solution:
The probability mass function for binomial distribution is,
Where,
X=0,1,2,3,…..; q=1-p
find the probability that (p∧ ≤ 0.06) , substitute the values of sample units (n) , and the probability of nonconformities (p) in the probability mass function of binomial distribution.
Consider x to be the number of non-conformities. It follows a binomial distribution with n being 50 and p being 0.03. That is,
binomial (50,0.02)
Also, the estimate of the true probability is,
p∧ = x/50
The probability mass function for binomial distribution is,
Where,
X=0,1,2,3,…..; q=1-p
The calculation is obtained as
P(p^ ≤ 0.06) = p(x/20 ≤ 0.06)
= 50cx ₓ (0.03)x ₓ (1-0.03)50-x
= (50c0 ₓ (0.03)0 ₓ (1-0.03)50-0 + 50c1(0.03)1 ₓ (1-0.03)50-1 + 50c2 ₓ (0.03)2 ₓ (1-0.03)50-2 +50c3 ₓ (0.03)3 ₓ (1- 0.03)50-3 )
=( ₓ (0.03)0 ₓ (1-0.03)50-0 + ₓ (0.03)1 ₓ (1-0.03)50-1 + ₓ (0.03)2 ₓ (1-0.03)50-2 ₓ (0.03)3 ₓ (1-0.03)50-3 )
The Range of a function is the set of all values that that function can take.
Given the sine function f(x)=sinx,
This function is the function which calculates the sine of the values of x.
According to the definition of the sine of an angle x in the unit circle,

,
so the sine of an angle is always larger or equal to -1, and smaller or equal to 1.
This means that the values that the sine function takes are any values between -1 and 1, inclusive.
This determines the Range of the sine function.
So the Range of the sine function is [-1, 1]
This is an isosceles right triangle (AB = BC & ∠ B=90° - Given)
Then the angles at the base are equal and ∠ CAB = ∠ ACB = 45°
Theorem: Segment DE, joining the midpoints of 2 sides is:
1st) parallel to the 3rd side and
2nd) equal to half the measurement of the 3rd side
So if the 3rd side (hypotenuse) = 9 units, DE = 9/2 = 4.5 units
Answer:
The width of the pathway is:
Step-by-step explanation:
To identify the width of the pathway, you must remember the area formula of a rectangle:
- Area of a rectangle = length * width.
From which the width can be cleared:
- Width of a rectangle = area / length.
We know that the length of the terrain was not modified since the pathway is in the perimeter of the rectangle (16 m) and that the new area is 240 m^2, so we only have to replace the cleared formula:
- Width of a rectangle = 240 m^2 / 16 m = 15 m.
The new width is equal to 15 meters, but since the question is not the total width but the width of the pathway, the width of the previously provided land must be subtracted from the value obtained.
- <u>Pathway width = Total width - Garden width.
</u>
- <u>Pathway width = 15m - 8m = 7 meters.</u>
9×2=18. add the tow zeros like this 9×2=18+00=1,800