A rhombus has diagonals of 10cm and 6cm. Find the angles of the rhombus and its area.
1 answer:
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Answer:
(a) 0.94
(b) 0.20
(c) 90.53%
Step-by-step explanation:
From a population (Bernoulli population), 90% of the bearings meet a thickness specification, let be the probability that a bearing meets the specification.
So,
Sample size, , is large.
Let X represent the number of acceptable bearing.
Convert this to a normal distribution,
Mean:
Variance:
(a) A shipment is acceptable if at least 440 of the 500 bearings meet the specification.
So,
Here, 440 is included, so, by using the continuity correction, take x=439.5 to compute z score for the normal distribution.
.
So, the probability that a given shipment is acceptable is
Hence, the probability that a given shipment is acceptable is 0.94.
(b) We have the probability of acceptability of one shipment 0.94, which is same for each shipment, so here the number of shipments is a Binomial population.
Denote the probability od acceptance of a shipment by .
The total number of shipment, i.e sample size,
Here, the sample size is sufficiently large to approximate it as a normal distribution, for which mean, , and variance,
.
Mean:
Variance:
.
In this case, X>285, so, by using the continuity correction, take x=285.5 to compute z score for the normal distribution.
.
So, the probability that a given shipment is acceptable is
Hence, the probability that a given shipment is acceptable is 0.20.
(c) For the acceptance of 99% shipment of in the total shipment of 300 (sample size).
The area right to the z-score=0.99
and the area left to the z-score is 1-0.99=0.001.
For this value, the value of z-score is -3.09 (from the z-score table)
Let, be the required probability of acceptance of one shipment.
So,
On solving
Again, the probability of acceptance of one shipment, , depends on the probability of meeting the thickness specification of one bearing.
For this case,
The area right to the z-score=0.97790
and the area left to the z-score is 1-0.97790=0.0221.
The value of z-score is -2.01 (from the z-score table)
Let be the probability that one bearing meets the specification. So
On solving
Hence, 90.53% of the bearings meet a thickness specification so that 99% of the shipments are acceptable.
Observe the graph below. This graph represents the scenario.
The question is ill formated, the complete question is
In a simulation, a moving object accelerates from rest to 4 meters per second in 2 seconds. For the following three seconds, it increases linearly until it reaches a speed of 10 meters per second. Following three seconds at that speed (acceleration = 0), the item progressively decelerates until it comes to rest two seconds later. Draw the graph of this scenario for 10 seconds?
I'll describe how the graph may show.
It will move diagonally upward from time 0 to 2 seconds until it reaches the y axis at a speed of 4 m/s.
Then, from 2 to 5, the position will move up diagonally until it reaches the y axis at a speed of 10 m/s.
The next 5 to 8 seconds will be horizontal.
After that, it will descend diagonally.
Observe the graph below. This graph represents the scenario.
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