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Complete the justification column for the following proof:
(1) BP
(2) (RDP)
(3) RD B
(4) ROP
(5) T
T
/T
Answers
Justification:
(1) BP | Premise
(2) (RDP) | Premise
(3) RD B | Modus Ponens (1), (2)
(4) ROP | Premise
(5) T | Modus Ponens (3), (4)
T | Conclusion (the desired statement to be proved)
The given proof is presented in the format of a deductive argument, where each line represents a statement that either follows logically from previous statements (i.e., by a rule of inference) or is assumed to be true (i.e., a premise). The objective of the proof is to demonstrate that the conclusion, represented by the symbol "/T", is a logical consequence of the premises.
The justification column of the proof provides an explanation of why each statement in the argument is true or valid. In this proof, the first four lines are premises that are assumed to be true, and their justifications are simply labeled as "Premise". The last two lines of the proof represent the application of a rule of inference called modus ponens, which states that if we have two statements A and A -> B, we can infer B. The justification for line 3 is modus ponens with lines 1 and 2 as antecedent and consequent respectively, and the justification for line 5 is modus ponens with lines 3 and 4 as antecedent and consequent respectively.
The conclusion of the proof, represented by "/T", is reached by applying modus ponens with lines 3 and 4 as antecedent and consequent respectively. The conclusion follows logically from the premises and the application of the modus ponens rule, which justifies the truth of the conclusion. Therefore, we can conclude that the argument is valid, and the conclusion can be accepted as true.
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Related Questions
what is greater -19/2 or -1.2
Answers
Answer:
-1.2 is greater than -19/2.
THe blanks for 1 Pt 2 are both , Mean, Median, mode, standard devidation, range.
Answers
The Mean = 9.778
The Median = 9
The Mode = 5 and 10
The Standard deviation = 6.21
The Range = 22
What are the Mean, Median, Mode, Standard Deviation and Range?Mean:
To get, we will sum up all the values and divide by the total number of values.
Mean - Ef/n
Mean = (4 + 5 + 5 + 8 + 9 + 10 + 10 + 11 + 26) / 9
Mean = 88 / 9
Mean = 9.778
Median:
This means middle value of a dataset when arranged in ascending order. If there are two middle values, median is average of the two.
Arranging dataset in ascending order: 4, 5, 5, 8, 9, 10, 10, 11, 26. The Median is 9.
Mode:
The mode is the value that occur(s) most frequently in the dataset. In this dataset, the mode is 5 and 10 as both occur twice.
Standard Deviation:
Variance = [[tex](4 - 9.778)^2 + (5 - 9.778)^2 + (5 - 9.778)^2 + (8 - 9.778)^2 + (9 - 9.778)^2 + (10 - 9.778)^2 + (10 - 9.778)^2 + (11 - 9.778)^2 + (26 - 9.778)^2] / 9[/tex]
Variance = 38.617284
Variance = 38.62
Standard Deviation = √Variance
Standard Deviation = √38.62
Standard Deviation = 6.21449917532
Standard Deviation = 6.21
Range:
The range is difference between maximum and minimum values
Range = 26 - 4
Range = 22
b. The outline for the data set is as follows:
Minimum value: 4First quartile (Q1): 5Median: 9Third quartile (Q3): 10Maximum value: 26Read more about centre of measures
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PLEASE HELP! I WILL GIVE BRAINLIEST!! A worker at an animal shelter recorded data about the adoption of cats in the table shown below.
Based on the table, which of these statements are true? Choose all that are correct.
a
Of all the cats adopted, 34.9% are between 6 months and 1 year old
b
Of the cats 1 year or older, about 58% took more than 1 month to be adopted.
c
Of all the cats adopted, about 66% were adopted in a month or less.
d
Of the cats that took more than a month to adopt, 12.5% were younger than 6 months
e
Of the cats who took 1 to 7 days to be adopted, 25% were between 6 months and 1 year old.
Answers
You got a new TV. The dimensions of the TV are 48 inches by 27 inches. What is the size of
the TV?
Answers
1,3,5,7,9…. What is the next number
Answers
Answer: 11
Step-by-step explanation:
this is a sequence of odd numbers.
it goes;
1,3,5,7,9,11,13,15,17,19,21,23....
There are 16 equally likely outcomes on a spinner, numbered 1 through 16. What are the odds against stopping on a number less than 12?
Answers
The odds against stopping on a number less than 12 is 5 ; 11
How to determine the odds against stopping on a number less than 12?From the question, we have the following parameters that can be used in our computation:
Sections in the spinner = 16
This means that the probability of getting a number less than 12 is
P(Number less than 12) = Sections less than 12/Sections in the spinner
There are 11 sections less than 12
So, we have
P(Number less than 12) = 11/16
When represented as odds, we have
P(Number less than 12) = 16 - 11 : 11
Evaluate the difference
P(Number less than 12) = 5 : 11
Hence, the odds against stopping on a number less than 12 is 5 ; 11
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QUESTION 3
Elvis Louw has organized a hall for Mother's day celebration. He invited 150 guests and 2 motivational
3.2
Table
1,8 m
Walking space
Chair 45 cm
Chair 45 cm
NOTE:
Dimensions of the hall: 23 m x 18 m.
The venue includes round tables with a diameter of 1,8 m that can each seat 10 persons.
Use the information above to answer the questions that follow.
3.1
Define the term "Diameter" according to the given context.
Elvis Louw calculated that they need 9 m² per round table. He claims that 30 of the
(2)
(5)
round tables will fit into the space.
Verify Elvis Louw's claim that 30 tables will fit into the space.
You may use the following formula: Area of a rectangle length x breadth
3.3 Calculate the amount of walking space between two tables at the point where they are (5)
the closest, if the space allowed per chair is 45 cm.
(12)
Answers
The amount of walking space between two tables at the point where they are the closest is 0.9 m.
We are given that;
The space allowed per chair = 45 cm.
Number of tables=30
Now,
we find the length of a side of a square that contains a table by adding twice the radius of a table to twice the space allowed per chair. The formula is: side length=2×radius+2×space per chair
Plug in the given values and simplify. The calculation is: side length=2×0.9+2×0.45=2.7
Now subtract the diameter of a table from the side length to get the walking space between two tables. The formula is: walking space=side length−diameter
Plug in the given values and simplify. The calculation is: walking space=2.7−1.8=0.9
To express our answer in meters. walking space=0.9 m
Therefore, by the algebra the answer will be 0.9 m.
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Pls help me with this im struggling
Answers
RQT = 159
RQS = 69
==============================================
Explanation:
Draw a segment connecting R and S.
Triangle SRQ is a right triangle due to Thale's Theorem. That theorem is a special case of the inscribed angle theorem. The 90 degree angle R is opposite the diameter SQ.
Minor arc QR = 42 degrees. Half of this is 42/2 = 21, which is the measure of inscribed angle RSQ. This inscribed angle subtends minor arc QR.
Focus on triangle SRQ. We have two known angles (R = 90 and S = 21). Let's use them to find the missing angle.
The inside angles of any triangle always add to 180 degrees.
S+R+Q = 180
21+90+Q = 180
111+Q = 180
Q = 180-111
Q = 69
Angle RQS is 69 degrees.
----------------
We'll add angle SQT onto the previous result to get angle RQT.
angle RQT = (angle RQS) + (angle RQT)
angle RQT = (69) + (90)
angle RQT = 159 degrees
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
You pick a card at random. Without putting the first card back, you pick a second card at random.
3
4
5
6
What is the probability of picking an odd number and then picking an odd number?
Write your answer as a fraction or whole number.
Answers
The probability of picking an odd number and then picking an odd number when two cards are drawn without replacement from a set of four cards labeled 3, 4, 5 and 6 is 1/6 or approximately 1667/10000 .
The probability of picking an odd number and then picking an odd number when two cards are drawn without replacement from a set of four cards labeled 3, 4, 5 and 6 can be found by using conditional probability.
The probability of the first card being odd is 2/4 (since there are two odd numbers out of four cards). If the first card was odd and not replaced, the number of cards remaining is three, with only one odd card. Therefore, the probability of picking an odd number again is 1/3.
So, the probability of picking an odd number and then picking an odd number is the product of the probabilities of picking an odd number in the first draw and picking an odd number in the second draw, given that the first draw resulted in an odd number.
P(Odd, Odd) = P(Odd on the first draw) * P(Odd on the second draw given that the first draw was odd)
P(Odd, Odd) = (2/4) * (1/3)
P(Odd, Odd) = 2/12
P(Odd, Odd) = 1/6 or approximately 0.1667
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Fred has a great idea for a new product. However, he can only invest $11,919 to start up the company. He asks a three other
individuals to invest in his company. The other three investors bring the total investment to start the company to $285,763.
What percent of the company does the three other individuals own? Round your answer to the nearest tenth of a percent.
Answers
Answer:
He owns about 4.17% or 4% so the others own about 95.83% or 96% but sense it rounds to the nearest tenth your answer would be 95.8%
Step-by-step explanation:
You can figure this out by doing 11,919 divided by 285,763 in order to figure out the percentage of the company he owns and then just do 100 - your answer.
Step-by-step explanation:
First, we need to find out how much money the three other individuals invested in the company. To do that, we'll subtract Fred's investment from the total investment:
Total investment = 285,763
Fred's investment = 11,919
Investment from the three other individuals = Total investment – Fred's investment
Investment from the three other individuals = 285,763 – 11,919
Investment from the three other individuals = 273,844
Now, to calculate the percentage of ownership for the three individuals, we'll divide their combined investment by the total investment and multiply by 100:
Percentage of ownership = (Investment from the three other individuals / Total investment) * 100
Percentage of ownership = (273,844 / 285,763) * 100
Percentage of ownership ≈ 95.8%
So, the three other individuals own approximately 95.8% of the company. Since the question asks to round to the nearest tenth, the answer is 95.8%.
if 12 people get a collective number of 775 questions in a 7 day period how man questions are being asked in a day
Answers
The number of questions asked in a day is A = 110
Given data ,
To determine the number of questions being asked in a day, we need to divide the total number of questions by the number of days.
Now , 12 people are collectively asking 775 questions in a 7-day period.
So , the number of questions being asked in a day, we divide 775 by 7
A = 775 / 7
On simplifying the equation , we get
A ≈ 110.71
Hence , 110.71 questions are being asked in a day
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Need help in this question please
Answers
a. The values of k for which points A, B, and C are collinear are k = 3 and k = -2.
b. The value of k for which AB is parallel to CD is k = 13.
How to calculate the valuea. slope AB = (k+4-9)/(k+1-0) = (k-5)/(k+1)
The slope of AC is:
slope AC = (k+3-9)/(2k-0) = (k-6)/(2k)
Since A, B, and C are collinear, slope AB = slope AC. Therefore, we have:
(k-5)/(k+1) = (k-6)/(2k)
2k(k-5) = (k+1)(k-6)
2k^2 - 10k = k² - 5k - 6
k = 3 or k = -2
(b) The slope of AB is:
= (k+4-9)/(k+1-0) = (k-5)/(k+1)
The slope of CD is:
= (k+6-k-3)/(2k+2-2k) = 3/2
Since AB is parallel to CD, slope AB = slope CD. Therefore, we have:
(k-5)/(k+1) = 3/2
2(k-5) = 3(k+1)
k = 13
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Give the coordinates of the point in the graph below.
-5
A
32
-3 -2
-1
-4
-3-
2-
0
-1-
--2-
-3-
-4
-5
-N-
2
3
4
5.
Answers
The coordinates of the point in the graph is (3, 2)
How to determine the coordinates of the point in the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following
The point is 3 units to the right of the x-axisThe point is 2 units above the y-axisRepresent the point with x
So, we have
X = (3, 2)
Hence, the coordinates of the point in the graph is (3, 2)
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How can I do this math ?
Answers
53 = 43 + v, so substitute each number for V and see if it equals 53.
v = 8 >>> NO
53 = 43 + 8 >>> Nope. This is 51
v = 10 >>> YES
53 = 43 + 10 = 53 >>> Yup! This works.
v = 96 >>> NO
53 = 43 + 96 >>>> Nope, this doesn't add up.
V = 6 >>> NO
53 = 43 + 6 = 49 >>> Nope this doesn't add up.
The total of individual weights of garbage discarded by 20 households in one week is normally distributed with a mean of 32.9 lbs with a sample standard deviation of 14.8 lbs. Find the 95% confidence interval of the mean.
< Select an answer <
Do not round in between steps. Round answers to at least 4 decimal places.
Answers
The 95% confidence interval of the mean is approximately (26.4121, 39.3879) lbs.
How to solve for the confidence intervalsince df = n - 1 = 20 - 1 = 19). You can find this value using a t-distribution table or an online calculator.
For a 95% confidence level and 19 degrees of freedom, the t-score is approximately 2.093.
Now, let's calculate the margin of error (E):
E = 2.093 * (14.8 / √20)
E ≈ 6.4879
Finally, we'll find the confidence interval:
Lower Bound = x - E = 32.9 - 6.4879 ≈ 26.4121 lbs
Upper Bound = x + E = 32.9 + 6.4879 ≈ 39.3879 lbs
The 95% confidence interval of the mean is approximately (26.4121, 39.3879) lbs.
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I need help with part C. Statistics-based.
Answers
10.8
.......................................
HELP PLEASE URGENT!!!!
Answers
The difference between the interquartile range of Matt's remaining vacation days an Linda's remaining vacation days is given as follows:
-3.5.
How to obtain the interquartile range?The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.
Matt's ordered data-set is given as follows:
5, 9, 11, 12.
Hence the quartiles are:
Q3 = 11.5 -> Mean of the last two elements.Q1 = 7 -> Mean of the first two elements.Hence the IQR is of:
IQR = 11.5 - 7 = 4.5.
Linda's ordered data-set is given as follows:
0, 6, 9, 13.
The quartiles aret
Q3 = 11.Q1 = 3.The IQR is of:
IQR = 11 - 3 = 8.
Hence the difference is of:
4.5 - 8 = -3.5.
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19. Randomly assigning the _____ units across the treatment groups is called randomization.
A partial
B experimental
C whole
D population
Answers
The correct answer is A) partial.
Randomization is the process of randomly assigning the study participants or experimental units to the different treatment groups.
This helps to ensure that any differences observed between the groups are due to the treatment and not some other extraneous factor. Partial randomization refers to the random assignment of a subset of units to the treatment groups, while other units may be assigned in a non-randomized manner, such as based on convenience or some other criteria. Experimental, whole, and population randomization are not commonly used terms in research methodology.
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The table shows the median annual salaries for two different jobs. Median Annual Salaries Job Marketing Manager Financial Analyst Median Annual Salary (dollars) 115,750 76,950 Based on the information in the table, how much more money would a marketing manager earn than a financial analyst over 10 years.
F $38,800
G $1,927,000
H $388,000
J $192,700
pls help!
Answers
The amount that Marketing Manager earn more than a Financial Analyst over 10 years is $388,000. The Option H.
How much more will Marketing earn than Financial Analyst?To get how much more a Marketing Manager will earn than a Financial Analyst, we have to calculate the difference in their median annual salaries and multiply by 10.
The difference in median annual salaries is:
= $115,750 - $76,950
= $38,800
The amount earned more by a Marketing Manager over 10 years is:
= $38,800 x 10
= $388,000.
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|7+(-12)|+|-16| add this together
Answers
Answer: 21
Step-by-step explanation:Given:
|7 + (-12)| + |-16|
Absolute value of -16:
|7 + (-12)| + 16
Addition times subtraction is subtraction:
|7 - 12| + 16
Subtract:
|-5| + 16
Absolute value of -5:
5 + 16
Add:
21
-
-
A dairy needs 372 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 3% butterfat must be used to obtain the desired 372 gallons?
Answers
We know that we need a total of 372 gallons of milk.
So, x + y = 372
We also know that the final mixture must contain 6% butterfat.
To find the amount of butterfat in the final mixture, we can multiply the percentage of butterfat in each milk by the number of gallons of that milk, add the two amounts of butterfat, and divide by the total number of gallons:
0.07x + 0.03y = 0.06(372)
Now we have two equations with two variables:
x + y = 372
0.07x + 0.03y = 22.32
We can solve for one of the variables in terms of the other in the first equation:
y = 372 - x
We can substitute this expression for y into the second equation:
0.07x + 0.03(372 - x) = 22.32
Simplifying and solving for x:
0.07x + 11.16 - 0.03x = 22.32
0.04x = 11.16
x = 279
So we need 279 gallons of milk containing 7% butterfat and 93 gallons of milk containing 3% butterfat to obtain 372 gallons of milk containing 6% butterfat.
Answer: 279 gallons of milk containing 7% butterfat and 93 gallons of milk containing 3% butterfat.
HELP WILL GIVE BRAINLESS IF U ANSWER THIS ONE'S AND THE OTHER ONES
Answers
Answer:
c. 3 ft by 4 ft by 5 ft
Step-by-step explanation:
You want to know which sets of measurements can form a triangle.
Triangle inequalityThe triangle inequality requires ...
a + b > c
for any assignment of a, b, c to side lengths. If 'a' and 'b' are the two shortest sides, satisfying this inequality will also satisfy any other arrangement.
Choicesa. 3 + 4 > 9 . . . . falseb. 5 + 5 > 10 . . . . falsec. 3 + 4 > 5 . . . . TRUEd. 9 + 11 > 20 . . . . falseOnly the side lengths 3 ft, 4 ft, 5 ft will form a triangle.
__
Additional comment
As we said the other arrangements of the triangle inequality are also satisfied for these numbers:
4 + 5 > 3
3 + 5 > 4
The garden with side lengths 3, 4, 5 will have the shape of a right triangle.
What is a the center and radius
Answers
A rectangular prism with a 8-centimeter length, a 4-centimeter width,
and a 5-centimeter height is placed on a rectangular prism with a 14-
centimeter length, a 8-centimeter width, and a 1-centimeter height.
6 cm
4 cm
5 cm
14 cm
1 cm
8 cm
What is the volume of the composite solid?
The volume is cubic centimeters.
Answers
plss help me for brainleist
Answers
[tex]\large \maltese \:{ \underline { \underline{ \pmb{ \sf{SolutioN }}}}} : -[/tex]
we have given ,
∠ A = 60°∠ B = 60°∠ C = ?? ( to be calculated)★ According to Angle sum property of triangle, the sum of interior angles of a triangle is 180°.
➝ ∠ A + ∠ B + ∠ C = 180°
➝ 60° + 60° + ∠ C = 180°
➝ 120° + ∠ C = 180°
➝ ∠ C = 180° - 120°
➝ ∠ C = 60°
Now,
★ Calculating for x :-
↝ ∠ C + x = 180°
↝ 60° + x = 180°
↝ x = 180° - 60°
↝ x = 120°
Hence, The value of x will be 120°.
Answer:
The major of the exterior angle is 120°
Step-by-step explanation:
In given triangle we have to find the value of exterior angle and in interior of the triangle there are two angles 60 degree and second one is also 60 degree and we have to find value of exterior angle which is x.
So, here we apply exterior angle property which is exterior angle is equal to the sum of the two interior opposite angles. Here, there are two opposite interior angles so we have to add these two and we get the value of exterior angle.
Exterior angle property :-
[tex] \implies \sf \angle60 \degree + \angle60 \degree[/tex]
[tex] \implies\angle120 \degree[/tex]
Additional information :-Some important properties :-
Exterior angle property :- An exterior angle of a triangle is equal to the sum of its interior opposite angles.
Angle sum property :- The total measure of the three angles of a triangle is 180°
Za kingdom charges according to this table. how much does Za Kingdom charge for each pizza
Answers
The amount that Za Kingdom charges for each pizza is $8.
How to determine the amount charged by Za kingdomTo determine the amount charged by Za Kingdom, we first note that the cost of each pizza plus the delivery fee is $21.
Assuming the basic price to be $8 and the delivery fee of $13, we have the sum of $21. So, for 3 pizzas, we will have 8 times 3 = 24 + 13 = 37
Also, the amount for 10 pizzas will be 8 times 10 = 80 + 13 = 93. So, the price of each pizza is $8.
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Based on the model, the company hired approximately workers in 2019.The r2 value for this model is 0,56, indicating that this functions good model of the data
Answers
Answer:
Step-by-step explanation:
so how to help you but you do a good job
A circle has a radius of 30 cm and a central angle that measures 312 degrees. Find the length of the arc defined by this central angle
Answers
The length of the arc defined by the central angle of 312 degrees is 26π cm.
The formula for the arc length of a circle is given by:
L = (θ/360) × 2πr
where L is the length of the arc, θ is the central angle in degrees, and r is the radius of the circle.
Substituting the given values, we get:
L = (312/360) × 2π(30)
L = (26/30) × π × 30
L = 26π cm
Therefore, the length of the arc defined by the central angle of 312 degrees is 26π cm.
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5C1 evaluate need quick
Answers
The combination is evaluated to give 20
How to evaluate the combinationFrom the information given, we have the expression as;
⁵C₁
The formula for calculating combination is expressed as;
ⁿCᵣ = n! / (r!(n-r)!)
Such that the parameters of the formula are expressed as;
n = 5 r = 1Now, substitute the values into the formula, we have;
⁵C₁ = 5! / (1!(5-1)!)
= 5! / (1! × 4!)
Find the permutation, we have;
= (5 × 4 × 3 ×2 × 1) / (1 × (4 × 3 × 2 × 1))
Divide the values, we get;
= 20 / 1
Find the value
= 20
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Mr. Lucci put together 5 bags of pens. He put 19 black pens and 12 red pens in each bag.
Which expression shows the total number of pens Mr. Lucci put into bags?
A. (5x 19) + 12
B. 5x (1912)
C. 5+ (19 x 12)
D. (5+19) x 12
Answers
Answer:
5 (19 + 12)
Step-by-step explanation:
You add up the red and black pens and multiply by 5, which indicates the 5 bags