As the question is not clear about the calculation needed, so i will calculate in both ways - compound interest and simple interest.
Given are:
Amount = $500
Rate of interest = 4% or 0.04
Time = 25
n = 1(compounded annually)
Formula for compound interest :
Putting values in the formula:
A= 
= 
= 500*2.665 = $ 1332.50
Hence, amount in the account after 25 years = 500+1332.50= $1832.50
Formula for simple interest:
S.I.=
= 
Interest = 500
Hence, amount in the account after 25 years = 500+500 = $1000
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
Is it a picture or an answer or something
Tan (Ф/2)=⁺₋√[(1-cosФ)/(1+cosФ)]
if π<Ф<3π/2;
then, Where is Ф/2??
π/2<Ф/2<3π/4; therefore Ф/2 is in the second quadrant; then tan (Ф/2) will have a negative value.
tan(Ф/2)=-√[(1-cosФ)/(1+cosФ)]
Now, we have to find the value of cos Ф.
tan (Ф)=4/3
1+tan²Ф=sec²Ф
1+(4/3)²=sec²Ф
sec²Ф=1+16/9
sec²Ф=(9+16)/9
sec²Ф=25/9
sec Ф=-√(25/9) (sec²Ф will have a negative value, because Ф is in the sec Ф=-5/3 third quadrant).
cos Ф=1/sec Ф
cos Ф=1/(-5/3)
cos Ф=-3/5
Therefore:
tan(Ф/2)=-√[(1-cosФ)/(1+cosФ)]
tan(Ф/2)=-√[(1+3/5)/(1-3/5)]
tan(Ф/2)=-√[(8/5)/(2/5)]
tan(Ф/2)=-√4
tan(Ф/2)=-2
Answer: tan (Ф/2)=-2; when tan (Ф)=4/3
