Answer:
Binomial distribution requires all of the following to be satisfied:
1. size of experiment (N=27) is known.
2. each trial of experiment is Bernoulli trial (i.e. either fail or pass)
3. probability (p=0.14) remains constant through trials.
4. trials are independent, and random.
Binomial distribution can be used as a close approximation, with the usual assumption that a sample of 27 in thousands of stock is representative of the population., and is given by the probability of x successes (defective).
P(x)=C(N,x)*p^x*(1-p)^(n-x)
where N=27, p=0.14, and C(N,x) is the number of combinations of x items out of N.
So we need the probability of <em>at most one defective</em>, which is
P(0)+P(1)
= C(27,0)*0.14^0*(0.86)^(27) + C(27,1)*0.14^1*(0.86^26)
=1*1*0.0170 + 27*0.14*0.0198
=0.0170+0.0749
=0.0919
Using proportions, the coordinates of the point 3/4 of the way from P to Q are: (0,4).
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We want to find the coordinates of point M(x,y) 3/4 of the way from P to Q, hence the rule is given by:
M - P = 3/4(Q - P)
For the x-coordinate, we have that:
x + 6 = 3/4(2 + 6)
x + 6 = 6
x = 0.
For the y-coordinate, we have that:
y + 5 = 3/4(7 + 5)
y + 5 = 9.
y = 4.
The coordinates are (0,4).
More can be learned about proportions at brainly.com/question/24372153
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Answer:
Option 3
Step-by-step explanation:
It is the only one that increases by 8 just like the pattern
There are 4 triangles with base of 5 and height of 8.4
Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 5 x 8.4 = 21 m^2
Multiply by 4 = 21 x 4 = 84 m^2
Area of the base = length x width = 5 x 5 = 25 m^2
Total area = 84 + 25 = 109 m^2
7 x 500,080=7 x (500,000+80)=7 x 500,000+7 x 80=3,500,000+560=3,500,560
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