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REY [17]
2 years ago
14

Determine whether line AB and line CD are parallel, perpendicular, or neither. A( 4, 2), B(-3, 1), C(6, 0), D(-10, 8)

Mathematics
1 answer:
Lapatulllka [165]2 years ago
6 0

Answer:

<h2>neither</h2>

Step-by-step explanation:

If AB an CD are parallel, then their slopes are the same.

If AB and CD are perpendicular, then the product of their slopes is equal -1.

The formula of a slope:

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

Calculate the both slope:

A(4,\ 2),\ B(-3,\ 1)\\\\m_{AB}=\dfrac{1-2}{-3-4}=\dfrac{-1}{-7}=\dfrac{1}{7}\\\\C(6,\ 0),\ D(-10,\ 8)\\\\m_{CD}=\dfrac{8-0}{-10-6}=\dfrac{8}{-16}=-\dfrac{1}{2}\\\\=============================

m_{AB}\neq m_{CD}

The line AB and line CD are not parallel

m_{AB}\cdot m_{CD}=\left(\dfrac{1}{7}\right)\left(-\dfrac{1}{2}\right)=-\dfrac{1}{14}\neq-1

The line AB and line CD are not perpendicular.

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Step-by-step explanation:

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4 0
2 years ago
Use the information provided to determine a 95% confidence interval for the population variance. A researcher was interested in
Leno4ka [110]

Answer:

The 95% confidence interval for the population variance is (8.80, 32.45).

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for the population variance is given as follows:

\frac{(n-1)\cdot s^{2}}{\chi^{2}_{\alpha/2}}\leq \sigma^{2}\leq \frac{(n-1)\cdot s^{2}}{\chi^{2}_{1-\alpha/2}}

It is provided that:

<em>n</em> = 20

<em>s</em> = 3.9

Confidence level = 95%

⇒ <em>α</em> = 0.05

Compute the critical values of Chi-square:

\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.05/2, (20-1)}=\chi^{2}_{0.025,19}=32.852\\\\\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{1-0.05/2, (20-1)}=\chi^{2}_{0.975,19}=8.907

*Use a Chi-square table.

Compute the 95% confidence interval for the population variance as follows:

\frac{(n-1)\cdot s^{2}}{\chi^{2}_{\alpha/2}}\leq \sigma^{2}\leq \frac{(n-1)\cdot s^{2}}{\chi^{2}_{1-\alpha/2}}

\frac{(20-1)\cdot (3.9)^{2}}{32.852}\leq \sigma^{2}\leq \frac{(20-1)\cdot (3.9)^{2}}{8.907}\\\\8.7967\leq \sigma^{2}\leq 32.4453\\\\8.80\leq \sigma^{2}\leq 32.45

Thus, the 95% confidence interval for the population variance is (8.80, 32.45).

4 0
2 years ago
What is the formula for the area A of a trapezoid with parallel sides of length B and D, nonparallel sides of length A and C and
loris [4]

Answer:

(B) \dfrac12H (B+D)

Step-by-step explanation:

\text{Area of a trapezoid }= \dfrac12 ($Sum of the parallel sides) \times $Height\\Parallel Sides = B and D\\Height =H\\Therefore:\\\text{Area of the trapezoid }= \dfrac12 (B+D) H

The correct option is B.

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3 years ago
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Afina-wow [57]

Answer:

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