Answer:
(1) For x = –12, g (x) = -9
For x = –9, g (x) = -3
For x = –6, g (x) = 3
For x = –3, g (x) = 9
(2) The principal amount of money is $80.
Step-by-step explanation:
(1)
The expression of g (x) is,
The complete table is:
x g (x)
-15 
-12 
-9 
-6 
-3 
0 
(2)
The formula for simple interest is:
Given:
I = $40
r = 10%
t = 5 years.
Compute the value of <em>P</em> as follows:
Thus, the principal amount of money is $80.
Newton's Law of Cooling states that the change
of the temperature of an object is proportional to the difference between its
own temperature and the ambient temperature over time.
Therefore when expressed mathematically, this is equivalent
to:
dT = - k (T – Ts) dt
dT / (T – Ts) = - k dt
Integrating:
ln [(T2– Ts) / (T1– Ts)] = - k (t2 – t1)
Before we plug in the values, let us first convert the
temperatures into absolute values R (rankine) by adding 460.
R = ˚F + 460
T1 = 200 + 460 = 660 R
Ts = 70 + 460 = 530 R
ln [(T2– 530) / (660 – 530)] = - 0.6 (2 - 0)
T2 = 569.16 R
T2 = 109 ºF
Answer: After 2 hours, it will be 109 ºF
Answer:
d. The random variable is the number of years in which the temperature increased from the previous year.
Step-by-step explanation:
The random variable is the amount of years that have higher average temperatures than its previous year.
As the sample is from 5 years, the random variable can take values from 0 (where none of the years increase their average temperature from its previous year) to 4 (where every year increases the average temperature).
To answer this question, an assumption must be made, that Eva spends 8 hours a day working. If this is the case, then Eva will complete jobs w, x, and v on day one, for a total of six hours. Since the next job (y) requires 4 hours, she will spend two hours working that day, leaving 2 more hours to go on that job. The next day she will spend 2 hours finishing job y, completing it, and finish the longest job z (hours) that day. This means she had 4 jobs on day one, and 2 jobs on day 2 for and average of 3 jobs per day.
This answer assumes an 8 hour work day, and that Eva can start a job she cannot finish that day.
