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scoundrel [369]
3 years ago
7

80% of an airline's flights depart on-time and 20% do not. Of those that depart on-time, 95% arrive on-time. Of those that depar

t late, 10% arrive on-time. What is the chance of someone taking a flight that will arrive on-time?
Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
4 0

Answer:

0.78

Step-by-step explanation:

given that 80% of an airline's flights depart on-time and 20% do not.

Of those that depart on-time, 95% arrive on-time. Of those that depart late, 10% arrive on-time

Let A be the event that flight departs on time.

Now A and A' are mutually exclusive and exhaustive

Let B be the event the flight arrives on time

Using total probability calculation we have

the chance of someone taking a flight that will arrive on-time

= P(B)

=P(A)+P(A'B)\\= 0.80(0.95) +0.20(0.10)\\= 0.76+0.02\\=0.78

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A clothier who only makes shirts and pants can make a shirt in 4 hours and a pair of pants in 6
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The amount of shirts and pants the clothier makes is an illustration of a linear equation

The equation that represents the number of shirts, and the number of pants is 4s + 6p = 40

<h3>How to determine the equation</h3>

The rates are given as:

Shirts = 4 hours

Pants = 6 hours

In time t, the shirts and pants made is represented with:

t = 4s + 6p

Given that the time is 40 hours, the equation becomes

4s + 6p = 40

Hence, the equation that represents the number of shirts, and the number of pants is 4s + 6p = 40

Read more about linear equations at:

brainly.com/question/14323743

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2 years ago
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Step-by-step explanation:

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3 years ago
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Find a vector equation and parametric equations for the line segment that joins p to q.P(0, - 1, 1), Q(1/2, 1/3, 1/4)
lakkis [162]

Answer:

vector equation:

\overrightarrow{PQ}=\begin{bmatrix}1/2}\\4/3\\-3/4\end{bmatrix}

parametric equations:

r_x = \dfrac{1}{2}t\\r_y = -1 +\dfrac{4}{3}t\\r_z = 1=\dfrac{3}{4}t

Step-by-step explanation:

The coordinates of the points are given as:

P(0,-1,1) and Q(1/2,1/3,1/4)

the coordinates of any points are also position vectors (vectors starting from the origin to that point), and can be represented as:

\overrightarrow{OP} = 0\hat{i}-1\hat{j}+1\hat{k}

or

\overrightarrow{OP} = \begin{bmatrix}0\\-1\\1\end{bmatrix}

similarly,

\overrightarrow{OQ} =\dfrac{1}{2}\hat{i}+\dfrac{1}{3}\hat{j}+\dfrac{1}{4}\hat{k}

or

\overrightarrow{OQ} = \begin{bmatrix}1/2}\\1/3\\1/4\end{bmatrix}

the vector PQ can be described as:

\overrightarrow{PQ}=\overrightarrow{OQ}-\overrightarrow{OP}

\overrightarrow{PQ}=\begin{bmatrix}1/2}\\1/3\\1/4\end{bmatrix}-\begin{bmatrix}0\\-1\\1\end{bmatrix}

\overrightarrow{PQ}=\begin{bmatrix}1/2}\\4/3\\-3/4\end{bmatrix}

this is the vector equation of the line segment from P to Q.

to make the parametric equations:

we know that the general equation of a line is represented as:

\overrightarrow{r} = \overrightarrow{r_0} + t\overrightarrow{d}

here, \overrightarrow{r_0}: is the initial position or the starting point. in our case it is the position vector of P

and \overrightarrow{d}: is the direction vector or the direction of the line. in our case that's PQ vector.

\overrightarrow{r} = \begin{bmatrix}0\\-1\\1\end{bmatrix} + t\begin{bmatrix}1/2}\\4/3\\-3/4\end{bmatrix}

that parametric equations can now be easily formed:

\begin{bmatrix}r_x\\r_y\\r_z\end{bmatrix} = \begin{bmatrix}0\\-1\\1\end{bmatrix} + t\begin{bmatrix}1/2}\\4/3\\-3/4\end{bmatrix}

r_x = \dfrac{1}{2}t\\r_y = -1 +\dfrac{4}{3}t\\r_z = 1=\dfrac{3}{4}t

these are the parametric equations of the line PQ

4 0
3 years ago
60 x 60 - 500 +40 + (120000000000 x 200) x 10 + 500000 =
olga55 [171]

Answer:

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or

\frac{6}{x+5} + \frac{5}{x - 8}

Step-by-step explanation:

i am not sure which answer you are looking for...so i hope this helps!

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3 years ago
Which table contains only values that satisfy the equation<br><br><br>y = 0.25x + 8?
sdas [7]

Answer:

Step-by-step explanation:

y = 0.25x + 8

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y = 0.25 × 2 + 8 = 8.50

(2, 8.50)

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