Step-by-step explanation:
Angle EGF = 0.5(180° - 50°) = 65°.
Angle CGF = 180° - Angle EGF = 115°.
Solution:
Given,
Volume of the-
First cube box=1728 in³
Second cube box=13824in³
We know that volume of cube =a³
So for the first box
a³= 1728 in³
a= 12 in
Now, surface area of the first box
6a²= 6×(12)²
= 864 in²
and for the second box
b³= 13824 in³
b= 24 in
Now, the surface area of the second box
6b²= 6×(24)²
= 3456 in²
Now, the ratio of the surface area of first box to the second box will be
864:3456
=1:4
The surface area of the larger of two boxes is
3456 in²
Answer:
Margin of error for a 95% of confidence intervals is 0.261
Step-by-step explanation:
<u>Step1:-</u>
Sample n = 81 business students over a one-week period.
Given the population standard deviation is 1.2 hours
Confidence level of significance = 0.95
Zₐ = 1.96
Margin of error (M.E) = 
Given n=81 , σ =1.2 and Zₐ = 1.96
<u>Step2:-</u>
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On calculating , we get
Margin of error = 0.261
<u>Conclusion:-</u>
Margin of error for a 95% of confidence intervals is 0.261
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There is a theorem that says that this angle (formed by thre points on the circumference) is half such arc called EF.
We can deduct it as well.
1) Call O the center of the circle. The central angle (EOF) = arc EF = 151°
2) Draw a chord from F to D and other chord from D to E.
You have constructed two triangles, FOD and DOE.
3) Triangle FOD has two sides equals (because both are the radius of the circcle). Then, this is an isosceles triangle and it has two angles of the same measure. Call this measure a.
4) Triangle DOE is also isosceles, for the same reason explained in the poiint 3. Call the measure of its equal angles b.
5) The sum of the angles of the two triangles is 180° + 180 ° = 360°.
This is a + a + b + b + (360 - central angle) = 360°
=> 2a + 2b = central angle
=> 2(a+b) = cantral angle
=> (a+b) = central angle / 2 = 151° / 2 =71.5°
(a+b) is the angle that you are looking for.
Then the answer is 71.5°
