Answer:
Modus Tollens
Step-by-step explanation:
Consider the following argument: If we put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase, the bookcase collapses. We do not put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase. Hence, the bookcase does not collapse.
The logical form of this argument is Modus Tollens.
Modus Tollens is a mode of argumentation that involves affirming the consequent of a conditional statement. In this argument, the conditional statement is "If we put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase, the bookcase collapses." The antecedent of this statement is "we put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase," and the consequent is "the bookcase collapses."
Modus Tollens is used to prove the negation of the consequent by negating the antecedent. In other words, if the consequent is not true, then the antecedent must also not be true. Thus, in this argument, since we know that the bookcase does not collapse, we can conclude that we did not put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase.
Therefore, the logical form of this argument is Modus Tollens.
Graph the following feature
Y intercept =2
Slope = -6/5
The equation of line is y = ( -6/5 )x + 2 , where the slope is m = ( -6/5 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( -6/5 )
The y intercept of the line is b = 2
So , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
On simplifying , we get
y = ( -6/5 )x + 2
Hence , the equation of line is y = ( -6/5 )x + 2 and the graph is plotted
To learn more about equation of line click :
https://brainly.com/question/14200719
#SPJ1
the electronic grading machine at john adams elementary can grade 52 multiple choice tests in minute. How long will it take to grade 338 tests
It will take 6.5 minutes to grade 338 test by the electronic grading machine.
What are some elements that impact grading system's accuracy?The quality of the answer papers is a key element. The machine might not be able to reliably scan and evaluate the answers if the answer sheets are not filled out completely or if the paper has rips or smudges on it. Similar to this, the computer might not be able to recognize the right answers if the answer sheets are not properly aligned.
Given that, the machine can grade 52 test in 1 minute.
The, we can calculate the time taken to grade 338 test as follows:
time = number of tests / rate of grading
Plugging in the given values, we get:
time = 338 / 52 = 6.5 minutes
Hence, it will take 6.5 minutes to grade 338 test by the electronic grading machine.
Learn more about rate here:
https://brainly.com/question/29518179
#SPJ1
If a system has no solution, what do you know about the lines being graphed?
PART B:
If a system has 1 solution, what do you know about the lines being graphed?
PART C:
If a system has infinitely many solutions, what do you know about the lines being graphed?
If a system has nο sοlutiοn, it means that the lines being graphed are parallel and dο nοt intersect at any pοint.
If a system has 1 sοlutiοn, it means that the lines being graphed intersect at a single pοint.
If a system has infinitely sοlutiοns, it means that the lines being graphed are cοincident, i.e., they lie οn tοp οf each οther.
What is Linear Equatiοn in Twο Variables?A linear equatiοn in 2 variables is an algebraic expressiοn that represents a straight line οn a 2D cοοrdinate plane.
It can be written in the fοrm οf y = mx + b, where m is the slοpe οf the line, b is the y-intercept, and x and y are the twο variables.
PART A:
If a system has nο sοlutiοn, it means that the lines being graphed are parallel and dο nοt intersect at any pοint. This implies that there are nο values οf the variables that can satisfy bοth equatiοns simultaneοusly.
PART B:
If a system has one sοlutiοn, it means that the lines being graphed intersect at a single pοint. This implies that there is οnly οne unique sοlutiοn that satisfies bοth equatiοns simultaneοusly.
PART C:
If a system has infinitely many sοlutiοns, it means that the lines being graphed are cοincident, i.e., they lie οn tοp οf each οther. This implies that there are an infinite number οf values οf the variables that can satisfy bοth equatiοns simultaneοusly since every pοint οn the shared line is a valid sοlutiοn tο the system.
To learn more about Linear Equations from the given link
https://brainly.com/question/13951177
#SPJ1
ermesyo brings his dogs to traing classes the equation -60+2y 0120=0 re;ates y the total cost of pets training and x the number of classess thanken
The line that the equation represents has a y-intercept of.
What is an example of a y-intercept?
Here are several y intercept instances. So we obtain y = 5(0)2 + 2 = 2 when we replace x = 0, so y-intercept of y Equal 5x2 + 2 is (0, 2). Because we obtain y = -5e0 = -5 when we try substituting x = 0, this same y-intercept of y Equal -5ex is (0, -5).
Y-intercept: Is it 0 or 1?
The point where a straight line intersects the X-axis is known as the Y interception. In the picture above, the line intersects the Value of y at 1. The point is shown by and the value of the Variable y is 1. (0,1). Remember that for the y-intercept, the point's such and such is always zero.
On this note, we must recall that the y-intercept of an equation is the value of when.
Therefore, we have;
-60(0) + 2y -120 = 0
2y = 120
y = 60
Hence, the y-intercept of the line represented by the equation is; 60.
To learn more about y-intercept visit:
https://brainly.com/question/25722412
#SPJ1
The complete question is:
Ernesto brings his dog to training classes. The equation -60x + 2y - 120 =0 relates y, the total cost of a pet's training, and x, the number of classes taken Ernesto states that the y-intercept of the line represented by the equation is 30. is he correct?
There are 9 game pieces on each tic-tac-toe board. The third grade class has 4 tic-tac-toe boards. How many game pieces does the class have for all of their tic-tac-toe boards?
A) 13
B) 27
C) 36
D) 45
Answer:
C) 36.
Step-by-step explanation:
Since there are 9 game pieces in each tic-tac-toe board and the class has 4 tic-tac-toe boards, the total number of game pieces the class has is:
9 pieces/board x 4 boards = 36 pieces
Therefore, the answer is C) 36.
Which expression is the simplest form of 223-22 + 3 (23 - 422)?
O A. 23 - 13x2
O B. 523 - 1322
О c. 323 - 1222
O D. 523 - 522
The simplification value of the expression is,
⇒ 5x³ - 12x²
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 2x³ - x² + 3 (x³ - 4x²)
Now, We can simplify the expression as;
⇒ 2x³ - x² + 3 (x³ - 4x²)
⇒ 2x³ - x² + 3x³ - 12x²
⇒ 5x³ - 12x²
Thus, The simplification value of the expression is,
⇒ 5x³ - 12x²
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
graph system of equations to determine solution
y=1/2x+3
2y=x+6
The system of linear equation has infinitely number of solutions
What is the graph of system of linear equationThe collection of all ordered pairs that concurrently fulfill both equations makes up the graph of a system of linear equations. It is the collection of all points that are the solutions to both equations, in other words.
The system of linear equations in this issue is stated as
y = 1/2x + 3...eq(i)
2y = x + 6...eq (ii)
The graph demonstrates that the system has an infinite number of solutions and that both lines cross one another. This demonstrates that the system is intractable.
Learn more on graph of system of linear equation here;
https://brainly.com/question/14323743
#SPJ1
Q.4. Mandy babysits and makes $8.50 per hour. To commute to the job, she spends $40 per
week on the bus and subway. Which inequality can be used to determine how many hours,
h, she must work to make more than $300 per week?
A. 8.50x + 40 > 300
B. 8.50x40 > 300
C. 40x+8.50 > 300
D. 40x8.50 > 300
Answer:
A is the correct answer
Step-by-step explanation:
The question is present in the problem
The solution to the given equation √(2x + 9) = 7 is x = 20.
What is the radical equation?Any equation that contains a radical symbol is considered a radical equation. To find the square roots, cubic roots, and higher, radical symbols are used.
The equation is given as follows:
√(2x + 9) = 7
Square both sides of the above equation,
2x + 9 = 7²
2x + 9 = 49
Subtract 9 from both sides of the above equation,
2x = 49 - 9
2x = 40
Divide by 2 into both sides of the equation,
x = 40/2
x = 20
Thus, the solution to the given equation is x = 20.
Learn more about radical expressions here:
https://brainly.com/question/3796764
#SPJ1
What is five percent of $97.25
Answer: 4.8625
Step-by-step explanation:
Lily has read 3/4 of her book. Sophie has read 2/6 of her book. Which girl has read more of her book?
Answer: Lily
Step-by-step explanation:
3/4 is larger than 2/6
Answer: Lily
Step-by-step explanation: 3/4 > 2/6
3/4 = 0.75
2/6= 0.33
compare the two decimal places, 0.75 > 0.33
50 Points!!! Solve each inequality. Then graph the solution set on a number line. Photo attached
50
Step-by-step explanation:
plot it on the number line
8(3n-2) + 1/2 (10n-7)
Answer:
29n - 39/2.
Step-by-step explanation:
To simplify the expression 8(3n-2) + 1/2 (10n-7), we can start by using the distributive property of multiplication over addition to simplify the terms inside the parentheses:
8(3n-2) + 1/2 (10n-7) = (83n - 82) + (1/2 * 10n - 1/2 * 7)
This gives us:
24n - 16 + 5n - 7/2
Next, we can combine like terms:
24n + 5n - 16 - 7/2 = 29n - 16 - 7/2
Finally, we can simplify the expression by finding a common denominator for -16 and -7/2:
29n - 16 - 7/2 = 29n - 32/2 - 7/2 = 29n - 39/2
Therefore, 8(3n-2) + 1/2 (10n-7) simplifies to 29n - 39/2.
I need help its due today
Answer: the image didnt send with this try reposting
Step-by-step explanation:
this is a little funny out of context tho, best of luck be upon you
What is the diffrence between b and 9
Answer: b-8
Step-by-step explanation:
b-9=b-9
b-9+1=b-8
Which expression represents the distance between Q and R
Answer:
Translation
Step-by-step explanation:
Translation
Find the slope of the line of fit and explain its meaning in the context of the data.
80 a student who studies for 0 hours is predicted to earn 80% on the test
70 a student who studies for 0 hours is predicted to earn 70% on the test
10 for each additional hour a student studies, their grade is predicted to increase by 10% on the test
5 for each additional hour a student studies, their grade is predicted to increase by 5% on the test
The slope of the line of fit is 7.5% per hour.
What is slope ?In mathematics, slope refers to the measure of steepness or incline of a line. It is the ratio of the vertical change between two points on the line (the rise) to the horizontal change between the same two points (the run).
According to given conditions:To find the slope of the line of fit, we need to use the formula:
slope = change in y / change in x
In this case, the change in y represents the change in the predicted grade on the test, and the change in x represents the change in the number of hours studied. From the given data, we can see that:
The predicted grade for a student who studies for 0 hours is 80%.
The predicted grade for a student who studies for 1 hour is 90% (80% + 10%).
The predicted grade for a student who studies for 2 hours is 95% (90% + 5%).
Using this information, we can calculate the slope of the line of fit:
slope = (95% - 80%) / (2 hours - 0 hours) = 15% / 2 hours = 7.5%/hour
The slope of the line of fit is 7.5% per hour. This means that for each additional hour a student studies, their predicted grade on the test is expected to increase by an average of 7.5%. The slope represents the rate of change of the predicted grade with respect to the number of hours studied. In this case, a positive slope indicates that there is a positive correlation between the number of hours studied and the predicted grade on the test. The higher the slope, the steeper the line of fit, and the greater the impact of studying on the predicted grade.
Therefore, the slope of the line of fit is 7.5% per hour
To know more about slope visit :
https://brainly.com/question/16949303
#SPJ1
What is the y-value of the solution of the given
system?
(4x + 3y = 1
-4x + 3y = -7
(F) -1
(G) 0
(H) 1
(J) 2
(K) 6
The y-value of the solution of the system of equations is given as follows:
y = -1.
How to solve the system of equations?The system of equations for this problem is defined as follows:
4x + 3y = 1.-4x + 3y = -7.Adding the two equations, the value of y can be obtained as follows, as the x-variable is eliminated:
6y = -6
y = -6/6
y = -1.
Hence option F is correct.
More can be learned about a system of equations at https://brainly.com/question/30374328
#SPJ1
A bin of soccer balls, basketballs, and volleyballs contains 112 balls. For every 3 soccer balls there are 5 basketballs and 6 volleyballs. How many more basketballs are there than soccer balls?
[tex]112 : ( 3 + 5 + 6)= 112 : 14 = 8[/tex]
basketballs = 8(5) = 40
soccer balls = 8(3) = 24
→ basketballs - soccer balls = 40 - 24 = 16
Suppose that the relation H is defined as follows.
H = {(−3, 8) , ( 0, -3) , (1, 3) , (1, -1)}
Give the domain and range of H.
Write your answers using set notation.
Domain = ?
Range = ?
The highest value and lowest value of x is domain, here domain is [1, -3]
The highest value and lowest value of y is range, here range is [8, -3].
What is domain and range?Mathematical operations are comparable to those of a soda vending machine. You can choose from a variety of sodas when you deposit a certain sum of money. Similar to how we input different numbers into functions, we also receive new numbers as the outcome. The two main characteristics of functions are domain and range.
A soda can be purchased with quarters and one dollar bills. If pennies are put into the machine, no soda flavour will be provided. As a result, the domain represents the possible inputs, which are quarters and one-dollar bills. No matter how much you pay, a soda machine won't give you a cheeseburger. The range represents the potential outputs we can have in this situation, that is, the flavors of soda in the machine.
Learn more about domain and range
https://brainly.com/question/29452843
#SPJ1
The question is present in the image
The value of variables are,
a = 0
c = 7
d = 2
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ [tex]\frac{32x^{4} y^{3} z^{- 6} }{(4x^{2} y^{-2} z^{-2})^2 } = \frac{Ax^ay^c}{z^d}[/tex]
Now, We can simplify as;
⇒ [tex]\frac{32x^{4} y^{3} z^{- 6} }{(4x^{2} y^{-2} z^{-2})^2 } = \frac{Ax^ay^c}{z^d}[/tex]
⇒ [tex]\frac{32x^{4} y^{3} z^{- 6} }{(16x^{4} y^{-4} z^{-4}) } = \frac{Ax^ay^c}{z^d}[/tex]
⇒ [tex]\frac{2x^0y^7}{z^2} = \frac{Ax^ay^c}{z^d}[/tex]
By comparing, we get;
a = 0
c = 7
d = 2
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
At Northern High School the ratio of boys to girls in intramural sports is 2 to 3. There are 230 students involved in intramural sports.
a. Write the proportion that would find the number of girls in intramural sports.
b. Find the number of girls in intramural sports.
Answer:
Step-by-step explanation:
to write the proportion is a number of the girl in intramural sport is [tex]\frac{x}{y} 2/3=230[/tex]
and find the number a girl in intramural sport is 90
Plot the point (4.5, −2.25) on the coordinate plane.
In response to the supplied query, we may state that Draw a dot to coordinates indicate the position (4.5, -2.25) where the two lines cross after finding the points on the x-axis and the y-axis.
what are coordinates?A coordinate system is a technique used in geometry to precisely locate points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers or coordinates. A point or item on a two-dimensional plane is located using a pair of numbers known as coordinates. The x and y coordinates are two numbers that describe a point's location on a 2D plane. a collection of integers that indicate exact locations. Typically, the figure has two numbers. The first number represents the front-to-back distance, while the second number represents the top-to-bottom distance. When there are 12 units below and 5 above, as in (12.5), this is an example.
Plotting the coordinates of the point (4.5, -2.25) requires the following actions:
Create the x- and y-axes.
Identify the intersection of the x and y axes. The coordinates of this place, which is known as the origin (0, 0).
Find the coordinates (4.5, -2.25) on the x- and y-axes.
Move 4.5 units to the right of the origin to find the point on the x-axis.
Go 2.25 units down from the origin to find the point on the y-axis.
Draw a dot to indicate the position (4.5, -2.25) where the two lines cross after finding the points on the x-axis and the y-axis.
To know more about coordinates visit:
https://brainly.com/question/27749090
#SPJ1
what is the area and formula for this question?
The total area of the given figure is found to be 96 m².
Explain about the area of the rectangle?The quantity of unit squares that could also fit inside a rectangle called its area. The quantity of space a flat surface of a specific form occupies is known as its area. The product of a rectangle's length and width is the formula for calculating its area (breadth). This is stated as follows: Rectangle area equals length x widthTotal area = area of rectangle + area of triangle
Total area = length x breadth + 1/2 x base x height
Total area = 12 x 7 + 1/2 x 6 x (11 - 7)
Total area = 84 + 12
Total area = 96
Thus, the total area of the given figure is found to be 96 m².
know more about the area of the rectangle
https://brainly.com/question/2607596
#SPJ9
You have a portfolio consisting solely of Stock A and Stock B. The portfolio has an expected return of 10.2 percent. Stock A has an expected return of 11.7 percent while Stock B is expected to return 8.3 percent. What is the portfolio weight of Stock A?
The portfolio weight of Stock A is 0.625 for the given situation.
What use do portfolio weights serve?The percentage of a portfolio's investments that are assigned to each asset or security is shown by the portfolio weights. Investors can meet their chosen risk and return objectives by varying the weights of various assets in their portfolios. Portfolio weights are a key component of asset allocation and portfolio optimization methodologies since they are used to determine the expected return and risk of a portfolio.
Let w be the weight (proportion) of Stock A in the portfolio.
The weight of Stock B would be (1-w).
Given that, the portfolio has an expected return of 10.2 percent.
0.102 = w(0.117) + (1-w)(0.083)
w = (0.102 - 0.083)/(0.117 - 0.083) ≈ 0.625
Hence, the portfolio weight of Stock A is 0.625 for the given situation.
Learn more about percent error here:
https://brainly.com/question/3670306
#SPJ1
What is the volume of the composite figure?
The volume of the composite figure is 408 cm³
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.
The volume of the composite figure is:
Volume = area of base * height
Substituting:
Base area = (14 * 3) + (1/2)(5 + (14-6))(7 - 3) = 68 cm²; height = 6 cm
Volume = area of base * height = 68 cm² * 6 cm = 408 cm³
The volume is 408 cm³
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
15 POINTS
Identify the roots in the given
{-8}
{-2, 4}
{0,-8}
{-2, -8,4}
The set containing the roots of the graphed quadratic function is given as follows:
{-3, 1}
How to obtain the roots of a function?The roots of a function can be obtained from the graph of the function, as they also represent the x-intercepts of the function.
The x-intercepts of a function are given by the values of x at which the graph of the function crosses the x-axis, which is the horizontal axis.
The values of x for which the graphed function crosses the x-axis are given as follows:
x = -3 -> 3 units to the left of the y-axis.x = 1 -> 1 unit to the right of the y-axis.Hence the set containing the roots of the graphed quadratic function is given as follows:
{-3, 1}
More can be learned about the roots of a function at https://brainly.com/question/10702726
#SPJ1
Given matrices
�
=
[
−
1
0
]
X=[
−1
0
] and
�
=
[
−
2
−
1
]
Y=[
−2
−1
] , which of the following matrices is
�
�
XY ?
From the given scenario, AB = [17 + 28, 47 + 58] = [23, 64]
How to calculate the product of matrices XY,To calculate the product of matrices XY, the number of columns in X must match the number of rows in Y. In this case, X has 1 column and Y has 2 rows, so the product XY is undefined.
A general example of this with matrices is:
Let A be a 2x3 matrix:
A = [1 2 3; 4 5 6]
Let B be a 1x2 matrix:
B = [7 8]
To calculate the product AB, we need the number of columns in A to match the number of rows in B.
In this case, A has 3 columns and B has 1 row, so the product AB is:
AB = [17 + 28, 47 + 58] = [23, 64]
P.S Your question is incomplete, so I showed how to calculate the product of matrices XY,
Read more about matrices here:
https://brainly.com/question/1279486
#SPJ1
Please help!
The terminal side of passes 0 through the point (-9, 10).
What is the exact value of sin in simplified form?
9 √181/181
10 √181/181
-10 √181/181
-9 √181/181
As a resuIt, 10 (181)/181 is the sin vaIue that cοmes cIοsest tο 10 √(181)/√181. B is the apprοpriate answer, sο.
Hοw dο yοu define vaIue?The cοst οr price οf sοmething, aIsο knοwn as its mοnetary vaIue.
The right-angIed triangIe fοrmed by the angIe's terminaI side and the pοints (-9, 10) can be caIcuIated using the Pythagοrean Theοrem tο determine the Iength οf a hypοtenuse:
h = √((-9)² + 10²) = √(81 + 100) = √(181)
Sin is pοsitive because the pοsitiοn (-9, 10) οccupies the secοnd quadrant. We are abIe tο determine the actuaI amοunt οf sin that use the definitiοn οf sin:
sin(theta) = οppοsite/hypοtenuse = 10/√(181)
We can cοmbine the twο parts οf this fοrmuIa by √181 tο οbtain the fοIIοwing resuIt:
sin(theta) = 10 × √(181)/√(181)√(181) = 10√(181)/181
To know more about Pythagorean Theorem visit:
https://brainly.com/question/14930619
#SPJ1
in need of help! thank you in advance
Answer:
1. 12
2. 6
3. 4.5
4. 7
Don't quite under #5
Explanation:
Sample mean = ΣX / n
1. 108 / 9 = 12
2. 72 / 12 = 6
3. 2 + 7 + 9 + 4 + 5 + 3 + 0 + 6 = 36 / 8 = 4.5
4. 8 + 2 + 5 + 7 + 12 + 9 + 11 + 3 + 6 = 63 / 9 = 7
