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3 years ago

What is the equation of the line that passes through the point (2,−4) and has a slope of 2?

Mathematics

1 answer:

vivado [14]3 years ago

3 0

Answer:

y = 2x - 8

Step-by-step explanation:

Since you have the slope of the line and point that the line passes through, you can use "point-slope form", hence the name.

Point-slope form is: $y-y_1=m(x-x_1)$

Substitute the slope (2) into m, and substitute the x-value of the point into $x_1$ and the the y-value of the point into $y_1$ .

$y-(-4)=2(x-(2))$

Simplify this equation.

$y+4=2(x-2)$

Distribute 2 inside the parentheses.

$y+4=2x-4$

Subtract 4 from both sides.

$y=2x-8$ is the final answer.

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According to a polling organization, 24% of adults in a large region consider themselves to be liberal. A survey asked 200 resp

Varvara68 [4.7K]

Answer:

$z=\frac{0.375 -0.24}{\sqrt{\frac{0.24(1-0.24)}{200}}}=4.47$

Now we can calculate the p value based on the alternative hypothesis with this probability:

$p_v =P(z>4.47)=0.00000391$

The p value is very low compared to the significance level of $\alpha=0.05$ then we can reject the null hypothesis and we can conclude that the true proportion of people liberal is higher than 0.24

Step-by-step explanation:

Information given

n=200 represent the random sample taken

X=75 represent the number of people Liberal

$\hat p=\frac{75}{200}=0.375$ estimated proportion of people liberal

$p_o=0.24$ is the value that we want to test

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to verify if the true proportion of adults liberal is higher than 0.24:

Null hypothesis: $p \leq 0.24$

Alternative hypothesis: $p > 0.24$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the info given we got:

$z=\frac{0.375 -0.24}{\sqrt{\frac{0.24(1-0.24)}{200}}}=4.47$

Now we can calculate the p value based on the alternative hypothesis with this probability:

$p_v =P(z>4.47)=0.00000391$

The p value is very low compared to the significance level of $\alpha=0.05$ then we can reject the null hypothesis and we can conclude that the true proportion of people liberal is higher than 0.24

6 0

3 years ago

Pls help me answer this question i need it asap. This is a good offer :)

tensa zangetsu [6.8K]

Answer:

The product is 21/32.

Step-by-step explanation:

Write the product:

=> 2 5/8 x 2/8

Convert it to improper fraction:

=> 21/8 x 2/8

Multiply:

=> 42/64

Simplify:

=> 21/32

Hence, the product is 21/32.

Hoped this helped.

$BrainiacUser1357$

7 0

3 years ago

Read 2 more answers

The measure of an angle in standard position is given. Find two positive angles and two negative angles that are coterminal with

Pani-rosa [81]

Notice the picture below

negative angles, are just angles that go "clockwise", namely, the same direction a clock hands move hmmm so.... and one revolution is just 2π

now, you can have angles bigger than 2π of course, by simply keep going around, so, if you go around 3 times on the circle, say "counter-clockwise", or from right-to-left, counter as a clock goes, 3 times or 3 revolutions will give you an angle of 6π, because 2π+2π+2π is 6π

now... say... you have this angle here... let us find another that lands on that same spot

by simply just add 2π to it :)

$\bf \cfrac{7}{6}+2=\cfrac{19}{6}\qquad thus\qquad \cfrac{7\pi} {6}+2\pi =\cfrac{19\pi }{6}
\\\\\\
\cfrac{19\pi }{6}\impliedby co-terminal\ angle$

now, that's a positive one
and $\bf \cfrac{7}{6}-2=-\cfrac{5}{6}\qquad thus\qquad \cfrac{7\pi} {6}-2\pi =-\cfrac{5\pi }{6}
\\\\\\
-\cfrac{5\pi }{6}\impliedby \textit{is also a co-terminal angle}$

to get more, just keep on subtracting or adding 2π