NEED HELP ASAP !! NEED ANSWERS

You make one pitcher of iced tea and one pitcher of lemonade for a party. Just before the party starts, you catch a little misch

mario62 [17]

Answer:

Each pitcher has the same fraction of the other drink.

Step-by-step explanation:

After 1 cup of tea is added to x cups of lemonade, the mix has the ratio 1:x of tea to lemonade. So, the fraction of mix that is tea is 1/(x+1).

The 1 cup of mix contains 1/(x+1) cups of tea and so x/(x+1) cups of lemonade. When that amount of lemonade is added to the tea, it brings the proportion of lemonade in the tea to (x/(x+1))/x = 1/(x+1), the same proportion as that of tea in the lemonade.

_____

You can consider the degenerate case of one cup of drink in each pitcher. Then when the 1 cup of tea is removed from its pitcher and added to the lemonade, you have a 50-50 mix of tea and lemonade. Removing 1 cup of that mix and putting it back in the tea pitcher makes there be a 50-50 mix in both pitchers.

Increasing the quantity in each pitcher does nothing to change the fact that the mixes end up in the same ratio:

tea:lemonade in Pitcher 1 = lemonade:tea in Pitcher 2

6 0

3 years ago

After graduating from college, Jane has two job offers to consider. Job A is compensated at $100,000 a year but

vaieri [72.5K]

Answer: (a) Job A , by approximately $69, 482

$\\$ (b) Job A , by approximately $6,867

$\\$ (c) Job B , by approximately $ 767,362

$\\$ (d) Job A

Step-by-step explanation:

JOB B

$\\$ The starting Salary is $ 10,000

Since there is an increment of 25% at the beginning of each new year. The breakdown of the increment is as follow:

$\\$ First year : 125% of $ 10,000 = $12,500

$\\$ Second year : 125% of $ 12,500 = $15,625

$\\$ Third year : 125% of $15,625= $19,531.25

$\\$ Fourth year: 125% of $19,531.25 = $24,414.06

$\\$ Fifth year : 125% of $24,414.06 = $30,517.58

$\\$ Sixth year: 125% of $30,517.58 = $38,147.00

$\\$ Seventh year: 125% of $38,147.00 = $47,683.75

$\\$ Eight year: 125% of $47,683.75 = $59,604.69

$\\$ Ninth year: 125% of $59,604.69 = $74,505.86

$\\$ Tenth year: 125% of $74,505.86 = $93,132.32

$\\$ Following the same procedure:

$\\$ Eleventh year = $116,415.40

$\\$ Twelfth year = $145,519.25

$\\$ Thirteenth year = $181,899.06

$\\$ Fourteenth year = $227,373.82

$\\$ Fifteenth year = $ 284,217.29

$\\$ Sixteenth year = $355,271.61

$\\$ Seventeenth year = $444,089.51

$\\$ Eighteenth year = $555,111.89

$\\$ Nineteenth year = $693,889.86

$\\$ Twentieth year = $867,362.32

$\\$ (a) Following the analysis above, at the beginning of the fifth year Job A will have a greater annual salary

$\\$ Difference: Salary of Job A at the beginning of fifth year remains $ 100,000 while that of Job B resulted into $ 30,517.58, the difference implies

$100,000 - $ 30,517.58 = $69,482

$\\$ (b) At the beginning of tenth year, Job A is still $100,000, Job B resulted into $93,132.32. Job A is still greater by approximately $6,867

$\\$ (c) At the beginning of the twentieth year, the annual salary of A is still $ 100,000 while the annual salary of B is $ 867,362.32. Job B annual salary is greater by approximately $ 767,362

$\\$ (d) If I were in Jane’s shoe I will take Job A and work for few years to gain more experience the look for a job that pays better. Waiting for many years in case of Job B is risky , market situation is uncertainty.