dave picked 1/5 of a pound strawberries.that afternoon daves sister ate 4/5 of the strawberries.how many pounds of strawberries
1 answer:
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For a better understanding of the solution provided here please find the diagram in the attached file.
In the diagram, A is the intersection. B is the position of the first car and C is the position of the second car. As can be clearly seen, as per the directions given in the question, the cars and the intersection make a right triangle.
The distance between the first car and the intersection is and the distance between the second car and the intersection is
. The distance between the two cars is depicted by
. As we can see,
is the hypotenuse of the right triangle. At the given instance the distances are 8 meters and 6 meters respectively. Thus, by the Pythagorean Theorem the hypotenuse will be:
...............(Equation 1)
Now, we know that at any instant the Pythagorean Theorem holds and so we will have, in general:
Now, implicitly differentiating the above formula with respect to time, we get:
This can be further simplified by dividing both the sides by the common factor 2 as:
.................(Equation 2)
As we can see from the questions and the diagram, and
. The negative sign is there because the distances y and x are reducing as the cars approach the intersection.
Applying this knowledge to (Equation 2) along with the fact that as per (Equation 1), , we get (Equation 2) to become:
Therefore,
Thus, the rate of change of the distance between the cars at the given instant (in meters per second) is .
Therefore, out of the given options, option D is the correct one.
Answer:
The probability is 0.971032
Step-by-step explanation:
The variable that says the number of components that fail during the useful life of the product follows a binomial distribution.
The Binomial distribution apply when we have n identical and independent events with a probability p of success and a probability 1-p of not success. Then, the probability that x of the n events are success is given by:
In this case, we have 2000 electronics components with a probability 0.005 of fail during the useful life of the product and a probability 0.995 that each component operates without failure during the useful life of the product. Then, the probability that x components of the 2000 fail is:
(eq. 1)
So, the probability that 5 or more of the original 2000 components fail during the useful life of the product is:
P(x ≥ 5) = P(5) + P(6) + ... + P(1999) + P(2000)
We can also calculated that as:
P(x ≥ 5) = 1 - P(x ≤ 4)
Where P(x ≤ 4) = P(0) + P(1) + P(2) + P(3) + P(4)
Then, if we calculate every probability using eq. 1, we get:
P(x ≤ 4) = 0.000044 + 0.000445 + 0.002235 + 0.007479 + 0.018765
P(x ≤ 4) = 0.028968
Finally, P(x ≥ 5) is:
P(x ≥ 5) = 1 - 0.028968
P(x ≥ 5) = 0.971032