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:
E) 35°, 70°.
Step-by-step explanation:
Given that the triangle has angles of a°, 2a° and 75°.
A triangle is a polygon shape that has three sides and three angles. The sum of angles in a triangle is 180°. There are different types of triangles such as scalene triangle, isosceles triangle, equilateral triangle e.t.c.
In the triangle:
a + 2a + 75 = 180° (sum of angles in a triangle)
3a + 75 = 180
adding -75 to both sides:
3a + 75 - 75 = 180 - 75
3a = 105
a = 105/3
a = 35°
Hence 2a = 2(35) = 70°
Therefore a = 35° and 2a = 70°
0 lol this is funny thanks for free points
Answer:
-4/3
Step-by-step explanation:
give 90°<Ø<180° show in Q2
and cscØ=5/4
tanØ in Q2 is minus
so tanØ is -4/3 #
Answer:
Step-by-step explanation:
let the national average be x
11/100 * x = 11x/100
25.47 - x = 11x/100
100(25.47-x) = 11x
2547 - 100x = 11x
2547 = 11x + 100x
2547 = 111x
x = 2547/111
x = 22.945945945946
22.95