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zhannawk [14.2K]
3 years ago
11

A sequence is recursively defined by f(1)=3,f(n)=2* f(n-1) for n >=2. Write the equation for the nth term

Mathematics
1 answer:
GarryVolchara [31]3 years ago
3 0

Given:

f(1)=3,f(n)=2\times f(n-1)         ...(i)

For n\geq 2.

To find:

The nth term for the given recursive formula.

Solution:

The given recursive formula is of the form of

f(n)=r\times f(n-1)            ...(ii)

It is the recursive formula of a GP, where r is common ratio.

On comparing (i) and (ii), we get

r=2

Now,

First term: a=f(1)=3

Common difference: r=2

nth term of a GP is

f(n)=ar^{n-1}

Putting a=3 and r=2, we get

f(n)=3(2)^{n-1}

Therefore, the equation for the nth term is f(n)=3(2)^{n-1}.

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A soft drink machine outputs a mean of 27 ounces per cup. The machine's output is normally distributed with a standard deviation
postnew [5]

Answer: P(22 ≤ x ≤ 29) = 0.703

Step-by-step explanation:

Since the machine's output is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

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µ = mean output

σ = standard deviation

From the information given,

µ = 27

σ = 3

The probability of filling a cup between 22 and 29 ounces is expressed as

P(22 ≤ x ≤ 29)

For x = 22,

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Looking at the normal distribution table, the probability corresponding to the z score is 0.047

For x = 29,

z = (29 - 27)/3 = 0.67

Looking at the normal distribution table, the probability corresponding to the z score is 0.75

Therefore,

P(22 ≤ x ≤ 29) = 0.75 - 0.047 = 0.703

6 0
3 years ago
Which could be the graph of the equation below<br> Y = 4 - x
Gelneren [198K]
The graph that has a slop of -1 and the y-interecept is 4
that graph is the 1st picture and top one
4 0
3 years ago
Read 2 more answers
Give the first 4 terms of a sequence who has the explicit formula an = 4n – 13
andreev551 [17]

Step-by-step explanation:

from,

An = 4n -13

A1 = 4 (1) - 13

> A1 = -9

A2 = 4(2) - 13

> A2 = -5

A3 = 4(3) - 13

> A3 = -1

A4 = 4(4) - 13

> A4 = 3

5 0
3 years ago
The second side of a triangular deck is 4 feet longer than the shortest side. The third side that is 4 feet shorter than twice t
Svetlanka [38]

The second side of a triangular deck is 4 feet longer than the shortest side

(s+4) = the 2nd side

and a third side that is 4 feet shorter than twice the length of the shortest side.

(2s-4) = the 3rd side

If the perimeter of the deck is 48 ​feet, what are the lengths of the three​ sides?

s + (s+4) + (2s-4) = 48

Combine like terms

s + s + 2s + 4 - 4 = 48

4s = 48

s = 48/4

s = 12 ft is the shortest side

I'll let you find the 2nd and 3rd sides, ensure they add up to 48

Hope this helps!

5 0
3 years ago
A public health department wants to determine the rate that parents of teen boys are choosing to vaccinate their sons for HPV wi
viktelen [127]

Answer:

The correct option is  B

Step-by-step explanation:

From the question we are told that

   The  sample size is  n  =  64

    The  proportion that choose to vaccinate the teen boys is  \r p =  0.12

considering the first statement

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The 95% confidence interval is is  %12 ± the margin of error

considering the second statement

The confidence interval should not be calculated due to the small sample size is true because from the central limit theorem

   np =  64 * 0.12 =  7.68

and this value is  less than 10  hence the confidence interval should not be calculated

considering the third statement

A 99% confidence interval will be smaller than the 90% confidence interval is false

  This is because as the confidence level increase (for example  from 90% to  99%) the margin of error increase which increases the confidence interval  

 

5 0
3 years ago
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