Answer:
is there a question ?
Step-by-step explanation:
Answer:
Step-by-step explanation:
Box plot is enclosed.
To find out 5 number summary
3.0, 3.5, 4.5, 5.5, 6.5, 6.5, 7.0, 7.0, 7.0, 7.0, 7.0, 7.5, 8.0, 9.0, 9.0, 9.0, 9.5, 9.5, 9.5, 9.5}
Minimum: 3.0
Quartile Q1: 6.5
Median: 7
Quartile Q3: 9
Maximum: 9.5
Besides we find that
Average (mean): μ=7.25
Absolute deviation: 30.5
Mean deviation: 1.525
Minimum: 3.0
Maximum: 9.5
Variance: 3.7125
Standard deviation σ=1.926
Perpendicular lines will have negative reciprocal slopes. What that means is if u have a slope of 1/2, to find the negative reciprocal, flip the slope and change the sign.......flip 2/1, change the sign -2/1 or just -2. So the negative reciprocal for the slope of 1/2 is -2.
A. y = 1/5x + 3.....slope here is 1/5, so for a perpendicular line, u r gonna need an equation with the slope of -5.....and that would be : y + 3 = -5(x + 2).
B. Parallel lines will have the same slope. y = 5x - 2...the slope here is 5...so a parallel line will have a slope of 5.
y = mx + b
slope(m) = 5
(8,-2)...x = 8 and y = -2
now we sub, we r looking for b, the y intercept
-2 = 5(8) + b
-2 = 40 + b
-2 - 40 = b
-42 = b
so ur parallel equation is : y = 5x -42
Answer:
0 is an inflection point
1/4 is a local maximum.
Step-by-step explanation:
To begin with you find the first derivative of the function and get that

to find the critical points you equal the first derivative to 0 and get that

To find if they are maximums or local minimums you use the second derivative.

since
is neither an inflection point, and since
then 1/4 is a maximum.
Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.
Step-by-step explanation:
Salt in the tank is modelled by the Principle of Mass Conservation, which states:
(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)
Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

By expanding the previous equation:

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

Since there is no accumulation within the tank, expression is simplified to this:

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:
, where
.

The solution of this equation is:

The salt concentration after 8 minutes is:

The instantaneous amount of salt in the tank is: