Write a quadratic function f whose zeros are -2 and 12.<br> f(x) = 0

Suppose A = {x |x ≤ −2, x ≥ 3} and B = {x | −1 ≤ x < 5}. Which statement is true?

vagabundo [1.1K]

A.A∪ B is real numbers

3 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

Three boards are placed end to end to make a walkway. The first board is 4 feet 5 inches long, the second board is 6 feet 9 inch

Kazeer [188]

Answer:

15 feet and 1 inch long

Step-by-step explanation:

add up the feet: 4+6+3= 13 feet

add up the inches: 5+9+11 = 25 inches

25/12= 2 feet 1 inch

13 feet + 2 feet + 1 inch= 15 feet 1 inch

7 0

2 years ago

A DVD player was marked down by 30 percent from its original price of $75. Including a 7 percent sales tax, what is the final co

jok3333 [9.3K]

Answer:

Step-by-step explanation:

D is your answer

$56.18

6 0

2 years ago

A deck of playing cards has four suits, with thirteen cards in each suit consisting of the numbers 2 through 10, a jack, a queen

Rudik [331]

A. True. There are 52 cards total and you only pick 5. Order doesn't matter.

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B. False. Order doesn't matter so you use a combination (instead of a permutation) as choice A shows.

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C. False. The answer is roughly 0.000858 as shown by the calculation below

(13/52)*(12/51)*(13/50)*(12/49)*(11/48) = 0.000858

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D. False. See calculation below

(13/52)*(12/51)*(11/50)*(10/49)*(9/48) = 0.000495

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E. True. See calculation below

(13/52)*(12/51)*(11/50)*(10/49)*(9/48) = 0.000495
this value rounds to roughly 0.0005

6 0

2 years ago

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Write a quadratic function f whose zeros are -2 and 12. f(x) = 0