4x + 3 < 3x + 6 a. x < 9/7 b. x > 9 c. x < 9 d. x

How do you find area and perimeter of a rectangle with the side lengths of 5x^2 and 12x?

valentinak56 [21]

Answer:

The area can be found by multiplying the two terms, and the perimeter by doubling and adding them.

Using this, we find that the area of the rectangle is 60x³, and the perimeter is 10x² + 24x.

Step-by-step explanation:

First let's find the area:

5x² × 12x

= 60x³

Now the perimeter:

2(5x² + 12x)

= 10x² + 24x

8 0

3 years ago

Define z_alpha to be a z-score with an area of alpha to the right. For Example: z_0.10 means P(Z > z_0.10) = 0.10. We would a

Reptile [31]

Answer:

a) P(-z_0.025 < Z < z_0.025)

For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(0.025,0,1)"

And for this case the two values are : $z_{crit}= \pm 1.96$

b) P(-z_{\alpha/2} < Z < z_{\alpha/2})

For this case we want a quantile that accumulates $\alpha/2$ of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(alpha/2,0,1)"

c) For this case we want to find a value of z that satisfy:

P(Z > z_alpha) = 0.05.

And we can use the following excel code:

"=NORM.INV(0.95,0,1)"

And we got $z_{\alpha/2}=1.64$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Part a

P(-z_0.025 < Z < z_0.025)

For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(0.025,0,1)"

And for this case the two values are : $z_{crit}= \pm 1.96$

Part b

P(-z_{\alpha/2} < Z < z_{\alpha/2})

For this case we want a quantile that accumulates $\alpha/2$ of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(alpha/2,0,1)"

Part c

For this case we want to find a value of z that satisfy:

P(Z > z_alpha) = 0.05.

And we can use the following excel code:

"=NORM.INV(0.95,0,1)"

And we got $z_{\alpha/2}=1.64$

6 0

4 years ago

The equation 3s equals 21 can be used to find the number of students s and each van on a field trip how many students are in eac

zubka84 [21]

3s=21
s=7
7 students are in each van.

6 0

4 years ago

Factoring using GCF 15cd + 30c^2d^2

olchik [2.2K]

Answer:

15cd(1 + 2cd)

Step-by-step explanation:

greatest common factor is 15cd

$15cd*1 + 15cd*2cd\\= 15cd(1 + 2cd)$

8 0

2 years ago

What percent of 26 is 4 A. 0.26 = n x 4 B. N= 0.26 ×4 C. 4 = n x 26 D. 26 = 4n

Anna11 [10]

the answer is 0.24=n×4

3 0

3 years ago

4x + 3 < 3x + 6 a. x < 9/7 b. x > 9 c. x < 9 d. x < 3