Solution
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data
STEP 2: Find the mean
mean is 87.33
STEP 3: Find the median
Answer:
15.7
Step-by-step explanation:
The equation for finding the circumference of a circle is
2 x pi x r(radius). Radius is half the diameter.
5/2=2.5
2 x 3.14 x 2.5
=15.7
Answer:
x = 23
y = 7
z = 11
Step-by-step explanation:
Since ∆PRS ≅ ∆CFH, therefore,
m<R = m<F
13y - 1 = 90° (substitution)
Add 1 to both sides
13y - 1 + 1 = 90 + 1
13y = 91
Divide both sides by 13
13y/13 = 91/13
y = 7
Since ∆PRS ≅ ∆CFH, therefore,
PS = CH
2x - 7 = 39 (substitution)
Add 7 to both sides
2x - 7 + 7 = 39 + 7
2x = 46
Divide both sides by 2
2x/2 = 46/2
x = 23
Since ∆PRS ≅ ∆CFH, therefore,
m<S = m<H
Find m<S
m<S = 180 - (m<P + m<R) (sum of ∆)
m<S = 180 - (28 + (13y - 1)) (substitution)
Plug in the value of y
m<S = 180 - (28 + (13)(7) - 1))
m<S = 180 - (28 + 91 - 1)
m<S = 180 - 118
m<S = 62°
Therefore, since m<S = m<H,
62° = 6z - 4 (substitution)
Add 4 to both sides
62 + 4 = 6z - 4 + 4
66 = 6z
Divide both sides by 6
66/6 = 6z/6
11 = z
Answer:
a) P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90
a= μ-3.16*σ , b= μ+3.16*σ
b) P(Y≥ μ+3*σ ) ≥ 0.90
b= μ+3*σ
Step-by-step explanation:
from Chebyshev's inequality for Y
P(| Y - μ|≤ k*σ ) ≥ 1-1/k²
where
Y = the number of fish that need be caught to obtain at least one of each type
μ = expected value of Y
σ = standard deviation of Y
P(| Y - μ|≤ k*σ ) = probability that Y is within k standard deviations from the mean
k= parameter
thus for
P(| Y - μ|≤ k*σ ) ≥ 1-1/k²
P{a≤Y≤b} ≥ 0.90 → 1-1/k² = 0.90 → k = 3.16
then
P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90
using one-sided Chebyshev inequality (Cantelli's inequality)
P(Y- μ≥ λ) ≥ 1- σ²/(σ²+λ²)
P{Y≥b} ≥ 0.90 → 1- σ²/(σ²+λ²)= 1- 1/(1+(λ/σ)²)=0.90 → 3= λ/σ → λ= 3*σ
then for
P(Y≥ μ+3*σ ) ≥ 0.90
Here in this question, we are to solve for x and get the measure of Angle A
Mathematically,
∠A = ∠B
The reason for this is because both are corresponding angles and corresponding angles are equal.
Since they are equal in value, we can equate the given expressions for each of the two angles
Thus;
7x + 40 = 3x + 112
Let us collect like terms
7x-3x = 112 - 40
4x = 72
x = 72/4
x = 18
But the question asks to get the value of ∠A
From the questionn, we are told that ∠A = 7x + 40
To get the value of ∠A, we need to substitute x
∠A = 7(18) + 40
∠A = 126 + 40
∠A = 166
∠A = 166 and x = 18
