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3 years ago

Simplify 2^-6 times 2^3

Mathematics

2 answers:

MAVERICK [17]3 years ago

5 0

Answer:

0.125

Step-by-step explanation:

$(2^{-6})(2^{3})\\$

$(2^{-6})=(\frac{1}{2^{6}} )=(\frac{1}{(2)(2)(2)(2)(2)(2)})=\frac{1}{64}=0.015625$

$(2^{3})=((2)(2)(2))=8$

$(0.015625)(8)=0.125$

IgorC [24]3 years ago

3 0

Answer:

(2^-6)*(2^3)

=2^(-6+3)

=2^-3

=1/(2^3)

=1/8

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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

Can someone give me the answers plz:)

Alborosie

Remark

There is no short way to do this problem and no obvious way to get the answer other that to solve each part.

Solve

$\dfrac{x + 1.6}{2} =\text{x + 0.1}$ Multiply by 2

x + 1.6 = 2(x + 0.1) Remove the brackets

x + 1.6 = 2x + 0.1*2

x + 1.6 = 2x + 0.2 Subtract x from both sides

1.6 = x + 0.2 Subtract 0.2 from both sides

1.6 - 0.2 = x

1.4 = x

Circle A

Subtract 2x from both sides.

3x - 2x = 1.4

Circle B

Remove the brackets.

4x + 6 = 2x - 6 Add 6 to both sides

4x + 12 = 2x Subtract 4x from both sides.

12 = -2x Divide by - 2

12/-2 = x

x = - 6 Don't circle C

I'm going to be very scant in my solution of this. You can fill in the steps.

3x = 4.2

x = 4.2/3

x = 1.4

Circle D

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