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3 years ago

3.

Mathematics

1 answer:

baherus [9]3 years ago

5 0

Answer:

3. $\overline{PM}\cong \overline{ON}$ Distances between two parallel lines $\overline{MN} \ and\ \overline{PO}$

4. $\overline{AC}$ = $\overline{CE}$ : Reason; Corresponding part of ΔACB and ΔDCE

C is the midpoint of $\overline{AE}$ : Reason; $\overline{AC}$ = $\overline{CE}$ : Definition of midpoint

Step-by-step explanation:

3. A parallelogram is defined as a quadrilateral with two opposite sides equal and parallel and having equal opposite interior angles

MNOP is a parallelogram: Reason; Given

$\overline{PM}\left | \right |\overline{ON}$ : Reason; Opposite sides of a parallelogram

∠NOM ≅ ∠OMP: Reason Alternate interior angles

$\overline{MN}\left | \right |\overline{PO}$ : Reason; Opposite sides of a parallelogram

∠NMO ≅ ∠MOP: Reason Alternate interior angles

$\overline{PM}\cong \overline{ON}$ Distances between two parallel lines $\overline{MN} \ and\ \overline{PO}$

4. $\overline{AB}\left | \right |\overline{DE}$ : Reason; Given

∠EAB ≅ ∠AED: Reason; Alternate int. ∠s Thm

∠ABC ≅ ∠EDB : Reason; Alternate int. ∠s Thm

C is the midpoint of $\overline{BD}$ : Reason; Given

$\overline{BC}$ = $\overline{CD}$ : Reason; Definition of midpoint

Therefore, ΔACB ≅ ΔDCE: Reason Angle Angle Side (AAS) Theorem

$\overline{AC}$ = $\overline{CE}$ : Reason; Corresponding part of ΔACB and ΔDCE

C is the midpoint of $\overline{AE}$ : Reason; Definition of midpoint

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Suppose small aircraft arrive at a certain airport according to a Poisson process with rate a 5 8 per hour, so that the number o

timurjin [86]

Answer:

(a) P (X = 6) = 0.12214, P (X ≥ 6) = 0.8088, P (X ≥ 10) = 0.2834.

(b) The expected value of the number of small aircraft that arrive during a 90-min period is 12 and standard deviation is 3.464.

Step-by-step explanation:

Let the random variable X = number of aircraft arrive at a certain airport during 1-hour period.

The arrival rate is, λt = 8 per hour.

(a)

For t = 1 the average number of aircraft arrival is:

$\lambda t=8\times 1=8$

The probability distribution of a Poisson distribution is:

$P(X=x)=\frac{e^{-8}(8)^{x}}{x!}$

Compute the value of P (X = 6) as follows:

$P(X=6)=\frac{e^{-8}(8)^{6}}{6!}\\=\frac{0.00034\times262144}{720}\\ =0.12214$

Thus, the probability that exactly 6 small aircraft arrive during a 1-hour period is 0.12214.

Compute the value of P (X ≥ 6) as follows:

$P(X\geq 6)=1-P(X$

Thus, the probability that at least 6 small aircraft arrive during a 1-hour period is 0.8088.

Compute the value of P (X ≥ 10) as follows:

$P(X\geq 10)=1-P(X$

Thus, the probability that at least 10 small aircraft arrive during a 1-hour period is 0.2834.

(b)

For t = 90 minutes = 1.5 hour, the value of λ, the average number of aircraft arrival is:

$\lambda t=8\times 1.5=12$

The expected value of the number of small aircraft that arrive during a 90-min period is 12.

The standard deviation is:

$SD=\sqrt{\lambda t}=\sqrt{12}=3.464$

The standard deviation of the number of small aircraft that arrive during a 90-min period is 3.464.

(c)

For t = 2.5 the value of λ, the average number of aircraft arrival is:

$\lambda t=8\times 2.5=20$

Compute the value of P (X ≥ 20) as follows:

$P(X\geq 20)=1-P(X$

Thus, the probability that at least 20 small aircraft arrive during a 2.5-hour period is 0.5298.

Compute the value of P (X ≤ 10) as follows:

$P(X\leq 10)=\sum\limits^{10}_{x=0}(\frac{e^{-20}(20)^{x}}{x!})\\=0.01081\\\approx0.0108$

Thus, the probability that at most 10 small aircraft arrive during a 2.5-hour period is 0.0108.

8 0

3 years ago

What is an equation of the line that passes through the points (-8, 1) and(7,1)?

likoan [24]

Answer:

y=1

Step-by-step explanation:

you can use those points to find the slope

use the equation $\frac{y_{1} - y_{2}}{x_{1}-x_{2}}$ then plug in the numbers

so (1-1)/(-8-7) = 0/15 so the slope is zero meaning it is a horizontal line which we can tell logically because the y coordinates of both points are 1.

so if you plug those numbers into the formula y=mx+b where m is slope and b is the y intercept then

you get y=0*x+1

then 0*x is just zero and it goes away so the equation for this line is y=1

Hope this helps! :)

8 0

3 years ago

Read 2 more answers

Solve the system of equations. – 3y + 5x = 26 - 2 - 5x = -16

mylen [45]

Answer:

$y=-4,\:x=\frac{14}{5}$

Step-by-step explanation:

$\begin{bmatrix}-3y+5x=26\\ -2-5x=-16\end{bmatrix}$

Isolate x for -2-5x=-16:

$x=\frac{14}{5}$

$\mathrm{Substitute\:}x=\frac{14}{5}$

$\begin{bmatrix}-3y+5\cdot \frac{14}{5}=26\end{bmatrix}$

$Simplify$

$\begin{bmatrix}-3y+14=26\end{bmatrix}$

Isolate y for -3y+14=26:

$y=-4$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$y=-4,\:x=\frac{14}{5}$

7 0

3 years ago

How do you do this?????

o-na [289]

$y = 2x - 9$

Step-by-step explanation:

Let's rewrite the given equation such that only y is on the left side and everything else on the right side:

$3x + 6y = -30 \Rightarrow 6y = -3x - 30$

Simplifying this by dividing by 6, we get

$y = -\frac{1}{2}x - 5$

This line has a slope of -1/2, which means that a line perpendicular to this has a slope of 2 (i.e., negative reciprocal). So we can write its equation as

$y = 2x + b$

This is the slope-intercept form of the equation of the line perpendicular to our given line. To complete this form, we need to find the value of b. Since this line passes through (1, -7), put these numbers into our equation to get

$-7 = 2(1) + b \Rightarrow b = -9$