Help please due today

shutvik [7]

Answer:

Given: $r || s$ and q is a transversal.

Alternative Interior Angle states that a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal are equal.

By alternative interior angle;

$\angle 3 \cong \angle 6$

Definition of Congruent angles are angles that have the same degree of measurement.

Therefore, $m\angle 3 = m\angle 6$ [By definition of Congruent] .....[1]

Linear Pair states that a pair of adjacent angles formed when two lines are intersect.

therefore, $\angle 4$ and $\angle 3$ are a linear pair. [by definition of linear pair]

Two angles of linear pairs are always supplementary , which means their measure are add up to 180 degree.

By the definition of supplementary angles, $m\angle 4 + m\angle 3 = 180^{\circ}$ .....[2]

Substitute equation [1] in [2] we get,

$m\angle 4 +m\angle 6 =180^{\circ}$

By the definition of supplementary angles,

$\angle 4$ is supplementary to $\angle 6$ Hence proved!

8 0

4 years ago

Read 2 more answers

Maria cut 5 1/2 yards of string to attach to her kite. How many inches is that

ivolga24 [154]

You answer 72 let me know if I was right

8 0

3 years ago

Read 2 more answers

The set of data in the table below represents a linear function.

Vinil7 [7]

Answer:

y = 2x - 19

Step-by-step explanation:

Graph the points on the table and you'll be able to see the answer. That's how I went about it.

or use m = y^2 - y^1 divided by x^2 - x^1 to find the slope, then solve for the initial value from there

8 0

1 year ago

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

What is the value of the expression below (-64)^2/3

damaskus [11]

Answer:

16

Step-by-step explanation:

$(-64)^2/3$