Answer:
$7.62 per hour
Step-by-step explanation:
Since, Heather gets a raise every 3 months, in 2 years, she will get a raise 8 times (2years = 24 months, 24 divided by 3 is 8).
Now it becomes a compound growth problem. We can use the formula shown below to solve these type of problems.
Where,
- F is the future value (what we want to find)
- P is the present rate ($6.5)
- r is the rate of growth, in decimal (2% growth means 0.02)
- t is the time frame, number of times compounding occurs (for our case we have figured it to be 8)
<u>Now plugging in all the info, we get the value of F:</u>
Thus, after 2 years, Heather's hourly rate will be $7.62
The product is 
Explanation:
The given expression is 
We need to determine the product of the given expression.
First, we shall simplify the given expression.
Thus, we have,
Expanding the expression, we have,
Now, we shall apply FOIL, we get,
Simplifying the terms, we have,
Multiplying, we get,
Adding the like terms, we get,
Thus, the product of the given expression is
Answer:
x = 5
Step-by-step explanation:
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ N(\stackrel{x_1}{-3}~,~\stackrel{y_1}{10})\qquad A(\stackrel{x_2}{6}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ NA=\sqrt{(6+3)^2+(3-10)^2}\implies NA=\sqrt{130} \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_2}{6}~,~\stackrel{y_2}{3})\qquad D(\stackrel{x_1}{6}~,~\stackrel{y_1}{-1}) \\\\\\ AD=\sqrt{(6-6)^2+(-1-3)^2}\implies AD=4 \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20N%28%5Cstackrel%7Bx_1%7D%7B-3%7D~%2C~%5Cstackrel%7By_1%7D%7B10%7D%29%5Cqquad%20A%28%5Cstackrel%7Bx_2%7D%7B6%7D~%2C~%5Cstackrel%7By_2%7D%7B3%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20NA%3D%5Csqrt%7B%286%2B3%29%5E2%2B%283-10%29%5E2%7D%5Cimplies%20NA%3D%5Csqrt%7B130%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20A%28%5Cstackrel%7Bx_2%7D%7B6%7D~%2C~%5Cstackrel%7By_2%7D%7B3%7D%29%5Cqquad%20D%28%5Cstackrel%7Bx_1%7D%7B6%7D~%2C~%5Cstackrel%7By_1%7D%7B-1%7D%29%20%5C%5C%5C%5C%5C%5C%20AD%3D%5Csqrt%7B%286-6%29%5E2%2B%28-1-3%29%5E2%7D%5Cimplies%20AD%3D4%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
now that we know how long each one is, let's plug those in Heron's Area formula.
![\bf \qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{130}\\ b=4\\ c=\sqrt{202}\\[1em] s=\frac{\sqrt{130}+4+\sqrt{202}}{2}\\[1em] s\approx 14.81 \end{cases} \\\\\\ A=\sqrt{14.81(14.81-\sqrt{130})(14.81-4)(14.81-\sqrt{202})} \\\\\\ A=\sqrt{324}\implies A=18](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Ctextit%7BHeron%27s%20area%20formula%7D%20%5C%5C%5C%5C%20A%3D%5Csqrt%7Bs%28s-a%29%28s-b%29%28s-c%29%7D%5Cqquad%20%5Cbegin%7Bcases%7D%20s%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20a%3D%5Csqrt%7B130%7D%5C%5C%20b%3D4%5C%5C%20c%3D%5Csqrt%7B202%7D%5C%5C%5B1em%5D%20s%3D%5Cfrac%7B%5Csqrt%7B130%7D%2B4%2B%5Csqrt%7B202%7D%7D%7B2%7D%5C%5C%5B1em%5D%20s%5Capprox%2014.81%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20A%3D%5Csqrt%7B14.81%2814.81-%5Csqrt%7B130%7D%29%2814.81-4%29%2814.81-%5Csqrt%7B202%7D%29%7D%20%5C%5C%5C%5C%5C%5C%20A%3D%5Csqrt%7B324%7D%5Cimplies%20A%3D18)
<span>Given that A
dataset shows that, on average, smokers do not live as long as
nonsmokers and heavy smokers do not live as long as light smokers.
If
you compute the least squares line for y = age at time of death and x =
number of packets per day typically smoked, you will notice that as the number of packets per day a person smokes increases, the age at time of death of the person decreases.
Thus, the graph wil have a negative slope.
Therefore, the slope of your
regression line will be less than 0.</span>
