The measure of 1/2 of the circumference of a circle is 157 feet. What is the radius of the circle, to the nearest foot?

The possible solutions to the equation are:

3π/4

π/4

Trigonometric equations involve trigonometric functions such as sine, cosine, tangent, etc. The goal is to solve for the unknown variable in the equation.

csc²x - 2 = 0

csc²x = 2

csc x = √2

sin x = 1/√2    (Remember: csc x  = 1/sinx)

x = sin⁻¹(1/√2 )

x = 90° or 135°  (sine is positive in 1st and 2nd quadrants)

x = π/4 or 3π/4

Thus, the possible solutions to the equation are x = π/4 or 3π/4.

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Answer:

2,000

Step-by-step explanation:

The value of X in the given fraction is 1/12

A fraction is a mathematical expression that represents a part of a whole or a quotient of two numbers. It is expressed as one integer or number (called the numerator) divided by another integer or number (called the denominator), separated by a line or a slash.

Here, we are going to find the LCM of both 4 and 6 to determine the value of X.

LCM = 12

X = 1/4 - 1/6

X = (3 - 2)/12

X = 1/12

Therefore, we can conclude that the value of X in the given fraction is 1/12.

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The equation of the graph is

The table is completed by substituting the x to the function y = sqrt(x) + 2

When x = 0:

y = sqrt(0) + 2

y = 0 + 2

y = 2

When x = 1:

y = sqrt(1) + 2

y = 1 + 2

y = 3

When x = 4:

y = sqrt(4) + 2

y = 2 + 2

y = 4

When x = 9:

y = sqrt(9) + 2

y = 3 + 2

y = 5

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Answer: 1,024 different ways

Step-by-step explanation:

      We will use the Fundamental Counting Principle. There are 5 questions, each with 4 possible answers. To use the principle and answer the question, we will multiply 4 by itself 5 times.

             4 * 4 * 4 * 4 * 4 = 1,024 different ways

Think of it like this:

            you have 4 objects (the 4 answer options, a, b, c, and d)

            You are going to chose a group of 5, and the order matters (your         answer to question #1 is independent of your choice on #3)

             Repetition is allowed (you can answer "c" on all of the questions if you want to)

This is a simple permutation. Use the formula:

       [tex]\bold{n^r}[/tex]

       where n is the number of objects (the number of answer choices)

       and r is the number of objects you will choose (5, one answer for each question)

To solve:

[tex]4^5[/tex]

[tex]1,024 \longleftarrow[/tex] your answer!

Hope this helps! Feel free to ask any follow up questions, and please "vote up" :)

Answer:

Step-by-step explanation:

area of trapezoid

[tex]= \frac{sum~of~parallel~sides}{2} \times altitude\\69.6=\frac{sum~of~parallel~sides}{2} \times 8.7\\139.2=sum~of~parallel~sides \times 8.7\\sum~of~parallel~sides=\frac{139.2}{8.7} =16[/tex]

minimum parameter=16+2(8.7)=16+17.4=33.4 in

Answer:

Sequence A is defined by subtracting 6 from the previous term and taking the absolute value, while Sequence B is the sum of the first n odd integers. B(9) > A(9).

To produce each new term from the previous term, subtract 6 from the previous term, then take the absolute value of the result. That is, if the previous term is x, then the next term is |x - 6|.

To find A(9) and B(9), we can apply the rules we have for each sequence:

A(0) = 19

A(1) = |19 - 6| = 13

A(2) = |13 - 6| = 7

A(3) = |7 - 6| = 1

A(4) = |1 - 6| = 5

A(5) = |5 - 6| = 1

A(6) = |1 - 6| = 5

A(7) = |5 - 6| = 1

A(8) = |1 - 6| = 5

A(9) = |5 - 6| = 1

B(0) = 0 (the sum of the first 0 odd integers)

B(1) = 1

B(2) = 1 + 3 = 4

B(3) = 1 + 3 + 5 = 9

B(4) = 1 + 3 + 5 + 7 = 16

B(5) = 1 + 3 + 5 + 7 + 9 = 25

B(6) = 1 + 3 + 5 + 7 + 9 + 11 = 36

B(7) = 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49

B(8) = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64

B(9) = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81

Answer:

Step-by-step explanation:

d.

The potential rational zeros of the given polynomial are ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±15, ±20, ±30, ±60, ±1/2, ±1/3, ±2/3, ±5/2, ±4/3, ±5/3, ±10/3, ±1/6, ±5/6, ±1/10, ±2/5, ±4/15, ±1/15, ±2/15.

How to calculate potential rational zeroes?

The Rational Zero Theorem states that if a polynomial with integer coefficients has any rational zeros, then they must have the form of a fraction p/q, where p is a constant term factor and q is a leading coefficient factor.

For the given polynomial q(x)=6x^3+31x^2+23x−20, the constant term is -20, and the leading coefficient is 6. Therefore, the potential rational zeros can be expressed as follows:

p/q = ± {factors of the constant term (-20)}/{factors of the leading coefficient (6)}

Possible factors of -20: ±1, ±2, ±4, ±5, ±10, ±20

Possible factors of 6: ±1, ±2, ±3, ±6

Therefore, the potential rational zeros are:

±1/1, ±2/1, ±4/1, ±5/1, ±10/1, ±20/1,

±1/2, ±2/2, ±4/2, ±5/2, ±10/2, ±20/2,

±1/3, ±2/3, ±4/3, ±5/3, ±10/3, ±20/3,

±1/6, ±2/6, ±4/6, ±5/6, ±10/6, ±20/6.

Simplifying and eliminating duplicates, we get:

±1, ±2, ±4, ±5, ±10, ±20,

±1/2, ±2/2, ±4/2, ±5/2, ±10/2, ±20/2 (which simplifies to ±1, ±2, ±3, ±5, ±10, ±20),

±1/3, ±2/3, ±4/3, ±5/3, ±10/3, ±20/3 (which simplifies to ±1/3, ±2/3, ±4/3, ±5/3, ±10/3),

±1/6, ±2/6, ±4/6, ±5/6, ±10/6, ±20/6 (which simplifies to ±1/6, ±1/3, ±2/3, ±5/6, ±5/3, ±10/3).

Therefore, the potential rational zeros of the given polynomial are ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±15, ±20, ±30, ±60, ±1/2, ±1/3, ±2/3, ±5/2, ±4/3, ±5/3, ±10/3, ±1/6, ±5/6, ±1/10, ±2/5, ±4/15, ±1/15, ±2/15.

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the distance between the points P=(-7, -2) and E=(1,-9) in the coordinate plane is √113

The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.

We have two points p=(-7,-2) and E=(1,-9)

then the distance between PE is

d=√(1+7)²+(-9+2)²

d= √(64+49)

d=√113

the distance between the points P=(-7, -2) and E=(1,-9) in the coordinate plane is √113

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Answer:

Step-by-step explanation:

Table A is showing the correct relation of equation y=1.5x

An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). They are used to model real-world phenomena, to solve problems, and to make predictions. Examples of equations include linear equations, quadratic equations, systems of equations, and differential equations.

Using the relation;

y=1.5x

Putting the value x=9

y=1.5×9

y=13.5

Putting the value x=11

y=1.5×11

y=16.5

On observing the tables, option A is satisfying the relation

Hence, Table A is showing the correct relation of equation y=1.5x.

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The complete question is:

Image is attached below.

Answer:

Step-by-step explanation:

scalar factor= 2, in order to find the scalar factor between two triangle  we need to get the ratio between any of thier side of both the triangle on same side

what is scalar factor?

In mathematics, a scalar factor is a numerical value that scales or stretches a vector or a matrix by a certain factor. In other words, a scalar factor is a constant that is multiplied to a given vector or matrix to change its size or magnitude.

In the given question,

In mathematics, a scalar factor is a numerical value that scales or stretches a vector or a matrix by a certain factor. In other words, a scalar factor is a constant that is multiplied to a given vector or matrix to change its size or magnitude.

For instance, if we have a vector v = (x, y, z), then multiplying it by a scalar factor k will result in a new vector kv = (kx, ky, kz), which is stretched or shrunk according to the value of k. Similarly, if we have a matrix A, multiplying it by a scalar factor k will result in a new matrix kA, where each element of A is multiplied by k.

in order to find the scalar factor between two triangle  we need to get the ratio between any of thier side of both the triangle on same side

scalar factor= opposite side of bigger triangle / opposite side of smaller triangle

scalar factor= 20/10

scalar factor= 2

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The weight of the pumpkins that Gina's class grew was measured.

a) There is a total of 23 pumpkins.

b) 7 pumpkins weigh 10 pounds.

c) The number of pumpkins that weigh 6 pounds is equal to 3 times the number of pumpkins that weigh 9 pounds.

Based on the given information, we can complete the sentences as follows:

a) There is a total of 23 pumpkins.

To get this number, we need to add up the number of dots for each weight:

3 + 5 + 1 + 7 + 4 + 2 + 1 = 23

b) 7 pumpkins weigh 10 pounds.

To find the weight with the most dots, we look for the peak in the line plot, which corresponds to 10 pounds, and count the number of dots on this peak, which is 7.

c) The proportion of pumpkins that weigh 6 pounds to those that weigh 9 pounds is 3 times.

To find the number of pumpkins that weigh 6 pounds, we count the number of dots on the peak corresponding to 6 pounds, which is 3. To find the number of pumpkins that weigh 9 pounds, we count the number of dots on the peak corresponding to 9 pounds, which is 1. Multiplying the number of pumpkins at 9 pounds by 3, we get 3 x 1 = 3, which is the same as the number of pumpkins at 6 pounds. Therefore, the statement is true.

The complete question is:-

Gina's class measured the weights of the pumpkins that they grew.

A line plot named “Pumpkin Weights” shows data from six to fourteen pounds. Six has three dots. Eight has five dots. Nine has one dot. Ten has seven dots. Twelve has four dots. Thirteen has two dots. Fourteen has one dot. Fill in the boxes to complete the sentences below to make each statement true.

a)there is a total of ____ pumpkins.

b) 7 pumpkins weigh _____ pounds.

c) the number of pumpkins that weigh ____ pounds is equal to 3 times the number of pumpkins that weigh 9 pounds.

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Answer:

Step-by-step explanation:

Applying absolute value rule the solutions are:

x + 1/2 = 3/2/3       or        x + 1/2 = -3 2/3

Changing to fractions:

x + 1/2 = 11/3   or   x + 1/2 = -11/3

and then changing to a common denominator

x + 3/6 = 22/6    or    x + 3/6  = -22/6

Solve left equation first:

x + 3/6 - 3/6 = 22/6 - 3/6

x = 19/6 or 3 1/6

Solve the right equation:

x + 3/6 - 3/6 = -22/6 - 3/6

x = -25/6 or  -4 1/6

So the two solutions are:

19/6 and -25/6 as improper fractions

And

as mixed numbers:  3 1/6 and -4 1/6

Here, a a⁻¹ b = 1b = b shows that a⁻¹ is indeed inverse of a, and x = a⁻¹b is a valid solution to the equation ax = b.

An equation is a statement that two expressions are equal. A solution of an equation is a value (or a set of values) that makes the equation true.

In the equation ax = b, the solution x = a⁻¹b means that if we multiply a by its inverse a⁻¹, we get 1, the multiplicative identity. So, when we multiply both sides of the equation by a⁻¹, we get:

a⁻¹(ax) = a⁻¹b

Multiplying a⁻¹ and a on the left side of the equation gives:

1x = a⁻¹b

which simplifies to x = a⁻¹b. This shows that x = a⁻¹b is a solution to the equation ax = b.

The statement "a a⁻¹ b = 1b = b" means that when we multiply a by its inverse a⁻¹, we get the multiplicative identity 1, and when we multiply 1 by b, we get b. So, a a⁻¹ b = 1b = b shows that a⁻¹ is indeed the inverse of a, and x = a⁻¹b is a valid solution to the equation ax = b.

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The fifth multiple of each fraction is shown as follows:

1. 2/6 = 5/3

2. 7/10 = 7/2

3. 3/8 = 15/8

4. 5/12 =25/12

5. 7/6 = 35/6

To get the multiple of a fraction, the best thing to do will be to multiply the fraction by the whole number in question. In this case, the whole number is five.

So, to get the right answers, you can begin by multiplying the functions with the whole number five. The values obtained are the fifth multiples. for the fraction, 2/6, the fifth multiple is 5/3.

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Therefore , the solution of the given problem of equation comes out to be  line passing through the spot (-4,1) and perpendicular to [tex]y = 1/3x + 5[/tex] is [tex]y = -3x - 11.[/tex]

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of a different method that could split 12 to two parts, consider the data supplied by y + 7,.

Here,

[tex]Y = mx + b[/tex], where m is the line's slope and b is its y-intercept, is the given equation in slope-intercept notation.

Provided that the slope of the provided line is 1/3, the slope of a line perpendicular to it will be the reciprocal of the negative of 1/3, or -3.

=> [tex]y - y_{1} = m(x - x_{1} )[/tex]

in which m [tex]= -3, x_{1} = -4,[/tex] and y1 = 1.

By replacing these numbers, we obtain:

=>[tex]y - 1 = -3(x - (-4))[/tex]

By condensing and figuring out x, we arrive at:

=> [tex]y - 1 = -3(x + 4)[/tex]

=>[tex]y - 1 = -3x - 12[/tex]

=> [tex]y = -3x - 11[/tex]

Consequently, the equation of the line passing through the spot (-4,1) and perpendicular to y = 1/3x + 5 is y = -3x - 11.

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The interest is $9.To find the interest, we can use the simple interest formula:

I = P * r * t

what is interest ?

Interest is the amount of money charged by a lender to a borrower for the use of money, usually expressed as a percentage of the amount borrowed. In other words, it is the cost of borrowing money.

In the given question,

To find the interest, we can use the simple interest formula:

I = P * r * t

where I is the interest, P is the principal, r is the annual interest rate as a decimal, and t is the time in years.

Here, the principal is $200, the annual interest rate is 9%, and the time is 1/2 year.

Converting the annual interest rate to a decimal, we get:

r = 9% = 0.09

And, converting the time to years, we get:

t = 1/2 year

Substituting the values into the formula, we get:

I = $200 * 0.09 * (1/2) = $9

Therefore, the interest is $9.

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The series [tex]a_n=\frac{(-1)^{n+1}}{n}[/tex] is converges.

What is a series?

An n-arithmetic sequence is a sequence in which the difference d of successive terms is constant.

The general term of the arithmetic progression can be written using its first term [tex]a_1[/tex], tolerance [tex]d[/tex], and index [tex]n[/tex] as [tex]a_n=a_1+(n-1)d[/tex].

According to the alternating series test, if a sequence {b_n} satisfies the following three conditions:

[tex]b_n[/tex] is positive for all [tex]n[/tex].

[tex]b_n[/tex] is decreasing (i.e., [tex]b_n > = b_{n+1}[/tex] for all n).

[tex]\lim_{n \to \infty} b_n =0\\[/tex]

Then the alternating series [tex](-1)^n b_n[/tex] converges.

To apply the alternating series test to the sequence {a_n}, we first note that [tex]a_n = (-1)^{n+1}/n[/tex] satisfies condition 3, since [tex]\lim_{n \to \infty} \frac{1}{n} =0[/tex].

Next, we observe that [tex]a_n[/tex] is positive for n = 1, 3, 5, ... and negative for n = 2, 4, 6, ..., so [tex](-1)^n a_n = (-1)^{n+1}/n[/tex] is an alternating sequence.

Finally, we show that a_n is decreasing by considering the difference between successive terms,

[tex]a_{n+1} - a_n = (-1)^n/n - (-1)^{n+1}/(n+1)\\ = (-1)^{n} [(n+1)/(n(n+1))] \\= (-1)^{n}/n(n+1) < 0[/tex]

since n and n+1 are both positive. Therefore, a_n is decreasing.

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Answer:

yes

Step-by-step explanation:

The mean of the set is 1/2.

The mean is a statistical measure that represents the average value of a set of numbers. To calculate the mean, you add up all the values in the set and then divide by the total number of values in the set.

To find the mean of a set of numbers, you add up all the numbers in the set and then divide the result by the total number of numbers in the set.

In this case, the set has six numbers:

2/3, 1/6, 1/3, 2/3, 7/9, 1/3

Adding them up, we get:

(2/3) + (1/6) + (1/3) + (2/3) + (7/9) + (1/3) = 3

So the sum of the numbers in the set is 3.

To find the mean, we divide this sum by the total number of numbers in the set, which is 6:

3/6 = 1/2

Therefore, the mean of the set is 1/2.

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We need a sample size of at least 879 to be 99.5% confident that our estimate of the population mean will be within 1 of the true population mean.

To determine the required sample size, we use mathematical formula:

[tex]n = (z * σ / E) ^ 2[/tex]

Where:

n: sample size

z: z-score corresponding to desired level of confidence (99.5%)

σ: population standard deviation

E: margin of error (1 in this case)

Substitute given values into formula:

[tex]n = (2.807 * 29.6 / 1) ^ 2\\n = 878.3[/tex]

Hence, in order to be 99.5% confident that our estimate of the population mean would be within 1 of the actual population mean, we need a sample size of at least 879.

It's vital to remember that the estimate will be more accurate the larger the sample size. Larger sample numbers might, however, also be more costly and time-consuming to gather. Hence, while choosing the sample size, researchers must carefully weigh the trade-offs between the required level of confidence, the margin of error, and the resources at their disposal.

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Justin is 14 years old, and Hassan is 15 years old.

What are integers?

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

Let's assume that Justin's age is x. Then, Hassan's age is x + 1, since their ages are consecutive integers and Hassan is older than Justin.

We are given that the product of their ages is 210:

x(x + 1) = 210

Expanding the left-hand side and simplifying, we get:

x² + x - 210 = 0

This is a quadratic equation in standard form. We can solve for x by using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 1, and c = -210.

Plugging these values into the formula, we get:

x = (-1 ± √(1² - 4(1)(-210))) / 2(1)

x = (-1 ± √(1 + 840)) / 2

x = (-1 ± √(841)) / 2

We take the positive root because x represents Justin's age, which is a positive integer. Therefore:

x = (-1 + 29) / 2 = 14

So, Justin is 14 years old, and Hassan is 15 years old.

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Overall, the Perez family likely benefited both financially and emotionally from each of these sources during their time of need.

The Perez family likely benefited in different ways from each of these sources during their time of need:

Insurance: If the Perez family had insurance, it is likely that they were able to receive financial assistance to cover some of their expenses. Depending on the type of insurance they had, they may have been able to receive money to pay for medical bills, property damage, or other expenses related to their time of need.

Non-profits: Non-profits may have provided the Perez family with resources such as food, clothing, and shelter during their time of need. These organizations may have also provided emotional support to the family, helping them feel less alone during a difficult time.

Family and friends: Family and friends likely provided the Perez family with emotional support during their time of need, as well as practical assistance such as meals, childcare, and help with household tasks. Financially, family and friends may have also helped the Perez family by providing loans or gifts of money.

Government: The government may have provided the Perez family with financial assistance through programs such as unemployment benefits, food stamps, or housing assistance. Additionally, the government may have provided emotional support to the family through counseling services or other resources.

Overall, the Perez family likely benefited both financially and emotionally from each of these sources during their time of need.

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The exact value of the trigonometric expression, given the conditions of sin and sec is -85/36.

The exact value of the trigonometric expression with u and v in Quadrant III is 304/425.

We are given sin(u) = -3/5 with 3π/2 < u < 2π and cos(v) = 15/17 with 0 < v < π/2.

cos(v - u) = cos(v)cos(u) + sin(v)sin(u)

We are given cos(v) = 15/17 and sin(u) = -3/5. To find sin(v) and cos(u), we can use the Pythagorean identities:

sin^2(v) + cos^2(v) = 1

sin(v) = sqrt(1 - (15/17)^2) = 8/17

Similarly, for cos(u):

sin^2(u) + cos^2(u) = 1

cos(u) = -sqrt(1 - (-3/5)^2) = -4/5

Now we can find cos(v - u):

cos(v - u) = cos(v)cos(u) + sin(v)sin(u)

cos(v - u) = -36/85

Since sec(v - u) = 1/cos(v - u), we have:

sec(v - u) = 1/(-36/85) = -85/36

Since both u and v are in Quadrant III, sin(u) and cos(u) are both negative, and sin(v) and cos(v) are both negative. We are given sin(u) = -7/25 and cos(v) = -15/17.

To find sin(v) and cos(u), we can use the Pythagorean identities:

sin^2(u) + cos^2(u) = 1

cos(u) = -sqrt(1 - (-7/25)^2) = -24/25 (since u is in Quadrant III)

Similarly, for sin(v):

sin^2(v) + cos^2(v) = 1

sin(v) = -sqrt(1 - (-15/17)^2) = -8/17 (since v is in Quadrant III)

Now we can find cos(u + v):

cos(u + v) = (-24/25)(-15/17) - (-7/25)(-8/17)

cos(u + v) = 304/425

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It would cost $282.60 to fill a cylindrical tank with a diameter of 6 feet and a height of 2 feet.

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of equal size and shape, connected by a curved side.

To calculate the cost of filling a tank with a diameter of 6 feet and a height of 2 feet, assuming a cost of $5 per cubic foot and using the value of pi as 3.14, we first need to calculate the volume of the tank.

The volume of a cylinder (which is the shape of the tank) is given by the formula:

V = π[tex]r^2h[/tex]

where V is the volume, r is the radius (half the diameter), and h is the height.

Since the diameter of the tank is 6 feet, the radius is 3 feet. Therefore:

V = 3.14 x [tex]3^2[/tex] x 2

= 56.52 cubic feet

Multiplying the volume of the tank by the cost per cubic foot gives us the total cost of filling the tank:

Total cost = 56.52 x $5

= $282.60

Therefore, it would cost $282.60 to fill a tank with a diameter of 6 feet and a height of 2 feet, assuming a cost of $5 per cubic foot and using the value of pi as 3.14.

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The total number of college students is 204,700,000.

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Here, Percentage of enrolled student for part time = 23%

         Total enrolled students = 8.9 millions

Number of part time student = 23% x 8.9 million

                                              [tex]= 0.23 \times 8900000[/tex]

                                             [tex]=204,700,000[/tex]

Thus, the total number of college students is 204,700,000.

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This argument is invalid because the premises do not logically lead to the conclusion. The conclusion is simply a repetition of the first premise and does not follow from the second premise. The argument lacks coherence and fails to establish a clear relationship between the premises and the conclusion. Therefore, we cannot accept the conclusion as a logical consequence of the premises.