Answer:
s(15)= 
Step-by-step explanation:
Before to getting started ,we have to consider the function which represents sleep decline rate S'(t) =
Since this function is interpreted in this case as a rate of change, we can deduce this funcion is the first derivative of the function of average amount of sleep (S(t)).
In order to find S(t), we will integrate S'(t)
This case corresponds to intergration by substitution
Substituting u=
Computting the differential of u
Now, let's go back to our integral and write it in terms of u, using both definition of u and its defferential.
The integral of a exponential function is itself. So the result is:
Now substitute u back in:
This answer correspond to function of average amount of sleep.
We know that when the semester begins (t=0) , math students sleep an average of 8.1 hours per day so we will use this info in order to find the value of c.
Solve this equation
c=8.1+
c=9.6
Replacing the value of c on S(t)
S(t)= 
Now, let's to find the average of amount of sleep when 15 weeks has elapsed since the start date of the semester.
s(15)=
Answer:
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Answer:
To find the percetage of data points that lie between the points -3.01 and 2.61, on a normal distribution we're going to need the help of a calculator. The result is: 99.42%
Attached you will find the graph that represents the result.
Answer:
x = -3
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do t one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and equals:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction.
Isolate the x. First, add 9 and subtract 4x from both sides:
6x (-4x) - 9 (+9) = 4x (-4x) - 15 (+9)
6x - 4x = -15 + 9
Combine like terms:
6x - 4x = -15 + 9
2x = -6
Next, divide 2 from both sides of the equation:
(2x)/2 = (-6)/2
x = -6/2
x = -3
x = -3 is your answer.
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Important things to note:
- PEMDAS is the order of operation, and equals Parenthesis, Exponents (& Roots), Multiplication, Division, Addition, Subtraction.
- If there is an equal sign and the same variable on both sides, you are trying to isolate that variable.
- Remember to follow the division rule. If you are dividing two negative numbers, your answer will be positive. If you are multiplying two negative numbers, your answer will be positive. If you are dividing or multiplying one positive and one negative number, your answer will be negative.
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