Answer:
$69.21
Step-by-step explanation:
Since the box has a square base the length and breadth of the box will be equal. Let it be [tex]x[/tex]
Let h be the height of the box
V = Volume of the box = [tex]620\ \text{cm}^3[/tex]
[tex]x^2h=620\\\Rightarrow h=\dfrac{620}{x^2}[/tex]
Now surface area of the box with an open top is given
[tex]s=x^2+4xh\\\Rightarrow s=x^2+4x\dfrac{620}{x^2}\\\Rightarrow s=x^2+\dfrac{2480}{x}[/tex]
Differentiating with respect to x we get
[tex]\dfrac{ds}{dx}=2x-\dfrac{2480}{x^2}[/tex]
Equating with zero
[tex]0=2x-\dfrac{2480}{x^2}\\\Rightarrow 2x^3-2480=0\\\Rightarrow x^3=\dfrac{2480}{2}\\\Rightarrow x=(1240)^{\dfrac{1}{3}}\\\Rightarrow x=10.74[/tex]
Double derivative of the function
[tex]\dfrac{d^2s}{ds^2}=2+\dfrac{4960}{x^3}=2+\dfrac{4960}{1240}\\\Rightarrow \dfrac{d^2s}{ds^2}=6>0[/tex]
So, x at 10.74 is the minimum value of the function.
[tex]h=\dfrac{620}{x^2}\\\Rightarrow h=\dfrac{620}{10.74^2}\\\Rightarrow h=5.37[/tex]
So, minimum length and breadth of the box is 10.74 cm while the height of the box is 5.37 cm.
The total area of the sides is [tex]4xh=4\times 10.74\times 5.37=230.7\ \text{cm}^2[/tex]
The area of the base is [tex]x^2=10.74^2=115.35\ \text{cm}^2[/tex]
Cost of the base is $0.40 per square cm
Cost of the side is $0.10 per square cm
Minimum cost would be
[tex]230.7\times 0.1+0.4\times 115.34=\$69.21[/tex]
The minimum cost of the box is 69.21 dollars.
Which equation represents a linear function?
Group of answer choices
y – 5 = x(–x + 2)
y – 5 = x – 20
y(x – 1) = 9
y(y – 1) = x + 25
Given 2x+4y=12 what is the x and y int
A pharmacologist measured the concentration of dopamine in the brains of several rats. The mean concentration was 1,269 ng/gm and the standard deviation was 145 ng/gm.4 What was the standard error of the mean if:_______.(a) 8 rats were measured?
(b) 30 rats were measured?
Answer:
51.265242 ng/gm ; 26.473257 ng/gm
Step-by-step explanation:
The standard error of the mean = standard deviation / √sample size
Given that:
mean concentration = 1,269 ng/gm
Standard deviation (s) = 145 ng/gm
Standard Error if 8 rats were measured :
Sample size (n) = 8
Standard Error = s / √n
Standard Error = 145 / √8
Standard Error = 145 / 2.8284271
Standard Error = 51.265242 ng/gm
If 30 rats were measured :
Standard Error = 145 / √30
Standard Error = 145 / 5.4772255
Standard Error = 26.473257 ng/gm
Mrs canales class is selling pizza to earn money for a field trip. For every pizza sold the class makes $5.35. They have already earned $182.90 toward their $750 goal. How many more pizzas must they sell to earn $750 (algebraic approach) Thanks
Answer:
They still have to earn:
$750 - $182.9 = $567.1
and if they make $5.35 for every pizza sold:
$567.1 : $5.35 = 106
They must sell 106 pizzas more.
Step-by-step explanation:
Write an equation and solve. Round to the nearest hundredth where necessary. What is 35% of 63?
⚠️⚠️⚠️⚠️NEED HELP MARKING PEOPLE AS BRAINLIST!
I believe its a reflection
Sorry if im wrong
Homer is 30 feet below sea level and Marge is 45 feet above sea level. Bart’s elevation is at the exact midpoint of those two values. What is the expression that model this problem, and which is Bart’s elevation?
Answer:
14.5 feet
Step-by-step explanation:
the midpoint is halfway from 30 to 45 so be(bart elevation) b.e = 45 - 30 / 2
7.5 m above sea level
__________________________________________________________
Step-by-step explanation:We are given:
The elevation of Homer = -30 feet [30 feet below sea level]
The elevation of Marge = +45 feet [45 feet above sea level]
The elevation of Bart is at the exact mid-point of the elevations of Homer and Marge
The elevation of Bart:
We are given that the elevation of Bart is at the exact mid-point of the elevations of Homer and Marge
So, Half the distance between the elevation of Homer and Marge is the elevation of Bart
Elevation of Bart (with respect to the elevation of Homer) =
(elevation of Marge - Elevation of Homer) / 2
replacing the variables with the suitable values:
(+45 - (-30))/2
(45 + 30) / 2
75 / 2
Elevation of Bart (w.r.t. Homer) = 37.5 feet
Since this is the elevation of Bart with respect to Homer, we can say that Bart is 37.5 m above Homer
So, we can say that:
Elevation of Bart (w.r.t Homer) = Elevation of Bart - Elevation of Homer
replacing the values
37.5 = Elevation of Bart -(-30)
37.5 = Elevation of Bart + 30
Elevation of Bart = 7.5 m above sea level [subtracting 30 from both sides]
help pls
What is the solution to this system of equations?
x = 12 − y
2x + 3y = 29
Answer:
Step-by-step explanation:
I have $100 and I want to buy tshirt that cost $10 and sweatshirts that cost $20 how many tshirts and sweatshirts can I buy
Answer:
10 tshirts or 5 sweatshirts
Step-by-step explanation:
One t-shirt + one sweatshirt = $30.
We know that $100 ÷ $30 = 3 times with $10 left over.
This leads to the conclusion that you can buy 4 t-shirts and 3 sweatshirts.
the ratio 60 miles per hour is an example of a because it has two measurements having different units of measure
Answer:
180
Step-by-step explanation:
Answer: ejejejwjfmfmdnc
Step-by-step explanation:
Jack has a saving account of value $65,550 at the start. The saving account has an interest rate of 3% that is compounded every six months. How long will it take Jack to have $100,000 in his account?
Given:
Principal value = $65,550
Rate of interest = 3% compounded every six month
To find:
The taken to have $100,000 in Jack's account.
Solution:
The formula for amount is
[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]
where, P is principal, r is rate of interest, n is number of times interest compounded in an year, t is time in number of years.
Interest compounded every six month. It means, interest compounded 2 times in an year.
Substitute A=100000, r=0.03 and n=2 in the above formula.
[tex]100000=65550(1+\dfrac{0.03}{2})^{2t}[/tex]
[tex]\dfrac{100000}{65550}=(1+0.015)^{2t}[/tex]
[tex]1.525553=(1.015)^{2t}[/tex]
Taking log on both sides.
[tex]\log (1.525553)=\log (1.015)^{2t}[/tex]
[tex]\log (1.525553)=2t\log (1.015)[/tex]
[tex]\dfrac{\log (1.525553)}{2\log (1.015)}=t[/tex]
[tex]t=14.1838928[/tex]
[tex]t\approx 14.18[/tex]
Therefore, after 14.18 year the amount will reach at $100,000 or we can say that in 15th year the amount will reach at $100,000.
I need help answering. Thanks.
Answer:
28
Step-by-step explanation:
C or B's so 30% + 40% = 70% so:
70/100 multiplied by 40 because 40 students
7/10 times 40 = 28
Find the value of K. The diagram is not to scale. Explain your answer.
Answer:
639 lo hago para conseguir puntos ;V
Step-by-step explanation:
In how many ways can you arrange the books A, B, C, and D on a bookshelf if books A and C must remain neighboring?
OK THIS IS MAH 3rd QUESTION CAN SOMEONE PLS HELP MEH?
I REALLY NEED HELP PLS!
:3
Answer:
The earthquake was a magnitude 6.8, which describes the relative size of the earthquake at the spot where it occurred. Earthquakes with a magnitude larger than 6 tend to be severe and cause damage.
Step-by-step explanation:
Now that i wrote this passage you have to figure out which one it is
How many times larger is 4 x 10 ^16 than 4 x 10^6?
Answer:
10^10 timesStep-by-step explanation:
To find it we will divide:
4 x 10^16 / 4 x 10^6 = 4/4 x 10^(16 - 6) = 1*10^10=10^10 timesThe first number is 10^10 times larger
Answer:
1e+16 and 1000000 multiply it then divide...
Step-by-step explanation:
is -3/4 rational or irrational?
is the square root of 2 rational or irrational?
is 2π rational or irrational?
is 3.75 rational or irrational?
is 2 1/8 rational or irrational?
Help guyssssssssssssss
Answer:
1
Step-by-step explanation:
Jason buys a jar of vitamins that contains 180 tablets. He
saves $5 by using a coupon. He pays $11.20. What is the cost
of each tablet for someone who does not have a coupon?
Write and solve an equation for this situation. Solve the
problem.
Answer: 11 cents
Step-by-step explanation:
add 11.20 +5=16.20, then dived by 180, which equals .11
A.4
B.3
C.6
D.5........ please help
Answer:
The answer is
A. 4
Step-by-step explanation:
hey guys what is this type of equation/ question called 1 < x < 30
Answer:
2,3,4,5,6,7,8,9,10,...29
Step-by-step explanation:
Find the distance of a line given the following points. R(3, 1), W(-1, -2)
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
we can solve this using the distance formula: [tex]\sqrt{(x_{2}-x_1)^{2} + (y_{2}-y_1)^{2}}[/tex]
[tex]x_1, y_1[/tex] is (3, 1)
[tex]x_2, y_2[/tex] is (-1, -2)
[tex]\sqrt{(1-3)^2 + (-2-1)^2}[/tex]
which simplifies to: [tex]\sqrt{(-2)^2 + (-3)^2}[/tex]
then: [tex]\sqrt{2^2 + 3^2}[/tex] or: [tex]\sqrt{4+9}[/tex]
your final answer is: [tex]\sqrt{13}[/tex] or about 3.61
Sarah has saved 254 pound coins. She puts the pound coins into bags.
There are 20 pound coins in each full bag of coins. Sarah is going to take all her full bags of coins to the bank.
She can only take up to 5 full bags of coins to the bank each day.
Sarah wants to go to the bank on as few days as possible.
On how many days will Sarah need to go to the bank?
Answer:
Step-by-step explanation:
So for the fewest days it would be 3 days. The reason for that is because she has 254 pound coins. And she can inly take 5 bags to the bank a day, all of those 5 bags have 100 pound coins in them. If she take 2 days and get 200 pound coins to the bank. Then on the third day she would only have to bring three bags. So your answer for the fewest days possible is three days!
Hope it helps
convert the common fraction into decimal fraction
[tex] \frac{3}{4} [/tex]
Answer:
We know that 3/4=0.75.When expressed as decimal fraction it is 75/100
What is an equation of the line that passes through the points (4,1) and (8,-3)?
PLZZ HELPP MEE!!
Answer:
y=-x+5
Step-by-step explanation:
(4,1)
(8,-3)
1)a slope of a line is (y2-y1)/(x2-x1)
so (-3-1)/(8-4)
-4/4=>m=-1
2)to find y-int replace any points in the equation by x and y
so 1=-1(4)+b
1=-4+b
1+4=b
so b= 5
therefore the equation is y=-x+5 so d
Megan makes and sell slime online.
Answer:
44 containers
what makes this number special 8549176230
Uhm hope this help (:
8,549,176,320 What makes this number unique? Answer: The said number has all the numbers from 0-9 exactly once and what is special is they are in lexicographical order of their English words.
There are 33 students in your class. Yesterday, 9 students were absent. What decimal represents the students were absent? *
Answer:
27.27% of the class was absent
Step-by-step explanation
Write a like term to: -5y
Answer:
-7y
Step-by-step explanation:
As long as the variable and exponent is the same, they are like terms
Answer: 68y
There are infinitely many ways to answer this. All you need to do is pick your favorite number and then stick y at the end of it. The terms -5y and 68y are like terms because they have the same variable attached.
You can think of 68y-5y as having 68 yoyos and then subtracting off 5 yoyos to get 63 yoyos when all is said and done. In terms of algebra, we would write 68y-5y = 63y.
What is the measure of an angle if the measures of its two adjacent supplementary angles add up to 100°?
The answer is not 80 btw
Explanation:
Let x be the unknown angle we want to find.
Let y be adjacent and supplementary to x. This means x+y = 180
Let z also be adjacent and supplementary to x. So x+z = 180 also
Subtracting the two equations leads to y-z = 0 and y = z. So effectively we've proven the vertical angle theorem.
Since the supplementary angles to x add to 100, we know that y+z = 100. Plug in y = z and solve for z
y+z = 100
z+z = 100
2z = 100
z = 100/2
z = 50
Therefore,
x+z = 180
x+50 = 180
x = 180-50
x = 130
Answer:
130°
Step-by-step explanation:
Let x be the unknown angle we want to find.
Let y be adjacent and supplementary to x. This means x+y = 180
Let z also be adjacent and supplementary to x. So x+z = 180 also
Subtracting the two equations leads to y-z = 0 and y = z. So effectively we've proven the vertical angle theorem.
Since the supplementary angles to x add to 100, we know that y+z = 100. Plug in y = z and solve for z
y+z = 100
z+z = 100
2z = 100
z = 100/2
z = 50
Therefore,
x+z = 180
x+50 = 180
x = 180-50
x = 130