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Bond [772]
2 years ago
6

A pair of perpendicular lines intersect at the point (5,9). Write

Mathematics
1 answer:
maw [93]2 years ago
6 0

Answer:

The equation of the line that is perpendicular to the line that passes through the point (-4, 2) is y = -9·x/5 + 18

Step-by-step explanation:

The coordinates of the point of intersection of the two lines = (5, 9)

The coordinates of a point on one of the two lines, line 1 = (-4, 4)

The slope of a line perpendicular to another line with slope, m = -1/m

Therefore, we have;

The slope, m₁, of the line 1 with the known point = (9 - 4)/(5 - (-4)) = 5/9

Therefore, the slope, m₂, of the line 2 perpendicular to the line that passes through the point (-4, 4) = -9/5

The equation of the line 2 is given as follows;

y - 9 = -9/5×(x - 5)

y - 9 = -9·x/5 + 9

y =  -9·x/5 + 9 + 9

y = -9·x/5 + 18

Therefore, the equation of the line that is perpendicular to the line that passes through the point (-4, 2) is y = -9·x/5 + 18.

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A College Alcohol Study has interviewed random samples of students at four-year colleges. In the most recent study, 494 of 1000
Vinil7 [7]

Answer:

The 95% confidence interval for the difference between the proportion of women who drink alcohol and the proportion of men who drink alcohol is (-0.102, -0.014) or (-10.2%, -1.4%).

Step-by-step explanation:

We want to calculate the bounds of a 95% confidence interval of the difference between proportions.

For a 95% CI, the critical value for z is z=1.96.

The sample 1 (women), of size n1=1000 has a proportion of p1=0.494.

p_1=X_1/n_1=494/1000=0.494

The sample 2 (men), of size n2=1000 has a proportion of p2=0.552.

p_2=X_2/n_2=552/1000=0.552

The difference between proportions is (p1-p2)=-0.058.

p_d=p_1-p_2=0.494-0.552=-0.058

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

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{494+552}{1000+1000}=\dfrac{1046}{2000}=0.523

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{0.523*0.477}{1000}+\dfrac{0.523*0.477}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.000249+0.000249}=\sqrt{0.000499}=0.022

Then, the margin of error is:

MOE=z \cdot s_{p1-p2}=1.96\cdot 0.022=0.0438

Then, the lower and upper bounds of the confidence interval are:

LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.058-0.0438=-0.102\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.058+0.0438=-0.014

The 95% confidence interval for the difference between proportions is (-0.102, -0.014).

7 0
2 years ago
Write the equation for Chelsea's graph in
xeze [42]

Answer:

y=-4x+16.

Step-by-step explanation:

From the given graph it is clear that the y-intercept is 16.

The line passes through (-2,24) and (2,8). So, slope of line is

Slope=\dfrac{y_2-y_1}{x_2-x_1}

Slope=\dfrac{8-24}{2-(-2)}

Slope=\dfrac{-16}{4}

Slope=-4

Slope intercept form of a line is

y=mx+b

where, m is slope and b is y-intercept.

Substitute m=-4 and b=16 in the above equation.

y=(-4)x+(16)

y=-4x+16

Therefore, the required equation is y=-4x+16.

6 0
3 years ago
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Rufina [12.5K]

Answer:

  d. Anthony rode 14 more miles per week than Malique.

Step-by-step explanation:

Anthony rode (141 mi)/(3 wk) = 47 mi/wk.

Malique rode (165 mi)/(5 wk) = 33 mi/wk.

Anthony rode more miles per week by ...

  (47 -33) mi/wk = 14 mi/wk

Anthony rode 14 more miles per week than Malique.

5 0
2 years ago
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dolphi86 [110]
$5 per Hour because the number keeps changing 5 dollars the first hour 10 the next... 15, 20... the number keeps climbing.
5 0
3 years ago
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Sloan [31]

Answer:

The volume is 75

Step-by-step explanation:

because the volume is the width, length, and height, add them together.

7 0
3 years ago
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