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3 years ago

Use identities to simplify

Mathematics

1 answer:

lianna [129]3 years ago

3 0

(B)

Explanation:

$(\sec \beta + 1)(\tan \beta \csc \beta - 1)$

$=\left(\dfrac{1}{\cos\beta} + 1 \right) \left(\dfrac{\sin \beta}{\cos \beta} \dfrac{1}{\sin \beta} - 1 \right)$

$=\left(\dfrac{1}{\cos\beta} + 1 \right) \left(\dfrac{1}{\cos \beta} - 1 \right)$

$= \left(\dfrac{1}{\cos^2 \beta} - 1 \right)$

$= \left(\dfrac{1 - \cos^2 \beta}{\cos^2 \beta} \right)$

$= \dfrac{\sin^2 \beta}{\cos^2 \beta}$

$= \tan^2 \beta$

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Answer:

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Geometry Special Quadrilaterals show work please

Charra [1.4K]

Answer:

a = 16

w = 125

x = 120

y = 55

Step-by-step explanation:

FINDING 'a'

31 = a + 46 / 2

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* This section looks Non-Isosceles trapezoid so I will be following the rule according it

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FINDING 'y'

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The answer is 10. If you replace the number letters with the numbers you get 6 + 10 / 2 - 1. Then you follow PEMDAS, so first divide 10 with 2 to get five (6 + 5 - 1). Add 6 and 5 to get 11 and subtract 1 to get the final answer of 10.

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A molecule of butane contains 10 atoms of hydrogen to every 4 atoms of hydrogen to every 4 atoms of carbon. Could a compound con

Naily [24]

Answer:

Yes this compound could be shown to be butane, specifically, it can be shown to be 9 molecules of butane. Check Explanation for more.

Step-by-step explanation:

Butane contains 10 hydrogen atoms for every 4 carbon atoms. It's molecular formula is C₄H₁₀

The hydrocarbon compound presented has 36 carbon atoms and 90 hyfrogen atoms

If the ratio of each of these atoms present is also in the ratio 4:10 like C:H, then, it can be inferred that the compound is indeed Butane

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36 | 90

dividing through by 9, we have

C | H

4 | 10

which is the exact ratio of Carbon to Hydrogen in butane.

Hence, the unknown compound is most likely 9 molecules of butane

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3 years ago

Random samples of students were compared to see whether or not there was a difference in the proportion favoring the university'

Nimfa-mama [501]

Answer:

There is enough evidence to support the claim that there is a significant difference in the proportion of residents and commuters who prefer the switch.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that there is a significant difference in the proportion of residents and commuters who prefer the switch.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0$

The significance level is 0.05.

The sample 1 (residents), of size n1=200 has a proportion of p1=0.4.

$p_1=X_1/n_1=80/200=0.4$

The sample 2 (conmuters), of size n2=200 has a proportion of p2=0.6.

$p_2=X_2/n_2=120/200=0.6$

The difference between proportions is (p1-p2)=-0.2.

$p_d=p_1-p_2=0.4-0.6=-0.2$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{80+120}{200+200}=\dfrac{200}{400}=0.5$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.5*0.5}{200}+\dfrac{0.5*0.5}{200}}\\\\\\s_{p1-p2}=\sqrt{0.0013+0.0013}=\sqrt{0.0025}=0.05$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.2-0}{0.05}=\dfrac{-0.2}{0.05}=-4$

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=2\cdot P(z$

As the P-value (0.00008) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that there is a significant difference in the proportion of residents and commuters who prefer the switch.

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4 years ago