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Lelechka [254]
3 years ago
5

Can someone help please

Mathematics
1 answer:
sineoko [7]3 years ago
3 0

A: Commutative Property of Addition

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The inequality is < so 2/4 < 5/6.
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I have two proof questions and I don't really know how to do them.
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\angle1\cong\angle2 corresponding angles, therefore

m∠1 = m∠2 → m∠2 = 130°

\angle2\cong\angle3 vertical angles, therefore

m∠2 = m∠3 → m∠3 = 130°


If ∠1 and ∠2 are complementary, then m∠1 + m∠2 = 90°.

If ∠2 and ∠3 are complementary, then m∠2 + m∠3 = 90°

Therfore

m\angle1 + m\angle2 = m\angle2 + m\angle3\qquad|\text{subtract}\ m\angle2\ \text{ from both sides}\\\\m\angle1 = m\angle3\to\angle1\cong\angle3

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3 years ago
In a random sample of students who took the SAT test, 427 had paid for coaching courses and the remaining 2733 had not. Calculat
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Answer:

The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

427 had paid for coaching courses and the remaining 2733 had not.

This means that n = 427 + 2733 = 3160, \pi = \frac{427}{3160} = 0.1351

95% confidence level

So \alpha = 0.05, z is the value of Z that has a p-value of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 - 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.1232

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 + 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.147

The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).

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3 years ago
Tamara has decided to start saving for spending money for her first year of college. Her money is currently in a large suitcase
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Answer:

She can create a function for the total savings in terms of the time x by adding the two functions together. The new function should look like this:

T(x)=S(x)+a(x)

So now we can substitute the given functions:

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But this function can be simplified for it to be easier for her to calculate her total amount of savings. We can do that by distributing the 6 into the parenthesis. This is, multiply the 6 by both the x and the -2, so we get:

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and now we can combine like terms. We can subtract 12 from 450 so we get:

T(x)=6x+438

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