Total arrangement = Case 1 + Case 2 – Case 3
Total arrangement = 15 + 15 - 81 = -51
What is Sitting Arrangement ?
In mathematics, seating arrangement refers to the various ways in which individuals can be seated in a certain arrangement or order. This term is often encountered in combinatorics, which is a branch of mathematics that deals with counting arranging objects.
To find the number of seats satisfying a given condition, we can approach the problem using the inclusion-exclusion principle.
Let's look at these two cases: no girls are sitting together and no boys are sitting together.
Case 1: No girls are sitting together
In this case, we have to divide the five girls into three rows so that no two girls sit in any row. We can use a technique called stars and bars. Think of the girls as stars and the spaces between them and the ends as rods. We need to divide the five girls between the three rows, so we have four spaces between the stars and two ends, giving us (4 + 2)C2 = 15 ways to divide the girls.
Case 2: No boys sit together
Similarly, we have to divide the five boys among three rows so that no two boys sit in any row. Using the same stars and bars technique, we have (4 + 2)C2 = 15 ways to divide the boys.
However, we must exclude cases where boys and girls sit together. To find this, we need to find the number of arrangements where both conditions are violated.
Case 3: Boys and girls are sitting together
In this case, we can consider the pair of boy and girl sitting together as one entity. So we have four pairs (BB, GG, GB, BG) to split between the three rows, giving us 3^4 = 81 ways to split these pairs.
Now we can use the inclusion-exclusion principle to find the number of arrangements that satisfy at least one of the conditions. The total number of arrangements is the sum of arrangements without girls together, arrangements without boys, minus arrangements where both boys and girls sit together:
Total arrangement = Case 1 + Case 2 – Case 3
Total arrangement = 15 + 15 - 81 = -51
However, a negative value has no meaning in this context. It means that there are no valid seating arrangements that meet the given conditions. It may not be possible to seat students in such a way as to prevent two girls or two boys from sitting together in any row of five seats. The teacher may need to explore alternative seating arrangements or adjust conditions to find a suitable solution.
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Here are the ingredients needed to makes 12 shortcakes:
50g of sugar
200g of butter
200g of flour
10ml of milk.
Robert has
500g of sugar
1000g of butter
1000g of flour
500ml of milk
Work out the greatest number of shortcakes Robert can make.
Answer:
He can make a maximum of 60 shortcakes
Step-by-step explanation:
With the sugar alone he has enough to make:
500/50=10×12=120 shortcakes
Taking the butter into account he can make a maximum of:
1000/200=5×12=60 shortcakes
Now taking the flour into account he can still make a maximum of 60 shortcakes before running out of supply.
However, with the milk alone, he can make up to
500/10=50×12=600 shortcakes
All we need to do is find the minimum number of shortcakes he can make before running out of supply.
In this case he would make 60 shortcakes
Hope this helps!
Pump A and Pump B fill the pool in 35 minutes, Pump B and Pump C fill it in 40
minutes, and Pump A and Pump C fill it in 56 minutes. How many minutes will it take
all three pumps, working together, to fill the pool?
It will take all three pumps, Working together, 1.56 minutes to fill the pool.
The given information, we can write three equations as follows:
1) (1/A + 1/B)*35 = C ---(Equation 1)
2) (1/B + 1/C)*40 = C ---(Equation 2)
3) (1/A + 1/C)*56 = C ---(Equation 3)
We want how many minutes it will take all three pumps, working together, to fill the pool, so let's represent the time taken by all three pumps working together as "t".
When all three pumps work together, they can fill the pool in one minute, so their combined rate is 1/C.
Using the rate formula, we can write the following equation:
1/A + 1/B + 1/C = 1/t ---(Equation 4)
We have four unknowns (A, B, C, and t), so we need to solve for one of them to get the answer. Let's solve for "t".
First, we can simplify Equations 1, 2, and 3 as follows:
1) 1/A + 1/B = C/35
2) 1/B + 1/C = C/40
3) 1/A + 1/C = C/56
Next, we can substitute these equations into Equation 4 to get:
(C/35) + (C/40) + (C/56) = 1/t
Now, we can simplify and solve for "t":
LCD = 39200
1120C + 980C + 700C = 39200
2800C = 39200
C = 14
Substituting this value of "C" into any of the simplified equations, we can solve for "A" and "B". Let's use Equation 1:
1/A + 1/B = 14/35
5(A+B) = 98
A+B = 19.6
Now we can use A+B+C = 1/t to solve for "t":
t = 1 / (A+B+C) = 1 / (19.6 + 14) = 0.026 hours = 1.56 minutes
Therefore, it will take all three pumps, working together, 1.56 minutes to fill the pool.
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Blake recorded the high temperatures each day for a month in two different cities.
For City A, the mean high temperature was 59°F with a mean absolute deviation of 3.2.
For City B, the mean high temperature was 71°F with a mean absolute deviation of 2.9.
Compare the difference of the means in terms of the mean absolute deviations
Answer:
City B is significantly higher than in City A.
Step-by-step explanation:
To compare the difference of the means in terms of the mean absolute deviations, we can use the concept of standard deviation units. We divide the difference of the means by the average of the mean absolute deviations of the two cities:
D = (71 - 59) / ((3.2 + 2.9) / 2)
D = 12 / 3.05
D ≈ 3.934
The value of D tells us that the difference of the means between the two cities is almost 4 standard deviation units, which is a large difference. This means that the mean high temperature in City B is significantly higher than in City A.
Forty volunteer drivers are separated into two groups of 20 drivers each at random. The first group is asked to pay particular attention to braking smoothly when approaching a red light or stop sign. The second group is given no special instructions. All drivers report, at the end of a month, the gallons of gasoline used. The mean for the first group is 43.16 gallons of gas. The mean for the second group is 54.63 gallons of gas. The difference in means for the two groups is -11.47 gallons of gas. The data for both groups are combined and redistributed at random into two groups of 20. The means for each redistributed group are calculated, and the difference in means is recorded. The differences are represented in the histogram.
Which of these conclusions and justifications is the most reasonable?
The most reasonable conclusion is that the instruction to brake smoothly resulted in a decrease in gas consumption, as evidenced by the lower mean and negative difference in means between the two groups.
Based on the information provided, the most reasonable conclusion would be that the instruction given to the first group of drivers to brake smoothly when approaching a red light or stop sign resulted in a decrease in the mean gallons of gas used compared to the second group.
The justification for this conclusion is supported by the fact that the mean for the first group is 43.16 gallons of gas, which is lower than the mean for the second group, which is 54.63 gallons of gas. This indicates that the first group, who received the specific instruction to brake smoothly, consumed less gas on average.
The histogram displaying the differences in means after the data for both groups were combined and redistributed also supports the conclusion. It likely shows a distribution that is centered around a negative value, indicating that the majority of the redistributed groups had a lower mean gas consumption compared to the initial second group.
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What is the answer to this?
The value of x in the parallel lines is 15.
Option C is the correct answer.
We have,
The concept being used here is the concept of alternate exterior angles and the parallel lines property.
Alternate exterior angles are pairs of angles that lie on opposite sides of a transversal and are located outside the two parallel lines.
According to the property of alternate exterior angles, when two parallel lines are intersected by a transversal, the alternate exterior angles are congruent or equal in measure.
Since lines s and t are parallel lines,
8x + 7 and 127 are alternate exterior angles.
So,
8x + 7 = 127
Now,
Solve for x.
8x + 7 = 127
8x = 127 - 7
8x = 120
x = 120/8
x = 15
Thus,
The value of x in the parallel lines is 15.
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priya is comparing two functions: f(x)= 25x^(2) and g(x) =3*3^(x) to find out which has greater output values as x gets very large
it has a input table using inputs from 0 to 5 and then on top it says f(x) and g(x) and you have to find the outputs with that
Answer:
Step-by-step explanation:
Sure, here is the input table for f(x) and g(x) using inputs from 0 to 5:
| Input (x) | f(x) = 25x^(2) | g(x) = 3*3^(x) |
|-----------|----------------|----------------|
| 0 | 0 | 3 |
| 1 | 25 | 9 |
| 2 | 100 | 27 |
| 3 | 225 | 81 |
| 4 | 400 | 243 |
| 5 | 625 | 729 |
As x gets very large, g(x) will have greater output values than f(x). This is because the function g(x) has an exponential growth while f(x) only has quadratic growth. As x gets larger, the base of the exponent in g(x) becomes more significant and results in a much larger output value compared to f(x).
Find the angles plssss hurry
Answer:
a = 157
b = 23
c = 157
Step-by-step explanation:
Angle b is a vertical angle to the angle measuring 23 so they are equal.
b = 23
Angle c and the angle measuring 23 forms a straight line so they add to 180.
c+23 =180
c = 180-23
c = 157
Angle c and a are vertical angles so they are equal.
c = a = 157
Answer:
a = 157°
c = 157°
b = 23°
Step-by-step explanation:
We know that vertically opposite angles are equal.
∴ b = 23°
We know that angles in a straight line are added up to 180°.
∴ b + c = 180
23 + c = 180
c = 180 - 23
c = 157°
a = 157° ( vertically opposite angles ⇒ c = a )
a manufacturer of shoes wanted to reduce the number of flaws per pair of shoes. data gathered from quality control measures indicated that brand a typically had 2.5 flaws per pair of shoes. a mechanical engineer for the company developed a modification of the current process that she thought might reduce the number of flaws. to determine if this was true, one of the machines in the plant was modified according to her specifications. a sample of 30 pairs of shoes was analyzed for flaws. the sample yielded a mean of 2.2 flaws per pair of shoes. assume the standard deviation of the measurements is 0.66. find the p-value of the test.
The p-value of the test is approximately 0.299.
To find the p-value of the test, we need to conduct a hypothesis test. Let's set up the hypotheses first:
Null Hypothesis (H0): The modification of the process did not reduce the number of flaws per pair of shoes.
Alternate Hypothesis (Ha): The modification of the process did reduce the number of flaws per pair of shoes.
We can use a one-sample t-test to analyze the data. The test statistic can be calculated using the formula:
t = ( - μ) / (s / √n),
where is the sample mean, μ is the population mean (2.5 flaws), s is the sample standard deviation (0.66), and n is the sample size (30).
Substituting the values into the formula, we get:
t = (2.2 - 2.5) / (0.66 / √30) ≈ -1.054
To find the p-value associated with this test statistic, we need to consult the t-distribution table or use statistical software. The p-value represents the probability of observing a test statistic as extreme as the one calculated under the null hypothesis.
Assuming a two-tailed test, the p-value is the probability of observing a t-value more extreme than -1.054 or more extreme than 1.054. Looking up the p-value in the t-distribution table or using software, we find that the p-value is approximately 0.299.
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A utility worker must reach the top of a telephone pole to fix an electric wire. if the pole casts a 39 foot 6 inch shadow at the same time the 6 foot 2inch man casts a 9 foot 4 inch shadow, how tall is the telephone pole? round to the nearest whole foot.
The height of the telephone pole is approximately 26 feet.
How to solve for the heightAccording to the given information, the height of the man is 6 feet 2 inches, which we can represent as 6.17 feet, and his shadow is 9 feet 4 inches, which is 9.33 feet.
Using the concept of similar triangles, we can set up the following proportion:
(man's height) / (man's shadow) = (pole's height) / (pole's shadow)
Simplifying the proportion:
6.17 / 9.33 = h / 39.5
To solve for 'h', we can cross-multiply:
6.17 * 39.5 = 9.33 * h
243.215 = 9.33 * h
Dividing both sides by 9.33:
h ≈ 26.06
Rounding to the nearest whole foot, the height of the telephone pole is approximately 26 feet.
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URGENT!! Please help for brainliest :)
Select the correct word or phrase that completes this sentence.
Least squares regression is a method that minimizes the sum of the
between the points on a
scatterplot and the regression line.
A. squared distances
B. median points
C. distances
D. average distances
Answer:
The correct answer is:
A. squared distances
a test requires that you answer first part a and then either part b or part c, but not both part b and part c. part a consists of 5 true-false questions, part b consists of 4 multiple choice questions with one correct answer out of 5 possible answers, and part c requires you to match 6 questions with 6 different answers. how many different completed (no blanks allowed) answer sheets are possible?
There are 250,000 different completed answer sheets possible using counting principle.
For part a, there are 2 choices for each of the 5 questions, so there are a total of 2^5 = 32 ways to complete part a.
For part b, there are 5 choices for each of the 4 questions, so there are a total of 5^4 = 625 ways to complete part b.
For part c, there are 6 choices for the first question, 5 choices for the second question (since one of the answers has already been used), 4 choices for the third question, and so on. So there are a total of 6 x 5 x 4 x 3 x 2 x 1 = 720 ways to complete part c.
To find the total number of possible completed answer sheets, we need to multiply the number of choices for each part. However, since part b and part c are mutually exclusive (you can only choose one of them), we need to add their totals together. Therefore, the total number of possible completed answer sheets is:
32 x (625 + 720) = 70,240
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Aiden is going to make concrete.
Answer:
8 bags of cement
9 bags of sand
3 bags of stone
Step-by-step explanation:
Hope this helps :)
Need Help ASAP! :(((
Answer:
look up a slope calculator insert x2 and y-3 for example and it will do it for u
Step-by-step explanation:
haylee Rolls two number cubes. what is the probability she rules two numbers whose sum is greater than 9?
Answer:
1/6 or 16.67%-------------------
There are 6 sides on each cube, so there are a total of 6 x 6 = 36 possible outcomes.
The combinations that result in a sum greater than 9 are:
(4,6), (5,5), (5,6), (6,4), (6,5), and (6,6)There are 6 favorable outcomes.
Therefore, the probability of two numbers whose sum is greater than 9 is:
6/36 = 1/6 or ≈ 16.67%.the test statistic calculated in the process of a kruskall-wallis test is h.
T/F
The Kruskal-Wallis test is a non-parametric test used to compare three or more independent groups to determine if there is a significant difference between the medians of the groups. The test statistic used in this test is denoted by the letter "H," which is calculated based on the ranks of the data.
True. The test statistic calculated in the Kruskal-Wallis test is denoted by the symbol H, not to be confused with the Shapiro-Wilk test statistic denoted by W. The Kruskal-Wallis test is a non-parametric test used to compare the median ranks of three or more independent groups. The test statistic H is calculated by comparing the between-group sum of squares to the total sum of squares. H follows a chi-squared distribution with degrees of freedom equal to the number of groups minus one. The p-value obtained from the chi-squared distribution is used to determine whether to reject or fail to reject the null hypothesis that there is no significant difference between the groups.
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Consider the relations shown in the table.
Which relations represent functions?
Answer: D
Step-by-step explanation: Got it right on test
Use the compound interest formula A = P(1 + r) to find the annual interest rate, r, if in 2 years an investment of $5,000 grows to $6,050.
The annual interest rate, r, is 0.1 or 10%. A 10% annual interest rate resulted in the investment growing from $5,000 to $6,050 in 2 years.
To find the annual interest rate, r, we can rearrange the compound interest formula A = P(1 + r) and solve for r.
Given that an investment of $5,000 grows to $6,050 in 2 years, we can substitute these values into the formula:
$6,050 = $5,000
[tex] {1 + r}^{2}[/tex]
Dividing both sides by $5,000, we have:
1.21 =
[tex](1 + r)^2[/tex]
Taking the square root of both sides, we get:
√1.21 = 1 + r
Simplifying, we have:
1.1 - 1 = r
0.1 = r
This means that the investment grew by 10% annually over the 2-year period. Compound interest is calculated by adding the interest earned to the initial amount, and as time passes, the interest is earned on both the initial amount and the accumulated interest from previous periods. In this case, a 10% annual interest rate resulted in the investment growing from $5,000 to $6,050 in 2 years.
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a random sample of size 28 is collected from a normal population with unknown variance. the sample has the mean of 108.127 and the standard deviation of 30.4888. construct a 98% confidence interval for a population mean. group of answer choices (105.546, 110.707) (94.725, 121.529) (93.878, 122.376) (105.235, 111.018)
The correct confidence interval for a population mean at a 98% confidence level is approximately (94.685, 121.569). Therefore, the correct choice is (94.725, 121.529).
To construct a confidence interval for a population mean, we can use the formula:
Confidence Interval = sample mean ± (critical value * standard error)
First, we need to determine the critical value for a 98% confidence level. Since the sample size is large (n = 28), we can use the z-table to find the critical value. For a 98% confidence level, the critical value is approximately 2.33.
Next, we calculate the standard error using the formula:
Standard Error = sample standard deviation / √(sample size)
In this case, the sample standard deviation is 30.4888 and the sample size is 28. Therefore:
Standard Error = 30.4888 / √(28) ≈ 5.769
Now we can construct the confidence interval:
Confidence Interval = 108.127 ± (2.33 * 5.769) = (108.127 ± 13.442) = (94.685, 121.569)
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PLSSS HELP IF YOU TURLY KNOW THISSS
Answer:
0.714
Step-by-step explanation:
5/7
(5X100) / 7 = 500/7.
50/7 = 7 remainder 1. carry that one over and place it before last zero in 500.
10/7 = 1 remainder 3.
we have 71 remainder 3.
3/7: 300/7 = 42.83
we now have answer of 0.714282
= 0.714 to nearest thousandth
use suitable property
(-128 x 46 )+ (128 x -36)
please answer the question I will mark them brainliest
The distributive property allows the formula (-128 x 46) + (128 x -36) to be simplified to -10496.
We may use the distributive property of multiplication over addition/subtraction, which asserts that an x (b + c) = an x b + an x c, to simplify the above calculation (-128 x 46) + (128 x -36).
Let's dissect the expression in detail:
(-128 x 46) + (128 x -36)Let's first assess the goods:
-128 x 46 = -5888
128 x -36 = -4608
Reintroduce these values into the phrase now:
(-5888) + (-4608)
We simply add the absolute values of the two negative numbers while maintaining the sign of the negative:
-5888 + (-4608) = -10496
Consequently, -10496 is the reduced expression.
Last but not least, the phrase (-128 x 46) + (128 x -36) becomes -10496. .By applying the distributive property and carrying out the required multiplication, addition, and subtraction, the result is -10496.
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pls help <3 Explain how to locate the foci of an ellipse from the graph.
Answer:
First take the difference between the squares of the semi-major axis and the semi-minor axis: (13 cm)² - (5 cm)² = 144 cm².
Then, take the square root of their difference to obtain the distance of the foci from the ellipse's center along the major diameter to be √144 = 12 cm.
Step-by-step explanation:
Your welcome
The formula PV - FV(1 + n) will determine the present value of $1. True/False
False. The formula PV - FV(1 + n) does not determine the present value of $1.
But rather it is a formula used to calculate the present value of a future cash flow or investment. PV stands for present value, FV stands for future value, and n represents the number of periods for which the investment will be held. The formula states that the present value of an investment or cash flow is equal to the future value of that investment or cash flow, discounted at a specified rate of return over a specific period of time.
In other words, the formula is used to determine the value today of a future cash flow or investment based on the time value of money. By discounting the future value of the cash flow or investment at a specified rate, the formula calculates the present value that would be equivalent to receiving that cash flow or investment at a future date.
Therefore, the correct statement would be: The formula PV - FV(1 + n) is used to determine the present value of a future cash flow or investment.
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if the standard error is smaller than the standard deviation when conducting a regression, what can you conclude?
If the standard error is smaller than the standard deviation when conducting a regression, it can be concluded that the model is more precise and reliable in predicting the outcome variable.
When conducting a regression, the standard error is a measure of the precision of the estimated regression coefficient. On the other hand, the standard deviation is a measure of the variability of the data points from the mean. If the standard error is smaller than the standard deviation, it means that the estimated regression coefficient is more precise than the variation of the data points. This indicates that the model is more reliable and accurate in predicting the outcome variable.
In practical terms, a smaller standard error means that the predicted values of the outcome variable will be closer to the actual values, resulting in more accurate predictions. However, it is important to note that a smaller standard error does not necessarily mean that the regression model is better. Other factors such as the goodness of fit, significance of the coefficients, and the overall explanatory power of the model should also be considered when evaluating the performance of a regression model.
In conclusion, if the standard error is smaller than the standard deviation when conducting a regression, it can be concluded that the model is more precise and reliable in predicting the outcome variable. However, other factors should also be taken into account to evaluate the overall performance of the model.
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A number tripled is equal to 57. Let n be the number. Which equation can be used to find the value of n and what is its solution? K OA) n + 3 = 57; n = 54 OB) n-3 = 57; n = 60 OC) 3 = 57; n = 171 OD) 3n = 57; n = 19
Answer:
[tex]3n = 57[/tex]
[tex]n = 19[/tex]
D is the correct answer.
given f(x)=3x+2 and g(x)= √x-1, determine the following: (f•g)(5) =
The value of (f•g)(5) is 21.
Given are two functions f(x) = 3x+2 and g(x)= √x-1, we need to determine (f•g)(5),
So, firstly determine (f•g)(x),
Therefore,
(f•g)(x) = (3x+2)(√x-1)
Now for, (f•g)(5) put x = 5,
We get,
(f•g)(5) = (3·5+2)(√5-1)
(f•g)(5) = 17 × 1.23
(f•g)(5) = 21
Hence the value of (f•g)(5) is 21.
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what is the surface area
The total surface area of the pyramid is: 208.88 m²
What is the surface area of the pyramid?The surface area of the pyramid is simply the sum of the areas of all the given surfaces.
Formula for the area of a triangle is:
Area = ¹/₂bh
where:
b is base
h is height
Area of four side triangles = 4(¹/₂ * 8 * 12) = 192 m²
Using Pythagoras theorem, the height of the base triangle is:
x = 4.22
Area of base = ¹/₂ * 8 * 4.22 = 16.88 m²
Total surface area = 192 + 16.88
= 208.88 m²
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Someone please help...
If the chicken crosses the road at 7.35 miles every 30 minutes exactly how fast would it take to find out the answer of why he crossed in the first place. Please answer mathematically (And leave the reason why...! )
We can deduce here that the chicken is traveling at a speed of 0.245 miles per minute.
What is speed?Speed is the amount of ground a thing covers in a predetermined period of time. It has magnitude but no direction because it is a scalar quantity. Meters per second (m/s), kilometers per hour (km/h), or miles per hour are used to express speed (mph).
In order to find the speed of the chicken, here is the formula to make use of:
Speed = distance / time
Speed = 7.35 miles / 30 minutes = 0.245 miles per minute.
The chicken might have crossed the first place because it is being chased.
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PLEASE HELP I AM GROUNDED AND NEED THIS ANSWER
Answer: 39
Step-by-step explanation: 180-141= 39
5x-4y=34
-x+8y=22
find the solution of the system of equations.
The solution of the system of equations 5x-4y=34 and -x+8y=22 is x = -6 and y = 4, or (x, y) = (-6, 4).
What is the solution to the system of equation?Given the system of equation in the question;
5x - 4y = 34 _____1
-x + 8y = 22 _____2
To solve the system of equation, first solve for x in equation 2 and plug it into equation 1.
-x + 8y = 22
x = 8y - 22 _____ 3
Plug equation 3 into equation 1
5x - 4y = 34
Plug in x = 8y - 22
5( 8y - 22 ) - 4y = 34
Solve for y
40y - 110 - 4y = 34
40y - 4y = 34 + 110
36y = 144
y = 144/36
y = 4
Plug y = 4 into equation 3
x = 8( 4 ) - 22
x = 32 - 22
x = 10
Therefore, the solution is x = 10 and y = 4.
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11. You and your friend ordered a pizza with 1 inch wide cheesy crust.
The total diameter of the pizza (including the cheesy crust) is 16 inches.
a) If you are given 1/6 of the pizza, what is the area of your slice? Lave exact answer.
b) What is the length of the outside cheesy crust that belongs to your friend? Leave exact answer
Answer:
Therefore:
a) The area of your slice is 32/3π square inches (exact answer).
b) The length of the outside cheesy crust that belongs to your friend is 16/3π inches (exact answer).
Step-by-step explanation:
a) To find the area of 1/6 of the pizza, we need to determine the area of the entire pizza and then divide it by 6.
The diameter of the pizza (including the cheesy crust) is 16 inches, which means the radius is half of the diameter, so the radius is 16/2 = 8 inches.
The formula for the area of a circle is A = πr², where A is the area and r is the radius.
Therefore, the area of the entire pizza is A = π(8 inches)² = 64π square inches.
To find the area of 1/6 of the pizza, we divide the area of the entire pizza by 6:
Area of 1/6 of the pizza = (64π square inches) / 6
b) The cheesy crust is located on the outer edge of the pizza, forming the circumference of the circle. The circumference is calculated using the formula C = 2πr, where C is the circumference and r is the radius.
The length of the outside cheesy crust that belongs to your friend is 1/6 of the circumference. So, we divide the circumference by 6:
Length of the outside cheesy crust for your friend = (2π(8 inches)) / 6
To get the exact answers, we leave the values in terms of π:
a) Area of 1/6 of the pizza = (64π square inches) / 6 = 32/3π square inches (exact answer)
b) Length of the outside cheesy crust for your friend = (2π(8 inches)) / 6 = 16/3π inches (exact answer)
Therefore:
a) The area of your slice is 32/3π square inches (exact answer).
b) The length of the outside cheesy crust that belongs to your friend is 16/3π inches (exact answer).
