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]
In a watch, the minute hand crosses the hour hand for the third
time exactly after every 3 hr 18 min and 15 s of watch time. What
is the time gained or lost by this watch in one day?
Determine the x- and y-intercepts of the graph of x−4y=8 . HURRY!!!
the answer in point-slope form is y = 1/4x-2 so your y-intercept is -2 and from there, move up one and right four. your points would be (0, -2) and (4, -1)
hope this helped! :)
Jamal buys 33 bolts that cost $0.38 each,hich equation represents the best estimate for the total cost of all of the bolts
Answer:
12.54
Step-by-step explanation:
The director of the library believes that 13% of the library's collection is checked out. If the director is right, what is the probability that the proportion of books checked out in a sample of 774 books would be less than 10%
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
What is 3 ÷ 2/5??
The quotient is 7 and ???
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.
Taylor buys dog food for $1.25 a pound. How much will he pay for 8.6 pounds of dog?
Answer:
Taylor will pay $10.75
Step-by-step explanation:
If 1.25 PER/for each/for one pound that means you would multiply. So the equation is 8.6 x 1.25 = 10.75
Hope that helps and have a great day!
Answer:
10.75
Step-by-step explanation: 1.25 times 8.6 is 10.75 so that is the answer.
who ever answers first i will give brainily!!!!
Answer:
85
Step-by-step explanation:
Answer:
30$*3=90$ - its the answer
Step-by-step explanation:
To get the answer we can first divide 60 by 2 to see how much cost 5 burgers. Then we have to multiply that result times 3 to get the answer.
60:2=30$ ----- 5 burgers.
30$*3=90$ - its the answer
A ball is thrown vertically upwards with an initial velocity of 22 m/s. When will its speed be 10
m/s?
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
Which value is a solution to the inequality 2x − 5 < −12?
Question 21 options:
0
−4
−2
3
ill mark brainleist
A department store sells logo shirts at an original price of $20. Every month that a shirt doesn’t sell, the store reduces the selling price by 25%. The store employees get a 50% markdown off the current price. Macy works at the store and sees the shirts going into the second markdown month. She decides that since 25% + 25% + 50% = 100%, the shirts must be free to employees. What is Macy’s error?
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.
The smallest angle in a triangle is 1/3 as large as the largest angle. The third angle is twice the smallest angle. Find the three angles.
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]
Therefore :-The measure of the largest angle = 90°
The measure of the smallest angle = 30°
The measure of the third angle = 60°
If 4 adult elephants eat 320 pounds of food, how many ounces of food should the zookeeper purchase?
Answer:
Step-by-step explanation:
y/15- 2/3= 4/5
Whats the answer for y
How do you solve substitution to the equation y=-2x +1 4x+y=9
Answer:
Step-by-step explanation: 2x+y=1
4x+y=9
we substract equals. 2x=8 so x=4 , y=-7
Please Answer ASAP!!
Answer:
0.17
Step-by-step explanation:
hope i helped
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Answer:
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Step-by-step explanation:
PLZ HELP FAST
Enter an algebraic expression to model the given context. Give your answer in simplest form. The original price p of an item less a discount of 10%. The algebraic expression is
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
3 step equations, I really need help on these with all the work:
1.
4x+y+5z=-9
x-4y-2z=-2
2x+3y-2z=21
2.
x-7y+3z=17
5x+2y-2z=-57
3x-10y-z=-11
Answer:
fdsfskdfdsjg,dgkdfjkgjkdfgjkfjkdghdkj
Step-by-step explanation:
Question a) Compare the Variability of Expenditure of Families in Two Towns given as follows: Number of families Expenditure (Rupees) 21-30 31-40 41-50 51-60 61-70 71-80 81-90 Town A 3 61 132 153 140 51 2 Town B 2 14 20 27 28 7 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.
In a multiple linear regression analysis, statistical model utility is determined by the value of R2 and 2s, while practical model utility is determined by the Global F-test p-value.
a) true
b) false
Answer:
This statement is true because if F statistics is significant, then the entire multiple regression model is useful for the prediction of y.
Step-by-step explanation:
Solution:
In a multiple linear regression analysis, the statistical model utility is determined by the value of R2 and ∂2, while the Global F test p-value determines the practical model.
This statement is true because if F statistics is significant, then the entire multiple regression model is useful for the prediction of y.
The F test is a statistical test that is very flexible. F test can evaluate multiple model terms.
The F test indicates whether a linear regression model provides a better fit to data than a model that contains no independent variable.
The F test for overall significance has two hypotheses:
1- Null hypothesis:
The fit of the intercept only model and your model are equal.
2- Alternative hypothesis:
The fit of the intercept-only model is significantly reduced compared to your model.
Compare p-value for the F test,
If the p-value is less than the significance level, the sample data provide sufficient evidence that the regression model fits the data better with no independent variable.
Pretest 5. In a group of 250 students, 40 are seniors. What percentage of the group are seniors?
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]
The signal from a certain satellite takes 0.06384 seconds to reach Earth. Estimate using scientific notation:
Answer: -63E2
Step-by-step explanation: i think
Write an inequality for the following statement.
5 is less than or equal to y
Answer:
5 ≤ y
Step-by-step explanation:
PLEASE HELP ASAP
IT AN EMERGENCY
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.
The NFL regulation extra point is kicked 12 yards from the goal how many inches away from the goal is the extra point kick
Answer: 432 inches
Step-by-step explanation: 12 x 36 = 432.
Answer:
88
Step-by-step explanation:
100 - 12
Will you do the same thing these students did? What are the other ways that you can help less fortunate people?
What is 13 5/8 - 3 2/3?
I really need help i will mark u as brainliest
Answer:
1.23
Step-by-step explanation:
103.32/(7*12)
103.32/84
1.23
How can you represent a rate with 100 as the whole?
Please need help
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:
Help please I need the answer ASAP
Answer:
j
Step-by-step explanation: