Answer:
d=1
Step-by-step explanation:
Factor d^2 - 2d - 8 into (d-4)(d+2)
Move -2/d+2 onto the other side, changing it into 2/d+2.
Let the empty side equal zero.
Add 3/d-4 and 2/d+2
Then add that to -3d.
Multiply 0 by d+2 and d-4 to get 2d-2 by itself.
2d=2
d=1
I can't edit the equation, but it's d-4 althroughout the question. Sorry for being so slow.
Answer:
below
Step-by-step explanation:
that is the procedure above
Answer:
a. 0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.
b. 0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.
c. 0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute
Step-by-step explanation:
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean:
(95% of data) range from 19 to 75 beats per minute.
This means that between 19 and 75, by the Empirical Rule, there are 4 standard deviations. So
a. What is the probability that the heart rate is less than 25 beats per minute?
This is the p-value of Z when X = 25. So
has a p-value of 0.0582.
0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.
b. What is the probability that the heart rate is greater than 60 beats per minute?
This is 1 subtracted by the p-value of Z when X = 60. So
has a p-value of 0.8238.
1 - 0.8238 = 0.1762
0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.
c. What is the probability that the heart rate is between 25 and 60 beats per minute?
This is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 25. From the previous two items, we have these two p-values. So
0.8238 - 0.0582 = 0.7656
0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute
Answer:
32760 ways
Step-by-step explanation:
Given
Number of Candidates = 15
Job Positions = 4
Required:
Number of outcomes
This question represent selection; i.e. selecting candidates for job positions;
This question can be solved in any of the following two ways
Method 1.
The first candidate can be chosen from any of the 15 candidates
The second candidate can be chosen from any of the remaining 14 candidates
The third candidate can be chosen from any of the remaining 13 candidates
The fourth candidate can be chosen from any of the remaining 12 candidates
Total Possible Selection = 15 * 14 * 13 * 12
<em>Total Possible Selection = 32760 ways</em>
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Method 2:
This can be solved using permutation method which goes thus;
Where n = 15 and r = 4
So;
becomes
<em>Hence, there are 32760 ways</em>