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3 years ago

Linear Transformations To reflect a linear function about the y-axis, the slope is what

Mathematics

1 answer:

baherus [9]3 years ago

4 0

Answer: Multiplied by -1

Example:

Let's say we had the linear function y = 2x+5

Reflecting this over the y axis means we replace every x with -x and simplify

y = 2x+5 becomes y = 2(-x)+5 and that simplifies to y = -2x+5

The y intercept stays the same the whole time. This is because the y intercept is on the mirror line of the y axis. Stuff on the mirror line does not move.

Notice the jump from the old slope (2) to the new slope (-2) has us multiply by -1.

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Consider the following data to determine whether there is a significant difference between the values of Group 1 and Group 2. Le

cestrela7 [59]

Using the t-distribution, it is found that since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.

At the null hypothesis, we test if the groups have the same values, that is, the subtraction of their means is 0:

$H_0: \mu_2 - \mu_1 = 0$

At the alternative hypothesis, we test if the groups have different values, that is, the subtraction of their means is different of 0:

$H_1: \mu_2 - \mu_1 \neq 0$

First, we have to find the mean and the standard deviation for both samples, hence, using a calculator:

$\mu_1 = 18.75, \sigma_1 = 6.2507, \mu_2 = 19.75, \sigma_2 = 4.2678$

The standard errors are:

$s_1 = \frac{\sigma_1}{\sqrt{n_1}} = \frac{6.2507}{\sqrt{8}} = 2.21$

$s_2 = \frac{\sigma_2}{\sqrt{n_2}} = \frac{4.2678}{\sqrt{8}} = 1.5089$

For the distribution of differences, we have that:

$\overline{x} = \mu_2 - \mu_1 = 19.75 - 18.75 = 1$

$s = \sqrt{s_1^2 + s_2^2} = \sqrt{2.21^2 + 1.5089^2} = 2.676$

We have the standard deviation for the samples, hence, the t-distribution is used. The test statistic is given by:

$t = \frac{\overline{x} - \mu}{s}$

In which $\mu$ is the value tested at the null hypothesis, which is 0 for this problem. Hence, the value of the test statistic is:

$t = \frac{\overline{x} - \mu}{s}$

$t = \frac{1 - 0}{2.676}$

$t = 0.37$

To find the p-value, we have a two-tailed test, as we test if the means are different from a value, with t = 0.37 and 8 + 8 - 2 = 14 df.

Using a t-distribution calculator, this p-value is of 0.72.

Since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.

A similar problem is given at brainly.com/question/15682365

3 0

3 years ago

Assume that y varies inversely

Marina86 [1]

Answer:

y = 2

Step-by-step explanation:

y varies inversely with x setup is:

y = k/x

7 = $\frac{k}{2/3}$ (find 'k')

k = 7/1 · 2/3

k = 14/3

use what you know about 'k' and 'x' to solve for 'y'

y = 14/3 ÷ 7/3 (remember to multiply by the reciprocal when dividing fractions)

y = 14/3 · 3/7

y = 2

3 0

3 years ago

Rotate RST 90° counterclockwise around the origin.

Nostrana [21]

The image of the triangle RST when rotated 90° counterclockwise around the origin is (-15,5), (-15,15) and (-5,10)

<h3>
How to rotate the triangle?</h3>

The coordinates of RST are given as:

R = (5,15)

S = (15,15)

T = (10,5)

The rule of 90° counterclockwise around the origin is:

(x,y) -> (-y,x)

So, we have:

R' = (-15,5)

S' = (-15,15)

T' = (-5,10)

Hence, the image of the triangle when rotated 90° counterclockwise around the origin is (-15,5), (-15,15) and (-5,10)