded below the line.
1. 0.91<0.93; 0.91 is farther away from the whole number 1 so it is less than 0.93.
2. 0.5=0.50; 0.5 and 0.50 are the same, since the decimal can be written with or without the zero.
3. 1.08<1.6; 1.08 is farther away from the whole number 2, so it is less than 1.6.
The 85th percentile is the cutoff time
such that
In other words, the 85th percentile refers to the time needed to belong to the top 15% of the distribution; more generally, the
percentile is the top
of the distribution.
Anyway, to find this value of
, transform
to a random variable
with the standard normal distribution using
where
is the mean of
and
is the standard deviation of
.
Here
is used to denote the z-score corresponding to the cutoff time
. Referring to a z-score table, you find that this occurs for
. So,
Answer: 0.9746
Step-by-step explanation:
Given : A normally distributed population has a mean of 250 pounds and a standard deviation of 10 pounds.
i.e. 
Sample size : n= 20
Let 
sample mean values.
Then, the probability that this sample will have a mean value between 245 and 255 be
Hence , the probability that this sample will have a mean value between 245 and 255 is 0.9746 .
