if a bag contains 18 red, 6yellow, 24blue 8white balloons what is the part to whole ratio of white ballons to all ballons

Answer:

X to power 3is=2 while y to power 3is=5so5-2=3

Step-by-step explanation:

x cubed is =8 so cube root of 8is 2

y cubed is =125so cube root of 125is 5

therefore 5-2=3

Answer:

69

Step-by-step explanation:

Answer:

69

Step-by-step explanation:

Answer:

the partial derivatives are

fx =5/9

fy =(-13/18)

Step-by-step explanation:

defining the vector v (from (2,1) to (1,3))

v=(1,3)-(2,1) = (-1,2)

the unit vector will be

v'=(-1,2)/√5 = (-1/√5,2/√5)

the directional derivative is

fv(x,y) = fx*v'x + fy*v'y = fx*(-1/√5)+fy(2/√5) =-2/√5

then defining the vector u ( from (2, 1) toward the point (5, 5) )

u=(5,5)-(2,1) = (3,4)

the unit vector will be

u'=(3,4)/5 = (3/5,4/5)

the directional derivative is

fu(x,y) = fx*ux + fy*uy = fx*(3/5)+fy(4/5)=1

thus we have the set of linear equations

-fx/√5*+2*fy/√5 =(-2/√5) → -fx + 2*fy = -2

(3/5) fx+(4/5)*fy=1 → 3* fx+4*fy = 5

subtracting the first equation twice to the second

 3*fx+4*fy -(- 2fx)*-4*fy = 5 -2*(-2)

5*fx=9

fx=5/9

thus from the first equation

-fx + 2*fy = -2

fy= fx/2 -1 = 5/18 -1 = -13/18

thus we have

fx =5/9

fy =(-13/18)

To answer this question it is necessary to find the volume of the box as a function of "x", and apply the concepts of a maximum of a function.

The solution is:

a) V (max) = 36.6 in³

b) x = 1.3 in

The volume of a cube is:

V(c) = w×L×h  ( in³)

In this case, cutting the length  "x" from each side, means:

wide of the box    ( w - 2×x )   equal to  ( 7 - 2×x )

Length of the box ( L - 2×x )   equal to  ( 9 - 2×x )

The height  is  x

Then the volume of the box,  as a function of x is:

V(x) = ( 7 - 2×x ) × ( 9 -2×x ) × x

V(x) = ( 63 - 14×x - 18×x + 4×x²)×x

V(x) = 4×x³ - 32×x² + 63×x

Tacking derivatives,  on both sides of the equation

V´(x) = 12×x² - 64 ×x + 63

If   V´(x) = 0      then      12×x² - 64 ×x + 63 = 0

This expression is a second-degree equation, solving for x

x₁,₂ = [ 64 ± √ (64)² - 4×12*63

x₁ =  ( 64 + 32.74 )/ 24

x₁ = 4.03     this value  will bring us an unfeasible solution,  since it is not possible to cut 2×4 in from a piece of paper of 7 in ( therefore we dismiss that value)

x₂ = ( 64 - 32.74)/24

x₂ = 1.30 in

The  maximum volume of the box is:

V(max) = ( 7 - 2.60) × ( 9 - 2.60)×1.3

V(max) = 4.4 × 6.4 × 1.3

V(max) = 36.60 in³

To chek for maximum value of V when x = 1.3

we find the second derivative of V  V´´,  and substitute the value of x = 1.3,    if the relation is smaller than 0,  we have a maximum value of V

V´´(x) = 24×x - 64 for x = 1.3

V´´(x) = 24× 1.3 - 64            ⇒   V´´(x) < 0

Then the value  x = 1.3 will bring maximum value for V

Related Link: brainly.com/question/13581879

Final answer:

The maximum volume of the box that can be formed is approximately 17.1875 cubic inches. The cutout length that would result in this maximum volume is approximately 1.25 inches.

Explanation:

To solve this problem, we will use optimization in calculus. Let's denote the length of the square cutout as 'x'. When you cut out an x by x square from each corner and fold up the sides, the box will have dimensions:

• Length: 9 inches (the original length) - 2x (the removed parts)
• Width: 7 inches (the original width) - 2x
• Height: x inches (the height is the cutout's length)

So the volume V of the box can be given by the equation: V = x(9-2x)(7-2x). We want to maximize this volume.

To find the maximum, differentiate V with respect to x, equate to zero and solve for x. V' = (9-2x)(7-2x) + x(-2)(7-2x) + x(9-2x)(-2) = 0. We obtain x=1.25 inches, but we need to verify whether this value gives us a maximum. Second differentiation, V'' = -12 is less than zero for these dimensions so the V is maximum.

a. So, when we solve, the maximum volume will be approximately 17.1875 cubic inches.

b. The cutout length that would produce the maximum volume is therefore about 1.25 inches.

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Answer:

21

best of luck!

Answer:

21

Step-by-step explanation:

1 + 2 = 3

3 + 3 = 6

6 + 4 = 10

10 + 5 = 15

15 + 6 = 21

Hope it helps

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Answer:

(a) P(X = 18) = 0.25

(b) P(X > 18) = 0.53

(c) P(X ≤ 18) = 0.47

(d) Mean = 19.76

(e) Variance = 22.2824

(f) Standard deviation = 4.7204

Step-by-step explanation:

We are given that discrete random variable X has the following probability distribution:

            X                    P (x)             X * P(x)                         * P(x)

           13                    0.22              2.86              169              37.18

           18                    0.25              4.5                324               81

           20                   0.20               4                  400               80

           24                    0.17              4.08              576              97.92

           27                    0.16              4.32              729             116.64

(a) P ( X = 18) = P(x) corresponding to X = 18 i.e. 0.25

     Therefore, P(X = 18) = 0.25

(b) P(X > 18) = 1 - P(X = 18) - P(X = 13) = 1 - 0.25 - 0.22 = 0.53

(c) P(X <= 18) = P(X = 13) + P(X = 18) = 0.22 + 0.25 = 0.47

(d) Mean of X, = ∑X * P(x) ÷ ∑P(x) = (2.86 + 4.5 + 4 + 4.08 + 4.32) ÷ 1

                                                         = 19.76

(e) Variance of X, = ∑ * P(x) -

                                 = 412.74 - = 22.2824

(f) Standard deviation of X, = = = 4.7204 .

Final answer:

The probabilities for the given X values are calculated by summing the relevant given probabilities. The mean of X is computed as a weighted average, and the variance and standard deviation are calculated using formula involving the mean and the individual probabilities.

Explanation:

The probability P(18) is given as 0.25 according to the distribution. The probability P(X > 18) is the sum of the probabilities for all x > 18, so we add the probabilities for x=20, x=24, and x=27, giving us 0.20 + 0.17 + 0.16 = 0.53. The probability P(X ≤ 18) includes x=18 and any values less than 18. As 18 is the lowest value given, P(X ≤ 18) is just P(18), or 0.25.

The mean μ of X is the expected value of X, computed as Σ(xP(x)). That gives us (13*0.22) + (18*0.25) + (20*0.20) + (24*0.17) + (27*0.16) = 2.86 + 4.5 + 4 + 4.08 + 4.32 = 19.76.

The variance σ 2 of X is computed as Σ [ (x - μ)^2 * P(x) ]. That gives us [(13-19.76)^2 * 0.22] + [(18-19.76)^2 * 0.25] + [(20-19.76)^2 * 0.20] + [(24-19.76)^2 * 0.17] + [(27-19.76)^2 * 0.16] = 21.61. The standard deviation σ of X is the sqrt(σ^2) = sqrt(21.61) = 4.65.

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