13. suppose that we color each of the eight corners of a cube. using three different colors, how many ways can the corners be colored up to a rotation of the cube?

After solving equation , the plumber put in 3.1 hours of work (or 3 hours, 6 minutes).

A mathematical assertion that demonstrates the equality of two expressions is called an equation The equals symbol (=) is used to denote the separation of two phrases. Numerous mathematical ideas and relationships, including linear functions, quadratic functions, and trigonometric functions, can be represented by equations.

Let's use the letter 'h' to indicate how many hours the plumber put in.

The plumber costs $35 to come to Jerald's residence and $50 for every hour they work. If Jerald is charged a total of $190 by the plumber, the following equation can be written:

$50h + $35 = $190

To solve for 'h,' we obtain:

$50h = $190 - $35

$50h = $155

h = 155 / 50

h = 3.1

Consequently, the plumber put in 3.1 hours of work (or 3 hours, 6 minutes).

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The prism has an 8/27 cubic centimetre volume.

The following formula determines a cube's volume:

V = s³

where V is the volume of the cube and s is the length of one of its sides.

In other words, to find the volume of a cube, you simply need to raise the length of one of its sides to the third power (cube it).

The volume of a cube = s³

Given that the prism is composed of cubes with a one-third-centimeter side measurement.

Volume of a cube = (1/3)³ = 1/27

There are 8 cubes in the prism.

Therefore, the volume of the prism is;

=8(1/27)

= 8/27 cubic centimeter.

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The complete question is:

The prism below is made of cubes which measure of a centimeter on one side. What is the volume?

Note: Figure is not drawn to scale.

The prism below is made of cubes which measure 1/3 of a centimeter on one side. What is the volume?

Image is attached below.

If M is the midpoint of the leg CG, then the

a) Area of ABD = 18.75 ft^2

b) Area of MOC = 15 ft^2

To solve this problem, we need to use the properties of trapezoids and their diagonals. Let's start with finding the area of ABD.

First, notice that ABD and COD are similar triangles because they share angle O. Thus, we can write

AB/CD = AD/CO

Since AD = BC (opposite sides of a trapezoid are parallel), we can simplify to:

AB/CD = BC/CO

We also know that the area of AOD is 15 ft^2

Area of ABD/ Area of COD = AB/CD

We can substitute the ratio AB/CD from the similarity relation above to get

Area of ABD/ Area of COD = BC/CO

Since the bases of the trapezoids are parallel

Area of ABD/ Area of COD = BD/CO

Finally, we can use the fact that the altitudes from B and O to the longer base are in a 5:3 ratio to write

Area of ABD/ Area of COD = 5/3

Area of ABD = 5/8 × Area of COD

We know that the area of AOD is 15 ft^2, so the area of COD is twice that, or 30 ft^2. Therefore

Area of ABD = 5/8 × 30 = 18.75 ft^2

Next, we need to find the area of MOC. To do this, we can use the fact that the diagonals of a trapezoid divide it into four triangles, and the areas of these triangles are proportional to the lengths of the diagonals.

Let x be the length of OC, and let y be the length of OG. Then we have

Area of MOC/ Area of MOG = x/y

Also, since M is the midpoint of CG, we have

x = 2y

Substituting this into the first equation, we get

Area of MOC/ Area of MOG = 2

We know that the area of MOG is half the area of AOD, so

Area of MOG = 15/2 ft^2

Therefore, we have

Area of MOC = 2 × Area of MOG = 15 ft^2

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39 degrees of freedom will be used to find the t-critical statistic value.

We need to find degrees of freedom for the t-critical statistic value with 40 sample towers and a normally distributed population. According to the given dataset we can assume that we have the 95% confidence interval which is taken as default if nothing is mentioned about it.

The degrees of freedom (df) for a t-distribution are calculated as given below:

df = n - 1

where n is the sample size of the problem.

In this case, the sample size is 40, so the degrees of freedom would be:

df = 40 - 1 = 39

Therefore, we would use 39 degrees of freedom to find the t-critical statistic value for a 95% confidence interval.

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Answer:

see what you got to do is you have to find n

the new club sent out 50 coupons to existing members and 150 coupons to potential members to boost sales for next year's memberships.

How to solve the question?

Let x be the number of coupons sent to existing members. Then the number of coupons sent to potential members is 3x, as they provided 3 times as many coupons to potential members than to existing members.

According to the problem, the total number of coupons sent is 200. Therefore, we can write the following equation:

x + 3x = 200

Simplifying this equation, we get:

4x = 200

Dividing both sides by 4, we get:

x = 50

Therefore, the number of coupons sent to existing members is 50, and the number of coupons sent to potential members is 3 times as many, or 150.

In conclusion, the new club sent out 50 coupons to existing members and 150 coupons to potential members to boost sales for next year's memberships.

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The equation when solved for b gives ± 7√a/3. Option C

Algebraic expressions are defined as expressions that are composed of terms, variables, constants, coefficients and factors.

They are also composed of arithmetic operations, such as;

From the information given, we have;

9ab² = 49

To determine the value of b, take the following steps

Divide both sides by 9a

b² = 49/9a

Now, find the square root of both sides, we have;

b = [tex]\sqrt{\frac{49}{9a} }[/tex]

b = ± 7√a/3

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If you are trying to determine if an input variable may affect your key characteristic (output variable) by examining the

correlation between variables, you should use the tool: D. Scatter plot diagram. therefore, option D.Scatter plot

diagram is correct.

A scatter plot diagram is a graphical representation of the relationship between two variables. It can help you visualize

the correlation between the input and output variables, making it easier to determine if there is a potential cause-and-

effect relationship.

The tool that you should use to examine the correlation between variables is D. Scatter plot diagram.

A scatter plot diagram is a graphical representation that displays the relationship between two variables.

The x-axis represents the input variable, while the y-axis represents the output variable.

By plotting the data points on the scatter plot diagram, you can visually analyze the correlation between the variables.

If there is a strong positive or negative correlation between the variables, it suggests that the input variable may affect

the key characteristic (output variable).

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D. Scatter plot diagram is the tool that should be used to examine the correlation between variables to determine if an input variable may affect your key characteristic (output variable).

The scatter plot diagram is a graphical representation that displays the relationship between two variables, and it is commonly used to identify patterns, trends, and correlations between variables. By examining the scatter plot diagram, you can determine whether there is a positive, negative, or no correlation between the variables, which can help you to identify potential cause-and-effect relationships.
 To determine if an input variable may affect your key characteristic (output variable) by examining the correlation between variables, you should use:

A scatter plot diagram is a graphical tool that helps visualize the relationship between two variables, allowing you to identify any correlation between the input and output variables.

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Answer:

In its simplest form, the ratios of the length of sides in a 45 45 90 special right angle triangles should be 1 : 1 : 2 1:1:\sqrt{2} 1:1:2on:

And because this is a 30-60-90 triangle, and we were told that the shortest side is 8, the hypotenuse must be 16 and the missing side must be 8 * 3 , or 8 3 . Our final answer is 8√3

The statement is true. The DecimalFormat class is part of the Java API, specifically within java.text package, so it is automatically available to your programs. You can use it to format numbers in various ways, such as for displaying currency or percentages.

DecimalFormat is a concrete subclass of NumberFormat that formats decimal numbers. It has a variety of features designed to make it possible to parse and format numbers in any locale, including support for Western, Arabic, and Indic digits. It also supports different kinds of numbers, including integers (123), fixed-point numbers (123.4), scientific notation (1.23E4), percentages (12%), and currency amounts ($123). All of these can be localized.

To obtain a NumberFormat for a specific locale, including the default locale, call one of NumberFormat's factory methods, such as getInstance(). In general, do not call the DecimalFormat constructors directly, since the NumberFormat factory methods may return subclasses other than DecimalFormat. If you need to customize the format object, do something like this:

NumberFormat f = NumberFormat.getInstance(loc);

if (f instanceof DecimalFormat) {

    ((DecimalFormat) f).setDecimalSeparatorAlwaysShown(true);

}

A DecimalFormat comprises a pattern and a set of symbols. The pattern may be set directly using applyPattern(), or indirectly using the API methods. The symbols are stored in a DecimalFormatSymbols object. When using the NumberFormat factory methods, the pattern and symbols are read from localized ResourceBundles

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True. The Decimal Format class is a part of the Java API and is included in the java.text package.

It is automatically available to Java programs without the need for any additional installations or imports.

The Decimal Format class is part of the Java API, and it is automatically available to your programs.

The Java API is a collection of pre-written classes, methods, and interfaces that are part of the Java Development Kit (JDK).

These classes and methods provide a wide range of functionalities that can be utilized by Java developers to build robust applications.
The Decimal Format class, specifically, is a subclass of the Number Format class and is used to format decimal numbers according to a specific pattern.

The class provides methods to format and parse decimal numbers and can be used to specify the number of digits after the decimal point, the use of a thousand separator, and the currency symbol.
The Decimal Format class in your Java program, you simply need to import the class using the import statement, and then create an instance of the class.

For example:
import java. text. Decimal Format.
public class MyClass

{
public static void main (String [] args) {
Decimal Format df = new Decimal Format("#.00");
double num = 1234.5678
System.out.println(df.format(num));
}
}
The Decimal Format class using the import statement, and then create an instance of the class called df.

We then use the format method of the class to format the decimal number 1234.5678 with two decimal places.
The Decimal Format class is an essential part of the Java API and is automatically available to your programs.

Its inclusion in the Java API makes it easier for Java developers to format decimal numbers in their applications.

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The interest she will have to pay is $28.

Answer:

x = 7 years

Step-by-step explanation:

The mean (M) is defined as the average of the sum of all the data points in a set:

[tex]M=\frac{r_{1}...r_{n} }{n}[/tex]

Thus, since there are five data points and we're given the mean, we can use the following formula to find x:

[tex]M=10\\10=\frac{(8+x+13+12+10)}{5}\\ 50=43+x\\7=x[/tex]

Answer:

y = [tex]\frac{x(k+1)}{k-1}[/tex]

Step-by-step explanation:

First, recall that in a proportion (a set of equivalent ratios), the product of means is equal to the product of extremes. For example,

if [tex]\frac{a}{b} = \frac{c}{d}[/tex] (or a:b = c:d) the product of means (b and c) is equal to the product of extremes (a and d), and we have ad = cb.

Using this knowledge, in the proportion (y+x):(y-x) = k:1, let us find the product of means and extremes and set them equal, like so:

(y+x):(y-x) = k:1 =

k(y-x) = y+x =

ky - kx = y+x

To solve for y, move all terms including y to one side, like so:

ky - kx = y+x =

ky - y = kx + x

Now, factor out y.

ky - y = kx + x =

y(k - 1) = kx + x

Then, factor out the common term x.

y(k - 1) = kx + x =

y(k - 1) = k(x + 1)

Now, finish isolating the variable by dividing by (k-1), and we have:

y =  [tex]\frac{x(k+1)}{(k-1)}[/tex]

Answer:

Step-by-step explanation:

1 + 1 divided by 3 x 3.5 = 4.66 or 4 2/3

Answer:

To find the values of f(g(x)) for the given values of x, we need to first evaluate g(x) for each value of x, and then plug the result into f(x).

Using the given functions:

g(x) = 2x - 5

f(x) = √(x+1)

Therefore, we have:

f(g(x)) = √(g(x) + 1) = √(2x - 5 + 1) = √(2x - 4) = 2√(x - 2)

So, we can complete the table as follows:

x f(g(x))

4 2

10 4

20 6

34 8

52 10

Therefore, the completed table is:

x f(g(x))

4 2

10 4

20 6

34 8

52 10

Each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.

Let's consider the number of ways to seat n couples around a circular table without any restrictions first.

Since there are 2 people in each couple, there are a total of 2n people. The number of ways to seat 2n people around a circular table is (2n-1)!/2n,

where we divide by 2n to account for rotations of the same seating arrangement.

Now, let's consider the restriction that no couple can sit together.

We can start by fixing one person in a couple, and then there are (2n-2) ways to seat the other person in that couple so that they don't sit together.

After that, we can fix another person and their partner, and there are (2n-4) ways to seat the remaining two people in their couple so that they don't sit together.

We can continue this process until all couples are seated.

Therefore, the total number of ways to seat n couples around a circular table so that no couple sits together is:

[tex](2n-2)(2n-4)(2n-6)...2 = 2^{n-1} * (n-1)![/tex]

We multiply by[tex]2^{n-1}[/tex] to account for the fact that each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.

Note that reflected seatings are considered to be different, so we don't need to worry about dividing by 2 as we did in the unrestricted case.

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The compound interest investment earns more interest than the simple interest investment, and the difference becomes more significant over time.

After 10 years, the difference is relatively small, but after 20 years, the compound interest investment has earned over $3,700 more than the simple interest investment.

To calculate the amount after 10 and 20 years, we can use the following formulas:

Simple Interest: A = P * (1 + r * t)

Compound Interest: A = P * (1 + r/n)^(n*t)

Where:

Using these formulas and the information given in the table, we can calculate the amount after 10 years and 20 years for each type of investment.

For simple interest, the interest is not compounded, so we just add the interest to the principal:

Amount after 10 years: A = $50,000 * (1 + 0.0275 * 10) = $68,750

Amount after 20 years: A = $50,000 * (1 + 0.0275 * 20) = $87,500

For compound interest, we need to use the formula above with n=12 (since the interest is compounded monthly):

Amount after 10 years: A = $50,000 * (1 + 0.0275/12)^(12*10) = $68,704.23

Amount after 20 years: A = $50,000 * (1 + 0.0275/12)^(12*20) = $91,262.47

To compare the two investments, we can look at the difference between the amounts after 10 and 20 years:

Difference after 10 years: $68,750 - $68,704.23 = $45.77

Difference after 20 years: $87,500 - $91,262.47 = $3,762.47

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From the figures, AB is a tangent to the C because they make a right angles (90⁰)

Recall that in n Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs.

We shall be determining the angle at C to see if it gives 90⁰

Using trigonometrical ratios of tangent

TanB = Opposite/Adjacent

Tan B. = 4.8/7.2

Tan B = 0.6667

B = Tan⁻¹0.6667

<B = 33.69⁰

Also in the same manner,

TanS = opp/Adj

Tan S = 7.2/4.8

Tan S = 1.5

S = Tan⁺¹1.5

< S = 56.31⁰

Npw <S + <B = 56.32 + 33.69 = 89.9999247 = 90⁰

Therefore AB makes tangent at C

20.  

Tan C = Opp/Adj

Tan C = 15/11.2

Tan C = 1.3393

C = Tan⁺¹1.3393

< C = 53.25

Also, Tan B = 11.2/15

Tan B = 0.7467

B = 36.75

<B + <C = 36.75 + 53.25 = 89.9986 = 90⁰

Therefore AB makes a tangent at C

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Answer:

The correct answer is:

10√2

Explanation:

In a right triangle, the hypotenuse is the side opposite the right angle and is also the longest side. The other two sides are called the legs.

In this problem, the hypotenuse of the resulting triangles is given as 20 inches. Since the quilt squares are cut on the diagonal to form triangular quilt pieces, the hypotenuse of each triangle is formed by the diagonal cut of a square.

Let's denote the side length of each square as "s" inches.

According to the Pythagorean Theorem, which relates the sides of a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

In this case, the hypotenuse is 20 inches, so we have:

20^2 = s^2 + s^2 (since the two legs of the right triangle are the sides of the square)

400 = 2s^2

Dividing both sides by 2, we get:

200 = s^2

Taking the square root of both sides, we get:

s = √200

Since we are looking for the side length of each piece in simplified radical form, we can further simplify √200 as follows:

√200 = √(100 x 2) = 10√2

So, the side length of each quilt piece is 10√

The side length of each piece of the triangular pieces of quilt cut from squares will be 10√2 inches.

This is a simple mathematics problem that can be solved using the Pythagoras theorem. This theorem states that in a right-angled triangle, the square root of the sum of the two perpendicular sides (p,b) is equal to the longest side, called the hypotenuse (h).

[tex]h = \sqrt{p^2 + b^2}[/tex]

Since the triangle pieces have been cut from a square, they will be right-angled triangles, and the two perpendicular sides will be equal, i.e., p = b.

20 = √2p²  (since p and b are equal, b can be taken as p)

On squaring both sides,

400 = 2p²

p² = 400/2

p² = 200

p = √200

p = 10√2 = b

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There are 64 degrees of freedom for the test for independence in this contingency table.

To find the degrees of freedom for a test for independence in a contingency table, you can use the following formula:
Degrees of freedom (df) = (number of rows - 1) * (number of columns - 1).
In your case, the contingency table has nine rows and nine columns. Using the formula:
df = (9 - 1) * (9 - 1)
df = 8 * 8
df = 64.

In a contingency table, the degrees of freedom (df) for the test of independence are calculated as:

df = (number of rows - 1) x (number of columns - 1)

In this case, the contingency table has nine rows and nine columns, so the degrees of freedom are:

df = (9-1) x (9-1) = 64

This means that there are 64 degrees of freedom for the test of independence.

Degrees of freedom are important because they determine the critical values for the test statistic, which in turn affects the decision to reject or fail to reject the null hypothesis.

In general, as the degrees of freedom increase, the critical values decrease, making it easier to reject the null hypothesis.

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There are 64 degrees of freedom for the test for independence in a contingency table with nine rows and columns.

To determine the degrees of freedom for the test for independence in a contingency table with nine rows and columns, we use the formula df = (r-1)(c-1), where r is the number of rows and c is the number of columns.

Substituting in the values, we get:df = (9-1)(9-1)df = 8 x 8df = 64A contingency table is a table that shows the frequency distribution of two or more categorical variables.

A test for independence is a statistical test that checks whether the variables are related or not.

Therefore, there are 64 degrees of freedom for the test for independence in a contingency table with nine rows and columns.

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The bank's claim is exaggerated and not entirely accurate.

The bank's claim that virtually all of its customers are served in less than 11 minutes is misleading, as it implies that almost all customers are served in 11 minutes or less. However, based on the given information that service times follow an exponential distribution with a mean of 4.5 minutes, we can calculate the probability that a customer will be served in less than 11 minutes using the cumulative distribution function of the exponential distribution:

P(X < 11) = 1 - [tex]e^{(-11/4.5)[/tex] = 0.956

This means that approximately 95.6% of customers will be served in less than 11 minutes, not "virtually all." Therefore, the bank's claim is exaggerated and not entirely accurate.

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The resistance of each bulb that is connected in series with a 110 V line is 24.55 Ω with a 13.75 V Voltage difference across each bulb. The power dissipated in each bulb is 7.7 W, if 0.56 A current flows through them.

The voltage across 8 identical bulbs is 110 V

Since they are connected in a series and identical, the Voltage difference across each bulb is [tex]\frac{110}{8}[/tex] V which is 13.75 V

According to the question,

The current flowing through the bulb = 0.56 A

So according to Ohm's Law,

V = IR

13.75 = 0.56 * R

R = 24.55 Ω

The power dissipated in each bulb can be calculated as

P = VI

P = 13.75 * 0.56 = 7.7 W

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In summary, the voltage across each bulb is 13.75V, the resistance of each bulb is 24.55Ω, and the power dissipated in each bulb is 7.7W.

When eight identical lights are connected in series across a 110-V line, the voltage across each bulb will be 110/8 = 13.75 V.
To find the resistance of each bulb, we can use Ohm's law, which states that resistance is equal to voltage divided by current (R = V/I). Therefore, the resistance of each bulb is 13.75/0.56 = 24.55 ohms.
To find the power dissipated in each bulb, we can use the formula P = VI, where P is power, V is voltage, and I is current. Therefore, the power dissipated in each bulb is 13.75 x 0.56 = 7.7 watts.
To find the voltage across each bulb, divide the total voltage by the number of bulbs:

Voltage across each bulb = Total Voltage / Number of Bulbs = 110V / 8 = 13.75V per bulb

Next, use Ohm's Law to find the resistance of each bulb:

Resistance (R) = Voltage (V) / Current (I) = 13.75V / 0.56A = 24.55Ω per bulb

Finally, find the power dissipated in each bulb using the formula:

Power (P) = Voltage (V) x Current (I) = 13.75V x 0.56A = 7.7W per bulb

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Step-by-step explanation:

Volume of a sphere is given by the formula

4/3 pi r^3       diameter = 6.3 cm  so radius, r = 3.15 cm

4/3 * pi * (3.15)^3 = 130.9 cm^3

Based on the given scenario, Steve who manages the property is a real estate agent.

The correct answer choice is option A

A real estate agent is a person who serves as n intermediary between tenant and landlord, buyers and sellers of properties. They collect rent, make little repairs and screen interested people. The real estate agent receives their reward based on commission, that is, a particular percentage of the property.

Therefore, Jordan is the tenant, Dave is the landlord and Steve is the real estate agent.

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The statement " Some irrational numbers do not have an additive inverse" is false because every real number, whether rational or irrational, has an additive inverse.

Every real number, whether rational or irrational, has an additive inverse. The additive inverse of a real number x is the number that, when added to x, gives zero as the result. For any real number x, its additive inverse is -x.

This is a fundamental property of the real numbers and is true regardless of whether a number is rational or irrational. Therefore, any irrational number, such as the square root of 2 or pi, also has an additive inverse. For example, the additive inverse of the irrational number √2 is -√2, since √2 + (-√2) = 0.

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Answer: The function that has real zeros at x = 3 and x = 7 is:

f(x) = (x - 3)(x - 7)

Expanding this function using FOIL (First, Outer, Inner, Last) method:

f(x) = x^2 - 10x + 21

Therefore, the answer is:

f(x) = x^2 - 10x + 21

Step-by-step explanation:

Since quadrilateral H'I'J'K' is a translation of quadrilateral HIJK, the translation rule include the following: (x, y)  → (x - 8, y + 10).

In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.

By translating the pre-image of quadrilateral HIJK horizontally left by 8 units and vertically up by 10 units, the coordinate J of quadrilateral H'I'J'K' include the following:

(x, y)                               →                  (x - 8, y + 10)

J (8, -2)                        →                  (8 - 8, -2 + 10) = J' (0, 8).

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In both cases, the subject term (S) and the predicate term (P) are distributed, which means that the proposition makes a claim about the entire class of S and the entire class of P.

Traditional categorical logic, a proposition with both of its terms (subject and predicate) distributed is called a universal proposition.

Stronger claim than a particular proposition.

A universal proposition is a statement that applies to all members of a category or class.

Asserts that the subject term is either entirely included or entirely excluded from the predicate term.

There are two types of universal propositions:

Universal affirmative proposition (A): All S are P.

Universal negative proposition (E): No S are P.

"All mammals are warm-blooded" is a universal affirmative proposition (A) because it claims that the subject term (mammals) is entirely included in the predicate term (warm-blooded).

It distributes both terms and claims the most knowledge.

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Answer: I'll have to say it's C or D but I think it's D

Hope it helped :D