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FrozenT [24]
3 years ago
11

For each geometric sequence, write a recusive rule by finding the commom ratio by calculating the ration of consecutive terms. W

rite an exlicit rule for the sequence by writing each term as the product of the first tern and a power of the common ratio.
n- 1, 2, 3, 4, 5
An- 2, 6, 18, 54, 162
Mathematics
1 answer:
Inessa05 [86]3 years ago
3 0

Answer:

a_n=2.(3)^{n-1}

Step-by-step explanation:

Given sequence is:

2,6,18,54,162

So the common ratio can be found by dividing the second term by first term:

r = 6/2 = 3

The standard formula for geometric sequence is:

a_n=a_1r^{n-1}

Putting the value of r

a_n=2.(3)^{n-1}

So,

a_1=2.(3)^{1-1} => 2.3^0 = 2*1 = 2\\a_2=2.(3)^{2-1} => 2.3^1 = 2*3 = 6\\a_3=2.(3)^{3-1} => 2.3^2 = 2*9 = 18\\a_4=2.(3)^{4-1} => 2.3^3 = 2*27 = 54\\a_5=2.(3)^{5-1} => 2.3^4 = 2*81 = 162

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Sati [7]
Answer: B) 16 units

Step-by-Step Explanation:

As we can observe from the graph,

Length (l) = 5 units
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6 0
3 years ago
Three identical fair coins are thrown simultaneously until all three show the same face. What is the probability that they are t
mixer [17]

Answer:

The probability that the coins are thrown more than three times to show the same face is 0.3164.

Step-by-step explanation:

The problem is related to Geometric distribution.

The Geometric distribution defines the probability distribution of <em>X</em> failures before the first success.

The probability distribution function is:

P(X=k)=(1-p)^{k}p;\    k = 0, 1, 2, ...

First compute the probability that in the i^{th} throw all the three coins will show the same face.

P (All the 3 coins shows the same face) = P (All the three coins shows Heads) + P (All the three coins shows Tails)

                      =(\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2} )+(\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2} )\\=\frac{1}{8}+\frac{1}{8}\\  =\frac{2}{8} \\=\frac{1}{4}

Now compute the probability that it takes more than 3 throws for the coins to show the same face.

P (<em>X</em> > 3) = 1 - P (<em>X</em> ≤ 3)

=1-[P(X=1)+P(X=2)+P(X=3)]\\=1-[[(1-\frac{1}{4} )^{0}\times\frac{1}{4}]+[(1-\frac{1}{4} )^{1}\times\frac{1}{4}]+ [(1-\frac{1}{4} )^{2}\times\frac{1}{4}]+[(1-\frac{1}{4} )^{3}\times\frac{1}{4}]]\\=1-[0.2500+0.1875+0.1406+0.1055]\\=1-0.6836\\=0.3164

Thus, the probability that it takes more than 3 throws for the coins to show the same face is 0.3164.

8 0
3 years ago
How many solutions does this system of equations have?
viktelen [127]

Answer:

Infinitely

Step-by-step explanation:

Solutions to a system are the intersection points. Since these two lines are the same line they intersect everywhere. There are infinitely many solutions.

4 0
4 years ago
7.
Serjik [45]

Answer:

Probability that a customer pays the bill by mail, given that the customer is female is 0.20.

Step-by-step explanation:

The complete question is:

                               Online                             By Mail            Total

             Male             12                                      8                   20

           Female           24                                     6                   30      

             Total             36                                     14                  50    

A utility company asked 50 of its customers whether they pay their bills online or by mail. What is the probability that a customer pays the bill by mail, given that the customer is female.

Probability that a customer pays the bill by mail, given that the customer is female is given by = P(Pays bill by mail / Customer is female)

\frac{6}{50}P(Pays bill by mail/Customer is female) = \frac{P(\text{Pays bill by Mail}\bigcap \text{ Customer is Female})}{P(\text{ Customer is Female})}

Now, Probability that customer is female =  \frac{30}{50}

Also, Probability that customer pays bill by mail and is female =   \frac{6}{50}

So, Required probability =  \frac{\frac{6}{50} }{\frac{30}{50} }

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Hence, probability that a customer pays the bill by mail, given that the customer is female is 0.20.

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3 years ago
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laila [671]

Answer: the answer is 0.3 but the the is ongoing so 0.33

Step-by-step explanation:

3 0
3 years ago
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