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Anastasy [175]
3 years ago
5

In how many ways can 2 singers be selected from 4 who came for an audition?

Mathematics
1 answer:
Triss [41]3 years ago
7 0

\displaystyle \binom{4}{2}=\dfrac{4!}{2!2!}=\dfrac{3\cdot4}{2}=6

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Help! If you know this can you tell me how to do it?
aleksandr82 [10.1K]

Answer:

c

Step-by-step explanation:

Here's how this works:

Get everything together into one fraction by finding the LCD and doing the math.  The LCD is sin(x) cos(x).  Multiplying that in to each term looks like this:

[sin(x)cos(x)]\frac{sin(x)}{cos(x)}+[sin(x)cos(x)]\frac{cos(x)}{sin(x)} =?

In the first term, the cos(x)'s cancel out, and in the second term the sin(x)'s cancel out, leaving:

\frac{sin^2(x)}{sin(x)cos(x)}+\frac{cos^2(x)}{sin(x)cos(x)}=?

Put everything over the common denominator now:

\frac{sin^2(x)+cos^2(x)}{sin(x)cos(x)}=?

Since sin^2(x)+cos^2(x)=1, we will make that substitution:

\frac{1}{sin(x)cos(x)}

We could separate that fraction into 2:

\frac{1}{sin(x)}×\frac{1}{cos(x)}

\frac{1}{sin(x)}=csc(x)  and  \frac{1}{cos(x)}=sec(x)

Therefore, the simplification is

sec(x)csc(x)

5 0
3 years ago
Determine if the following series converges or diverges. Show steps!
MAXImum [283]
Converges by p series test
top section is almost constant, can never be larger than 3
so, compare degrees of their exponents, in this case it’s at a maximum of 3/1000n^2. the same as saying (3/1000)*summation of p series.
converges absolutely.
3 0
3 years ago
Please help immediately! thanks
Eva8 [605]

Answer:

pretty sure its 9 : 4

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
I need help with the bottom section b
d1i1m1o1n [39]

Answer:

Interior Angle Theorem

x=5

measure of angles: 46, 46, 134

Step-by-step explanation:

Interior angle theorem

12x-14=5x+21

7x=35

x=5

12x-14=12(5)-14=46

5x+21=5(5)+21=46

20x+34=20(5)+34=134

4 0
3 years ago
Need an answer thanks in advance​!
slamgirl [31]

Answer:

1806 seats.

Step-by-step explanation:

From the question given above, the following data were obtained:

Row 1 = 24 seats

Row 2 = 27 seats

Row 3 = 30 seats

Total roll = 28

Total number of seat =?

From the above data, we can liken the roll to be in arithmetic progress.

Also, we are asked to determine the total number of seats in the theater.

Thus the sum of the sequence can be written as:

Roll 1 + Roll 2 + Roll 3 +... + Roll 28 i.e

24 + 27 + 30 +...

Thus, we can obtain obtained the total number of seats in the theater by applying the sum of arithmetic progress formula. This can be obtained as follow:

First term (a) = 24

Common difference (d) = 2nd term – 1st term

Common difference (d) = 27 – 24 = 3

Number of term (n) = 28

Sum of the 28th term (S₂₈) =?

Sₙ = n/2 [2a + (n –1)d]

S₂₈ = 28/2 [2×24 + (28 –1)3]

S₂₈ = 14 [48 + 27×3]

S₂₈ = 14 [48 + 81]

S₂₈ = 14 [129]

S₂₈ = 1806

Thus, the number of seats in the theater is 1806.

6 0
2 years ago
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