Find the value of K , if x-1 is a factor of x^3+3x^2-4x+k

Your chance of being chosen to attend the festival is approximately: Probability = 1 / 23 ≈ 0.0435 or 4.35% when rounded to four decimal places.

To determine your chance of being chosen to attend the festival, you need to find the probability of your name being

drawn from the basket.

There are 22 other people in class, and each person, including you, will have their name on a piece of paper.

Total number of names in the basket = 22 (other people) + 1 (you) = 23

Since each person has an equal chance of being chosen, the probability of your name being drawn is:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

Probability = 1 (your name) / 23 (total names)

So, your chance of being chosen to attend the festival is approximately:

Probability = 1 / 23 ≈ 0.0435 or 4.35% when rounded to four decimal places.

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Answer:

radius of circle T/smaller circle = 4 units

Diameter of larger circle is 10units

radius of larger circle = D/2

= 10/2 = 5units

CIRCUMFERENCE OF SMALLER CIRCLE =

2πr = 2 × 3.14 × 4

= 25.12 units

Area of smaller Circle =

πr² = 3.14 × 4 × 4

= 50.24 units²

CIRCUMFERENCE OF LARGER CIRCLE =

2πr = 2 × 3.14 × 5

= 31.4 units

Area of larger circle =

πr² = 3.14 × 5 × 5

= 78.5 units²

Check the picture below.

The given statement "In the unit method of proportioning, the longest dimension of an object is set equal to one unit." is False because the unit method of proportioning does not require the longest dimension.

In the unit method of proportioning, a chosen dimension of an object is set equal to one unit, and then all other dimensions are expressed in terms of that unit, regardless of whether it is the longest dimension or not.

For example, if a rectangle has a width of 4 cm and a length of 6 cm, we could choose to set the length as the unit and express the width as a fraction of the unit: 4/6 or 2/3 of a unit.

Alternatively, we could choose to set the width as the unit and express the length as a fraction of the unit: 6/4. In either case, the longest dimension of the object is not necessarily the unit.

The unit method of proportioning is commonly used in art and design to help maintain consistent proportions between different elements of a composition. It allows for easy scaling and adjustment of proportions while preserving the overall relationships between the different elements.

Rather, any dimension can be chosen as the unit, and the other dimensions are expressed in terms of that unit.

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Naomi walks a total of 6 + 4 + 7.2 ≈ 17.2 meters.

How to calculate?

Naomi walks the length of the room, which is 6 meters, then across the width, which is 4 meters.

Using the Pythagorean theorem, the length of the diagonal can be found:

diagonal = √(6²2 + 4²2)

diagonal = √(36 + 16)

diagonal = √52

diagonal ≈ 7.2 meters

Therefore, Naomi walks a total of 6 + 4 + 7.2 ≈ 17.2 meters.

The Pythagorean theorem is a fundamental concept in mathematics that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

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Answer:

PQ = 165.60m

Step-by-step explanation:

Since triangles are similar

PQ/70 + 210 = 124.2/210

PQ = 124.2 (70 + 210)/210 = 165.60m

The measure of angle Q is equal to 40°.

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. In Geοmetry, triangles are the type οf pοlygοns, which have three sides and three vertices.

This is a twο-dimensiοnal figure with three straight sides. A triangle is cοnsidered a 3-sided pοlygοn. The sum οf all the three angles οf a triangle is equal tο 180°. The triangle is cοntained in a single plane. Based οn its sides and angle measurement, the triangle has six types.

Using Cos θ = adjacent/ Hypotenuse

Cos Q = 720/ 940

Cos Q = 36/47

Q = arccos 36/47

Q = 40.007793734°

Thus, The measure of angle Q is equal to 40°.

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Answer:

[tex] \sf \: 6x + 14 [/tex]

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The property we use,

→ Distributive property.

The expression is,

→ 2(3x + 7)

Let's simplify the expression,

→ 2(3x + 7)

→ 2(3x) + 2(7)

→ (2 × 3)x + 14

→ 6x + 14

Hence, the answer is 6x + 14.

Answer: 200 teachers attended the conference

Step-by-step explanation:

        To answer this question, we will find 5% of 4,000. A percent divided by 100 becomes a decimal, and "of" means multiplication in mathematics.

        5% / 100 = 0.05

        4,000 * 0.05 = 200 teachers attended the conference

The answer is 200

If 5% of teachers at a university attended a conference and 4000 teachers are enrolled at the university, about 200 teachers attended the conference. What is the problem asking for? The problem is asking us to calculate how many teachers attended a conference given that 5% of the total number of teachers at a university attended the conference and that the university has 4000 teachers .What is the formula for percentage? The formula for percentage is given by:(Part/Whole)*100Let T be the total number of teachers at the university, and let x be the number of teachers that attended the conference. We know that 5% of teachers at a university attended a conference, therefore:(5/100)*T = x,. Given that there are 4000 teachers in the university, we can substitute this value into the equation: (5/100)*4000 = x. Simplifying the equation, we get: x = 0.05 * 4000x = 200.

Therefore, about 200 teachers attended the conference.

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The diameter of the lens of a particular telescope is approximately 4 feet.

The circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line, then the length of that line will be the circle's circumference.

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, d is the diameter, and π is approximately equal to 3.14.

In this case, we are given that the circumference of the lens is 12.56 feet. So we can plug in the values:

12.56 = 3.14d

To solve for d, we need to isolate it on one side of the equation. We can do this by dividing both sides by 3.14:

d = 12.56/3.14

Simplifying, we get:

d ≈ 4

Therefore, the diameter of the lens is approximately 4 feet

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The three numbers are:

(-1 + √(97))/2, (-1 ± √(97))/2, (-1 ± 7√(97))/2

What is an arithmatic progression?

An arithmetic progression is a sequence of numbers in which each term after the first is obtained by adding a fixed constant to the preceding term. The fixed constant is called the common difference, denoted by d.

Let the three numbers in the GP be a/r, a, and ar, where a is the middle term.

Then we have:

a/r + a + ar = 26 (sum of GP)

(a/r + 5) + (a + 9) + (ar + 5) = 3(a + 4) (sum of AP)

Simplifying the second equation, we get:

a(r - 1) = 3

Substituting this into the first equation, we get:

a/r + a + ar = 26

1/r + 1 + r = 26/a

r^2 + r - 26/a = 0

Solving for r using the quadratic formula, we get:

r = (-1 ± √(1 + 104/a))/2

Since r > 0 (because the terms are in GP), we take the positive root:

r = (-1 + √(1 + 104/a))/2

Substituting this into the equation a(r - 1) = 3, we get:

a(-1 + √(1 + 104/a))/2 - a = 3

-a + a √(1 + 104/a) - 2 = 0

a √(1 + 104/a) = -a + 2

a² (1 + 104/a) = a² - 4a + 4

104a = 4a² - 4a + 4

a² - a + 1 = 26

(a - 1/2)² + 3/4 = 26

(a - 1/2)² = 97/4

a - 1/2 = ±√(97)/2

a = (1 ± √(97))/2

Since the terms are in GP, we can use the value of a to find the other two terms:

a/r = (1 ± √(97))/(2(-1 + √(1 + 104/a))/2) = (-1 ± √(97))/2

ar = (1 ± √(97))/(2(-1 - √(1 + 104/a))/2) = (-1 ± 7√(97))/2

Therefore, the three numbers are:

(-1 + √(97))/2, (-1 ± √(97))/2, (-1 ± 7√(97))/2

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The required volume of the cube is increasing at a rate of 15,000 cubic centimeters per second when the length of each edge is 50 centimeters and the edges are increasing at a rate of 2 centimeters per second.

Let us consider V be the volume of the cube,

And s be the length of one edge of the cube.

Volume of a cube is equal to,

V = s^3

To find how fast the volume is changing with respect to time,

Use the chain rule of differentiation,

dV/dt = dV/ds × ds/dt

where dV/dt is the rate of change of volume with respect to time,

dV/ds is the rate of change of volume with respect to the length of one edge of the cube,

And ds/dt is the rate of change of the length of one edge of the cube with respect to time.

ds/dt = 2 cm/s,

find dV/dt when s = 50 cm.

First, find dV/ds,

dV/ds = 3s^2

Then, we can plug in s = 50 cm,

dV/ds = 3(50)^2

          = 7500 cm^2

Finally, we can plug in the values we have to find dV/dt,

dV/dt = (dV/ds) × (ds/dt)

         = 7500 cm^2/s × 2 cm/s

         = 15,000 cm^3/s

Therefore, the volume of the cube is increasing at a rate of 15,000 cubic centimeters per second .

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Answer:

(6-3)

Step-by-step explanation:

The difference between the perimeter and area of the figure is -20 square units.

In geometry, the perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.

The figure is a rectangle with sides DE and FG measuring 8 units, and sides EF and GD measuring 6 units.

To find the perimeter of the figure, we can add up the lengths of all four sides:

Perimeter = DE + EF + FG + GD

Perimeter = 8 + 6 + 8 + 6

Perimeter = 28

To find the area of the figure, we can use the formula for the area of a rectangle:

Area = length * width

Area = DE * EF

Area = 8 * 6

Area = 48

Therefore, the difference between the perimeter and area of the figure is:

Perimeter - Area = 28 - 48

Perimeter - Area = -20

The difference between the perimeter and area of the figure is -20 square units.

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Answer:

The answer to your problem is, B. y=11.8x+29.2

Step-by-step explanation:

Determine the line of the best fit grpahically

Find the problem:

y = 11 x 8x + 29 x 2 B.

The approximate probability that x is between 15 and 25 (inclusive) is 0.3026.

To solve this problem, we will use the binomial distribution, since we are dealing with a binary outcome (nonconforming vs. conforming) and a fixed sample size. Let p = 0.11 be the probability of a nonconforming shaft and q = 1 - p = 0.89 be the probability of a conforming shaft. Then, the probability mass function of x is given by:

P(X = x) = (200 choose x) * p^x * q^(200-x)

(a) To find the probability that x is at most 30, we can compute:

P(X ≤ 30) = Σ P(X = x) for x from 0 to 30

However, this is quite tiresome to tally by hand, so we can instead use a normal approximation to the binomial distribution. Specifically, if np and nq are both at least 10, then we can approximate the binomial distribution with a normal distribution with mean μ = np and standard deviation σ = sqrt(npq). In this case, we have np = 22 and nq = 178, both of which are at least 10.

Thus, we can approximate X with a normal distribution:

[tex]X ~ N(mu, σ^2) = N(22, 3.8004)[/tex]

Then, we can compute the probability that X is at most 30 by standardizing and using the standard normal distribution:

[tex]P(X ≤ 30) ≈ P(Z ≤ (30 - mu) / σ) = P(Z ≤ (30 - 22) / 1.9488) = P(Z ≤ 4.1142) = 0.9997[/tex]

(b) To find the probability that x is less than 30, we can use the same normal approximation and compute:

[tex]P(X < 30) ≈ P(Z < (30 - mu) / σ) = P(Z < (30 - 22) / 1.9488) = P(Z < 4.1142) = 0.9997[/tex]

(c) To find the probability that x is between 15 and 25 (inclusive), we can either use the binomial distribution directly or use the normal approximation as before:

P(15 ≤ X ≤ 25) = Σ P(X = x) for x from 15 to 25

However, we can use the normal approximation instead. Using the same approach as before, we get:

[tex]P(15 ≤ X ≤ 25) ≈ P((15 - μ) / σ ≤ Z ≤ (25 - μ) / σ) = P(-3.0806 ≤ Z ≤ -0.5145) = P(Z ≤ -0.5145) - P(Z ≤ -3.0806) = 0.3035 - 0.0009 = 0.3026[/tex]

Therefore, the approximate probability that x is between 15 and 25 (inclusive) is 0.3026.

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The percent error of the measurement is 1.9%.

What is the percent error?

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error. Measurement mistakes or computation machine precision can generate an approximation error.

Here, we have

Given: Mackenzie measured a line to be 5.3 inches long. If the actual length of the line is 5.4 inches.

We have to find the percent error of the measurement.

If the actual length of the line is 5.4 inches

So, the difference in length of the line = 5.4-5.3

= 0.1

Now, the percent error = Difference in length of line/Actual length × 100

= 0.1/5.3 × 100

= 0.01887 × 100

= 1.9 %

Hence,  the percent error of the measurement is 1.9%.

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The planning value for the population standard deviation ,a sample size of 677 graduates is needed to estimate the population mean starting salary with a margin of error of $200.

We need to use the range of the expected starting salaries, which is between $42,000 and $59,800. The formula for calculating the planning value is:
Planning value = (range of salaries) / (6)
Therefore, the planning value for the population standard deviation is:
Planning value =[tex]($59,800 - $42,000) / (6) = $2,967[/tex]
To determine the sample size needed for a desired margin of error, we need to use the following formula:
Sample size = (Z-score)^2 * (planning value)^2 / (margin of error)^2
For a margin of error of $600 and a 95% confidence level, the Z-score is 1.96. Plugging in the values, we get:
Sample size =[tex](1.96)^2 * ($2,967)^2 / ($600)^2 = 113[/tex]
Therefore, a sample size of 113 graduates is needed to estimate the population mean starting salary with a margin of error of $600.
For a margin of error of $200, the Z-score is still 1.96. Plugging in the new margin of error, we get:
Sample size =[tex](1.96)^2 * ($2,967)^2 / ($200)^2 = 677[/tex]
Therefore, a sample size of 677 graduates is needed to estimate the population mean starting salary with a margin of error of $200
In summary, the planning value for the population standard deviation is $2,967. The sample size needed for a margin of error of $600 is 113, while the sample size needed for a margin of error of $200 is 677. These calculations can help organizations determine the appropriate sample size needed to accurately estimate the starting salaries of business administration graduates.

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To solve the problem, we can use the formula for the future value of an annuity:

FV = PMT * ( (1 + r)^n - 1 ) / r

where:

- PMT is the periodic payment

- r is the periodic interest rate

- n is the number of periods

In this case,

- PMT = $475 (the monthly payment)

- r = the monthly interest rate

- n = 24 (the number of months in the agreement)

We first need to calculate the monthly interest rate. We can find this by dividing the yearly interest rate by 12 months:

r = 18% / 12 months = 0.015

Now we can calculate the future value (FV) of the annuity using the above formula:

FV = $475 * ( (1 + 0.015)^24 - 1 ) / 0.015 = $13,237.19

This is the amount that Christopher would owe after 24 months if he made monthly payments of $475.

However, Christopher pays off the loan after 18 months. To find out how much he owes at this point, we can calculate the future value after 18 months:

FV = $475 * ( (1 + 0.015)^18 - 1 ) / 0.015 = $10,198.66

So, after 18 months, Christopher owes approximately $10,198.66.

The distance between the points H (-9, 1), and K (-1, 8) in the coordinate plane, obtained using the distance formula is; Distance: 10.63

The distance formula is a formula that is used to find the distance between two points on the coordinate plane.

The specified points are; H = (-9, 1), and K = (-1, 8)

The distance formula can be used to calculate the distance between the points as follows;

The distance formula is; d = √((x₂ - x₁)² + (y₂ - y₁)²)

Where; (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

When, (x₁, y₁) = (-9, 1), and (x₂, y₂) = (-1, 8), we get;

d = √((-1 - (-9))² + (8 - 1)²) = √(8² + 7²) =

√(8² + 7²) = √(64 + 49) = √(113) ≈ 10.63 (rounded to the nearest hundredth)

The distance between the points is about 10.63 units

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The probability of rolling a six when spinning the spinner shown twice, assuming that the outcomes 1, 2, 3, and 4 are equally likely for each spin is 3/16.

A robot spins the spinner shown twice. Assume that the outcomes 1, 2, 3, and 4 are equally likely for each spin.

What is the probability that the sum of the two outcomes will be 6?

The probability that the sum of the two outcomes will be 6 when a robot spins the spinner shown twice, assuming that the outcomes 1, 2, 3, and 4 are equally likely for each spin, is 2/16 or 1/8.However, before determining the probability, we should first determine the possible outcomes of the spinner. When a spinner is spun twice, the possible outcomes are: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, and 44.There are 16 possible outcomes. Of these 16 possible outcomes, only two add up to six. These two possible outcomes are: 33,24,42. Therefore, the probability of rolling a six is 3/16 .

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Answer:

The last option/option D/2 over 7/(2/7)

Step-by-step explanation:

There are 3 $10 bills.
There are 4 $1 coins.

3/7=Pull out one $10 dollar bill

However, it is less likely to get the same answer twice.
A Root Graph (or what you like to call it):


As you can see, there are 3 instances where you wound up with 10 BOTH ROUNDS. There are also an additional 11 that DON'T wound up with 10 in both rounds. The ratio is 3/11. 3 divided by 11 is 0.27 (or 0.28). The last option, 2/7 is the one that I think is the answer. It is because 2 divided by 7=0.28...

Therefore our answer is the last option?

When a study sample is representative of the target population, it allows for the results to be generalizable, meaning they can be applied to the broader population.

This is an important aspect of research, as it ensures the study's findings are relevant and useful beyond the specific sample studied.

When a study sample shows representativeness, it means that the sample accurately reflects the characteristics of the target population.

In this case, the study is most likely generalizable, with results that can be applied to the target population.
To achieve representativeness, researchers often use random sampling techniques, which help minimize the potential for sampling bias.

Sampling bias occurs when certain groups within the target population are over- or under-represented in the sample, which can lead to inaccurate conclusions.

In contrast, if a study used strict inclusion and exclusion criteria to limit the sample size or relied on specific inclusion criteria, it could result in a sample that is not representative of the target population.

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After answering the presented question, we can conclude that To pay the $19.60 weekly cost for your cell phone Internet access, you would need to save $2.80 (or $2.86 if you round up) per day.

The internet is a vast network of interconnected computers and devices that communicate with each other using a common set of protocols and technologies. It allows people to share information, communicate with each other, and access a wide range of digital services and resources. The internet is a global network that spans across the world, connecting people and businesses across different geographic locations and time zones. It has revolutionized the way people communicate and access information, enabling unprecedented levels of connectivity, collaboration, and innovation.

You can use the following steps to calculate how much you need to save per day to pay the bill:

Divide your weekly bill by the number of days in a week to see how much you need to save per day:

$19.60 ÷ 7 = $2.80

You can round up to the closest cent if you want to be more precise:

$19.60 divided by 7 equals $2.80 per day

$2.80 rounded up to $2.86

To pay the $19.60 weekly cost for your cell phone Internet access, you would need to save $2.80 (or $2.86 if you round up) per day.

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Answer:

To find the number of years it will take for the population of the colony to grow from 80,000 to 92,610 with a growth rate of 5% per annum, we can use the formula for compound interest:

Final Population = Initial Population * (1 + Growth Rate) ^ Number of Years

92,610 = 80,000 * (1 + 0.05) ^ t

Now, we can solve for t:

(92,610 / 80,000) = (1.05) ^ t

1.157625 = (1.05) ^ t

To find t, we can use logarithms:

t = log(1.157625) / log(1.05)

t ≈ 2.967

So, it will take approximately 2.967 years for the population to grow from 80,000 to 92,610 at a 5% growth rate.

Now, let's consider a 2% lower growth rate (5% - 2% = 3%). We can use the same formula to find the final population after the same time (2.967 years):

Final Population = Initial Population * (1 + Growth Rate) ^ Number of Years

Final Population = 80,000 * (1 + 0.03) ^ 2.967

Final Population ≈ 80,000 * 1.09364

Final Population ≈ 87,491.2

To find the difference in population for the same time, we can subtract the population with the lower growth rate from the population with the higher growth rate:

Difference in population = 92,610 - 87,491.2

Difference in population ≈ 5,118.8

So, the difference in population for the same time with a 2% lower growth rate would be approximately 5,118.8.

it depends on the shape. There are yt videos you could watch that would explain how to solve the perimeters of that specific shape

OK what are you wanting to find the perimeter to?

Add up all the sides:

EX:

Square: 3+3+3+3

Rectangle: 4+2+4+2

Triangle [Equilateral]: 2+2+2

You get the gist?

The margin of error for a 90% confidence interval for the proportion of all employees dissatisfied with their jobs, based on a survey of 200 employees where 44% reported dissatisfaction, is  0.068.

We can use the formula for the margin of error for a proportion:

ME = zsqrt((p_hat(1-p_hat))/n)

where z is the z-score associated with the desired level of confidence (90% in this case), p_hat is the sample proportion (0.44), n is the sample size (200), and sqrt is the square root.

From a standard normal distribution table, the z-score for a 90% confidence level is approximately 1.645.

Plugging in the values, we get:

ME = 1.645sqrt((0.44(1-0.44))/200)

ME ≈ 0.068

So the margin of error for a 90% confidence interval is approximately 0.068 or 0.068/1= 0.068 = 0.068 = 6.8% (rounded to 3 decimal places).

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--The given question is incomplete, the complete question is given

"A human resources consulting firm conducted a survey of 200 employees to determine how dissatisfed they were with their jobs. 44% of the employees said they were dissatisfied, what is the margin of error for a 90% confidence interval for the proportion of all employees that are dissatisfied with their jobs? Answer to 3 decimal places"--

The model shaded to show the fraction of the pizza that both boys ate is option C, 7/12.

To find the fraction of the pizza that both boys ate, we need to find the intersection of the two fractions that represent the amount each boy ate.

We can represent each boy's portion of the pizza using the following models:

Simon = 3/12

Luke = 4/12

When these fractions are added, we have

Total = 3/12 + 4/12

Evaluate the sum

Total = 7/12

Hence, the model is 7/12

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As a result, more students than or equal to 41 can be added to the current student body by inequality.

A mathematical statement known as an inequality compares two expressions using one of the following symbols:, >,, or.

For instance:

x + 2 < 5

2y - 3 > 7

3z ≤ 9

4w + 1 ≥ 13

Now,

The disparity that indicates the extra students who can be seated is as follows:

350 - 309 ≤ x

where x is the maximum number of extra pupils who can sit in a classroom.

When we simplify this inequality, we obtain:

41 ≤ x

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Step-by-step explanation:

The total number of pens in the box is:

Total number of pens = 11 black pens + 8 blue pens + 6 red pens

Total number of pens = 25 pens

The probability of Roxy selecting a blue pen can be expressed as the ratio of the number of blue pens to the total number of pens:

Probability of selecting a blue pen = Number of blue pens / Total number of pens

Probability of selecting a blue pen = 8 / 25

So, the probability that the pen Roxy selects is blue is 8/25 or approximately 0.32 (rounded to two decimal places).

Answer:8/25

Step-by-step explanation: