Answer:
EF is the longest side of △DEF,
DF = 6 cm and
DE = 6 StartRoot 3 EndRoot cm.
Step-by-step explanation:
The angle ∠ EDF = 90° of the right triangle Δ DEF and ∠ DEF = 30° and ∠ EFD = 60°.
The hypotenuse EF is 12 cm.
Now, Sin ∠ EFD = DE/EF
⇒
⇒ DE = 6√3 cm.
Again, Cos ∠EFD = DF/EF
⇒
⇒ DF = 6 cm.
Therefore, EF is the longest side of △DEF, DF = 6 cm and DE = 6 StartRoot 3 EndRoot cm. (Answer)
Answer:
E. The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is greater than the confidence level used for the interval constructed from Y
Step-by-step explanation:
Confidence interval formula is given as
CI = \bar{x} \pm z*(\sigma/\sqrt{n})
Here, we can see that the width of confidence interval is z*(\sigma/\sqrt{n}) , which is dependent only on z critical value, standard deviation (sigma) and sample size (n)
This simply entails that either z or n or both are greater for x as compared to y.
Option E is correct answer because x and y can have sample sizes, but if the z critical is greater for x, then the width will be larger.
There are 7 games in each case.
4+10 = 14
14 ÷2= 7 games
now in a kite, the ∡x and the angle on the opposite side are twins.
the sum of all interior angles in a polygon are 180(n - 2), n = number of sides.
so a kite is a quadrilateral, 4 sides, so its interior angles add up to 180( 4 - 2) = 360°.
we know one side is 26°, and the opposite side is 90°, so the slack is 360 - 26 - 90 = 244°.
so the twins will take half each of that, namely each one takes 244/2 = 122° = ∡x.
6000x = 135000; x ≈ 23.
We are required to have one fire extinguisher for every 6000 ft of space in the building; this means we need to find out how many 6000-ft spaces we have in 135000.
Solving this equation, we divide both sides by 6000:
6000x/6000 = 135000/6000 = 22.5 ≈ 23