A box with a square base and open top must have a volume of 256000 c m 3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x , the length of one side of the square base.
Answers
Answer:
Follows are the response to the given question:
Step-by-step explanation:
The volume of the box:
[tex]V = x\times x \times h = 256000 \ cm^3\\\\\to x^2 \times h = 256000\\\\\to h = \frac{256000}{x^2}[/tex]
The surface area of the open box is:
[tex]A(x) = x \times x + 2 \times (x \times h +x \times h)\\\\A(x) = x^2 + 4 \times x \times h\\\\A(x) = x^2 + \frac{1024000}{x}\\\\\frac{d(x^n)}{dx} = n \times x^{(n - 1)}\\\\[/tex]
Use above formula
[tex]A'(x) = 2 \times x - \frac{1024000}{x^2}\\\\[/tex]
[tex]A'(x) = 0\\\\2\times x - \frac{1024000}{x^2} = 0\\\\2x = \frac{1024000}{x^2}\\\\x^3 = 512000\\\\x = (512000)^{(\frac{1}{3})} = 80\ cm\\\\[/tex]
Now
[tex]A''(x) = 2\times 1 + 2\times \frac{1024000}{x^3}\\\\A''(x) = 2 + \frac{2048000}{x^3}\\\\x = 80 \ cm\\\\A''(80) = 2 + \frac{2048000}{80^3} = 6\\\\[/tex]
therefore [tex]A"(x) > 0,[/tex] x amount of material used in minimum.
[tex]h = \frac{256000}{80^2} = 40\ cm[/tex]
Related Questions
GIVEN a = (2 -3) and b = (1 -5 ) find 3a - b
Answers
Answer:
3a - b = 1
Step-by-step explanation:
a = (2-3)
b = (1-5)
Substitute the values of a and b to the 3a-b.
3(2-3) - (1-5)
6-9 - (-4)
6 - 9 + 4
-3 + 4
= 1
Therefore, 1 is the answer.
Step-by-step explanation:
Solution :
Given,
a= (2 - 3)
b= (1 - 5)
Now,
3a-b
= 3(2 - 3) -(1 - 5)
= 3×(-1) - (-4)
= -3+4
= 1
.
. .The value of 3a-b is 1
A,B and C are the vertices of a triangle,
A has coordinates (4,6)
B has coordinates (2,-2)
C has coordinates (-2,-4)
D is the midpoint of AB.
E is the midpoint of AC.
prove that DE is parallel to BC.
Answers
Answer:
SSS (side, side, side)
hope it helps:))!!!
A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 15 mph, find the speed of the plane in still air.
Answers
Answer:
161 speed of plain in still air
Mark in brainlist
can anyone please help me with this?
Answers
Answer:
I believe that It would be b
o perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one, two, or three steps. The second procedure requires either one or two steps. Answer the first and second questions using this information.List the experimental outcomes associated with performing the blood analysis. (Hint: The first procedure has three possible outcomes (steps needed), the second procedure has two possible outcomes (steps needed)).(1), (2), (3), (1,1), (2,1), (3,1), (1,2), (2,2), (3,2), (1,3), (2,3), (3,3)(1), (2), (3), (1,1), (2,1), (3,1), (1,2), (2,2), (3,2)(1,1), (2,1), (3,1), (1,2), (2,2), (3,2), (1,3), (2,3), (3,3)(1,1), (2,1), (3,1), (1,2), (2,2), (3,2)
Answers
Answer:
11, 12, 13, 21, 22 and 23
Step-by-step explanation:
Given
[tex]Procedures = 2[/tex]
[tex]1 \to[/tex] Step 1
[tex]2 \to[/tex] Step 2
[tex]3 \to[/tex] Step 3
Required
List all possible experimental outcomes
From the question, we understand that:
[tex]Procedure\ 1 = 3\ steps[/tex]
[tex]Procedure\ 2 = 2\ steps[/tex]
So, the total possible steps (n) are:
[tex]n=Procedure\ 1 * Procedure\ 2[/tex]
[tex]n = 3 * 2[/tex]
[tex]n = 6\ steps[/tex]
Such that the 2nd steps cannot take the value of 3.
So, the outcomes are: 11, 12, 13, 21, 22 and 23
A biologist is studying the migratory patterns of sandhill cranes. His study focuses only on sandhill cranes that are bred and hatched in Alaska, and eventually migrate south to warmer climates. Each year he randomly tags a sample of 50 cranes with GPS trackers to gather data about their migratory patterns.
In this scenario, the population is
.
In this scenario, the sample is
Answers
Answer:
Population = All Sandhill cranes bred and hatched in Alaska that migrate south
Sample = The 50 crane samples which are tagged yearly.
Step-by-step explanation:
The population refers to all members or subjects which belongs to a defined study. Each and every subject which meets the requirement of a study makes up the population.
The sample however, is a subset of the population, the sample is a smaller group of subject which is selected from the population randomly to for a representative sample of the population. Here, it is the 50 sampled sandhill cranes bed per year.
Answer:
These are the answers
Step-by-step explanation:
Do 5, 5, and 5 form a right triangle?
Answers
25 + 25 = 50
50 is not the square of 5
Calculate the mean and median of the list of numbers below: 3, 5, 2, 10, 6, 3, 7, 3
Answers
Answer:
Step-by-step explanation:
mean = sum of data / no of data
=3 + 5 + 2 + 10 + 6 + 3 + 7 + 3/8
=36/8
4.5
to calculate the given data must be arranged in ascending to descending order . So , the data are
2 , 3 , 3 , 3 , 5 , 6 , 7 , 10
Median = N + 1/2 (N means no of data)
=8 + 1/2
=9/2
=4.5
=(4 + 5) th term / 2
=3 + 5/2
=8/2
=4
QUESTION 1
The adult dosage of a medication is 15 mg** per day.
1. What is the pediatric dosage of that same medication for a child weighing 52 pounds? Refer to the formula below:
(Child weight divided by 150 lbs.) x Adult Dose = Pediatric Dosage
2. Explain in a well-written paragraph
Answers
Answer:
Step-by-step explanation:
Given that the adult dosage = 15 mg/day.
1. The pediatric dosage for a child weighing 52 pounds can be determined by;
Pediatric Dosage = (Child weight divided by 150 lbs.) x Adult Dose
= [tex]\frac{52}{150}[/tex] x 15 mg/day
= 5.2 mg/day
The pediatric dosage of the medication for a child weighing 52 pounds is 5.2 mg per day.
2. The medication can be consume by either an adult or a pediatric at a measured quantity. If an adult takes 15 mg of the medication per day, then any child whose weight is 52 pounds can take a maximum quantity of 5.2 mg of the medication per day. This implies that a child of the measured weight should not take more than 5.2 mg of the medication per day, and probably not at once.
The dosage of the medication for a pediatric can be determined by;
Pediatric Dosage = (Child weight divided by 150 lbs.) x Adult Dose
That is, once the weight of a child is determined, the dosage can be calculated.
A researcher investigated whether following a vegetarian diet could help to reduce blood pressure. For a sample of 85 people who followed a vegetarian diet for 4 months, the mean systolic blood pressure was 124 mmHg. For a sample of 75 people who followed a non-vegetarian diet for 4 months, the mean systolic blood pressure was 138 mmHg. Methods of statistics show that if a vegetarian diet had no effect on blood pressure, there would be less than 1 chance in 100 of getting these results. Does the result have statistical significance? Why or why not? Does the result have practical significance?
Answers
Answer:
Yes, the result does not have statistical significance
Yes, the result has practical significance
Step-by-step explanation:
An experiment or claim may be said to be statistically significant if it's occurence is likely not due to chance for a certain level of stated significance. From the scenario described, it is stated that if vegetarian diet has no effect on blood, then the result obtained wipukd likely occur in less Than 1 of 100 ; this is < 0.01. This means that the effect of vegetarian diet on blood could not have occurred by chance. Hence, result is statistically significant.
The result does have practical significance too, since there is a distinctive difference in blood pressure of non - vegetarians(138mmHg) and Vegetarians (124mmHg).
which of the following steps were applied to ABCD to obtain A' B'C'D'
Answers
Answer:
Thus, The steps applied to ABCD to obtain A'B'C'D' is shifted x coordinate 2 units to right and y coordinate 3 units down
Explain why the square root of a number is defined to be equal to that number to the 1/2 power
Answers
9514 1404 393
Answer:
(x^(1/2))(x^(1/2)) = x^(1/2 +1/2) = x^1 = x
Step-by-step explanation:
The rule of exponents is ...
(x^a)(x^b) = x^(a+b)
From which ...
(x^a)(x^a) = x^(a+a) = x^(2a)
So, if we want two identical factors that have a product of x = x^1, then the exponents of those factors will be such that ...
x^(2a) = x^1
2a = 1
a = 1/2
The square root is defined as one of two identical factors that have a product equal to the specified value. That is ...
(√x)(√x) = x
Above, we have shown that ...
(x^(1/2))(x^(1/2)) = x
so, we can conclude ...
√x = x^(1/2)
_____
Additional comment
In like fashion, we can show that the n-th root of a number is the same as that number to the 1/n power. It's really a matter of definition. Since the square of x^(1/2) is x, we call x^(1/2) the square root. It is used commonly enough that it has its own symbol: √x.
Answer:
Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.
Step-by-step explanation:
I have a mix of 12 nickels and dimes in my pocket. All together I have $1 . How many nickles and dimes do I have?
(Create a system of equations and solve that system)
Answers
Answer:
Step-by-step explanation:
n + d = 12
0.05n + 0.1d = 1 ║ × ( - 10 )
n + d = 12 ..... (1)
- 0.5n - d = - 10 ..... (2)
(1) + (2)
0.5n = 2 ⇒ n = 4
d = 12 - 4 = 8
There are 4 nickels and 8 dimes in the pocket.
given f(x) = 5x + 7,g(x) = 3x-1 find f(g(x))
Answers
Answer:
f(g(x)) = 15x + 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
FunctionsFunction NotationComposite FunctionsStep-by-step explanation:
Step 1: Define
Identify
f(x) = 5x + 7
g(x) = 3x - 1
Step 2: Find
Substitute in functions: f(g(x)) = 5(3x - 1) + 7[Distributive Property] Distribute 5: f(g(x)) = 15x - 5 + 7[Addition] Combine like terms: f(g(x)) = 15x + 2you can never divide any one angle into smaller angle. true or false
Answers
Answer:
true.
hope it helps..
474 ( ) 548 42. - 8 how do I arrive at this answer.
Answers
9514 1404 393
Answer:
(64x^28)/(5y^22)
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)
__
First, eliminate the outside exponent on the left factor. Then use the above rules to combine factors with the same base.
[tex]\displaystyle\left(\frac{4x^4}{5y^6}\right)^5\cdot\left(\frac{5^4y^8}{4^2x^{-8}}\right)=\frac{(4^5x^{20})(5^4y^8)}{(5^5y^{30})(4^2x^{-8})}=4^{5-2}5^{4-5}x^{20-(-8)}y^{8-30}\\\\=4^35^{-1}x^{28}y^{-22}=\boxed{\frac{64x^{28}}{5y^{22}}}[/tex]
There are twelve empty rooms in the office of Acme Softwares, inc. Alif and Laila joins the company. How many ways can they be assigned a room each from these twelve
Answers
Answer:
132.
Step-by-step explanation:
That would be the number of permutations of 2 from 12.
12P2 = 12! / (12-2)!
= 132.
An analyst must decide between two different forecasting techniques for weekly sales of roller blades: a linear trend equation and the naive approach. The linear trend equation is Ft = 124 + 2t, and it was developed using data from periods 1 through 10.
t units sold
11 147
12 148
13 151
14 145
15 155
16 152
17 155
18 157
19 160
20 165
Based on data for periods 11 through 20 as shown in the table, which of these two methods has the greater accuracy if MAD and MSE are used? (Round your answers to 2 decimal places.)
MAD (Naive)=
MAD (Linear)=
MSE (Naive)=
MAD (Linear)=
Answers
Answer:
Following are the responses to the given question:
Step-by-step explanation:
Mean Absolute Deviation MAD
[tex]MAD = \sum_{i=1}^{n} \frac{\left | actual_{i}-forecast_{i} \right |}{n}[/tex]
Mean squared error
[tex]MSE=\Sigma^{n}_{i=1} \frac{(Actual_i - Forecast_i)^2}{(n - 1)}[/tex]
linear trend equation is [tex]Ft = 124 + 2t[/tex]
[tex]MAD = \frac{23}{10} = 2.3\\\\MSE = \frac{91}{9}= 10.11\\\\[/tex]
Naive method
[tex]MAD = \frac{36}{9} = 4\\\\MSE = \frac{202}{8}=25.25\\\\MAD (Naive) = 4\\\\MAD (Linear) =2.3\\\\MSE (Naive)=25.25\\\\MSE (Linear)=10.11\\\\[/tex]
Please find the attached file.
at sunrise, the outside temperature was 3 below zero by lunchtime the temperature rose by 27 and fell by 10 by night what was the temperature at the end of the day?
Answers
Answer:11 degrees at sunrisde the temp was -1 degree
Step-by-step explanation:
I need help please I dont understand
Answers
Solve 3(5x + 7)= 9x + 39
Answers
Answer:
x=3
Step-by-step explanation:
If Clive was charged $3.92 for a minute 38 call, what is Clive's per minute base rate?
Answers
The strongest winds of Hurricane Isabel extended 50 miles in all directions from the center.
What is the area of the hurricane in square miles? Leave your answer in terms of Pi
Answers
Answer:
20
Step-by-step explanation:
your mom
What is MS Word?
O It is a computerized tool.
O It is a calculating tool
O It is a graphic design tool.
O Its is a typing tool.
Answers
some one plz help its algebra 1
Answers
Listed below are the commissions earned ($000) last year by a sample of 15 sales representatives at Furniture Patch Inc.
$4.3 $6.1 $7.4 $10.7 $13.1 $13.6 $14.7 $16.5 $17.1 $17.4 $18.7 $22.3 $36.7 $43.2 $79.4
Required:
a. Determine the mean, median, and the standard deviation.
b. Determine the coefficient of skewness using Pearson.
Answers
Answer:
Mean = 21.413
Median = 16.5
Standard deviation = 19.182
0.768
Step-by-step explanation:
Given the data :
Ordered data, X : 4.3 6.1 7.4 10.7 13.1 13.6 14.7 16.5 17.1 17.4 18.7 22.3 36.7 43.2 79.4
The sample size, n = 15
The mean, m= ΣX / n = 321.2 / 15 = 21.413
The median, Md:
1/2(n + 1)th term
1/2 (15 +1) th term
1/2(16) = 8th term
Median = $16.5
The standard deviation, s = √[Σ(x - m)²/ n]
The standard deviation obtained using a calculator is ; 19.182
Coefficient of skewness : = 3(m - Md) / s
= 3(21.413 - 16.5) / 19.182
= 14.739 / 19.182
= 0.768
The solution for 7x + 4 = x – 2
Answers
Answer:
x = -1
Step-by-step explanation:
Add two on both sides. This makes the equation 7x + 6 = x. Now subtract 7x on both sides. This equals 6 = -6x. Divide by -1 on both sides. x = -1.
Answer fast please and thank you!
Answers
Step-by-step explanation:
everything can be found in the picture
Solve the quadratic function by graphing.
-4x^2 + 16x - 16 = 0
0,-4)
(-4,0)
(2,0)
(0,2)
Answers
-4x²+16x-16=0
X=2
The choose (2,0)
Samples of rejuvenated mitochondria are mutated (defective) in 2% of cases. Suppose 12 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities.
(a) No samples are mutated.
(b) At most one sample is mutated.
(c) More than half the samples are mutated.
(c) is 0.00
Round your answers to two decimal places
Answers
Answer:
a) 0.7847 = 78.47% probability that no samples are mutated.
b) 0.9769 = 97.69% probability that at most one sample is mutated.
c) 0% probability that more than half the samples are mutated.
Step-by-step explanation:
For each sample, there are only two possible outcomes. Either they are mutated, or they are not. The probability of a sample being mutated is independent of any other sample, 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.
2% of cases.
This means that [tex]p = 0.02[/tex]
12 samples are studied
This means that [tex]n = 12[/tex].
(a) No samples are mutated.
This is [tex]P(X = 0)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.02)^{0}.(0.98)^{12} = 0.7847[/tex]
0.7847 = 78.47% probability that no samples are mutated.
(b) At most one sample is mutated.
This is:
[tex]P(X \geq 1) = P(X = 0) + P(X = 1)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.02)^{0}.(0.98)^{12} = 0.7847[/tex]
[tex]P(X = 1) = C_{12,1}.(0.02)^{1}.(0.98)^{11} = 0.1922[/tex]
[tex]P(X \geq 1) = P(X = 0) + P(X = 1) = 0.7847 + 0.1922 = 0.9769[/tex]
0.9769 = 97.69% probability that at most one sample is mutated.
(c) More than half the samples are mutated.
This is:
[tex]P(X > 6) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,7}.(0.02)^{7}.(0.98)^{5} \approx 0[/tex]
So the others(greater than 7) wil be 0 too
0% probability that more than half the samples are mutated.