The dimensions of the box that minimize the total cost of materials used are:
L = W = 16 cm
H = 32 cm
What is the rectangular dimension?
Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth. A triangle's or an oval's interior likewise has two dimensions.
We have,
volume L* W * H = 512 cm³
sides of the box cost = 1 cent/cm²
top and bottom cost 2 cent/cm²
to find out
dimensions of the box that minimize the total cost of material use
we know here,
L* W * H = 512 cm³
where,
L is length and W is width and H is the height
so when we minimize the cost function
C( L, W, H ) = (1) 1 H ( L + W ) + (2) 1 L W
so put here H
substitute [tex]H = \frac{512}{LW}[/tex] we get,
C(L, W) = 512([tex]\frac{1}{l}, \frac{1}{W}[/tex]) + 2LW
so
minimum cost will be when the two partial derivatives is 0
dC/dL = 2W - 512/L² = 0
so
dC/dW = 2L - 512/W² = 0
L = 256/W²
so
by solving the above equation we get
L = W = (256)⁻³ = 16cm
and
H = 512/16 = 32
H = 32 cm
Hence, the dimensions of the box that minimize the total cost of materials used are:
L = W = 16 cm
H = 32 cm
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A piece of paper is to display ~150~ 150 space, 150, space square inches of text. If there are to be one-inch margins on the sides and the top and a two-inch margin at the bottom, what are the dimensions of the smallest piece of paper that can be used?.
The paper's smallest dimensions are height=8.660in and width=17.321in.
What are dimensions?In physics and mathematics, the dimension of space is the smallest set of coordinates needed to specify any point within a mathematical space.
A line has a dimension of one because only one coordinate is needed to specify a point on a line, such as a point at 5 on a number.
So, we have:
Area = 150in²
Side margin = 1 in
Top and Bottom Margin = 2 in
To obtain the smallest dimensions, calculate as follows:
The printed material's area is:
Area = l*w
A1 = h*w
A1 should be changed to 150:
150 = h*w
h = 150/w
The complete paper's topic is:
Area = l*w
A2 = (w+2+2)*(H+1+1)
A2 = (w+4)*(H+2)
For H, substitute 150/W:
A2 = (w+4)*(150/w+2)
A2 = w(150/w+2) + 4(150/w+2)
A2 = 150 + 2w + 600w + 8
A2 = 2w = 600/w + 8 + 150
A2 = 2w = 600/w + 158
Calculate a difference with regard to w and set the outcome to 0:
A'2 = 2-600/w²+0
A'2 = 2-600/w²
0 = 2 - 600/w²
2 = 600/w²
2*w² = 600
w² = 600/2
w² = 300
w = 17.321
Remember that:
h = 150/w
h = 150/17.321
h = 8.660
Therefore, the paper's smallest dimensions are height=8.660in and width=17.321in.
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THIS IS URGENT!!!
A cube has 54 colored stickers across all six of its faces. Each face has the same number of stickers in the same format. On each face, each column and row has the same number of stickers.
The number of stickers in each row and column is
.
Answer:
3
Step-by-step explanation:
We know a cube has six sides.
Using this logic, we can divide 54 by 6.
54 ÷ 6 = 9
We can conclude that each side has 9 stickers.
If we think of a square, and the area of that square is 9,
3 × 3 = 9
The number of stickers in each row and column is 3
Answer:
3 stickers in each row and column
Step-by-step explanation:
so i divided 54 by 6 and that equals 9 and since you said there was the same number of stickers on each column and rows that would be 9 separated into a even amount of rows and columns would be 3
a survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools. two of the questions concerned eye and hair color. in the survey, the following codes were used:
a survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools The U.S. Population Census is an example of a census
Census means the procedure of counting, calculating and recording the number and information about the members of the nation's.
Generally, population census are conducted every 10 years although some nations conduct their's every 5 years.
The primary objective of population census is to know the total size of the population of a country.
Population census also enable the government to appropriate resources fairly based on the number of people in a geographical area.
In conclusion, the U.S. population census is the only example of census.
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Please help now asap !!!!!!!!!
Answer:
80
usually estimate is rounded 1 significant figure, 0.9 is rounded to 1, and 82 is rounded to 80.
1*80 is 80
Mites are discovered in a peach orchard. The Department of Agriculture has determined that the population of mites t hours after the orchard has been sprayed is approximated by N(t)=1600−3tln(0.07t)−t N ( t ) = 1600 − 3 t ln ( 0.07 t ) − t , where 0What is the maximum number of mites in the peach orchard? Round to the nearest whole number.
The maximum number of mites in the peach orchard are 1564
Given that,
There are found to be mites in a peach orchard. According to research conducted by the Department of Agriculture, the number of mites t hours after the orchard has been sprayed is roughly represented by the equation N(t)=1600-3tln(0.07t)-t
To find : What is the maximum number of mites in the peach orchard? Round to the nearest whole number.
N(t)=1600-3tln(0.07t)-t
N(19)=1600-3(19)ln(0.07(19))-(19)
N(19)=1600- 16.255 - 19
N(19)=1564.74
N(19)≈1564
Therefore, the maximum number of mites in the peach orchard are 1564
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Write code using the range function to add up the series 15, 20, 25, 30,. 50 and print the resulting sum each step along the way.
The range function to add up the series is 15 ,35 ,60 ,90, 125,165,210 ,260
What is a python function?
A unit of code with a name is referred to as a function in Python. We utilize functions anytime we need to repeat a process repeatedly without writing the same code.
Given: Series 15, 20, 25, 30,.. 50
Program (Pascal ABC) and Result:
Program:
Var i, Summ : integer;
begin
i : = 15;
Summ : = 15;
While i <= 50 do
begin
WriteIn ( ' ' , Summ) ;
i : = i + 5 ;
Summ : = Summ + i ;
end ;
end.
Result : 15 ,35 ,60 ,90, 125,165,210 ,260
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suppose our student center published data that the average starting salary for college graduates is 59k. you randomly sampled 49 college graduates and calculated the sample average salary is 44k. what test can you use to check whether the true average is 59k?
To check whether the true average is 59k or not, A sample mean T-Test needs to be conducted. The true value of 59k is 44k after the test.
What is an Average?In the field of statistics, average means that the ratio of the sum of the numbers of a given set, to the total number of characters in a given set. It is also called as the Arithmetic mean.
Equating :
It is given that the student center has published the data that the average salary of the college graduates is 59k. Accordingly, the sample of 49 college students were verified and the sample average salary came out to be 44k.
When we analyze the given question, we find that,
The total number of students were 49,The true average was found to be 59k,and the Sample average is found to be 44k.
Thus, in the present question we will use the One- sample T-test.
We used this test, as the statistical hypothesis test is used to find if the unrecognized population mean is different from the specific value.
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The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 20. 820. 820, point, 8 years; the standard deviation is 3. 13. 13, point, 1 years.
A z-score of 23.9 years must be located in the gorillas' lifespans in a specific zoo's typical normal distribution.
Define the term normal distribution?A data collection with a normal distribution is put up so that the majority of the values cluster as in midpoint of the range and the remaining values taper off symmetrically in either direction.The equation can be used to determine the z score.
z = (x - μ)/σ
In which,
X is age 23.9.The typical gorilla life span is M. (20.8 years).The standard deviation is s. (3.1 years).Then,
z = (23.9 - 20.8)/3.1
z = 1
According to the empirical rule, 68% of lifespans are within one standard deviation of the mean.
Half of it, 68/2 = 34% %, is on the right side of the mean's standard deviation.
Given that the likelihood of a gorilla lasting less than 23.9 years is 50%.
A gorilla's lifespan being less than the norm means is;
50% + 34% = 84% sits below z-score 1.
Thus, the probability of a gorilla living less than 23.9 years is 84%.
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The correct question is-
The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 20.8 years; the
standard deviation is 3.1 years.
Use the empirical rule (68 – 95 - 99.7%) to estimate the probability of a gorilla living less than 23.9 years.
Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.)
The integration by part is [tex]\frac{x^{3}In x }{3} -\frac{x^{3} }{9} +C[/tex] with indicated choices of u and dv.
What is integration by parts?
The method Integration by Parts is known to be a special method of integration that is often useful. In calculus, definite integrals are referred to as the integral with limits such as upper and lower limits. It is also possible to derive the formula of integration by parts with limits.
Given: ∫ [tex]x^{2} In x dx[/tex] ; [tex]u=In x[/tex] ; [tex]dv=x^{2} dx[/tex]
Consider [tex]u=In x[/tex] and [tex]dv=x^{2} dx[/tex]
⇒ [tex]u=In x[/tex] ⇒ [tex]dv=x^{2} dx[/tex]
⇒ [tex]du= \frac{1}{x} dx[/tex] ⇒ [tex]v=\frac{x^{3} }{3}[/tex]
Now, apply integration by parts to solve the integral
∫ u dv = uv - ∫ v du
the antiderivative of [tex]x^{n}[/tex][tex]=\frac{x^{n+1} }{n+1}[/tex] and the derivative of In x = [tex]\frac{1}{x}[/tex] .
⇒ ∫ [tex]x^{2} In x dx =[/tex][tex]\frac{x^{3} In x}{3} -\frac{x^{3} }{3} .\frac{1}{x} dx[/tex]
= [tex]\frac{x^{3}In x }{3}[/tex] [tex]-\frac{x^{2} }{3} dx[/tex]
= [tex]\frac{x^{3}In x }{3}[/tex] [tex]-\frac{x^{3} }{9} +C[/tex]
Hence, the final integration is [tex]\frac{x^{3}In x }{3}[/tex] [tex]-\frac{x^{3} }{9} +C[/tex]
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Im so confused with this question 21≥3(a-7)+9
Answer:
I got you!
a ≤ 11
For more info, look at the steps in the attached image!
Step-by-step explanation:
Answer:
a ≥11
Step-by-step explanation:
[tex]21 \geqslant 3a - 21 + 9 \\ 21 \geqslant 3a - 12 \\ 21 + 12 \geqslant 3a - 12 + 12 \\ 33 \geqslant 3a \\ 3a \leqslant 33 \\ a \geqslant 11[/tex]
Assuming that each of the 121212 customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?.
The probability that at least one customer will report a food allergy is; 0.6323
How to find the probability?The formula for Binomial probability distribution is;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
Where;
P(X = x) is the probability of getting success.
x is number of trials
n is sample size
p is the probability of getting success in each event.
We are given;
n = 12
p = 0.08
Let x denotes the customer will report a food allergy.
Then, the probability that at least one customer will report a food allergy will be :
P(X ≥ 1) = 1 - P(X < 1)
P(X < 1) IS P(X = 0)
Thus;
P(X ≥ 1) = 1 - 0.3677
P(X ≥ 1) = 0.6323
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Complete question is;
When a customer places an order at Ying Ying's bakery, there is an 8 percent probability that the customer will report a food allergy. One day, 12 customers place orders at Ying Ying's bakery.
Assuming that each of the 12 customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?
The functions f(x) and g(x) are graphed. On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). Which represents where f(x) = g(x)? Group of answer choices f(2) = g(0) and f(0) = g(4) f(2) = g(4) and f(1) = g(1) f(2) = g(2) and f(0) = g(0) f(2) = g(0) and f(4) = g(2)
f(2) = g(2) and f(0) = g(0) is representation of f(x) = g(x)
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
the curved red line represents g(x) and the straight blue line represents f(x) .
The important thing here is that the equality of functions f(x)=g(x) is represented as a common function between their curves. So, we just need to find such a common point for both.
f(x) has points (0, 4) and (2, 0).
g(x) has points (0,4) and (2,0).
Notice that both functions have the same y-value for x=0 and x=2, that means f(0)=g(0) and f(2)=g(2)
Hence, f(2) = g(2) and f(0) = g(0) is representation of f(x) = g(x)
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the standard error of estimate measures the accuracy of a prediction. group startstrue or falsetrue, unselectedfalse, unselected
The statement is true that is the standard error of estimate measures the accuracy of a prediction.
Given that,
We have a statement that is the standard error of estimate measures the accuracy of a prediction.
We have to find is the statement is true are false.
We know that,
What is standard error?The SE formula is used to determine how accurately a sample represents a population. The sample mean's departure from the specified population is provided as follows,
Formula for standard error
S.E=S/√n
Where, n is the number of observations and S is the standard deviation.
Therefore, The statement is true that is the standard error of estimate measures the accuracy of a prediction.
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Find the volume of a right circular cone that ha a height of 13,8 cm and a bae with a circumference of 15. 8 m
Answer: V=πr2h
3
Step-by-step explanation: Your spelling is a bit off
Find the value of the product (4a2 + 3b) (4a2+36) at a = 1, b = 2.
The final value of the product = 292
According to the given equation -
= (4a2+3b)x(4a2+36)
multiply the whole equation-
= 16a4+144+12a2b+108
as we can see that the values of a and b are given 1 and 2 respectively,
so putting the values of a and b in the equation we get -
= 16(1)4+144+12(1)2(2)+108
= 292
The product of the following equation will be = 292
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PLEASE HELP!!!!!!
I need this answered ASAP
Abiona cannot decide which of two bicycles to buy. The original price of each is $380. The first bicycle is marked down by 50%. The second bicycle is marked down by 30% first and then an additional 20% off. Which bicycle should Abiona buy if the bicycles are the same except for the selling price? Explain your answer.
Abiona should buy the first bicycle ($190) because it is cheaper than the second bicycle ($212.8)
How to determine which bicycle Abiona should buy?Given that:
The original price of each is $380
The first bicycle is marked down by 50%
The second bicycle is marked down by 30% first and then an additional 20% off
The price of the first bicycle after the discount will be:
price = 380 - (0.5×380)
price = $190
The price of the second bicycle after the discount will be:
After 30% discount:
price = 380 - (0.3×380) = $266
After 20% discount:
price = 266 - (0.2×266) = $212.8
Thus, the price after the discount is $212.8
Therefore, Abiona should buy the first bicycle because it is cheaper
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Solve for the variable. 2(k+8) = 44
Answer:
k = 14
Step-by-step explanation:
2(k+8) = 44
2*k + 2*8 = 44
2k + 16= 44
2k = 44 - 16
2k = 28
k = 28/2
k = 14
Check:
2(14+8) = 44
2*22 = 44
If the original quantity i 5 and the new quantity i 3, what i the percent decreae?
The percentage reduction is 40% if the original number was 5 and the new quantity is 3.
What is the percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.
If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
A percentage is a value expressed as a decimal. Divide the percentage value by 100 to convert percentages to decimals and fractions.
The Latin word per centum, which means "hundred" or "by the hundred," is where the word "percent" originates.
The Italian word per cento, which means "for a hundred," gradually shrank to become the symbol for "percent."
Per was frequently shortened to "p" and eventually vanished entirely. The contemporary "%" symbol was created by condensing the "cento" to two circles divided by a horizontal line.
According to our question-
5 were originally ordered, however only 3 were added, resulting in a net drop of 1.
(5 - 3) = 2.
Now, we'll divide net change by the initial amount and multiply it by 100% to get the percentage change, which is,
(2/5)×100%.
= 40%,
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PLEASE HELP I AM CONFUSE!!!!!!!!!!
Answer:
A = $285.45
A = P + I where
P (principal) = $200.00
I (interest) = $85.45
Step-by-step explanation:
there I hope this helps!
Here is a graph of a logarithmic function.
what is the base of the logarithm? explain how you know.
Answer:
base = 10
Step-by-step explanation:
Make a conjecture about the value
Points A, B, and C are collinear,
and D is between B and C.
Answer :not fully correct
cStep-by-step explanation:
A baker uses 2 cups of vanilla to make 24 donut. how many ounces vanilla are there per donut?
The two polygons are similar . Solve for x
Your team has contracted to design and build a 500 ft, square-based, open-top, rectangular steal holding tank for a paper company. The tank is to be made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weight as little as possible.
For dimensions of x =10 and y=5 for the base and height that will make the tank weight as little as possible.
Here we are given the information of a square-based, open-top, rectangular steel holding tank, so here the tank is in the shape of a cuboid and we know the formula for :
volume = x*y*z, as here it is a square base, so the volume will be
volume = x²*y, where x and y are the dimension of the base and height
So for the given reason,
=>x²*y = 500
=> y = 500/x²
Again, the surface area formula will be
S=x²+4xy, substituting the value of y in this question
=>S=x²+4x(500/x²)
=>S=x²+2000/x
Differentiating the above formula with respect to x, we get
=>2x-2000/x²=0
=>2x³= 2000
=>x³= 1000
=>x =10
so the substituting the x values of x in the equation y , we get
y = 500/x²
=>y = 5
so the dimensions are x= 10 and y=5
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aurelio is purchasing carpet tiles to cover an area of his living room floor that is 813 feet wide by 10 feet long. each carpet tile is a square 20 inches wide by 20 inches long. what is the minimum number of carpet tiles that aurelio must purchase to cover this area of his living room floor?
30 inches many carpet tiles will Aurelio need to buy at the very least to cover this portion of the floor in his living room.
Given that,
To cover an area of his living room floor that is 8 1/3 feet wide by 10 feet long, Aurelio is buying carpet tiles. The dimensions of each carpet tile are 20 inches broad by 20 inches long.
We have to find how many carpet tiles will Aurelio need to buy at the very least to cover this portion of the floor in his living room.
We know that,
1 feet=12 inches.
So,
8 1/3 feet = 25/3 feet =100 inches.
10 feet =120 inches.
=100+120 inches
=12000 inches.
So, now
20×20=400
We get
12000/400= 30
Therefore, 30 many carpet tiles will Aurelio need to buy at the very least to cover this portion of the floor in his living room.
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Joey's boat weighs 0.62 tons. What is he weight of the boat measured in pounds?
Answer:
The answer would be 1240 pounds. The conversion that you would make would be to multiply 0.62 by 2000.
Hope this helps, Have a wonderful day! :D
Step-by-step explanation:
A class trip to a beach has been planned for your senior trip. The resort only allows swimming when the temperature is between 75 degrees and 110 degrees. There is room for 50 people on your trip. Write the constraints to represent this real-world problem, where x is the temperature and y is the number of people on your trip.
The correct answer is (C) since the limitations to depict this real-world problem in inequality are 75 < x < 110 and 0 < y ≤ 50.
What is inequality?The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity.
This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.
So, our senior trip will be a group excursion to a beach.
Only when the temperature is between 75 and 110 degrees does the resort permit swimming.
On your excursion, there is space for 50 people.
Let y represent the number of travelers and x represent the temperature.
The temperature ranges from 75 to 110 degrees:
75 < x < 110
On your excursion, there is space for 50 persons:
0 < y ≤ 50
Therefore, the correct answer is (C) since the limitations to depict this real-world problem in inequality are 75 < x < 110 and 0 < y ≤ 50.
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Complete question:
A class trip to a beach has been planned for your senior trip. The resort only allows swimming when the temperature is between 75 degrees and 110 degrees. There is room for 50 people on your trip. Write the constraints to represent this real-world problem, where x is the temperature and y is the number of people on your trip.
a. 0 < x ≤ 50 and 75 < y < 110
b. x > 75 and y < 110
c. 75 < x < 110 and 0 < y ≤ 50
d. x < 110 and y > 75
Consider a right-tailed test (upper tail) and a sample size of 40 at the 95% confidence level. Which one of the following is the value of t?.
The value of t while considering a right-tailed test (upper tail) and a sample size of 40 at the 95% confidence level is ±1.685.
Given:
Consider a right-tailed test (upper tail) and a sample size of 40 at the 95% confidence level.
we are asked to determine the t value:
The directional hypothesis is:
Hₐ : µ > µ₀
The sample size is, n = 40.
The significance level is:
α = 1-0.95 = 0.05
Use the t-table to compute the right-tailed t-critical value as follows:
tₐ,₍ₙ₋₁₎ = t₀.₀₅,₍₄₀₋₁₎
= t₀.₀₅,₃₉
≈ t₀.₀₅,₄₀
= 1.684
≈ 1.685
The value is positive since the directional hypothesis suggests that the test is right tailed.
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9 questions for 30 points!
Answer:
1. The solution to question one = (2, -6)
2. The solution to question two = (-1, 7)
3. The solution to question three = (1, 12)
4. The solution to question four = (2, -12)
5. The solution to question five = (3, 12)
6. The solution to question six = (-3, 12)
7. The solution to question seven = (-2, -8)
8. The solution to question eight = (-3, 21)
9. The solution to question nine = (2, 16)
Step-by-step explanation:
Steps to solve question 1:
Step 1: Substitute 5x for y in y = x - 8 and solve for y
1. (5x) = x - 8 → 4x = 8 → x = 2
Step 2: Plug 2 in for x in y = x - 8 and solve for x
2. y = (2) - 8 → y = -6
The solution to question one: (2, -6)
Steps to solve question 2:
Step 1: Substitute 3x for y in y = -x - 4 and solve for y
1. (3x) = -x - 4 → 4x = -4 → x = -1
Step 2: Plug -1 in for x in y = -x - 4 and solve for x
2. y = -(-1) - 8 → y = 7
The solution to question two: (-1, 7)
Steps to solve question 3:
Step 1: Substitute 12x for y in y = x + 11 and solve for y
1. (12x) = x + 11 → 11x = 11 → x = 1
Step 2: Plug 1 in for x in y = x + 11 and solve for x
2. y = (1) + 11 → y = 12
The solution to question three: (1, 12)
Steps to solve question 4:
Step 1: Substitute -6x for y in y = x - 14 and solve for y
1. (-6x) = x - 14 → -7x = -14 → x = 2
Step 2: Plug 2 in for x in y = x - 14 and solve for x
2. y = (2) - 14 → y = -12
The solution to question four: (2, -12)
Steps to solve question 5:
Step 1: Substitute 2x for y in y = -x + 9 and solve for y
1. (2x) = -x + 9 → 3x = 9 → x = 3
Step 2: Plug 3 in for x in y = -x + 9 and solve for x
2. y = (3) + 9 → y = 12
The solution to question five: (3, 12)
Steps to solve question 6:
Step 1: Substitute -4x for y in y = x + 15 and solve for y
1. (-4x) = x + 15 → -5x = 15 → x = -3
Step 2: Plug -3 in for x in y = x + 15 and solve for x
2. y = (-3) + 15 → y = 12
The solution to question six: (-3, 12)
Steps to solve question 7:
Step 1: Substitute 4x for y in y = -x - 10 and solve for y
1. (4x) = -x - 10 → 5x = -10 → x = -2
Step 2: Plug -2 in for x in y = -x - 10 and solve for x
2. y = -(-2) - 10 → y = -8
The solution to question seven: (-2, -8)
Steps to solve question 8:
Step 1: Substitute -7x for y in y = x + 24 and solve for y
1. (-7x) = x + 24 → -8x = 24 → x = -3
Step 2: Plug -3 in for x in y = x + 24 and solve for x
2. y = (-3) + 24 → y = 21
The solution to question eight: (-3, 21)
Steps to solve question 9:
Step 1: Substitute 8x for y in y = -x + 18 and solve for y
1. (8x) = -x + 18 → 9x = 18 → x = 2
Step 2: Plug 2 in for x in y = -x + 18 and solve for x
2. y = -(2) + 18 → y = 16
The solution to question nine: (2, 16)
Hope this helps you out :)