Answer:
9
Step-by-step explanation:
The length of the paper , x, can be obtained using Pythagoras :
Width = 12 ; length = 15
x² = 15² - 12²
x² = 225 - 144
x² = 81
x = sqrt(81)
x = 9
Hence, length of the paper = 9 inches
These are four questions and four answers:
Question 1. What is the petrochemical production in 2005?
Solution:
1) The table reports the the annual Petrochemical Production p (Billion metric tons) for 2005 - 2011.
2) The years are indicated as 0, 1, 2, 3, 4, 5, 6.
3) There is a contradiction in the stament because there is a note telling that t = 0 is year 2002, which meant that the years are from 2002 - 2008, contradicting that the years are 2005 - 2011.
4) If you take for good the note the t = 3 is year 2005 and the corresponding production is 12.0, which is the option A).
5) If you take for good the initial statement that the years are 2005 - 2011, then t = 0 is 2005 and the corresponding production is 10.8
So you have to clarify with your teacher which is the right statement.
Question 2. What are the units.
Solution:
The units are indicated in parenthesis after the label of the row.
The label of the row is Petrochemical production p and the units are Billion metric tons.
So, the answer is the option D) billion metric tons.
Question 3. Graph the function f(x) = log base 2 of x
Solution:
You might create a table with some four points or use the knowledge about logarithm function.
Thiis is the knowledge you need to answer the question:
1) logarithm is an increasing function: as x increase f(x) increase)
2) log base a of a = 1
3) limit of log base a of x when x approaches 0 is negative infinity.
With those three properties you know that the answer is the first figure with certainty.
Question 4. Graph the function f(x) = 2^x
Solution:
These properties will give you the answer:
1) 2^x is the inverse function of log base 2 of x (the function of the question 2)
2) 2^0 = 1
3) 2^x is a growing function (as x increases 2^x increases)
4) 2^x is always positive.
5) limit of 2^x when x approaches negative infinity is 0.
With that you are sure that the graph of 2^x is the second figure.
Answer:
![\displaystyle greater\:than \\ Line\:B: [-6, 0] \\ Line\:A: [2, 0]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20greater%5C%3Athan%20%5C%5C%20Line%5C%3AB%3A%20%5B-6%2C%200%5D%20%5C%5C%20Line%5C%3AA%3A%20%5B2%2C%200%5D)
Step-by-step explanation:
The x-intercept of Line B is already given to you because it is where the graph intersects the x-axis.
Now, to get the x-intercept of Line A, plug 0 in for <em>y</em><em> </em>to get this:
0 = −2x + 4
- 4 - 4
_____________
So, the x-intercept of Line A is ![\displaystyle [2, 0],](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5B2%2C%200%5D%2C)
and since 2 is greater than −6, <em>greater than</em> would be your answer.
I am joyous to assist you anytime.
Answer:
12.5%
Step-by-step explanation:
Answer:
a) 0.2416
b) 0.4172
c) 0.0253
Step-by-step explanation:
Since the result of the test should be independent of the time , then the that the test number of times that test proves correct is independent of the days the river is correct .
denoting event a A=the test proves correct and B=the river is polluted
a) the test indicates pollution when
- the river is polluted and the test is correct
- the river is not polluted and the test fails
then
P(test indicates pollution)= P(A)*P(B)+ (1-P(A))*(1-P(B)) = 0.12*0.84+0.88*0.16 = 0.2416
b) according to Bayes
P(A∩B)= P(A/B)*P(B) → P(A/B)=P(A∩B)/P(B)
then
P(pollution exists/test indicates pollution)=P(A∩B)/P(B) = 0.84*0.12 / 0.2416 = 0.4172
c) since
P(test indicates no pollution)= P(A)*(1-P(B))+ (1-P(A))*P(B) = 0.84*0.88+ 0.16*0.12 = 0.7584
the rate of false positives is
P(river is polluted/test indicates no pollution) = 0.12*0.16 / 0.7584 = 0.0253
