as you should know, to get the inverse of any expression, we start off by doing a quick switcheroo on the variables and then solve for "y".
![\stackrel{f(x)}{y}=\sqrt{x}-5\implies \stackrel{\textit{quick switcheroo}}{x=\sqrt{y}-5}\implies x+5=\sqrt{y} \implies (x+5)^2=y \\\\\\ \stackrel{F~O~I~L}{(x+5)(x+5)}=y\implies x^2+10x+25=\stackrel{f^{-1}(x)}{y}](https://tex.z-dn.net/?f=%5Cstackrel%7Bf%28x%29%7D%7By%7D%3D%5Csqrt%7Bx%7D-5%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bquick%20switcheroo%7D%7D%7Bx%3D%5Csqrt%7By%7D-5%7D%5Cimplies%20x%2B5%3D%5Csqrt%7By%7D%20%5Cimplies%20%28x%2B5%29%5E2%3Dy%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7BF~O~I~L%7D%7B%28x%2B5%29%28x%2B5%29%7D%3Dy%5Cimplies%20x%5E2%2B10x%2B25%3D%5Cstackrel%7Bf%5E%7B-1%7D%28x%29%7D%7By%7D)
Answer:
$33,090.
Step-by-step explanation:
The formula is A = P( 1 + r/2)^2n so we have:
50,000 = P(1 + 0.07/2)^(6*2)
50000 = P * 1.035^12
P = 50000/ 1.035^12
= $33,090 to the nearest dollar.
Answer:
False, the angles remain unchanged
Step-by-step explanation:
Answer:
The margin of error for this estimate is of 14.79 yards per game.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
T interval
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 20 - 1 = 19
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 19 degrees of freedom(y-axis) and a confidence level of
. So we have T = 2.093
The margin of error is:
![M = T\frac{s}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20T%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D)
In which s is the standard deviation of the sample and n is the size of the sample.
You randomly select 20 games and see that the average yards per game is 273.7 with a standard deviation of 31.64 yards.
This means that ![n = 20, s = 31.61](https://tex.z-dn.net/?f=n%20%3D%2020%2C%20s%20%3D%2031.61)
What is the margin of error for this estimate?
![M = T\frac{s}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20T%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D)
![M = 2.093\frac{31.61}{\sqrt{20}}](https://tex.z-dn.net/?f=M%20%3D%202.093%5Cfrac%7B31.61%7D%7B%5Csqrt%7B20%7D%7D)
![M = 14.79](https://tex.z-dn.net/?f=M%20%3D%2014.79)
The margin of error for this estimate is of 14.79 yards per game.
Answer:
1 simply 1
Step-by-step explanation:
1*1*1=1