How can I use context clues and keywords to translate situations into inequalities? Explain with an example of your own.

If the following statements are true, use the Law of Detachment to derive a new true statement.

1) If you are a penguin, then you live in the Southern Hemisphere.

2) You are a penguin.

Remember if p then q

The law of detachment, or modus ponens, doesn't apply when the antecedent is false or when premises lack conditional statements, making deductions invalid in these cases.

The law of detachment, also known as modus ponens, is a fundamental principle in classical logic that allows us to make valid deductions. However, there are situations where it does not apply:

Invalid Antecedent: In modus ponens, we start with a conditional statement (if-then statement) as our premise and then affirm the consequent. If the antecedent (the "if" part) of the conditional statement is false, the law of detachment cannot be applied. For example, if we have the statement "If it is raining, then the ground is wet" and we know that the ground is not wet, we cannot conclude anything about whether it's raining or not, as the antecedent is false.

Lack of a Conditional Statement: Modus ponens requires a conditional statement as its premise. If we are given unrelated or non-conditional premises, we cannot apply this rule. For instance, if we know that "John is a doctor" and "The sun is shining," we cannot use modus ponens to deduce anything because there is no conditional relationship between the statements.

In summary, while modus ponens is a valid and powerful inference rule in classical logic, it cannot be applied when the antecedent is false or when the premises do not involve conditional statements.

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Complete question below:

Could you provide two examples where the law of detachment does not apply in logic?

Answer:

The volume is equal to [tex]18\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of each figure is equal to

[tex]V=LWH[/tex]

where

L is the length

W is the width

H is the height

Step 1

Find the volume of figure N 1

[tex]V1=1.5*2*3=9\ cm^{3}[/tex]

Step 2

Find the volume of figure N 2

[tex]V2=1.5*2*2=6\ cm^{3}[/tex]

Step 3

Find the volume of figure N 3

[tex]V3=1.5*2*1=3\ cm^{3}[/tex]

Step 4

Find the total volume

[tex]V=V1+V2+V3=9+6+3=18\ cm^{3}[/tex]

Answer:

[tex]\text{Volume of podium}=18\text{ ft}^3[/tex]

Step-by-step explanation:

We have been given a graph of podium for a track meet and we are asked to find the volume of our given podium.

To find the volume of podium we will find volume of each podium using volume of cuboid formula.

[tex]\text{Volume of cuboid}=l*b*h[/tex], where,

[tex]l=\text{ Length of cuboid}[/tex],

[tex]b=\text{ Breadth of cuboid}[/tex],

[tex]h=\text{ Height of cuboid}[/tex].

Upon substituting our given values in cuboid formula we will get,

[tex]\text{Volume of cuboid 1}=\text{3 ft*2 ft*1.5 ft}[/tex]    

[tex]\text{Volume of cuboid 1}=9\text{ ft}^3[/tex]    

[tex]\text{Volume of cuboid 2}=\text{2 ft*2 ft *1.5 ft}[/tex]

[tex]\text{Volume of cuboid 2}=6\text{ ft}^3[/tex]

[tex]\text{Volume of cuboid 3}=\text{1 ft*2 ft *1.5 ft}[/tex]

[tex]\text{Volume of cuboid 3}=6\text{ ft}^3[/tex]

Let us add volume of each cuboid to find the volume of our given podium.

[tex]\text{Volume of podium}=9\text{ ft}^3+6\text{ ft}^3+3\text{ ft}^3[/tex]

[tex]\text{Volume of podium}=18\text{ ft}^3[/tex]

Therefore, volume of our given podium is 18 cubic feet.

For Penn Foster the answer you find the answer to this qrestion In the section called Analysis of “ Paul’s Case” 4 th paragraph an Archetype appears repeatedly throughout history -It’s a prototype . So the qrestion people are asking is. Archetypes are a type of _______ that appear throughout history? A. foreshadowing B. prototype C. subgenre D. motif

Answer true and correct B. PROTOTYPE

I made a hundred on this test for pf

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a=adult

c=child

a+c=214

c=214-a

9c+14a=2081

9(214-a)+14a=2081

1926-9a+14a=2081

5a=155

a=155/5=31

31 adults

183 children

check

31*14 = 434

183*9=1647

1647+434=2081

side 1 = x

side 2 = x+5

side 3 = x+14

perimeter = side 1 + side 2 + side 3

133 = x + (x+5) + (x +14)

133=3x + 19

114=3x

x=114/3 = 38

side 1 = 38

side 2 = x+5 = 38+5 = 43

side 3 = x+14 = 38+14 = 52

38+43+52 = 133

side lengths are 38, 43 & 52

Answer:

3

Step-by-step explanation:

took quiz on edge

Answer:

Move all terms not containing x to the right side of the inequality. x≥8

Closed circle on 8, shading to the right.

Answer:

Answer is C

Step-by-step explanation:

Area of an equilateral triangle can be found by the following formula,

A=[tex]\frac{\sqrt{3}} {4} a^{2}[/tex]

Where "a" is the length of one side of the triangle.

Now we can substitute the value given to the equation above and find the area of the given equilateral triangle.

A=[tex]\frac{\sqrt{3}} {4}(14\sqrt{3})^ {2}[/tex]

=[tex]\frac{\sqrt{3}} {4} 196*3[/tex]

=[tex]\frac{\sqrt{3}*196*3} {4}[/tex]

=[tex]254.611[/tex]

A=[tex]255[/tex] square feet.

Answer is C

In this case, we have two different brands of thread and we have data about their tensile strength. We calculate the standard error of the difference between their means and use that to construct a 95% confidence interval. The result suggests the average tensile strength of Brand B is significantly higher than that of Brand A.

To construct a 95% confidence interval for the difference of the population means between the two types of threads, we first need to calculate the standard error of the difference which is the square root of the sum of the squares of the standard deviations divided by the respective sample sizes. In this case, the sample sizes for brands A and B are both 50.

The standard error of the difference = sqrt[(5.6^2/50) + (6.3^2/50)] = approximately 1.18

Since we are trying to build a 95% confidence interval, we have to look at the z-score corresponding to this confidence level. A 95% confidence interval corresponds to 1.96 standard deviations either side of the mean, thus the z-score is 1.96.

We can then calculate the confidence interval as:
Lower limit = (78.3 - 87.2) - 1.96 x 1.18 = -11.52
Upper limit = (78.3 - 87.2) + 1.96 x 1.18 = -7.08

So the 95% confidence interval for the difference between the mean tensile strengths of the two thread types is approximately (-11.52, -7.08) kilograms.

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86/7 = 12.28 days worth

 so they will run out on the 13th day of the next month

The unit price of a towel is calculated by dividing the total cost of the pack ($15.20) by the number of towels in the pack (8), which equals $1.90 per towel.

In order to find the unit price in dollars per towel, we simply divide the total cost of the pack by the number of towels in the pack. So for Rachel who paid $15.20 for a pack of 8 towels, to find the cost per towel, you'd divide $15.20 by 8.

To calculate:

Divide the total cost by the number of items: $15.20 / 8

This equals $1.90. So, the cost per towel, or unit price, is $1.90.

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693-57 = 636

636/2 = 318

cheeseburgers sold = 318

 hamburgers sold = 318 + 57 = 375

To determine the number of hamburgers sold on a specific day, an equation is set up and solved to find the value of hamburgers. In this scenario, 375 hamburgers were sold on Wednesday.

The question is asking how many hamburgers were sold on a specific Wednesday given the total combined sales of hamburgers and cheeseburgers and that fewer cheeseburgers were sold than hamburgers. To find the number of hamburgers sold, we can set up a system of equations. Let's define H as the number of hamburgers and C as the number of cheeseburgers. From the information provided, we have the following equations:

Substituting the second equation into the first gives us:

H + (H - 57) = 693

2H - 57 = 693

Adding 57 to both sides, we get:

2H = 693 + 57

2H = 750

Now divide both sides by 2:

H = 375

Therefore, 375 hamburgers were sold on Wednesday.

Answer:

9cm

Step-by-step explanation:

If the given equation is represented as "2(x - 1) = 14", then the value of the variable "x" is 8.

To solve the equation 2(x - 1) = 14 for x, we use algebraic techniques to separate x.

First, we distribute the 2 to both terms inside the brackets;

2x - 2 = 14,

Next, we separate the variable x by adding 2 to both sides of the equation:

2x - 2 + 2 = 14 + 2,

Simplifying the equation:

2x = 16,

At last , to solve for x, we divide both sides of the equation by 2:

We get,

(2x) / 2 = 16 / 2,

x = 8,

Therefore, the solution to the equation 2(x - 1) = 14 is x = 8.

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Answer:

608.33

108.33

Step-by-step explanation:

Found answer in above answer.

To determine the intersection points of the helix and the sphere, we substitute the helix's parametric expressions into the sphere's equation, simplify, and solve for t, resulting in two points of intersection upon further substitution back into the helix's equation.

The question asks at what points the helix r(t) = (sin t, cos t, t) intersects the sphere x2 + y2 + z2 = 65. To find the intersections, we substitute the parametric equations of the helix into the equation of the sphere. Thus, we get (sin2t) + (cos2t) + t2 = 65. Using the Pythagorean identity sin2t + cos2t = 1, the equation simplifies to 1 + t2 = 65, which further simplifies to t2 = 64. Solving for t, we find t = ±8. Thus, the helix intersects the sphere at the points generated by these t values, which can be found by substituting t back into the helix equations, resulting in (sin(8), cos(8), 8) and (sin(-8), cos(-8), -8), with approximate numerical values after calculations.