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shtirl [24]
3 years ago
14

A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and vot

ing rights. There are 8 faculty members and 13 students eligible to serve on the committee. In how many ways can the committee be formed?
Mathematics
1 answer:
MArishka [77]3 years ago
8 0

Answer:

Step-by-step explanation:

This question bothers on combination. combination has to do with selection.

If 4 faculty members are chosen from total of  8 faculty members, this can be done in 8C4 number of ways.

8C4 = 8!/(8-4)!4!

8C4 = 8!/4!4!

8C4 = 8*7*6*5*4!/4!*4*3*2

8c4 = 8*7*6*5/24

8C4 = 7*5*2

8C4  =70 ways

Similarly,  5 students are to be selected from a pool of 13 students, this can be done in 13C5 number of ways.

13C5 = 13!/(13-5)!5!

13C5 = 13!/8!5!

13C5 = 13*12*11*10*9*8!/8!*5*4*3*2

13C5 = 13*12*11*10*9/120

13C5 = 1,287 ways

The total number of ways the committee can be formed is 8C4 * 13C5 = 70*1287

The total number of ways the committee can be formed is 90,090 ways

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2. A right triangle has a hypotenuse of 15 cm. What are possible lengths for the two legs of the triangle? Explain your reasonin
dolphi86 [110]

Answer:

Two possible lengths for the legs A and B are:

B = 1cm

A = 14.97cm

Or:

B = 9cm

A = 12cm

Step-by-step explanation:

For a triangle rectangle, Pythagorean's theorem says that the sum of the squares of the cathetus is equal to the hypotenuse squared.

Then if the two legs of the triangle are A and B, and the hypotenuse is H, we have:

A^2 + B^2 = H^2

If we know that H = 15cm, then:

A^2 + B^2 = (15cm)^2

Now, let's isolate one of the legs:

A = √( (15cm)^2 - B^2)

Now we can just input different values of B there, and then solve the value for the other leg.

Then if we have:

B = 1cm

A = √( (15cm)^2 - (1cm)^2) = 14.97

Then we could have:

B = 1cm

A = 14.97cm

Now let's try with another value of B:

if B = 9cm, then:

A = √( (15cm)^2 - (9cm)^2) = 12 cm

Then we could have:

B = 9cm

A = 12cm

So we just found two possible lengths for the two legs of the triangle.

4 0
3 years ago
At 55 mph it will take you approximately _____ feet to stop the car. A. 5 feet B. 100 feet C. 228 feet
ololo11 [35]

Answer:

The correct answer is option C, 228 feet

Step-by-step explanation:

As per Newton’s third law of motion:

V2 – U2 = 2 x a x S

Where V = final velocity

U = Initial Vlocity

a = acceleration (-ve)

S= distance travelled

V= 0 mph

U= 55 mph = 80.6667 ft /sec

0 – (80.6667 ft /sec)2 = 2 x (-g/2) x S

S = (80.6667 ft /sec)2 /(32.2 feet per second per second x0.5)

S = 202.1 feet

So the most nearest option is option C

6 0
3 years ago
James has a board that is 3/4 foot long. He wants to cut the board into pieces that are each 1/8 foot long
mina [271]
Answer=6 pieces

First lets convert 3/4 to ?/8...

\frac{3}{4}= \frac{6}{8}

3/4 is equivalent to 6/8. 

Now we can divide 6/8 by 1/8

\frac{6}{8}/ \frac{1}{8}=6


Answer=6 pieces
4 0
3 years ago
Read 2 more answers
The following graph represents an inequality.
Leni [432]

Answer:

Opt. 1 -3 ≤ x ≤ 3

Step-by-step explanation:

Inequalities are regions, the attached picture shows us a region located between -3 and 3, the dots used are solid, this means that the value '3' is include in the region.

Hence the variable is narrowed to -3 and 3.

8 0
3 years ago
Let a be a real number and n a positive integer . show that x-a is a factor of x^n- a^n
nikklg [1K]

Answer:

steps below

Step-by-step explanation:

x-a=0

x=a   plug in xⁿ - aⁿ

xⁿ - aⁿ = aⁿ - aⁿ = 0

(x-a) must be a factor of xⁿ - aⁿ

6 0
3 years ago
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