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4 years ago

John makes 35% of his free throw shots.

Mathematics

1 answer:

Minchanka [31]4 years ago

8 0

Answer:

(1)0.39

(2)0.14

(3)0.21

(4)0.26

Step-by-step explanation:

John makes 35% of his free throw shots.

The probability that John makes his shot =0.35
The probability that John misses his shot =1-0.35=0.65

Sue makes 40% of her free throw shots.

The probability that Sue makes her shot =0.4
The probability that Sue misses her shot =1-0.4=0.6

(1)John and sue both miss their shots

P(John and sue both miss their shots)

=P(John miss his shot) X P(Sue misses her shot)

=0.65 X 0.6 =0.39

(2)John and Sue both make their shots

P(John and Sue both make their shots)

=P(John makes his shot) X P(Sue makes her shot)

=0.35 X 0.4=0.14

(3)John makes his shot and Sue misses hers

P(John makes his shot and Sue misses hers)

=P(John makes his shot) X P(Sue misses her shot)

=0.35 X 0.6=0.21

(4)John misses his shot and Sue makes hers

P(John misses his shot and Sue makes hers)

=P(John miss his shot) X P(Sue makes her shot)

=0.65 X 0.4 =0.26

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Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:

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To solve, we can simply substitute $l -14$ in for $s$ in the second equation and solve.

$\dfrac{1}{l - 14} + \dfrac{5}{l} = \dfrac{1}{4}$

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$\dfrac{l}{l(l - 14)} + \dfrac{5(l - 14)}{l(l - 14)} = \dfrac{1}{4}$

Get terms on the left side to a common denominator for easier addition

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Simplify

$4(6l - 70) = l(l - 14)$

Cross multiplication ( $\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc$ )

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Simplify

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Factor left side of the equation

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Zero Product Property

Now, notice that we have found two solutions, but the problem is only asking for one. This <em>likely </em>means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,

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Since $s$ is not positive in this case, $l = 10$ is not a solution.

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which means that the smaller number is 14 and the larger number is 28.

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