All categories

4 years ago

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Mathematics

1 answer:

Alja [10]4 years ago

3 0

Answer: $\bold{a_1=6,\quad a_n=-3a_{n-1}}$

Step-by-step explanation:

The recursive rule for a general geometric sequence is: $a_n=a_{n-1}(r)\quad \text{where}\ a_{n-1}\ \text{is the previous term and r is the ratio}$

Given the sequence {6. -18, 54, -162, ... }, we can see that

$\text{the first term}\ (a_1)\ \text{is 6}$
$\text{the common ratio (r) is:}\ \dfrac{-18}{6}=-3$

So, the recursive rule is: $a_n=-3a_{n-1}$

You might be interested in

(2a)3 = _____ This expression without exponents is?

Natalka [10]

(2a)^3 =8a^3

hope it helps

4 0

3 years ago

Read 2 more answers

f) The life of a power transmission tower is exponentially distributed, with mean life 25 years. If three towers, operated indep

Step2247 [10]

Answer:

15.24% probability that at least 2 will still stand after 35 years

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution and the exponential distribution.

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.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Probability of a single tower being standing after 35 years:

Single tower, so exponential.

Mean of 25 years, so $m = 25, \mu = \frac{1}{25} = 0.04$

We have to find $P(X > 35)$

$P(X > 35) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-0.04*35} = 0.2466$

What is the probability that at least 2 will still stand after 35 years?

Now binomial.

Each tower has a 0.2466 probability of being standing after 35 years, so $p = 0.2466$

3 towers, so $n = 3$

We have to find:

$P(X \geq 2) = P(X = 2) + P(X = 3)$

In which

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

$P(X = 2) = C_{3,2}.(0.2466)^{2}.(0.7534)^{1} = 0.1374$

$P(X = 3) = C_{3,3}.(0.2466)^{3}.(0.7534)^{0} = 0.0150$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.1374 + 0.0150 = 0.1524$

15.24% probability that at least 2 will still stand after 35 years

4 0

3 years ago

Write the point-slope form of the line passing through (2, -12) and parallel to y=3x.

dsp73

Answer:

y = 3x - 18

Step-by-step explanation:

The line passes through (2,-12) and;

Its parallel to line y = 3x

The slope of our line is 3

Taking another point (x,y) on the line

Slope = change in y ÷ change in x

3 = $\frac{y - -12}{x - 2}$

y + 12 = 3x - 6

y = 3x - 18

3 0

3 years ago

At the time of her grandson’s birth, a grandmother deposits $13,000 in account that pays 2.5% compounded monthly. What will be t

sergeinik [125]

Answer:

19, 300 i think thats correct im sorry if not

Step-by-step explanation:

5 0

3 years ago

You sight the top of a 50-ft tree from a point on the ground 50 ft from the base of the tree. What is your angle of elevation?

nikitadnepr [17]

Answer:

45°

Tan‐¹ 50÷50

Step-by-step explanation:

7 0

3 years ago