Answer:
Positive and negative intervals on a graph
Step-by-step explanation:
The positive regions of a function are those intervals where the function is above the x-axis. It is where the y-values are positive (not zero). The negative regions of a function are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero). hope this helps you :)
Answer: B
Step-by-step explanation:
In the systems of equation it already gives you the solution for x which is -2 so all you have to do is substitute -2 into the first equation and solve for y.
y= 2/3x + 3
x= -2
Substitute x for -2
y = 
y= 
+ 
y = 
so now you have the solution like this 
Answer:
(a) 1.5 inches
(b) 2.5 inches
(c) 5 inches
Step-by-step explanation:
speed of first turtle = 4 1/2 inches per minute = 9/2 inches per minute
speed of the second turtle = 5inches per minute
distance = speed x time
(a) Distance traveled by first turtle in 3 minutes
s = 9/2 x 3 = 13.5 inches
distance traveled by second turtle in 3 minutes
s' = 5 x 3 = 15 inches
So, the gap is
s'- s = 15 - 13.5 = 1.5 inches
(b) Distance traveled by first turtle in 5 minutes
s = 9/2 x 5 = 22.5 inches
distance traveled by second turtle in 5 minutes
s' = 5 x 5 = 25 inches
So, the gap is
s'- s = 25 - 22.5 = 2.5 inches
(c) Distance traveled by first turtle in 10 minutes
s = 9/2 x 10 = 45 inches
distance traveled by second turtle in 10 minutes
s' = 5 x 10 = 50 inches
So, the gap is
s'- s = 50 - 45 = 5 inches
Answer:
a) P ( E | F ) = 0.54545
b) P ( E | F' ) = 0
Step-by-step explanation:
Given:
- 4 Coins are tossed
- Event E exactly 2 coins shows tail
- Event F at-least two coins show tail
Find:
- Find P ( E | F )
- Find P ( E | F prime )
Solution:
- The probability of head H and tail T = 0.5, and all events are independent
So,
P ( Exactly 2 T ) = ( TTHH ) + ( THHT ) + ( THTH ) + ( HTTH ) + ( HHTT) + ( HTHT) = 6*(1/2)^4 = 0.375
P ( At-least 2 T ) = P ( Exactly 2 T ) + P ( Exactly 3 T ) + P ( Exactly 4 T) = 0.375 + ( HTTT) + (THTT) + (TTHT) + (TTTH) + ( TTTT)
= 0.375 + 5*(1/2)^4 = 0.375 + 0.3125 = 0.6875
- The probabilities for each events are:
P ( E ) = 0.375
P ( F ) = 0.6875
- The Probability to get exactly two tails given that at-least 2 tails were achieved:
P ( E | F ) = P ( E & F ) / P ( F )
P ( E | F ) = 0.375 / 0.6875
P ( E | F ) = 0.54545
- The Probability to get exactly two tails given that less than 2 tails were achieved:
P ( E | F' ) = P ( E & F' ) / P ( F )
P ( E | F' ) = 0 / 0.6875
P ( E | F' ) = 0
