Answer:
Step-by-step explanation:
All we have to do is input the given values of x into the functions.
The first function:
f(x) = x^2 - 5x - 6
f(0) = 0^2 - 5(0) - 6 = 0 - 0 - 6 = -6
f(0) = -6
f(2) = 2^2 - 5(2) - 6 = 4 - 10 - 6 = -12
f(2) = -12
f(-1) = -1^2 - 5(-1) - 6 = 1 + 6 - 6 = 1
f(-1) = 1
f(6) = 6^2 -5(6) - 6 = 36 - 30 - 6 = 0
f(6) = 0
The second function:
f(x) = x^3 - x^2 - 12
f(0) = 0^3 - 0^2 - 12 = 0 - 0 - 12 = -12
f(0) = -12
f(2) = 2^3 - 2^2 - 12 = 8 - 4 - 12 = -8
f(2) = -8
f(-1) = -1^3 - (-1)^2 - 12 = -1 - 1 - 12 = -14
f(-1) = -14
f(6) = 6^3 - 6^2 - 12 = 216 - 36 - 12 = 168
f(6) = 168
The third function:
f(x) = 5 * 2^x
f(0) = 5 * 2^0 = 5 * 1 = 5
f(0) = 5
f(2) = 5 * 2^2 = 5 * 4 = 20
f(2) = 20
f(-1) = 5 * 2^-1 = 5 * 0.5 = 2.5
f(-1) = 2.5
f(6) = 5 * 2^6 = 5 * 64 = 320
f(6) = 320
Answer:
a. A and B are disjoint
Step-by-step explanation:
We know that P(A and B)=0, It means that event A and event B have nothing in common and it means that event A and event B are disjoints events.
The event A and event B are independent if
P( A and B)= P(A)*P(B)
P(A)*P(B)=0.3*0.2=0.06
So, P(A and B)≠P(A)*P(B)
Hence events A and B are not independent.
Option a is A and B are disjoints which is correct
Option b is A and B are neither disjoints nor independent which is partially false as A and B are disjoints event.
Option c states that A and B are independent which is clearly false.
Option d states that A and B are disjoints and independent which is partially false as A and B are not independent.
Hence the correct option is option A.
Answer:
The answer is
and 
Step-by-step explanation:
Given:
-4x-2y=14
-10x+7y=-24
Now, to solve it by elimination:
......(1)
......(2)
So, we multiply the equation (1) by 7 we get:

And, we multiply the equation (2) by 2 we get:

Now, adding both the new equations:




<em>Dividing both the sides by -8 we get:</em>

Now, putting the value of
in equation (1):




<em>Subtracting both sides by 25 we get:</em>

<em>Dividing both sides by -2 we get:</em>

Therefore, the answer is
and 
Solution:
Given:
A table representing an exponential function.
The x-values represent the terms, while the y-values represent the numbers.
The common ratio is gotten from the numbers (y-values).
The formula for common ratio is given by;

Therefore, the common ratio is 3.