1. 200% =2
5000 multiplied by 2 equals 10000
2.50% = 0.5
10000 multiplied by 0.5 equals 5000
Answer:
The earnings gap, over a career spanning 30 years, between men and women totals $1,200,150
Step-by-step explanation:
Calculated annually.
The typical male earns $90,761 each year.
The typical female earns $50,756 per annum.
Therefore, the annual difference is:
90,761 - 50,756 = 40,005
Across 30 years:
30*40,005 = 1,200,150
The earnings gap over a 30-year career, when comparing men and women, is $1,200,150
Answer:
Given that the frog jumps every 10 seconds
(using digits from a random number table)
- It requires 7 jumps with 2 in the reverse direction (either left or right) for the frog to get off the board in 60 seconds.
- Alternatively, 3 jumps in the same direction will also lead to the frog being off the board.
- Furthermore, it would take 5 jumps with one in the opposite direction within the time limit of 60 seconds to leave the board.
Step-by-step explanation:
A frog positioned right at the center of a 5ft long board is 2.5 ft away from either edge.
Every 10 seconds, the frog jumps left or right.
If the frog's jumps are LLRLRL, it will remain on the board at the leftmost square.
If it jumps as LLRLL, it will jump off the board after fifty seconds.
Given that the frog jumps every 10 seconds
(using digits from a random number table)
- It requires 7 jumps with 2 in reverse direction (either left or right) for the frog to get off the board in 60 seconds.
- Alternatively, 3 jumps in the same direction will also lead to the frog being off the board.
- Furthermore, it would take 5 jumps with one in the opposite direction within the time limit of 60 seconds to leave the board.
To determine the rates at which the inlet and outlet pipes fill and empty the reservoir, we remember that work done equals rate multiplied by time. Let’s denote the inlet rate as i and for the outlet pipe as 0. Therefore,
i(24) = 1
o(28) = 1
In this context, the '1' represents the total number of reservoirs, since the problem states the time needed for each pipe to either fill or empty a singular reservoir. Solving for rates yields:
i = 1/24 reservoirs/hour
o = 1/28 reservoirs/hour
Over the first six hours, the inlet pipe fills (1/24)(6) = 1/4 reservoirs and during the same period, the outlet pipe empties (1/28)(6) = 3/14 reservoirs. To calculate the net volume of the reservoir filled, we subtract the emptying total from the filling total:
1/4 - 3/14 = 1/28 reservoirs (note that if emptying exceeds filling, a negative value results. In such cases, treat that negative value as zero, indicating that the outlet rate surpasses the inlet rate, leading to an empty reservoir).
Now we need to find out how long it will take to fill up one reservoir since we’ve already partially filled 1/28 of it, after closing the outlet pipe. In simpler terms, we need to determine the time required for the inlet pipe to finish filling the remaining 27/28 of the reservoir. Fortunately, we have already established the filling rate for the inlet pipe, leading to the equation:
(1/24)t = 27/28
Solving for t gives us 23.14 hours. Remember to add the initial 6 hours to this result since the question seeks the total time. Thus, the final total is 29.14 hours.
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P(S) = Probability of Smash = 0.05 (5%)
P(M) = Probability of Modest = 0.5 (50%)
P(F) = Probability of Flop = 0.45 (45%)
Based on this, we utilize the model for discrete random variables, leading to:
E(X) = (0.05 * 5.2) + (0.5 * 0.9) + (0.45 * 0)
= 0.26 + 0.45 + 0
= 0.71 Mill'
