The logical statement [tex]$(a \wedge b) \rightarrow(b \vee c)$[/tex] is a tautology. Hence, Option B is the most appropriate answer to the given question.
A tautology is a logical statement where the conclusion is always equivalent to the premise. No matter what the individual parts are, the result is always a true statement; i.e. a tautology is always true. The opposite of tautology is either a contradiction or a fallacy.
a. let us check the first option.
[tex](a \vee b) \rightarrow(b \wedge c)=(a+b)^{\prime}+b c[/tex]
[tex](a \vee b) \rightarrow(b \wedge c)=a^{\prime} b^{\prime}+b c[/tex]
Therefore, [tex]$(a \vee b) \rightarrow(b \wedge c)$[/tex] is a contingency and not a tautology.
b. let us check the second option.
[tex](a \wedge b) \rightarrow(b \vee c)=a b \rightarrow b+c[/tex]
[tex](a \wedge b) \rightarrow(b \vee c)=(a b)^{\prime}+b+c[/tex]
[tex](a \wedge b) \rightarrow(b \vee c)=a^{\prime}+b^{\prime}+b+c[/tex]
[tex](a \wedge b) \rightarrow(b \vee c)=a^{\prime}+1+c[/tex] (since, b' + b = 1)
[tex](a \wedge b) \rightarrow(b \vee c)=1.[/tex]
Therefore, [tex]$(a \wedge b) \rightarrow(b \vee c)$[/tex] is a tautology.
c. let us check the third option.
[tex](a \wedge b) \rightarrow(b \rightarrow c)=(a+b) \rightarrow\left(b^{\prime}+c\right)[/tex]
[tex](a \wedge b) \rightarrow(b \rightarrow c)=(a+b)^{\prime}+b^{\prime}+c[/tex]
[tex](a \wedge b) \rightarrow(b \rightarrow c)=a^{\prime} b^{\prime}+b^{\prime}+c[/tex]
[tex](a \wedge b) \rightarrow(b \rightarrow c)=b^{\prime}+c[/tex]
Therefore, [tex]$(a \wedge b) \rightarrow(b \rightarrow c)$[/tex] is contingency but not a tautology.
d. let us check the fourth option.
[tex](a \rightarrow b) \rightarrow(b \rightarrow c)=\left(a^{\prime}+b\right) \rightarrow\left(b^{\prime}+c\right)[/tex]
[tex](a \rightarrow b) \rightarrow(b \rightarrow c)=\left(a^{\prime}+b\right)+b^{\prime}+c[/tex]
[tex](a \rightarrow b) \rightarrow(b \rightarrow c)=a b^{\prime}+b^{\prime}+c[/tex]
[tex](a \rightarrow b) \rightarrow(b \rightarrow c)=b^{\prime}+c[/tex]
Therefore, [tex]$(a \rightarrow b) \rightarrow(b \rightarrow c)$[/tex] is contingency but not a tautology.
Hence, option B is the only example of tautology.
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02.03 Focus Questions- please help 50+ points
What are linear equations and functions?
What are the different ways of representing a linear function?
How are key features of a linear function identified and interpreted from a graph?
How are key features of a linear function identified and interpreted from a table?
How are key features of a linear function identified and interpreted from an equation?
How are key features of a linear function identified and interpreted from a description?
Step-by-step explanation:
first of all, a function is an equation.
it associates a function result variable (typically called y) with a calculation based on an input variable (usually caked x), or in more complex mathematics based on a group of input variables.
but not every equation is a function. to be a function every valid x value must have exactly one associated y value.
e.g. x = 5 is an equation. but it does not restrict y in any way. so, any value of y (infinitely many) is valid for x = 5.
therefore, this is not a function.
a linear equation/function is a straight line (hence the name).
it is characterized by an inclination (typically called slope or rate of change) and its absolute position typically incentives by the interception points particularly with the y-axis on a coordinate grid.
there are various ways to describe a line in a formal way.
the slope-intercept form :
y = ax + b
a being the slope, b being the y-intercept (y-value when x = 0).
the point-slope form
y - y1 = a(x - x1)
again, a is the slope, (x1, y1) is an identified point (coordinates) on the line.
the general (often called standard) form
gx + hy = c
g, h, c are not describing anything directly, but after transforming this standard form they build the "a" and "b" terms of the other forms.
the slope is the ratio of (y coordinate change / x coordinate change) when going from one point on the line to another. for a line this is constant for any pair of points you can pick on the line.
in other words it tells us how many units y changes, when x changes by a certain amount of units
basically, a line is the collection of all the points for which the given equation is true (when using the x coordinate in the equation we get the corresponding y as calculation result, or when using x and y of any point on the line in the equation, then the equation is true).
graph :
the slope is found by checking 2 points and calculating the y diff / x diff ratio. e.g. starting with (0, 0) if that point is in the line, we increase x by 1 and check the y value there : (1, y).
so, the slope is for that example (y - 0)/(1 - 0) = y.
the y-intercept is found by checking the y-value for x = 0.
the y-interception point is therefore (0, b).
the x-intercept is the x-value when y = 0.
the x-interception point is therefore (x-intercept, 0).
table :
for the slope we pick again 2 data points of the table and calculate y diff / x diff.
as explained this has to be constant for any picked pair of data points of the table. then you know it is a linear equation.
if we are lucky, the table contains data points with x = 0 and/or y = 0. then we have the corresponding intercept values.
but if not, we need to use the coordinates of 1 point in the e.g. slope-intercept form to create an equation with 1 variable : b. and then we solve it to get b.
equation :
we need to bring the equation into a form that we get
y = ...
then the factor of x is the slope. and the constant term (even if it is not there, as it means it is 0) defines the y-intercept
everything else is as described above
description :
the description needs to give us either data points or an indication about the slope and the y-intercept.
when we have 2 points, we can define a line through them. in other words, any pair of points defines a line.
points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints. is the meaning of _____
Points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints is the meaning of perpendicular bisector theorem
The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment ,then it is equidistant from the segment's endpoints.
The perpendicular bisector of a triangle is the line segment that is drawn from a vertex to the opposite side bisecting the side at a right angle. The perpendicular of a triangle is perpendicular to the sides drawn from the opposite vertices and divides the sides into two equal parts. The point at which all the three perpendicular bisectors of a triangle meets is called the circumcenter of a triangle.
It is the meaning of perpendicular bisector theorem.
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Sam tested every 50th candy bar from the assembly line to make sure there were enough peanuts in each bar. He found 15% did not have enough peanuts. How many candy bars do not have enough peanuts if the factory produces 20,000 candy bars?.
Here every 50th candy bar is tested . It is a sampling interval .
What does "systematic sampling" mean?
Systematic sampling is a probability sampling technique where researchers choose individuals from the population at regular intervals, such as every 15th person on a population list.
The advantages of simple random sampling can be imitated if the population is arranged randomly.
Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval.
Here every 50th candy bar is tested . It is a sampling interval .
Therefore he use systematic sampling plan.
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Shawna bought an antique writing
desk marked down from $6,116 to
$1,951. What percentage is the
discount?
(round your answer to the nearest percent)
Percent changes are measured by (the change in amount) divided by (the starting amount).
In this case, you'd have
[tex]\dfrac{6116-1951}{6116}=\dfrac{4165}{6116}\approx 0.6810[/tex]
This is about a 68% discount.
All the gummy machines at a candy factory work at the same rate: Six machines working simultaneously can complete big order in 22 hours. How many hours would it take t0 fill the order if the number of working machines decreased by a factor of 2? er: hours
The numbers of hours taken to fill the order if the number of working machines decreased by a factor of 2 is; 44 hours
How to find the rate of work?We are given;
Numbers of hours a work is complete by 6 machines = 22 hours
Now, we know that the number of hours required to complete a work is inversely proportional to the number of machines used.
Therefore, If the number of working machines decreased by a factor of 2, then the number of hours will be increased twice.
Therefore, we can say that;
The numbers of hours taken to fill the order = (22 * 6)/3
= 44 hours
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part 2 of important test, all solutions need to be the same
helppp
The solution of the quadratic equation using the quadratic formula is
x = 4 + 2√6 or 4 - 2√6
How to solve a quadratic equation using quadratic formula?The quadratic formula is a formula used to solve quadratic equations, which are equations of the form ax² + bx + c = 0 where a, b, and c are constants. The quadratic formula is:
x = (-b±√(b²-4ac))/(2a)
Given: x² - 8x - 84 = 0
Here, a = 1, b = -8 and c = -84
x = (-b±√(b²-4ac))/(2a)
x = [-(-8)±√((-8)²-[4×1×(-8)])]/(2a)
x = [8±√(96)]/2
x = (8± 4√6)/2
x = 4 ± 2√6
x = 4 + 2√6 or 4 - 2√6
Thus, the solution is x = 4 + 2√6 or 4 - 2√6
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Help me please…20points!!
Answer:
The answer is b . the first was appel and the second was blackberry
1. Given the data: 12, 14, 21, 19, 25, 29, 26,
21, 15, and 18. Calculate the standard deviation,
the mean, and the interquartile range using the
calculator.
For the data 12, 14, 21, 19, 25, 29, 26, 21, 15, and 18.
the mean is 20
the standard deviation is 3.7
the interquartile is 10
How to solve for the meanFor the data 12, 14, 21, 19, 25, 29, 26, 21, 15, and 18. the mean is calculated as follows
= sum of data / number of data
sum = 200
number of data = 10
mean (x bar) = 200 / 10
= 20
standard deviation
standard deviation is the square root of the ratio of sum of squares to number of samples
sum of squares = (x - x bar)²
= (12 - 20)² + (14 - 20)² + (21 - 20)² + ......+(21 - 20)² + (15 - 20)² + (18 - 20)²
= 274
standard deviation = √(274 / 20) = 3.7
Interquartile range = upper quartile - lower quartile
raw data = 12, 14, 21, 19, 25, 29, 26, 21, 15, and 18
arranged data = 12, 14, 15, 18, 19, 21, 21, 25, 26, 29,
upper quartile = 25
lower quartile = 15
Interquartile range = 25 - 15 = 10
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The price of a new phone is $960.00 and the rate of tax is 7.6%.what is the amount of sales tax?
Answer: $72.96
Step-by-step explanation:
7.6% = 0.076
Take 960.00 times 0.076 = $72.96
a party store has 54 packs of plates in stock. the packs are either sets of 8 or sets of 12. if the store has 496 total plates in stock, how many plates would a customer but if he or she buys all of the packs of 12 that the store has in stock?
If the customer purchases every pack of 12 which the shop has 192 plates in stock.
Explain the method of substitution?Three steps make up the substitution technique: For each of the variables, solve one equation. Put this expression (or plug it in) into the other equation, then solve it. To identify the matching variable, rewrite the value's original equation.Total number of packs of plates = 54.
The set are either sets of 8 or sets of 12.
Let x represent the overall number of 12-plate packets.
There will therefore be in total packs of 8 plates: 54 - x.
Thus,
8(54−x) + 12x = 496
432 − 8x + 12x = 496
4x = 64
x = 16
Thus, there are 16 packs of 12 plates in the store.
So, if a consumer purchases all of the 12-packs of plates, he will ultimately purchase 1216 = 192 plates.
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write an equation of the circle with center (-6,8) and radius 9
Answer:
(x + 6)^2 + (y - 8)^2 = 81
Step-by-step explanation:
6(x - 3)2(4x - 3) = 6
0x = 3
0x = -9
0x = 4
0x = 9
The two possible solutions for the given equation are -
[x] = 0.696 and [x] = 3.054.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is the equation as follows -
6(x - 3).2(4x - 3) = 6
We have the equation as -
6(x - 3).2(4x - 3) = 6
12(x - 3)(4x - 3) = 6
(x - 3)(4x - 3) = 6/12
(x - 3)(4x - 3) = 1/2
x(4x - 3) - 3(4x - 3) = 1/2
4x² - 3x - 12x + 9 = 1/2
4x² - 15x + 9 = 1/2
2(4x² - 15x + 9) = 1
8x² - 30x + 18 = 1
8x² - 30x + 17 = 0
(x - 0.696)(x - 3.054) = 0
(x - 0.696) = 0 and (x - 3.054) = 0
x = 0.696 and x = 3.054
Therefore, the two possible solutions for the given equation are -
[x] = 0.696 and [x] = 3.054.
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A cell phone is originally priced at $120. The store owner gives a discount and the cell phone is now priced at $90. Find the percentage discount for the cost of the cell phone,.
Answer:
25%
Step-by-step explanation:
To find the percentage discount for the cost of the cell phone, we need to first find the difference between the original price and the discounted price:
$120 - $90 = $30
Then we need to divide this amount by the original price and multiply by 100% to express the result as a percentage:
($30 / $120) * 100% = 25%
Therefore, the percentage discount for the cost of the cell phone is 25%.
Simplify: -3x + 6 - 3x - 24 + 2y
-6x + 2y - 18
2y - 18
6x + 2y - 30
None of these choices are correct.
Answer:
To simplify the expression -3x + 6 - 3x - 24 + 2y, you can start by combining like terms.
-3x and -3x are both negative, so they can be combined to give -6x.
6 and -24 are both constants, so they can be combined to give -18.
So the simplified expression is: -6x - 18 + 2y
If you want to write the expression in standard form, you can rearrange the terms to give: 2y - 6x - 18
CORRECT ME IF I'M WRONGthe interest charged on a $50,000, 60-day note payable, at the rate of 6%, would be
If the interest charged on a $50,000, 60-day note payable, at the rate of 6%, would be $500.
In the given question, we have to find the interest charged on a $50,000, 60-day note payable, at the rate of 6%.
The note payable = $50,000
Rate = 6% = 0.06
Period outstanding = 60
The total interest formula is a way to calculate the total simple interest on a sum of money over time at a specific interest rate.
Total Interest charged = Note Payable * rate * period outstanding
Total Interest charged = $50,000 * 0.06 * 60/360
Total Interest charged = $500
Hence, if the interest charged on a $50,000, 60-day note payable, at the rate of 6%, would be $500.
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A questionnaire was given to students. The first question asked was "How stressed have
you been in the last week on a scale of 0 to 10 with O being not stressed at all and 10
being as stressed as possible?" The responses are shown to the right.
a. Stress rating describes the greatest number of students is: 8 out of 10
b. There are 156 students that responded with this rating.
How to calculate the stress rating?A questionnaire is a research tool made up of a list of questions used to collect data from respondents during a survey or statistical analysis. Typically, a research questionnaire will contain both closed-ended and open-ended questions.
From the table, the total students will be the addition and this will be:
= 6 + 2 + 5 - 16 + 20 + 20 + 11 + 21 + 24 + 19 + 12
= 156
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Find the lengths of the hypotenuses (x) of the triangle whose legs are given
1) 8cm,15cm
Answer:
hypotenuse is 17cm
Step-by-step explanation:
According to Pythagoras theorem,
AC²=AB²+BC²
AC² = 8²+15²
AC = √64+225
AC =√ 289
AC =17cm
45 − (−28) = A) −73 B) −17 C) 63 D) 73
Answer:
(d) 73
- and - are plus so 45+28
Step-by-step explanation:
Answer:
D) 73
Step-by-step explanation:
-)- basically means plus so 45 + 28 is ... 73,so that's your answer!
In the figure above, is AB || CD?
1. If m 2 5 = 30 and m 2 3 = 150?
A. Yes because angles 5 and 3 are same-side interior angles.
B. Yes because angles 5 and 3 are alternate interior angles.
C. Yes because angles 5 and 3 are vertical angles.
OD. No because angles 5 and 3 are vertical angles.
O E. No because angles 5 and 3 are corresponding angles.
F. No because angles 5 and 3 are alternate interior angles.
Answer:
the answer is yes because angles 5 and 2 are same side interior angles and same side interior angles add up to 180*.
Step-by-step explanation:
Make sure not to be fooled by the "it looks like it" theorem. Teachers will try to trick you by making the lines look not parallel. All you need to look at are if the angles are congruent or supplementary based on the theorems you hopefully were taught in class. Wow what has brainly done I sound like a teacher lol.
Select all the correct answers. which two equations can you use to find the adult and child admission fees for a puppet show? let a represent the fee for adults and c represent the fee for children. adults children admissions collected day 1 45 30 $315 day 2 50 40 $370 45c 30a = 315 45a 50c = 315 45a 30c = 315 50c 40a = 370 50a 40c = 370
The two equations can you use to find the adult and child admission fees for a puppet show are 45a + 30c = 315 and 50a + 40c = 370
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, two equations can you use to find the adult and child admission fees for a puppet show
Let a represent the fee for adults
Let c represent the fee for children.
On day 1 number of adults = 45
So, fees of 45 adults = 45a
On day 1 number of children= 30
So, fees of 30 children = 30c
Total collection on day 1 = 315
Therefore, equation is 45a + 30c = 315
On day 2 number of adults = 50
So, fees of 50 adults = 50a
On day 2 number of children = 40
So, fees of 40 children = 40c
Total collection on day 2 = 370
So, equation = 50a + 40c = 370
Hence, The two equations can you use to find the adult and child admission fees for a puppet show are 45a + 30c = 315 and 50a + 40c = 370
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The three perpendicular bisectors of a triangle intersect in one point called the: _______
Mr. Croland aked tudent to factor the expreion 28x−8
28
x
−
8. The tudent offered the anwer hown in the box. Which tudent() offered anwer() equivalent to the original expreion?
The students who offered the answer equivalent to original expression are Carlos and Irene.
The original expression can be traced back by solving the solution of each student. Thus, taking each solution.
Carlos
Performing multiplication of the solution
Expression = 2(14x - 4)
Expression = 28x - 8
Danny
Performing multiplication of the solution
Expression = 7(4x - 1)
Expression = 28x - 7
Irene
Performing multiplication of the solution
Expression = 4(7x - 2)
Expression = 28x - 8
Thus, Carlos and Irene gave the correct factors of the original expression.
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The complete question is -
Mrs. Crosland asked students to factor the expression 28 x − 8 . The students offered the answers shown in the box
Carlos: 2(14x - 4)
Danny: 7(4x - 1)
Irene: 4(7x - 2)
Consider the values shown. What
place value must the answer be
reported to?
67.4 +43 +30 + 42.10 =
A. tens place B. ones place
C. tenths place
D. hundredths place
4 1/7 divided by 2/3
Exact Form: 87/14
Decimal Form: 6.21428571... or 6.21
Answer: 6.21
Step-by-step explanation:
80085
Henry read for 20 minute each day alicia rate for 30 minute each day they both read 7 Day of a week how many more doe Alicia read then Henry in 2 week
Alicia read 140 minutes more then Henry in 2 week .
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.
Main body:
Henry read for 20 minute each day.
Alicia rate for 30 minute each day.
as they read 7 day of a week , so
total minutes read by Henry = 2 *7 *20
= 280 minutes
total minutes read by Alicia = 2 *7 *30
=420 minutes
difference between henry , alicia reading = 420 - 280 = 140 minutes.
Hence , Alicia read 140 minutes more then Henry in 2 week .
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Which of the following government agencies does not regulate banking or financial markets?
a.
The NCUA
b.
The Federal Reserve
c.
The FCC
d.
The OCC
The government agency that does not regulate banking or financial market is the The FCC. option C
What is the meaning of FCC?The term FCC stands federal Communication Commission. We should know that the duty of the federal communication Commission not to regulate finance in the society or regulate banking activities rather than to regulate Communication
It is the duty of the Commission to report on chain broadcasting, assign television stations to private and government individuals in the state.
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Write in standard form:
8.254 x 10^6
•Type your answer using commas to show place value.
•Type your answer with NO spaces
The number is the standard from is given by the equation A = 8.254 x 10⁶
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 8.254 x 10⁶
On simplifying the equation , we get
A = 8.254 x 1000000
Multiplying the number , we get
A = 8,254,000
Now , the number can also be written as
A = 8254000
So , the standard form of the number A is given by the equation
A = 8.254 x 10⁶
Hence , the number is A = 8.254 x 10⁶
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Can anyone please help me out with this question?
a) The percentile rank of a score of 71 on this test is given as follows: 33rd percentile.
b) Victor's score, which is the 60th percentile, is given as follows: 84.
What is a percentile?A measure is said to be in the xth percentile of the data-set if it the bottom separator of the bottom x% of measures of the data-set and the top (100 - x)% of measures, that is, it is greater than x% of the measures of the data-set.
The ordered data-set in this problem is given as follows:
58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96.
The data-set is composed by 15 scores, and 5 is the 5th score in the data-set, hence the percentile rank of a score of 71 on this test is calculated as follows:
5/15 = 0.33 = 33rd percentile.
The 60th percentile is the score at the position given as follows:
0.6 x 15 = 9th score = 84.
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PLEASE HELP ASAP
90 students sat a Maths exam. On the way out of the hall, they were asked whether they found it hard, OK or easy. Here are the results:
Show the results on a pie chart. Remember to include full workings, so it is clear how you have calculated each angle.
Answer:
Hey, answer is attached.
Step-by-step explanation:
Hope this helps.
PLS HELP FOR 100 POINTS PLS
Answer:
it is 3
Step-by-step explanation:
I don't know I would
Answer:
it is 3
Step-by-step explanation:
It Basile 9 divide by 4