........................................
2 answers:
<u>Answer:</u>
vii. x = 70° viii. x = 60°
<u>Step-by-step explanation:</u>
vii.
The purple line drawn is parallel to the lines PQ and ST.
∴ ∠ a + 130° = 180° [alternate angles]
⇒ ∠ a = 50°
x = a + 20° [Co-interior angles with angle ]
⇒ x = 50° + 20°
⇒ x = 70°
viii.
The yellow line drawn and the line AB are parallel.
∴ n° + 130° = 180° [Co-interior angles]
n = 50°
The green line and line DE are parallel.
∴ m° + 110° = 180° [Co-interior angles]
m = 70°
n + m + x = 180° [Angles on a straight line]
⇒ 50° + 70° + x = 180°
⇒ x = 60°
Answer:
vii) x = 70° viii) x = 60°
Step-by-step explanation:
Please refer to the attached photos for better understanding (Apologies for the terrible drawing.)
vii) Angle RSV + Angle RST = 180° (Sum of angles in a straight line)
Angle RSV + 130° = 180°
Angle RSV = 180° - 130°
= 50°
Angle RVS + Angle RSV + Angle SRV = 180° (Sum of angles in a triangle)
Angle RVS + 50°+ 20° = 180°
Angle RVS = 180° - 70° = 110°
Angle RVX + Angle RVS = 180° (Sum of angles in a straight line)
Angle RVX + 110° = 180°
Angle RVX = 180° - 110° = 70°
Angle x = Angle RVX = 70° (Corresponding Angles)
viii) Angle FDG + Angle CDE = 180° (Sum of angles in a straight line)
Angle FDG + 110° = 180°
Angle FDG = 180° - 110°
= 70°
Angle BGC = Angle FDG = 70° (Corresponding Angles)
Angle CBG + Angle ABC = 180° (Sum of angles in a straight line)
Angle CBG + 130° = 180°
Angle CBG = 180 - 130°
= 50°
Angle x + Angle CBG + Angle BGC = 180° (Sum of angles in a triangle)
Angle x + 50° + 70° = 180°
Angle x = 180° - 120° = 60°
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Step-by-step explanation:
Given:
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Now, to find the surface area(SA) of the right regular hexagonal pyramid.
So, we find the area of the base(b) first:
Area of the base =
=
On solving we get:
Area of the base(b) =
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Perimeter = s × 6
Now, putting the formula for getting the surface area:
Surface area = perimeter × height/2 + Area of the base.
As, <em>the surface area is 50.784 and rounding to nearest hundredth becomes 50.78 because in hundredth place it is 8 and in thousandth place it is 4 so rounding to it become 50.78.</em>
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Answer:
If the observed sample mean is greater than 17.07 minutes, then we would reject the null hypothesis.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 15 minutes
Sample size, n = 10
Alpha, α = 0.05
Population standard deviation, σ = 4 minutes
First, we design the null and the alternate hypothesis
Since the population standard deviation is given, we use one-tailed z test to perform this hypothesis.
Formula:
Now,
Thus, we would reject the null hypothesis if the z-statistic is greater than this critical value.
Thus, we can write:
Thus, the decision rule would be if the observed sample mean is greater than 17.07 minutes, then we would reject the null hypothesis.