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BigorU [14]
3 years ago
5

The business department at a university has 18 faculty members. Of them, 11 are in favor of the proposition that all MBA student

s should take a course in ethics and 7 are against this proposition. If 5 faculty members are randomly selected from the 18, what is the probability that the number of faculty members in this sample who are in favor of the proposition is exactly two
Mathematics
1 answer:
drek231 [11]3 years ago
8 0

Answer:

0.225

Step-by-step explanation:

Total outcomes of choosing 5 out of 18 members = 18C5

Outcomes of choosing 2 out 11 favourers, 3 out of 7 members  =          11C2 & 7C3

Probability = Favourable outcomes / Total outcomes

= ( 11C2 x 7C3 ) / 18C5

<u>[ { 11 ! / 2! 9! } {7 ! / 3! 4! } ] </u>

       [ 18 ! / 5! 13! ]

( 55 x 35 ) /  8568

1925 / 8568

= 0.2246 ≈ 0.225

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the expression 42 + 57 shows how much money nate spent at the store. which expression also shows how much money nate spent.​
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2 years ago
A circle is inscribed in an equilateral triangle. A point in the figure is selected at random. Find the probability that the poi
liubo4ka [24]

Answer:

The correct answer is first option 60%

Step-by-step explanation:

The radius of a circle is inscribed in an equilateral triangle with side a = a/2√3

<u>To find the area of equilateral triangle</u>

Here side be 'a'

Area of equilateral = √3a²/4

<u>To find the area of circle</u>

Here radius = a/2√3

Area = πr²

 = π(a/2√3)

 = 3.14a²/12

<u>To find the probability</u>

probability = area of circle/area of triangle

   = 3.14a²/12/ √3a²/4

   = 3.14/3√3

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The correct answer is first option 60%

 

8 0
2 years ago
Consider the graph of the line y = x – 4 and the point (−4, 2).
Hitman42 [59]

Answer:

a. The slope  of a line parallel to the given line is 1

b. A point on the line parallel to the given line, passing through (−4, 2), is  (1,7)

c. The slope of the line perpendicular to the given line is -1

d. A point on the line perpendicular to the given line, passing through (−4, 2), is (3,-5)

Step-by-step explanation:

The equation of the line in Slope-intercept form  is:

y=mx+b

Where m is the slope and b is the y-intercept.

a. For the line y = x - 4

You can identify that:

m=1

 By definition, two lines are parallel if they have the same slope. Then, the  slope of a line parallel to the given line is:

m=1

b. The equation of the line in Point-slope form is:

y -y_1 = m(x - x_1)

Where m is the slope and (x_1,y_1)  is a point of the line.

Given the point (-4,2), substitute this point and the slope of the line into the equation:

 y -2 = (x +4)

Give a value to "x", substitute it into this equation and solve for "y":

For x=1 :

y -2 = (1 +4)

y= 5+2

y= 7

Then, you get the point (1,7)

c. The slopes of perpendicular lines are negative reciprocals, then the  slope of a line perpendicular to the given line is:

m=-\frac{1}{1}\\\\m=-1

d. Given the point (-4,2), substitute this point and the slope of the line into the equation:

 y -2 = -1(x +4)

 y -2 = -(x +4)

Give a value to "x", substitute it into this equation and solve for "y":

For x=3 :

y -2 = -(3 +4)

y= -7+2

y= -5

Then, you get the point (3,-5)

8 0
3 years ago
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