A movie earned $40 million in its first week of release. Earnings decreased each successive week by 40%. Which recursive formula
1 answer:
You might be interested in
Answer:
0.2%
Step-by-step explanation:
The given parameters are;
The percentage of product within the correct range = 95%
The percentage of the times the sensor reject boxes of incorrect weight = 98%
The percentage of the times the company reject boxes with correct weight = 1%
We have, FN = 0.9, TN = 9.8, TP = 90 - 0.9 = 89.1, FP = 10 - 9.8 = 0.2
FNR = FN/(FN + TP) = 0.9/(0.9 + 89.1) = 0.01
FPR = 0.2/(0.2 + 9.8) = 0.02
TPR = 89.1/(89.1 + 0.9) = 0.99
TNR = 9.8/(9.8 + 0.2) = 0.98
P(C/A) = TPR × P(C)/((TPR × P(C) + FPR×(1 - P(C)))
Where;
P(C/A) = The probability that a correct weight package is accepted
∴ P(C/A) = 0.99*0.9/(0.99*0.9 + 0.02*0.1) ≈ 0.99776
The probability that a correctly weighed package is rejected, P(C/R), is given as follows;
P(C/R) = 1 - P(C/A)
∴ P(C/R) ≈ 1 - 0.99776 = 0.00224 ≈ 0.2%
The probability that a correctly weighed package is rejected, P(C/R) ≈ 0.2%
<u>Solution- </u>
A researcher placed a petri dish with 32,000 bacterial cells. One hour after being placed in the vacuum chamber, the number of cells in the petri dish had halved. Another hour later, the number of cells had again halved.
This can be represented as exponential decreasing function,
Where,
- a = starting amount = 32000
- r = rate = 50% = 0.5 as the sample becomes halved in each hour
- x = hours
Putting the values,
y-intercept means, where x=0, so
The coordinate of this poin will be (0, 32000)
This means when x=0 or at the starting of the research, the number of bacteria cells was 32000.
After 3 hours, number of bacteria cells will be,
The coordinate of this point will be (3, 4000)
