if the canonical sum of an n-input logic function is itself a minimal sum, how many literals are in each product term of the minimal sum? give an example of such a function.
Answers
If the canonical sum of an n-input logic function is itself a minimal sum, then each product term in the minimal sum has n literals. The canonical sum of this function is: f(A,B,C) = A'B'C' + A'B'C + A'BC' + AB'C' + AB'C
In Boolean algebra and digital logic, a canonical sum of a logic function is a sum of minterms that covers all possible combinations of inputs that produce a logic 1 output.
A minterm is a product of literals, where a literal is either an input variable or its complement. The number of literals in a product term corresponds to the number of input variables in the function.
A minimal sum is a sum of product terms that is equivalent to the original function and has the minimum number of terms possible. The number of literals in each product term of a minimal sum depends on the structure of the function and how it is expressed.If the canonical sum of an n-input logic function is itself a minimal sum, then it already has the minimum number of terms and literals.
This means that the product terms in the minimal sum each have n literals, one for each input variable.
For example, consider the 3-input function f(A,B,C) = Σ(1,2,3,5,6), which has a canonical sum of:f(A,B,C) = A'B'C' + A'B'C + A'BC' + AB'C' + AB'C
This sum has 5 product terms, each with 3 literals, corresponding to the 3 input variables A, B, and C. Since this canonical sum is already a minimal sum, there is no other sum of product terms with fewer terms or literals that is equivalent to the original function.
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Related Questions
One unit of A is composed of two units of B and three units of C. Each B is composed of one unit of F. C is made of one unit of D, one unit of E, and two units of F. Items A,B,C, and D have 20,50,60, and 25 units of on-hand inventory, respectively. Items A,B, and C use lot-for-lot (L4L) as their lot-sizing technique, while D,E, and F require multiples of 50,100 , and 100 , respectively, to be purchased. B has scheduled receipts of 30 units in period 1. No other scheduled receipts exist. Lead times are one period for items A, B, and D, and two periods for items C,E, and F. Gross requirements for A are 20 units in period 1,20 units in period 2, 60 units in period 6, and 50 units in period 8. Find the planned order releases for all items.
Answers
The planned order releases for each item are as follows: A: 20 units in period 1, B: 10 units in period 1, C: 40 units in period 3, D: No planned order release, E: 100 units in period 5, F: 100 units in period 5
To determine the planned order releases for all items, we need to calculate the net requirements for each period based on the given information. We will start with the highest-level item and work our way down the bill of materials.
Item A:
Period 1: Gross requirement of 20 units.
Since A uses lot-for-lot (L4L) as the lot-sizing technique, we release an order for 20 units of A.
Item B:
Item B is a component of A, and each A requires 2 units of B.
We need to calculate the net requirements for B based on the planned order release for A.
Period 1: Gross requirement of 20 units * 2 (requirement multiplier for B) = 40 units.
B has a scheduled receipt of 30 units in period 1.
Net requirement for B in period 1: 40 units - 30 units = 10 units.
Since B also uses L4L as the lot-sizing technique, we release an order for 10 units of B.
Item C:
Item C is a component of A, and each A requires 3 units of C.
We need to calculate the net requirements for C based on the planned order release for A.
Period 1: Gross requirement of 20 units * 3 (requirement multiplier for C) = 60 units.
C has a lead time of two periods, so we need to account for that.
Net requirement for C in period 3: 60 units - 20 units (scheduled receipt for A in period 1) = 40 units.
Since C uses L4L as the lot-sizing technique, we release an order for 40 units of C.
Item D:
Item D is a component of C, and each C requires 1 unit of D.
We need to calculate the net requirements for D based on the planned order release for C.
Period 3: Gross requirement of 40 units * 1 (requirement multiplier for D) = 40 units.
D has a lead time of one period, so we need to account for that.
Net requirement for D in period 4: 40 units - 60 units (scheduled receipt for C in period 3) = -20 units (no requirement).
Since the net requirement is negative, we do not release any planned order for D.
Item E:
Item E is a component of C, and each C requires 1 unit of E.
We need to calculate the net requirements for E based on the planned order release for C.
Period 3: Gross requirement of 40 units * 1 (requirement multiplier for E) = 40 units.
E has a lead time of two periods, so we need to account for that.
Net requirement for E in period 5: 40 units - 0 units (no scheduled receipt for E) = 40 units.
Since E requires a multiple of 100 to be purchased, we release an order for 100 units of E.
Item F:
Item F is a component of B and C, and each B requires 1 unit of F, while each C requires 2 units of F.
We need to calculate the net requirements for F based on the planned order releases for B and C.
Period 1: Gross requirement for B = 10 units * 1 (requirement multiplier for F) = 10 units.
Period 3: Gross requirement for C = 40 units * 2 (requirement multiplier for F) = 80 units.
F has a lead time of two periods, so we need to account for that.
Net requirement for F in period 5: 10 units + 80 units - 0 units (no scheduled receipt for F) = 90 units.
Since F requires a multiple of 100 to be purchased, we release an order for 100 units of F.
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Yesterday, 20 bakery customers bought muffins and 11 of those customers bought banana muffins. If 100 customers buy muffins tomorrow, how many would you expect to buy a banana muffin?
Answers
Answer:
55
Step-by-step explanation:
Make a proportion.
11/20=x/100
20*5=100, 11*5=55
Kuta Software Infinite Algebra 1. Solving Systems of Equations by Substitution. Solve each system by substitution. 1) y=6x-11. -2x-3y=-7. -2x-3(60x-11)=-7
Answers
the solution to the system of equations is x = 2 and y = 1.
To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.
Given the system of equations:
1) y = 6x - 11
2) -2x - 3y = -7
Step 1: Solve equation (1) for y.
y = 6x - 11
Step 2: Substitute the value of y from equation (1) into equation (2).
-2x - 3(6x - 11) = -7
Step 3: Simplify and solve for x.
-2x - 18x + 33 = -7
-20x + 33 = -7
-20x = -7 - 33
-20x = -40
x = (-40)/(-20)
x = 2
Step 4: Substitute the value of x into equation (1) to find y.
y = 6(2) - 11
y = 12 - 11
y = 1
Therefore, the solution to the system of equations is x = 2 and y = 1.
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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.
Explanation:To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.
Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.
Therefore, the solution to the system of equations is x = 2 and y = 1.
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A grocery store clerk can scan 1 product every
1
2
of a second. At what rate can she scan products?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
products per second
Answers
Answer:
2 products per second.
Step-by-step explanation:
help me please answer 1-10 and also the guide question
Answers
This prompt is about prioritization, time management and order. It also speaks to the way a project manager should think about events and their importance.
How would one place the given tasks according to order of importance?
The tasks are placed in order of importance as follows:
Entering PIN of your ATM card. - OIIWinning in a swimming contest. - ONIOpening a combination lock of a vault. - OIISelecting 3 posters to hang out of 6 different places. - ONISelecting 7 people to form a committee for contact tracing. - ONIDrawing a set of 4 numbers in a lottery containing numbers I — 42. - ONIAssigning rooms to parents who will get modules for their students. - OIISelecting 3 among 7 nurses to be assigned in an emergency room. - OIIChoosing 5 questions to answer out of 15 questions in a test. - ONIChoosing 4 books to borrow out of 7 books of his interest in the library. - ONI.The response categorizes each task as OII (Order Is Important) or ONI (Order Is Not Important) based on whether the sequence of steps affects the outcome of the task or not. For example;
The order in which you enter your PIN is crucial because entering the wrong PIN too many times could lock your card. The correct sequence is essential for accessing your account and completing transactions.
Selecting 7 people to form a committee for contact tracing - ONI (Order Is Not Important)The order in which the seven people are selected for the committee does not matter as long as the selected individuals meet the necessary qualifications for contact tracing. Any combination of seven qualified individuals will suffice.
Choosing 5 questions to answer out of 15 questions in a test - ONI (Order Is Not Important)The order in which the questions are answered does not matter as long as the required number of questions is answered correctly. Any five questions can be selected and answered in any order to achieve the desired result.
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Divide and answer in simpilist form: 1/2 ÷4
Answers
Answer:
1/8
Step-by-step explanation:
1/2 ÷4
Copy dot flip
1/2 * 1/4
1/8
Answer:
1/8
I want brainliest!!! :)
Step-by-step explanation:
1/2 divided by 4
1/2/4 = 1/8
I need help with my Geometry. Can you help?
Thanks.
Answers
Answer:
1. 32 units
2. C(-15, -4) and D(17, -4)
Step-by-step explanation:
1.The midpoint divides CD into two segments that are the same length:
CM = MD
8(x -2) = 4(5x -16)
8x -16 = 20x -64 . . . eliminate parentheses
48 = 12x . . . . . . . . . add 64 -8x
x = 4 . . . . . . . . . . . divide by 12
Then the length of CD is ...
CD = 2·CM = 2(8(x -2)) = 2(8(4-2))
CD = 32
__
2.If we put C and D on the same horizontal line as M, their coordinates are ...
C = M -(16, 0) = (1,-4) -(16, 0) = (-15, -4)
D = M +(16, 0) = (1, -4) +(16, 0) = (17, -4)
Coordinates C and D that have M(1, -4) as a midpoint are ...
C(-15, -4) and D(17, -4).
Angle S measures 137°.
What type of angle is angle S?
Responses
acute
obtuse
right
Answers
Answer:
Obtuse
Step-by-step explanation:
Right angles are 90° so incorrect
Acute angles are less than 90°, also incorrect
Obtuse angles are between 90 and 180. And this is the range which 137 is found
So angle S is obtuse
Answer:
B) Obtuse
Step-by-step explanation:
Let's look at the definitions for each answer choice:
Acute: An acute angle is an angle that measures less than 90°.
Obtuse: An obtuse angle is an angle that measures more than 90°.
Right: A right angle is an angle that measures exactly 90°.
Given that Angle S is 137°, we can classify this angle as an obtuse angle, as 137>90.
Hope this helps! :)
Find the solution
of this system of linear
equations. Separate the x- and y- values with a
comma. Enclose them in a pair of parantheses.
-6x = 24 - By
12x = -72 + 8y
Answers
MATH HELP PLEASE HELP
Answers
Answer:
75 cm
Step-by-step explanation:
150÷2 = 75
Good luck with your exam :)
Answer:
75
Step-by-step explanation:
Essentially this question for the radius as it ask for the distance from the middle of the pit to the outside of the pit.
We are given the diameter (150) which is a straight line through the middle from one end to the other
To find the radius given the diameter you simply divide by 2
So answer = 150/2 = 75
write the equation of the line passing through points (2,-2) and (1,0) in the slope intercept form
Answers
Answer:
y=-2x+2
Step-by-step explanation:
Just follow the slope-intercept form formula-
Formula: y= mx+b
Key:
y = y-coordinate
m = slope
x = x-coordinate
b = y-intercept
Feel free to ask if you have any questions, hope this helps!(:
What addition doubles fact can help you solve 4 5?.
Answers
The addition doubles fact used here is 4+4 =8 or 5+5=10
Given,
Double facts;-
Remind your kids that a double fact is a mathematical expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16. Give children the chance to practize combining groups of the same number using manipulatives or other classroom supplies.
Here,
We have to find the addition doubles fact that can help us to solve 4 + 5
Then,
⇒4+5
=4+4+1----[5=4+1]
=2 × 4 +1
=8+1
= 9
Now,
→4+5
=(5-1)+5
=5+5-1
=10-1
=9
Therefore,
The addition doubles fact used here is;
→4+4 =8
or
→5+5=10
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find the area of the surface. the part of the surface z = 5 5x 3y2 that lies above the triangle with vertices (0, 0), (0, 1), (2, 1).
Answers
To find the area of the surface z = 5 + 5x + 3y^2 above the triangle with vertices (0, 0), (0, 1), and (2, 1), we need to use the surface integral formula.
First, calculate the partial derivatives with respect to x and y:
∂z/∂x = 5
∂z/∂y = 6y
Now, compute the magnitudes of the cross product of the gradient vectors:
|∂z/∂x × ∂z/∂y| = √((5^2) + (6y)^2) = √(25 + 36y^2)
The area of the surface can be found using the double integral of the magnitudes over the triangle:
Area = ∬(√(25 + 36y^2)) dA
We'll use the triangle's vertices to set the integration limits for x and y:
x: 0 to 2 - y
y: 0 to 1
Area = ∫(y=0 to 1) ∫(x=0 to 2-y) (√(25 + 36y^2)) dx dy
Evaluating this integral will provide the area of the surface above the given triangle.
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A grocery store finds that the number of boxes of new cereal sold increases each week. In the 1st week, 24
boxes of cereal were sold. In the 2nd week, 39 boxes of cereal were sold and in the 3rd week 54 boxes of
cereal were sold. The number of boxes of cereal sold each week represents an arithmetic sequence.
A) Write the explicit rule in simplified form for the arithmetic sequence that defines the number of boxes
of cereal sold in week n. Make sure to show all steps
B) Use this rule to calculate how many boxes of cereal will be sold during the 10th week.
Answers
Answer: a)159 boxes of cereal will be sold during the 10th week, b) an = 15n + 9
Step-by-step explanation:
Given the regression equation y-hat = 15.6 - 3.8x, the predicted y for x = 3 is ___________.
Answers
Work Shown:
y = 15.6 - 3.8x
y = 15.6 - 3.8*3
y = 4.2
-3x + 5x - 2x + 5x simplifies to
Answers
Answer:
5x
Step-by-step explanation:
have a good day! :)
If there is no joint variability between two variables, then the r value will be?
Answers
Answer:
If r=0, there is absolutely no relationship between the two variables.
Step-by-step explanation:
This is 9th-grade math
Answers
The range and domain of the exponential function graphed above include:
Range = [-4, ∞].
Domain = [-∞, ∞].
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph of the exponential function above, we can reasonably and logically deduce the following domain and range:
Range = [-4, ∞] or -4 ≤ y ≤ ∞.
Domain = [-∞, ∞] or -∞ ≤ x ≤ ∞.
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Plsssssssssssssssssssssss help
This rectangular prism was built with cubes that each have a volume of one cubic centimeter. What is the volume of the rectangular prism?
Plssssssssssssssss help!!!!!!!
Answers
Answer:
32 cubic \(cm^{3}\)
Step-by-step explanation:
Since each cube is 1 by 1 we can just count blocks to get its width length and height.
Width = 2
Length = 4
Height = 4
Volume= LxWxH
Volume= 4x2x4
Volume = 32 cubic \(cm^{3}\)
HELP!!
Find the mean, median, and mode of the data.
mean:
median:
mode:
Answers
Answer: mean:4 Median: 3 mode:10
Step-by-step explanation:
Answer:
mean:4 Median: 3 mode:10
Step-by-step explanation:
Always remember this saying if you ever have this question again.
Hey diddle diddle, the median in the middle, you add and divide for the mean, the mode is the one that shows up the most, and the range is the difference in between.
if an equilaterl triangle is inscribed in a circle of a radius 8cm.then what is the area of the triangle?
Answers
The area of the triangle is 83.14 square centimeters.
How to get the area of the triangle?If an equilateral triangle is inscribed in a circle of radius R, each side of the triangle measures:
S = R*√3
In this case R = 8cm.
And we know that the area of an equilateral triangle of side length S is:
\(A = \frac{\sqrt{3} }{4} *S^2\)
Replacing what we know in the area formula:
\(A = \frac{\sqrt{3} }{4} *(\sqrt{3}*8cm)^2 = 83.14 cm^2\)
The area of the triangle is 83.14 square centimeters.
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Which three (3) characteristics are found in ALL proportional equations.
Answers
Answer: A, C and E
Step-by-step explanation:
All proportional equations or lines always go through the origin because when it's x coordinate is 0, it's y coordinate has to be 0 too.
It is also a straight line .
And k will always be the constant value, as if y = kx. K is the constant change or the slope.
C) a straight line
E)contains the point (1,k) where k is the constant
1. (2x+5)+(3x-2)=
2. (3x-2)-(2x+5)=
3. (2x+5)-(3x-2=
Answers
Answer:
5x+3x -7-x +7Step-by-step explanation:
Combine like terms. The associative and commutative properties of addition apply, as does the distributive property.
__
1. (2x+5)+(3x-2) = (2x +3x) +(5 -2) = 5x +3
__
2. (3x-2)-(2x+5) = 3x -2 -2x -5 = (3x -2x) +(-2 -5) = x -7
__
3. (2x+5)-(3x-2) = 2x +5 -3x +2 = (2x -3x) +(5 +2) = -x +7
_____
Additional comment
Note that swapping the order of operands in a subtraction problem (problems 2 and 3) will cause the sign of the result to reverse.
Answer:
1. = 5x+3
Step-by-step explanation:
Write each equation in slope intercept formI need it fast please thank you
Answers
Answer:
\(y(x)=-\frac{6}{5}x-3\)Explanation: The slope-intercept form of the linear equation is the standard form, and is written as follows:
\(y(x)=mx+b\)The given equation can be converted into slope-intercept form as follows:
\(\begin{gathered} 6x+5y=-15 \\ 5y=-6x-15 \\ y(x)=-\frac{6}{5}x-3 \end{gathered}\)Simplify \(\frac{sec(a)-csc(a)}{sec(a)+csc(a)}\)
Answers
The simplified version of (sec a - cosec a) / (sec a + cosec a) is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).
What is trigonometry?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.
Given:
(sec a - cosec a) / (sec a + cosec a)
Multiply the numerator and denominator by (sec a - cosec a)
(sec a - cosec a) / (sec a + cosec a) × (sec a - cosec a)
(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)
As we know,
\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)
sec² a cosec² a - 2sec a cosec a / (sec²a - cosec²a)
sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)
cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)
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the chart gives prices and output information for the country of new zealand. use this information to calculate real and nominal gdp for both years. use 2017 as the base year.
Answers
The nominal GDP for the year 2017 is $87,000, and the real GDP for the year 2017 is $87,000.
How to calculate real and nominal GDP?Using a base year,the formula to calculate the Real GDP is given below:
Real GDP = Nominal GDP ÷ Deflator (in decimal)
Where, Deflator = (Price of base year goods and services ÷ Price of current year goods and services) × 100
Nominal GDP for the year 2017= 1,650 × 10 + 2,820 × 25= 16,500 + 70,500= 87,000
Nominal GDP for the year 2019= 1,900 × 12 + 3,250 × 27= 22,800 + 87,750= 110,550 Using the above formula,
Deflator for the year 2017 can be calculated as:
Deflator for 2017= (P2017 / P2017) × 100= (1 × 10 + 2 × 25) / (1 × 10 + 2 × 25) × 100= 100
Similarly, Deflator for the year 2019 can be calculated as:
Deflator for 2019= (P2019 / P2017) × 100= (1.10 × 12 + 2.75 × 27) / (1 × 10 + 2 × 25) × 100= 120.25
Now, Real GDP for the year 2017= 87,000 / 100= $87,000 Real GDP for the year 2019= 110,550 / 120.25= $917.54 million.
Thus, the nominal GDP for the year 2017 is $87,000, and the real GDP for the year 2017 is $87,000. The nominal GDP for the year 2019 is $110,550, and the real GDP for the year 2019 is $917.54 million.
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Question 3 of 10
Which method for calculating credit card balances is best for consumers who
make large payments?
A. Average monthly balance method
B. Previous balance method
ОООО
C. Average daily balance method
D. Adjusted balance method
SUBMIT
Answers
Answer:
D. Adjusted balance method
Step-by-step explanation:
Which of the equations or inequalities below are true?
9 - 6 = 3
-9 + 6 > 0
-9 + 6 = 3
-9 + 6 < 0
Answers
Which is the best estimate of?
square root 35
Answers
The temperature on Wednesday was −5 degrees Celsius. By Friday the temperature fell to −10 degrees Celsius. Write and solve an equation that shows the change in temperature.
Answers
Answer: -5 + (10) = 5
Step-by-step explanation:
keep change flip -5 - (-10) you get -5 + (10) = 5