I tried using the standard deviation formula but still got the wrong answer. How would I solve this?

Let (x, y, z) be a point on the plane in the first octant. The box formed by this point has volume xyz, and you want to maximize this subject to the equation of the plane.

Use the method of Lagrange multipliers: the Lagrangian is

L(x, y, z) = xyz - λ (x + 2y + 3z - 6)

Find its critical points:

∂L/∂x = yz - λ = 0

∂L/∂y = xz - 2λ = 0

∂L/∂z = xy - 3λ = 0

∂L/∂λ = -(x + 2y + 3z - 6) = 0

Solving the first three equations for λ gives

λ = yz = xz/2 = xy/3

Solve these equations for y and z :

• yz = xz/2   =>   y = x/2   =>   2y = x

• yz = xy/3   =>   z = x/3   =>   3z = x

Substitute these solutions into the last equation and solve for x, then again for y and z :

x + 2y + 3z - 6 = 3x - 6 = 0   =>   3x = 6   =>   x = 2, y = 1, z = 2/3

At this critical point, the maximum volume is

xyz = 2*1*2/3 = 4/3

Answer:

5196

Step-by-step explanation:

So it's 5040+(-156)

We have to find the absolute value

|-156|=156

5040+156=5196

Answer:

i know im cool...you don't gotta tell me

2847474747273747474747477754523970+72r7573747473747362538492949276​

have a nice day

Answer:

Step-by-step explanation:

hope it may help u

please mark as brainlist

(๑˙❥˙๑)

Answer:

m<D = 120°

Step-by-step explanation:

Adjacent angles are supplementary in a parallelogram.

Thus:

2x + 12 + 5x = 180°

Collect like terms

7x + 12 = 180

7x = 180 - 12

7x = 168

x = 168/7

x = 24

✔️m<D = 5x° (opposite angles in a parallelogram are equal)

Plug in the value of x

m<D = 5(24)

m<D = 120°

Answer:

As the volume approaches 0,

The density approaches infinity

Step-by-step explanation:

The graph of the equation is a hyperbola with the asymptote at v = 0. This means that when the value of v is very close to 0, the value of the density is very large.

As the volume approaches 0,

The density approaches infinity

Answer:

The density approaches infinity.

Step-by-step explanation:

Answer:

Sales tax=31.16, total price=359.16

Step-by-step explanation:

Price x sales tax rate -=sales tax

328 x .095(9.5%)=31.16 sales tax

price + sales tax = total price

328 + 31.16=359.16

Answer:

y = 3/5x - 1

Step-by-step explanation:

y = mx + b

m = slope

m = 3/5

to find the y - intercept we have to make x = 0 by adding or subtracting

in this case it is +5

add five to both x and y

[tex](-5, -6) + (5, 5) = (0, -1)[/tex]

the y intercept focuses on what y is when x is 0

the y intercept in this case is -1

Answer:

h = 33 hours

Step-by-step explanation:

Given that,

Addison worked 6 more hours this week than last week. In total, she worked 72 hours this week and last week.

The equation is :

2h + 6 = 72

We need to find the number of hours

2h = 72 - 6

2h = 66

h = 33

Hence, Adison worked for 33 hours last week.

Answer:

See answers below

Step-by-step explanation:

Volume of the box = length * width * height

Volume of the box = 15 * 12 * 20

Volume of the box = 300 * 12

Volume of the box = 3600 cubic cm

Area of rectangle = Length * Width

Area of rectangle A = 20cm * 12cm

Area of rectangle A = 240sq.cm

Area of rectangle B = 15cm * 20cm

Area of rectangle B = 300 sq.cm

Area of rectangle C = 15cm * 12cm

Area of rectangle C = 180 sq.cm

Answer:

the last one is a polynomial

Step-by-step explanation:

Answer:

[tex] \displaystyle x = 2 \sqrt{3} [/tex]

Step-by-step explanation:

we would like to solve the following equation:

[tex] \displaystyle \sqrt{3} = \frac{6}{x} [/tex]

in order to do so do cross multiplication:

[tex] \displaystyle x \sqrt{3} = 6[/tex]

divide both sides by √3:

[tex] \displaystyle x = \frac{6}{ \sqrt{3}} [/tex]

since we ended up with a square root on the denominator so we can consider rationalising the denominator to do so multiply both numerator and denominator by √3 which yields:

[tex] \displaystyle x = \frac{6}{ \sqrt{3}} \times \frac{ \sqrt{3} }{ \sqrt{ 3} } [/tex]

simplify multiplication:

[tex] \displaystyle x = \frac{6 \sqrt{3} }{ 3} [/tex]

reduce fraction:

[tex] \displaystyle x = 2 \sqrt{3} [/tex]

and we are done!

Answer: I only need the points :) <3

Step-by-step explanation: Two competing companies are having sales on laptops. Laptop #AX330M has a retail price of $2,100. The Buy Less is advertising #AX330M for 15% off, while Sell More has stated they will match any competitor’s advertised special and take an additional 10% off of the competitor’s advertised price. How much money is saved by purchasing the laptop from Sell More instead of Buy Less?

Answers:

==========================================================

Explanation:

For now, focus on the triangle with angles 'a', 71 and 40 degrees.

Recall that for any triangle, the inside angles always add to 180

a+71+40 = 180

a+111 = 180

a = 180-111

a = 69

---------------

Notice how angles b and 133 are adjacent and form a straight angle. This makes them supplementary. Meaning they add to 180

b+133 = 180

b = 180-133

b = 47

---------------

Let angle f be adjacent to angle c, and part of the triangle with angles 'a' and b.

Use the rule mentioned in the first section

a+b+f = 180

69+47+f = 180

116+f = 180

f = 180-116

f = 64

Now we can find angle c, because angles f and c are supplementary

c+f = 180

c+64 = 180

c = 180-64

c = 116

We could also use the remote interior angle theorem to say that a+b = c, so c = a+b = 69+47 = 116

---------------

Next, focus your attention on the 140 degree angle. The missing adjacent angle to this is 180-140 = 40 degrees

Now focus on the triangle that has angles d, 40, and 47. The "40" being what we just calculated in the previous paragraph.

We'll do the same thing as before

d+40+47 = 180

d+87 = 180

d = 180-87

d = 93

---------------

The angle just above angle d is also the same (vertical angles). This upper triangle has angles 40, d and g, where g is unknown. Let's find it.

40+d+g = 180

40+93+g = 180

133+g = 180

g = 180-133

g = 47

The vertical angle across from this is also 47 degrees.

Similarly, we can move that angle b over to its vertical pairing counterpart.

The smallest triangle at the very top has angles e, b, and g

e+b+g = 180

e+47+47 = 180

e+94 = 180

e = 180-94

e = 86

1. The given series is

 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) =  

For n=1

L.H.S=4.6=24

R.H.S=[4×5×15]÷6

      =300÷6

      =50

So, for n=1,

L.H.S≠ R.H.S

Since the given expression is true for n=1 ,

So , the given series is untrue.

we should replace R.H.S by=4(n+1)(n+2)(4n-3)²

2.

12+42+72+.......+(3 n -2)2=

For n=1,

L.H.S=12

R.H.S=1×(6-3-1)/2

       =2/2

      =1

As L.H.S≠ R.H.S

We should Replace R.H.S by [(3 n-1)(3 n-2)]2

3.The given sequence is

2+4+6+....+2n=n(n+1)

L.H.S

P(1)=2

R.H.S

1×(1+1)

=1×2

=2

( b)  L.H.S

P(n)=2+4+6+.....2 k

This is an A.P having n terms.

tex]S_{n}=

              = n(n+ 1)

R.H.S=n(n+1)

So, P(k)=k(k+1)

(c) P(k+1)=2+4+6+.......+2(k+1)

This is an A.P having (k+1) terms.

              =(k+1)(k+2)

So, P(k+1)= (k+1)(k+2)

(Btw this is not my answer)

9514 1404 393

Answer:

  (-2, -2)

Step-by-step explanation:

The midpoint M is calculated from end points A and B as ...

  M = (A +B)/2

Solving for end point B, we get ...

  2M = A +B . . . . . . multiply by 2

  B = 2M -A . . . . . . subtract A

Then the other end point is ...

  B = 2(4, 3) -(10, 8) = (2·4 -10, 2·3 -8) = (8-10, 6-8)

  B = (-2, -2)

The other end point has coordinates (-2, -2).

Answer:

undefined in the set of real numbers

Step-by-step explanation:

See image below:)

Answer:f(g)=2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

there is 2:   3  1  

                      4

Answer:

The answer is B--> 111 degrees

Answer:

Here

X=75+36(Exterior angle of a triangle is equal to sum of interior opposite angle)

X=111

Answer:

7.35

Step-by-step explanation:

m^2+10m-24

=m^2+12m-2m-24

=m (m+12)-2 (m+12)

=(m-2)(m+12)

Answer:(m-2)(m+12)

if wrong correct me pls

I hope it helps mate

HAVE A GREAT DAY

#Liliflim

we learned this in our lower i dont remember exactly but i think~

the probability that it will land on an even number will be 3 as there are 3 odd number and 3 even number

Answer:

1/2

Step-by-step explanation:

n(E) = 9

n(S) = 18

p(E1) = [tex]\frac{n(E1)}{n(S)}[/tex]

=9/18

=1/2

Answer:

1/12

Step-by-step explanation:

The first time the person picks a magazine, they have a 5/10 chance of drawing an architecture magazine.

The second time, they have a 4/9 chance because they have already removed one magazine from the bookshelf

The third time, they have a 3/8 chance because they have already removed 2 magazines.

Multiply all of the probabilities together

5/10 * 4/9 * 3/8 = 60/720

Simplify:

60/60 / 720/60 = 1 / 12

Hope this helps!

Answer:

5 Hundredths

Step-by-step explanation:

The place value of 5 in 624.95 in 5 Hundredths or 0.05

Answer:

0.3164 = 31.64% probability that none of the selected adults say that they were too young to get tattoos.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either the say their were too young to get tattoos, or they do not say it. The answers for each adult is independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

25​% say that they were too young when they got their tattoos.

This means that [tex]p = 0.25[/tex]

Four adults who regret getting tattoos are randomly​ selected

This means that [tex]n = 4[/tex]

a. Find the probability that none of the selected adults say that they were too young to get tattoos.

This is P(X = 0). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{4,0}.(0.25)^{0}.(0.75)^{4} = 0.3164[/tex]

0.3164 = 31.64% probability that none of the selected adults say that they were too young to get tattoos.

Answer:

125

Step-by-step explanation:

120 units cost 15000.

so, 1 unit is then the 120th part of the total costs.

price of 1 unit = 15000/120 = 1500/12 = 125

Answer:

[tex]volume = \pi {r}^{2} h \\ = 3.14 \times {6}^{2} \times 12 \\ = 1357.2 \: {ft}^{3} [/tex]