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3 years ago

5

The value of a professional basketball player's autograph rose 30% in the last year. It is now worth $286.00. What was it worth

a year ago?

2 answers:

solong [7]3 years ago

8 0

Answer:

$220

Step-by-step explanation:

Let one year ago, worth of a professional basketball player's autograph=x

After increasing worth by 30%

Now, worth of a professional basketball player's autograph=$286

We have to find the worth of a professional basketball player's autograph a year ago.

30% of x= $\frac{30}{100}\time x=\frac{30x}{100}$

According to question

$x+\frac{30x}{100}=286$

$\frac{100x+30x}{100}=286$

$\frac{130x}{100}=286$

$x=\frac{286\times 100}{130}$

$x=220$

Hence, a year ago the worth of a professional basketball player's autograph=$220

charle [14.2K]3 years ago

4 0

X+0.30x=286
Solve for x
X=220

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Answer:

Step-by-step explanation:

(a)

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By the multiplication rule, the number of possible ways can one component of each type be selected is,

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Part a

Therefore, the number of possible ways can one component of each type be selected is 240.

(b)

The number of Sony receivers is 1.

The number of Sony CD players is 1.

The number of speakers is 3.

The number of cassettes is 4.

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Select one Sony CD player out of 1 Sony CD players in ways.

Select one speaker out of 3 speakers in ways.

Select one cassette out of 4 cassettes in $4C_1$ ways.

Find the number of ways can components be selected if both the receiver and the CD player are to be Sony.

By the multiplication rule, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is,

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Therefore, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is 12.

(c)

The number of receivers without Sony is 4.

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The number of cassettes without Sony is 3.

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Select one speaker out of 3 speakers in 3C_1 ways.

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By the multiplication rule, the number of ways can components be selected if none is to be Sony is,

$=4C_1*3C_1*3C_1*3C_1\\\\=108$

[excluding sony from each of the component]

Therefore, the number of ways can components be selected if none is to be Sony is 108.

(d)

The number of ways can a selection be made if at least one Sony component is to be included is,

= Total possible selections -Total possible selections without Sony

= 240-108

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Therefore, the number of ways can a selection be made if at least one Sony component is to be included is 132.

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If someone flips the switches on the selection in a completely random fashion, the probability that the system selected contains at least one Sony component is,

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= 132 / 240

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The probability that the system selected contains exactly one Sony component is,

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Therefore, if someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains at least one Sony component is 0.55.

If someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains exactly one Sony component is 0.4125.

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