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2 years ago

The expression 27 + 45 as a product using the GCF and distributive property.

Mathematics

1 answer:

Bogdan [553]2 years ago

5 0

Answer:

(a) By Greatest Common Factor: (27 + 45 ) = 3( 9 + 15)

(b) By distributive property: (27 + 45 ) = 9(3) + 9(5)

Step-by-step explanation:

Here, the given expression is 27 + 45 .

Now, by Prime Factorization:

27 = 3 x 3 x 3

45 = 3 x 3 x 5

Here, the 3 is the ONLY prime common factor.

So, the Greatest Common Factor = 3

⇒ (27 + 45 ) = 3( 9 + 15)

Hence, by Greatest Common Factor: (27 + 45 ) = 3( 9 + 15)

Now, by distributive property:

A( B + C) = AB + AC

Here, in the given expression:

(27 + 45 ) = 9 ( 3 + 5) = 9(3) + 9(5)

or, (27 + 45 ) = 9(3) + 9(5)

Hence, by distributive property: (27 + 45 ) = 9(3) + 9(5)

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The Slow Ball Challenge or The Fast Ball Challenge.

cupoosta [38]

Answer:

Fast ball challenge

Step-by-step explanation:

Given

Slow Ball Challenge

$Pitches = 7$

$P(Hit) = 80\%$

$Win = \$60$

$Lost = \$10$

Fast Ball Challenge

$Pitches = 3$

$P(Hit) = 70\%$

$Win = \$60$

$Lost = \$10$

Required

Which should he choose?

To do this, we simply calculate the expected earnings of both.

Considering the slow ball challenge

First, we calculate the binomial probability that he hits all 7 pitches

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

Where

$n = 7$ --- pitches

$x = 7$ --- all hits

$p = 80\% = 0.80$ --- probability of hit

So, we have:

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

$P(7) =^7C_7 * 0.80^7 * (1 - 0.80)^{7 - 7}$

$P(7) =1 * 0.80^7 * (1 - 0.80)^0$

$P(7) =1 * 0.80^7 * 0.20^0$

Using a calculator:

$P(7) =0.2097152$ --- This is the probability that he wins

i.e.

$P(Win) =0.2097152$

The probability that he lose is:

$P(Lose) = 1 - P(Win)$ ---- Complement rule

$P(Lose) = 1 -0.2097152$

$P(Lose) = 0.7902848$

The expected value is then calculated as:

$Expected = P(Win) * Win + P(Lose) * Lose$

$Expected = 0.2097152 * \$60 + 0.7902848 * \$10$

Using a calculator, we have:

$Expected = \$20.48576$

Considering the fast ball challenge

First, we calculate the binomial probability that he hits all 3 pitches

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

Where

$n = 3$ --- pitches

$x = 3$ --- all hits

$p = 70\% = 0.70$ --- probability of hit

So, we have:

$P(3) =^3C_3 * 0.70^3 * (1 - 0.70)^{3 - 3}$

$P(3) =1 * 0.70^3 * (1 - 0.70)^0$

$P(3) =1 * 0.70^3 * 0.30^0$

Using a calculator:

$P(3) =0.343$ --- This is the probability that he wins

i.e.

$P(Win) =0.343$

The probability that he lose is:

$P(Lose) = 1 - P(Win)$ ---- Complement rule

$P(Lose) = 1 - 0.343$

$P(Lose) = 0.657$

The expected value is then calculated as:

$Expected = P(Win) * Win + P(Lose) * Lose$

$Expected = 0.343 * \$60 + 0.657 * \$10$

Using a calculator, we have:

$Expected = \$27.15$

So, we have:

$Expected = \$20.48576$ -- Slow ball

$Expected = \$27.15$ --- Fast ball

<em>The expected earnings of the fast ball challenge is greater than that of the slow ball. Hence, he should choose the fast ball challenge.</em>

5 0

2 years ago

A function f(x) s defined as f(x)=-8x^2. What is f(-3)?

Semenov [28]

$f(-3)=-8\cdot(-3)^2\\
f(-3)=-8\cdot9\\
f(-3)=-72
$

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2 years ago

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How long will it take $3000 to earn $900 interest at 6% simple interest?

a_sh-v [17]

Answer:

5 years

Step-by-step explanation:

3000x.06=180 interest per year.

900/180 =5 years to earn 900 interest.

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2 years ago

What is 83 times 13?

Alexxx [7]

Answer:

1079

Step-by-step explanation:

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1 year ago

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What is the area of the trapezoid

topjm [15]

Answer:

24 in

Step-by-step explanation:

Add up all the inches. voila!

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