Answer:
The number of ways this can be done is 1,260 ways
Step-by-step explanation:
In this question, we are asked to calculate the number of ways in which the letters of the word balloon can be arranged.
To do this, we take into consideration those letters that are repeated and the number of times repeated. The letters are l and o and are repeated two times each.
The number of ways = 7!/2!2! = 5040/4 = 1,260 ways
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.
Multiply each of the numbers by a ten to a power that they both become whole numbers.
0.67 *
= 67
0.3 *
= 30
Divide as usual.
67 / 30 = 2
So, the answer is 2 1/3.
Answer:one solution
Step-by-step explanation:
Given
a=42
b=34
angle A=117
using sine rule
sinB=0.7212
and A+B+C=180
Thus 2 triangles can be formed with given value
