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3 years ago

Help with writing the set from an interval notation.

Mathematics

1 answer:

Nikitich [7]3 years ago

5 0

Answer:

(-oo, 1) U (1, 3) U (3, oo)

Step-by-step explanation:

We have a line with two arrowheads. The arrow heads show us that the numbers in the set continue forever in the negative direction past -5 and in the positive direction past 5. In this case, the set consists of all real numbers except 1 and 3 since they have open circles.

That means the set is from negative infinity to 1, from 1 to 3, from 3 to positive infinity, but leaving out 1 and 3.

Remember that a regular parentheses symbols, ( and ), do not include the number near them and are used for open circles.

Square brackets, [ and ], do include the number near them and are used for closed circles.

Also, infinity and negative infinity are not numbers, so we always use regular parentheses when dealing with infinity or negative infinity.

We need the union of three sets:

from negative infinity to 1, from 1 to 3, from 3 to positive infinity

Answer: (-oo, 1) U (1, 3) U (3, oo)

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Do political science classes require less writing than history classes? The 55 randomly selected political science classes assig

saul85 [17]

Answer:

We conclude that political science classes require less writing time than history classes at 0.01 level of significance.

Step-by-step explanation:

We are given that the 55 randomly selected political science classes assigned an average of 16.3 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages.

The 54 randomly selected history classes assigned an average of 18.9 pages of essay writing for the course. The standard deviation for these 54 classes was 5 pages.

Let $\mu_1$ = average writing time required by political science classes.

$\mu_2$ = average writing time required by history classes.

So, Null Hypothesis, $H_0$ : $\mu_1\geq\mu_2$ {means that political science classes require more or equal writing time than history classes}

Alternate Hypothesis, $H_A$ : $\mu_1$ {means that political science classes require less writing time than history classes}

The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t__n_1_-_n_2_-_2$

where, $\bar X_1$ = sample average pages of essay writing for political science classes = 16.3 pages

$\bar X_2$ = sample average pages of essay writing for history classes = 18.9 pages

$s_1$ = sample standard deviation for political science classes = 4.8 pages

$s_2$ = sample standard deviation for history classes = 5 pages

$n_1$ = sample of political science classes = 55

$n_2$ = sample of history classes = 54

Also, $s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(55-1)\times 4.8^{2}+(54-1)\times 5^{2} }{55+54-2} }$ = 4.90

So, test statistics = $\frac{(16.3-18.9)-(0)}{4.9 \sqrt{\frac{1}{55}+\frac{1}{54} } }$ ~ $t_1_0_7$

= -2.77

The value of t test statistics is -2.77.

Now, at 0.01 significance level the t table gives critical value of -2.365 at 107 degree of freedom for left-tailed test.

Since our test statistics is less than the critical value of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that political science classes require less writing time than history classes.

3 0

3 years ago

The great pyramids at giza were built during which of the following periods

olya-2409 [2.1K]

You didn't provide any answer choices so this is what I found...

The Great Pyramid of Giza was built for the Fourth Dynasty Pharaoh Khufu (or Cheops), and was completed around 2560 BCE.

This is mathematics, I think you meant to put this in History, lol. I hope my answer helps. I'm not sure if it was the answer you were looking for though. :)

7 0

4 years ago

Read 2 more answers

A cellphone company offers four choices for purchasing talk time. Which of the following has the lowest cost per minute?

g100num [7]

H you divide 80.50/700 and will give you the rate for minute

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3 years ago

A soccer team is having a car wash. The team spent $45 on supplies. They earned $350, including tips. The team's profit is the a

umka21 [38]

The profit is going to be the total amount made, so you are going to subtract $350 - $45 = $305. $305. I hope this helps!

5 0