Answer:
Step-by-step explanation:
The solution of a system of linear equations is the point of intersection of their graphs because the intersection represents the only x or y values that will satisfy both/all equations. The graph visually shows that the intersection of these equations is the only spot on the graph that all of the equations have in common. This means that only this spot will satisfy all equations. For example, the intersection may be (0,1); this means that for all equations an x value of 0 will always result in the y value of 1. However, an x or y value that satisfies one equation may not satisfy the others if they do not lead to the desired outcome.
Answer:Decay
Step-by-step explanation: because of perenthesis
<span>The variance method is as follows.
-Sum the squares of the values in data set, and then divide by the number of values in data set
- From that, subtract the square of the mean (add all values and divide by number of values in the data set)
Our variance is
<span>
![\displaystyle\sigma^2 = \frac{2^2 + 5^2 + m^2}{3} - \left(\frac{2 + 5 + m}{3}\right)^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csigma%5E2%20%3D%20%5Cfrac%7B2%5E2%20%2B%205%5E2%20%2B%20m%5E2%7D%7B3%7D%20-%20%5Cleft%28%5Cfrac%7B2%20%2B%205%20%2B%20m%7D%7B3%7D%5Cright%29%5E2)
Since variance has to be 14, we set
![\sigma^2 = 14](https://tex.z-dn.net/?f=%5Csigma%5E2%20%20%3D%2014)
and solve for m
![14= \frac{4 + 25 + m^2}{3} - \left(\frac{7 + m}{3}\right)^2\ \Rightarrow \\ \\ 14 = \frac{29}{3} + \frac{1}{3}m^2 - \frac{1}{9}(7+m)^2 \\ \\ 14 = \frac{29}{3}+ \frac{1}{3}m^2 - \frac{1}{9}(49 + 14m + m^2) \\ \\ 14 = \frac{29}{3}+ \frac{1}{3}m^2 - \frac{49}{9}- \frac{14}{9}m- \frac{1}{9}m^2 \\ \\ 0 = \frac{-88}{9} -\frac{14}{9}m + \frac{2}{9}m^2 ](https://tex.z-dn.net/?f=14%3D%20%5Cfrac%7B4%20%2B%2025%20%2B%20m%5E2%7D%7B3%7D%20-%20%5Cleft%28%5Cfrac%7B7%20%2B%20m%7D%7B3%7D%5Cright%29%5E2%5C%20%5CRightarrow%20%5C%5C%20%5C%5C%0A14%20%3D%20%5Cfrac%7B29%7D%7B3%7D%20%2B%20%5Cfrac%7B1%7D%7B3%7Dm%5E2%20-%20%5Cfrac%7B1%7D%7B9%7D%287%2Bm%29%5E2%20%5C%5C%20%5C%5C%0A14%20%3D%20%5Cfrac%7B29%7D%7B3%7D%2B%20%5Cfrac%7B1%7D%7B3%7Dm%5E2%20-%20%5Cfrac%7B1%7D%7B9%7D%2849%20%2B%2014m%20%2B%20m%5E2%29%20%5C%5C%20%5C%5C%0A14%20%3D%20%5Cfrac%7B29%7D%7B3%7D%2B%20%5Cfrac%7B1%7D%7B3%7Dm%5E2%20-%20%5Cfrac%7B49%7D%7B9%7D-%20%5Cfrac%7B14%7D%7B9%7Dm-%20%5Cfrac%7B1%7D%7B9%7Dm%5E2%20%5C%5C%20%5C%5C%0A0%20%3D%20%5Cfrac%7B-88%7D%7B9%7D%20%20-%5Cfrac%7B14%7D%7B9%7Dm%20%2B%20%5Cfrac%7B2%7D%7B9%7Dm%5E2%0A)
quadratic formula
![m = \displaystyle\frac{-b \pm \sqrt{b^2 -4ac}}{2a} \\ m = \frac{-(-\frac{14}{9}) \pm \sqrt{\left(-\frac{14}{9}\right)^2 - 4(2/9)(-88/9)} }{2(2/9)} \\ m = \frac{\frac{14}{9} \pm \sqrt{ \frac{196}{81} + \frac{704}{81} } }{\frac{4}{9} } \\ m = \frac{\frac{14}{9} \pm \sqrt{ \frac{900}{81} } }{\frac{4}{9} } \\ m = \frac{\frac{14}{9} \pm \sqrt{ \frac{100}{9} } }{\frac{4}{9} } \\ m = \frac{\frac{14}{9} \pm \frac{10}{3} }{\frac{4}{9} } \\ m = 11, -4](https://tex.z-dn.net/?f=m%20%3D%20%5Cdisplaystyle%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2%20-4ac%7D%7D%7B2a%7D%20%5C%5C%0Am%20%3D%20%5Cfrac%7B-%28-%5Cfrac%7B14%7D%7B9%7D%29%20%5Cpm%20%5Csqrt%7B%5Cleft%28-%5Cfrac%7B14%7D%7B9%7D%5Cright%29%5E2%20-%204%282%2F9%29%28-88%2F9%29%7D%20%7D%7B2%282%2F9%29%7D%20%5C%5C%0Am%20%3D%20%5Cfrac%7B%5Cfrac%7B14%7D%7B9%7D%20%5Cpm%20%5Csqrt%7B%20%5Cfrac%7B196%7D%7B81%7D%20%2B%20%5Cfrac%7B704%7D%7B81%7D%20%7D%20%7D%7B%5Cfrac%7B4%7D%7B9%7D%20%7D%20%5C%5C%0Am%20%3D%20%5Cfrac%7B%5Cfrac%7B14%7D%7B9%7D%20%5Cpm%20%5Csqrt%7B%20%5Cfrac%7B900%7D%7B81%7D%20%20%7D%20%7D%7B%5Cfrac%7B4%7D%7B9%7D%20%7D%20%5C%5C%0Am%20%3D%20%5Cfrac%7B%5Cfrac%7B14%7D%7B9%7D%20%5Cpm%20%5Csqrt%7B%20%5Cfrac%7B100%7D%7B9%7D%20%20%7D%20%7D%7B%5Cfrac%7B4%7D%7B9%7D%20%7D%20%5C%5C%0Am%20%3D%20%5Cfrac%7B%5Cfrac%7B14%7D%7B9%7D%20%5Cpm%20%5Cfrac%7B10%7D%7B3%7D%20%20%7D%7B%5Cfrac%7B4%7D%7B9%7D%20%7D%20%5C%5C%0Am%20%3D%2011%2C%20-4)
-4 doesnt' work as it is not a positive integer
m = 11
</span></span>
Step-by-step explanation:
you can open the file I gave you now. the answer is there
Answer:
$755.80
Step-by-step explanation:
Determine the compound amount first and then subtract the principal from it, to find the amount of interest.
The compound amount formula is A = P (1 + r/n)^(nt), where
P is the initial principal, r is the interest rate as a decimal fraction, n is the number of compounding periods per year, and t is the number of years. Here, P = $2179; t = 5 yrs; r = 0.06; and n = 4 (quarterly compounding).
We get:
A = $2179(1 + 0.06/4)^(4*5), or $2179(1.015)^20, or $2179(1.347) = $2937.80.
The compound amount is $2934.80. Subtracting the $2179 principal results in the interest earned: $755.80.