Answer:
[tex]\begin{array}{c|c|c||c}X & Y & Z & (X \to Y) \lor (Z \to \lnot X) \\ \cline{1-4} \rm T & \rm T & \rm T & \rm T\\ \rm T & \rm T & \rm F & \rm T \\ \rm T & \rm F & \rm T & \rm F \\ \rm T & \rm F & \rm F & \rm T \\ \cline{1-4} \rm F & \rm T & \rm T & \rm T \\ \rm F & \rm T & \rm F & \rm T \\ \rm F & \rm F & \rm T & \rm T \\ \rm F & \rm F & \rm F & \rm T\end{array}[/tex].
[tex]\begin{array}{c|c|c||c}X & Y & Z & (X \to Y) \lor (Z \to \lnot X) \\ \hline \rm T & \rm T & \rm T & \rm T\\ \rm T & \rm T & \rm F & \rm T \\ \rm T & \rm F & \rm T & \rm F \\ \rm T & \rm F & \rm F & \rm T \\ \hline \rm F & \rm T & \rm T & \rm T \\ \rm F & \rm T & \rm F & \rm T \\ \rm F & \rm F & \rm T & \rm T \\ \rm F & \rm F & \rm F & \rm T\end{array}[/tex].
Step-by-step explanation:
Let [tex]A[/tex] denote a Boolean variable.
The negation of [tex]A[/tex] ([tex]\lnot A[/tex]) is false if when [tex]\!A[/tex] is true, and true when [tex]A\![/tex] is false. In a truth table:
[tex]\begin{array}{c||c} A & \lnot A \\ \cline{1-2} \rm T & \rm F \\ \rm F & \rm T\end{array}[/tex].
[tex]\begin{array}{c||c} A & \lnot A \\ \hline \rm T & \rm F \\ \rm F & \rm T\end{array}[/tex].
Let [tex]B[/tex] denote another Boolean variable. The material implication "[tex]A[/tex] implies [tex]\!B[/tex]" ([tex]A \to B[/tex]) is true unless [tex]B\![/tex] is false when [tex]A\![/tex] is true.
[tex]\begin{array}{c|c||c} A & B & A \to B \\ \cline{1-3} \rm T & \rm T & \rm T \\ \rm T & \rm F & \rm F \\ \rm F & \rm T & \rm T \\ \rm F & \rm F & \rm T\end{array}[/tex].
[tex]\begin{array}{c|c||c} A & B & A \to B \\ \hline \rm T & \rm T & \rm T \\ \rm T & \rm F & \rm F \\ \rm F & \rm T & \rm T \\ \rm F & \rm F & \rm T\end{array}[/tex]
The logical or "[tex]A[/tex] or [tex]B[/tex]" is true when either [tex]A\![/tex] or [tex]B\![/tex] is true (and also when both are true.)
[tex]\begin{array}{c|c||c} A & B & A \lor B \\ \cline{1-3} \rm T & \rm T & \rm T \\ \rm T & \rm F & \rm T \\ \rm F & \rm T & \rm T \\ \rm F & \rm F & \rm F\end{array}[/tex]
[tex]\begin{array}{c|c||c} A & B & A \to B \\ \hline \rm T & \rm T & \rm T \\ \rm T & \rm F & \rm F \\ \rm F & \rm T & \rm T \\ \rm F & \rm F & \rm T\end{array}[/tex].
Start by finding the value of [tex]\lnot X[/tex], [tex](X \to Y)[/tex], and [tex](Z \to \lnot X)[/tex] for each of the [tex]2^3 = 8[/tex] possible combinations of [tex]X[/tex], [tex]Y[/tex], and [tex]Z[/tex].
[tex]\begin{array}{c|c|c||c||c|c}X & Y & Z & \lnot X & (X \to Y) & (Z \to \lnot X) \\ \cline{1-6} \rm T & \rm T & \rm T & \rm F & \rm T & \rm F\\ \rm T & \rm T & \rm F & \rm F & \rm T & \rm T \\ \rm T & \rm F & \rm T & \rm F & \rm F & \rm F \\ \rm T & \rm F & \rm F & \rm F & \rm F & \rm T \\ \cline{1-6} \rm F & \rm T & \rm T & \rm T & \rm T & \rm T \\ \rm F & \rm T & \rm F & \rm T & \rm T & \rm T \\ \rm F & \rm F & \rm T & \rm T & \rm T & \rm T \\ \rm F & \rm F & \rm F & \rm T & \rm T & \rm T \end{array}[/tex].
[tex]\begin{array}{c|c|c||c||c|c}X & Y & Z & \lnot X & (X \to Y) & (Z \to \lnot X) \\ \hline \rm T & \rm T & \rm T & \rm F & \rm T & \rm F\\ \rm T & \rm T & \rm F & \rm F & \rm T & \rm T \\ \rm T & \rm F & \rm T & \rm F & \rm F & \rm F \\ \rm T & \rm F & \rm F & \rm F & \rm F & \rm T \\ \hline \rm F & \rm T & \rm T & \rm T & \rm T & \rm T \\ \rm F & \rm T & \rm F & \rm T & \rm T & \rm T \\ \rm F & \rm F & \rm T & \rm T & \rm T & \rm T \\ \rm F & \rm F & \rm F & \rm T & \rm T & \rm T \end{array}[/tex].
The value of [tex](X \to Y) \lor (Z \to \lnot X)[/tex] is true whenever either [tex](X \to Y)[/tex] or [tex](Z \to \lnot X)[/tex] is true (or both.) The combination [tex]X = \rm T[/tex], [tex]Y = \rm F[/tex], and [tex]Z = \rm T[/tex] is the only one among the eight where neither [tex](X \to Y)\![/tex] nor [tex](Z \to \lnot X)\![/tex] is true. [tex](X \to Y) \lor (Z \to \lnot X)\![/tex] would evaluate to true for all other combinations.
Hence, the truth table would be:
[tex]\begin{array}{c|c|c||c}X & Y & Z & (X \to Y) \lor (Z \to \lnot X) \\ \cline{1-4} \rm T & \rm T & \rm T & \rm T\\ \rm T & \rm T & \rm F & \rm T \\ \rm T & \rm F & \rm T & \rm F \\ \rm T & \rm F & \rm F & \rm T \\ \cline{1-4} \rm F & \rm T & \rm T & \rm T \\ \rm F & \rm T & \rm F & \rm T \\ \rm F & \rm F & \rm T & \rm T \\ \rm F & \rm F & \rm F & \rm T\end{array}[/tex].
[tex]\begin{array}{c|c|c||c}X & Y & Z & (X \to Y) \lor (Z \to \lnot X) \\ \hline \rm T & \rm T & \rm T & \rm T\\ \rm T & \rm T & \rm F & \rm T \\ \rm T & \rm F & \rm T & \rm F \\ \rm T & \rm F & \rm F & \rm T \\ \hline \rm F & \rm T & \rm T & \rm T \\ \rm F & \rm T & \rm F & \rm T \\ \rm F & \rm F & \rm T & \rm T \\ \rm F & \rm F & \rm F & \rm T\end{array}[/tex].
Suppose box A contains 4 red and 5 blue poker chips and box B contains 6 red and 3 blue poker chips. Then a poker chip is chosen at random from box A and placed in box B. Now, a poker chip is chosen at random from those now in box B. What is the probability a blue poker chip was transferred from box A to box B, given that the coin just chosen from box B is red?
Answer:
0.5172 = 51.72% probability a blue poker chip was transferred from box A to box B, given that the coin just chosen from box B is red
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Coin chosen from box B is red.
Event B: Blue poker chip transferred.
Probability of choosing a red coin:
7/10 of 4/9(red coin from box A)
6/10 of 5/9(blue coin from box A). So
[tex]P(A) = \frac{7}{10}*\frac{4}{9} + \frac{6}{10}*\frac{5}{9} = \frac{28 + 30}{90} = 0.6444[/tex]
Blue chip transferred, red coin chosen:
6/10 of 5/9. So
[tex]P(A \cap B) = \frac{6}{10}*\frac{5}{9} = \frac{30}{90} = 0.3333[/tex]
What is the probability a blue poker chip was transferred from box A to box B, given that the coin just chosen from box B is red?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3333}{0.6444} = 0.5172[/tex]
0.5172 = 51.72% probability a blue poker chip was transferred from box A to box B, given that the coin just chosen from box B is red
Help me ASAP for heart, 5 star rating and comment
There is 8 questions which will be posted one after the other. Questions 1-7 the person who answers correctly and quickly will get a heart and 5 star rating and comment and for the 8th question the correct person will get the rewards + brainiest.
1. If U = 35 and V = 7 and T =4 and V = U + AT. How much Is A worth
This question is worth 10 points numbers WILL get higher
Answer:
A=-7
Step-by-step explanation:
7=35+A4
4A=-28
A=-7
Connor’s temperature was 0.7 degrees higher last night than it was this morning. His temperature this morning was 101.2 degrees. What was his temperature last night?
Answer:
101.9 degrees
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Let's define what we have:
Conner's morning temperature: 101.2 degrees
Conner's last night temperature: morning temperature + 0.7 degrees
We know that Conner's last night temperature is addition because it was higher (key word) than the morning temperature.
Therefore, we simply add the values together to get our answer:
101.2 + 0.7 = 101.9 degrees
Which statement is correct?
Thank you for anyone who answers
Answer:
I believe the correct answer is C
Which two prisms have the same height
Answer:
The height of prism A is 4, the height of prism B is 5, the height of prism C is 4, and the height or prism D is 2. Since 4=4, prisms A and C have the same height.
Hope this helped! If it did, please give me brainliest! It would help a lot! Thanks! :D
please help !!!! asap
Answer:
y = 1
Step-by-step explanation:
-3y + 14 + y = 12
-3y + y + 14 = 12
-2y + 14 = 12
-2y + 14 - 14 = 12 - 14
-2y = -2
-2y/-2 = -2/-2
y = 1
Answer:
y=1
Step-by-step explanation:
Hey There!
So to solve this type of problem we use inverse operations
-3y+14+y=12
step 1 subtract 14 from each side
14-14
12-14=-2
now we have
-3y+y=-2
step 2 combine like terms
-3y+y=-2y
now we have -2y=-2
step 3 divide each side by -2
-2/-2=1
so we can conclude that y=1
Find the missing sides of the triangle. Leave your answers in simplest radical form.
Answer:
B) x=2, y=2
Step-by-step explanation:
B.
It’s a 90-45-45 triangle, so the hypotenuse is x√2, and the other two sides are x. Since this x is 2, the other two sides are 2.
Use the number line to answer the questions that follow
Answer:
A. make a point on the line to the right 2 units from 0
B. the opposite of 2 isn't located at the same place as point P on the number line because the opposite of 2 is -2 and the point P is the opposite of negative 2 which would be positive 2. So the two points are not in the same place because they have different signs.
Step-by-step explanation:
hope this helps
I know the wording is a bit complicated lol <3
If an exterior angle measure of a regular polygon is 60°, how many sides does the polygon have? What is the measure of each interior angle?
9514 1404 393
Answer:
6 sides120°Step-by-step explanation:
The sum of the measures of the exterior angles of a convex polygon is always 360°. If each is 60°, there are 360°/60° = 6 of them.
There are 6 sides.
The adjacent interior angle is the supplement of the exterior angle, so is ...
180° -60° = 120°.
Each interior angle measures 120°.
24=3(n-5) what does n equal
Answer:
The answer is n = 13
Step-by-step explanation:
1) Divide both sides by 3.
[tex] \frac{3}{24} = n - 5 [/tex]
2) Simplify 24/3 to 8.
[tex]8 = n - 5[/tex]
3) Add 5 to both sides.
[tex]8 + 5 = n[/tex]
4) Simplify 8 + 5 to 13.
[tex]13 = n[/tex]
5) Switch sides.
[tex]n = 13[/tex]
Therefor, the answer for this equation is n = 13.
Which of the following circles has an area greater than 400 square meters and less than 600 square meters? Use 3.14 for π. Select all that apply.
A.Radius: 8 meters
B.Radius: 12 meters
C.Radius: 14 meters
D.Diameter: 12 meters
E.Diameter: 22 meters
F.Diameter: 26 meters
Answer:d
Step-by-step explanation:fkjfkjfkjfkjfkjf
There are 420 students at Virginia Middle School. The ratio of girls to boys is 4 to 3. HELPPPPPPPP
Answer:
60 more girls are there than boys at Virginia Middle School.Find the positive of x that makes the equation true.
x^2 = 225
Answer:
x = 15
Step-by-step explanation:
15 * 15 = 225
Answer:
X = 15
Step-by-step explanation:
This is because if you square 15, you get 225.
A) Jerry wants to open a bank account with his money. He will deposit $60.75
per month. If m represents the number of months, write an algebraic expression to
represent the total amount of money he will deposit
Answer:
$60.75×m
Step-by-step explanation:
'5'5"5"5""55
Slove for the value of x to the nearest whole number?
Answer:
Hello good afternoon
Step-by-step explanation:
you have to put this link
9−z9, minus, z when z = 8z=8z, equals, 8.
Kobe drove 240 miles in 6 hours. To find the unit rate, you should determine how many miles Kobe drove
in hour(s).
Answer:
40 miles per hour
Step-by-step explanation:
Answer:
40 mph
Step-by-step explanation:
240 / 6 = 40
en la pastelería de Luisa le regalan a una casa hogar 18 galletas dé cada 60 que se hornean a la semana si la semana pasada hornearon 720 galletas Cuántas regalaron
Answer:
La pastelería de Luisa regaló 216 galletas a la casa hogar.
Step-by-step explanation:
De acuerdo con el enunciado, la pastelería de Luisa regalan 18 galletas a una casa hogar por cada 60 galletas horneadas en una semana. El total de galletas regaladas por hornear 720 galletas se determina por la siguiente Regla de Tres Simple:
[tex]x = \frac{18}{60}\times 720[/tex]
[tex]x = 216[/tex]
La pastelería de Luisa regaló 216 galletas a la casa hogar.
of Kayla has a bowl of beads that contalns 42 yellow beads, 28 green beads, 12 white beads, and 18 red beads. She randomly draws a bead from
the bowl.
The probability of Kayla not drawing yellow or a green bead is
%. The probability of Kayla drawing red or a green bead is
%.
Answer:
a) You have a 30% of not drawing yellow or green
b) You'd have a 46% of frawing a red or green bead
Step-by-step explanation:
Total beads: 42 + 28 + 12 + 18 = 100
Green beads + yellow beads = 28 + 42 = 70
100 - 70 = 30
30/100 = 0.3 or 30%
Red beads + green beads = 18 + 28 = 46
46/100 = 0.46 or 46%
Answer:
1. 30%
2.46%
Step-by-step explanation:
The probability of Kayla not drawing a yellow or a green bead is 30 %. The probability of Kayla drawing a red or a green bead is 46 %.
Correct for plato! :)
PLEASE HELP ME.............
Answer:
[tex]g(x)=3x^2[/tex]
How many joules of gravitational potential energy does a 15 kg object have when it is lifted from the floor and held 0.6 meters above the ground?
Answer:
88.29joules
Step-by-step explanation:
mgh=gravitational potential energy
(15kg)(9.81)(0.6)= 88.29joules
What is the area of the shaded region?
Answer:
65
Step-by-step explanation:
( (23 * 13) / 2 ) - ( (13 * 13) / 2 ) = ( 299 / 2 ) - ( 169 / 2 ) = 149.5 - 84.5 = 65
Numbers are slightly unclear but I think this is right.
Divide twice the variable p by the product of 5 and q
Answer:
Step-by-step explanation:Solution :
Given variable = p
According to the problem given ,
Twice the variable p divided by the
product of 5 and q
= ( 2p )/ ( 5q )
= 2p/5q
Which expression is equivalent to the expression 6h + 2?
(2 + 4h) + 2
(2 + 4h) + h
(1 + 5h) + 2
(2 + 5h) + h
Answer:
D
Step-by-step explanation:
Movie Theaters There are two movie theaters in a town. A student wants to compare the amount of
money each theater makes over a period of days. The following box plots show the data for the
amount of money each theater makes over a period of days. Compare the median of each box plot.
Click here to see the box plot for movie theater 1.
Click here to see the box plot for movie theater 2.
Vhich of the following is the best description of the medians?
A. The median for Movie Theater 1 is greater.
B. The median for Movie Theater 2 is greater.
C. The medians are about the same.
The medians are about the same.
Option C is the correct answer.
What is a median?It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
Movie theater 1.
From the box plot given,
The median is 995.
Movie theater 2.
From the box plot given,
The median is 995.
Thus,
The median in both the box plot is the same.
Learn more about the median here:
https://brainly.com/question/28060453
#SPJ2
M = 19 - 3 please ANSWErrrr
Answer:
16
Have a great day!
PLEASE HELP MEEEEE ASAP 100 POINTS
Answer:
3. D 4. B
Step-by-step explanation:
3. e^2 = g^2 + f^2, answer is d
4. Let a = 3, b = 4, c = 5
2c = 10
2b = 8
2a = 6
10^2 = 8^2 + 6^2
answer is b
3. The Pythagorean theorem states the hypotenuse squared is equal to each side squared added to each other.
The answer is D. E^2 = f^2 + g^2
4.
To keep the proportion you could multiply the sides by the same numbers . The answer would be 2A, 2b, 2c
what is the volume of this object just tell me no explashiom
Answer:
29 I think
Step-by-step explanation:
Plz help me !!!! I’m not sure if it’s 20 !
Answer:
D) 20º
Step-by-step explanation:
if one angle is 70º, and the other is 90º, that means that the first two angles equal 160º. since all three interior angles of a triangle have to add up to 180º, the third angle must be 20º.
What is one thing that you found interesting about future value and present value for compound interest? 100 words ^
Answer:
Compound interest is that which, once generated, is added to the capital, in order to expand the calculation base on which, in turn, new interests will be generated. Thus, in short, if the interest is, for example, 5 percent, said interest will be added to the initial capital, with which that 5% generated will be increasing, since it will be calculated on an increasingly large basis.
Compound interest is very important for financial investments, as it maximizes the results of said investments, even more so when compared to simple interest, in which the interest generated is not added to the initial capital.