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3 years ago

Find the slope of a line perpendicular to y=-2/5x+4/5.

Mathematics

1 answer:

Inga [223]3 years ago

7 0

For two lines to be perpendicular their slopes must be negative reciprocals of one another, mathematically:

m1*m2=-1

In this case, our reference line has a slope of -2/5 so our perpendicular slope must satisfy:

-2m/5=-1

-2m=-5

m=-5/-2

m=5/2

....

The negative reciprocal property can be more easily understood by realizing that the angle of a line is:

tanα=m

α=arctanm

So if one line, A, has a slope of m and the other, B, has a slope of -1/m

A=arctan m, B=arctan -1/m

B-A=90° (feel free to use any value for m that you choose to see that this is true, so if the two lines differ by 90°, they are indeed perpendicular)

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OverLord2011 [107]

Answer:

1) p1=0.83

2) p2=0.81

3) Option B

4) p=0.82

5) s=0.03

6) z=0.67

7) P=0.50

8) Do not reject H0

Step-by-step explanation:

1) The proportion of Republicans who think the full-body scans should be applied in airports is equal to the ratio between the republicans that think it should over the total Republicans in the poll:

$p=X/n=258/311=0.83$

2) The proportion of Democrats who think the full-body scans should be applied in airports is equal to:

$p=X/n=294/363=0.81$

3) As we want to know if there is a difference in the proportions calculated, not if one is higher or lower than the other, the correct option is B:

$H_0:p_1-p_2=0\\\\H_a:p_1-p_2\neq0$

4) The pooled estimate of a proportion is the average of both proportions:

$\bar{p}=\frac{p_1+p_2}{2}= \frac{0.83+0.81}{2}=0.82$

5) The standard error can be calculated as:

$s=\sqrt{\frac{\bar{p}(1-\bar{p})}{n_1} +\frac{\bar{p}(1-\bar{p})}{n_2}} \\\\s=\sqrt{\frac{0.82*0.18}{311} +\frac{0.82*0.18}{363}} \\\\s=\sqrt{0.00047+0.00041} =\sqrt{0.00088}=0.03$

6) The z-statistic can be calculated as:

$z=\frac{p_1-p_2}{s}=\frac{0.83-0.81}{0.03}=\frac{0.02}{0.03}=0.67$

7) The P-value for z=0.67 is P=0.50 (from the standard normal distribution table).

$2P(Z>|z|)=0.50286$

8) If the significance level is 0.01, the P-value is bigger than the significance level. The effect is not significanct. The null hypothesis is not rejected.

There is not enough evidence to say that both proportions are different.

A. Do not reject H0

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2 years ago

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mario62 [17]

Answer:

315-90 = 15x-6x

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9x/225

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3 years ago

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Y_Kistochka [10]

Let's do this step by step:
Our objective is to find out x.

First, we have to take the '-3' to the right side, and put it next to the 11. When we do this its operation reverses, so it becomes 11 + 3, which is 14.
So we have 9x > 2x + 14.
Then we do the same to the numbers with X, but this time we take the number from the right side to the left. So 2x to the left (reversed) becomes 9x-2x which is 7x.
So 7x > 14
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