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3 years ago

HELP ME PLS BBRAINLIESST AND 10 POINTS

Mathematics

1 answer:

Effectus [21]3 years ago

7 0

P(not like black | not like pink) = 9/32 ≈ 28.1%

Look on the row for "not like pink". Your probability is the number under "not like black" divided by the total for "not like pink".

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First one and last one

Step-by-step explanation:

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3 years ago

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X²-y², x²+xy and x² + 2xy + y² plz fast full formula givee

Scorpion4ik [409]

Answer:

Step-by-step explanation:

x²- y² = (x+y) (x-y)

x² + xy = x(x+y)

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3 years ago

How to simplify fractions ti its lowest terms

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Divide the top number and the bottom number by a number they both have in common

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3 years ago

Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinat

tensa zangetsu [6.8K]

Answer:

The volume of the largest rectangular box (V) = 81/4

Step-by-step explanation:

Step 1:-

Given volume of the largest rectangular box in the first octant

V = l b h

let (x ,y, z) be the one vertex in the given plane

V = f(x, y, z) = x y z

given plane. Ф (x, y, z) = x + 9y + 4z = 27 ........(1)

Step( ii):

By using Lagrange multipliers

Suppose it is required to find the extreme for the function f(x, y, z) subject to the condition Ф (x, y, z) =0

Form Lagrange function F(x, y, z) = f(x, y, z) + λ Ф (x, y, z) where λ is called the Lagrange multipliers

F(x, y, z) = x y z+ λ ( x + 9y + 4z - 27) ......(2)

Obtain the equations are δ F / δ x = 0

δ f / δ x +λ δ Ф / δ x =0

⇒ y z + λ ( 1) = 0

⇒ y z = - λ ......(a)

Obtain the equations are δ F / δ y = 0

δ f / δ x +λ δ Ф / δ x =0

⇒ x z + λ ( 9) = 0

⇒ $\frac{xz}{9}$ = - λ .......(b)

Obtain the equations are δ F / δ z = 0

δ f / δ x +λ δ Ф / δ z =0

x y + λ ( 4) = 0

⇒ $\frac{xy}{4}$ = - λ .......(c)

Step (iii):-

Equating (a) and (b) equations

we get $y z = \frac{xz}{9}$

cancel 'z' value we get x = 9y .......(d)

Equating (b) and (c) equations

we get $\frac{xy}{4} = \frac{xz}{9}$

cancel 'x' value on both sides , we get

4z =9y ......(e)

substitute (d) (e) values in equation (1) we get

x + 9y + 4z -27 = 0

9y + 9y + 9y -27 =0

27y -27 =0

y = 1

substitute y =1 in x = 9y

x = 9

substitute y =1 in 4z =9y

z = 9 /4

therefore the dimensions are x =9 , y=1 and z = 9 /4

Conclusion:-

The largest volume of the rectangular box V = x y z

substitute x =9 , y=1 and z = 9 /4

V = 9(1)(9/4) =81/4

The largest volume of the rectangular box (V) = 81/4

Verification :-

Given plane x + 9y + 4z = 27

substitute x =9 , y=1 and z = 9 /4

9 + 9 + 4(9/4) = 27

27 =27

so satisfied equation

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3 years ago

The time between calls made to Amazon's customer service is exponentially distributed with a mean of 10 minutes (taken between e

daser333 [38]

Answer:

The probability that the time between the next two calls is between 3 minutes and 7 minutes is 0.2442.

Step-by-step explanation:

Let X = time between calls made to Amazon's customer service.

The average time between calls is, β = 10 minutes.

The random variable X follows an Exponential distribution with parameter $\lambda=\frac{1}{\beta}=\frac{1}{10}=0.10$

The probability distribution function of X is:

$f_{X}(x)=\left \{ {{\lambda e^{-\lambda x};\ x>0}} \atop {0;\ otherwise}} \right.$

Compute the probability that the time between the next two calls is between 3 minutes and 7 minutes as follows:

$P(3$

Thus, the probability that the time between the next two calls is between 3 minutes and 7 minutes is 0.2442.

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4 years ago

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