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3 years ago

The dimensions of a box are x, 2x, and 3x. Each dimension is increased by 3. Calculate the volume of the box.

Mathematics

2 answers:

Tema [17]3 years ago

6 0

Answer:

The volume of the box would be 6x³+33x²+54x+27.

Step-by-step explanation:

The new dimensions of the box would be (x+3), (2x+3), and (3x+3). Since the volume of a rectangular prism are calculated by multiplying the length, width, and depth, we can just multiply all three of these dimensions together to come up with the answer.

Using foil on the first two terms originally you get (x+3)×(2x+3)= 2x²+3x+6x+9 which can be simplified to 2x²+9x+9.

Then you multiply this equation by (3x+3). (2x²+9x+9)×(3x+3)= 6x³+6x²+27x²+27x+27x+27 which can be simplified to 6x³+33x²+54x+27.

NISA [10]3 years ago

4 0

Answer:

6x³+33x²+54x+27

Step-by-step explanation:

dimensions are now:

x+3, 2x+3, 3x+3

Volume

V=lwh
V= (x+3)(2x+3)(3x+3)=
3(x+1)(x+3)(2x+3)=
3( x² + 4x+3)(2x+3)=
3(2x³+11x²+18x+9)=
6x³+33x²+54x+27

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3 years ago

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Bogdan [553]

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3 years ago

Translate and solve: 46 less than y is at least -184

natima [27]

Translate: y - 46 > -184

Possible answer: y > - 138

Solution:

y - 46 > -184

= y > - 184 + 46

= y > - 138

#CarryOnLearning

8 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

Solve for s. s+24=90

-Dominant- [34]

S + 24 = 90

This is a one-step problem. so, all you have to do is subtract 24 on both sides:

s + 24 - 24 = 90 - 24

s = 66

Check your work:

66 + 24 = 90

90 = 90

Hope this helps!!
~Kiwi

8 0

3 years ago

Read 2 more answers