Answers
The value of x will be 1.17 inches and the maximum volume of the box is 1.6 cubic inches.
What is volume?Volume is a measurement of three-dimensional space that is occupied. It is frequently numerically quantified using SI-derived units or various imperial or US customary units. The definition of length is linked to the definition of volume.
Given that the rectangular box is made from cardboard the thickness is x.
The length of the box will be,
L = 4.5 - 3x
The width of the box will be,
W = 4 - 2x
The thickness of the box is,
H = x
The volume of the box will be calculated as,
V = ( 4.5 - 3x) ( 4 - 2x ) (x)
V = ( 4.5 - 3x) ( 4 - 2x ) (x)
V = ( 18 - 12x - 9x + 6x² ) x
V = 6x³ -21x² + 18x
For maximum volume differentiate the volume with respect to x and get the value of x,
dV / dx = d / dx ( 6x³ -21x² + 18x ) = 0
d / dx ( 6x³ -21x² + 18x ) = 0
18x² - 42x + 12 = 0
3x² - 7x + 6 = 0
Solve the above quadratic equation as,
x = [ -b ±√(b² - 4ac) ] / 2a
x = [ -7 ± √ (-7² - 4 x 3 x 6 ) ] / ( 2 x 3 )
x = 1.17
The value of x is 1.17 inches by solving the above quadratic equation. The maximum volume will be calculated as,
V = 6x³ -21x² + 18x
V = 6(1.17)³ -21(1.17)² + 18(1.17)
V = 9.6 - 28.7 + 21.06
V = 1.96 cubic inches
The maximum volume is 1.96 cubic inches and the value of x is 1.17 inches.
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Related Questions
Ryanne is 14. Her brother's age is three more than half her age. How old is her brother?
OA 7
OB. 8.5
OC. 10
OD. 31
Question
Answers
Answer:
10 years old
Step-by-step explanation:
Madelyn and Kaia are competing to see who can sell the most tickets for the Winter Dance. On Monday, Madelyn sold 22 and then sold 30 per day after that.
Kaia sold 53 on Monday and then sold 20 per day after that.
Write an equation to represent the number of tickets that Madelyn sold.
Write an equation to represent the number of tickets that Kaia sold.
Write a system of equations. What is the appropriate method for solving the system?
Solve the system of equations. Explain the meaning of your solution.
Answers
The equations found for the number of tickets sold when 22 tickets are sold on Monday and 30 per day after are sold by Madelyn, and 53 tickets are sold on Monday and 20 per day after that are;
Tickets sold by Madelyn is; y = 22 + 30·x
Tickets sold by Kaia is; y = 53 + 20·x
A system of equation obtained from the details in the question can be presented as follows
y = 22 + 30·x...(1)
y = 53 + 20·x...(2)
The appropriate method for solving the system is to equate equivalent values of one of the variable obtained from each equation in the system.
The solution of the system of equation is; x = 3.1, which indicates that it takes about 3.1 days for the number of tickets sold by Madelyn and Kaia to be equivalent.
What is an equation?An equation consists of two expressions that are joined by the 'equals to' (=) sign.
The number of tickets for the Winter Dance Madelyn sold = 22
Number of tickets per day Madelyn sold after that = 30 per day
Number of tickets Kaia sold on Monday = 53
Number of tickets per day Kaia sold after that = 20 per day
Let x represent the number of days since Monday, and let y represent the number of tickets sold
Therefore;
The number of tickets Madelyn sold, y = 22 + 30·x
The number of tickets Kaia sold, y = 53 + 20·x
The system of equations from the specified information is the equation for the number of tickets Madelyn sold and the number of tickets Kaia sold combined, which can be presented as follows;
y = 22 + 30·x...(1)
y = 53 + 20·x...(2)
The method of solving the equations is by plugging in the value of y from equation (1) in equation (2), as follows;
22 + 30·x = 53 + 20·x
30·x - 20·x = 53 - 22 = 31
10·x = 31
x = 31 ÷ 10 = 3.1
The meaning of the solution of the system of equation, x = 3.1, is that the number of days for the number of tickets sold by Madelyn and Kaia to be the same is about 3 days
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luka is making lemonade to sell at a school fundraiser. his recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. he uses 3 cups of lemon juice. how many cups of water does he need?
Answers
Luka will require 24 cups of water to make lemonades as calculated from the data given.
The quantity of sugar which he use is twice the amount of lemon which he us ,
= 2 x 3 = 6
and ,
as we know the amount of water is 4 times as much as lemon juice
Therefore, amount of water
= 4 * 6
= 24
A quantity in a Maths equation is a number or variable plus any algebraic combination of additional quantities. In an equation like x + 6 = 15, four values are represented.
A quantity can be described as the amount of something or how much of it there is. Quantity can also be used to refer to the size of something (its magnitude), whether in terms of numbers, units of measurement, or just relative size.
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cross-tabulation can only be used for two variables; each variable must have well-defined labels. true false
Answers
The statement "cross-tabulation can only be used for two variables; each variable must have well-defined labels " is false
The cross tabulation is defined as the tool that is used in statistics to categorical data. We can also says that that present the results of the entire group of respondents
The given statement is "cross-tabulation can only be used for two variables; each variable must have well-defined labels "
The cross tabulation method can be used to represent two or more variables. The cross tabulation table has x axis as one variable and y axis as another variables
The cross tabulation can be used for two or more variables
Therefore, the the given statement is false
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In a group of 500 people determine how many are suspects in the following scenario.
A wallet was stolen from an office in a building with 500 employees. The suspect was wearing black pants, a white button-down shirt, and a multicolored tie. In one of the offices in the building, the following data was collected.
30 people total in the office
22 wearing a white button down shirts
16 wearing black pants
7 wearing a multicolored tie
Using the data, how many suspects are there?
Answers
Using the given data, the number of suspects is; 7
How to find the intersection of mathematical sets?
The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.
However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.
Now, we are told that;
Total number of people in the office = 30 people
Number of people wearing a white button down shirts = 22
Number of people wearing black pants = 16
Number of people wearing a multicolored tie = 7
Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;
The number of suspects = A ∩ B ∩ C = 7 people
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Given the functions f(x) = x3 + x2 – 3x + 4 and g(x) = 2x – 4, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)
Answers
1. f(x) - cubic function -- polynomial , g(x) - linear function
similar
domain all real numbers (?)range is all real number, end behavior is the sameThe function f(x) = x³+x²-3x+4 is a polynomial function and g(x) = 2ˣ-4 is an exponential function.
Domain: -∞ < x < ∞
Range: -∞ < y < ∞
y-intercept = 4
x - intercepts = -2.68
Function g(x)
Domain: x > 0
Range: -4 < y < ∞
y - intercept = -4
x - intercepts = none
By comparing the key features above, we can conclude that the common features in both functions are their range
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Nick has two pet rabbits.His Flemish giant rabbit weighs 5 times as much as his Holland lop rabbit,If nich's Flemish rabbit weighs 12 more pounds than his Holland lop rabbit,how much does his Flemish giant rabbit weight?
Answers
Answer:The Flemish giant rabbit weighs 32 pounds.
Step-by-step explanation:
What is the solution of the equation x2 - 12x = 8?
Answers
The solution of the equation is x = 6±2√11.
What is a quadratic equation?
The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem. In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.
Here, we have
Given: x² - 12x = 8
Now, we factorize the given equation and find the solution.
x² - 12x = 8
x² - 12x - 8 = 0
We apply here the quadratic formula.
= (-b ±√b²-4ac)/2
= (12 ±√12²-4×1×(-8))/2
= (12±√144+32)/2
= (12±√176)/2
= (12±4√11)/2
= 6±2√11
Hence, the solution of the equation x² - 12x = 8 is 6±2√11.
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Please help! Division of Polynomials, Find the quotient and remainder.
Answers
First:
Quotient: [tex]2x^{2} -11x+58[/tex]
Remainder: [tex]-294[/tex]
Second:
Quotient: [tex]x^{3} -5x^{2} +17x-83[/tex]
Remainder: [tex]422[/tex]
Third:
Quotient: [tex]2x-3[/tex]
Remainder: [tex]12[/tex]
Hi sorry for the mistake this is the photo I was meant to post and I need help with number 6(iii)
Answers
Answer:
-2
Step-by-step explanation:
Given,
g(x) = f(4)
or, 2 - 4x = 3*4 - 2
or, 2 - 4x = 10
or, 2 - 10 = 4x
or, -8 = 4x
or, x = -2
Which statement can you conclude is true from
the given information?
Given: AB is the perpendicular bisector of IK.
( please help me , answers my questions )
Answers
As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.
What is perpendicular bisector?A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.
What is the perpendicular of two points?A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.
Option J can not be true as A can not be the midpoint of IK as A is not on IK. Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.
Option H i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.
Option G i.e m∠IAJ also does not true necessarily true. The reason is simple i.e AJ is arbitrary.
So, Option f i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ is true.
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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.
What is perpendicular bisector?
A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.
What is the perpendicular of two points?
A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.
Option J can not be true as A can not be the midpoint of IK as A is not on IK. Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.
Option H) i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.
Option G) i.e m∠IAJ also does not true necessarily true. The reason is simple i.e AJ is arbitrary.
So, Option f) i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ is true.
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a car manufacturer wants to learn more about the brand preferences of electric car owners. there are millions of electric car owners in the world. who should the company survey? 1 point the entire population of electric car owners a sample of car owners who have owned more than one electric car a sample of all electric car owners a sample of car owners who most recently bought an electric car
Answers
A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.
What is Survey?A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.
Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.
As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.
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The following figure was drawn using a straightedge and a compass. Where was the point of the compass located in order to make the arcs?
1. points X and Y
2. point D
3. point C
4. points A and B
Answers
The point of the compass located in order to make the arcs is points X and Y.
Define arc.An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc. A circle contains an arc. For instance, a quarter-circle and a semicircle are both examples of arcs. A minor arc is one that is smaller than half of the circle it is a part of, or less than a semicircle, whereas a major arc is one that is more than half of its circle.
Given
The following figure was drawn using a straightedge and a compass.
The point of the compass located in order to make the arcs:
1. points X and Y
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fast as you can. point slope form. algebra 1)
Answers
Answer: Y=mx+b
Step-by-step explanation:
the perimeter of a square is 48 centimeters, what is the area in square centimeters
Answers
Answer:
144cm²
Step-by-step explanation:
If the square is perfectly even on all sides, the you first need to divide 48 by 4, as a square has 4 sides.
48/4 = 12cm
Then, to find the area, you need to multiply 12 by 12.
12 cm x 12 cm = 144cm²
Hope this helps :)
If you vertically compress the absolute value parent function, F(x) = |x|, by multiplying by 3/4, what is the equation of the new function?
A. G(x) = | 3/4 x |
B. G(x) = |x| - 3/4
C. G(x) = 3/4 |x|
D. G(x) = | x + 3/4 |
Answers
Answer:G(x) = 3/4 |x|, nevertheless that is the same that G(x) = |3/4x|.
Step-by-step explanation:
Note that given that 3/4 is less than 1 the original function is compressed.
- Take care <3
Write the answer in the blank.
What number is 280 more than 220?
Answers
Answer: 500
Step-by-step explanation:
280 + 220 is 500
Answer:
The number is 500.
Step-by-step explanation:
Let's assume that,
→ Missing number = x
Forming the equation,
→ x = 220 + 280
Now the value of x will be,
→ x = 220 + 280
→ [ x = 500 ]
Hence, the number is 500.
suppose that a product is designed to function for 10,000 hours with a 3% chance of failure. find the average number of failures per hour and the mttf.
Answers
A product is designed to function for 10,000 hours with a 3% chance of failure , then Average number of failures per hour = 0.03/10000 = 0.000003 and MTTF = 1/0.000003 = 333,333 hours
Given,
Chance Product is designed to function for 10,000 hours
of failure is 3%
To find,
Average number of failures per hour
MTTF
Solution,
Average number of failures per hour = Chance of failure/Total hours of function
= 3%/10000
= 0.03/10000
= 0.000003
MTTF = 1/Average number of failures per hour
= 1/0.000003
= 333,333 hours
The product is designed to function for 10,000 hours with a 3% chance of failure. This means that the average number of failures per hour is 0.000003 and the Mean Time To Failure (MTTF) is 333,333 hours. This means that, on average, the product should last 333,333 hours before it fails.
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solve for x.
enter your answer as a mixed number in simplest form in the box.
x =
Answers
Answer:
x + x - x = x
explanation:
give us the actual formula lol
Graph the inequality on the axes below
x+ 5y <-30
Answers
The points where the inequality x+ 5y <-30 intercepts is ( 30, 0 ) and (0,6).
What is an inequality?Inequality is defined as a relationship between two expressions or values that are not equal to each other.In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).Here given the inequality.
x + 5y ≤ 30
To find the x-intercepts.
We have to substitute 0 for y and solve x to determine the x-intercepts.
x + 5 × 0 = 30
By solving the equation.
x = 30
( 30, 0 ) is the x-intercepts.
To find the y-intercepts.
By substituting 0 for x and solving y will get the y-intercept(s).
0 + 5y = 30
5y =30
y = 30/5
y = 6
In the point form, y-intercept.
Y-intercept(s): ( 0, 6 )
(30, 0) is the x-intercept.
Y-intercepts at : ( 0, 6 ).
The points in which the inequality x+ 5y <-30 intercepts is (30, 0) and (0,6).
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the table shows the number of stickers three friends have, Hannah has fewer stickers than Marco but more stickers than Addison. how many stickers could Hannah have?
Answers
A cryotherapy chamber uses extreme cold to reduce muscle soreness. A chamber is currently 0°F. The temperature in the chamber is dropping 2.5°F every second. Identify an inequality that represents the numbers of seconds $s$ that can pass for the temperature to drop below -20 °F
Answers
Answer: The answer is $s$ > 7, which represents the number of seconds that can pass for the temperature in the cryotherapy chamber to drop below -20°F.
Step-by-step explanation: The temperature in the chamber will drop below -20°F when it reaches -20°F + 2.5°F = -17.5°F.
The temperature in the chamber is currently 0°F, so we can represent this situation with the inequality 0 - (2.5 * $s$) < -17.5, where $s$ is the number of seconds that can pass.
We can simplify this inequality by multiplying both sides by -1 to get the following: 2.5 * $s$ > 17.5.
Dividing both sides by 2.5, we get the final inequality: $s$ > 7.
Therefore, the number of seconds $s$ that can pass for the temperature in the cryotherapy chamber to drop below -20°F is greater than 7 seconds.
Helppppp meeeee guyssss
Answers
25.) 4•4•4•4•4 = 1024
27.) 1/3^7= 1/2187
29.) 476500
31.) 4.26 x 10^7
Brainly pls
Here is the graph for one equation in a system of equations:
a) Write a second equation for the system so it has infinitely many solutions.
b) Write a second equation whose graph goes through (0, 1) so the system so it has no
solutions.
Answers
The answer to each part is -
for infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.What is the general form of a straight line? What is a mathematical function, equation and expression?straight line equation : The general equation of a straight line equation is given byy = mx + c
where -
[m] : slope of line
[c] : y - intercept
Given is the graph of a straight line as shown.
[A] - A second equation for the system so it has infinitely many solutions can be the one that overlaps the line given. So the second equation can be written as follows. The points are -
(0, 4) and (4, 1)
Let the line be -
y = mx + c
m = (1 - 4)/(4 - 0) = -3/4
m = -3/4
So, the equation will be -
y = (-3/4)x + 4
[B] -
For no solution, the line will be parallel to the given line. The equation of the line is → y = (-3/4)x + 4. The equation whose graph goes through (0, 1) so the system has no solutions as : y = (-3/4)x + 1.
Therefore, the answer to each part is -
for infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.To solve more questions on functions, expressions and polynomials, visit the link below -
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what does a z-score tell us about an individual observation in a data set? it is the number of standard deviations an observation is away from the mean. the midpoint of the sorted sample data set the sum of all data values divided by the number of data items. the average. the most frequently occurring data value in the set. none of the above
Answers
A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.
The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.
A z-score is the value of an observation expressed in standard deviation units. The sign of the score indicates whether it is above (positive) or below (negative) the mean, and the value quantifies how many standard deviations the score is from the mean.
The purpose of z-scores is to identify and describe the exact location of each score in a distribution & to standardize an entire distribution to understand & compare scores from different tests.
Z-scores or Z-statistics represent a statistical technique of measuring the deviation of data from the mean. There are different formula used for Z-score or Z-statistics depending upon what is measured. Z-statistics is generally used with Z-test which is a hypothesis testing statistical technique.
Therefore,
A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.
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let g be a polynomial function of x where g(x) = 2x^3 + 5x^2 - 28x - 15 Given (x - 3) is a factor of g, what is the reminder of g(x) + (x - 3)?
Answers
The remainder of polynomial g(x) divides (x - 3) that is g(x) / (x - 3) is 0.
What is polynomial?
A polynomial is a mathematical expression made up of variables, constants, and exponents that are combined using addition, subtraction, multiplication, and division operations.
Given: g(x) = 2x^3 + 5x^2 - 28x - 15
(x - 3) is a factor of g(x).
We have to find the remainder of g(x) / (x - 3).
Consider,
2x^2 + 11x + 5
[tex]\sqrt[(x-3)]{2x^3+5x^2 -28x -15}[/tex]
- 2x^3 -6x^2
____________________________
11x^2 - 28x
- 11x^2 - 33x
____________________________
5x - 15
- 5x - 15
_______________________________
0
Hence, the remainder of polynomial g(x) divides (x - 3) that is
g(x) / (x - 3) is 0.
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maria has type b blood. she can safely receive blood transfusions from people with blood types o and b. what is the probability that a randomly chosen person from the united states can donate blood to maria?
Answers
The probability that a randomly chosen person from the united states can donate blood to maria is 0.50
considering blood to be of types A,B,AB and O
further all blood groups are equi probable
Probability of blood type A = probability of blood type B = probability of blood type AB = probability of blood type O = x
Probability of blood type A + probability of blood type B + probability of blood type AB + probability of blood type O = 1
⇒ 4x = 1
⇒ x = 1/4
Probability that a random person will have blood of type B or O = x+x
= 1/4 + 1/4
= 1/2
= 0.50
Hence we get the required answer.
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please help, this is my finals & i don’t know it
Answers
Answer:
i think that answer is correct
Step-by-step explanation:
Solve the equation -3.5(x-14)+9x=5.5x + 49. Which statement is true ?
Answers
Answer:
Step-by-step explanation:
Answer:
-3.5(x-14)+9x=5.5x + 49 is a TRUE statement that equals 0. It has infinite solutions.
Step-by-step explanation:
What is the cubic polynomial with zeros (3,0), (-6,0), and (1,0)?
(Question 15)
Answers
Answer:
D
Step-by-step explanation:
when we have the zeroes, we can build the polynomial by multiplying factors that will turn the functional value to 0 at exactly these points.
f(x) = (x - 3)(x + 6)(x - 1)
we don't need to do the full multiplications to see that the constant term of the polynomial is the result of the multiplication of all 3 constant terms of the factors :
-3 × +6 × -1 = +18
and therefore, D is the correct answer (as it is the only answer option with +18 as constant term).
