Answer:
(A)The northern lighthouse is 8.2 miles closer than the southern lighthouse.
Step-by-step explanation:
The triangle attached represents the given problem.
First, let us determine the distance of the Boat from each of the lighthouse.
In Triangle ABC,
∠A+∠B+∠C=180 degrees
21+∠B+16=180
∠B=180-37=143 degrees.
Using Law of Sines
![\frac{a}{Sin A}=\frac{b}{Sin B}\\\frac{a}{Sin 21^0}=\frac{60}{Sin 143^0} \\\text{Cross Multiply}\\a*sin143=60*sin21\\a=60*sin21\div sin143\\a=35.73 miles](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7BSin%20A%7D%3D%5Cfrac%7Bb%7D%7BSin%20B%7D%5C%5C%5Cfrac%7Ba%7D%7BSin%2021%5E0%7D%3D%5Cfrac%7B60%7D%7BSin%20143%5E0%7D%20%5C%5C%5Ctext%7BCross%20Multiply%7D%5C%5Ca%2Asin143%3D60%2Asin21%5C%5Ca%3D60%2Asin21%5Cdiv%20sin143%5C%5Ca%3D35.73%20miles)
Similarly
![\frac{c}{Sin C}=\frac{b}{Sin B}\\\frac{c}{Sin 16^0}=\frac{60}{Sin 143^0} \\\text{Cross Multiply}\\c*sin143=60*sin16\\c=60*sin16\div sin143\\c=27.48 miles](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7BSin%20C%7D%3D%5Cfrac%7Bb%7D%7BSin%20B%7D%5C%5C%5Cfrac%7Bc%7D%7BSin%2016%5E0%7D%3D%5Cfrac%7B60%7D%7BSin%20143%5E0%7D%20%5C%5C%5Ctext%7BCross%20Multiply%7D%5C%5Cc%2Asin143%3D60%2Asin16%5C%5Cc%3D60%2Asin16%5Cdiv%20sin143%5C%5Cc%3D27.48%20miles)
Difference in Distance =35.73-27.48=8.25 miles
Therefore, the northern lighthouse is 8.2 miles closer than the southern lighthouse.
Answer: 4/7
Step-by-step explanation:
A p e x
Centre of the circle (-6,-4) and radius =6 units :)
f(n) is the nth term
Each term f(n) is found by adding the terms just prior to the nth term. Those two terms added are f(n-1) and f(n-2)
The term just before nth term is f(n-1)
The term just before the (n-1)st term is f(n-2)
----------------
For example, let's say n = 3 indicating the 3rd term
n-1 = 3-1 = 2
n-2 = 3-2 = 1
So f(n) = f(n-1) + f(n-2) turns into f(3) = f(2) + f(1). We find the third term by adding the two terms just before it.
f3) = third term
f(2) = second term
f(1) = first term
Answer:
Step-by-step explanation:
We would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = randomly chosen values.
µ = mean
σ = standard deviation
From the information given,
µ = 9
σ = 5
1) The proportion of the population that is less than 20 is expressed as
P(x < 20)
For x = 20
z = (20 - 9)/5 = 2.2
Looking at the normal distribution table, the probability corresponding to the z score is 0.986
P(x < 20) = 0.986
2) The probability that a randomly chosen value will be greater than 6 is expressed as
P(x > 6) = 1 - P(x ≤ 6)
For x = 6
z = (6 - 9)/5 = - 0.6
Looking at the normal distribution table, the probability corresponding to the z score is 0.27
P(x > 6) = 1 - 0.27 = 0.73