Yes, the product of (x - 3)^2 is a perfect square trinomial because it can be written as the square of the binomial (x - 3).
A perfect square trinomial is a trinomial of the form a^2 + 2ab + b^2, where a and b are terms that can be squared. When we expand the square of a binomial, we get a perfect square trinomial.
In this case, the binomial is (x - 3), and its square is (x - 3)^2. When we expand this expression, we get:
(x - 3)^2 = (x - 3)(x - 3) = x^2 - 6x + 9
This is a perfect square trinomial, because it can be written as the square of the binomial (x - 3). Specifically, we can write:
(x - 3)^2 = (x - 3)(x - 3) = (x - 3)^2
Therefore, the product of (x - 3)^2 is a perfect square trinomial.
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Use Table B in your Student Guide to answer the questions about ion concentrations.
A solution with a pH = 13 has approximately how many moles of OH ions per liter?
How many moles of H* would this same solution have per liter?
(Use the decimal form of your answer.)
A different solution with an H+ concentration of 1.0 x 10-4 would have a pH =
Considering the definition of pH and pOH, you obtain that:
a solution with a pH = 13 has 0.1 moles of OH⁻ ions per liter.a solution with a pH = 13 has 1×10⁻¹³ moles of H⁺ ions per liter.a different solution with an H⁺ concentration of 1.0×10⁻⁴ would have a pH= 4.What is the pH?pH is the Hydrogen Potential. It is a measure of acidity or alkalinity that indicates the amount of hydrogen ions present in a solution or substance.
Mathematically, pH is calculated as the negative base 10 logarithm of the activity of hydrogen ions, that is, the concentration of hydrogen ions:
pH= - log [H⁺]
Similarly, pOH is a measure of hydroxyl ions in a solution and is expressed as the logarithm of the concentration of OH⁻ ions, with the sign changed:
pOH= - log [OH⁻]
The following relationship can be established between pH and pOH:
pOH + pH= 14
In this case, you know that a solution has a pH = 13. So, the pOH can be calculated as:
pOH + 13= 14
pOH= 14 -13
pOH= 1
Then, the concentration of OH⁻ can be calculated as:
1= - log [OH⁻]
[OH⁻]= 10⁻¹
[OH⁻]= 0.1
Finally, a solution with a pH = 13 has 0.1 moles of OH⁻ ions per liter.
On the other side, remembering that pH = 13, the concentration of H⁺ can be calculated as:
13= - log [H⁺]
[H⁺]= 10⁻¹³
[H⁺]= 1×10⁻¹³
So, a solution with a pH = 13 has 1×10⁻¹³ moles of H⁺ ions per liter.
Finally, you have a different solution with an H⁺ concentration of 1.0×10⁻⁴. Replacing in the definition of pH:
pH= - log (1.0×10⁻⁴)
Solving:
pH= 4
Then, a different solution with an H⁺ concentration of 1.0×10⁻⁴ would have a pH= 4.
In summary, you obtain that:
a solution with a pH = 13 has 0.1 moles of OH⁻ ions per liter.a solution with a pH = 13 has 1×10⁻¹³ moles of H⁺ ions per liter.a different solution with an H⁺ concentration of 1.0×10⁻⁴ would have a pH= 4.Read more about molar mass here:
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What is the answer for -6+3a+4-5a+0
Answer:
-2a-2
Step-by-step explanation:
We can start solving this expression by combining like terms: Constants, or the number values, and Variables(the letters)
We can combine -6, 4, and 0 to get -2.
We can combine 3a and -5a to get -2a.
-2a + (-2) is the expression we are left with.
We can simplify this to
-2a - 2.
It can't be simplified further, so our answer is
-2a-2.
HELP
WHICH IS NOT A PROPIETY OF PARALLELOGRAM
According to the given information Congruent diagonals is not a property of parallelogram.
Why not? A kite is not a parallelogram.A kite's opposing forces aren't always parallel, just like not every kite is just a parallelogram. Trapezoids are quadrilaterals having a single pair of parallel sides. The parallel sides make up the bases. If somehow the foundation angles are equal, the trapezoid is said to be an isosceles trapezoid.
Do parallelograms count as diamonds?Since a diamond has four slanted, equal-length sides, it is an example of a rhombus. They are also both parallelograms since a parallelogram is indeed a rhombus and a diamond is one as well.
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Combine the like terms to simplify this expression: ( the 2 to the right of the x, is an exponent)
10y - 14x² + 3x - 4x² + 4y - 6
Answer: -18x² + 3x +14y - 6
10y - 14x² + 3x - 4x² + 4y - 6
- 14x²- 4x² + 3x + 10y + 4y -6
-18x² + 3x +14y - 6
10. at a pizza shop there is a deal going on that you can get a pizza for $3.00. you can choose thick or thin crust, red or white sauce, and one topping of either pepperoni, sausage, or vegetarian. create a tree diagram to display the sample space on your worksheet. how many total outcomes are there?
The number of total outcomes is 12.
Here is a tree diagram for the pizza options:
Copy code
/ | \
Thick Thin
/ | \
Red White Red White
/ | \ / | \ / | \
Pep Saus Veg Pep Saus Veg Pep Saus Veg
There are two (2) options for the crust, two (2) options for the sauce, and three (3) options for the topping. Therefore, the total number of outcomes is:
Total Outcomes = 2 (options for crust) x 2 (options for sauce) x 3 (options for topping)
Total Outcomes = 12
Therefore, there are 12 total outcomes.
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`h\left(x\right)=\frac{1}{2}x-14`
`h\left(-4\right)=`
Answer:
-16
Step-by-step explanation:
[tex]h\left(x\right)=\frac{1}{2}x-14\\h\left(-4\right)=-4/2-14=-2-14=-16[/tex]
A gardener wants to divide a square piece of lawn in half diagonally. what is the length of the diagonal side of the square is 8 fr. leave your answer in simplest radical form.
Answer:
8√2 feet
Step-by-step explanation:
You want the length of the diagonal of a square that is 8 ft on a side.
DiagonalThe diagonal of a square is the hypotenuse of the isosceles right triangle with leg lengths equal to the sides of the square. The ratios of side lengths in such a triangle is ...
1 : 1 : √2
Then the lengths of the sides of that triangle are ...
8 ft : 8 ft : 8√2 ft . . . . . multiply ratio values by 8 ft
The diagonal length is 8√2 feet.
__
Additional comment
If you use the Pythagorean theorem to find the diagonal length, you will determine it is ...
d = √(8² +8²) = 8√(1+1) = 8√2 . . . . feet
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double d, then subtract 6 from the result
Do not simplify any part of the expression.
Answer:
2d-6
Step-by-step explanation:
Since the d is doubled you are multipling then subtracting 6 from the result
Fifteen gallons of gas cost $50.25. What is the price per gallon
Answer:
$3.35
Step-by-step explanation:
$50.25 ÷ 15 gallons = $3.35 a gallon
3.8 liters = ____ deciliters?
Answer:
Step-by-step explanation:
3.8 liters = 38deciliters
Answer:
3.8 litres =38 deciliters
Mrs. Thapa wishes to grow flowers on the hanging bowls at her home. She bring hemispherical bowls from the market having internal diameter 21 cm and thickness 0.5 cm each and fills the bowls with compost completely. (i) If 1 cm³ of compost weighs 2.31 gm, find the total weight of required comp (ii) If she covers outer curved surface of each bowl with polythene sheet, find Width of the c Length of the Now the area of Hence, the cost o Also, the area of total amount of polythene.
The total volume of compost required for 16 bowls is 67,493.33 cm³
The total weight of compost required for 16 bowls is 155,906.67 gm
The total amount of polythene required for 16 bowls is: 6400π cm²
How to solve for this(i) The volume of compost required per bowl can be calculated as follows:
V = (4/3)πr^3, where r is the radius of the sphere
The radius of each bowl can be calculated as:
r = (d/2) - t, where d is the diameter (21 cm) and t is the thickness (0.5 cm)
So, r = (21/2) - 0.5 = 10 cm
Plugging the value of r into the formula for volume:
V = (4/3)πr^3 = (4/3)π * 10^3 = 4186.67 cm³
The total volume of compost required for 16 bowls is:
16 * 4186.67 = 67,493.33 cm³
The total weight of compost required for 16 bowls is:
67,493.33 cm³ * 2.31 gm/cm³ = 155,906.67 gm
(ii) To find the total amount of polythene required to cover the outer surface of 16 bowls, we first need to calculate the surface area of one bowl.
The surface area of a sphere can be calculated as follows:
A = 4πr^2
Plugging the value of r into the formula for surface area:
A = 4πr^2 = 4π * 10^2 = 400π cm²
The total amount of polythene required for 16 bowls is:
16 * 400π cm² = 6400π cm²
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Solve four-ninths plus five-eighteenths equals blank.
14 Jun 2018 · Norman is 12 years older than Michael. In 6 years, he will be twice as old as Michael. How old is Michael now? (A) 3 (B) 6 (C) 12
Michael is now (B) 6 years old.
Let's start by defining variables for the current ages of Norman and Michael.
Let N be Norman's current age, and M be Michael's current age.
From the problem statement, we know that N = M + 12 (Norman is 12 years older than Michael).
We also know that in 6 years, Norman will be twice as old as Michael.
So we can set up the following equation:
N + 6 = 2(M + 6)
Substituting N = M + 12 into the equation, we get:
M + 12 + 6 = 2(M + 6)
Simplifying:
M + 18 = 2M + 12
M = 6
Therefore, Michael is currently 6 years old.
Answer: (B) 6
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in a game of chance, a fair die is tossed. if the number is 1 or 2, you will win $3. if the number is 3, you win $5. if the number is 4 or 5, you win nothing, and if the number is 6 you lose $2. should you play the game, based on the long run expected amount you would win?
Answer:
Expected amount = $1.50
Step-by-step explanation:
Let's get a couple of definitions out of the way to understand how to compute the expected value given probabilities
Random Variable is a set of possible values from a random experiment.
We usually denote a random variable using the sets of possible values that the variable can take.
When we toss a fair die, the probability of getting a single number = 1/6 since there are 6 possible outcomes
The probability of getting 2 given numbers say 1 or 2 is twice 1/6 = 2 x 1/6 = 2/3 and so on
The expected value of each outcome is the value attached to each outcome x probability of that outcome
As an example, P(1 or 2) = 2/6 = 1/3
Payout = $3
Expected payout = 3 x 1/3 = $1
The table below summarizes the outcomes, probabilities, payouts and expected payouts
Outcome Probability Payout Expected Payout
(Payout x probability)
X = {1 or 2} 2/6 = 1/3 $3 $3 x 1/3 = $1
X = {3} 1/6 $5 $5 x 1/6 = $5/6
X = {4 or 5} 2/6 = 1/3 $0 $0 x 1/3 = $0
X = {6} 1/6 -2$ -$2 x 1/6 = -$2/6
The expected payout in the long run is the sum of the individual expected payouts
= $1 + $5/6 + $0 - $2/6 (5/6 - 2/6 = 3/6)
= $1 + $3/6 (3/6 = $0.50)
= $1 + $0.50
= $1.50
The expected value of the game is $2. This means that if you play the game many times, you can expect to win an average of $2 per game in the long run.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
To determine whether you should play the game, we need to calculate the expected value of the game.
The expected value is the sum of the product of each outcome and its probability.
The outcomes and their corresponding probabilities are:
Win $3 with probability 1/3 (if the number is 1 or 2)
Win $5 with probability 1/6 (if the number is 3)
Win $0 with probability 2/6 = 1/3 (if the number is 4 or 5)
Lose $2 with probability 1/6 (if the number is 6)
Using these probabilities and outcomes, we can calculate the expected value as:
Expected value = (3 × 1/3) + (5 × 1/6) + (0 × 1/3) + (-2 × 1/6)
= 1 + 5/6 - 1/6
= 1.666
= 2
Hence, the expected value of the game is $2. This means that if you play the game many times, you can expect to win an average of $2 per game in the long run.
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Pls help me this is very hard
Answer:
Step-by-step explanation:
35tu
(5 and 7 are like terms, and you put the 't' and 'u' in alphabetical order)
Answer:
ut=35
Step-by-step explanation:
5×u×t×7=0
collect like terms
ut=5×7
ut=35
There are 9 times as many strawberries as plums in a fruit basket. What is the ratio of the number of plums to the total number of strawberries and plums.
Answer:
Below
Step-by-step explanation:
strawberries to plums 9:1 then total would be 10 parts of which 1 is plums so 1 : 10
A square lawn has an area of 1922 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle?
A. 43. 84 B. 21. 92 C. 62 D. 31
The radius of the circle such that it just covers the lawn is B. 21.92.
The circular pattern just covering the square lawn will have one thing in common. It is the length or width of square which will be equal to diameter of the circle. So, finding the same to calculate our answer.
Area of square = side²
Side = ✓area
Keep the values
Side = ✓1922
Side = 43.84 feet
The side of the square will be the diameter. We know diameter is double of radius. So,
radius = 43.84/2
Performing division
Radius = 21.92 feet
Hence, correct option is B. 21.92
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in what way can a truthful set of statistics regarding a rise in vehicle theft over the course of a year in a city not reflect the actual situation?
A truthful set of statistics regarding a rise in vehicle theft over the course of a year in a city might not reflect the actual situation in several ways.
Here are a few possible examples:
Underreporting or overreporting: The statistics might be based on police reports of stolen vehicles, which may not capture all incidents of vehicle theft in the city. For instance, some victims may not report the theft to the police, or some incidents may be misclassified as other types of crime. Similarly, the statistics might include some incidents that are not actually vehicle thefts, such as cases where the vehicle was recovered undamaged or cases where the vehicle was not actually stolen, but rather borrowed without permission.
Geographical bias: The statistics might show an overall rise in vehicle thefts, but fail to capture the fact that the increase is concentrated in certain parts of the city. For example, a rise in thefts in a particular neighborhood might be masked by a decrease in thefts in other areas of the city.
Seasonal or temporal bias: The statistics might show an increase in vehicle thefts over the course of a year, but fail to account for seasonal or temporal factors that could be driving the increase. For instance, thefts might be more common during certain times of year (e.g., the summer) or on certain days of the week (e.g., weekends). If the statistics do not adjust for these factors, they might misrepresent the true trend in vehicle thefts.
Demographic bias: The statistics might show an increase in vehicle thefts overall, but fail to capture the fact that the rise is driven by thefts of certain types of vehicles or in certain neighborhoods. For example, if the increase is largely driven by thefts of high-end vehicles or in affluent areas, the statistics might not reflect the experiences of people who own less expensive vehicles or live in less affluent areas.
Overall, it's important to interpret statistical data with a critical eye and consider the limitations of the data source and methodology before drawing conclusions about the real-world situation.
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And i dont get this aswell
Answer:5
Step-by-step explanation:
This is a variation question.
When m is inversely proportional to n,
m ∝ 1/n
Now, there is a constant of 100.
So the formula connecting m and n is
m=k/n where k is the constant
=>m=100/n
Now, n= 20 ( 20 printers)
Thus, m=
100/20=5 minutes.
Hope this helps :)
the median should often be used to describe: select one: a. normal distributions. b. skewed distributions. c. large distributions. d. percentages.
The median should be used to describe a normal or skewed distribution, as it is a better measure of the central tendency than the mean for these types of distributions.
The median is a better measure of the central tendency than the mean when describing a normal or skewed distribution. A normal distribution is a symmetrical distribution of data in which values are evenly spread around the mean. A skewed distribution is when one side of the distribution is longer than the other, with the mean being pulled away from the center. The median is the most appropriate measure of central tendency for both normal and skewed distributions because the mean can be distorted by outliers and extremes in the data. The median is the midpoint in the data and provides a better representation of the middle of the distribution, which can be useful in interpreting the data. Using the median to describe a large distribution or percentage is not as common as it is better to use the mean or mode for these types of distributions.
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The science club and the math club each bought plain pizzas for their end of the year
parties from the same pizza parlor.
The science club paid $79.00 for 5 large pizzas and 2 medium pizzas.
The math club paid $86.00 for 4 large pizzas and 4 medium pizzas.
What is the price, in dollars, of a medium pizza? Enter your answer as $0.00
The price of medium pizza paid by both the science and maths clubs found using linear equations is $9.50.
What is meant by equation?
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Given,
Cost of 5 large pizzas and 2 medium pizzas paid by the science club = $79.00
Cost of 4 large pizzas and 4 medium pizzas paid by the math club = $86.00
Let the cost of medium pizza = x
Cost of large pizza = y
Now using the above equation we can write two linear equations.
2x + 5y = 79
4x + 4y = 86
Solving the above system of linear equations.
We are making the coefficient of the x variable the same.
Multiplying the first equation by 2.
4x + 10y = 158
4x + 4y = 86
Subtracting the equations.
6y = 72
y = 12
Now substituting in any one equation, we get the value of x.
2x + 5 * 12 = 79
2x = 19
x = 9.5
Therefore the price of medium pizza found using linear equations is $9.50.
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2v+12≥16 pls need help
Please help with left hand limit problem. When I plug in the values from the bottom graph (left hand limit) into the function I don’t get the same f(x) values as my teacher but 1.9 for the first one
Answer:
Step-by-step explanation:
your picture is blur. can you repost it?
The cylinder shown here has a height of 7 centimeters and a radius of 4 centimeters.
1. What is the area of the base of the cylinder? Express your answer in terms of .
2. How many cubic centimeters of fluid can fill this cylinder? Express your answer in terms of .
3. Give a decimal approximation of your answer to the second question using 3.14 to approximate n.
Answer:
1) 16pi square cm
2) 112pi cubed cm
3) 351.68 cubed cm
Step-by-step explanation:
Question 1: The base of a cylinder is a circle. To find the area of a circle, we can use the formula A = pi(r^2). the radius is 4 centimeters. 4^2 = 16.
The answer to the question is 16pi square cm
Question 2: This question is asking for the volume of the cylinder. To find the volume of the cylinder, we must multiply the area of the base by its height. we know the area of the base is 16pi. 16pi x 7(the height) = 112 pi.
The answer to the question is 112 pi cubed cm
Question 3: If pi were to be 3.14, we just need to substitute pi in the equation for question two with 3.14:
16(3.14) x 7 = 351.68
The answer is 351.68 cubed cm
Can somebody help me out here, please?
The addition and subtraction of the fractions by finding the LCD gives:
NUMBER 1: (8y-49) /(y²-49)
NUMBER 2: (x+10) /(2x+8)
NUMBER 3: (7a-2)/10b
NUMBER 4: 1
How to add and subtract the fractions by finding the LCD?Least Common Denominator (LCD) refers to the smallest multiple that two or more denominators have in common, and is used in operations involving fractions.
NUMBER 1
y/(y²-49) - 7(y+7) = y/[(y+7)(y-7)] - 7(y+7)
LCD of (y+7)(y-7) and (y+7) is (y+7)(y-7):
= [y + 7(y-7)] / [(y+7)(y-7)]
= [y + 7y-49)] / [(y+7)(y-7)]
= (8y-49) / (y+7)(y-7)
= (8y-49) /(y²-49)
NUMBER 2
1/2 + 3/(x + 4) = [1(x+4) + 3*2] /[2(x+4)]
= [x+4 + 6] /[2(x+4)]
= (x+10) /(2x+8)
NUMBER 3
(a+2)/4b + (a-1)/10b + (a-3)/5b = [5(a+2) + 2(a-1) + 4(a-3)]/20b
= [5a+10 + 2a-2 + 4a-12]/20b
= (14a-4)/20b
= 2(7a-2)/20b
= (7a-2)/10b
NUMBER 4
x/(x+1) - 1/(x-1) + 2x/(x²-1) = [x(x-1) - 1(x+1) + 2x]/(x²-1)
= [x²-x -x-1 + 2x]/(x²-1)
= (x²-1)/(x²-1)
= 1
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The Martinez family just bought 6 crates of eggs, and each crate had 12 eggs. The family already had 9eggs in their refrigerator. How many eggs do they have now?
The Martinez family just bought 6 crates of eggs, and each crate had 12 eggs. The family already had 9 eggs in their refrigerator. Total number of eggs they have now is 81.
The problem states that the Martinez family bought 6 crates of eggs, and each crate had 12 eggs. So, we can start by multiplying the number of crates by the number of eggs per crate to find out how many eggs they bought in total:
6 crates x 12 eggs/crate = 72 eggs
This tells us that the family now has 72 eggs. However, the problem also states that the family already had 9 eggs in their refrigerator. To find out how many eggs they have now in total, we need to add the number of eggs they bought to the number of eggs they already had:
72 eggs + 9 eggs = 81 eggs
So the answer is that the Martinez family now has a total of 81 eggs.
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A math test has 12 multiplication problems and 24 division problems.
What is the ratio value of division problems to multiplication problems?
Answer as a fraction in simplest form.
Answer:2\1
Step-by-step explanation:24\12 then simplify and get 2\1
The total mass of a box and some oranges was 25kg. The total mass of the same box and some apples was 11kg. The mass of the oranges was 3 times the mass of apples
From The total mass of orange and box, the mass of oranges are 2kg and the mass of empty box is 23kg.
Let's use "o" to represent the mass of one orange and "a" to represent the mass of one apple.
We can set up two equations based on the information given:
Box + Oranges = 25 kg (equation 1)
Box + Apples = 11 kg (equation 2)
Oranges = 3 x Apples (equation 3)
We can substitute equation 3 into equation 1 to eliminate "oranges":
Box + 3a = 25 kg
We can substitute equation 3 into equation 2 to eliminate "oranges" again:
Box + a = 11/3 kg
Now we have two equations with two unknowns. We can solve for "Box" and "a" using either substitution or elimination. For example, we can multiply the second equation by 3 and subtract it from the first equation:
Box + 3a = 25
3(Box + a = 11)
-2Box + 2a = 2
Simplifying, we get:
Box - a = -1
We can add this equation to the second equation to get:
2Box = 11 - 1 = 10
So, Box = 5 kg.
Now we can substitute this value back into equation 2 to find "a":
5 + a = 11/3
a = 2/3 kg
Finally, we can use equation 3 to find the mass of the oranges:
Oranges = 3 x Apples = 3 x (2/3) = 2 kg.
Therefore, the mass of the oranges is 2 kg.
The mass of the empty box is the difference between the total mass of the box and the fruit and the mass of the fruit:
Mass of box = Total mass - Mass of fruit
From equation 1, we know that the total mass of the box and the oranges is 25 kg. From part a, we know that the mass of the oranges is 2 kg. Therefore:
Mass of box = 25 kg - 2 kg = 23 kg.
So, the mass of the empty box is 23 kg.
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____The given question is incomplete, the complete question is given below:
The total mass of a box and some oranges was 25kg . The total mass cii N the same box and some apples was 11kg . The mass of the oranges was 3 times the mass of the apples. (a) Find the mass of the oranges.. (b) Find the mass of the empty box.
what is the value of y?
Answer:
y = 43
Step-by-step explanation:
47° , y and 90° lie on the straight line AB and sum to 180° , that is
47 + y + 90 = 180
y + 137 = 180 ( subtract 137 from both sides )
y = 43
consider the two statements a. a iff b. b. (not a) iff (not b). under what circumstances are these statements true? under what circumstances are they false? explain why these statements are, in essence, identical.
The two statements a iff b and (not a) iff (not b) has been explained
The two statements are known as biconditionals, which state that two statements are true if and only if each other.
"a iff b" means that "a" is true if "b" is true, and "a" is false if "b" is false. In other words, "a" and "b" have the same truth value.
"(not a) iff (not b)" means that "not a" is true if and only if "not b" is true, and "not a" is false if and only if "not b" is false.
Therefore, these two statements are equivalent because they express the same idea: "a" and "b" have the same truth value. If "a" is true, then "b" is true, and if "a" is false, then "b" is false. Similarly, if "b" is true, then "a" is true, and if "b" is false, then "a" is false.
These statements are true in cases where both "a" and "b" have the same truth value. If both are true or both are false, then the statements are true. If "a" is true and "b" is false, or vice versa, then the statements are false.
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