Answer:
13, 4, and 4
Step-by-step explanation:
The absolute value of a difference measures the discrepancy between the two numbers inside. The 13 represents the ideal amount of biscuits and x represents the actual number of biscuits in the package. So the difference between the actual and the ideal is 4 (whether it's 4 more of 4 less than 13).
The situation described doesn't actually match the wording, because this says there'll either be 9 or 17 biscuits in the package, due to the "=". If you wanted to have "as many as," then this should be "≤", allowing for 4 or fewer in either direction.
Answer:
see attached for sketch of Empirical Rule
Step-by-step explanation:
The Empirical Rule (also known is the "68-95-99.7" rule) states that nearly all of the data will fall within three standard deviations of the mean.
![\bf \begin{cases} t=tacos\\ m=milk \end{cases}~\hspace{7em} \begin{cases} \stackrel{1~taco}{t}+\stackrel{1~glass}{m}=\stackrel{\$}{2.10}\\[0.8em] \stackrel{2~tacos}{2t}+\stackrel{3~glasses}{3m}=\stackrel{\$}{5.15} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{array}{llll} t+m=2.10&\stackrel{multiplied~by}{\times -3}\implies &\stackrel{notice}{-3t\stackrel{\downarrow }{-3m}=-6.3}\\[0.8em] 2t+3m=5.15&\implies &~~2t+3m=5.15\\ \cline{3-3} &&-t+0m=-1.15 \end{array} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0At%3Dtacos%5C%5C%0Am%3Dmilk%0A%5Cend%7Bcases%7D~%5Chspace%7B7em%7D%0A%5Cbegin%7Bcases%7D%0A%5Cstackrel%7B1~taco%7D%7Bt%7D%2B%5Cstackrel%7B1~glass%7D%7Bm%7D%3D%5Cstackrel%7B%5C%24%7D%7B2.10%7D%5C%5C%5B0.8em%5D%0A%5Cstackrel%7B2~tacos%7D%7B2t%7D%2B%5Cstackrel%7B3~glasses%7D%7B3m%7D%3D%5Cstackrel%7B%5C%24%7D%7B5.15%7D%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Cbegin%7Barray%7D%7Bllll%7D%0At%2Bm%3D2.10%26%5Cstackrel%7Bmultiplied~by%7D%7B%5Ctimes%20-3%7D%5Cimplies%20%26%5Cstackrel%7Bnotice%7D%7B-3t%5Cstackrel%7B%5Cdownarrow%20%7D%7B-3m%7D%3D-6.3%7D%5C%5C%5B0.8em%5D%0A2t%2B3m%3D5.15%26%5Cimplies%20%26~~2t%2B3m%3D5.15%5C%5C%0A%5Ccline%7B3-3%7D%0A%26%26-t%2B0m%3D-1.15%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A~%5Cdotfill)
notice, we used -3 in the multiplication to <u>eliminate</u> the m's.
If the <em>n</em>-th term of the sequence is given by <em>n</em> ² - 2, then the 5th term is obtained by simply replacing <em>n</em> with 5 :
5² - 2 = 25 - 2 = 23
