d ( f o c) / dt = 9
( solution is attached below)
Answer:
The number of deliveries that are predicted to be made to homes during a week with 50 deliveries to business is 87 deliveries
Step-by-step explanation:
The data categorization are;
The number of home deliveries = x
The number of delivery to businesses = y
The line of best fit is y = 0.555·x + 1.629
The number of deliveries that would be made to homes when 50 deliveries are made to businesses is found as follows;
We substitute y = 50 in the line of best fit to get;
50 = 0.555·x + 1.629 =
50 - 1.629 = 0.555·x
0.555·x = 48.371
x = 48.371/0.555= 87.155
Therefore, since we are dealing with deliveries, we approximate to the nearest whole number delivery which is 87 deliveries.
Answer:
the probability that the project will be completed in 95 days or less, P(x ≤ 95) = 0.023
Step-by-step explanation:
This is a normal probability distribution question.
We'll need to standardize the 95 days to solve this.
The standardized score is the value minus the mean then divided by the standard deviation.
z = (x - xbar)/σ
x = 95 days
xbar = mean = 105 days
σ = standard deviation = √(variance) = √25 = 5
z = (95 - 105)/5 = - 2
To determine the probability that the project will be completed in 95 days or less, P(x ≤ 95) = P(z ≤ (-2))
We'll use data from the normal probability table for these probabilities
P(x ≤ 95) = P(z ≤ (-2)) = 0.02275 = 0.023
Answer: at 11:54
Step-by-step explanation:
Let's define the 10:30 as our t = 0 min.
We know that Train A stops every 12 mins, and Train B stops every 14 mins, they will stop at the same time in the least common multiple of 12 and 14.
To find the least common multiple of two numbers, we must do:
LCM(a,b) = a*b/GCD(a,b)
Where GCD(a, b) is the greatest common divisor of a and b.
In this case the only common divisior of 12 and 14 is 2.
So we have:
LCM(12, 14) = 12*14/2 = 84.
Then the both trains will stop 84 minutes after 10:30
one hour has 60 mins, so we can write 84 minutes as:
1 hour and 24 minutes = 1:24
Then they will stop at the same time at 10:30 + 1:24 = 11:54
Since 25% is smack in the middle between 20% and 30%, it will take equal volumes of ech to make a 25% solution.
Since 4 gallons of 30% solution was used, so 4 gallons of 20% solution will be needed.
