Answer:
Riley will earn interest of $1706.86 in 15 years. But when the same problem solved for interest compounded annually we get,
c)1663.90
The options does not match with answer
Step-by-step explanation:
Given
principal amount P = $ 1000
rate of interest r = 6.75 % = 6.75/100 =0.0675
time t = 15
compounded semi annually, hence
no. of times interest is compounded, n = 2
We know that the formula for deriving final amount (A) is
A = P![(1+\frac{r}{n} )^{nt}](https://tex.z-dn.net/?f=%281%2B%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D)
Substituting the known values , we get
A = 1000 x ![(1 + \frac{0.0675}{2} )^{2 * 15}](https://tex.z-dn.net/?f=%281%20%2B%20%5Cfrac%7B0.0675%7D%7B2%7D%20%29%5E%7B2%20%2A%2015%7D)
= $2706.86
Hence the interest earned = A - P
= $2706.86 - $ 1000
= $1706.86
The answer is $1706.86
But when the same problem solved for interest compounded annually we get, n=1 and so
A = 1000 x ![(1 + 0.0675)^{15}](https://tex.z-dn.net/?f=%281%20%2B%200.0675%29%5E%7B15%7D)
= 2663.90
Hence interest earned = $2663.90 - $ 1000
= 1663.90
The first one is 9/16 you have to make 54 and 96 a fraction such as 54/96 then simplify
the second one is 1/5 you have to make 4 and 20 a fraction like this 4/20 then simplify
hope this helps!!
Use the formula (b/2)^2 in order to create a new term. Solve for x by using this term to complete the square.
x = 1 ±![\frac{\sqrt{6} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B6%7D%20%7D%7B2%7D)
It is given in the question , that Simon has 160 meters of fencing to build a rectangular garden. the garden's area (in square meters) as a function of the garden's width w (in meters) is modeled by
![A(w) = -w(w-80) \\ A(w) = -w^2 + 80w](https://tex.z-dn.net/?f=%20A%28w%29%20%3D%20-w%28w-80%29%0A%5C%5C%0AA%28w%29%20%3D%20-w%5E2%20%2B%2080w%20)
Which represents parabola and the parabola is maximum at its vertex, that is
![w = -\frac{b}{2a} = - \frac{80}{2} = 40 meters](https://tex.z-dn.net/?f=%20w%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D%20%3D%20-%20%5Cfrac%7B80%7D%7B2%7D%20%3D%2040%20meters%20)
Therefore the width is 40 meters and the area is
![A(40) = -40(40-80) = -40*-40 = 1600 meter ^2](https://tex.z-dn.net/?f=%20A%2840%29%20%3D%20-40%2840-80%29%20%3D%20-40%2A-40%20%3D%201600%20meter%20%5E2%20)