Answer:
(B) 
General Formulas and Concepts:
<u>Calculus</u>
Limits
Derivatives
- The definition of a derivative is the slope of the tangent line.
Derivative Notation
Instantaneous Rates
- Tangent Line:
Step-by-step explanation:
Since we are trying to find a <em>rate</em> at which W(t) changes, we must find the <em>derivative</em> at <em>t</em> = 3.
We are given 2 close answer choices that would have the same <em>numerical</em> answer but different <em>meanings</em>:
- (A)
- (B)
If we look at answer choice (A), we see that our units would simply just be volume. It would not have the units of a rate of change. Yes, it may be the closest numerically correct answer, but it does not tell us the <em>rate</em> at which the volume would be changing and it is not a derivative.
If we look at answer choice (B), we see that our units would be cm³/s, and that is most certainly a rate of change. Answer choice (B) is also a <em>derivative</em> at <em>t</em> = 3, and a derivative tells us what <em>rate</em> something is changing.
∴ Answer choice (B) will give us the best estimate for the value of the instantaneous rate of change of W(t) when <em>t</em> = 3.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
Using the Empirical Rule, it is found that:
- a) Approximately 99.7% of the amounts are between $35.26 and $51.88.
- b) Approximately 95% of the amounts are between $38.03 and $49.11.
- c) Approximately 68% of the amounts fall between $40.73 and $46.27.
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The Empirical Rule states that, in a <em>bell-shaped </em>distribution:
- 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.
-----------
Item a:
Within <em>3 standard deviations of the mean</em>, thus, approximately 99.7%.
-----------
Item b:
Within 2<em> standard deviations of the mean</em>, thus, approximately 95%.
-----------
Item c:
- 68% is within 1 standard deviation of the mean, so:
Approximately 68% of the amounts fall between $40.73 and $46.27.
A similar problem is given at brainly.com/question/15967965
Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = $300
r = 10% = 10/100 = 0.1
n = 2 because it was compounded 2 times in a year(6 months).
t = 3 years
Therefore,
A = 300(1 + 0.1/2)^2 × 3
A = 300(1 + 0.05)^6
A = 300(1.05)^6
A = $402.03
Answer:
x = 4, TU = 22
Step-by-step explanation:
Given that TS bisects TU at Q , then
TQ = QU , substitute values
5x - 9 = 15 - x ( add x to both sides )
6x - 9 = 15 ( add 9 to both sides )
6x = 24 ( divide both sides by 6 )
x = 4
Thus
TU = 5x - 9 + 15 - x = 4x + 6 = 4(4) + 6 = 16 + 6 = 22
This is the simplest proportion i have seen.
This is how we do it:
=
The answer surprisingly is obvious,
z = 1But we can still do cross multiplication
7z = 7
Divide by 7 to isolate z
7 and 7 cancels out
z = 1
