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2 years ago

What is the value of W in a exterior angle theorem

Mathematics

1 answer:

malfutka [58]2 years ago

8 0

Answer:

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.

so:

30 + 2w - 8 = w + 48

22 + 2w = w + 48 export like terms to the same side of the equation

2w - w = 48 - 22 subtract

w = 26

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$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}\quad 
\begin{cases}
r=radius\\
------\\
r=4
\end{cases}\implies V=\cfrac{4\pi 4^3}{3}\implies V=\cfrac{256\pi }{3}\\\\
-------------------------------\\\\
\cfrac{sphere}{cylinder}\qquad \cfrac{2}{3}\impliedby ratio~thus\implies \cfrac{2}{3}=\cfrac{\stackrel{sphere}{v}}{\stackrel{cylinder}{v}}
\implies 
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3 years ago

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Step-by-step explanation:

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2 years ago

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A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at th

Natalija [7]

Answer:

Step-by-step explanation:

given that a certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 6 students' scores on the exam after completing the course:

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3 years ago

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3 years ago

A past survey of 1, 068,000 students taking a standardized test revealed that 8.9% of the students were planning on studying eng

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Complete Question

The complete question is shown on the first uploaded image

Answer:

The interval is $-0.0037 < p_1-p_2$

Step-by-step explanation:

From the question we are told that

The first sample size is $n _1 = 1068000$

The first sample proportion is $\r p_1 = 0.089$

The second sample size is $n_2 = 1476000$

The second sample proportion is $\r p_2 = 0.092$

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = (100 - 95 )\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table

The value is

$Z_{\frac{\alpha }{2} } =z_c= 1.96$

Generally the 95% confidence interval is mathematically represented as

$(\r p_1 - \r p_2 ) -z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}} < (p_1 - p_2 ) < (\r p_1 - \r p_2 ) +z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}}$

Here $\r q_1$ is mathematically evaluated as $\r q_1 = (1 - \r p_1)= 1-0.089 =0.911$

and $\r q_2$ is mathematically evaluated as $\r q_2 = (1 - \r p_2) = 1- 0.092 = 0.908$

$(0.089 - 0.092 ) -1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}} < (p_1 - p_2 ) < (0.089 - 0.092 ) +1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}}$

$-0.0037 < p_1-p_2$

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3 years ago