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2 years ago

12

Use prime factorization to find the GCF of 18c cubed and 24c cubed

2 answers:

satela [25.4K]2 years ago

5 0

The GCF is 6c^3

18/6 = 3
24/6 = 4

6c^3(3+4)

Lera25 [3.4K]2 years ago

3 0

18x18x18
9x2 x 9x2 x 9x2
3x3 x 2 x 3x3 x 2 x 3x3 x 2
(3^6) x (2^3)

24x24x24
12x2 x 12x2 x 12x2
6x2 x 2 x 6x2 x 2 x 6x2 x 2
3x2 x2 x2 x 3x2 x 2 x 2 x 3x2 x 2 x2
(3^3) x (2^9)

at least (3^3) are in each and at least (2^3) are in each
the greatest common factor will be 3^3 x 2^3 = 216

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The following results come from two independent random samples taken of two populations.

photoshop1234 [79]

Answer:

$(a)\ \bar x_1 - \bar x_2 = 2.0$

$(b)\ CI =(1.0542,2.9458)$

$(c)\ CI = (0.8730,2.1270)$

Step-by-step explanation:

Given

$n_1 = 60$ $n_2 = 35$

$\bar x_1 = 13.6$ $\bar x_2 = 11.6$

$\sigma_1 = 2.1$ $\sigma_2 = 3$

Solving (a): Point estimate of difference of mean

This is calculated as: $\bar x_1 - \bar x_2$

$\bar x_1 - \bar x_2 = 13.6 - 11.6$

$\bar x_1 - \bar x_2 = 2.0$

Solving (b): 90% confidence interval

We have:

$c = 90\%$

$c = 0.90$

Confidence level is: $1 - \alpha$

$1 - \alpha = c$

$1 - \alpha = 0.90$

$\alpha = 0.10$

Calculate $z_{\alpha/2}$

$z_{\alpha/2} = z_{0.10/2}$

$z_{\alpha/2} = z_{0.05}$

The z score is:

$z_{\alpha/2} = z_{0.05} =1.645$

The endpoints of the confidence level is:

$(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$

$2.0 \± 1.645 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}$

$2.0 \± 1.645 * \sqrt{\frac{4.41}{60}+\frac{9}{35}}$

$2.0 \± 1.645 * \sqrt{0.0735+0.2571}$

$2.0 \± 1.645 * \sqrt{0.3306}$

$2.0 \± 0.9458$

Split

$(2.0 - 0.9458) \to (2.0 + 0.9458)$

$(1.0542) \to (2.9458)$

Hence, the 90% confidence interval is:

$CI =(1.0542,2.9458)$

Solving (c): 95% confidence interval

We have:

$c = 95\%$

$c = 0.95$

Confidence level is: $1 - \alpha$

$1 - \alpha = c$

$1 - \alpha = 0.95$

$\alpha = 0.05$

Calculate $z_{\alpha/2}$

$z_{\alpha/2} = z_{0.05/2}$

$z_{\alpha/2} = z_{0.025}$

The z score is:

$z_{\alpha/2} = z_{0.025} =1.96$

The endpoints of the confidence level is:

$(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$

$2.0 \± 1.96 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}$

$2.0 \± 1.96* \sqrt{\frac{4.41}{60}+\frac{9}{35}}$

$2.0 \± 1.96 * \sqrt{0.0735+0.2571}$

$2.0 \± 1.96* \sqrt{0.3306}$

$2.0 \± 1.1270$

Split

$(2.0 - 1.1270) \to (2.0 + 1.1270)$

$(0.8730) \to (2.1270)$

Hence, the 95% confidence interval is:

$CI = (0.8730,2.1270)$

8 0

2 years ago

Consider this cube with a volume of 64 cubic centimeters. A cube with volume 64 centimeters cubed. What can be concluded of this

BabaBlast [244]

Answer: B) this is a perfect cube. D )the side length is 4. E)taking the cube root of the volume will determine the side length.

Step-by-step explanaion: just guessed and it told me it was right on edunuity 2020.

HOPE I HELPED PLZ GIVE BRAINLIEST:)

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2 years ago

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Ms.stoner purchased a new computer for $1,150 at the apple store. If sales tax is 7.5% what was the total of her purchase

enyata [817]

First convert 7.5% into a decimal (.075)
1,150 * .075 = 86.25
1,150 + 86.25 = 1,236.25

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2 years ago

What is the volume of a square pyramid with base side length of 22 cm and height of 8cm?

Inessa05 [86]

Answer is 1290.67. I rounded to the nearest tenth but it goes on.

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2 years ago

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12 is 60% of what number?

goldenfox [79]

Answer: 20

<u>Step-by-step explanation:</u>

12 is 60% of what number

12 = 0.60 * n

20 = n

8 0

2 years ago