Answer:
4, 4, and 8
Step-by-step explanation:
2 cups * 2 marshmallows per cup = 4 marshmallows
8 marshmallows / 2 marshmallows per cup = 4 cups of hot cocoa
16 marshmallows / 2 marshmallows per cup = 8 cups of hot cocoa
Answer:
The linear regression equation that represents the set of data is:
![y=1083.48+23.73x](https://tex.z-dn.net/?f=y%3D1083.48%2B23.73x)
The predicted number of new cases for 2013 is 1368.
Step-by-step explanation:
The general form of a linear regression is:
![y=a+bx](https://tex.z-dn.net/?f=y%3Da%2Bbx)
Here,
<em>y</em> = dependent variable
<em>x</em> = independent variable
<em>a</em> = intercept
<em>b</em> = slope
Compute the values of <em>a</em> and <em>b</em> as follows:
![\begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6857 \cdot 55 - 15 \cdot 17558}{ 6 \cdot 55 - 15^2} \approx 1083.476 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6 \cdot 17558 - 15 \cdot 6857 }{ 6 \cdot 55 - \left( 15 \right)^2} \approx 23.743\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%09%09%09%09%09%09%09a%20%26%3D%20%5Cfrac%7B%5Csum%7BY%7D%20%5Ccdot%20%5Csum%7BX%5E2%7D%20-%20%5Csum%7BX%7D%20%5Ccdot%20%5Csum%7BXY%7D%20%7D%7Bn%20%5Ccdot%20%5Csum%7BX%5E2%7D%20-%20%5Cleft%28%5Csum%7BX%7D%5Cright%29%5E2%7D%20%3D%09%09%09%09%09%09%09%20%20%20%20%20%20%5Cfrac%7B%206857%20%5Ccdot%2055%20-%2015%20%5Ccdot%2017558%7D%7B%206%20%5Ccdot%2055%20-%2015%5E2%7D%20%5Capprox%201083.476%20%5C%5C%20%5C%5Cb%20%26%3D%20%5Cfrac%7B%20n%20%5Ccdot%20%5Csum%7BXY%7D%20-%20%5Csum%7BX%7D%20%5Ccdot%20%5Csum%7BY%7D%7D%7Bn%20%5Ccdot%20%5Csum%7BX%5E2%7D%20-%20%5Cleft%28%5Csum%7BX%7D%5Cright%29%5E2%7D%20%09%09%09%09%09%09%09%3D%20%5Cfrac%7B%206%20%5Ccdot%2017558%20-%2015%20%5Ccdot%206857%20%7D%7B%206%20%5Ccdot%2055%20-%20%5Cleft%28%2015%20%5Cright%29%5E2%7D%20%5Capprox%2023.743%5Cend%7Baligned%7D)
The linear regression equation that represents the set of data is:
![y=1083.48+23.73x](https://tex.z-dn.net/?f=y%3D1083.48%2B23.73x)
Compute the predicted value of the number of new cases for 2013 (i.e. <em>x</em> = 12) as follows:
![y=1083.48+23.73x](https://tex.z-dn.net/?f=y%3D1083.48%2B23.73x)
![=1083.48+(23.73\times12)\\\\=1083.48+284.76\\\\=1368.24\\\\\approx 1368](https://tex.z-dn.net/?f=%3D1083.48%2B%2823.73%5Ctimes12%29%5C%5C%5C%5C%3D1083.48%2B284.76%5C%5C%5C%5C%3D1368.24%5C%5C%5C%5C%5Capprox%201368)
Thus, the predicted number of new cases for 2013 is 1368.
Answer:
wish i coul d help
Step-by-step explanation:
3^n=27
Solve Exponent.
3^n=27
log(3n)=log(27)(Take log of both sides)
n*(log(3))=log(27)
n=log(27) / log(3)
n=3