Use DeMorgan's theorems to prove that the expression A’
+ (A’ . B’ . C) is equivalent to the original expression
(A’ + B’ . C). (A’ + B’ . C’)
Answers
To prove the equivalence of the expressions \(A' + (A' \cdot B' \cdot C)\) and \((A' + B' \cdot C) \cdot (A' + B' \cdot C')\) using De Morgan's theorems, we need to apply the following two theorems:
1. De Morgan's Theorem for OR (Union):
\((X + Y)' = X' \cdot Y'\)
2. De Morgan's Theorem for AND (Intersection):
\((X \cdot Y)' = X' + Y'\)
Let's proceed with the proof:
Starting with the expression \(A' + (A' \cdot B' \cdot C)\):
1. Apply De Morgan's Theorem for AND to \(A' \cdot B' \cdot C\):
\((A' \cdot B' \cdot C)' = A'' + B'' + C' = A + B + C'\)
Now, the expression becomes \(A' + (A + B + C')\).
2. Apply De Morgan's Theorem for OR to \(A + B + C'\):
\((A + B + C')' = A' \cdot B' \cdot C'' = A' \cdot B' \cdot C\)
Now, the expression becomes \(A' \cdot B' \cdot C\).
Now, let's consider the expression \((A' + B' \cdot C) \cdot (A' + B' \cdot C')\):
1. Apply De Morgan's Theorem for OR to \(B' \cdot C'\):
\(B' \cdot C' = (B' \cdot C')'\)
Now, the expression becomes \((A' + B' \cdot C) \cdot (A' + (B' \cdot C')')\).
2. Apply De Morgan's Theorem for AND to \((B' \cdot C')'\):
\((B' \cdot C')' = B'' + C'' = B + C\)
Now, the expression becomes \((A' + B' \cdot C) \cdot (A' + B + C)\).
Expanding the expression further:
\((A' + B' \cdot C) \cdot (A' + B + C) = A' \cdot A' + A' \cdot B + A' \cdot C + B' \cdot C' + B' \cdot B + B' \cdot C + C \cdot A' + C \cdot B + C \cdot C\)
Simplifying the terms:
\(A' \cdot A' = A'\) (Law of Idempotence)
\(B' \cdot B = B'\) (Law of Idempotence)
\(C \cdot C = C\) (Law of Idempotence)
The expression becomes:
\(A' + A' \cdot B + A' \cdot C + B' \cdot C' + B' + B' \cdot C + C \cdot A' + C \cdot B + C\)
Now, let's compare this expression with the original expression \(A' + (A' \cdot B' \cdot C)\):
\(A' + A' \cdot B + A' \cdot C + B' \cdot C' + B' + B' \cdot C + C \cdot A' + C \cdot B + C\)
This expression is equivalent to the original expression \(A' + (A' \cdot B' \cdot C)\).
Therefore, we have proven that the expression ’
+ (A’ . B’ . C) is equivalent to the original expression
(A’ + B’ . C). (A’ + B’ . C’)
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Related Questions
A number reduced by two, then multiplied by 9
Answers
(x-2)9
9x-18
good luck <33
3. Find the value of x and explain your reasoning
(4x - 8)
(3x + 10) (11x + 2y)º
Answers
The question is an illustration of angles on a straight line
The value of x is 25.4
How to determine the value of xIn the figure, angles 1 and 2 are angles on a straight line
Where:
Angle 1 = 4x - 8Angle 2 = 3x + 10So, we have:
\(4x - 8 + 3x + 10=180\)
Collect like terms
\(4x + 3x =180 - 10 + 8\)
\(7x =178\)
Divide through by 7
\(x =25.4\)
Hence, the value of x is 25.4
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When Mr. Tallchief reaches his retirement age of 65, he expects to have a retirement account worth of about $400,000. One month after he retires, and every month thereafter, he intends to withdraw 4,000 from the account. The balance will be invested at 9% anual interest compounded monthly.
a. Let An represent the amount in the account n months after Mr. Tallchief's retirement. Give a recursive definition for An
b. When will there be no money left in the account
Answers
The amount will become zero after 400 months.
Given that, Mr. Tallchief have $400,000 in his account after his retirement,
He intends to withdraw 4,000 from the account every month after the retirement,
We need to find the equation that represents the amount in the account n months after his retirement.
So,
f(n) = 400,000 - 4000n
This equation will give the withdrawal of money each month,
Now, when the account will have no money in it,
A = 0,
0 = 400,000 - 4000n
400,000 = 4000n
n = 400
Hence, the amount will become zero after 400 months.
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A new Outdoor Recreation Center is being built in Hadleyville. The perimeter of the rectangular playing field is 318 yards. The length of the field is 5 yards less than
triple the width. What are the dimensions of the playing field?
yards.
Answers
Answer:
41 yards by 118 yards
Step-by-step explanation:
Let W and L be the Width and Length of the playing field:
The perimeter, P, would be P = 2W + 2L
We are told that P = 318 yards.
We learn that L = 3W - 5
Combining this information, we can say:
P = 2W + 2L [Oriinal equation]
318 = 2W + 2L [P is 318]
318 = 2W + 2(3W-5) [ Use the definition of L = 3W - 5]
318 = 2W + 6W - 10
328 = 8W
W = 41 yards
Use this value of W to find L:
L = 3W - 5
L = 3(41) - 5
L = 123 - 5
L = 118
CHECK
Does 2*(118) + 2*(41) = 318? YES
Is the length 5 yards less than triple the width?
3*(41) - 5 = 118 YES
What happened
Ok so I logged off an hour ago and had 1000 points and 100 questions answered and 12 BRAINLIEST
Why is it now 24 points 0 answers and 0 BRAINLIEST
Srry it’s only for 10 points I don’t have a lot of points
Also I’m still an expert
Answers
a schematic diagram that uses symbols to represent the parts of a system is a(n) ____.
Answers
A schematic diagram that uses symbols to represent the parts of a system is called a schematic or a circuit diagram.
A schematic diagram is a type of diagram that represents a system or process using symbols, lines, and other graphical elements. The purpose of a schematic diagram is to convey information about a system or process in a clear and concise manner, making it easier to understand and analyze.
Schematic diagrams are commonly used in fields such as electrical engineering, mechanical engineering, and process engineering. They may be used to depict a wide range of systems or processes, including electronic circuits, hydraulic systems, HVAC systems, and manufacturing processes, among others.
In a schematic diagram, symbols are used to represent various components or elements of the system or process being depicted. For example, in an electrical circuit schematic, symbols might be used to represent resistors, capacitors, diodes, and other electronic components. Lines and other graphical elements are used to show the connections and interactions between the different components.
Schematic diagrams are an important tool in the design, analysis, and troubleshooting of systems and processes. They allow engineers and other professionals to quickly and easily understand the workings of complex systems, identify potential problems, and develop solutions.
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Determine the cost of the points given the loan, interest rate, and number of points
purchased. Assume each point costs 1% of the loan amount:
$300,000, 4.4% APR, 1 points with 0.125% discount
Answers
The borrower would pay $3,000 for one point, which would result in a reduction of 0.125% on the interest rate, bringing it down to 4.3945%.
To determine the cost of the points in this scenario, we need to calculate 1% of the loan amount ($300,000), which is $3,000. Since the borrower is purchasing one point, the cost of the point would be $3,000.
Additionally, the borrower is receiving a discount of 0.125% on the interest rate for purchasing this point. To calculate the new interest rate after the discount, we can multiply the original interest rate (4.4%) by the discount percentage (0.125%), which gives us a reduction of 0.0055. We can then subtract this reduction from the original interest rate to get the new rate:
4.4% - 0.0055 = 4.3945%
So the borrower would pay $3,000 for one point, which would result in a reduction of 0.125% on the interest rate, bringing it down to 4.3945%.
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After t seconds the height s of an object propelled upward with an initial velocity of 3200 feet per second is given by s = 3200t - 16t^2. How long after the object is propelled upward will it first reach an altitude of 51,000 feet? (Round your answer to two decimal places.)
Answers
The object will first reach an altitude of 51,000 feet approximately 199.24 seconds after it is propelled upward.
To find the time it takes for the object to reach an altitude of 51,000 feet, we need to set the height equation equal to 51,000 and solve for time (t):
\(s = 3200t - 16t^2\\51,000 = 3200t - 16t^2\)
To solve this quadratic equation, we rearrange it to the standard form:
16t^2 - 3200t + 51,000 = 0
Next, we can either factorize or use the quadratic formula. Let's use the quadratic formula:
\(t = (-b \pm \sqrt(b^2 - 4ac)) / (2a)\)
Plugging in the values from the equation:
\(t = (-(-3200) \pm \sqrt((-3200)^2 - 4(16)(51,000))) / (2(16))\)
Simplifying:
\(t = (3200 \pm \sqrt(10,240,000 - 32,640)) / 32\\t = (3200 \pm \sqrt10,207,360) / 32\\t = (3200 \pm 3,195.80) / 32\)
Now we solve for the two possible values of t:
t₁ = (3200 + 3,195.80) / 32 ≈ 199.24
t₂ = (3200 - 3,195.80) / 32 ≈ 0.05
The negative value of t₂ is not physically meaningful in this context, so we discard it.
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Yosef typed a 48-word paragraph in 1/3 minute. What is his typing speed, in words per minute? I’m desperate please help me
Answers
Answer:
54 Words Per Minute
Hope I helped!
Please help me with this!!!
Answers
Answer:
x = 3 and y = 8
Step-by-step explanation:
The Opposite sides of a parallelogram are equal and parallel. It means,
\(\dfrac{y}{2}=4\\\\y=8\)
Also,
5x - 6 = 3x
Taking like terms together,
5x -3x = 6
2x = 6
x = 3
So, the values of x and y are 3 and 8 respectively.
simplify. 5 - 8 ÷ 2 + 4
Answers
Answer:
5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
5 - 8 ÷ 2 + 4
Step 2: Simplify
Division: 5 - 4 + 4Subtract: 1 + 4Add: 5Katie and Lukas write equations showing the proportional relationship between the number of ants, a, and the number of ant legs, 1. Katie writes a=6•1 and Lukas writes a=1/6•1 whose equation do u agree with
Answers
the number of ants is equal to 6 times the number of ant legs. Therefore, I agree with Katie's equation
Katie's equation is a=6•1, which states that the number of ants (a) is equal to 6 times the number of ant legs (1). Lukas's equation is a=1/6•1, which states that the number of ants (a) is equal to 1/6 of the number of ant legs (1). Since it is known that each ant has 6 legs, Katie's equation is correct, and therefore I agree with it.
The correct equation for the proportional relationship between the number of ants and the number of ant legs is a=6•1, which states that the number of ants is equal to 6 times the number of ant legs. Therefore, I agree with Katie's equation
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Answer the photo below thanks
Answers
Answer:
A . 496 ft²
Step-by-step explanation:
Area = ½ × base × height
= ½ × 62 × 16
=496 ft²
A car dealership is holding a contest for people who are in line before 6 a.m. The people who are 57 places before and after the 153rd
person win a new car. Based on this information, which equation can be used to find the two winners of the new car?
Answers
The equations x - 57 and x + 57 can be used to find the positions of the two winners of the new car, where x represents the Position of the 153rd person in line.
Based on the given information, we can determine the equations to find the two winners of the new car.
The position of the 153rd person in line as x. Since the people who are 57 places before and after the 153rd person win the new car, we can write the following equations:
1. For the person 57 places before the 153rd person: x - 57
This equation represents the position of the person who is 57 places before the 153rd person in line.
2. For the person 57 places after the 153rd person: x + 57
This equation represents the position of the person who is 57 places after the 153rd person in line.
By substituting the value of x (the position of the 153rd person) into these equations, we can find the positions of the two winners in line.
For example, if the 153rd person is in the 200th position in line (x = 200), we can determine the winners as follows:
1. For the person 57 places before the 153rd person: 200 - 57 = 143
The person in the 143rd position is the winner of the new car.
2. For the person 57 places after the 153rd person: 200 + 57 = 257
The person in the 257th position is the second winner of the new car.
Thus, the equations x - 57 and x + 57 can be used to find the positions of the two winners of the new car, where x represents the position of the 153rd person in line.
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Find the critical value a corresponding to a sample size of 10 R and a confidence level of 95 percent. O 0.103 7.378 3.325 19.023
Answers
The critical value 'a' for a 95% confidence level and sample size 10 (n=10) is 2.306. Therefore, none of the above options is correct.
Given information:
Sample size (n) = 10
Confidence level = 95%
The critical value 'a' for a 95% confidence level and sample size 10 (n=10) is 2.306.
Therefore, none of the above options is correct.
The critical value is the z-score that separates the middle 95% of the normal distribution from the outer 5% of the normal distribution. The z-score can be calculated using the following formula:
z = (x - μ) / σ
Where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.In this case, we do not have the population mean (μ) and standard deviation (σ).
But since n = 10, we can use the t-distribution instead of the standard normal distribution.
The formula for the t-score is: z = (x - μ) / s/√n
Where s is the sample standard deviation.In this case, we do not have the sample standard deviation either. So we need to use the t-distribution with n-1 degrees of freedom to estimate the critical value 'a'. The critical value 'a' for a 95% confidence level and sample size 10 (n=10) is 2.306.
Therefore, none of the above options is correct.
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I WILL MARK BRAIN HELPP!!Lucas wants to write
3
÷
2
as a mixed number. He performs the division below.
3
÷
2
=
1
R
1
Explain how to write the quotient as a mixed number.
Drag the words to complete the explanation. Words may be used once or not at all.
quotientremainderdivisordividend
Use the whole number part of the
as the whole number part of the mixed number.
Write the
in the numerator of the fraction and write the
in the denominator of the fraction.
Answers
Answer:
1st blank: quotient
2nd blank: remainder
3rd blank: divisor
Step-by-step explanation:
This is saying the whole part of the division answer is the big number of the mixed number. The remainder goes on top of the fraction part of the answer and the "dividedby" guy (or the outside number if you do that kind of division) is the bottom number of the fraction part of the mixed number.
Please help me with this math problem!! :) Will give brainliest!!
Answers
Answer:
Step-by-step explanation:
it is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant. it is linear because the function is continuous. it is nonlinear because the final cost is determined by multiplying each price tag by 0.75. it is nonlinear because the price tag and final cost columns do not have the same common difference.
Answers
A statement which best describes the function that represents the situation include the following: A) It is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant.
What is a linear function?In Mathematics and Geometry, a linear function refers to a type of function whose equation is graphically represented by a straight line on the xy-plane or cartesian coordinate.
This ultimately implies that, a linear function has the same (constant) slope or ratio of change and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.
In this context, we have the following linear function;
F = 0.75x
where:
F represents the final cost in dollars.
x represents the price on the tag in dollars.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
2. compute the following summary statisticsa) the mean for the low income group is: b) the median for the low income group is: c) the standard deviation for the low income group is: d) the mean for the high income group is: e) the median for the high income group is: f) the standard deviation for the high income group is:
Answers
The mean for the low income group is the average of all the values in the group.
It is calculated by adding up all the values and then dividing by the total number of values. In the low income group, the mean is calculated by adding up all the incomes, and then dividing by the total number of people.
The median for the low income group is the middle value when all the values are arranged in order. To calculate the median, first arrange the incomes in order from lowest to highest, and then find the middle value.
The standard deviation for the low income group is a measure of how spread out the values are. It is calculated by taking the square root of the variance, which is calculated by taking the average of the squared difference between each value and the mean, and then dividing by the number of values.
The mean for the high income group is the average of all the values in the group. It is calculated by adding up all the values and then dividing by the total number of values. In the high income group, the mean is calculated by adding up all the incomes, and then dividing by the total number of people.
The median for the high income group is the middle value when all the values are arranged in order. To calculate the median, first arrange the incomes in order from lowest to highest, and then find the middle value.
The standard deviation for the high income group is a measure of how spread out the values are. It is calculated by taking the square root of the variance, which is calculated by taking the average of the squared difference between each value and the mean, and then dividing by the number of values.
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Markus decides to return 4 shirts costing $19 each to a clothing store. While there, he decides to purchase 2 pairs of shoes at $45 each and a raincoat for $62.75. The clerk charges him 5% tax on the amount due after returns. What amount does he owe the clerk?
Answers
Answer:
$80.59
Step-by-step explanation:
You add the price of the raincoat and shoes to get 152.75, you then subtract the price of the 4 shirts you returned to get 76.75. The 5% tax for this is 3.84 so you add the two together and you get $80.59.
check your solution for 12(2w-3)=6w
Answers
Answer:
w=2
and how I got the answer is here
i just wanted to say thank you to everyone who helped me with my exam questions yesterday & this whole school year and i appreciate you all :)
i passed because of you guys!
Answers
Answer:
Hey, I'm so happy for you! :D
Step-by-step explanation:
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Mia's food delivery service is $0.65 per mile. She also charges an $8 fee for gas needed to get there. Write an expression to show the cost of her services per mile, m.
Answers
The cost of Mia's food delivery service per mile is $8.65.
To calculate the cost of Mia's food delivery service per mile, we need to consider two components: the cost per mile and the fixed gas fee.
Let's define the cost per mile as 'C' and the fixed gas fee as 'F'. Given that Mia's food delivery service is $0.65 per mile and she charges an $8 fee for gas, the expression for the cost of her services per mile, 'm', can be written as follows:
m = C + F
Substituting the given values into the expression:
m = $0.65 per mile + $8
Simplifying, we have:
m = $0.65 + $8
Combining the terms, the expression for the cost of Mia's services per mile is:
m = $8.65
Therefore, the cost of Mia's food delivery service per mile is $8.65.
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What are the two components of the EIA and what is the role in
planning a dam projects? Discuss NEMA.What is EMP and EA?
Answers
The two components of the EIA (Environmental Impact Assessment) are the Environmental Management Plan (EMP) and the Environmental Assessment (EA).
the role of the EIA in planning dam projects is to assess the potential environmental impacts of the project and propose measures to mitigate or minimize these impacts. The EIA helps in identifying potential environmental risks, evaluating the project's potential effects on ecosystems, and suggesting ways to manage and reduce negative impacts.
NEMA (National Environmental Management Authority) is a regulatory body responsible for overseeing and enforcing environmental policies and regulations in a country. In the context of dam projects, NEMA plays a crucial role in ensuring that the project complies with environmental standards and regulations. NEMA reviews and approves the EIA reports submitted by project developers and ensures that the proposed measures in the EMP are adequate for mitigating the project's environmental impacts.
The EMP (Environmental Management Plan) is a document that outlines the specific actions and measures that will be implemented during and after the project to minimize and manage the environmental impacts. It includes strategies for monitoring, control, and mitigation of potential adverse effects on the environment. The EMP provides a roadmap for environmental management throughout the project's lifecycle, ensuring that environmental concerns are addressed effectively.
The EA (Environmental Assessment) is the process through which the potential environmental impacts of a proposed project are identified, evaluated, and communicated. It involves collecting data, conducting studies, and assessing the potential effects on various aspects such as air quality, water resources, biodiversity, and social aspects. The EA also involves engaging stakeholders and seeking their inputs to ensure a comprehensive evaluation of the project's impacts.
In summary, the EIA consists of the EMP and EA. The EMP focuses on the management and mitigation of environmental impacts, while the EA is the process of assessing and evaluating the potential environmental effects of a project. NEMA plays a crucial role in overseeing the implementation of the EIA process and ensuring compliance with environmental regulations.
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whats the opposite of -3 pls :)
Answers
Answer:
positive 3
Step-by-step explanation:
answer- positive 3
Answer:
Th opposite is positive 3
Step-by-step explanation:
Since it is -3 the opposite of a positive, it would be positive 3 (3)
Hope this helps!
Can anyone help with this? Thanks
Answers
The surface area of the prism is 1440 mm²
Given,
Triangular prism
Height of the prism = 32 mm
Base of the prism = 24 mm
Length of the prism = 7 mm
We have to find the surface area of the prism;
Surface area, SA = bh + (b₁ + b₂ + b₃) l
Here,
Base, b = 24 mm
Height, h = 32 mm
Length, l = 7 mm
b₁ = 24 mm
b₂ = 32 mm
b₃ = \(\sqrt{b_{1} ^{2} + b_{2} ^{2} }\) = \(\sqrt{24^{2}+ 32^{2} }\) = \(\sqrt{576 + 1024}\) = √1600 = 40 mm
Then,
Surface Area = bh + (b₁ + b₂ + b₃) l
SA = 24 x 32 + (24 + 32 + 40) 7
SA = 768 + 96 x 7
SA = 768 + 672
SA = 1440 mm²
That is,
The surface area of the prism is 1440 mm²
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Is the equation 3x² 7y 13 a linear equation in 2variables?
Answers
This is not a two-variable linear equation.
If an equation is written in the form axe + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., When both a and b, in turn, do not equal zero, an equation with two variables is said to be linear. Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalizes the two sides of the equation.
Given equation,
\(3x^{2} -7y=13\)
In this case, the variable x's degree is 2.
Hence, this is not a two-variable linear equation.
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AYUDAAAA, LES DOY CINCO ESTRELLAS SI LO RESUELVEN BIEN
Answers
dividido por la epotenusa es 7 :v
how many permutations are there of the letters in the word ""peppermint""?
Answers
There are a total of 720 permutations of the letters in the word "peppermint".
To calculate this, we use the formula n!/(r! * (n-r)!) where n is the number of objects (in this case, letters) and r is the number of objects chosen from that set. In this case, n = 10 (10 letters in "peppermint") and r = 10 (all 10 letters are chosen).
So, 10!/(10! * (10-10)!) = 10!/(10! * 0!) = 10!/(10!) = 1, which simplifies to 1. That means that there is one way to choose all 10 letters from the word "peppermint", so the total number of permutations is 1 * 10! = 10! = 3628800, or 720.
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Solve
x2 + x - 56 = 0
Answers
The answer would be 2x1=x so x would be 2
Step-by-step explanation:
Answer:
x = 7, - 8
Step-by-step explanation:
x^2 + x - 56 = 0
x^2 + 8x - 7x - 56 = 0
x ( x + 8 ) - 7 ( x + 8 ) = 0
( x - 7 ) ( x + 8 ) = 0
x - 7 = 0
x = 7
x + 8 = 0
x = - 8