Sally wants 3 dozen peanut butter cookies, 4 dozen snickerdoodles, and a dozen chocolate chip cookies. How many cookies will Sal
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Answer:
a. distance of the surveyor to the base of the building = 2051.90 ft
b. height of the building = 1384 ft
c. Angle of elevation from the surveyor to the top of the antenna = 38.31°
d. Height of antenna = 237.08 ft
Step-by-step explanation:
The picture above is a illustration of the described event.
a = the height of the flag
b = the height of the building
c = distance of the surveyor from the base of the building
the angle of elevation from the position of the surveyor on the ground to the top of the building = 34°
distance from her position to the top of the building = 2475 ft
distance from her position to the top of the flag = 2615 ft
(a) How far away from the base of the building is the surveyor located?
using the SOHCAHTOA principle
cos 34° = c/2475
c = 0.8290375726 × 2475
c = 2051.8679921
c = 2051.90 ft
(b) How tall is the building
The height of the building = b
sin 34° = opposite /hypotenuse
0.5591929035 = b/2475
b = 0.5591929035 × 2475
b = 1384.0024361
b = 1384.00 ft
(c) What is the angle of elevation from the surveyor to the top of the antenna?
let the angle = ∅
cos ∅ = adjacent/hypotenuse
cos ∅ = 2051.90/2615
cos ∅ = 0.784665392
∅ = cos-1 0.784665392
∅ = 38.310258303
∅ = 38.31°
(d) How tall is the antenna?
height of the antenna = a
sin 38.31° = opposite/hypotenuse
sin 38.31° = (a + b)/2615
sin 38.31° × 2615 = (a + b)
(a + b) = 0.6199159917 × 2615
(a + b) = 1621.0803182
(a + b) = 1621. 08 ft
Height of antenna = 1621. 08 - 1384.00 = 237.08031822 ft
Height of antenna = 237.08 ft
Answer:
The answer is below
Step-by-step explanation:
A sugar refinery has three processing plants, all receiving raw sugar in bulk. The amount of raw sugar (in tons) that one plant can process in one day can be modelled using an exponential distribution with mean of 4 tons for each of three plants. If each plant operates independently,a.Find the probability that any given plant processes more than 5 tons of raw sugar on a given day.b.Find the probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day.c.How much raw sugar should be stocked for the plant each day so that the chance of running out of the raw sugar is only 0.05?
Answer: The mean (μ) of the plants is 4 tons. The probability density function of an exponential distribution is given by:
a) P(x > 5) =
b) Probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day can be solved when considered as a binomial.
That is P(2 of the three plant use more than five tons) = C(3,2) × [P(x > 5)]² × (1-P(x > 5)) = 3(0.2865²)(1-0.2865) = 0.1757
c) Let b be the amount of raw sugar should be stocked for the plant each day.
P(x > a) =
But P(x > a) = 0.05
Therefore:
a ≅ 12