Let D be the set of weekdays, Monday through Friday, let W be a set of employees {1, 2, 3} of a tutoring center, and let V be a set of computer languages for which tutoring is offered, {A(P L), B(asic), C(++), J(ava), L(isp), P(ython)}. We define s (schedule) from D into W by dsw if w is scheduled to work on day d. We also define r from W into V by wrl if w can tutor students in language l. If s and r are defined by matrices (1 2 3
M 1 0 1 A B C J L P
S = T 0 1 1 and R = 1 (0 1 1 0 0 1
W 1 0 1 2 1 1 0 1 0 1
R 0 1 0 3 0 1 0 0 1 1)
F 1 1 0)
a. compute SR using Boolean arithmetic and give an interpretation of the relation it defines
b. compute SR using regular arithmetic and give an interpretation of what the result describes.

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!

(x, y)→(x − 8, y − 7)

step-by-step explanation:

enjoy!

step-by-step explanation:

for exempl this   system of equations   y = x - 3

                                                                y = 2x - 5

look   the line : y = x -3     ( red)

                            the line : y = 2x -5 ( bleus)

the answer is:

the correct option is the option b.

to calculate the surface area of the right cylinder, we need to use the following formula:

from the picture we know that:

so, substituting and calculting we have:

hence, we have that the correct option is the option b.

have a nice day!