What must be your car's average speed in order to travel 227 km in 3.22 h ?

A certain restaurant always overbooks. If possible. At 7:00 pm the restaurant can seat 50 parties, but takes reservations for 53

oee [108]

Answer:

The probability that the restaurant can accommodate all the customers who do show up is 0.3564.

Step-by-step explanation:

The information provided are:

At 7:00 pm the restaurant can seat 50 parties, but takes reservations for 53.
If the probability of a party not showing up is 0.04.
Assuming independence.

Let X denote the number of parties that showed up.

The random variable X follows a Binomial distribution with parameters n = 53 and p = 0.96.

As there are only 50 sets available, the restaurant can accommodate all the customers who do show up if and only if 50 or less customers showed up.

Compute the probability that the restaurant can accommodate all the customers who do show up as follows:

$P(X\leq 50)=1-P(X>50)\\=1-P(X=51)-P(X=52)-P(X=53)\\=1-[{53\choose 51}(0.96)^{51}(0.04)^{53-51}]-[{53\choose 52}(0.96)^{52}(0.04)^{53-52}]\\-[{53\choose 53}(0.96)^{53}(0.04)^{53-53}]\\=1-0.27492-0.25377-0.11491\\=0.3564$

Thus, the probability that the restaurant can accommodate all the customers who do show up is 0.3564.

7 0

3 years ago

Write the slope-intercept form of the equation of the line passing through the point (-5.-4) and parallel to the

LenKa [72]

Answer:

all work is shown/pictured

5 0

3 years ago

Find the slope of the line using the points indicated. Then write an equation for the line.

Kryger [21]

The slope of the line is -2/2

5 0

2 years ago

5\7m-2-6\7m=-13 what is the answer

Butoxors [25]

5/7m - 2 - 6/7m = -13
5/7m - 6/7m - 2 = -13
-1/7m - 2 = -13
-1/7m = -11
-m/7 = -11
-m = -77
m = 77

7 0

3 years ago

find the standard form of equation of a line perpendicular to 4X plus 5Y equals 40 that includes the point -10, -3

snow_tiger [21]

The equation of line in standard form is 5x - 4y = -38

Solution:

Given that we have to find the equation of line perpendicular to 4x + 5y = 40 that includes the point (-10, -3)

The equation of line in slope intercept form is given as:

y = mx + c ------ eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Given equation of line is:

4x + 5y = 40

Rearranging to slope intercept form, we get

5y = -4x + 40

$y = \frac{-4}{5}x + \frac{40}{5}\\\\y = \frac{-4}{5}x + 8$

On comparing the above equation with eqn 1,

$m = \frac{-4}{5}$

We know that product of slope of line and slope of line perpendicular to given line is equal to -1

Therefore,

$\frac{-4}{5} \times \text{ slope of line perpendicular to it } = -1\\\\\text{ slope of line perpendicular to it } = \frac{5}{4}$

Now find the equation of line with slope 5/4 and passing through (-10, -3)

Substitute $m = \frac{5}{4}$ and (x, y) = (-10, -3) in eqn 1

$-3 = \frac{5}{4}(-10) + c\\\\-3 = \frac{-25}{2} + c\\\\c = -3 + \frac{25}{2}\\\\c = \frac{-6 + 25}{2}\\\\c = \frac{19}{2}$

Substitute $c = \frac{19}{2}$ and $m = \frac{5}{4}$ in eqn 1

$y = \frac{5}{4}x + \frac{19}{2}$

The standard form of an equation is Ax + By = C

Therefore,

$\frac{5}{4}x - y = -\frac{19}{2}\\\\\frac{5x - 4y}{4} = \frac{-19}{2}\\\\5x - 4y = -38$

Thus the equation of line in standard form is found

4 0

3 years ago