The decay of 192 mg of an isotope is given by A(t)= 192e-0.015t, where t is time in years. Find the amount left after 55 years.
1 answer:
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Answer:
168.7602 miles
Step-by-step explanation:
One way to solve this problem is by using an equation that describes the listening radius of the station, and another for the road, then the points where this two-equation intersect each other will represent when the driver starts and stops listening to the station, and the distance between the points is the miles that the driver will receive the signal.
The equation for the listening radius (the radio station is at (0,0)):
The equation for the road that past through the points (-120,0) and (80,100) (Collinsville and Harmony respectively):
Substitutes the value of y in the equation of the circle:
The formula to solve second-degree equations:
Using the values in x to find the values in y:
The distance between the points (51.4718,85.7359) and (-99.4718,10.2641) :
Answer:
The cities are approximately 1452 km apart
Step-by-step explanation:
The two cities are on the same Longitude 90°W therefore the distance between them is on a great circle
Latitude of the first city = 23°N
Latitude of the second city = 36° N
Because their latitude are on the same polar axis, we subtract to get the angular difference
Angular Difference = 36 -23 =13°
where
The cities are approximately 1452 km apart
Answer:
- When Two containers are selected
(a) Probability that the second one selected is defective given that the first one was defective = 0.00450
(b) Probability that both are defective = 0.0112461
(c) Probability that both are acceptable = 0.986
2. When Three containers are selected
(a) Probability that the third one selected is defective given that the first and second one selected were defective = 0.002.
(b) Probability that the third one selected is defective given that the first one selected was defective and the second one selected was okay = 0.00451
(c) Probability that all three are defective = 6.855 x .
Step-by-step explanation:
We are given that a batch of 445 containers for frozen orange juice contains 3 defective ones i.e.
Total containers = 445
Defective ones = 3
Non - Defective ones = 442 { Acceptable ones}
- Two containers are selected, at random, without replacement from the batch.
(a) Probability that the second one selected is defective given that the first one was defective is given by;
<em>Since we had selected one defective so for selecting second the available </em>
<em> containers are 444 and available defective ones are 2 because once </em>
<em> chosen they are not replaced.</em>
Hence, Probability that the second one selected is defective given that the first one was defective = = 0.00450
(b) Probability that both are defective = P(first being defective) +
P(Second being defective)
= = 0.0112461
(c) Probability that both are acceptable = P(First acceptable) + P(Second acceptable)
Since, total number of acceptable containers are 442 and total containers are 445.
So, Required Probability = = 0.986
- Three containers are selected, at random, without replacement from the batch.
(a) Probability that the third one selected is defective given that the first and second one selected were defective is given by;
<em>Since we had selected two defective containers so now for selecting third defective one, the available total containers are 443 and available defective container is 1 .</em>
Therefore, Probability that the third one selected is defective given that the first and second one selected were defective = = 0.002.
(b) Probability that the third one selected is defective given that the first one selected was defective and the second one selected was okay is given by;
<em>Since we had selected two containers so for selecting third container to be defective, the total containers available are 443 and available defective containers are 2 as one had been selected.</em>
Hence, Required probability = = 0.00451 .
(c) Probability that all three are defective = P(First being defective) +
P(Second being defective) + P(Third being defective)
= = 6.855 x
.