Need help because I don't understand

Evaluate the following expression:<br> 30 = 5(8 – 6 + 1) - (2^2 - 3)^3

grin007 [14]

Answer:

30=15

Step-by-step explanation:

30=40-30+6-4-27

30=10+2-27

40=12-27

30=-15

7 0

3 years ago

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

The circumference of a circle exceeds the radius by 74 cm. Find the radius of the circle.

saw5 [17]

Answer:

14 cm.

Step-by-step explanation:

Let the radius of the circle = r cm.

Then circumference of circle = 2 π r.

Since circumference exceeds the radius by 74 cm

Therefore, according to the question,

$\sf \:2 π r = r+ 74$

$\sf \: = > 2 \times \frac{22}{7} \times r = r \: + 74$

$\sf \: = > \frac{44r}{7} -r = 74$

$\sf \: = > \frac{44r - 7r}{7} = 74$

$\sf \: = > \frac{37r}{7} = 74$

$\sf \: = > r = \frac{7 \times 74}{37}$

$\sf \: = > r = 14$

Hence, the radius of the circle is 14 cm.

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3 0

2 years ago

Read 2 more answers

What is the length of side AC of the triangle? Pls hurry

kodGreya [7K]

Answer:

Step-by-step explanation:

According to the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third side. This means that you cannot draw a triangle that has side lengths 2, 7 and 12, for instance, since 2 + 7 is less than 12.

3 0

3 years ago

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Question

ladessa [460]

Answer:

Step-by-step explanation:

4s + 2j = 68........2j = -4s + 68........j = -2s + 34

3s + 3j = 81

3s + 3(-2s + 34) = 81

3s - 6s + 102 = 81

3s - 6s = 81 - 102

-3s = - 21

s = -21/-3

s = 7 <==== shirts cost 7 bucks

j = -2s + 34

j = -2(7) + 34

j = -14 + 34

j = 20 <===== jeans cost 20 bucks

7 0

3 years ago