Answer:
(a)9
(b)I. 0.28125
II. 0.46875
III. 0.25
Step-by-step explanation:
There are a total of 32 students, therefore the number of elements in the Universal set, n(U)=32
(a)The Venn diagram is attached below.
Therefore, 9 students play both the violin and piano.
(b)
I. Probability that the student plays the violin but not the piano
Number of Students who play violin only =18-x=18-9=9
ii.Probability that the student does not play the violin
Number of Students who does not play violin only =17-x+7=17-9+7=15
P(does not play violin only)
iii.Probability that the student plays the piano but not the violin
Number of Students who play piano only =17-x=17-9=8
Let x be the amount of money, you fund in Fund A and y be the amount of mone yyou fund in Fund B.
1. You have 250,000 In an IRA at the time you retire and want to invest this money into Funds A and B, then
2. Fund A pays 1.2% (as a decimal 1.2% is 0.012) annually, then 
is annual interest income in Fund A.
Fund B pays 6.2% (as a decimal 6.2% is 0.062) annually, then 
is annual interest income in Fund B.
Since Fund A and Fund B produce an annual interest income of $8,000, then
3. Solve the system of equations:
Express x from first equation 
and substitute it into the second equation
Multiply this equation by 1000:
Then
Answer: you have to fund $150,000 in Fund A and $100,000 in Fund B.
<h3>Problem Solution</h3>
Assuming the spool is a cylinder and the circumference we're winding around is that of a circle with the given area, we can write the relation between circumference and area as
... C = 2√(πA)
10 times the circumference is then
... 10C = 20√(π·20 cm²) = 40√(5π) cm ≈ 159 cm
<h3>Formula Derivation</h3>
The usual formulas for circumference and area are
... C = 2πr
... A = πr²
If we multiply the area formula by π and take the square root, we get
... πA = (πr)²
... √(πA) = πr
Multiplying this by 2 gives circumference.
... C = 2√(πA) = 2πr
