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3 years ago

If f(x) = (x - 2) = x3 + 2x - 4 + 13 what is f(2)?

Mathematics

1 answer:

leva [86]3 years ago

8 0

Answer:

f(2)=21

Step-by-step explanation:

f(2)=2^3+2*2-4+13=8+4-4+13=8+13=21

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Please help me answer this question

sergejj [24]

Answer:

72km

Step-by-step explanation:

alex : tomos : annabelle = 2 : 3 : 4

if tomos drove 24km

tomos ratio is 3

so 3 --> 24

1 --> 8

total ratios --> 2 + 3 + 4 = 9

so total journey is 9 --> 9 * 8 = 72km

6 0

2 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

2.38+4.89=3+ _ changing expressions??

Lerok [7]

Add 2.38 and 4.89 then subtract 3 giving you 4.27

3 0

3 years ago

Find the number of terms, n, in the arithmetic series whose first term is 13, the common difference is 7, and the sum is 2613.

siniylev [52]

Answer:

Step-by-step explanation:

Recall that the sum of an arithmetic series is given by:

$\displaystyle S = \frac{n}{2}\left(a + x_n\right)$

Where n is the number of terms, a is the first term, and x_n is the last term.

We know that the initial term a is 13, the common difference is 7, and the total sum is 2613. Since we want to find the number of terms, we want to find n.

First, find the last term. Recall that the direct formula for an arithmetic sequence is given by:

$x_n=a+d(n-1)$

Since the initial term is 13 and the common difference is 7:

$x_n=13+7(n-1)$

Substitute:

$\displaystyle S = \frac{n}{2}\left(a + (13+7(n-1)\right)$

We are given that the initial term is 13 and the sum is 2613. Substitute:

$\displaystyle (2613)=\frac{n}{2}((13)+(13+7(n-1)))$

Solve for n. Multiply both sides by two and combine like terms:

$5226 = n(26+7(n-1))$

Distribute:

$5226 = n (26+7n-7)$

Simplify:

$5226 = 7n^2+19n$

Isolate the equation:

$7n^2+19n-5226=0$

We can use the quadratic formula:

$\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a = 7, b = 19, and c = -5226. Substitute:

$\displaystyle x =\frac{-(19)\pm\sqrt{(19)^2-4(7)(-5226)}}{2(7)}$

Evaluate:

$\displaystyle x = \frac{-19\pm\sqrt{146689}}{14} = \frac{-19\pm 383}{14}$

Evaluate for each case:

$\displaystyle x _ 1 = \frac{-19+383}{14} = 26\text{ or } x _ 2 = \frac{-19-383}{14}=-\frac{201}{7}$

We can ignore the second solution since it is negative and non-natural.

Therefore, there are 26 terms in the arithmetic series.

Our answer is A.

6 0

3 years ago

NEED HELP WITH THIS PLEASE. NEED THE ANSWER ASAP

padilas [110]

Answer:

PY = 8

Step-by-step explanation:

Lets run down the other three to show why they're wrong

MY=8

By P.T, that's wrong (PERPENDICULAR)

PM=MY

We can't prove that with the given

XY=42

Again, by P.T., this is false

BTW: You can prove PY=8 by proving XMP congruent to YMP by SAS

7 0

3 years ago