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Dominik [7]
2 years ago
6

A committee must be formed with 5 teachers and 4 students. If there are 6 teachers to choose from, and 15 students, how many dif

ferent ways could the committee be mad?
Mathematics
1 answer:
ZanzabumX [31]2 years ago
8 0

Answer:

8190 ways

Step-by-step explanation:

Given

Teachers = 6

Students = 15

Selection

Students = 4

Teachers = 5

Required

Number of ways of selection

4 students can be selected from 15 students in:

Students= ^{15}C_4

Similarly.

5 teachers can be selected from 6 teachers in:

Teachers= ^{6}C_5

So, the required number of selection is:

Selection = ^{15}C_4 * ^6C_5

Apply combination formula:

Selection = \frac{15!}{(15-4)!4!} * \frac{6!}{(6-5)!5!}

Selection = \frac{15!}{11!4!} * \frac{6!}{1!5!}

Selection = \frac{15*14*13*12*11!}{11!*4*3*2*1} * \frac{6*5!}{1*5!}

Selection = \frac{15*14*13*12}{4*3*2*1} * \frac{6}{1}

Selection = \frac{32760}{24} * 6

Selection = 1365 * 6

Selection = 8190

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Solve for the missing side labeled "x."
agasfer [191]

Answer:

x = 6.3375

Step-by-step explanation:

sin53 = 4/5 (roughly) = 5.07/x

=> 4x = 25.35

=> x = 6.3375

7 0
2 years ago
If y=kx, where k is a constant, and y=24 when x=6, what is the value of y when x=5?A. 6B. 15C. 20D. 23
Marizza181 [45]

First, we will find the value of k

We can do this by sybstituting y=24, x=6 in;

y=kx and then solve for k

24= k(6)

divide both-side of the equation by 6

24/6 = k

4 = k

k=4

Then when x = 5, we will substitute x=5 and k=4 in; y=kx and then solve for y

y= (4)(5)

y = 20

7 0
1 year ago
Arrange the parabolas represented by the equations in increasing order with respect to the y-values of their directrixes.
Alexus [3.1K]
(x-h)^2=4P(y-k), vertex is (h,k)
P is distance from vertex to directix
remember to subtract P from the y value of the vertex (p-k) and that y value is the directix, y=p-k

nut
ok so one way is to just graph them on a graphing utility
remember if the graph opens up, then the directix is below that
or we can convert to 4P(y-k)=(x-h)^2 form where P is distance from directix

I will only convert the 1st one fully, you should be able to do the rest

1. y=-x^2+3x+8
multiply both sides by -1 since we don't like the x^2 term negative
-y=x^2-3x-8
add8 to both sides
-y+8=x^2-3x
take 1/2 of linear coeficient and square it and add to both sides
-3/2=-1.5
 (-1.5)^2=2.25
-y+10.25=x^2-3x+2.25
factor perfect square
-y+10.25=(x-1.5)^2
force undistribute -1 in left side
(-1)(y-10.25)=something, we don't care anymore for now
factor out a 4 in -1
4(-1/4)(y-10.25)

k=10.25
p=-1/4=-0.25
directix=k-p=10.25-(-0.25)=10.5
directix is y=10.5

basically completee the square with x and find P by force factoring a 4 out

2.  directix: y=-1.75

3. directix: y=1.5

4. directix: y=17.25

5. d: -37.5

6. d: 9.25

7. d=2.625

order them yourself

7 0
3 years ago
Soo I need help... can u help?
Luda [366]

Answer:

I think its (6042 = 1780 + a) but I'm not really sure though but I hope if that helped somehow

6 0
3 years ago
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A potter can make 24 vases in 8 days. If the potter works 6 hours each day, how long does it take to make one vase?
NikAS [45]
Answer: 2
Explaintion/
24/8 =3
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7 0
3 years ago
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