Answer:
a) 
b) 
c) 
d) 
Step-by-step explanation:
For each container, there are only two possible outcomes. Either it is undefilled, or it is not. This means that we can solve this problem using the binomial probability distribution.
Binomial probability distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which 
is the number of different combinatios of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem
There are 10 containers, so 
.
A food-packaging apparatus underfills 10% of the containers, so 
.
a) This is P(X = 1)
b) This is P(X = 3)
c) This is P(X = 9)
d) This is 
.
Either the number is lesser than five, or it is five or larger. The sum of the probabilities of each event is decimal 1. So:
In which
So
Finally
Given that we assume that all the bases of the triangles are parallel.
We can use AAA or Angle-Angle-Angle to prove that these triangles are similar.
Each parallel line creates the same angle when intersecting with the same side.
For example:
The bases of each triangle cross the left side of all the triangle.
Each angle made by the intersecting of the the parallel base and the side are the same.
Thus, each corresponding angle of all the triangles are congruent.
If these angles are congruent, then we have similar triangles.
Answer:
36
Step-by-step explanation:
If you set the equation up, it would be n + 5 = 41. If you subtract the 5 from both sides to get n by itself, you get n = 36.
Solutions
To solve the problem the first step is to m<span>ultiply the whole number by the fraction's denominator (4 x 3).Add the numerator (2) to the product.
4 * 3 = 12
12 + 2 = 14
= 14/3 </span>
