Tom is preparing for a 100 meters race competition. During his practice last week, a sample of seven 100
meters races is reviewed, and the finishing times (in seconds) were as below:
13.4
15.6
13.1
14.5
14.2
13.3
15.3
It is reasonable to assume his finishing times are normally distributed.
(a) Construct a 99% confidence interval estimate of his population mean finishing time of 100 meters race.
(b) If the confidence interval estimate of his population mean finishing time of 100 meters is constructed at
95% instead of 99%, would the new confidence interval be (I) wider, (II) narrower, or (III) the same as
the interval constructed at part (a)? (Just state your answer, no calculation is needed in part (b))

Answer:

1  17/30.

Step-by-step explanation:

you can find this out by seeing how many 30s go into 47 which is 1.

Then subtract to find how much is leftover still over 30.

47 - 30 = 17

So 1 and 17/30

Answer:

The population of yeast cells is growing at a rate of approximately 46.41% per hour.

Step-by-step explanation:

To find the rate of growth of the yeast population, we can use the exponential growth formula:

P(t) = P₀ * e^(kt)

where P(t) is the population size at time t, P₀ is the initial population size, k is the growth rate constant, and t is the time elapsed.

In this case, the initial population size P₀ is 5, the final population size P(5) is 160, and the time elapsed t is 5 hours. We want to find the growth rate constant k.

Plugging in the values, we get:

160 = 5 * e^(5k)

Divide by 5:

32 = e^(5k)

Now, take the natural logarithm (ln) of both sides to isolate k:

ln(32) = ln(e^(5k))

Using the property that ln(a^b) = b * ln(a):

ln(32) = 5k * ln(e)

Since ln(e) = 1:

ln(32) = 5k

Now, divide by 5:

k = (ln(32)) / 5 ≈ 0.4641 (rounded to four decimal places)

So, the growth rate constant k is approximately 0.4641 per hour.

To express the rate of growth as a percentage, multiply the growth rate constant by 100:

0.4641 * 100 ≈ 46.41%

The population of yeast cells is growing at a rate of approximately 46.41% per hour.

The rate of growth of the yeast cells is 31 cells per hour.

The rate of growth of the yeast cells can be calculated by finding the average rate of change in the population over the given time period.

In this case, the population increased from 5 to 160 in 5 hours, so the average rate of growth can be calculated as (160 - 5) / 5 = 31. The rate of growth of the yeast cells is 31 cells per hour.

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The probability of drawing a black card is P(draw a black card) = 0.3 or 30%.

Probability is a branch of mathematics that deals with the study of random events and the likelihood or chance of their occurrence. It is the measure of how likely or unlikely it is for an event to happen. The probability of an event is a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to occur.

Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if we want to calculate the probability of flipping a coin and getting heads, we divide the number of ways to get heads (1) by the total number of possible outcomes (2), which gives us a probability of 1/2 or 0.5.

Probability is used in many real-world applications, such as in the fields of finance, insurance, and engineering, to make informed decisions based on the likelihood of an event occurring. It is also used in statistical analysis to make inferences about a population based on a sample of data.

The total number of cards in the deck is:

Total number of cards = number of black cards + number of red cards = 33 + 77 = 110

The probability of drawing a black card is given by:

P(draw a black card) = (number of black cards) / (total number of cards) = 33 / 110

Therefore, the probability of drawing a black card is:

P(draw a black card) = 0.3 or 30%

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The cost of pizza with no toppings is $6. So correct option is C.

A graph is a visual representation of data or information, typically shown on a coordinate plane or a network of nodes and edges. Graphs are used to help people understand complex information by presenting it in a clear and concise way.

There are many different types of graphs, including bar graphs, line graphs, scatter plots, pie charts, and network graphs. Each type of graph is best suited for representing different types of data. For example, bar graphs are used to represent discrete data or data that can be divided into categories, while line graphs are used to represent continuous data or data that changes over time. Scatter plots are used to represent the relationship between two variables, while pie charts are used to represent percentages or proportions. Network graphs are used to represent complex systems of relationships between objects or people.

Graphs are commonly used in fields such as business, economics, science, and engineering to help people understand trends, patterns, and relationships in data. They can also be used to make predictions, identify outliers or anomalies, and communicate results to others. In addition, graphs can be customized to suit the needs of different audiences, such as by adding labels, titles, and other visual elements to make the data more understandable.

Because when x is 0 ,y is 6. So, the y intercept is the cost of a pizza with no toppings is $6.

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The complete question is:

Answer:

-4 + 8 = 4

-2 + 6 = 4

-1 + 5 = 4

So the three pairs are -4 and 8; -2 and 6; and -1 and 5.

The range in ages for the middle 50% of viewers is the interquartile range (IQR), which is the height of the box in the box plot. The best approximation is C) 20.

The interquartile range (IQR) is a measure of statistical dispersion that represents the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a dataset. It is a useful measure of spread because it is not influenced by outliers.

Range is a statistical measure that represents the difference between the highest and lowest values in a set of data. It provides a simple indication of the spread or variability of the data.

According to the given information:

A box plot is a graphical representation of the distribution of a dataset. The box in the plot represents the middle 50% of the data, with the lower end of the box representing the 25th percentile (Q1) and the upper end of the box representing the 75th percentile (Q3). The distance between Q1 and Q3, which is represented by the height of the box, is called the interquartile range (IQR).

To answer the question, we need to find the best approximation for the range in ages for the middle 50% of viewers. From the box plot, we can see that the height of the box is approximately 20 units, which is the IQR. Therefore, the best approximation for the range in ages for the middle 50% of viewers is option C) 20. This means that 50% of viewers are between Q1-10 to Q3+10, where Q1 is the 25th percentile and Q3 is the 75th percentile.

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Answer:

circumference of a circle is

[tex]2\pi\:r[/tex]

And the area of the circle is

[tex]\pi \: r {}^{2} [/tex]

a. TRUE, b. TRUE, c. TRUE, d. TRUE, e. TRUE, f. FALSE, g. TRUE

a. TRUE: The probability of an event can never be negative, and can at most be equal to 1, which represents certainty.

b. TRUE: The sample space is the set of all possible outcomes of an experiment, and the probability of the sample space is always equal to 1, since one of the outcomes must occur.

c. TRUE: If the events in a sequence are disjoint, then they have no outcomes in common, so the probability of the union of the events is the sum of the probabilities of the individual events.

d. TRUE: If one event is a subset of another event, then the probability of the subset is less than or equal to the probability of the superset. This follows from the fact that the subset contains fewer outcomes than the superset.

e. TRUE: The probability of the union of two events is the probability of the first event plus the probability of the second event, minus the probability of the intersection of the events, which is the probability of both events occurring together. This is known as the inclusion-exclusion principle.

f. FALSE: The formula (P(A ∩ B) = P(A)P(B)) only applies to independent events, but not all independent events are mutually exclusive. For example, if A is the event of rolling a 4 on a die, and B is the event of rolling an even number, then A and B are independent, but not mutually exclusive.

g. TRUE: If two events are mutually exclusive, then they have no outcomes in common, so the occurrence of one event tells us that the other event cannot occur. This dependence means that the events are not independent.

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The effective tax rate for a taxable income of $115,500 is A) 18.71%

The introductory $10,275 is subjected to a 10% tax burden, with the converted dollar amount representing $1,027.50 in taxes. The additional taxable sum of $30,900 ($41,175 - $10,275) is accessed at a 12% charge and aggregates to $3,708 worth of duties. An extra levy of 22% is imposed on the total $47,900 that lies between the two stipulated ranges ($89,075 - $41,175). The final evaluation stands at 24%, which provides an identical tax rate for the remaining $25,350 ($115,500 - $89,075). ).

Effective Tax Rate = (Total Tax Paid / Taxable Income) x 100%; which further articulates to ($21,357.50 / $115,500) x 100%,

= 18%

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Answer:

a) To find the exponential growth function, we can use the formula:

P(t) = P0 * e^(rt)

Where:

P(t) = the population at time t

P0 = the initial population (in this case, 5.51 million)

e = the mathematical constant e (approximately 2.71828)

r = the annual growth rate (in decimal form)

t = the number of years

Substituting the given values, we have:

P(t) = 5.51 * e^(0.0382t)

b) To estimate the population of the city in 2018, we can substitute t = 6 (since 2018 is 6 years after 2012) into the exponential growth function:

P(6) = 5.51 * e^(0.0382*6) ≈ 6.93 million

Therefore, the estimated population of the city in 2018 is approximately 6.93 million.

c) To find when the population of the city will be 10 million, we can set P(t) = 10 and solve for t:

10 = 5.51 * e^(0.0382t)

e^(0.0382t) = 10/5.51

0.0382t = ln(10/5.51)

t ≈ 11.7 years

Therefore, the population of the city will be 10 million in approximately 11.7 years from 2012, or around the year 2023.

d) To find the doubling time, we can use the formula:

T = ln(2) / r

Where:

T = the doubling time

ln = the natural logarithm

2 = the factor by which the population grows (i.e., doubling)

r = the annual growth rate (in decimal form)

Substituting the given value of r, we have:

T = ln(2) / 0.0382 ≈ 18.1 years

Therefore, the doubling time for the population of the city is approximately 18.1 years.

The only observations that are correct are Grace's and Maddy's. The answer is Option C.

We can start by finding the perimeter, area, and volume of one face of the cube, and then see which observation is correct.

The perimeter of one face of the cube is 4 times the length of one edge, which is:

= 4 × 12 inches

= 48 inches. So Grace's observation is correct.

The area of one face of the cube is the length of one edge squared, which is:

= 12 inches × 12 inches

= 144 square inches. So Maddy's observation is also correct.

The volume of the cube is the length of one edge cubed, which is:

= 1 foot × 1 foot × 1 foot

= 1 cubic foot. So Elena's observation is not correct.

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Answer:

Step-by-step explanation:

4-10(9m-7)

4-90m+70

74-90m

56x+24/8

8(7x + 3)/8

7x + 3

24r + 16

8(3r + 2)

is 2m-3 same as 4(1/2m-3)

2m-3 = 2m-12

: no

-2(10-15x) same as 14x-20+16x

-20+30x = -20+30x

: yes

The range is expressed in interval notation as (-1, ∞)

To find the linear function f(x), let us use the table given.

A linear function with the following equation that passes through the points (a, g(a)) and (b, g(b)):

[tex]g(x) - g(a) = \frac{g(b)-g(a)}{b-a} (x-a)[/tex]

Because the g(x) line crosses through points (-6, 14) and (-3, 8), we have:

a = -6, g(a) = 16, b = -3 and, g(b) = 10

Therefore g(x)

[tex]g(x) - (16) = \frac{10-16}{-3-(-6)} (x--(6))\\g(x) - 16 = \frac{10-16}{-3+6} (x+6)\\g(x) - 16 = \frac{-6}{3} (x+6)\\g(x) - 16 = -2(x +6)\\g(x) = -2x -12+16\\g(x) = -2x+4[/tex]

now find the (f+g)(x).

[tex](f+g)(x) = f(x) + g(x) = x^{2} + 2x -5 -2x + 4\\(f+g)(x) = f(x) + g(x) = x^{2} - 1\\[/tex]

(f+g)(x) = (x-1)(x+1), therefore we get the values x = 1 and x = -1

The parabola's vertice has x-coordinate 0 (the midway between the roots). At x = 0, we get:

[tex](f +g)(x) = 0^{2} - 1 = -1[/tex]

Furthermore, because the coefficient of [tex]x^{2}[/tex] is 1, which is positive, this function indicates a parabola that has been opened upwards.

As a result, the function's minimal value is y = -1. As a result, the function's range includes all real numbers equal to or greater than -1.

The range is expressed in interval notation as (-1, ∞)

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Let x be the distance traveled on the first day. Then, the distance traveled on the second day is 1.1x, on the third day is 1.1(1.1x) = 1.21x, and so on. After 7 days, the total distance traveled is:

x + 1.1x + 1.21x + ... + (1.1)^6 x = 56.923

Using the formula for the sum of a geometric series, we have:

x(1 - (1.1)^7)/(1 - 1.1) = 56.923

x(1 - 1.1^7)/(-0.1) = 56.923

x = 56.923(-0.1)/(1 - 1.1^7) ≈ 4 miles

Therefore, the hiker traveled approximately 4 miles on the first day.

Sn = x(1 - r^n)/(1 - r)

where x is the first term, r is the common ratio (in this case, 1.1), and n is the number of terms.

S14 = x(1 - 1.1^14)/(1 - 1.1)

S14 ≈ 167.63

Therefore, the hiker will travel approximately 167.63 miles in 14 days.

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Answer:

Step-by-step explanation:

A=1/2(b1+b2)h

=1/2 (11yd+11yd)(7yd)

=1/2(22yd)(7yd)

=(11yd)(7yd)

=77yd

The ratio of US to British coins is 25 to 4.

The second term, £50, is a fixed sum she receives regardless of the number of hours worked.

The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.

1. The ratio of US to Euro coins is 5 to 2, and the ratio of Euro to British coins is 5 to 1. To find the ratio of US to British coins, we can combine these ratios.

First, we need to make sure that the ratios have a common term. We can do this by multiplying the first ratio (US to Euro) by 5, which gives us a ratio of 25 to 10.

Next, we can use the second ratio (Euro to British) to convert Euro coins to British coins. Since the ratio is 5 to 1, for every 5 Euro coins, there is 1 British coin. So for every 10 Euro coins, there are 2 British coins.

Finally, we can combine the US to Euro ratio (25 to 10) with the Euro to British ratio (10 to 2) to get the ratio of US to British coins.

25 : 10 :: 10 : 2

Multiplying both sides by 2, we get:

50 : 20 :: 10 : 2

Simplifying, we get:

The ratio of US to British coins is 25 to 4.

2. To calculate Amanda's monthly pay, we can use the formula:

m = 10h + 50

where m is the total money Amanda receives in a month, and h is the number of hours she works.

The first term, 10h, represents her pay for the number of hours she works, which is £10 per hour. The second term, £50, is a fixed sum she receives regardless of the number of hours worked.

3. To calculate the cost of the holiday package for d days, we can use the formula:

C = 190 + 50d

where C is the cost of the holiday package, and d is the number of days.

The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.

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The diagram of the Gateway Arch on the coordinate plane, analyzed using quadratic equations indicates;

1. The vertex point is (50, 630)

2. The solution point are; (20, 0), and (80, 0)

3. Vertex form; f(x) = -0.7·(x - 50)² + 630

4. Factored form; f(x) = -0.7·(x - 20)·(x - 80)

A quadratic equation is an equation of the form f(x) = a·x² + b·x + c

1. The vertex obtained from the graphical diagram of the Gateway Arch indicates that the point corresponding to the vertex point is; (50, 9 × 70 = 630)

The vertex point is; (50, 630)

2. The solution are the points the curve of the Gateway intersects the x-axis, which are points where the y-axis values are zero, therefore;

The solutions are; (20, 0), and (80, 0)

3. The vertex form of a quadratic equation is; f(x) = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex

Therefore;

(h, k) = (50, 630)

f(20) = 0 = a·(20 - 50)² + 630

a·(20 - 50)² = -630

a = -630/((20 - 50)²) = -630/900 = -7/10

a = -7/10 = -0.7

The vertex form quadratic equation is therefore; f(x) = -0.7·(x - 50)² + 630

4. The factored form of a quadratic equation is; f(x) = a·(x - r₁)·(x - r₂)

r₁ = 20, and r₂ = 80, a obtained from the vertex is; a = -0.7

The factored form is therefore; f(x) = -0.7·(x - 20)·(x - 80)

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The solution to the compound inequality 4p + 1 < −11 or 6p + 3 > 39 is p > 6 or p > -3.

A compound inequality is a mathematical statement that involves two or more inequalities joined by either the word "and" or "or". The solution set of a compound inequality is the set of all values that satisfy both (in the case of "and") or either (in the case of "or") of the individual inequalities.

Let's solve each inequality separately:

4p + 1 < −11

Subtracting 1 from both sides, we get:

4p < -12

Dividing both sides by 4 (and remembering to flip the inequality because we are dividing by a negative number), we get:

p > -3

So the solution to the first inequality is:

p > -3

Now let's look at the second inequality:

6p + 3 > 39

Subtracting 3 from both sides, we get:

6p > 36

Dividing both sides by 6, we get:

p > 6

So the solution to the second inequality is:

p > 6

Therefore, the solution to the compound inequality 4p + 1 < −11 or 6p + 3 > 39 is:

p > 6 or p > -3

This can be written more simply as:

p > -3

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In the equation 1 over 2 x + y=c, the constant proportionality is defined as c. It displays the line's y-intercept and slope.

If the ratio of one statistic to the other is constant, then there is a proportional relationship between the two variables.

The ratio of y to x is the constant of proportionality if x and y have a proportional connection. At times, we can also say that x is to y.

The proportionality constant, or c, in the equation 1 over 2 x + y = c serves as a gauge for how quickly two variables change. The proportionality constant's value doesn't change when the value of one of the variables does.

A linear equation with two variables, x and y, is 1 over 2x + y = c. In the x-y plane, it symbolises a straight line.

If x = 0

Then,

1/2(0) + y = c

y = c

The proportionality constant, c, can be seen in the equation

1 over 2 x + y = c.

This number, which is unrelated to the actual values of the variables, shows the relationship between the two variables x and y.

The slope of the line connecting the two variables is another name for the constant of proportionality.

Two variables, x and y, are included in the equation 1 over 2 x + y = c in addition to the proportionality constant. The two quantities that

are being compared are represented by these variables.

In the equation 1 over 2 x + y=c, the proportionality constant is defined as c. It displays the line's y-intercept and slope.

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The Complete questions as follows-

Explain what the constant of proportionality means in the equation 1 over 2 x + y = c

It should be noted that to select the location of -2 and -9 on the number line, the steps are given below.

Draw a number line with zero in the center and a positive direction to the right and a negative direction to the left.

Find the position of -9 by counting 9 units to the left of zero on the number line. Mark this point with a dot or a cross.

Find the position of -2 by counting 2 units to the left of zero on the number line. Mark this point with a dot or a cross.

Label the points as -9 and -2 to indicate their values.

Your number line should now have two marked points at positions -9 and -2.

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The measurements for area of Jacobs yard are;

Part A = 6m x 3m = 18m

Part B = 4.5m x 3m = 13 m

Part C = 1/2 x 3m x 3m = 4.5 m²

Total area = 18m² + 13.5m² + 4.5m² = 36m²

To identify sections that would help in calculating area, you need to look for shapes or figures that can be divided into simpler geometric shapes, such as squares, rectangles, triangles, and circles.

Once you have identified the simpler shapes, you can use their formulas to calculate their areas and then add them together to find the total area of the larger shape or figure.

For example, a rectangle can be divided into two triangles or two smaller rectangles, and a circle can be divided into a sector or a ring. Breaking down a larger shape into smaller, simpler shapes can make it easier to calculate their areas accurately.

Jacob is putting tiles on the section of his yard labeled A, B, C. What is the area of the parts that need tiles?

Part A = .............. x ........... = ...........m

Part B = + .............. x ............. = ............ m

Part C = 1/2 x ................. x ............ = ............... m²

Total area = ................... + ..................... + .................. = ..............m

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Answer:

42.15 as a decimal is 0.4215 and you can multiply 0.4215 by a number to get 42.15 percent of that number.

Step-by-step explanation:

So the answer is 0.4215

Hope this helps! =D

Answer:0.4215

Step-by-step explanation:

42.15%÷100=0.4215

The probability that the selected member is 21 or more is 88%.

The probability that the selected member is 55 or less is 86%.

The probability that the selected member is not in the 21 to 35 age group is 58%.

The basic probability formula of dividing the number of favorable outcomes by the total number of outcomes.

In this case, we are given the percentage of members in each age group, and we need to find the probability of selecting a member with a certain age range.

Here we have

The table shows the age distribution of members of a gym.  

Age -            Under 21      21 -35     36 - 55   Over 55

percentage       12                42            32          14  

a) To find the probability that the selected member is 21 or more,

Add the percentage of members who are 21-35, 36-55, and over 55 since all of these age groups are 21 or more.

Probability (21 or more)

= Percentage (21-35) + Percentage (36-55) + Percentage (Over 55)

= 42% + 32% + 14%

= 88%

b) To find the probability that the selected member is 55 or less,  

Add the percentage of members who are under 21, 21-35, and 36-55 since all of these age groups are 55 or less.

Probability (55 or less)

= Percentage (Under 21) + Percentage (21-35) + Percentage (36-55)

= 12% + 42% + 32%

= 86%

c) To find the probability that the selected member is not in the 21 to 35 age group,

Add the percentage of members who are under 21, 36-55, and over 55 since all of these age groups are not in the 21 to 35 age group.

Probability (not in the 21 to 35 age group)

= Percentage (Under 21) + Percentage (36-55) + Percentage (Over 55)

= 12% + 32% + 14%

= 58%

Therefore,

The probability that the selected member is 21 or more is 88%.

The probability that the selected member is 55 or less is 86%.

The probability that the selected member is not in the 21 to 35 age group is 58%.

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Therefore, 65% of all nurses have a starting salary of more than $71,725.31.

Random variable: X, the starting salary of a randomly selected nurse.

b) P(X ≥ 78371.8) = 1 - P(X < 78371.8)

Using the Z-score formula:

z = (X - μ) / σ = (78371.8 - 67694) / 10333 ≈ 1.03

Looking up the probability in the standard normal table or using a calculator, we get:

P (Z ≥ 1.03) ≈ 0.1492

Therefore, P (X ≥ 78371.8) ≈ 0.1492.

c) P (X ≤ 91407.1)

Using the Z-score formula:

z = (X - μ) / σ = (91407.1 - 67694) / 10333 ≈ 2.30

Looking up the probability in the standard normal table or using a calculator, we get:

P(Z ≤ 2.30) ≈ 0.9893

Therefore, P (X ≤ 91407.1) ≈ 0.9893.

d) P (78371.8 < X < 91407.1) = P(X < 91407.1) - P(X < 78371.8)

Using the Z-score formula:

z1 = (78371.8 - 67694) / 10333 ≈ 1.03

z2 = (91407.1 - 67694) / 10333 ≈ 2.30

Looking up the probabilities in the standard normal table or using a calculator, we get:

P(Z < 1.03) ≈ 0.8498

P(Z < 2.30) ≈ 0.9893

Therefore, P (78371.8 < X < 91407.1) ≈ 0.9893 - 0.8498 ≈ 0.1395.

e) P (X ≤ 41861.5)

Using the Z-score formula:

z = (41861.5 - 67694) / 10333 ≈ -2.50

Looking up the probability in the standard normal table or using a calculator, we get:

P (Z ≤ -2.50) ≈ 0.0062

Therefore, P (X ≤ 41861.5) ≈ 0.0062.

f) Yes, a starting salary of 41861.5 dollars is unusually low for a randomly selected nurse, because it is more than 3 standard deviations below the mean. A salary this low would be in the bottom 0.62% of all nurse salaries.

g) To find the starting salary that 65% of all nurses have more than, we need to find the z-score that corresponds to the 65th percentile, and then use the Z-score formula to solve for X.

Using a standard normal table or calculator, we find that the z-score corresponding to the 65th percentile is approximately 0.3853.

Using the Z-score formula:

z = (X - μ) / σ

Substituting μ = 67694, σ = 10333, and z = 0.3853, we get:

0.3853 = (X - 67694) / 10333

Solving for X, we get:

X = 10333(0.3853) + 67694 ≈ 71725.31

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Using curves, we can find that the value of y at the indicated point on the curve is √3.

What is the definition of curves?

A smooth-drawn figure or line with a bend or turns is referred to as a curve. A circle is an illustration of a curved shape. Geometry is a subfield of mathematics that examines the dimensions, characteristics, and shapes of figures.

Here in the question,

Given equation:

x = y² - 2

As a point (1, y) is on the curve, we can put the value of x coordinate in the equation:

1 = y² - 2.

Adding 2 on both sides:

1 + 2 = y² - 2 + 2

⇒ 3 = y²

⇒ y = √3.

Therefore, the value of y at the indicated point on the curve is √3.

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Answer: a. To find the number of barrels that should be refined to maximize profit, we need to find the critical point of the function P(x), which occurs where the derivative of P(x) equals zero.

P(x) = 8x - 0.02x²

P'(x) = 8 - 0.04x

Setting P'(x) = 0, we get:

8 - 0.04x = 0

Solving for x, we get:

x = 200

Therefore, 200 barrels should be refined to maximize the profit.

b. To find the maximum profit, we substitute x = 200 into the profit function P(x):

P(200) = 8(200) - 0.02(200)²

P(200) = 1600 - 800

P(200) = 800

Therefore, the maximum profit is $800.

Step-by-step explanation: