The mean diastolic blood pressure for a random sample of 80 people was 100 millimeters of mercury. If the standard deviation of
1 answer:
The confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41 where the lower limit is 97.59 and the upper limit is 102.41
<h3>How to determine the confidence interval?</h3>We have:
Mean = 100
Sample size = 80
Standard deviation = 11
At 95% confidence interval, the critical z value is:
z = 1.96
The confidence interval is then calculated as:
So, we have:
Evaluate the product
Divide
Split
CI = (100 - 2.41,100 + 2.41)
Evaluate
CI = (97.59,102.41)
Hence, the confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41
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= annually interest rate in decimal form.
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Where
= initial investment.
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And the exponent (4) the 4 quarters in the full year.
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Notice that we are not using the initial investment
since they are the same.
The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
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We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.
For the annually rate we have that:
Where
And the exponent (1) represents the full year.
For the quarterly interest rate we have that:
Where
And the exponent (4) the 4 quarters in the full year.
Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
Notice that we are not using the initial investment
The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.
Answer:
Step-by-step explanation:
Let , we proceed to transform the expression into an equivalent form of sines and cosines by means of the following trigonometrical identity:
(1)
(2)
Now we perform the operations:
(3)
By the quadratic formula, we find the following solutions:
and
Since sine is a bounded function between -1 and 1, the only solution that is mathematically reasonable is:
By means of inverse trigonometrical function, we get the value associate of the function in sexagesimal degrees:
Then, the values of the cosine associated with that angle is:
Now, we have that , we proceed to transform the expression into an equivalent form with sines and cosines. The following trignometrical identities are used:
(4)
(5)
If we know that and
, then the value of the function is: