A certain brand of automobile tire has a mean life span of 32,000 miles and a standard deviation of 2,450 miles. (Assume the life spans of the tires have a bell-shaped distribution.) (a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 31,000 miles. Find the z-score that corresponds to each life span.

a)

The z-score corresponds to 34000 is 0.816

The z-score corresponds to 37000 is 2.041

The z-score corresponds to 31000 is -0.408

Step-by-step explanation:

The z-score corresponds to 34000

Let x=34000

z-score=(x-mean)/standard deviation

z-score=34000-32000/2450=0.816

The z-score corresponds to 34000 is 0.816

The z-score corresponds to 37000

Let x=37000

z-score=(x-mean)/standard deviation

z-score=37000-32000/2450=2.041

The z-score corresponds to 37000 is 2.041

The z-score corresponds to 31000

Let x=31000

z-score=(x-mean)/standard deviation

z-score=31000-32000/2450=-0.408

The z-score corresponds to 31000 is -0.408

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!

-10i^2-4i

step-by-step explanation:

evaluate for p=2,q=5i

(2−4)(2+5i)i

(2−4)(2+5i)i

=−10i2−4i