Suppose that two teams called the Hogs and the Grunts are in a playoff series where the first team to win 2 games wins the series. For each game they play, the probability that the Hogs win is 0.53 and the probability the Grunts win is 0.47.(a) What is the probability that the Bears win the series in exactly 3 games (i. e. only 3 games are required to finish the series and the Bears are the ones that win)?
(b) What is the probability that the Wildcats win the series in exactly 3 games?
(c) What is the probability that the Bears win the series in exactly 4 games?
(d) What is the probability that the Wildcats win the series in exactly 4 games?
(e) What is the probability that the Bears win the series in exactly 5 games?
(f) What is the probability that the Wildcats win the series in exactly 5 games?
(g) What is the probability that the Bears win the series (i. e. the Bears win but we don't care how many games are required)?
(h) What is the probability that the Wildcats win the series?

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!

its the second choice.

step-by-step explanation:

the elements in the range will be 7 less than the elements in the domain.

explanation:

infrared radiation has wavelength in the range between 700 nm and 1 mm. lets' convert these values into scientific notation, keeping in mind that:

let's start from the lower value, we have:

(we moved the dot two places to the left, so we increased the exponent by 2 units, from -9 to -7)

the higher value is:

so, the range of wavelength of infrared radiation is: