Step-by-step explanation:
let us give all the quantities in the problem variable names.
x= amount in utility stock
y = amount in electronics stock
c = amount in bond
“The total amount of $200,000 need not be fully invested at any one time.”
becomes
x + y + c ≤ 200, 000,
Also
“The amount invested in the stocks cannot be more than half the total amount invested”
a + b ≤1/2 (total amount invested),
=1/2(x + y + c).
(x+y-c)/2≤0
“The amount invested in the utility stock cannot exceed $40,000”
a ≤ 40, 000
“The amount invested in the bond must be at least $70,000”
c ≥ 70, 000
Putting this all together, our linear optimization problem is:
Maximize z = 1.09x + 1.04y + 1.05c
subject to
x+ y+ c ≤ 200, 000
x/2 +y/2 -c/2 ≤ 0
≤ 40, 000,
c ≥ 70, 000
a ≥ 0, b ≥ 0, c ≥ 0.
The mode of a set of numbers is the number that occurs the most.
The numbers in this set are as follows,
26, 17, 9, 12, 18, 21, 9, 14, 18, 23, 15, 7, 20, 18, 17, and 12
26 I
17 II
9 II
12 II
18 III
21 I
14 I
23 I
15 I
7 I
20 I
The number that appears the most is 18!
So the mode of the set of numbers is 18!
Answer:
As both prism have the same base area and height there volumes are the same.
Step-by-step explanation:
Volume of the prism is given by
Volume of Prism A= base area* height
60 cubic units= base area* 12
base area= 60/12= 5 units
Volume of Prism B= base area* height
= 5 units*12 units
= 60 cubic units
As both prism have the same base area and height there volumes are the same.
The length of the longer side is the length of the triangle itself.
For example the length of longer side of prism A maybe 10 units but width may be 1/2 units
and
the length of longer side of prism B maybe 15 units but width may be 1/3 units
the total base area remains the same.
The answer is C because u multiply 16.50 and .20
Hello! For this question, you solve using order of operations, which you probably already have remembered as PEMDAS. Anytime a number is raised to the 0 power, that is equivalent to 1. 0.5^0 is 1. 250 * 1 is 250. x = 0 gives us the answer of 250. Now, let's solve for the number by the second power. 0.5² is 0.25. 250 * 0.25 is 62.5. x² gives us 62.5. Now, let's subtract the two numbers together. 250 - 62.5 is 187.5. Because the number is decreasing, the slope is negative, so the answer is -187.5. Your answer is correct.
