Let's find the rate that the inlet and outlet pipe can fill and empty the reservoirs. remember that rate*time = work done so if we let the rate of the inlet pipe be i and the outlet pipe be 0 we have
i(24) = 1
o(28) = 1
if you're confused about what the 1 is, it is the number of reservoirs because in the problem, it gives us the time it takes for each pipe to either empty or fill 1 reservoir. solving for r and t gives us:
i = 1/24 reservoirs/hour
o = 1/28 reservoirs/hour
in the first 6 hours the inlet pipe fills up (1/24)(6) = 1/4 reservoirs and the outlet pipe empties (1/28)(6) = 3/14 reservoirs so to find out how many reservoirs are filled we subtract emptied amount from filled amount:
1/4 - 3/14 = 1/28 reservoirs (note that if the amount emptied is greater than the amount filled you will obtain a negative answer. please just change that negative number to 0 because a negative answer simply means that emptying rate is greater than filling rate so you end up with no water).
now we need to figure out how long it will take to fill up 1 reservoir given we have already filled up 1/28 reservoirs and that the outlet pipe is finally closed. to put it in simple terms, how long will it take for the inlet pipe to fill up the rest of the 27/28 of the reservoir. good thing we've already found the rate the inlet pipe fills up reservoirs so we have the equation:
(1/24)t = 27/28
solving for t, we have 23.14 hours. make sure you remember to add 6 to the answer because the question wants us to include that time in our answer. doing so gives 29.14 hours.
let me know if you have any questions!
Given the table below comparing the marginal benefit Lucinda gets from
Kewpie dolls and Beanie Babies.
![\begin{tabular} {|p {2cm}|p {2cm}|p {2cm}|p {2cm}|} \multicolumn {4} {|c|} {Lucinda's Kewpie Doll and Beanie Baby Marginal Benefits}\\[1ex] \multicolumn {2} {|c|} {Kewpie Dolls}&\multicolumn {2} {|c|} {Beanie Babies}\\[1ex] 1&\$15.00&1&\$12.00\\ 2&\$12.00&2&\$10.00\\ 3&\$9.00&3&\$8.00\\ 4&\$6.00&4&\$6.00\\ 5&\$3.00&5&\$4.00\\ 6&\$0.00&6&\$2.00\\ \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cp%20%7B2cm%7D%7Cp%20%7B2cm%7D%7Cp%20%7B2cm%7D%7Cp%20%7B2cm%7D%7C%7D%0A%5Cmulticolumn%20%7B4%7D%20%7B%7Cc%7C%7D%20%7BLucinda%27s%20Kewpie%20Doll%20and%20Beanie%20Baby%20Marginal%20Benefits%7D%5C%5C%5B1ex%5D%0A%5Cmulticolumn%20%7B2%7D%20%7B%7Cc%7C%7D%20%7BKewpie%20Dolls%7D%26%5Cmulticolumn%20%7B2%7D%20%7B%7Cc%7C%7D%20%7BBeanie%20Babies%7D%5C%5C%5B1ex%5D%0A1%26%5C%2415.00%261%26%5C%2412.00%5C%5C%0A2%26%5C%2412.00%262%26%5C%2410.00%5C%5C%0A3%26%5C%249.00%263%26%5C%248.00%5C%5C%0A4%26%5C%246.00%264%26%5C%246.00%5C%5C%0A5%26%5C%243.00%265%26%5C%244.00%5C%5C%0A6%26%5C%240.00%266%26%5C%242.00%5C%5C%0A%5Cend%7Btabular%7D)
<span>If
lucinda has only $18 to spend and the price of kewpie dolls and the
price of beanie babies are both $6,
Lucinda will buy the combination for which marginal benefit is the same.
Therefore, Lucinda will buy </span><span>2 kewpie dolls and 1 beanie baby,</span><span>
if she were rational.</span>
Answer:
835.49
Step-by-step explanation:
selling price = original cost + markup value
We need to find the markup
markup = original cost * markup percent
= $784.50 * 6.5%
= $784.50 *.06.5
=50.9925
Rounding to the nearest cent
=50.99
selling price = original cost + markup value
=784.50+50.99
835.49
Answer:
ab/2 + 2c
Step-by-step explanation:
Half the product would be represented by “product/2”
The product of two numbers a and b can be represented by “ab”
Added to twice a third number c = + 2c
Before we figure out how many customers you will need to talk per day to reach your goal, let's calculate what is 20% of how many customers you normally talk to a day.
current no. = 8
goal = 8 + 20%
20% = 8 x 0.20
(a percent is really just a fraction with the percent number over 100)
20% = 1.60
goal = 8 + 1.60
goal = 9.60
However, there is no such thing as .60 of a person so we will have to round up. You will need to talk to 10 customers per day.
