Atul deposited 30% of his income in a bank. After spending 50% of the remaining ,he had ripped 10,500 left with

Mei and Anju are sitting next to each other on different horses on a carousel. Mei's horse is 3 meters from the center of the

SOVA2 [1]

Answer:

$2\pi \approx 6.28\ meters$

Step-by-step explanation:

Mei's horse is 3 meters from the center of the carousel. After one rotation, Mei travelled

$l_M=2\pi r=2\pi \cdot 3=6\pi\ meters$

Anju's horse is 2 meters from the center. After one rotation, Mei travelled

$l_A=2\pi r=2\pi \cdot 2=4\pi\ meters$

The difference in their travelled distances is

$l_M-l_A=6\pi -4\pi =2\pi \approx 6.28\ meters$

5 0

2 years ago

Read 2 more answers

One option in a roulette game is to bet $2 on red. (There are 18 red compartments, 18 black compartments, and two compartmen

aleksandrvk [35]

It cost $46.000 for the red.

4 0

2 years ago

A researcher gathers data on the length of essays (number of lines) and the SAT scores received for a sample of students enrol

LenaWriter [7]

Answer:

(C) The slope of the regression equation is not significantly different from zero

Step-by-step explanation:

Let's suppose that we have the following linear model:

$y= \beta_o +\beta_1 X$

Where Y is the dependent variable and X the independent variable. $\beta_0$ represent the intercept and $\beta_1$ the slope.

In order to estimate the coefficients $\beta_0 ,\beta_1$ we can use least squares estimation.

If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis: $\beta_1 = 0$

Alternative hypothesis: $\beta_1 \neq 0$

Or in other wouds we want to check is our slope is significant.

In order to conduct this test we are assuming the following conditions:

a) We have linear relationship between Y and X

b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable

c) We assume that the Y values are independent and the distribution of Y is normal

The significance level is provided and on this case is $\alpha=0.05$

The standard error for the slope is given by this formula:

$SE_{\beta_1}=\frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

Th degrees of freedom for a linear regression is given by $df=n-2$ since we need to estimate the value for the slope and the intercept.

In order to test the hypothesis the statistic is given by:

$t=\frac{\hat \beta_1}{SE_{\beta_1}}$

The confidence interval for the slope would be given by this formula:

$\hat \beta_1 + t_{n-2, \alpha/2} \frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

And using the last formula we got that the confidence interval for the slope coefficient is given by:

$-0.88 < \beta_1$

IF we analyze the confidence interval contains the value 0. So we can conclude that we don't have a significant effect of the slope on this case at 5% of significance. And the best option would be:

(C) The slope of the regression equation is not significantly different from zero

6 0

2 years ago

Find the common difference of the arithmetic sequence. 6,9.4,12.8,16.2

Blababa [14]

A sequence is said to be arithmetic if every couple of adjacent elements differ by the same number. If this is the case, that constant number is called the common difference.

This sequence is arithmetic, because the difference between every element and the previous one is