The dimensions of the box that minimize the amount of material used are approximately 39 cm by 39 cm by 39 cm.
To minimize the amount of material used, we need to minimize the surface area of the box.
Let's denote the dimensions of the box as x,y, and z, where x and y are the dimensions of the base (length and width), and z is the height.
The volume V of the box is given by:
[tex]\[ V = xyz \][/tex]
We're given that V = 62500 cubic cm.
The surface area A of the box (excluding the top) is given by:
[tex]\[ A = xy + 2xz + 2yz \][/tex]
To minimize the amount of material used, we need to minimize A subject to the constraint V = 62500 .
We can solve this problem using the method of Lagrange multipliers. First, let's define the Lagrangian function L as follows:
[tex]\[ L(x, y, z, \lambda) = xy + 2xz + 2yz + \lambda(62500 - xyz) \][/tex]
Now, we take partial derivatives of L with respect to x,y,z, and [tex]\( \lambda \),[/tex] and set them equal to zero:
[tex]\[ \frac{\partial L}{\partial x} = y + 2z - \lambda yz = 0 \]\[ \frac{\partial L}{\partial y} = x + 2z - \lambda xz = 0 \]\[ \frac{\partial L}{\partial z} = 2x + 2y - \lambda xy = 0 \]\[ \frac{\partial L}{\partial \lambda} = 62500 - xyz = 0 \][/tex]
Solving these equations will give us the dimensions that minimize the amount of material used.
However, this system of equations is quite complex to solve manually. Let's simplify the problem by recognizing that the dimensions that minimize the amount of material used will likely be those where the box is as close to a cube as possible. This means x=y to minimize the perimeter, and x=y=z to minimize the surface area.
So, let's find the cube root of 62500 :
[tex]\[ \sqrt[3]{62500} \approx 38.99 \][/tex]
Since [tex]\( 38^3 = 54872 \)[/tex] and [tex]\( 39^3 = 59319 \)[/tex], the closest perfect cube to 62500 is [tex]\( 39^3 \)[/tex]. Therefore, the dimensions of the box that minimize the amount of material used are approximately 39 cm by 39 cm by 39 cm.
Assume the random variable X is normally distributed with mean mu equals 50?=50 and standard deviation sigma equals 7?=7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. Upper P left parenthesis Upper X greater than 35 right parenthesisP(X>35) LOADING... Click the icon to view a table of areas under the normal curve. Which of the following normal curves corresponds to Upper P left parenthesis Upper X greater than 35 right parenthesisP(X>35)?? A. 35355050 A normal curve has a horizontal axis with two labeled coordinates, 35 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35 and 50. The area under the curve between the vertical line segments is shaded. B. 35355050 A normal curve has a horizontal axis with two labeled coordinates, 35 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35 and 50. The area under the curve to the right of the left vertical line segment is shaded. C. 35355050 A normal curve has a horizontal axis with two labeled coordinates, 35 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35 and 50. The area under the curve to the left of the left vertical line segment is shaded. Upper P left parenthesis Upper X greater than 35 right parenthesisP(X>35)equals=nothing ?(Round to four decimal places as? needed.)
Answer:
B. A normal curve has a horizontal axis with two labeled coordinates, 35 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35 and 50. The area under the curve to the right of the left vertical line segment is shaded; P(X > 35) = 0.9838
Step-by-step explanation:
The middle line in a normal distribution represents the mean. The mean of this distribution is 50; this means the peak of the curve will have a vertical line down to the horizontal axis at 50.
The value we are concerned with is anything more than 35. This means there will be a vertical line from the horizontal axis to the curve at 35. Since we want the probability X is greater than 35, the area to the right of this value under the curve will be shaded.
To find the probability, we use a z score. The formula for z scores is
[tex]x=\frac{X-\mu}{\sigma}[/tex]
Using our values for X, the mean and the standard deviation, we have
[tex]z=\frac{35-50}{7}=\frac{-15}{7}=-2.14[/tex]
Using a z table, we see that the area under the curve to the right of this value is 0.0162. This means the area to the left, the desired area, is
1-0.0162 = 0.9838.
Thad is riding his bike to the library,which is 3 kilometers away. How many meters away is the library?
Answer: The library is 3,000 meters away.
Step-by-step explanation:
The solution of this exercise can be obtained by making the conversion from kilometers to meters.
You know that the library is 3 kilometers away.
Let's remember that 1 kilometer has 1,000 meters.
Then, the conversion from 3 kilometers to meters can be made by this proccedure:
3 kilometers to meters:
[tex]=(3\ kilometers)(\frac{1,000\ meters}{1\ kilometers})\\\\=3,000\ meters[/tex]
Then the library is 3,000 meters away.
A census determines the number of people living in the United States. Identify the type of data.
A.
categorical data
B.
quantitative data
C.
continuous data
D.
attribute data
Answer with explanation:
Census Evaluates number of people Living in the United States.
There are two kinds of Data
1. Qualitiative----Which Says about the Quality Possessed by variate in Data set.
2. Quantitative----Variate in Data set is represented through numerical value.
Quantitative Data set has two attributes
(a) Discrete Data Set
(b) Continuous Data set
In this Question , it has been asked about number of people living in United states , which is Numerical Representation.As when number of People will get counted , it will keep on increasing, but population measurement which is represented by Natural number can't be continuous.
So, it is Quantitative data.
Option (B)--- Quantitative data.
Write the ratio as a fraction in simplest form. The ratio for 18 girls to 27 boys as a fraction is .
Answer:
2/3
Step-by-step explanation:
Reduce the fraction 18/27 into its lowest terms
since both 18 and 27 are divisible by 9, divide both terms by 9
18/9 = 2
27/9 = 3
18/27 reduced to lowest terms is 2/3
Jillian plays a game that involves stacking blocks in a tower.The graph show the height of the tower based on the number of blocks she uses.
Answer:
c)
{0,4,8,12,16,20,24,28,32,36,40}
Step-by-step explanation:
Given in the question is graph which shows height of tower depending on number of blocks use.
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain, x values.
By looking at graph
domain range
0 0
1 4
2 8
3 12
4 16
5 20
. .
. .
10 40
A field is to be fertilized at a cost of $0.07 per square yard. The rectangular part of the field is 125 yards long and the diameter of each semicircle is 40 yards. Find the cost of fertilizing the field. Use 3.14 for π.
Answer:
Total cost is $437.92
Step-by-step explanation:
Rectangular area=125•40=5000 yd²
Two equal semicircles=one single circle
Area of circle=πr²=20²•π=400•3.14=1256 yd²
Total field area=circle+rectangle=6256yd²
Cost=area•0.07yd²=6256•0.07=437.92
twice a number plus 5 equals 81
solution
2x+5=81
2x=81-5
2x=76
x=38
Answer:
[tex]38 = x[/tex]
Step-by-step explanation:
81 = 5 + 2x
- 5 - 5
___________
76 = 2x
__ __
2 2
[tex]38 = x[/tex]
I am joyous to assist you anytime.
Can you help me with this question? Complete the proof and show your work.
4. ∠FCB ≅ ∠GDC: Corresponding angles theorem (when two parallel lines are crossed by a transversal, the corresponding angles formed are congruent) (but to use this, you have to state that ∠BCF and ∠CDG are corresponding)
5. ∠FCB ≅ ∠GCD: Subst. POC (Because ∠FCB ≅∠GDC and ∠GDC≅∠GCD)
6. Converse of the corresponding angles theorem
I can not really show my work since most proofs are theoretical and hence most work is done in the head.
Solve the equation by using the basic properties of logarithms.
ln(x+4)=-1
Write both sides as powers of [tex]e[/tex]:
[tex]\ln(x+4)=-1\implies e^{\ln(x+4)}=e^{-1}\implies x+4=e^{-1}[/tex]
since [tex]b^{\log_ba}=a[/tex]. Then
[tex]x=e^{-1}-4\approx-3.63[/tex]
Answer:
-3.63
Step-by-step explanation:
What is the period for the tangent function? (Answer in radians and round to the hundreds place.)
Answer: _____
Answer:
π radians.
3.14.
Step-by-step explanation:
The period is π radians which is 3.14 radians to the nearest hundredth.
Andrea bought tacos from a food truck and left a 25% percent tip of $2.00. What was the price of Andrea's tacos before tip
$8.00. Hope this helps!
If P(A)=0.35, then the probability of the complement of A is
0.55
-0.35
0.35
0.65
Answer:
0.65
Step-by-step explanation:
Complement of an event is defined as "all the other outcomes that are not in the given event"
So complement of event A will be all the outcomes that are not in event A.
Probability of event A is given to be 0.35
P(A) = 0.35
The sum of probabilities of an event and its compliment is always equal to 1
So,
P(A) + P(A') = 1
Where, A' represents the compliment of A
So, from here we can write:
P(A') = 1 - 0.35
P(A') = 0.65
Therefore, the probability of the complement of A is 0.65
Answer:
0.65
Explanation:
Probability of an event P(A) shows the chances for this event to actually happen or occur
Probability of the complement of an event P'(A) shows the chances for this event not to happen or occur
The sum of the probability of a certain event and its complement is ALWAYS equal to 1
This means that:
P(A) + P'(A) = 1
In the problem, we are given that P(A) = 0.35
Substitute in the above equation to get P'(A) as follows:
P(A) + P'(A) = 1
0.35 + P'(A) = 1
P'(A) = 1 - 0.35
P'(A) = 0.65
Hope this helps :)
A full bag of dog food weighs 5 1/2 pounds. How much dog food do you have if there are 3 3/4 bags
Answer:
20 5/8 lbs
Step-by-step explanation:
Multiply 5 1/2 by 3 3/4
1. convert the mixed numbers to improper fractions
5 1/2 = 11/2
3 3/4 = 15/4
2. Multiply numerator by numerator and denominator by denominator
11*15 = 165
2*4 = 8
165/8
3. divide to convert back to mixed number:
165/8 = 20 5/8
To find out how much dog food you have, multiply the weight of one bag by the number of bags. The required answer will be 8 1/4 or 20.25 pounds of dog food.
Explanation:To find out how much dog food you have, you can multiply the weight of one bag by the number of bags. In this case, one bag weighs 5 1/2 pounds, and there are 3 3/4 bags. To multiply these fractions, convert them to improper fractions, multiply the numerators together, and multiply the denominators together. Then, divide the product of the numerators by the product of the denominators. So, 5 1/2 multiplied by 3 3/4 is equal to 33/4 pounds or 8 1/4 pounds of dog food.
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According to Cavaliert's Principle, which two triangles have the same area?
According to Cavaliert's Principle,
if two triangles are formed on base of equal length and are between same parallels, i.e have same height, then the triangles are of equal area.
help please thank you
Answer:
Step-by-step explanation:
The first two are incorrect. Only very special n's will work. (Every 10th one for n>0)
Just call A and B incorrect.
400o = 360 + 40
The answer is between C and D
The question is will a negative value for n work? Suppose n = - 1 That means you go around the circle clockwise 1 time and though the question does not say it, you must start at the positive x axis.
Having said that 40 is plus.
The 360 starts at the + x axis. It doesn't matter how it got there. 40 degrees from the +x axis is in the first quadrant. It always will be.
D is correct but C is the better answer because it includes D.
Is 30 a typical test score? If so, explain your reasoning. If not, what is a test score
A test score of 30 may not be typical as it falls within the lower 30% of scores achieved by students. Higher scores are generally preferred.
Explanation:30 may not be considered a typical test score because it falls within the range of scores that only 30% of students achieved. According to the given information, 70% of students answered 16 or fewer questions correctly, while only 30% answered 16 or more questions correctly.
In addition to this, higher percentiles that generally indicate higher scores, are typically considered better for most of the students. Therefore, a higher test score would be desirable for most students.
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What is the minute ventilation of an average adult male at rest breathing at a rate of 10 breaths per minute?
Answer:
5000 milliliters per minute
Step-by-step explanation:
Answer:
12 to 18
Step-by-step explanation:
Which three-dimensional figure is formed by the rotation given?
First picture is the rotation, and the rest are the answer choices.
Answer with explanation:
A circle is rotated around a vertical line which we call Y axis.
When we rotate the circle around y axis, and join each circle ,we get a closed shape resembling with the Cylinder, having height equal to Diameter of circle.
We can't Calculate Radius of shape resembling with Cylinder.
The circle is rotated about an axis it forms a circular ring of the thickness as the circle has.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Given
The picture is the rotation.
If the point is rotated about the axis it forms a circular ring of no thickness.
The circle is rotated about an axis it forms a circular ring of the thickness as the circle has.
It will look like a bangle.
Thus, the correct option is B.
More about the geometry link is given below.
https://brainly.com/question/7558603
All of the names of the polygon are correct EXCEPT for:
The correct answer would be c) GDFEABC
Please mark brainliest
Answer:
The third option: GDFEABC
Step-by-step explanation:
Just follow the letters around in a circle. ABCDEFG works, it goes from one point to the next, so does EDCBAGF, just in the other direction with a different start point. The second option also circles around perfectly fine. The third option, GDFEABC is the only one that jumps around, G to D skips over 2 points, F & E.
Solve for v
-(2/3)v-1=(7/2)v-(4/3)
Answer: [tex]v=\frac{2}{25}[/tex]
Step-by-step explanation:
To solve from v from the equation given in the problem you must apply the folowing proccedure:
- Add like terms:
[tex]-1+\frac{4}{3}=\frac{7}{2}v+\frac{2}{3}v\\\\ \frac{1}{3}=\frac{25}{6}v[/tex]
- Mulitply bot sides of thee equation by 6 and then divide both sids by 25.
Therefore you obtain:
[tex]\frac{1}{3}=\frac{25}{6}v\\\frac{6}{3}=25v\\v=\frac{2}{25}[/tex]
Answer:
v = 2/25
Step-by-step explanation:
We have given the equation:
-(2/3)v-1=(7/2)v-(4/3)
We have to solve it for v.
-(2/3)v-1=(7/2)v-(4/3)
(7/2)v+(2/3)v = -1+(4/3)
Multiply both sides of equation by 6 we get,
21v+4v = -6+8
25v = +2
Multiplying both sides by 1/25 we get,
v = 2/25
v = 2/25 is the answer.
Please help me and Simplify
Answer:
12a^3 b^4 c^5
Step-by-step explanation:
First you rewrite 144a^6 b^8 c^10 as (12a^3 b^4 c^5)^2.Pull terms out from under the radical, assuming positive real numbersGiven u=(1,3) and v=(2,6), find 2v+u
Options
(5,15)
(4,12)
(3,9)
(6,18)
ANSWER
[tex]2v + u = \binom{5}{15}[/tex]
EXPLANATION
It was given that:
[tex]u = \binom{1}{3} [/tex]
and
[tex]v = \binom{2}{6} [/tex]
[tex]2v + u =2 \binom{2}{6} + \binom{1}{3} [/tex]
Perform the scalar multiplication to obtain:
[tex]2v + u = \binom{4}{12} + \binom{1}{3} [/tex]
We add the corresponding components to get;
[tex]2v + u = \binom{4 + 1}{12 + 3}[/tex]
[tex]2v + u = \binom{5}{15}[/tex]
The first choice is correct.
Answer:
A
Step-by-step explanation:
PLEASE HELP!!!!!!
Which values of x are solutions to the equation below?
Check all that apply.
5x2 - 136 = 44
A. x = - sq root 12
B. x = sq root 12
C. x = -6
D. x = 6
E. x = -8
F. x = 8
Answer:
x=6
Step-by-step explanation:
5x^2-136=44
add 136 to both sides
5x^2=180
divide both sides by 5
x^2= 36
take square root of both sides
x=6
Answer: The correct options are
(C) x = -6
(D) x = 6.
Step-by-step explanation: We are given to select the values of x that are the solutions to the following equation :
[tex]5x^2-136=44~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
The solution of the given equation (i) is as follows :
[tex]5x^2-136=44\\\\\Rightarrow 5x^2=44+136\\\\\Rightarrow 5x^2=180\\\\\Rightarrow x^2=\dfrac{180}{5}\\\\\Rightarrow x^2=36\\\\\Rightarrow x=\pm\sqrt{36}~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=6,~-6.[/tex]
Thus, the solutions to the given equation are x = -6 and x = 6.
Option (C) and (D) are correct options.
in still water, the speed of the boat 10 mi/h. camilla drives the boat upstream for 60 min. and then downstream to her starting point in 20 min. what is the speed of the stream?
Answer:
5 mi/h
Step-by-step explanation:
S = v*t
S - space (miles)
v - velocity (mi/h)
t - time (h)
stream speed = x
The distance upstream(S_1) is expressed by :
60 min -> 1 hour
S_1 = (10-x)*1
The distance downstream is expressed by :
20 min -> 0.3(3) hour
S_2 = (10+x)*0.3(3)
The distance traveled upstream for 60 min is equal to the distance traveled downstream in 20 min. -> S_1 = S_2
(10-x) * 1 = (10+x)*0.3(3)
10 - x = 3.3(3) + 0.3(3)x
6.6(6) = 1.3(3)x
x = 6.6(6) / 1.3(3)
x = 5 mi/h
The speed of the stream is equal to 5.79 mi/h
Let the stream speed be s.Given the following data:
Speed of boat = 10 mi/hUpstream time = 60 minutes = 1 hour.Downstream time = 20 minutes = 0.3 hour.To calculate the speed of the stream:
What is speed?Speed can be defined as the distance covered by an object per unit time.
Mathematically, speed is given by the formula;
[tex]Speed = \frac{distance}{time}[/tex]
Note: The upstream distance of the boat must be equal to the downstream distance of the boat.
[tex]D_u = D_d\\\\(10-s) \times 1 = (10+s)0.33\\\\10-s=3.3+0.33s\\\\10-3.3=0.33s+s\\\\7.7=1.33s\\\\s=\frac{7.7}{1.33}[/tex]
Speed, s = 5.79 mi/h
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Flora's car is 59/100 of a meter longer than Sally's car. Sally's car is 2/10 of a meter longer than Trevor car. How much longer is Flora's car than Trevor's car?
Answer:
Flora's car is 79/100 of a meter longer than Trevor's car
Step-by-step explanation:
Let
x-----> Fiora's car
y-----> Sally's car
z-----> Trevor's car
we know that
[tex]x=y+\frac{59}{100}[/tex] -----> equation A
[tex]y=z+\frac{2}{10}[/tex] -----> equation B
substitute equation B in equation A
[tex]x=(z+\frac{2}{10})+\frac{59}{100}[/tex]
[tex]x=z+\frac{20+59}{100}[/tex]
[tex]x=z+\frac{79}{100}[/tex]
therefore
Flora's car is 79/100 of a meter longer than Trevor's car
Flora's car is 79/100 of a meter longer than Trevor's car.
We are given the following information:
Flora's car is 59/100 of a meter longer than Sally's car.
Sally's car is 2/10 of a meter longer than Trevor's car.
We need to find out how much longer Flora's car is than Trevor's car. To do so, we will add the differences in lengths given:
First, express both fractions with a common denominator:
Convert 2/10 to 20/100:
2/10 = 2 × 10 / 10 × 10 = 20/100
Then, add the lengths:
Add the fractions:
59/100 + 20/100 = 79/100
Therefore, Flora's car is 79/100 of a meter longer than Trevor's car.
Antoine is trying to find the roots for the quadratic function f(x)=x^2+25. He states that there is no solution. Is he correct? Justify your answer.
Answer: Yes, Atoine is correct.
Step-by-step explanation:
The roots of a quadratic function are also known as the solutions or the zeros of a function. Here is how we get them:
1. Let y=0 to find the x-intercept(s).
0=x^2+25
2. Subtract 25 from both sides.
−25=x&2
3. Take the square root of both sides.
±√−25
=x
4. Simplify √−25 to √25ı.
±√25ı=x
5. Since 5×5=25, the square root of 25 is 5.
±5ı=x
6. Switch sides.
x=±5ı
The equation above is not a real solution that represents a line.
Therefore, there are no x-intercepts.
In the given statement is "true".
Quadratic function:
[tex]\to f(x)=x^2+25[/tex]
Assuming "solution" refers to a real solution (it often does), then yes, he would be correct. However, there are complex solutions to the equation. Let's try to find the solution ourselves to understand the problem better:[tex]\to x^2+25=0\\\\\to x^2= -25\\\\\to x= \pm i\sqrt{25}\\\\[/tex]
Since[tex]\sqrt{-25}[/tex] is an imaginary number then
[tex]\to x=\pm 5i\\\\\to \sqrt{25}= 5[/tex]
Its equation's solutions are [tex]\pm 5i[/tex].
The problem is that such solutions are not true solutions because they require i. Although the equation contains complex solutions, it is frequently stated that it has no answer.Therefore, the final answer is "no solution".
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Subtract 3 x^2 + 7 x − 4 3x 2 +7x−43, x, start superscript, 2, end superscript, plus, 7, x, minus, 4 from 8 x^2 − 6 x + 2 8x 2 −6x+2
Answer is:5x ^2 −13x+6
Answer:
[tex]\large\boxed{5x^2-13x+6}[/tex]
Step-by-step explanation:
[tex](8x^2-6x+2)-(3x^2+7x-4)\\\\=8x^2-6x+2-3x^2-7x-(-4)\\\\=8x^2-6x+2-3x^2-7x+4\qquad\text{combine like terms}\\\\=(8x^2-3x^2)+(-6x-7x)+(2+4)\\\\=5x^2-13x+6[/tex]
To subtract polynomials, subtract the coefficients of the like terms. Start with the highest degree term and work your way down to the constant term.
Explanation:To subtract 3x^2 + 7x - 4 from 8x^2 - 6x + 2, you need to subtract the corresponding coefficients of the like terms. Start with the highest degree term, which is x^2. Subtract the coefficient of x^2 in the second polynomial from the coefficient of x^2 in the first polynomial: 8x^2 - 3x^2 = 5x^2. Next, move to the x term. Subtract the coefficient of x in the second polynomial from the coefficient of x in the first polynomial: -6x - 7x = -13x. Finally, subtract the constant term: 2 - (-4) = 6. Therefore, the result is 5x^2 - 13x + 6.
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Find the slope intercept equation that passes through (6,8) and is parallel to the line with the equation 3x+y=6
"y = -3x + 26" is the correct answer.
the answer would be "y = -3x + 26"
Drag the numbers to order them from greatest to least, with the greatest at the top.
9.92749.....
√101
0.99853.......
10√
Howdy!
I just finished taking the quiz and found that the correct answer is:
10[tex]\pi[/tex]
√101
9.92749...
0.99853...
I hope this helped! :D
The numbers, from greatest to least, are 9.92749....., √101 (approximately 10.0499), 10√ (approximately 3.1623), and 0.99853....... The principles of significant digits are important in ordering these numbers to ensure accuracy without introducing errors by rounding.
Explanation:First, we need to evaluate the values given to us:
9.92749..... (This is a repeating decimal, so it retains its value as 9.92749...)√101 (This is the square root of 101, which is approximately 10.0499.)0.99853....... (This is another repeating decimal, and it remains as 0.99853...)10√ (This likely means the square root of 10, which is approximately 3.1623.)Now we will order them from greatest to least:
9.92749.....√101 (Approximately 10.0499)10√ (Approximately 3.1623)0.99853.......We keep in mind the principles of significant digits when we compare or order these numbers.
As evident from the provided reference information, it is important not to introduce errors by unnecessary rounding.
Help 13 points!!!!!!!!
Replace x with a^2:
7(a^2)^2 - 8
Multiply the exponents:
7a^4 - 8