The table shows the results of (p ^ q) and results of (p ^ r) for all possible outcomes. We have to tell which of the outcomes of union of both these events will always be true.
(p ^ q) V (p ^ r) means Union of (p ^ q) and (p ^ r). The property of Union of two sets/events is that it will be true if either one of the event or both the events are true i.e. there must be atleast one True(T) to make the Union of two sets to be True.
So, (p ^ q) V (p ^ r) will be TRUE, if either one of (p ^ q) and (p ^ r) or both are true. From the given table we can see that only the outcomes A, B and C will result is TRUE. The rest of the outcomes will all result in FALSE.
Therefore, the answer to this question is option 2nd
Answer:
Step-by-step explanation:
Please consider the attached image as the given square.
We are asked to express the shaded area as a fraction, a decimal, and a percent of the whole.
We can see that in our figure there are 100 squares as there are 10 rows and each row contains 10 squares.
We can also see that there are 81 shaded squares out of 100 squares, so we can represent it as a fraction as:
To convert the shaded area into decimal, we need to divide 81 by 100.
To convert the shaded area into percent, we need to multiply 0.81 by 100.
Answer:
0.95 = 95% probability that the next person to purchase this car will request at least one of automatic transmission or built-in GPS
Step-by-step explanation:
We solve this question treating these probabilities as Venn sets.
I am going to say that:
Event A: Requesting automatic transmission
Event B: Requesting built-in GPS
90% of all buyers request automatic transmission
This means that 
82% of all buyers request built-in GPS
This means that 
77% of all buyers request both automatic transmission and built-in GPS.
This means that 
What is the probability that the next person to purchase this car will request at least one of automatic transmission or built-in GPS
This is
, which is given by:

So

0.95 = 95% probability that the next person to purchase this car will request at least one of automatic transmission or built-in GPS
Answer:
No complex roots; 3 real roots
Step-by-step explanation:
If a third order polynomial has any complex roots, then as a rule it has 1 real root and 2 complex roots. In this particular case, the polynomial has three real roots, as can be determined by graphing the function. The graph crosses the x-axis in 3 places.
Answer:
a. 5
Step-by-step explanation:
To find slope, subtract the y's.
5 - -5 is 10.
Put that on the top of a fraction.
Subtract the x's.
3 - 1 is 2, put that on the bottom of the fraction.
So the slope is 10/2. This simplifies to 5 (because 10÷2 is 5).
The slope is 5.