Зcx + cx = 7 solve for x if c represents a consonant
1 answer:
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Answer:
The length of the shadow is increasing with the rate of 1.5 feet per sec
Step-by-step explanation:
Let AB and CD represents the height of the lamppost and child respectively ( shown below )
Also, let E be a point represents the position of child.
In triangles ABE and CDE,
( right angles )
( common angles )
By AA similarity postulate,
∵ Corresponding sides of similar triangles are in same proportion,
We have, AB = 12 ft, CD = 4 ft, BE = BD + DE = 6 + DE,
Now, the speed of walking = 2 mph =
Note: 1 mile = 5280 ft, 1 hour = 3600 sec
Thus, the time taken by child to reach at E
= 2.045 hours
Hence, the change rate in the length of shadow
= 1.5 ft per sec.
Answer: The events are independent
a) p = 1/36 b) p = 5/216
Step-by-step explanation: both events are independent because the fact that the first die shows it sample space {1, 2, 3, 4, 5, 6} does not stop the second die from showing it own sample space too which is {1, 2, 3, 4, 5, 6}.
The sample space of first die = {1, 2, 3, 4, 5, 6}
The sample space of second die = {1, 2, 3, 4, 5, 6}
The sample space of 2 dice rolled at once is seen as attachment to this answer, find attachment below.
Probability that an event will occur = number of time the event will occur / total number of possible outcome of the event
a)
Probability that first die will show 3 = number of times 3 shows up in the event / total number of outcome of the die = P (3)
P (3) = 1/6
Probability that 2 dice sum up to give 7 = 6/ 36 = 1/6 ( from the sample space for 2 dice attached, it is seen that the sum of 7 comes out 6 times and the total sample space is 36)
P (first die show 3) = 1/6
P ( 2 dice sum to 7) = 1/6
P ( first die show 3) and P ( 2 dice sum to 7) = 1/6 * 1/6 = 1/36.
b)
Probability of the first die showing 4 = P(4) = 1/6
Probability of 2 die sum up to give 8 = 5/36
P ( first die show 8) and P ( 2 die sum up to give 8) = 1/6 * 5/36 = 5/216
