Answer:
Step-by-step explanation:
From the given information:
We are to find the following:
1)
Directional hypothesis: The directional hypothesis is the groups with different bedroom lightning conditions having a different proportion of eyesight proportions.
2)
The non directional hypothesis is each group having the same proportion of eyesight problems regardless and independent of the condition of the bedroom lightning.
3)
Control group: Children that slept in darkness
4)
Experimental groups: Children that slept in night light and those that slept with lamp.
5)
Independent variable: Light condition of the bedroom
Dependent variable: Eye sight problem.
Answer:
0.324
Step-by-step explanation:
So we are taking his hits and dividing by his attempts.
Number of hits was 156 and number attempts is 482.
So punch 156 (division sign) 482 into calculator.
You get 0.32365145 approximately.
So the answer to the nearest thousandths is 0.324.
The simplified expression of
is ![10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}](https://tex.z-dn.net/?f=10%5Csqrt%7B6%7D%20%2B%20%206%5Csqrt%7B20%7D%2B%20%2020%5Csqrt%7B3%7D%20%2B%20%2030%5Csqrt%7B2%7D)
The expression is given as:
![2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})](https://tex.z-dn.net/?f=2%5Csqrt%7B30%7D%20%5Ctimes%20%28%5Csqrt5%2B%20%5Csqrt6%2B%20%5Csqrt%7B10%7D%20%2B%20%5Csqrt%7B15%7D%29)
Expand the expression
![2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2\sqrt{30} \times \sqrt5+ 2\sqrt{30} \times \sqrt6+ 2\sqrt{30} \times \sqrt{10} + 2\sqrt{30} \times \sqrt{15}](https://tex.z-dn.net/?f=2%5Csqrt%7B30%7D%20%5Ctimes%20%28%5Csqrt5%2B%20%5Csqrt6%2B%20%5Csqrt%7B10%7D%20%2B%20%5Csqrt%7B15%7D%29%20%3D%202%5Csqrt%7B30%7D%20%5Ctimes%20%5Csqrt5%2B%20%202%5Csqrt%7B30%7D%20%5Ctimes%20%5Csqrt6%2B%20%202%5Csqrt%7B30%7D%20%5Ctimes%20%5Csqrt%7B10%7D%20%2B%20%202%5Csqrt%7B30%7D%20%5Ctimes%20%5Csqrt%7B15%7D)
Factor out 2
![2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{30} \times \sqrt5+ \sqrt{30} \times \sqrt6+ \sqrt{30} \times \sqrt{10} + \sqrt{30} \times \sqrt{15})](https://tex.z-dn.net/?f=2%5Csqrt%7B30%7D%20%5Ctimes%20%28%5Csqrt5%2B%20%5Csqrt6%2B%20%5Csqrt%7B10%7D%20%2B%20%5Csqrt%7B15%7D%29%20%3D%202%28%5Csqrt%7B30%7D%20%5Ctimes%20%5Csqrt5%2B%20%20%5Csqrt%7B30%7D%20%5Ctimes%20%5Csqrt6%2B%20%20%5Csqrt%7B30%7D%20%5Ctimes%20%5Csqrt%7B10%7D%20%2B%20%20%5Csqrt%7B30%7D%20%5Ctimes%20%5Csqrt%7B15%7D%29)
Combine the radicals
![2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{150} + \sqrt{180}+ \sqrt{300} + \sqrt{450})](https://tex.z-dn.net/?f=2%5Csqrt%7B30%7D%20%5Ctimes%20%28%5Csqrt5%2B%20%5Csqrt6%2B%20%5Csqrt%7B10%7D%20%2B%20%5Csqrt%7B15%7D%29%20%3D%202%28%5Csqrt%7B150%7D%20%2B%20%20%5Csqrt%7B180%7D%2B%20%20%5Csqrt%7B300%7D%20%2B%20%20%5Csqrt%7B450%7D%29)
Expand the expression
![2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{25 \times 6} + \sqrt{9 \times 20}+ \sqrt{100 \times 3} + \sqrt{225\times 2})](https://tex.z-dn.net/?f=2%5Csqrt%7B30%7D%20%5Ctimes%20%28%5Csqrt5%2B%20%5Csqrt6%2B%20%5Csqrt%7B10%7D%20%2B%20%5Csqrt%7B15%7D%29%20%3D%202%28%5Csqrt%7B25%20%5Ctimes%206%7D%20%2B%20%20%5Csqrt%7B9%20%5Ctimes%2020%7D%2B%20%20%5Csqrt%7B100%20%5Ctimes%203%7D%20%2B%20%20%5Csqrt%7B225%5Ctimes%202%7D%29)
Evaluate the roots
![2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(5\sqrt{6} + 3\sqrt{20}+ 10\sqrt{3} + 15 \sqrt{2})](https://tex.z-dn.net/?f=2%5Csqrt%7B30%7D%20%5Ctimes%20%28%5Csqrt5%2B%20%5Csqrt6%2B%20%5Csqrt%7B10%7D%20%2B%20%5Csqrt%7B15%7D%29%20%3D%202%285%5Csqrt%7B6%7D%20%2B%20%203%5Csqrt%7B20%7D%2B%20%2010%5Csqrt%7B3%7D%20%2B%20%2015%20%5Csqrt%7B2%7D%29)
Expand
![2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) =10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}](https://tex.z-dn.net/?f=2%5Csqrt%7B30%7D%20%5Ctimes%20%28%5Csqrt5%2B%20%5Csqrt6%2B%20%5Csqrt%7B10%7D%20%2B%20%5Csqrt%7B15%7D%29%20%3D10%5Csqrt%7B6%7D%20%2B%20%206%5Csqrt%7B20%7D%2B%20%2020%5Csqrt%7B3%7D%20%2B%20%2030%5Csqrt%7B2%7D)
Hence, the simplified expression of
is ![10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}](https://tex.z-dn.net/?f=10%5Csqrt%7B6%7D%20%2B%20%206%5Csqrt%7B20%7D%2B%20%2020%5Csqrt%7B3%7D%20%2B%20%2030%5Csqrt%7B2%7D)
Read more about simplified expressions at:
brainly.com/question/8008182
Answer:
{1,4}
Step-by-step explanation:
A={3,6,9}
B={2,3,5,7}
C={1,2,3,4,5}
AUB={2,3,5,6,7,9}
(AUB)'={1,4,8,10}
(AUB)'⋂C={1,4}
Answer:
1 cm
You are going to make one of these bags from a roll of cloth 1 meter wide. What
is the shortest length that you need to cut from the roll for the bag?
Step-by-step explanation: