How far and what direction the decimal move from meters to centimeters?

Can someone please help mee (20 points and i will give brainliest!!!)

FromTheMoon [43]

Answer:

a. y-intercept:(0, -6), x-intercepts: (3, 0) and (-2, 0). vertex: (0.5, -6.25)

b. y-intercept: (0, 6), x-intercepts(3, 0) and (-2, 0). vertex: (0.5, 6.25)

Step-by-step explanation:

a:

So finding the y-intercept is really easy and is simply when x=0. If you plug in 0 as x it makes $y=(0)^2-0-6$ which simplifies to -6, which is the y-intercept. As for the x-intercepts you can calculate that by using the quadratic equation $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\$ . In this case a=1, b=-1, c=-6. So plugging those values in you get $x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-6)}}{2(1)}$ , which simplifies to $x=\frac{1\pm5}{2}$ . This gives you the x-intercepts 6/2 and -4/2 which are 3 and -2. The vertex can be calculated by manipulating the equation so it's in the form of $y=(x-h)^2+k$ where (h, k) is the vertex of the parabola. This is done by moving c to the other side and then completing the square and the isolating y. So the first step will be

Move c to the other side

$y+6=x^2-x$

Complete the square by adding (b/2)^2

$y+6+0.25 = x^2-x+0.25$

Rewrite as square binomial

$y+6.25 = (x-0.5)^2$

Isolate y

$y=(x-0.50)^2-6.25$

(h, k) = 0.50, -6.25 which is the vertex

b: To identify the y-intercept you plug in 0 as x which will only leave c which in this case is 6 which is the y-intercept. (0, 6). To identify the x-intercepts you can simplify plug in the values a, b, c into the quadratic equation which was stated in the previous answer. In this case a, b, c = -1, 1, 6. Plugging these values in gives the equation $y=\frac{-(1)\pm\sqrt{1^2-4(-1)(6)}}{2(-1)}$ . which simplifies to $x=\frac{-1\pm5}{-2}$ which gives the values -2 and 3. To find the vertex it's the same process as before

Factor out -1

$y=-(x^2-x-6)$

Add 6 to both sides (on the left side add -6 since -1 was factored out).

$y-6=-(x^2-x)$

Complete the square by adding (b/2)^2 to both sides (add -(b/2)^2 to left side since -1 was factored out)

$y-6-0.25 = -(x^2-x+0.25)$

Rewrite as square binomial

$y-6.25=-(x-0.5)^2$

Add 6.25 to both sides

$y=(x-0.50)^2+6.25$

(h, k) = (0.50, 6.25)

When you graph the parabolas you'll notice there just flipped relative to the x-axis. This can be deduced by simply looking at the two equations, since the two equations have the same absolute value coefficients, the signs are just different, and more specifically they're all opposite. If you took the first equation and multiplied the entire right side by -1 you would get the same equation. And since that equation really represents the value of y (since it's equal to y) you're reflecting it across the x-axis.

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1 year ago

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The scientist performs additional analyses and observes that the number of major earthquakes does appear to be decreasing but wo

kifflom [539]

Answer:

Step-by-step explanation:

Hello!

A regression model was determined in order to predict the number of earthquakes above magnitude 7.0 regarding the year.

^Y= 164.67 - 0.07Xi

Y: earthquake above magnitude 7.0

X: year

The researcher wants to test the claim that the regression is statistically significant, i.e. if the year is a good predictor of the number of earthquakes with magnitude above 7.0 If he is correct, you'd expect the slope to be different from zero: β ≠ 0, if the claim is not correct, then the slope will be equal to zero: β = 0

The hypotheses are:

H₀: β = 0

H₁: β ≠ 0

α: 0.05

The statistic for this test is a student's t: $t= \frac{b - \beta }{Sb} ~~t_{n-2}$

The calculated value is in the regression output $t_{H_0}= -3.82$

This test is two-tailed, meaning that the rejection region is divided in two and you'll reject the null hypothesis to small values of t or to high values of t, the p-value for this test will also be divided in two.

The p-value is the probability of obtaining a value as extreme as the one calculated under the null hypothesis:

p-value: $P(t_{n-2}\leq -3.82) + P(t_{n-2}\geq 3.82)$

As you can see to calculate it you need the information of the sample size to determine the degrees of freedom of the distribution.

If you want to use the rejection region approach, the sample size is also needed to determine the critical values.

But since this test is two tailed at α: 0.05 and there was a confidence interval with confidence level 0.95 (which is complementary to the level of significance) you can use it to decide whether to reject the null hypothesis.

Using the CI, the decision rule is as follows:

If the CI includes the "zero", do not reject the null hypothesis.

If the CI doesn't include the "zero", reject the null hypothesis.

The calculated interval for the slope is: [-0.11; -0.04]

As you can see, both limits of the interval are negative and do not include the zero, so the decision is to reject the null hypothesis.

At a 5% significance level, you can conclude that the relationship between the year and the number of earthquakes above magnitude 7.0 is statistically significant.

I hope this helps!

(full output in attachment)