Answer:
a) The probability that the life of the component is less than or equal to 6000 hours is 58%
b) The probability that the life is greater than 4000 hours is 96%
Step-by-step explanation:
Let's define the variable time as 
, which is measured in hours. Then, according to the problem:
- The probability that the component survives for more than 6000 hours is 0.42
- The probability that the component survives no longer than 4000 hours is 0.04
a) The probability that the life of the component is less than or equal to 6000 needs to be equal to 
.
To see this, think of a full set, whose elements can be separate in two categories, the ones that survive more than 6000 hours (let's call them A and number of elements of this type Na) and the ones that survive less than or equal to 6000 (let's call them B and number of elements of this type Nb). Thus, the total number of elements can be calculate as 
, which represents the unit.
If you want to calculate the proportion of elements of type A, you need to divide the number of element of type A over the total number of elements, which is 
. And the same analysis applies to the proportion of elements of type B: 
. Hence, it is easy to see:
of course this only applies when the elements can be only categorized as one type or the other, which is call in probability, mutually exclusive events.
Using this for:
a) 
b) 
Answer:
Option A. 3.5x + 15 ≥ 55
Step-by-step explanation:
Points Rosh received for becoming a member = 15
Points Rosh received for visiting the moving theater = 3.5
Total points needed for a free movie ticket = 55
For each visit he receives 3.5 points, so for x visits he will receive 3.5x points.
Total points = Points received on becoming a member + Points received on x visits
So,
Total Points = 15 + 3.5x
These points must be at least 55 for a free movie ticket. At least means equal to or greater than. So the total points must be equal to or greater than 55 in order to earn a free movie ticket. This can be expressed as:
3.5x + 15 ≥ 55
So, option A gives the correct answer
Answer:
Step-by-step explanation:
The given options are:
The key to determining which product is negative is to understand the rule of sign multiplication.
Now:
- The product of even negative terms is positive
- The product of odd negative terms is negative.
- The product of positive will always be positive.
In Options A and B, the number of negative signs is even, therefore our result is positive.
In option C, all the terms are positive, therefore our result will be positive.
In Option D, the number of negative signs is odd, therefore our result is negative.
Answer:
error in step 1
Step-by-step explanation:
well where is does the step not make sense?
remember cos(pi) = -1 and sin(pi)=0
that means step 1 is strange... it didn't distribute properly
it should have been:
cos(pi) - cos(A)
hope that helps! ^-^
