Response:
Based on the anticipated number of individuals completing the form to claim the refund, the company ought to foresee its net profit decreasing to:
- $174.6 per computer tablet.
Detailed explanation:
Initially, the profit per tablet is $180, but after initiating the rebate program, it is expected that 18% of purchasers will fill out the forms and obtain the VISA card, which will lower the profit as demonstrated below:
- Calculation of the reduced benefit for 18% of computer tablets = original benefit - refund amount.
- Reduced benefit for 18% of tablets = $180 - $30 = $150
From here, we find that 18% of tablets will yield a benefit of $150, while the other 82% will maintain a benefit of $180. To ascertain an overall figure for the benefit, we must compute it as follows:
- Total benefit = Percentage of reimbursed tablets * Benefit of reimbursed tablets + Percentage of non-reimbursed tablets * Benefit of non-reimbursed tablets.
- Overall profit = 18% * 150 + 82% * 180
- Overall profit = $174.6
Thus, after the $30 rebate on 18% of the tablets, the total benefit amounts to $174.6.
Answer:
a) 0.216
b) 0.784
c) 0.288
d) 0.352
e) 0.784
Step-by-step explanation:
The steps for solving this are provided in an image.
m = 6.57 and n = -2
Detailed explanation:
To solve this question, convert the thickness of a dollar bill into standard notation and compare the two thicknesses.
0.07 compared to 0.0043 results in 0.0657
0.0657 = 6.57 x 10^-2
Thus, a quarter is thicker than a dollar by 6.57 x 10^-2.
m = 6.57 and n = -2
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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