Answer:
-25
Step-by-step explanation:
Answer:
The maximum value of z is 244 at x= 8 and y=49.
Step-by-step explanation:
We are given the system of equations as,
Maximize :
Subject to :
After plotting the inequalities to which the maximized function is subjected to, we get the following graph.
So, we will find the value of 'z' at the enclosing the solution region.
(2,4) z= 6×2+4×4= 12+16 = 28
(2.273,3.182) z= 6×2.273+4×3.182 = 13.64+12.73= 26.37
(8,49) z= 6×8+4×49 = 48+196= 244
Thus, we get that the maximum value of z is 244 at x= 8 and y=49.
Answer:
DE = 20 units
Step-by-step explanation:
<u><em>GIVEN</em></u><em> :-</em>
- D & E are the mid-points of AB & BC respectively.
- DE = 4x + 4
- AC = x + 36
<u><em>TO FIND</em></u><em> :-</em>
<u><em>FACTS TO KNOW BEFORE SOLVING</em></u><em> :-</em>
- The midsegment of a triangle is a line constructed by connecting the midpoints of any two sides of the triangle.
- The Triangle Midsegment Theorem tells us that a midsegment is one-half the length of the third side (the base), and it is also parallel to the base.
<u><em>PROCEDURE</em></u><em> :-</em>
According to Triangle Midsegment Theorem ,
Multiplying 2 on both the sides ,
∴ DE = 4×4 + 4 = 20 units
In order to determine the mean:
Add all of the numbers given and then divide the sum by the total amount of numbers in the equation.
5 + 8 + 4 + 7 = 24
There are 4 numbers, so:
24 / 4 = 6
The average number of books Vasquez reads per month is 6.
Answer:
a. x = 40 wpm
b. MOE = 4.4 wpm.
c. If you were to create many more confidence intervals from many different random samples, you would expect 95% all of the confidence intervals to have centers and widths that include the true mean.
d. About 5% of the confidence intervals would not capture the parameter (true mean) you are trying to estimate.
Step-by-step explanation:
We have a 95% confidence interval for the mean with bounds 35.6 and 44.4.
This is estimated from a sample that, in this case, has a sample size of n=54.
The value of x, used to construct the interval, will be at the center of the interval. Then we can calculate the value of x as the average between the two bounds:
The margin of error is equal to the difference between x and any of the bounds:
c. If you were to create many more confidence intervals from many different random samples, you would expect 95% all of the confidence intervals to have centers and widths that include the true mean.
d. About 5% of the confidence intervals would not capture the parameter (true mean) you are trying to estimate.