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Free_Kalibri [48]

3 years ago

6

A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fai

l on a one-hour flight is 0.037.What is the probability that both will fail? .0014What is the probability that neither will fail?What is the probability that at least one fails?

1 answer:

azamat3 years ago

3 0

Answer:

Probability (Both fail) = 0.001369

Probability (None fails) =0.927369

Probability (at least one fails) = 0.072631

Step-by-step explanation:

given data

Probability (fail) P = 0.037

two alternators is independent

solution

we get here first probability that both will fail will be

Probability (Both fail) = 0.045² ................1

Probability (Both fail) = 0.001369

and

now we get probability that neither will fail

Probability (None fails) = (1-0.037)² ...............2

Probability (None fails) =0.927369

and

now we get probability that at least one fails

Probability (at least one fails) = 1 - Probability (non fails) .................3

Probability (at least one fails) = 1 - 0.927369

Probability (at least one fails) = 0.072631

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

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

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

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BartSMP [9]

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mamaluj [8]

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2. Starting at a fixed time, each car entering an intersection is observed to see whether it turns left (L), right (R), or goes

jasenka [17]

Answer:

Natural numbers (integers greater than zero)

X = 3, 5, 4, 4, 3

Step-by-step explanation:

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The possible values of X are integers greater than zero, which are known as the Natural numbers.

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X = 3, 5, 4, 4, 3

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3 years ago