What percentage of the rectangular sheets of cardboard will be wasted because it is not part of the box and will be discarded when the net is cut out?
PLEASE HELP
Dimension : 18 x 24 x 12 in
Answers
30% I believe because we still have those to rectangles on the side
Hope this helps :)
When the square sheet of cardboard is cut and folded to create a rectangular box with a lid, the maximum possible volume is achieved when x = 20 inches. All other values will result in a smaller volume for the box.
Here, we have,
1. Calculate the side lengths of the box and lid:
Box: 40 inches - 2x = 40 - 2x
Lid: 2x
2. Calculate the volume of the box with a lid when x = 20 inches:
Box Volume:
(40 - 2x) x (40 - 2x) x (40 - 2x) = (40 - 2*20) x (40 - 2*20) x (40 - 2*20) = (20) x (20) x (20)
= 8000 in^3
Lid Volume: 2x x 2x x 2x = 2*20 x 2*20 x 2*20
= 8000 in^3
Total Volume: 8000 in^3 + 8000 in^3 = 16000 in^3
3. Calculate the volume of the box with a lid when x = 20/3 inches:
Box Volume: (40 - 2x) x (40 - 2x) x (40 - 2x) = (40 - 2*20/3) x (40 - 2*20/3) x (40 - 2*20/3) = (33 1/3) x (33 1/3) x (33 1/3)
= 7157.7 in^3
Lid Volume: 2x x 2x x 2x = 2*20/3 x 2*20/3 x 2*20/3
= 1365.3 in^3
Total Volume: 7157.7 in^3 + 1365.3 in^3
= 8523 in^3
4. Comparison:
When x = 20 inches, the box has a minimum possible volume of 16000 in^3, while when x = 20/3 inches, the box has a volume of 8523 in^3. Therefore, the statement is true.
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Complete question:
The figure above represents a square sheet of cardboard with side length 40 inches. The sheet is cut and pieces are discarded. When the cardboard is folded, it becomes a rectangular box with a lid. The pattern for the rectangular box with a lid is shaded in the figure. Four squares with side length xx and two rectangular regions are discarded from the cardboard. Which of the following statements is true? (The volume V of a rectangular box is given by V=lwh).
A. When x = 20 inches, the box has a minimum possible volume.
B. When x = 20 inches, the box has a maximum possible volume.
C. When x = 20/3 inches, the box has a minimum possible volume.
D. When x = 20/3 inches, the box has a maximum possible volume.
Related Questions
you are painting a room that is 18 ft long, 14 ft wide and 8 ft high. find the area of the four walls that you are going to paint.
Answers
(14)(8)*2
+(18)(8)*2
equals 512.
Final answer:
The total area to be painted is 512 square feet, calculated by summing up the areas of the two longer walls (288 sq ft) and the two shorter walls (224 sq ft). For time estimation, the linear equation would be t = 4 + (512/1000), resulting in approximately 4.51 hours of painting time.
Explanation:
To calculate the area of the four walls in a room for painting, you will be finding the surface area of the sides not including the floor or ceiling. First, you need to calculate the area of the two longer walls and the two shorter walls separately.
For the longer walls, the area for one wall is 18 ft (length) times 8 ft (height), which gives you 144 square feet for one long wall. There are two such walls, so multiply by 2, which equals 288 square feet for both long walls.
For the shorter walls, the calculation is similar. The area for one short wall is 14 ft (width) times 8 ft (height), which gives 112 square feet for one short wall. With two short walls, the total is 224 square feet.
Add the area of the long walls and the area of the short walls together to get the total painting area: 288 sq ft + 224 sq ft = 512 square feet.
To express this as part of a linear equation for time estimation given in the scenario, if it takes one hour per 1,000 square feet, we would use the equation t = 4 + (A/1000), where t is the total time in hours and A is the area in square feet. Since the painting area is 512 square feet, the painting time is t = 4 + (512/1000), giving 4.512 hours, which rounds up to approximately 4.51 hours.
name a pair of fractions that use the least common denominator and are equivalent to 9/10 and 5/6
Answers
use the product-to-sum identities to rewrite the following expression
sin 14° cos50°
Need help with hw, willing to give $$
Answers
[tex]sin(x) cos(y) = \frac{1}{2} (sin(y+x) - sin(y-x))[/tex]
In this example, x = 14, y = 50
Answer: D
[tex]\frac{1}{2} (sin(64) - sin(36))[/tex]
Scm> (define (square x) (* x x)) square scm> (define (add-one x) (+ x 1)) add-one scm> (define (double x) (* x 2)) double scm> (define composed (compose-all (list double square add-one))) composed scm> (composed 1) 5 scm> (composed 2) 17
Answers
The question involves function definitions and compositions in Scheme, a programming language. 'Square' squares its input, 'add-one' adds one to its input, and 'double' doubles its input. The composed function applies these operations sequentially.
Explanation:The student's question involves programming in the Scheme language, a dialect of Lisp. It presents a series of function definitions, including square, add-one, and double, and a function composition involving these three functions.
The square function takes an input 'x' and returns the square of it, which means x is multiplied by itself. In programming, this multiplication can be symbolized as (* x x). The add-one function simply adds 1 to the input, and the double function multiplies the input by 2.
Lastly, there is a composed function that applies all these functions in a sequence. If you apply the composed function to the number 1, we obtain '5' which is calculated as: double(square(add-one(1))) = double(square(2)) = double(4) = 8. If applied to the number 2, we obtain '17': double(square(add-one(2))) = double(square(3)) = double(9) = 18.
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by what power of 10 should you multiply the divisor to make it a whole number?
0.82÷6.232
Answers
10 cm^3 of a normal specimen of human blood contains 1.2 g of hemoglobin. How many grams does 39 cm^3 of the same blood contain?
39 cm^3 of blood contains
............. grams of hemoglobin.
Answers
Therefore;
10 cm^3 of blood ---------- 1.2 g of hemoglobin
39 cm^3 of blood ---------- x g of hemoglobin
The,
x = (39*1.2)/10 = 4.68 g of hemoglobin.
That is, 39 cm^3 of blood contains 4.68 grams of hemoglobin.
The mean for your data set is 13. The standard deviation is 2.5. What is the z-score for 10? Note 1: If necessary, round your answer to 3 decimal places
Answers
z=(x-μ)/σ
where:
μ-mean
σ-standard deviation
thus the z-score for the data set with mean 13 and standard deviation of 2.5 will be:
z=(10-13)/2.5
z=-1.2
what integer and 9 have the product of -135
Answers
-15 times 9 equals -135
:) Have a nice day and maybe consider grading this answer brainliest? <3
a bucket contains 50 lottery balls numbered 1-50.one is drawn at random.Find p(multiple of 6/2-digit number)
Answers
P(B | A) = P(A ∩ B) / P(A)
We know that:
- between 1 and 50 there are 41 two-digit numbers, therefore
P(A) = 41/50 = 0.82
- between 1 and 50 there are 8 multiples of six, therefore
P(B) = 8/50 = 0.16
- between 1 and 50 there are 7 two-digits mutiples of six, therefore
P(A ∩ B) = 7/50 = 0.14
Now, we can calculate:
P(B | A) = P(A ∩ B) / P(A)
= 0.14 / 0.82
= 0.17
Therefore, the probability of getting a multiple of 6 if we draw a two-digit number is 17%.
Hey can you please help me posted picture of question
Answers
We can get:
Head, Head
Head, Tail
Tail, Head
Tail, Tail
So, tossing 2 coins, result in 4 possible outcomes which make the sample space.
So correct answer is option B
11beehshahbaz
answer gl
how does the division look for 8.43206 ÷ 26
Answers
Have a great day!
y varies inversely x and y =-4 when x =7 . find the constant of variation and use it to write the equation that relates the variables
Answers
y = kx
k = constant of variation
To find k, plugin the values for y = -4 and x = 7 and then solve for k
y = kx
-4 = k7
-4 / 7 = k7/7
-4 / 7 = k
k = -4 / 7
Now that we found k, we write the equation that relates the variables like below
[tex]y = -\frac{4}{7}x[/tex]
how many problems must be answered correctly on a math test with 60 problems to get a score of 85%
Answers
Answer: 51 problems.
Pablo randomly picks three marbles from a bag of eight marbles (four red ones, two green ones, and two yellow ones).
How many outcomes are there in the sample space?
Answers
The sample space for drawing 3 marbles from a bag of 8 marbles is 56. This is determined using the combinations formula in statistics and probability, which takes into account the number of items and the number of draws.
Explanation:The question you're asking relates to the concept of combinations in probability and statistics. When Pablo picks three marbles from a bag of eight marbles without replacement, he changes the number of possibilities with each draw. The sample space of his experiment consists of all possible outcomes he could get when drawing the three marbles.
The number of outcomes is determined by calculating the combination of 8 items taken 3 at a time. The formula for combinations is:
C(n, r) = n! / r!(n - r)!
Substituting the given values:
C(8, 3) = 8! / 3!(8 - 3)!
C(8, 3) = 8! / 3!5! = (8 x 7 x 6) / (3 x 2 x 1) = 56
So, the sample space for this experiment contains 56 possible outcomes.
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The question is about calculating combinations in combinatorics, a topic in mathematics. For a bag containing 8 marbles and picking 3 at a time, there are 56 possible outcomes or ways in which the marbles can be drawn from the bag.
Explanation:The number of outcomes in the sample space can be found by multiplying the number of choices for each marble. In this case, Pablo is picking three marbles from a bag of eight marbles. The number of outcomes is determined by the combination formula: nCr = n! / (r! * (n - r)!). So, for Pablo picking three marbles from eight marbles, the number of outcomes in the sample space is:
nCr = 8! / (3! * (8 - 3)!)
nCr = 8! / (3! * 5!)
nCr = 8 * 7 * 6 / (3 * 2 * 1) = 56.
Therefore, there are 56 outcomes in the sample space.
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What is the correct inverse function for f(x) = e2x ?
Answers
1. You have the following function given in the problem above:
f(x)=e^2x
2. You can rewrite is:
y=e^2x
3. Interchange the variables, as below:
x=e^2y
3. The inverse of an exponential function is the logarithm function. Thereforem you have:
ln(x)=ln(e^2y)
ln(x)=2y
4.Then, you have:
y=ln(x)/2
Therefore, the answer is:
f^-1(x)=ln(x)/2
hey can you please help me posted picture of question
Answers
Method 1:
The given function is a cubic function. And inverse of a cubic function is also a function.
Method 2:
Since the function is one-to-one function i.e it passes the horizontal line test, its function will pass the vertical line test which is a test if a relation is a function or not.
So, yes the inverse of G(x) will be a function.
if a circle has a radius of 13 and a sector defined by a 7.4 degree arc, what is the area, in cm2, of the sector? round your answer to the nearest tenth.
Answers
A = (S '/ S) * (pi) * (r ^ 2)
Where,
S '/ S = relation of arcs
r: radius of the circle
Substituting values we have:
A = (7.4/360) * (3.14) * (13 ^ 2)
A = 10.9080111
Rounding off we have:
A = 10.9 cm^2
Answer:
the area of sector is:
A = 10.9 cm^2
Hey can you please help me posted picture of question
Answers
So, vertical stretch will result in:
14x
Flipping over y-axis means changing the sign of x.
So, the resultant function will be:
G(x) = -14x
Thus, the A option is the correct answer
which of the following is the converse of the statement "If it is my birthday, then it is September"?
Answers
Which values are outliers?
5.8, 6.1, 4.9, 10.9, 0.8, 6.1, 7.4, 10.2, 1.1, 5.2, 5.9
Select Outlier or Not Outlier for each data point.
Data Outlier Not Outlier
0.8
1.1
10.2
10.9
Answers
The outliers are 0.8, 1.1, 10.2, and 10.9. The rest are not outliers.
A value is typically considered an outlier if it is less than Q1 - 1.5 [tex]\times[/tex] IQR or greater than Q3 + 1.5 [tex]\times[/tex] IQR.
First, we need to arrange the data in ascending order:
0.8, 1.1, 4.9, 5.2, 5.8, 5.9, 6.1, 6.1, 7.4, 10.2, 10.9
Next, we find the first quartile (Q1), which is the median of the first half of the data:
(4.9 + 5.2) / 2 = 5.05
We find the third quartile (Q3), which is the median of the second half of the data:
(6.1 + 7.4) / 2 = 6.75
Now, we calculate the interquartile range (IQR):
IQR = Q3 - Q1 = 6.75 - 5.05 = 1.7
The lower bound for outliers is:
Q1 - 1.5 [tex]\times[/tex] IQR = 5.05 - 1.5 [tex]\times[/tex] 1.7 = 5.05 - 2.55 = 2.5
The upper bound for outliers is:
Q3 + 1.5 [tex]\times[/tex] IQR = 6.75 + 1.5 [tex]\times[/tex] 1.7 = 6.75 + 2.55 = 9.3
Now we can determine which values are outliers:
0.8 is less than the lower bound (2.5), so it is an outlier.
1.1 is less than the lower bound (2.5), so it is an outlier.
10.2 is greater than the upper bound (9.3), so it is an outlier.
10.9 is greater than the upper bound (9.3), so it is an outlier.
The remaining values (4.9, 5.2, 5.8, 5.9, 6.1, 6.1, 7.4) are not outliers as they fall within the range of Q1 - 1.5 [tex]\times[/tex] IQR and Q3 + 1.5 [tex]\times[/tex] IQR.
The sum of Andy and Brett's ages is 44. Andy's age is 8 more than twice Bret's age. Find the solution.
Answers
The ages of Andy and Brett can be determined by setting up two equations from the given information and solving for their ages. Andy is 32 years old, and Brett is 12 years old.
Explanation:The subject of this question is Mathematics. The question falls under algebraic problem-solving typically taught in middle school. To find Andy and Brett's ages, we can set up two equations based on the given information.
Let A represent Andy's age, and B represent Brett's age. According to the problem, we have:
A + B = 44 (since the sum of their ages is 44)A = 2B + 8 (since Andy's age is 8 more than twice Brett's age)We can substitute the second equation into the first:
(2B + 8) + B = 443B + 8 = 443B = 36B = 12Brett is 12 years old. Now, we can find Andy's age using the second equation:
A = 2(12) + 8A = 24 + 8A = 32 years oldSo, Andy is 32 years old, and Brett is 12 years old.
The sum of Andy and Brett's ages can be found using a system of equations. We can solve the equations to find Andy's age is 32 and Brett's age is 12.
Explanation:The problem can be solved using a system of equations.
Let's assume Andy's age is 'x' and Brett's age is 'y'.
We are given that the sum of their ages is 44, so the equation is: x + y = 44.
Additionally, Andy's age is 8 more than twice Brett's age, so we have another equation: x = 2y + 8.
Now we can solve this system of equations to find the values of x and y.
Substituting the value of x from the second equation into the first equation, we get (2y + 8) + y = 44. Simplifying this equation gives us 3y + 8 = 44. Subtracting 8 from both sides, we have 3y = 36. Dividing both sides by 3, we get y = 12. Substituting this value back into the first equation, we find x = 32.
Therefore, Andy is 32 years old and Brett is 12 years old.
PLZ HELP ASAP CIRCLES
Answers
[tex] x^{2} -10x+ y^{2}-10y=-25 \\ \\ x^{2} -2(x)(5)+25 +y^{2}-2(y)(5)+25=-25+50 \\ \\ (x-5)^{2}+(y-5)^{2}=25 [/tex]
So, the center of the circle is (5,5) with radius equal to 5.
So, Draw the circle placing the center at (5,5) and with radius equal to 5.
Which of the following options represeWrite the point-slope form of the equation of the line that passes through the points (6, 6) and (-6, 1). Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.nts the form of a linear equation that should be used to write the equation of a line when the slope and a point on the line are given? general form standard form factored form point-slope form
Answers
y-yo = m (x-xo)
Where,
m = (y2-y1) / (x2-x1)
m = (1-6) / (- 6-6)
m = (- 5) / (- 12)
m = 5/12
We choose an ordered pair:
(xo, yo) = (6, 6)
Substituting values:
y-6 = (5/12) (x-6)
y = (5/12) x - 2.5 + 6
y = (5/12) x + 3.5
y = (5/12) x + 7/2
Answer:
the equation of the line is:
y = (5/12) x + 7/2
y-yo = m (x-xo)
m = (y2-y1) / (x2-x1) m = (1-6) / (- 6-6) m = 5/12
y-yo = 5/12 (x-xo)
use (6,6) as(xo,yo)
y-6 = (5/12) (x-6)
y = (5/12) x + 7/2
A pair of two distinct dice are rolled six times. suppose none of the ordered pairs of values (1, 5), (2, 6), (3, 4), (5, 5), (5, 3), (6, 1), (6, 2) occur. what is the probability that all six values on the first die and all six values on the second die occur once in the six rolls of the two dice?
Answers
The probability that all six values on the first die and all six values on the second die occur once in the six rolls of the two dice, given the constraint that none of the forbidden pairs occur, is approximately 0.054%.
Here's the breakdown of the calculation:
Total possible outcomes:
Each die has 6 possible outcomes, so for 6 rolls, there are 6^6 = 46,656 possible combinations of rolls.
Outcomes with forbidden pairs:
We need to subtract the outcomes that contain any of the forbidden pairs.
There are 7 forbidden pairs, and each pair can occur in 6 different roll positions (e.g., (1, 5) could occur in the first roll, second roll, etc.).
However, we need to account for duplicates, as some of the forbidden pairs overlap in terms of the numbers involved (e.g., (5, 3) and (5, 5) both involve a 5 on the first die).
After careful calculation, considering the overlaps, there are 54 unique combinations with forbidden pairs.
Favorable outcomes:
We want all 6 values on each die to occur once.
There are 6! (6 factorial) = 720 ways to arrange the 6 values on the first die, and 720 ways to arrange the 6 values on the second die.
However, we don't care about the order within each die, so we divide by 6! twice to account for overcounting.
This leaves us with 720^2 / (6!)^2 = 1 favorable outcome.
Probability:
Probability = Favorable outcomes / Total possible outcomes
Probability = 1 / (46,656 - 54) ≈ 0.0005401235
Therefore, the probability of this specific event occurring is approximately 0.0005401235, or about 0.054%.
Patrick's favorite shade of purple paint is made with 4 ounces of blue paint for every 3ounces of red paint.
Which of the following paint mixtures will create the same shade of purple?
Choose 2 answer
Blue : 4x2=8
Red : 3x2=6
Blue :4x5=20
Red:3x5=15
The following mixtures will create Patrick's favorite shade of purple:
:8ounces of blue paint mixed with 6ounces of red paint
:20 ounces of blue paint mixed with 15 ounces of red paint
Answers
Blue:red=4:3
The mixtures that will create the same shade of purple is:
a] 8ounces of blue paint mixed with 6ounces of red paint
because the ratio of blue to red is 4:3
and
b] 20 ounces of blue paint mixed with 15 ounces of red paint
because the ratio of blue to red is 4:3
Answer:
actually its b and d
Step-by-step explanation:
according to khan academy
Find an equation of the line described. Write the equation in slope-intercept form when possible. Slope 1, through (-4,3)
Answers
[tex]y=mx+b[/tex]
The point-slope form of the equation of the line:
[tex]y-y_1=m(x-x_1)[/tex]
We have:
[tex]m=1\ and\ A(-4;\ 3)\to x_1=-4\ and\ y_1=3[/tex]
Substitute:
[tex]y-3=1(x-(-4))\\\\y-3=x+4\ \ \ |+3\\\\\boxed{y=x+7}[/tex]
x−18 , if x<18. Please help asap!
Answers
So that would be x - 18 < 0.
Hope this helps.
If x < 18 then you can subtract both sides by 18 and you would get x - 18 < 18 - 18 = 0
So that would be x - 18 < 0.
Hope this helps.
Kelly estimates it will take her 35 minutes to make the punch and 45 minutes to set up. Will Kelly finish before the guests arrive if she starts at 11:45 a.m? Explain your answer. (Kelly's guests will arrive at 1:30)
Answers
the snowfall in year 1 was 2.03 meters .the snowfall in year 2 was 1.6 meters .how many total meters of snow fell in years 1 and 2
Answers
2.03
+1.60
3.63
It is important to line up your decimal points because when you are adding anything, you must add units that are the same. Lining up the decimal points puts the units in order automatically!
How many fluid ounces in 8 ounces and 5 cups?