Answer:
- 5.8206 cm
- 10.528 cm
- 23.056 cm^2
Step-by-step explanation:
(a) The Law of Sines can be used to find BD.
BD/sin(48°) = BD/sin(50°)
BD = (6 cm)(sin(48°)/sin(60°)) ≈ 5.82064 cm
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(b) We can use the Law of Cosines to find AD.
AD^2 = AB^2 +BD^2 -2·AB·BD·cos(98°) . . . . . angle ABD = 48°+50°
AD^2 ≈ 110.841
AD ≈ √110.841 ≈ 10.5281 . . . cm
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(c) The area of ∆ABD can be found using the formula ...
A = ab·sin(θ)/2 . . . . . where a=AB, b=BD, θ = 98°
A = (8 cm)(5.82064 cm)sin(98°)/2 ≈ 23.0560 cm^2
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Angle ABD is the external angle of ∆BCD that is the sum of the remote interior angles BCD and BDC. Hence ∠ABD = 48° +50° = 98°.
Answer:
q1=11
q3= 33
Step-by-step explanation:
The data set has 44 number of students. The first quartile is 25 % of the numbers in the data set . So
25 % of 44 = 25/100 * 44= 0.25 *44 = 11
So the first quartile lies at 11.
Similarly the third quartile lies at the 75 % of the numbers of the data set . So
75 % of 44 = 75/100 * 44= 0.75 *44 = 33
So the third quartile lies at 33.
Answer:
35 is the integer that represents the change in number of gallons of water in the tank after 7 days
Step-by-step explanation:
The water tank leaks 5 gallons in one day.
So if there is leakage of 5 gallons a day, then after 7 days the total leakage will be:
Total Leakage = Leakage per day * Total number of days
= 5 Gal/day * 7 day
= 35 Gallons
So, 35 is the integer that represents the change in number of gallons of water in the tank after 7 days ..
The proportion of production that is defective and from plant A is
... 0.35·0.25 = 0.0875
The proportion of production that is defective and from plant B is
... 0.15·0.05 = 0.0075
The proportion of production that is defective and from plant C is
... 0.50·0.15 = 0.075
Thus, the proportion of defective product that is from plant C is
... 0.075/(0.0875 +0.0075 +0.075) = 75/170 = 15/34 ≈ 44.12%
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P(C | defective) = P(C&defective)/P(defective)
Answer:
Step-by-step explanation:
El diagrama trigonométrico que representa el enunciado es incluido abajo como adjunto. Las siguientes relaciones trigonométricas describen la localización del globo. (The trigonometric diagram representing the statement is included below as attachment. The following trigonometric relations describes the location of the balloon):
A continuación, se obtiene la distancia horizontal: (The horizontal distance is obtained hereafter):
La altura aproximada del globo es (The approximated height of the globe is):
