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Rus_ich [418]
3 years ago
6

Rectangle ABCD with coordinates A(1, 1), B(4, 1), C(4, 2), and D(1, 2) dilates with respect to the origin to give rectangle A'B'

C'D'. If = 6, what is the scale factor of the dilation?

Mathematics
1 answer:
Fed [463]3 years ago
3 0
I have attached a screenshot with the complete question.

Answer:
dilation factor is 2

Explanation:
First, we will need to find the distance of AB as follows:
distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}
AB = \sqrt{(4-1)^2 + (1-1)^2}
AB = √9 = 3 units

Dilation can be represented as follows:
A'B' = k * AB
where k is the dilation factor

We are given that:
A'B' = 6

We can note that:
A'B' = 2 * AB
Therefore, the dilation factor is 2.

Hope this helps :)

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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)

5 0
3 years ago
Are the fractions Name two fractions
scoundrel [369]

Answer:

1/2 and 4/8         1/2 and 3/8 are not equivalent.

Step-by-step explanation:

6 0
3 years ago
George bought 2.5 pounds of each type of fruit shown on the sign apples $1.30/lb,grapes $1.65/lb,bananas $0.49/lb.what was the t
Stella [2.4K]

Answer:

$8.60

Step-by-step explanation:

Let’s find the cost for each item

Apples: 2.5 x 1.30 = 3.25

Grapes: 2.5 x 1.65 = 4.125

Bananas: 2.5 x 0.49 = 1.225

Now we will add all the costs which will give use our total!

3.25 + 4.125 + 1.225 = 8.6

So the answer will be $8.60

5 0
2 years ago
Attila the Hun was a ruler of the Hunnic Empire. The Romans feared him greatly until his death since he made quite a habit of in
Bas_tet [7]
The inequality would be x > 453 because any year after he died would be more than the year he died. 
Also, if it helps, I think of inequalities as an alligator's mouth, trying to eat the bigger quantity. 
Hope this helps!
8 0
3 years ago
Eloise is planning on retiring soon. When she first began working she invested $1500 in a retirement fund. The percent increase
cupoosta [38]
$2925 she would have left in her account :)
6 0
3 years ago
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