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Margarita [4]
3 years ago
5

What is the sequence? 243, 81, 27, 9, 3, 1

Mathematics
1 answer:
katen-ka-za [31]3 years ago
5 0

9514 1404 393

Answer:

  an = 243·(1/3)^(n-1) = 3^(6-n)

Step-by-step explanation:

This geometric sequence has a first term of a1=243 and a common ratio of r = 81/243 = 1/3. The general term for it is ...

  an = a1·r^(n-1)

  an = 243·(1/3)^(n-1)

Making use of the rules of exponents, this can be simplified to ...

  an = 3^5·(3^-1)^(n-1) = 3^(5-n+1)

  an = 3^(6-n)

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ANGLE OF ELEVATION, ANGLE OF DEPRESSION​
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\:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \large \mathfrak{Together  \: We  \: Go  \: Far}

\rule{70mm}{2.9pt}

<h3>ANGLE OF ELEVATION</h3>

☞ An angle of elevation is the angle between the horizontal line of sight of the observer to the object above.

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Additional Information:-

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3 0
2 years ago
Is the function f(x) = 9x2 + 4x – 2 linear, quadratic, or exponential?
Fiesta28 [93]

Answer:

According to me it is quadratic function.

4 0
3 years ago
A.The Murray family has produced 8 children.
Vlad [161]

Answer:

A. 0.2734 = 27.34% probability that there are an equal number of boys and girls

B. 0.2753 = 27.53% probability that she’ll answer exactly 5 questions correctly

Step-by-step explanation:

In each of these questions, the binomial probability distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

A.The Murray family has produced 8 children.

What is the probability that there are an equal number of boys and girls?

8 children means that n = 8

Each children is equally as likely to be a boy or a girl, which means that p = 0.5

This probability is P(X = 4). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 4) = C_{8,4}.(0.5)^{4}.(0.5)^{4} = 0.2734

0.2734 = 27.34% probability that there are an equal number of boys and girls

B.Margie has the uncanny ability of being able to guess the correct answer to TRUE/FALSE questions with an 80% accuracy rate. Tomorrow’s test has 7 questions on it and she needs to answer 5 questions correctly in order to make the Honor Roll. If she guesses on every question, what is the probability that she’ll answer exactly 5 questions correctly?

80% accurracy rate means that p = 0.8

7 questions means that n = 7

The probability is P(X = 5). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 5) = C_{7,5}.(0.8)^{5}.(0.2)^{2} = 0.2753

0.2753 = 27.53% probability that she’ll answer exactly 5 questions correctly

7 0
3 years ago
40 POINTS AND BRAINLIEST
Korvikt [17]

Answer:

x = 13

Step-by-step explanation:

x = 13 ; y = -6

Double check

-6 + 2 = -4/5(13 - 8)

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7 0
3 years ago
Read 2 more answers
Solve for x
ludmilkaskok [199]

Answer:

x = 3/4

Step-by-step explanation:

Step 1: Write equation

5x - 2(x + 1) = 1/4

Step 2: Solve for <em>x</em>

  1. <u>Distribute -2:</u> 5x - 2x - 2 = 1/4
  2. <u>Combine like terms:</u> 3x - 2 = 1/4
  3. <u>Add 2 to both sides:</u> 3x = 9/4
  4. <u>Divide both sides by 3:</u> x = 3/4

Step 3: Check

<em>Plug in x to verify it's a solution.</em>

5(3/4) - 2(3/4 + 1) = 1/4

15/4 - 2(7/4) = 1/4

15/4 - 14/4 = 1/4

1/4 = 1/4

3 0
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