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LiRa [457]
2 years ago
9

The measure of three angles of a triangle are in the ratio 4:5:6, find the measure of each

Mathematics
1 answer:
Yuri [45]2 years ago
4 0

Answer:

4n+5n+6n=180

4+5+6=15n

180/15=12

4×12=48

5×12=60

6×12=72

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(Ross, 4.78) A jar contains 4 white and 4 black marbles. We randomly choose 4 marbles. If 2 of them are white and 2 are black, w
KATRIN_1 [288]

Answer:

Step-by-step explanation:

Given

Jar contains 4 white and 4 black marbles

We randomly select 4 marbles out of which 2 are white and 2 are black

Probability that 2 white and 2 black marbles are selected is

P=\frac{^4C_2\times ^4C_2}{^8C_4}

P=\frac{18}{35}

The process is continue for n trails until we choose the correct order

i.e. we have to fail in n-1 trails

For exact n selection Probability is given by

Req.\ Probability=Probability\ of\ failure\ in\ (n-1)\ trials\times Probability\ of\ getting\ exact\ order

=\left ( 1-\frac{18}{35}\right )^{n-1}\times \frac{18}{35}

8 0
3 years ago
The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.​
Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is \dfrac{15}{2}.

To find:

The sum of first six terms.​

Solution:

We have,

S_2=6

S_4=\dfrac{15}{2}

Sum of first n terms of a GP is

S_n=\dfrac{a(1-r^n)}{1-r}              ...(i)

Putting n=2, we get

S_2=\dfrac{a(1-r^2)}{1-r}

6=\dfrac{a(1-r)(1+r)}{1-r}

6=a(1+r)                    ...(ii)

Putting n=4, we get

S_4=\dfrac{a(1-r^4)}{1-r}

\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}

\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}

\dfrac{15}{2}=6(1+r^2)            (Using (ii))

Divide both sides by 6.

\dfrac{15}{12}=(1+r^2)

\dfrac{5}{4}-1=r^2

\dfrac{5-4}{4}=r^2

\dfrac{1}{4}=r^2

Taking square root on both sides, we get

\pm \sqrt{\dfrac{1}{4}}=r

\pm \dfrac{1}{2}=r

\pm 0.5=r

Case 1: If r is positive, then using (ii) we get

6=a(1+0.5)  

6=a(1.5)  

\dfrac{6}{1.5}=a  

4=a

The sum of first 6 terms is

S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}

S_6=\dfrac{4(1-0.015625)}{0.5}

S_6=8(0.984375)

S_6=7.875

Case 2: If r is negative, then using (ii) we get

6=a(1-0.5)  

6=a(0.5)  

\dfrac{6}{0.5}=a  

12=a  

The sum of first 6 terms is

S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}

S_6=\dfrac{12(1-0.015625)}{1.5}

S_6=8(0.984375)

S_6=7.875

Therefore, the sum of the first six terms is 7.875.

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Answer:

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Step-by-step explanation:

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