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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Answer:
550
Step-by-step explanation:
We know that 17% of the applicants (3,240) will receive acceptance.
0.17 * 3,240 = 550.8
Thus, 550 students will gain acceptance
we must round down since only 17% can be accepted, and having 0.8 of a person is not feasible
hope this helps
Answer:
In total, Henry requires 15 pints of paint.
Step-by-step explanation:
Henry starts with 2 pints of red and 3 pints of yellow to achieve a certain color, but he has already used 9 pints of yellow paint. Thus, this is represented by:
3 x 3 = 9 (yellow)
Since whatever is done on one side must also be applied to the other, we calculate the red paint:
2 x 3 = 6 (red)
Now we consolidate the amounts:
9 + 6 = 15. (Total red and yellow paint)
This leads to the conclusion that 15 pints are needed.
We opt to accept the null hypothesis. Given the following details provided: the Sample mean equals 28.8 miles per gallon, Sample size n is 120, and Alpha α is 0.01 with a sample standard deviation of 6.89 miles per gallon. Initially, we set up the null and alternative hypotheses. Utilizing a two-tailed t-test facilitates this hypothesis testing. By substituting the relevant values we calculate, and eventually conclude that we fail to reject the null hypothesis, endorsing that the average MPG for the Toyota Highlander Hybrid vehicles is indeed 28 miles per gallon.
A minimum sample size of 75 is necessary. Step-by-step explanation: We need to determine our level, which is calculated by subtracting 1 from the confidence interval divided by 2. Now, we need to find the z value in the Z table that corresponds to a p-value of [Z value]. Therefore, it is the z value with a p-value of [specific value]. Next, we calculate the margin of error M, where [insert equation], with [standard deviation] representing the population standard deviation and n as the sample size. The standard deviation equals the square root of the variance. With a 0.95 probability level, if the margin of error desired is 5 or below, a sample size of at least 75 is required.
