Answer:
1) Event A = 2/3
Event B = 1/2
2) 1/2
Step-by-step explanation:
1)
Event A :
No. we need on dice = 4
Total numbers on dice = 6
Hence sample space of the event = 6
P( getting 4) = 4/6 = 2/3
Event B :
A coin has a head & a tail.
Hence sample space of the event = 2
But as we need tail only ,
P ( getting Tail ) = 1/2 [ if only tossed once ]
2)
Total numbers on a die = 6
Total no. of odd numbers on die = 3 (∵ 1 , 3 & 5 are odd )
Sample space of this event = 6
P (getting an odd number) = 3/6 = 1/2
Answer:
The expression to compute the amount in the investment account after 14 years is: <em>FV</em> = [5000 ×(1.10)¹⁴] + [3000 ×(1.10)⁸].
Step-by-step explanation:
The formula to compute the future value is:
![FV=PV[1+\frac{r}{100}]^{n}](https://tex.z-dn.net/?f=FV%3DPV%5B1%2B%5Cfrac%7Br%7D%7B100%7D%5D%5E%7Bn%7D)
PV = Present value
r = interest rate
n = number of periods.
It is provided that $5,000 were deposited now and $3,000 deposited after 6 years at 10% compound interest. The amount of time the money is invested for is 14 years.
The expression to compute the amount in the investment account after 14 years is,
![FV=5000[1+\frac{10}{100}]^{14}+3000[1+\frac{10}{100}]^{14-6}\\FV=5000[1+0.10]^{14}+3000[1+0.10]^{8}](https://tex.z-dn.net/?f=FV%3D5000%5B1%2B%5Cfrac%7B10%7D%7B100%7D%5D%5E%7B14%7D%2B3000%5B1%2B%5Cfrac%7B10%7D%7B100%7D%5D%5E%7B14-6%7D%5C%5CFV%3D5000%5B1%2B0.10%5D%5E%7B14%7D%2B3000%5B1%2B0.10%5D%5E%7B8%7D)
The future value is:
![FV=5000[1+0.10]^{14}+3000[1+0.10]^{8}\\=18987.50+6430.77\\=25418.27](https://tex.z-dn.net/?f=FV%3D5000%5B1%2B0.10%5D%5E%7B14%7D%2B3000%5B1%2B0.10%5D%5E%7B8%7D%5C%5C%3D18987.50%2B6430.77%5C%5C%3D25418.27)
Thus, the expression to compute the amount in the investment account after 14 years is: <em>FV</em> = [5000 ×(1.10)¹⁴] + [3000 ×(1.10)⁸].
Answer:
16x^2 -8x +1
Step-by-step explanation:
The square of a binomial expands as ...
(a +b)^2 = a^2 +2ab +b^2
So, you need to look for a trinomial with first and last terms that are perfect squares and a middle term that is double the product of the roots of those terms.
This pattern matches ...
16x^2 -8x +1 = (4x -1)^2
Answer:
P=2 (a+b)=2•(7+15)=44
A= b h= 15•5=75