Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. The cafeteria manager in an office building surveyed workers in the office building about their soup preferences. The results are shown in the two-way relative frequency table below.

Lentil Mushroom Chicken Tomato Total
Part-time 85 40 35 70 230
Full-time 25 55 65 125 270
Total 110 95 100 195 500

Use the information provided in the table to match each description with the correct percentage of workers.

30%
38.6%
25.1%
35%
22.7%
20.4%
30.4%
18.3%
Percentage of full-time workers who prefer mushroom soup
arrowRight
Percentage of workers who prefer lentil soup who are full-time
arrowRight
Percentage of workers who prefer chicken soup who are part-time
arrowRight
Percentage of part-time workers who prefer tomato soup
arrowRight

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

answer: -1

step-by-step explanation:

d. corresponding side lengths in similar triangles are proportional in length.

step-by-step explanation:

the number 100 represents the number of trials in the experiment.

49/100 represents the experimental probability of the coin landing heads up.

step-by-step explanation: