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3 years ago

Which shows one way to determine the factors of 12x3 – 2x2 + 18x – 3 by grouping?

Mathematics

2 answers:

Debora [2.8K]3 years ago

6 0

Option A

$2x^2(6x-1) + 3(6x-1)$ is one way to determine the factors of $12x^3-2x^2+18x-3$ by grouping

Solution:

Factoring by grouping means that you will group terms with common factors before factoring

Given expression is:

$12x^3-2x^2+18x-3$

Group the first two terms together and then the last two terms together.

$(12x^3-2x^2)+(18x-3)$

We can see that $2x^2$ is common in first two terms

And 3 is common in last two terms

Factor them out

$(12x^3-2x^2)+(18x-3) = 2x^2(6x-1) + 3(6x-1)$

$2x^2(6x-1) + 3(6x-1)$

Thus option A is correct

Scorpion4ik [409]3 years ago

5 0

Answer:

is one way to determine the factors of by grouping

Solution:

Factoring by grouping means that you will group terms with common factors before factoring

Given expression is:

Group the first two terms together and then the last two terms together.

We can see that is common in first two terms

And 3 is common in last two terms

Factor them out

Step-by-step explanation:

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One measure of an athlete’s ability is the height of his or her vertical leap. Many professional basketball players are known fo

almond37 [142]

Answer:

(1) P( $\bar X$ < 26 inches) = 0.0436

(2) P(27.5 inches < $\bar X$ < 28.5 inches) = 0.2812

Step-by-step explanation:

We are given that the mean vertical leap of all NBA players is 28 inches. Suppose the standard deviation is 7 inches and 36 NBA players are selected at random.

Firstly, Let $\bar X$ = mean vertical leap for the 36 players

Assuming the data follows normal distribution; so the z score probability distribution for sample mean is given by;

Z = $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean vertical leap = 28 inches

$\sigma$ = standard deviation = 7 inches

n = sample of NBA player = 36

(1) Probability that the mean vertical leap for the 36 players will be less than 26 inches is given by = P( $\bar X$ < 26 inches)

P( $\bar X$ < 26) = P( $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{26-28}{\frac{7}{\sqrt{36} } }$ ) = P(Z < -1.71) = 1 - P(Z $\leq$ 1.71)

= 1 - 0.95637 = 0.0436

(2) Now, here sample of NBA players is 26 so n = 26.

Probability that the mean vertical leap for the 26 players will be between 27.5 and 28.5 inches is given by = P(27.5 inches < $\bar X$ < 28.5 inches) = P( $\bar X$ < 28.5 inches) - P( $\bar X$ $\leq$ 27.5 inches)

P( $\bar X$ < 28.5) = P( $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{28.5-28}{\frac{7}{\sqrt{26} } }$ ) = P(Z < 0.36) = 0.64058 {using z table}

P( $\bar X$ $\leq$ 27.5) = P( $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{27.5-28}{\frac{7}{\sqrt{26} } }$ ) = P(Z $\leq$ -0.36) = 1 - P(Z < 0.36)

= 1 - 0.64058 = 0.35942

Therefore, P(27.5 inches < $\bar X$ < 28.5 inches) = 0.64058 - 0.35942 = 0.2812

6 0

3 years ago

What is the sum of the geometric series

Sergio039 [100]

Answer: 2343 / 256

Explanation

I will do this for you in two forms: 1) adding each term, and 2) using the general formula for the sum of geometric series.

1) Adding the terms:

4
∑ 3 (3/4)^i = 3 (3/4)^0 + 3 (3/4)^1 + 3 (3/4)^2 + 3 (3/4)^3 + 3 (3/4)^4
i=0

= 3 + 9/4 + 27/16 + 81/64 + 243/256 = [256*3 + 27*16 + 64*9 + 4*81 + 243] / 256 =

= 2343 / 256

2) Using the formula:

n-1
∑ A (r^i) = A [1 - r^(n) ] / [ 1 - r]
i=0

Here n - 1 = 4 => n = 5

r = 3/4

A = 3

Therefore the sum is 3 [ 1 - (3/4)^5 ] / [ 1 - (3/4) ] =

= 3 [ 1 - (3^5) / (4^5) ] / [ 1/4 ] = 3 { [ (4^5) - (3^5) ] / (4^5) } / {1/4} =

= (3 * 781) / (4^5) / (1/4) = 3 * 781 / (4^4) = 2343 / 256

So, no doubt, the answer is 2343 / 256

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3 years ago

If a jogger jogs 6 kilometers in 45 minutes what is his speed

kaheart [24]

45 minutes = 3/4 hours

so his speed = 6 / 3/4 kph

= 8 km / h Answer

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3 years ago