Answer:
71.4699, 81.7301.
Step-by-step explanation:
So, the following are the scores: 74
90
84
78
61
65
62
67
73
75
76
95
71
98
80
![Let,\;the\;total\;sum\;of\;the\;scores\;be:\sum x =1149](https://tex.z-dn.net/?f=Let%2C%5C%3Bthe%5C%3Btotal%5C%3Bsum%5C%3Bof%5C%3Bthe%5C%3Bscores%5C%3Bbe%3A%5Csum%20x%20%3D1149)
![Then,\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\sum x^2=89795](https://tex.z-dn.net/?f=Then%2C%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5Csum%20x%5E2%3D89795)
The length of the score : 15
Then, let the size of the scores be n : 15.
Then, we have to find the mean.
![\bar{x}=\frac{\sum x}{n}](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%3D%5Cfrac%7B%5Csum%20x%7D%7Bn%7D)
![=\frac{1149}{15}=76.6](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1149%7D%7B15%7D%3D76.6)
![Then,\;we\;have\;to\;find\;standard\;deviation:S=\sqrt{\frac{\sum x^2-n.(\bar{x})^2}{n-1} }](https://tex.z-dn.net/?f=Then%2C%5C%3Bwe%5C%3Bhave%5C%3Bto%5C%3Bfind%5C%3Bstandard%5C%3Bdeviation%3AS%3D%5Csqrt%7B%5Cfrac%7B%5Csum%20x%5E2-n.%28%5Cbar%7Bx%7D%29%5E2%7D%7Bn-1%7D%20%7D)
![=\sqrt{\frac{89795-15\times(76.6)^2}{15-1} }=11.2808](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%5Cfrac%7B89795-15%5Ctimes%2876.6%29%5E2%7D%7B15-1%7D%20%7D%3D11.2808)
![The\;degree\;of\;freedom:n-1=14](https://tex.z-dn.net/?f=The%5C%3Bdegree%5C%3Bof%5C%3Bfreedom%3An-1%3D14)
![So,\;the\;significant\;level:\alpha=1-0.90=0.10](https://tex.z-dn.net/?f=So%2C%5C%3Bthe%5C%3Bsignificant%5C%3Blevel%3A%5Calpha%3D1-0.90%3D0.10)
![and\;the\;critical\;value:t_{\frac{\alpha}{2} }=1.7613](https://tex.z-dn.net/?f=and%5C%3Bthe%5C%3Bcritical%5C%3Bvalue%3At_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%20%7D%3D1.7613)
![Finally:\\=\bar{x}\;\pm\;t_{\frac{\alpha}{2} }\;\frac{S}{\sqrt{n} }\\=(71.4699, 81.7301)](https://tex.z-dn.net/?f=Finally%3A%5C%5C%3D%5Cbar%7Bx%7D%5C%3B%5Cpm%5C%3Bt_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%20%7D%5C%3B%5Cfrac%7BS%7D%7B%5Csqrt%7Bn%7D%20%7D%5C%5C%3D%2871.4699%2C%2081.7301%29)
Answer:
Step-by-step explanation:
![\frac{x}{6} =-\frac{15}{12} \\x=-\frac{15}{12} \times 6=-\frac{15}{2} \\\frac{x}{6} =\frac{29}{12} \\x=\frac{29}{12} \times 6\\x=\frac{29}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B6%7D%20%3D-%5Cfrac%7B15%7D%7B12%7D%20%5C%5Cx%3D-%5Cfrac%7B15%7D%7B12%7D%20%5Ctimes%206%3D-%5Cfrac%7B15%7D%7B2%7D%20%5C%5C%5Cfrac%7Bx%7D%7B6%7D%20%3D%5Cfrac%7B29%7D%7B12%7D%20%5C%5Cx%3D%5Cfrac%7B29%7D%7B12%7D%20%20%5Ctimes%206%5C%5Cx%3D%5Cfrac%7B29%7D%7B2%7D)
Answer:
False
Step-by-step explanation:
2 is a solution because to circle is closed. All answers including 2 and above are solutions.
Answer:
Minnesota and Iowa
Step-by-step explanation:
Divide each term in the y column by 2 to go from this list {8, 2, 0, 2, 8} to this list {4, 1, 0, 1, 4}
This list {4, 1, 0, 1, 4} is a bunch of perfect squares so it suggests that y = x^2
However we must double the values to get back to the original list. So the rule is y = 2*x^2