Struggling so hard on this

Two angles and one side in a triangle are equivalent to those in another triangle. Are the remaining sides and angles equivalent

butalik [34]

Only if the one side is between the two angles. If not, then we can't say. Maybe the rest are, and maybe they're not.

8 0

3 years ago

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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

Evaluate the following expression: 2^3

maw [93]

2^3=2×2×2
2^3=4×2
2^3=8

7 0

3 years ago

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Mark is in training for a bicycle race. He needs to ride 50 km a week as part of his training. He rode 18.23 km on Monday and 13

konstantin123 [22]

The answer is B-about 18km

This is because you round 18.23 to 18km

then you round 13.94 to 14km

you add these rounded numbers together

you take it away from 50km

the answer would then me 18km

but it be ABOUT because that was only a rough estimate because it was rounded

5 0

3 years ago

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Barry found a computer at Staples for $989. A week later, the computer went on sale for $849. What

JulijaS [17]

Barry found a computer at Staples for $989. A week later, the computer went on sale for $849. The percentage change is 14.156 % decrease

Solution:

Given that Barry found a computer at Staples for $989

A week later, the computer went on sale for $849

To find: percent of change

Percent change is the extent to which a variable gains or loses value. The figures are arrived at by comparing the initial (or before) and final (or after) quantities according to a specific formula.

THE PERCENT CHANGE IS GIVEN AS:

$\text{ percent change } =\frac{\text { final value - initial value }}{\text { initial value }} \times 100$

If the result is positive, it is percentage increase

If the result is negative, it is percentage decrease

Here initial value = 989 and final value = 849

Substituting the values in above formula,

$\begin{aligned}&\text { percent change }=\frac{849-989}{989} \times 100\\\\&\text { percent change }=-0.14155 \times 100=-14.156 \%\end{aligned}$

Here negative sign denotes percentage decrease

Thus percentage change is 14.156 % decrease

8 0

3 years ago