Answer: C.) 4/27
Step-by-step explanation:
Given that:
One out of three cards is a winner :
P(winning) = 1 / 3
Therefore, P(not winning) = P(losing) :
1 - P(winning) = 1 - 1/3 = 2/3
Probability that shenice will first win on her third try can be interpreted as:
1st try = lose, 2nd try: lose, 3rd try : win
P(losing) × p(losing) × p(winning)
(2/3) × (2/3) × (1/3)
4 / 27
Probability of first winning on third try = 4/27
It would be 5*5*5 which is 125 :D
Answer:
3,520 yds in 2 hours
Step-by-step explanation:
5,280:1 ; 1 mile an hour is 5,280 feet in an hour
10,560:2 ; 2 miles in 2 hours is 5,280+5,280 (10,560) feet in 2 hours
3 ft = 1 yd ; every 3 feet is a yard, so divide 10,560 by 3
10,560/3 = 3520 yds ; Jorge can walk 3,520 yds in 2 hours
cos4x = cos2x
We know that:
cos2x = 1-2cos^2 x
==> cos4x = 1-2cos^2 (2x)
Now substitute:
==> 1-2cos^2 (2x) = cos2x
==> 2cos^2 (2x) + cos2x - 1 = 0
Now factor:
==> (2cos2x -1)(cos2x + 1) = 0
==> 2cos2x -1 = 0 ==> cos2x =1/2 ==> 2x= pi/3
==> x1= pi/6 , 7pi/6
==> x1= pi/6 + 2npi
==> x2= 7pi/6 + 2npi
==> cos2x = -1 ==> 2x= pi ==> x3 = pi/2 + 2npi.
<span>==> x= { pi/6+2npi, 7pi/6+2npi, pi/2+2npi}</span>
When dilation is about the origin, as it is here in every case, the image point coordinates are the original (pre-image) coordinates multiplied by the scale factor.
1. Multiply every coordinate value by 5:
... W' = (-5, 10), X' = (-15, -5), Y' = (25, -5), Z' = (15, 10)
2. Multiply every coordinate value by 1/3:
... A' = (-2, 5), B' = (0, 5/3), C' = (1, 10/3)
3. A' = (2, 8), B' = (6, 2), C' = (2, 2)
4. The image coordinates are 5 times the original coordinates, so ...
... the scale factor of the dilation is 5.
