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4 years ago

Write the equation for the line that passes

Mathematics

1 answer:

Allushta [10]4 years ago

7 0

Answer:

y=-3x+7

Step-by-step explanation:

Parallel means the lines have the same slope.

So they practically give you the slope as -3

Now we can use the form of an equation of a line

Y=mx+b

now we have m- the slope we just need to plug in the coordinate values given- (2,1)

Y=-3x+b

1=(-3·2)+b

1=-6+b

b=7

now we add to our original equation

we know m= -3

we know b=7

that's all we need

substitute

y=mx+b

becomes

y=-3x+7

Hope this helps

~lalagrl

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A manufacturer of paper coffee cups would like to estimate the proportion of cups that are defective (tears, broken seems, etc.)

Maksim231197 [3]

Answer:

The 95% confidence interval is $0.0503 < p < 0.1297$

The sample proportion is $\r p = 0.09$

The critical value is $Z_{\frac{\alpha }{2} } = 1.96$

The standard error is $SE =0.020$

Step-by-step explanation:

From the question we are told that

The sample size is n = 200

The number of defective is k = 18

The null hypothesis is $H_o : p = 0.08$

The alternative hypothesis is $H_a : p > 0.08$

Generally the sample proportion is mathematically evaluated as

$\r p = \frac{18}{200}$

$\r p = 0.09$

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

$\alpha = 100 - 95$

$\alpha = 5\%$

$\alpha = 0.05$

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

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

Generally the standard of error is mathematically represented as

$SE = \sqrt{\frac{\r p (1 - \r p)}{n} }$

substituting values

$SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }$

$SE =0.020$

The margin of error is

$E = Z_{\frac{ \alpha }{2} } * SE$

=> $E = 1.96 * 0.020$

=> $E = 0.0397$

The 95% confidence interval is mathematically represented as

$\r p - E < \mu < p < \r p + E$

=> $0.09 - 0.0397 < \mu < p < 0.09 + 0.0397$

=> $0.0503 < p < 0.1297$

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The answer would be A. m= -3/5 and b=-4/5
"m= -5-1 divided by 7--3
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or, -3/5.

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Source: webmath

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