In what year will the two quantities be​ equal?

Answer:

12.54

Step-by-step explanation:

Answer:

The dimensions of the aquarium that minimize the cost of the materials:

[tex]x=y = \sqrt[3]{\frac{2V}{9}} , z = \sqrt[3]{\frac{81V}{4}}[/tex]

Step-by-step explanation:

Let x, y and z be the dimensions of aquarium .

Surface area of an aquarium = xy+2yz+2xz

Volume of aquarium V= [tex]Length \times Breadth \times Height =xyz----A[/tex]

We are given that slate costs five times as much (per unit area) as glass

So, Cost function : C=9xy+2yz+2xz

Now we will use langrage multiplier to find the dimensions of the aquarium that minimize the cost of the materials.

[tex]\nabla C = \lamda \nabla V\\(\frac{\partial C}{\patial x},\frac{\partial C}{\partial y}, \frac{\partial C}{\partial z})=\lambda(\frac{\partial V}{\patial x},\frac{\partial V}{\partial y}, \frac{\partial V}{\partial z})\\(9y+2z,9x+2z,2y+2x)=\lambda(yz+zx+xy)[/tex]

So,[tex]9y+2z=\lambda yz -----1\\9x+2z=\lambda zx -------2\\2y+2x=\lambda xy --------3[/tex]

Multiply 1 ,2 and 3 by x,y and z respectively.

[tex]9xy+2xz=\lambda xyz ------4\\9xy+2zy=\lambda zxy -------5\\2yz+2xz=\lambda xyz --------6[/tex]

Now equate 4 and 5

9xy+2xz=9xy+2yz

x=y

Substitute y=x in 5 and 6 and equate them

[tex]9x^2+2xz=2xz+2xz\\9x=2z\\\frac{9x}{2}=z[/tex]

Substitute the values in A

[tex]Volume = xyz=(x)(x)(\frac{9x}{2})\\Volume V = \frac{9x}{2}x^3\\\sqrt[3]{\frac{2V}{9}}=x\\x=y=\sqrt[3]{\frac{2V}{9}}\\z=\frac{9(\sqrt[3]{\frac{2V}{9}})}{2}\\z=\sqrt[3]{\frac{81V}{4}}[/tex]

Hence,

The dimensions of the aquarium that minimize the cost of the materials:

[tex]x=y = \sqrt[3]{\frac{2V}{9}} , z = \sqrt[3]{\frac{81V}{4}}[/tex]

Answer:

The ball's speed will be 10 m/s at t=1.22 seconds

Step-by-step explanation:

The vertical motion of an object is controlled by the force of gravity. This means that there is a non-zero net force acting on the object that makes it accelerate downwards.

If the object is thrown upwards at speed vo, its speed at time t is:

[tex]v_f=v_o-g.t[/tex]

Where g is the acceleration of gravity [tex]g=9.8 m/s^2.[/tex]

Our ball is thrown upwards with v0=22 m/s. We need to calculate the time when its speed is vf=10 m/s.

Solving the above equation for t:

[tex]\displaystyle t=\frac{v_o-v_f}{g}[/tex]

Substituting:

[tex]\displaystyle t=\frac{22-10}{9.8}=\frac{12}{9.8}[/tex]

t=1.22 seconds

The ball's speed will be 10 m/s at t=1.22 seconds

Answer:

How to Calculate a Rate. "Rate" simply means the number of things per some other number, usually 100 or 1,000 or some other multiple of 10. A percentage is a rate per 100. Infant mortality rates are calculated per 1,000.

Step-by-step explanation:

Answer:

The probability that the proportion of books checked out in a sample of 774 books would be less than 10% is 0.0066

Step-by-step explanation:

We are given that The director of the library believes that 13% of the library's collection is checked out.

[tex]\mu = p = 0.13[/tex]

Total no. of books = 774

Standard deviation =[tex]\sqrt{\frac{p(1-p)}{n}}[/tex]

Standard deviation = [tex]\sqrt{\frac{0.13(1-0.13)}{774}}=0.012[/tex]

We are supposed to find  the probability that the proportion of books checked out in a sample of 774 books would be less than 10%

[tex]P(\hat{p}<0.1)\\Z=\frac{x-\mu}{\sigma}\\Z=\frac{0.1-0.13}{0.012}\\Z=-2.48\\P(Z<-2.48)=0.0066[/tex]

So,[tex]P(\hat{p}<0.1)=0.0066[/tex]

Hence  the probability that the proportion of books checked out in a sample of 774 books would be less than 10% is 0.0066

Answer:

25%

Step-by-step explanation:

Macy’s error is that the store employees get a 25% markdown off the current price. In the first markdown (i.e 50%) should have been reduced to 25% in the second markdown, instead of being totally free.

Answer:

///////////////////

Step-by-step explanation:

Let the largest angle in a triangle be x .

Then :-

The smallest angle :-

[tex] \frac{1}{3} x[/tex]

The third angle :-

[tex] \frac{2}{3} x[/tex]

Let us find the measure of the three angles .

Sum of all angles in the interior of a triangle = 180°

An equation to find the value of each angle :-

[tex]x + \frac{1}{3} x + \frac{2}{3} x = 180[/tex]

[tex]x + \frac{3}{3} x = 180[/tex]

[tex]x + \frac{1}{1} x = 180[/tex]

[tex]x + 1x = 180[/tex]

[tex]x + x = 180[/tex]

[tex]2x = 180[/tex]

[tex]x = \frac{180}{2} [/tex]

[tex]x = 90[/tex]

Which means :-

Measure of the largest angle = 90°

Measure of the smallest angle :-

[tex] \frac{1}{3} \times 90[/tex]

[tex] = 30°[/tex]

Measure of the third angle :-

[tex] \frac{2}{3} \times 90[/tex]

[tex] = 60°[/tex]

The measure of the largest angle = 90°

The measure of the smallest angle = 30°

The measure of the third angle = 60°

Answer:

5 ≤ y

Step-by-step explanation:

Answer:

0.17

Step-by-step explanation:

hope i helped

We're given two pairs of congruent sides, and a pair of congruent angles. The angles are not between the two congruent sides. So we don't have enough information to know if the triangles are congruent or not. SSA is not a valid congruence theorem. This is because there are some cases where two triangles are possible leading to ambiguity.

If the marked angles were between the tickmarked sides, then we could use SAS.

Answer:

Step-by-step explanation:

Answer:

Taylor will pay $10.75

Step-by-step explanation:

If 1.25 PER/for each/for one pound that means you would multiply. So the equation is 8.6 x 1.25 = 10.75

Hope that helps and have a great day!

Answer:

10.75

Step-by-step explanation: 1.25 times 8.6 is 10.75 so that is the answer.

Answer:

7 and 5

Step-by-step explanation:

3 divided by 2/25 will be 15/2 in fraction form, and will be 7.5 in decimal form.

Answer:

The quotient is 7 1/2.

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Number of families __________Expenditure

______midpoint (x) ____Town A __Town B

21-30 __25.5____________3 _______2

31-40 __35.5____________61 ______14

41-50 __45.5___________132 _____ 20

51-60 __55.5__________ 153 ______27

61-70 __65.5__________ 140 ______ 28

71-80 __75.5___________ 51 _______ 7

81-90 __85.5___________ 2 _______ 2

The variability is the variance and standard deviation :

The variance (s):

√Σ(x - m)²/Σf(x)

Town A:

m = Σ(X * f(x)) / Σf ; Σf = 542

Σ x * f(x) = (25.5*3) + (35.5*61) + (45.5*132) + (55.5*153) + (65.5*140) + (75.5*51) + (85.5*2)

= 29931 / 542

= 55. 22

Σf(x - m)² / Σf - 1 = [3(25.5-55.22)^2 + 61(35.5-55.22)^2 + 132(45.5-55.22)^2 + 153(55.5-55.22)^2 + 140(65.5-55.22)^2 + 51(75.5-55.22)^2 + 2(85.5-55.22)^2] / 541

= 76458. 4928 / 541

Variance = 141.32808

Standard deviation = √variance

Standard deviation = √141.32808

Standard deviation = 11.89

TOWN B:

m = Σ(X * f(x)) / Σf ; Σf = 100

Σ x * f(x) = (25.5*2) + (35.5*14) + (45.5*20) + (55.5*27) + (65.5*28) + (75.5*7) + (85.5*2)

= 5490 / 100

= 54.90

Variance :

Σf(x - m)² / Σf - 1 = [2(25.5-54.90)^2 + 14(35.5-54.90)^2 + 20(45.5-54.90)^2 + 27(55.5-54.90)^2 + 28(65.5-54.90)^2 + 7(75.5-54.90)^2 + 2(85.5-54.90)^2] / 99

= 16764 / 99

= 169.33

Standard deviation = √variance

Standard deviation = √169.3333

Standard deviation = 13.013

From the result above, Town A has lesser variability than Town B due to the slightly lower variance and standard deviation values.

Answer: 432 inches

Step-by-step explanation: 12 x 36 = 432.

Answer:

88

Step-by-step explanation:

100 - 12

Answer:

The algebraic expression is​ 0.90p

Step-by-step explanation:

The presentation of the algebraic expression is​ shown below:

Let us assume that the original price is p.

So,

The Orginal price is P

and the item would be less a 10% discount

So it could be written as 0.10p

Now the required expression could be written as

p - 0.10 p = 0.90p

Hence the algebraic expression is​ 0.90p

The same is to be considered

Answer:

fdsfskdfdsjg,dgkdfjkgjkdfgjkfjkdghdkj

Step-by-step explanation:

Answer:

[tex]\%seniors = 16\%[/tex]

Step-by-step explanation:

Given

[tex]Students = 250[/tex]

[tex]Seniors = 40[/tex]

Required

Determine the percentage of seniors

This is calculated as thus;

[tex]\%seniors = \frac{Seniors}{Students} * 100\%[/tex]

[tex]\%seniors = \frac{40}{250} * 100\%[/tex]

[tex]\%seniors = \frac{4000\%}{250}[/tex]

[tex]\%seniors = 16\%[/tex]

Answer:

j

Step-by-step explanation:

Answer:

Step-by-step explanation:   2x+y=1

                                               4x+y=9        

we substract equals. 2x=8 so x=4 , y=-7

Answer: -63E2

Step-by-step explanation: i think

Answer:

c = 64

Step-by-step explanation:

I hope this helps!

Answer:

1.23

Step-by-step explanation:

103.32/(7*12)

103.32/84

1.23