Please help me?

otez555 [7]

In division, exponents with the same base are subtracted.
example:
$\frac{x^4}{x^2} = x^2 \\ \\ \frac{ x^{3} y^{2} }{ x^{6} y} = \frac{y}{ x^{3} } \\ \\ Negative-exponents \\ \\ x^{-2} = \frac{1}{ x^{2} }$

5 0

3 years ago

An auto company claims that the fuel efficiency of its sedan has been substantially improved. A consumer advocate organization w

zzz [600]

Answer:

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.983 -0}{\frac{1.685}{\sqrt{12}}}=2.021$

$df=n-1=12-1=11$

$p_v =P(t_{(11)}>2.021) =0.0342$

If we compare the the p value with the significance level provided $\alpha=0.1$ , we see that $p_v < \alpha$ , so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.

Step-by-step explanation:

Previous concepts

A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.

Let put some notation :

x=test value 2017 , y = test value 2019

x: 28.7 32.1 29.6 30.5 31.9 30.9 32.3 33.1 29.6 30.8 31.1 31.6

y: 31.1 32.4 31.3 33.5 31.7 32.0 31.8 29.9 31.0 32.8 32.7 33.8

Solution to the problem

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x \leq 0$

Alternative hypothesis: $\mu_y -\mu_x >0$

Because if we have an improvement we expect that the values for 2019 would be higher compared with the values for 2017

The first step is calculate the difference $d_i=y_i-x_i$ and we obtain this:

d: 2.4, 0.3, 1.7,3,-0.2, 1.1, -0.5, -3.2, 1.4, 2, 1.6, 2.2

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{11.8}{12}=0.983$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =1.685$

We assume that the true difference follows a normal distribution. The 4th step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.983 -0}{\frac{1.685}{\sqrt{12}}}=2.021$

The next step is calculate the degrees of freedom given by:

$df=n-1=12-1=11$

Now we can calculate the p value, since we have a right tailed test the p value is given by:

$p_v =P(t_{(11)}>2.021) =0.0342$

If we compare the the p value with the significance level provided $\alpha=0.1$ , we see that $p_v < \alpha$ , so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.

4 0

3 years ago

N 4(x + 2) + 50y + 3). An equivalent expression is Reset Next

natita [175]

Answer:

4x+50y+11

hope this helps :) plz brainliest

Step-by-step explanation:

7 0

3 years ago

Can someone please help me??

valkas [14]

The answer is 78 feet of fencing. This is because you need to find the perimeter of the yard. To find the perimeter of the yard, you add the sides together, so 21+21+18+18 = 78.

5 0

2 years ago

Read 2 more answers

Given: Triangle ABC : triangle ADB. AB =24, AD =16 <br> Find: AC

RoseWind [281]

Answer:

Step-by-step explanation:

Given ΔABC and ΔADB, since both triangles are right angled triangles then the following are true.

From ΔADB, AB² = AD²+BD²

Given AB = 24 and AD = 16

BD² = AB² - AD²

BD² = 24²-16²

BD² = 576-256

BD² = 320

BD = $\sqrt{320}$

BD = 17.9

from ΔABC, AC² = AB²+BC²

SInce AC = AD+DC and BC² = BD² + DC² (from ΔBDC )we will have;

(AD+DC)² = AB²+ (BD² + DC²)

Given AD = 16, AB = 24 and BD = 17.9, on substituting

(16+DC)² = 24²+17.9²+ DC²

256+32DC+DC² = 24²+17.9²+ DC²

256+32DC = 24²+17.9²

32DC = 24²+17.9² - 256

32DC = 640.41

DC = $\frac{640.41}{32}$

DC = 20.01

Remember that AC = AD+DC

AC = 16+20.01

AC = 36.01

6 0

3 years ago