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3 years ago

11

What is the greatest common factor for 21,24,27

1 answer:

True [87]3 years ago

6 0

So,

To find the GCF, you have to factor all of the numbers.

21 --> 3 * 7
24 --> 2 * 2 * 2 * 3
27 --> 3 * 3 * 3

Next, you find all the factors that they have in common.

They all have at least one 3, so that means that 3 is the greatest common factor of 21, 24, and 27.

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Complete Question

The complete question is shown on the first uploaded image

Answer:

a

$P(X < 4) = 0.4141$

b

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c

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d

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Step-by-step explanation:

From the question we are told that

The mean is $\mu = 4.5$

The standard deviation is $\sigma = 2.3$

Generally the probability that a randomly selected study participant's response was less than 4 is mathematically represented as

$P(X < 4) = P(\frac{X - \mu }{\sigma} < \frac{4 - 4.5}{ 2.3} )$

$\frac{X -\mu}{\sigma} = Z (The \ standardized \ value \ of\ X )$

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$P(X < 4) = P(Z < -0.217 )$

From the z-table $P(Z < -0.217 ) = 0.4141$

So

$P(X < 4) = 0.4141$

Generally the probability that a randomly selected study participant's response was between 4 and 6 is mathematically represented as

$P(4 < X < 6) = P( < \frac{4 - 4.5}{ 2.3} < \frac{X - \mu }{\sigma} < \frac{6 - 4.5}{2.3})$

=> $P(4 < X < 6) = P( \frac{4 - 4.5}{ 2.3} < \frac{X - \mu }{\sigma} < \frac{6 - 4.5}{2.3})$

=> $P(4 < X < 6) = P( -0.217 < Z< 0.6522$

=> $P(4 < X < 6) = (Z< 0.6522) -P( Z < -0.217)$

From the z-table

$(Z< 0.6522) = 0.74286$

So

$P(4 < X < 6) = 0.74286 -0.4141$

=> $P(4 < X < 6) = 0.74286 -0.4141$

=> $P(4 < X < 6) = 0.32876$

Generally the probability that a randomly selected study participant's response was more than 8 is mathematically represented as

$P(X > 8) = P(\frac{X - \mu }{\sigma} > \frac{8 - 4.5}{ 2.3} )$

$P(X > 8) = P(Z > 1.52174 )$

From the z-table $P(Z > 1.52174 ) = 0.064037$

So

$P(X >8) = 0.064037$

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