Answer:
12.61 miles
Step-by-step explanation:
The distance of lighthouse B from lighthouse A, the distance from lighthouse A to the boat and the distance of lighthouse B from the boat all form a triangle. Since lighthouse B is west of lighthouse A, and at a distance of 9 miles form lighthouse A, light house A is at a bearing of North 90° East of lighthouse B. The distance from lighthouse A to the boat is 6 miles, and the bearing of the boat from lighthouse B is North 64° East.
So, the angle between the distance from lighthouse B to the boat and lighthouse B to lighthouse A is 90° - 64° = 26°
Since we have two sides and an angle, we use the sine rule
a/sinA = b/sinB where a = 6, A = 26°, b = 9, B = unknown
So, sinB = bsinA/a
= 9sin26/6
= 3(0.4384)/2
= 1.3151/2
= 0.6576
B = sin⁻¹(0.6576)
= 41.11°
≅ 41.1°
We now find the third angle in the triangle, C(the angle facing the distance from lighthouse B to the boat) from
26° + 41.1° + C = 180° (sum of angles in a triangle)
67.1° + C = 180°
C = 180° - 67.1° = 112.9°
Using the sine rule again to find the third side, c(the distance from lighthouse B to the boat), we have
a/sinA = c/sinC
c = asinC/sinA
= 6sin112.9°/sin26°
= 6(0.9212)/0.4384
= 5.5271/0.4384
= 12.61 miles
Answer:
(d) The sale was for a 29% decrease.
Step-by-step explanation:
Original/Regular price = $42.25
New/Sale price = $29.95
Difference in prices = 42.25 - 29.95 = 12.3
Formula for finding the percentage decrease of the sale
= × 100
× 100
=
≈ 29.11 %
≈ 29 %
Therefore, the percent off the watch during the sale was approximately 29%.
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Answer: 1443
Step-by-step explanation:
Formula we use to find the sample size , if prior proportion is available :-
Given : Percent of the claims are covered : p= 60% =0.60
Margin of error : E=3% = 0.03
Critical value for 98 % confident :
Then , the required sample will be :
Hence, the required sample size = 1443