Given f(x) = 3x2 − 6x − 13, what is the domain of f(x)? all real numbers x ≥ 1 x ≤ −6 x ≥ −13

The height of the cone is 15cm.

From the question;

Height of cylinder = 28cm

Let the radius of the solid object = Rcm

The slant height of the cone = 17cm

Cost of painting = Rs. 140 per 100 sq cm

Cost of painting 1 cm² =  140/100 = RS1.4

The total cost of painting = Rs. 2851.2

Total area of the object =  total cost of painting/Cost of painting per sq cm

Total area of the object = 2851.2/1.4  = 2036.57143 cm²

Total surface area of object = CSA of Cylinder + CSA of cone + area of the circle at the bottom

Total surface area of the object = [tex]\pi rh + \pi rl + \pi r^2[/tex]

So, [tex]\frac{2851.2}{1.4}[/tex] =  [tex]\pi rh + \pi rl + \pi r^2[/tex]

[tex]\frac{2851.2}{1.4}[/tex] = [tex]2\pi r * 28 + \pi r * 17 + \pi r^2[/tex]

[tex]\frac{2851}{1.4}[/tex] = [tex]\frac{1232}{7}r =+\frac{374}{7} r + \frac{22}{7} r^2[/tex]

[tex]\frac{2851}{1.4}[/tex] = [tex]\frac{1606}{7} r + \frac{22}{7} r^2[/tex]

[tex]\frac{2851}{2}[/tex]= [tex]1606r + 22r^2[/tex]

[tex]14256 = 1606r + 22r^2[/tex]

[tex]22r^2 + 1606r - 14256 =0[/tex]

Solving the quadratic equation, the possible value of radius are:

r = 8cm

r = -81cm

r = -81cm will be neglected because radius can not be negative.

Therefore, the radius of the object is 8cm

To find the height of the cone, we should know that the relation between radius, height and slant height of the cone is:

[tex]l^2 = r^2 + h^2[/tex]

[tex]h=\sqrt{l^2 - r^2}[/tex]

[tex]h=\sqrt{17^2 - 8^2}[/tex]

[tex]h=\sqrt{225}[/tex]

[tex]h=15cm[/tex]

Therefore, height of  cone in the solid object is 15cm

Learn about radius here https://brainly.com/question/27696929

#SPJ1

According to the question the word "Liberty" on the quarter is about 0.872 inches long.

In geometry, a circle's diameter is any straight segment whose endpoint is on the circle and which passes through its centre. Another name for it is the circle's longest chord. Either idea can be used to determine a sphere's diameter. The diameter is indeed the length of both the line perpendicular to the two points at each end of the circle. If you think of length as the distance between two points, then diameter is length. The diameter of a circle is the separation between its two farthest points.

Since the quarter has a diameter of about 1 inch, we can use its diameter as a reference to estimate the length of the word "Liberty" on the quarter.

If the word "Liberty" makes about a 100° angle, that means it takes up about 100/360 or 5/18 of the circumference of the quarter. The circumference of a circle is given by:

C = 2πr

where C is indeed the circumference, pi (roughly 3.14), is a mathematical constant, and r is the circle's radius. The quarter's approximate 1 inch diameter means that the radius equals 1/2 inch, approximately 0.5 inches.

The circumference of the quarter is therefore:

C = 2π(0.5 inches) = π inches

The length of the word "Liberty" on the quarter is approximately 5/18 of this circumference, which is:

(5/18) × π inches ≈ 0.872 inches

So the word "Liberty" on the quarter is about 0.872 inches long.

To know more about diameter visit:

https://brainly.com/question/5501950  

#SPJ9

The transformation of the graph of f(x) to g(x) is defined as: 2 units shift on the left side and 5 units shift upward.

Think about the function f (x). We measure the movement using the x- and y-axes on a coordinate grid. The following are guidelines for function transformations that could be used with function graphs. All algebraic and graph of transformations are possible.

Transformations can be divided into four categories: translation, rotation, reflection, plus dilation.

Given :

Transformation of the graph of f(x) --->  g(x)

f(x) = x² g(x) = (x - 2)² + 5

There is a shift of 2 units on the left. Subtract 2 from x to get the value (x - 2)

There is a shift of 5 units upward. Add 5 on the function f(x)  to get the function g(x).

Thus, the transformation of the graph of f(x) to g(x) is defined as: 2 units shift on the left side and 5 units shift upward.

Know more about the transformation

https://brainly.com/question/30228009

#SPJ1

The probability shows that if the mean μ=1, then only 0.0027 is at least as small as the sample mean x=1.5. This also leads to the conclusion that if we believe that μ = 1, we must also believe that there is a 27 in 10,000 chance that our observed sample mean can be described as such.

To achieve the goal of this task, use the mean μ x and the standard deviation σ x.

The task has two conditions, the first is that the standard deviation σ is 1.3 days and the second is that the standard deviation σ is 1.8 days.

If the standard deviation σ is 1.3, then the mean μ is 1.4. And if the standard deviation is σ 1.8, then the mean is μ₁. In this case, the given standard deviation is μ 1.8, so use the second condition to achieve the task goal.

we know that:

μₓ = μ and σₓ = σ/√n

Given that:

μ = 1, σ = 1.8 and n = 100

So, by the formula of standard deviation σₓ,

σₓ = σ/√n = 1.8/√100

               = 0.18

Calculate the probability with the mean μ=1, and standard deviation

σₓ =0.18.

P(x > 1.5) = P(z > 0.5/0.18)

              = P( z > 2.78)

Looking at the z table, first, find the units and decimals in the first column of the z table. In this case, search for 2.7 first. Then look in which column the 100th value is placed. In this case, 0.08 and follow the number of lines placed 2.7.

Therefore, the value of 2.78 in table z is 0.9973 because z=0.9973, and the right tail area is 0.0027 or (1−0.9973).

Learn more about Probability:

https://brainly.com/question/30034780

#SPJ4

Answer:

The given equation is:

15x + 30 = 105

Here,

15x represents the total cost of the fruit baskets purchased, and

30 represents the cost of the membership fee.

To find the number of fruit baskets purchased (x), we must isolate the variable on one side of the equation.

Subtracting 30 from both sides, we get:

15x = 105 - 30

15x = 75

Dividing both sides by 15, we get:

x = 5

Therefore, Mrs. Williams purchased 5 fruit baskets for her coworkers.

The answer using probability are shown:

(A) 43/60 projection is used.

(B) He shouldn't alter the estimate in light of this knowledge.

Simply put, the probability is the likelihood that something will occur.

When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes.

Statistics is the study of occurrences that follow a probability distribution.

Mathematics' study of random events is known as probability, and there are four major kinds of probability: axiomatic, classical, empirical, and subjective.

So, he would calculate the amount by dividing the overall number of bricks by the proportion of green bricks. The likelihood of choosing a green block out of all 60 bricks would be that.

Then, the probability would be:

= 43/60

Andre shouldn't alter his assessment, in other words.

The explanation is that we do not know whether the bricks he saw were green in color; we are only told that she looked in the bag and found 6 bricks.

The only time Andre needs to adjust his guess is if it turns out that the six bricks Mai saw in the bag were, in fact, green.

The estimate should not be altered until this proof is received.

Therefore, the answer using probability are shown:

(A) 43/60 projection is used.

(B) He shouldn't alter the estimate in light of this knowledge.

Know more about probability here:

https://brainly.com/question/24756209

#SPJ1

Complete question:
Andre picks a block out of a bag 60 times and notes that 43 of them were green. What should Andre estimate for the probability of picking out a green block from this bag? Mai looks in the bag and sees that there are 6 blocks in the bag. Should Andre change his estimate based on this information? If so, what should the new estimate be? If not, explain your reasoning.

Answer:

Yes The set R = [(a,1),(b,2),(c,3)] is a Function.

Step-by-step explanation:

A function ia a relation between two sets ,where each element in domain is associated with only one range.

Some examples of function -

1- x2 (squaring) is a function

2- x3+1 is also a function

3- Sine, Cosine and Tangent are function

in the case the domain {a,b,c} and the range is {1,2,3}

IN R each domain is associated with only one element in range,So R SATISFIES the definiton of Function

To know more about Function:

brainly.com/question/14465109

brainly.com/question/4379163

A parabolic function is represented by h = -16T² + 32T + 151.

A function with the equation f(x) = ax²+ bx + c is said to be parabolic. It is a second-degree quadratic expression in x². A parabola-like form can be seen in the graph of a parabolic function. The range value for the parabolic function is the same for two different domain values. Parabolic motion refers to a variety of motions, such as the motion of a stone thrown under the influence of gravity.

. The function's greatest or minimum value is where the parabola's vertex is located. In this instance, the formula -b/2a,

where a = -16 and b = 321, can be used to get the vertex of the parabola. As a result, this parabola's vertex is located at t = 1 second and h = 31 feet.

The parabola's vertex is located at t = 1 second and h = 31 feet. These are the main characteristics of this graph.

The parabola's axis of symmetry is a vertical line that passes through its vertex.

Because the coefficient of t² is negative, the parabola begins to slope downward.

- The maximum height that Miyako reaches is 31 feet.

To know more about parabolic function visit:

brainly.com/question/29171945

#SPJ1

The type of sampling that assumes all members of a population have an equal chance of being selected for participation in the study is called Simple Random Sampling.

In Simple Random Sampling, each individual in the population has an equal probability of being chosen as a participant, and the selection process is unbiased. This method ensures that the sample is representative of the entire population, thus allowing for valid conclusions to be drawn about the population as a whole.

Here is a step-by-step explanation of how Simple Random Sampling is conducted:

1. Define the population: First, clearly identify the population you want to study.

2. Assign a unique number to each member: To ensure equal chances of selection, assign a unique number to every individual in the population.

3. Determine the sample size: Decide how many participants you need in your study based on factors like required level of accuracy and available resources.

4. Use a random selection method: Use a random selection method such as a random number generator, a lottery system, or a random number table to pick the required number of participants.

5. Collect data from the selected individuals: Once the participants are chosen, collect data from them using appropriate research methods like surveys, interviews, or experiments.

By using Simple Random Sampling, you can obtain a sample that is unbiased and representative of the entire population, which is essential for accurate and reliable research findings.

for such more questions on Simple Random Sampling

https://brainly.com/question/13219833

#SPJ11

From shortest to longest, the earthworms measure the following lengths:   B (3 cm), D (4.5 cm), C (9.23 cm) and A (10.2 cm)

A physical concept known as length measures the gap between two points or the expanse of an object in one dimension.

Common units used to measure it include metres (m), feet (ft), millimetres (in), centimetres (cm), etc. In several disciplines, including mathematics, engineering, physics, and engineering, length is a crucial concept.

given

From shortest to longest, the earthworms measure the following lengths:

B (3 cm), D (4.5 cm), C (9.23 cm) and A (10.2 cm)

To know more about length visit :-

brainly.com/question/30100801

#SPJ9

Answer:

x = 8

Step-by-step explanation:

The two sides equal each other

5x - 13 = x + 19  Subtract x from both sides

5x - x - 13 = x - x + 19

4x - 13 = 19  Add 13 to both sides

4x - 13 + 13 = 19 + 13

4x = 32  Divide both sides by 4

x = 8

Helping in the name of Jesus.

There is no real solution for X. This means that the given measurements do not form a valid right triangle.

Triangle KJL forms a right triangle, with length KL (hypothenuse side) = 10 and JL = X and KL = 24.

We can use the Pythagorean theorem to solve for the missing side, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Therefore, we have:

KL² = KJ² + JL²

Substituting the given values, we get:

10² = 24² + X²

Simplifying and solving for X, we get:

100 = 576 + X²

X² = 100 - 576

X² = -476

Since X² is negative, there is no real solution for X. This means that the given measurements do not form a valid right triangle.

Learn more about Pythagorean theorem here: https://brainly.com/question/231802

#SPJ1

Answer: If Amanda Bryan purchased a used car for $12,875 and made a 25% down payment, then she paid:

25% of $12,875 = 0.25 * $12,875 = $3,218.75

This means that the amount she financed (i.e. borrowed) to purchase the car is the difference between the total cost of the car and the down payment:

Amount financed = Total cost - Down payment

Amount financed = $12,875 - $3,218.75

Amount financed = $9,656.25

Therefore, Amanda Bryan financed $9,656.25 to purchase the used car.

Step-by-step explanation:

The conditional probability that the coin chosen is fake given that it was flipped three times and all three flips resulted in heads is higher than the initial probability.

Let A be the event that the coin chosen is fake, and B be the event that the three flips resulted in heads. We are given that the probability of choosing the fake coin is 0.1, i.e. P(A) = 0.1, and the probability of getting heads with the fake coin is 1, i.e. P(B|A) = 1. The probability of getting heads with the fair coin is 0.5, i.e. P(B|A') = 0.5, where A' is the event that the coin chosen is fair. Using Bayes' theorem, we can calculate the conditional probability of A given B:

P(A|B) = P(B|A) * P(A) / (P(B|A) * P(A) + P(B|A') * P(A'))

Plugging in the given values, we get:

P(A|B) = 1 * 0.1 / (1 * 0.1 + 0.5 * 0.9) = 0.18

Therefore, the conditional probability that the coin chosen is fake given that it was flipped three times and all three flips resulted in heads is 0.18, which is higher than the initial probability of 0.1. This means that the evidence of three consecutive heads increases the likelihood that the coin is fake.

To learn more about conditional probability here:

brainly.com/question/30144287#

#SPJ11

Answer:

2 Nd is in order from least to grater

The candy distributor needs to use 30 kilograms of 10% fat-content chocolate and 70 kilograms of 50% fat-content chocolate to create 100 kilograms of a 14% fat-content chocolate.

To solve this problem, we can use the method of mixture problems, which involves setting up a system of equations. Let x be the number of kilograms of the 10% fat-content chocolate and y be the number of kilograms of the 50% fat-content chocolate.

We have two equations based on the fat content and the total weight of the mixture:

0.1x + 0.5y = 0.14(100) (equation for fat content)

x + y = 100 (equation for total weight)

We can solve this system of equations using substitution or elimination. Using substitution, we can solve for x in terms of y from the second equation and substitute it into the first equation:

x = 100 - y

0.1(100 - y) + 0.5y = 0.14(100)

10 - 0.1y + 0.5y = 14

0.4y = 4

y = 10

Then we can substitute y = 10 back into the equation for x and get:

x = 100 - y = 100 - 10 = 90

To know more about elimination, refer here:

https://brainly.com/question/14619835#

#SPJ11

Answer: We can start by finding the width of the rectangular field using the formula for area of a rectangle:

Area = length x width

80 = 20 x width

width = 4 meters

Now we can use the formula for perimeter of a rectangle:

Perimeter = 2 x length + 2 x width

Perimeter = 2 x 20 + 2 x 4

Perimeter = 40 + 8

Perimeter = 48 meters

So, you would have traveled 48 meters if you walked the whole way around the field.

Step-by-step explanation:

The probability that a randomly selected newborn baby boy's weight is between 3682 and 4552 grams is approximately 0.1979, or 19.79% when rounded to four decimal places.

To find the probability that a newborn baby boy's weight  Convert the weights to z-scores:

z = (X - μ) / σ, where X is the weight, μ is the mean, and σ is the standard deviation.

First, calculate the standard deviation:

σ = √variance = √385,641 ≈ 621

Now, calculate the z-scores for the given weights:

z1 = (3682 - 3186) / 621 ≈ 0.7986

z2 = (4552 - 3186) / 621 ≈ 2.1965

Use a standard normal table or a calculator with a standard normal probability function to find the probabilities corresponding to these z-scores:

P(Z ≤ 0.7986) ≈ 0.7879

P(Z ≤ 2.1965) ≈ 0.9858

Find the probability that the weight is between the two z-scores:

P(0.7986 ≤ Z ≤ 2.1965) = P(Z ≤ 2.1965) - P(Z ≤ 0.7986) ≈ 0.9858 - 0.7879 ≈ 0.1979

So, the probability that a randomly selected newborn baby boy's weight is between 3682 and 4552 grams is approximately 0.1979, or 19.79% when rounded to four decimal places.

for such more question on probability

https://brainly.com/question/13604758

#SPJ11

Answer:

48 yards

Step-by-step explanation:

Use the Pythagorean theorem:

[tex] {a}^{2} = {52}^{2} - {20}^{2} = 2704 - 400 = 2304[/tex]

[tex]a > 0[/tex]

[tex]a = \sqrt{2304} = 48 \: yd[/tex]

For the first question, the measure of variability that should be used for both sets of data to determine the location with the most consistent temperature is IQR, because it is robust to outliers and can provide a better representation of the spread of data for skewed distributions. The option "IQR, because Desert Landing is symmetric" is incorrect because the graph of Desert Landing is not symmetric.

For the second question, we need to compare the measures of center (mean and median) of the two sets of data to determine which shop typically sells the most amount of coffee per hour. To do this, we can calculate the mean and median of each set of data:

For Coffee Ground, the mean is (1.5+20+3.5+12+2+5+11+7+2.5+9.5+3+5)/12 = 6.25 gallons and the median is the middle value of the ordered set, which is 5 gallons.

For Wide Awake, the mean is (2.5+10+4+18+4+3+6.5+15+6+5+2.5)/11 = 6.136 gallons and the median is the middle value of the ordered set, which is 4.5 gallons.

Therefore, we can conclude that Wide Awake typically sells the most amount of coffee per hour, with a median value of 4.5 gallons. The option "Wide Awake, with a mean value of about 4.5 gallons" is incorrect because the mean value of Wide Awake is slightly lower than 4.5 gallons. The option "Coffee Ground, with a median value of 5 gallons" is incorrect because the median value of Coffee Ground is lower than the median value of Wide Awake. The option "Coffee Ground, with a mean value of about 5 gallons" is incorrect because the mean value of Coffee Ground is higher than 5 gallons.

The concept of a complement of a set is the set of all elements in the universal set that are not in the original set. The answer is B) {1, 2, 3, 4, 5, 6, 7}.

It is denoted by U. Universal sets are used to define the scope of an expression or equation, as well as to denote sets of all objects, such as the set of real numbers or the set of natural numbers.

The complement of a set is also referred to as its opposite set. In this case, the universal set is {1, 2, 3, 4, 5, 6, 7}, and the set C is {1, 2, 3}.

The complement of C is {4, 5, 6, 7}.

The complement of the complement of C is the set of all elements that are not in the complement of C.

Since the complement of C is {4, 5, 6, 7}, the complement of the complement of C is the set of all elements in the universal set that are not in the complement of C, which is {1, 2, 3, 4, 5, 6, 7}.

Therefore, the answer is B) {1, 2, 3, 4, 5, 6, 7}.

To summarize, the complement of the complement of C is the set of all elements in the universal set that are not in the complement of C.

In this case, the complement of C is {4, 5, 6, 7}, so the complement of the complement of C is {1, 2, 3, 4, 5, 6, 7}.

For more questions related to Universal sets

https://brainly.com/question/29478291

#SPJ1

Since overtime is paid at one and one-half, Tonya's overtime pay for this week is $36.56.

The overtime pay is the product of the overtime pay rate and the number of overtime hours.

The normal work week is 40 hours.  The overtime hours, in this situation, are 2.5 hours.

The total number of hours Tonya worked this week = 42.5 hours

The hourly pay rate = $9.75

Overtime pay rate = $14.625 ($9.75 x 1.5)

Overtime hours worked = 2.5 hours (42.5 - 40)

Overtime pay = $36.56 ($14.625 x 2.5)

Learn more about overtime pay at https://brainly.com/question/901346.

#SPJ1

The speed of the copy machine is 30 pages per minute.

What is Fraction ?

A fraction is a way of representing a part of a whole or a division of a quantity into equal parts. It consists of two numbers, one written above the other and separated by a horizontal or diagonal line called a fraction bar. The number written above the fraction bar is called the numerator, and the number written below the fraction bar is called the denominator.

If the copy machine made a copy of Leslie's 3-page essay in just 1/10 of a minute, then it made a copy of one page in 1/10 ÷ 3 = 1/30 of a minute.

To find the speed of the copy machine, we can take the reciprocal of the time it takes to make one copy, which is:

1 ÷ (1/30) = 30

Therefore, the speed of the copy machine is 30 pages per minute.

To learn more about Fraction from given link.

https://brainly.com/question/29766013

#SPJ1

For the given values, the standard deviation for this data set is approximately 3.67 minutes.

What is standard deviation?

In statistics, standard deviation is a measure used to quantify the amount of spread or dispersion of a set of numerical data around the mean. This measure indicates how much the data values vary from the average value of the dataset.

To find the standard deviation, you can follow these steps:

Find the mean (average) of the data set:

mean = (11 + 7 + 14 + 2 + 8 + 13 + 3 + 6 + 10 + 3 + 8 + 4 + 8 + 4 + 7) / 15 = 7.2

Subtract the mean from each data point:

(11 - 7.2), (7 - 7.2), (14 - 7.2), (2 - 7.2), (8 - 7.2), (13 - 7.2), (3 - 7.2), (6 - 7.2), (10 - 7.2), (3 - 7.2), (8 - 7.2), (4 - 7.2), (8 - 7.2), (4 - 7.2), (7 - 7.2)

Simplifying, we get:

3.8, -0.2, 6.8, -5.2, 0.8, 5.8, -4.2, -1.2, 2.8, -4.2, 0.8, -3.2, 0.8, -3.2, -0.2

Square each result:

13.44, 0.04, 46.24, 27.04, 0.64, 33.64, 17.64, 1.44, 7.84, 17.64, 0.64, 10.24, 0.64, 10.24, 0.04

Find the mean (average) of the squared results:

(13.44, 0.04, 46.24, 27.04, 0.64, 33.64, 17.64, 1.44, 7.84, 17.64, 0.64, 10.24, 0.64, 10.24, 0.04) / 15 = 12.49

Take the square root of the mean:

[tex]\sqrt{(12.49)[/tex] ≈ 3.67

Therefore, the standard deviation for this data set is approximately 3.67 minutes.

To learn more about standard deviation visit:

https://brainly.com/question/475676

#SPJ1

Answer:

1)  5

Step-by-step explanation:

Trapezoid Midsegment Theorem:

EF = (DC + AB) / 2

2x + 2 = ((x + 3) +(5x - 9)) / 2

4x + 4 = 6x - 6

-2x = -10

x = 5

Answer:

126 meters squared

Step-by-step explanation:

To find the surface area

For the top and bottom it will be: l x w x 2(because there's a top and bottom)

3x6x2 = 36

For the sides (left and right) it will be: l x h x 2 (There's left and right)

3x5x2 = 30

For the front and back it will be w x h  x 2 (There's the front and the back)

6x5x2 = 60

Added it all together and you get 126

The surface area is 126 meters squared



The surface areas are 756.87 km², 2567.6 in², 853.91 yd², 749.72 cm² and the area to paint is 3268.60 in²

Figure 9

This is calculated as

Area = Base area + 1/2 * Perimeter * Slant height

So, we have

Surface area = (1/4 * 14² * √3) + 1/2 * (14 + 14 + 14) * 32

Surface area = 756.87 km²

Figure 10

This is calculated as

Area = Sum of side areas

So, we have

Surface area = 2 * 1/2 * (35 + 10) * 20.3 + 32 * 17 + 10 * 17 + 20.3 * 17 + 35 * 17

Surface area = 2567.6 in²

Figure 11

Start by calculating the radius using

(2r)² = 19.4² - 14.4²

2r = 13

So, we have

r = 6.5

This area is then calculated as

Area = 2πr(h + r)

So, we have

Area = 2 * 22/7 * 6.5(14.4 + 6.5)

Surface area = 853.91 yd²

Figure 12

This area is calculated as

Area = lw + l√[(w/2)² + h²] + w√[(l/2)² + h²]

So, we have

Area = 15 * 18 + 18√[(15/2)² + 12²] + 15√[(18/2)² + 12²]

Surface area = 749.72 cm²

Without painting the bottom, the area is

Area = 2 * 1/2 * 34 + 42.8 + 36 * √(34² + 42.8²) + 34 * 36

Evaluate

Area = 3268.60 in²

Unclear dimensions

Read more about surface areas at

https://brainly.com/question/26403859

#SPJ1

The probability of a measured value greater than 80 mm in a normal distribution with mean 20 mm and standard deviation 30 mm is (0.0228). The probability of a measured value between 50 and 80 mm is 0.1359.

Probability of a measured value greater than 80 mm:

We can use the standard normal distribution to find this probability, by standardizing the value of 80 mm:

z = (80 - 20) / 30 = 2

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being greater than 2 is approximately 0.0228. Therefore, the probability of a measured value of the polymer fiber being greater than 80 mm is approximately 0.0228.

Probability of a measured value between 50 and 80 mm:

Again, we can standardize the values of 50 mm and 80 mm:

z1 = (50 - 20) / 30 = 1

z2 = (80 - 20) / 30 = 2

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being between 1 and 2 is approximately 0.1359. Therefore, the probability of a measured value of the polymer fiber being between 50 and 80 mm is approximately 0.1359.

To know more about Probability:

https://brainly.com/question/11234923

#SPJ4