a) we can be 99% confident that the true mean tread wear index for tires produced by this manufacturer under this brand name is between 172.4 and 210.2., b) The answer is A., c) The answer is B.
a. To construct a 99% confidence interval estimate of the population mean tread wear index, we need to use the formula:
CI = x ± zα/2 * (σ/√n)
where x is the sample mean (191.3), zα/2 is the z-score corresponding to the desired confidence level (99% in this case, which is 2.576), σ is the population standard deviation (unknown in this case, so we use the sample standard deviation of 21.1 as an estimate), and n is the sample size (20). Plugging in the values, we get:
CI = 191.3 ± 2.576 * (21.1/√20) = (172.4, 210.2)
Therefore, we can be 99% confident that the true mean tread wear index for tires produced by this manufacturer under this brand name is between 172.4 and 210.2.
b. The answer is A. No, because a grade of 200 is not in the interval. Since the confidence interval does not include the claimed value of 200, the consumer organization cannot accuse the manufacturer of producing tires that do not meet the performance information on the sidewall of the tire based on this sample alone.
c. The answer is B. It is not unusual because it is just outside of the confidence interval. The confidence interval developed in part (a) only provides a range of values that we are 99% confident the population mean falls within. It does not mean that all individual observations within or outside the interval are unusual. In fact, there is still a small probability (1% in this case) that an individual observation could fall outside the interval by chance. As long as the observed tread wear index is not too far outside the interval, it is still plausible that it could be a representative value from the population. In this case, an observed value of 205 is only slightly above the upper bound of the confidence interval, so it is not unusual.
a. To construct a 99% confidence interval estimate of the population mean tread wear index, we can use the following formula:
CI = x ± (t * (s / √n))
Where CI is the confidence interval, x is the sample mean, t is the t-value for the desired confidence level (99% in this case), s is the sample standard deviation, and n is the sample size.
Using the given data, we have:
x = 191.3
s = 21.1
n = 20
For a 99% confidence level and a sample size of 19 degrees of freedom (n-1), the t-value is approximately 2.861.
Now, we can calculate the confidence interval:
CI = 191.3 ± (2.861 * (21.1 / √20))
CI = 191.3 ± (2.861 * 4.718)
CI = 191.3 ± 13.5
CI = (177.8, 204.8)
b. Based on the confidence interval (177.8, 204.8), we can see that the grade of 200 is within the interval. Therefore, the consumer organization should not accuse the manufacturer of producing tires that do not meet the performance information on the sidewall of the tire. The correct answer is C: No, because a grade of 200 is in the interval.
c. An observed tread wear index of 205 for a particular tire is not unusual even though it is outside the confidence interval developed in (a) because the confidence interval only estimates the population mean tread wear index. Individual tire tread wear indexes can vary from the mean, and 205 is just slightly outside of the confidence interval. The correct answer is B: It is not unusual because it is just outside of the confidence interval.
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At the local college, a study found that students had an average of 0.7 roommates per semester. A sample of 133 students was taken. What is the best point estimate for the average number of roommates per semester for all students at the local college?
The best point estimate for the average number of roommates per semester for all students at the local college is 0.7, based on the study conducted with a sample of 133 students.
The best point estimate for the average number of roommates per semester for all students at the local college is 0.7, which is the average found in the study of the sample of 133 students. Since the sample is representative of the population, we can use the sample mean as a point estimate for the population mean. Therefore, we can estimate that the average number of roommates per semester for all students at the local college is 0.7.
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determine the minimum and the maximum number of matches that can be played in a double-elimination tournament with n players, where after each game between two players, the winner goes on and the loser goes on if and only if this is not a second loss.
In a double-elimination tournament with n players, the minimum number of matches that can be played is 2n - 3, and the maximum number of matches is 3n - 3.
In a double-elimination tournament with n players, we need to determine the minimum and maximum number of matches that can be played. Here's the step-by-step explanation:
1. the Minimum number of matches:
In a double-elimination tournament, each player is eliminated after their second loss. The minimum number of matches occurs when all players except the eventual winner lose twice in succession. In this case, there will be (n-1) matches in the winner's bracket and (n-2) matches in the loser's bracket.
Minimum number of matches = (n-1) + (n-2)
= 2n - 3
2.The maximum number of matches:
In the maximum case scenario, each player has to be defeated twice except the eventual winner who will only have one defeat. This means there will be (n-1) matches in the winner's bracket and 2(n-1) matches in the loser's bracket.
Maximum number of matches = (n-1) + 2(n-1)
= 3n - 3
So, in a double-elimination tournament with n players, the minimum number of matches that can be played is 2n - 3, and the maximum number of matches is 3n - 3.
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The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 10 to 14.5 on the number line. A line in the box is at 12.5. The lines outside the box end at 5 and 20. The graph is titled Fast Chicken.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
Which drive-thru typically has less wait time, and why?
Fast Chicken, because it has a smaller median
Fast Chicken, because it has a smaller mean
Super Fast Food, because it has a smaller median
Super Fast Food, because it has a smaller mean
The drive-thru is able to estimate their wait time more consistently will be;
⇒ A. Burger Quick, because it has a smaller IQR.
Since, The range of values in the middle of the scores is known as the interquartile range, or IQR.
The appropriate measure of variability is the interquartile range when a distribution is skewed and the median is used instead of the mean to show a central tendency.
Since, IQR is the difference between the third quartile and the first quartile, which is represented by the box in the box plot.
Now, In this case, the IQR for Burger Quick is,
15.5 - 8.5 = 7.0,
while the IQR for Fast Chicken is,
14.5 - 10 = 4.5.
Hence, A smaller IQR indicates that the data is more consistent and less spread out.
Thus, The correct option here is Burger Quick, because it has a smaller IQR (Interquartile Range).
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How would I solve a problem like this?
The area of the shape is 843.76mm²
What is area of a shape?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.
The shape can be divided into a trapezoid , square and a semi circle.
The area of the trapezoid = 1/2(a+b) h
= 1/2( 55+12.5) ×12.5
= 1/2 × 67.5 × 12.5
= 421.88mm²
Area of square = 12.5 × 12.5
= 156.25mm²
Area of semi circle = 1/2πr²
= 1/2 × 3.14 × 12.5²
= 265.63mm²
Area of the shape = 265.63 + 421.88 + 156.25 = 843.76mm²
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find the domain and range. determine if the relation is a function. {(-1,1), (-1,-1),(-2,2), (-2,-2),(-3,3),(-3,-3),(-4,4), (-4,-4)}
The Domain of the function is Domain = {-1, -1, -2, -2, -3, -3, -4, -4}.
Yes the relation a function.
We have the set,
{(-1,1), (-1,-1),(-2,2), (-2,-2),(-3,3),(-3,-3),(-4,4), (-4,-4)}
We know that the domain is the input value or the x value.
So, Domain = {-1, -1, -2, -2, -3, -3, -4, -4}
and, the range is the output value or y value
So, Range = {1, -1, 2, -2, 3, -3, 4, -4}
As, each input value have distinct output s then the relation a function.
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Is my answer right or wrong click to see file
The given representation is a quadratic function.
The given table can be represented in the form of equation as,
y = x²
When x = 0, y = 0
When x = 1, y = 1
When x = 2, y = 2² = 4
When x = 3, y = 3² = 9
When x = 4, y = 4² = 16
This can be written as,
y = x² + 0x + 0
This is a quadratic function.
Hence the given representation is a quadratic function.
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find the lenght of side x
give your answer in simplist form
The length of side x based on the triangle given will be 26.2cm.
How to calculate the length of the triangleIt should be noted that the image of the triangle is missing, so i have attached it.
In this case, to find the value of x, we will use cosine rule;
x² = 15² + 18² - 2(15 × 18)cos105
x² = 225 + 324 - 540(-0.2558)
x² = 549 + 138.132
x² = 687.132
x ≈ 26.2 cm
Therefore, length of side x based on the triangle given will be 26.2cm.
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In right triangle DOG with the right angle O
find OG if DG = 4√5 and DO = 4.
The calclated length of segment OG is 8 units
Calculating the length OGFrom the question, we have the following parameters that can be used in our computation:
DG = 4√5
DO = 4.
The length OG is calculated as
OG^2 = DG^2 - DO^2
substitute the known values in the above equation, so, we have the following representation
OG^2 = (4√5)^2 - 4^2
Evaluate
OG^2 = 64
So, we have
OG = 8
Hence, the solution is 8
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I’ll give brainliest
The graph that shows the image of triangle LMN after a dilation with scale factor of 3, followed by a translation 4 units down and 2 units left is given as follows:
Graph D.
How to obtain the transformed figure?The vertices of the original figure are given as follows:
L(1,0), M(0,3), N(2,2).
The dilation by a scale factor of 3 means that each coordinate of each vertex is multiplied by 3, hence the vertices are given as follows:
L'(3,0), M'(0,9) and N'(6,6).
The rule for the translation 4 units down and 2 units left is given as follows:
(x,y) -> (x - 2, y - 4).
Hence the vertices of the image are given as follows:
L''(1,-4), M''(-2, 5) and N''(4, 2).
Which are shown on Graph D.
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1) Find the linearization L(x) of the function at a. f(x)= x^4 + 3x^2, a= -1
Therefore, the linearization of f(x) at a = -1 is L(x) = -10x - 6.
To find the linearization L(x) of the function f(x) = x⁴ + 3x² at a = -1, we need to use the formula:
L(x) = f(a) + f'(a)(x-a)
where f'(x) is the derivative of f(x) with respect to x.
First, we need to find f(-1) and f'(-1).
f(-1) = (-1)⁴ + 3(-1)²
= 1 + 3
= 4
f'(x) = 4x³ + 6x
f'(-1) = 4(-1)³ + 6(-1)
= -4 - 6
= -10
Now we can substitute these values into the linearization formula:
L(x) = f(-1) + f'(-1)(x - (-1))
L(x) = 4 - 10(x + 1)
L(x) = -10x - 6
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You would like to study all of the numbers that are at a distance 10 or less from a number -20. Write this using absolute value notation and use the variable x
Answer:
Step-by-step explanation:
dad hates me sorry bye
Checking for approximate normality in the population is essential for constructing a valid confidence interval, particularly when dealing with small sample sizes. This ensures the accuracy and reliability of the interval in estimating the true population parameter.
It's important to check whether the population is approximately normal before constructing a confidence interval because the accuracy and validity of the interval depend on the underlying distribution of the population. Here's a step-by-step explanation:
1. A confidence interval is a range of values within which the true population parameter (e.g., mean or proportion) is likely to fall, with a certain level of confidence (e.g., 95% or 99%).
2. The process of constructing a confidence interval relies on the Central Limit Theorem, which states that, for large sample sizes, the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution.
3. However, for small sample sizes, the distribution of the population needs to be approximately normal in order to obtain an accurate confidence interval. This is because the normality assumption is crucial for the proper interpretation of the interval.
4. If the population is not approximately normal, the confidence interval may not provide a reliable estimate of the true population parameter, leading to incorrect conclusions and potentially invalid results.
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The p-value is _____ or less if the chi-square statistic is 3.84 or more.
The p-value is 0.05 or less if the chi-square statistic is 3.84 or more.
The p-value is 0.05 or less if the chi-square statistic is 3.84 or more. This indicates that there is a statistically significant difference between the observed and expected frequencies, and we reject the null hypothesis at a 5% significance level.
A statistical technique called the chi-squared test is used to assess whether there is a significant discrepancy between observed and predicted data. The test is frequently employed in disciplines like biology, sociology, and psychology to analyse categorical data.
The chi-squared test's fundamental premise is to contrast observed frequencies of a collection of categorical data with expected frequencies that would be anticipated if the data were distributed in a particular way. The test determines whether there is a statistically significant difference between the observed and anticipated frequencies.
The goodness-of-fit test and the test of independence are the two primary categories of chi-squared tests.
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T/F : If det A is zero, then two columns of A must be the same, or all of the elements in a row or column of A are zero.
False. If Determinant A is zero, it does not necessarily imply that two columns of A must be the same or that all elements in a row or column of A are zero.
If det A is zero, it does not necessarily imply that two columns of A must be the same or that all elements in a row or column of A are zero.
For example, consider the following 2x2 matrix:
A = [1 2]
[2 4]
The determinant of A is det(A) = (1*4 - 2*2) = 0, but the columns of A are not the same, and not all elements in a row or column are zero.
However, it is true that if two columns of A are the same or all of the elements in a row or column of A are zero, then det A must be zero.
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Circle the greater fraction. Then subtract the
lesser fraction from the greater fraction.
4/5 8/9. What is it pls
Answer:
The greater fraction is 8/9. The difference is 4/45
Step-by-step explanation:
To compare we need a common denominator. That number is 45
[tex]\frac{4}{5}[/tex]·[tex]\frac{9}{9}[/tex] = [tex]\frac{36}{45}[/tex]
[tex]\frac{8}{9}[/tex]·[tex]\frac{5}{5}[/tex] = [tex]\frac{40}{45}[/tex] This has the largest value.
[tex]\frac{40}{45}[/tex] - [tex]\frac{36}{45}[/tex] = [tex]\frac{4}{45}[/tex]
Helping in the name of Jesus.
in person 1 can do a task in x hours and person 2 can do a task in y hours how many hours will it take to complete the same task together equation
the time it would take for person 1 and person 2 to complete the task together is 2xy / (x + y) hours
If person 1 can do a task in x hours and person 2 can do the same task in y hours, then the combined rate at which they can complete the task is:
rate = 1/x + 1/y
This is because each person's rate of completing the task is the reciprocal of their time to complete the task, and their combined rate is the sum of their individual rates.
To find the time it would take for both persons to complete the task working together, we can use the formula:
time = 1 / rate
Substituting the expression for the rate above, we get:
time = 1 / (1/x + 1/y)
Simplifying this expression, we can use the formula for the harmonic mean of two numbers:
time = 2xy / (x + y)
Therefore, the time it would take for person 1 and person 2 to complete the task together is 2xy / (x + y) hours
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Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 72 students in the highest quartile of the distribution, the mean score was x = 175.90. Assume a population standard deviation of σ = 8.35. These students were all classified as high on their need for closure. Assume that the 72 students represent a random sample of all students who are classified as high on their need for closure. How large a sample is needed if we wish to be 99% confident that the sample mean score is within 1.5 points of the population mean score for students who are high on the need for closure? (Round your answer up to the nearest whole number.) students
Rounding up to the nearest whole number, we get a sample size of 314 students. Therefore, if we randomly select 314 students who are classified as high on their need for closure. we can be 99% confident that the sample mean score is within 1.5 points of the population mean score.
To determine the sample size needed, we can use the formula:
n = (z * σ / E)^2
Where:
z = the z-score corresponding to the desired level of confidence (in this case, 2.576 for 99% confidence)
σ = the population standard deviation (8.35)
E = the maximum allowable error (1.5)
Plugging in these values, we get:
n = (2.576 * 8.35 / 1.5)^2
n = 313.15
To determine the required sample size for a 99% confidence interval within 1.5 points of the population mean score, follow these steps:
1. Identify the given information:
- Population standard deviation (σ) = 8.35
- Desired margin of error (E) = 1.5
- Confidence level (z-score) = 2.576 (for 99% confidence interval)
2. Use the formula for sample size calculation:
n = (Z * σ / E)^2
3. Plug in the values:
n = (2.576 * 8.35 / 1.5)^2
4. Calculate the result:
n ≈ 121.22
5. Round up to the nearest whole number:
n = 122 students
So, a sample size of 122 students is needed to be 99% confident that the sample mean score is within 1.5 points of the population mean score for students who are high on the need for closure.
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fsu statistics students' moms if there were only twenty-two students instead of fifty-two who contributed their moms' heights, what alternative assumption would we have had to make about the population of mom-heights if we wanted to use a one-sample confidence interval procedure (regardless of whether it would be z or t)? we would have had to assume that the population of mom-heights was ...
If there were only twenty-two students instead of fifty-two who contributed their moms' heights and we wanted to use a one-sample confidence interval procedure (whether it would be z or t), we would have had to assume that the population of mom-heights was normally distributed.
The one-sample confidence interval is used to estimate the true population mean based on a sample mean and standard deviation. The procedure assumes that the sample is a random sample from a normally distributed population. With a sample size of at least 30, the central limit theorem allows for the use of a z-test to construct the confidence interval. With a smaller sample size, a t-test would be more appropriate. However, the assumption of normality still needs to hold for the validity of the confidence interval.
If the sample size is smaller than 30, the assumption of normality can be replaced by the assumption of approximately normal data. This means that the data follows a distribution that is symmetric and bell-shaped, even if it is not exactly normal.
However, the validity of the confidence interval can be compromised if the data is highly skewed or contains outliers. In such cases, it may be necessary to use non-parametric methods to construct a confidence interval.
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This is a multi-part question. Once an answer is submitted, you will be unable to return to this part A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one- third of the time and a O two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.6 and the probability that it is received incorrectly (as a 1) is 0.4. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2. Find the probability that a 0 is received.
The probability that a 0 is received can be found using conditional probability. Let's denote the event that a 0 is sent as S0, and the event that a 0 is received as R0. We want to find P(R0), the probability that a 0 is received.
Using the law of total probability, we can express P(R0) as the sum of the probabilities of receiving a 0 given that a 0 or a 1 was sent, weighted by the probabilities of sending a 0 or a 1:
[tex]P(R0) = P(R0|S0)P(S0) + P(R0|S1)P(S1)[/tex]
We are given that the probe sends a 1 one-third of the time and a 0 two-thirds of the time, so we have:
P(S0) = 2/3
P(S1) = 1/3
We are also given the probabilities of receiving a 0 or a 1 correctly or incorrectly, so we have:
P(R0|S0) = 0.6
P(R1|S0) = 0.4
P(R0|S1) = 0.2
P(R1|S1) = 0.8
Plugging these values into the formula for P(R0), we get:
P(R0) = (0.6)(2/3) + (0.8)(1/3)
= 1/2
Therefore, the probability that a 0 is received is 1/2, or 50%.
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22. {(6,2), (9,5), (12,8), (15, 11)}
inverse of each function, determine domaine and range of inverse and function
The domain of the original function is all real numbers, and the range is also all real numbers. The domain of the inverse function is also all real numbers, and the range is also all real numbers.
How to explain the domainThe domain of the original function is all real numbers, and the range is also all real numbers. The domain of the inverse function is also all real numbers, and the range is also all real numbers.
For the third number, the domain of the original function is all real numbers, and the range is also all real numbers. The domain of the inverse function is also all real numbers, and the range is also all real numbers.
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A great egret has a wingspan of 180
centimeters. A red-tailed hawk has a
wingspan of 1,100 millimeters. Which has
bird has the greater wingspan? Explain.
The bird with the greater wingspan is the great egret
How to determine the greater wingspanTo determine the greater wingspan, we need to know the following conversion values, we have;
1 decimeter = 10 centimeters
1 decimeter = 100millimeters
1 centimeter = 10 millimeters
From the information given, we have;
The red-tailed hawk = 1,100 millimeters
The great egret = 180 centimeters
convert the millimeters to centimeters
if 1 centimeters = 10 millimeters
then, 180 centimeters = x
cross multiply
x = 1800 millimeters
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Multiple choice quiz: In a multiple choice quiz there are 5 questions and 4 choices for each question (a, b, c, d). Robin has not studied for the quiz at all, and decides to randomly guess the answers. Find the probabilities of each of the following events: (a) the first question she gets right is the 3rd question? (please round to four decimal places) (b) she gets exactly 3 or exactly 4 questions right? (please round to four decimal places) (c) she gets the majority of the questions right? (please round to four decimal places
The probability of getting the majority of the questions right is P(X>=3) = P(X=3) + P(X=4) + P(X=5) = 15/128 + 6/1024 = 0.2266, rounded to four decimal places.
(a) The probability of guessing the correct answer for any single question is 1/4. Since there are no dependencies between questions, the probability of guessing the third question correctly is also 1/4. The probability of getting the first two questions wrong is (3/4)^2 = 9/16. Therefore, the probability that the first question Robin gets right is the third question is the product of these probabilities, which is (1/4)*(9/16) = 9/64. Rounded to four decimal places, this is 0.1406.
(b) To find the probability that Robin gets exactly 3 or exactly 4 questions right, we can use the binomial distribution. Let X be the number of questions Robin gets right. Then X follows a binomial distribution with n=5 and p=1/4, since each question has a probability of 1/4 of being answered correctly, and there are 5 questions in total.
The probability of getting exactly 3 questions right is P(X=3) = (5 choose 3) * (1/4)^3 * (3/4)^2 = 15/128. Similarly, the probability of getting exactly 4 questions right is P(X=4) = (5 choose 4) * (1/4)^4 * (3/4)^1 = 5/1024. The probability of getting both exactly 3 and exactly 4 questions right is 0, since they are mutually exclusive events.
Therefore, the probability of getting exactly 3 or exactly 4 questions right is P(X=3) + P(X=4) = 15/128 + 5/1024 = 0.1719, rounded to four decimal places.
(c) The majority of the questions means getting at least 3 questions right. We can calculate this probability using the binomial distribution again. The probability of getting 3 questions right is P(X=3) = 15/128, as calculated above. The probability of getting 4 or 5 questions right is P(X=4) + P(X=5) = (5 choose 4) * (1/4)^4 * (3/4)^1 + (5 choose 5) * (1/4)^5 * (3/4)^0 = 5/1024 + 1/1024 = 6/1024. Therefore, the probability of getting the majority of the questions right is P(X>=3) = P(X=3) + P(X=4) + P(X=5) = 15/128 + 6/1024 = 0.2266, rounded to four decimal places.
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Part B: If Susan originally has 7 yards of fabric, how much is left over after making the aprons? Show every step of your work. (5 points).
Based on fractional values, if Susan originally has 7 yards of fabric, after making 3 aprons consuming 5⁵/₈ yards, the quantity of fabric left is 1³/₈ yards.
What are fractional values?Fractional values are the results of fractional computations.
Fractions may be proper, improper, and complex fractions, depending on the values of the denominators and the numerators.
Algebraic expressions that have fractions are stated as fractional values.
The original quantity of fabric that Susan has = 7 yards
The quantity of fabric used for the front of each apron = 1¹/₄ yards
The quantity of fabric used for the tie of each apron = ⁵/₈ yards
The total quantity of fabric used for each apron = 1⁷/₈ yards (1¹/₄ + ⁵/₈)
The total quantity of fabric used for the 3 aprons made = 5⁵/₈ yards (1⁷/₈ x 3)
Therefore, the remaining quantity of fabric that Susan has after making the 3 aprons = 1³/₈ yards (7 - 5⁵/₈).
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Question Completion:Susan first made 3 aprons using 1¹/₄ yards for the front and ⁵/₈ yards for the tie.
Use the general slicing method to find the volume of the following solid.
The solid with a semicircular base of radius 16 whose cross sections perpendicular to the base and parallel to the diameter are squares. Set up the integral and find an answer.
The volume of the solid is 17124 cubic units. To find the volume of the solid, we need to integrate the area of each cross-section perpendicular to the base and parallel to the diameter.
Since these cross-sections are squares. We can find their area by squaring the side length.
Let's call the side length of each square "x". We know that the diameter of the semicircle is 32 (twice the radius of 16), so the side length of each square is also 32.
Now we need to express the volume of the solid as an integral. We can do this by summing the areas of all the infinitesimal squares as we slice the solid perpendicular to the base.
The infinitesimal thickness of each slice is dx. The width of each slice is also dx, since the squares are perpendicular to the base. The height of each slice is the length of the chord of the semicircle that corresponds to the x-coordinate of the slice.
We can use the Pythagorean theorem to find this height. The chord has length 2(sqrt(16^2 - x^2)), so the height is sqrt(16^2 - x^2).
Therefore, the volume of the solid is given by the integral:
V = ∫(0 to 16) of [x^2 * (2sqrt(16^2 - x^2))] dx
Evaluating this integral, we get:
V = (2/3)(16^3)(pi) - (2/3)(16^3)
So the volume of the solid is approximately 17124 cubic units.
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What is 131 divided by 1.5?
Answer:
87.3
Step-by-step explanation:
131 ÷ 1.5 = 87.3
The answer will be 87.3 repeat.
131 divided by 1.5 is equal to 8 with a remainder of 11, or 8.7333 (rounded to four decimal places).
We have,
To divide 131 by 1.5, we can perform the division operation as follows:
131 ÷ 1.5
To make the calculation easier, we can convert 1.5 to an equivalent fraction with a denominator of 10.
We can multiply both the numerator and denominator by 10 to get 15.
So, the division becomes:
131 ÷ 15
When we divide 131 by 15, we get a quotient of 8 with a remainder of 11.
Therefore,
131 divided by 1.5 is equal to 8 with a remainder of 11, or 8.7333 (rounded to four decimal places).
131 ÷ 1.5 is approximately equal to 8.7333.
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Find the shaded area of 12ft 5ft 9ft 18ft 5ft
The area of the shaded region is 180 square feet.
What is the shaded area?The figiure in the image is a triangle inscribed in a rectangle.
To get area of the shaded region, we subtract the area of the triangle from the area of the rectangle.
For the triangle:
Base = 18 - (5+5) = 8ftHeight = 9ftFor the rectangle:
Length = 18 ftWidth = 12 ftHence:
Area of the shaded region = Area of rectangle - Area of triangle
Area of the shaded region = ( length × width ) - ( 1/2 × base × height )
Area of the shaded region = ( 18ft × 12ft ) - ( 1/2 × 8ft × 9ft )
Area of the shaded region = 216ft ²- 36ft²
Area of the shaded region = 180ft²
Therefore, the area is 180ft².
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Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 minutes, while it would take Simon 30 minutes to do the job working alone. If Sophie and Simon work together to peel the potatoes, how long will i
The time taken by them to complete the work is 18 minutes.
Time taken by Sophie to peel all the potatoes = 45 minutes
Time taken by Simon to peel all the potatoes = 30 minutes
Amount of work done by Sophie in one minute = 1/45
Amount of work done by Simon in one minute = 1/30
Let the time taken by both of them to complete the work together be x.
So, the time taken by them to complete the work,
1/x = (1/45) + (1/30)
x = 1350/75
x = 18 minutes
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A farmer purchased 275 acres of land for $4,300/acre. He paid 25% down and obtained a loan for the balance at 6. 75% APR over a 20-year period. How much is the annual payment? (Simplify your answer completely. Round your answer to the nearest cent. )
The annual payment is $7,351.98 if the APR rate is 6.75% over a 20-year period.
Area of land = 275 acres
Price = $4,300/acre
Time = 20-year
APR rate = 6.75%
down payment = 25% of the total cost
Total cost = 275 acres x $4,300/acre
Total cost = $1,182,500
Down payment = 0.25 x $1,182,500
Down payment = $295,625
The remaining amount = Total cost - Down payment
The remaining amount = $1,182,500 - $295,625
The remaining amount = $886,875
The present value of an annuity,
PMT = [tex](r * PV) / (1 - (1 + r)^{n} )[/tex]
The interest rate = 6.75% / 12 = 0.5625% per month
The total number of periods = 20 years x 12 months/year = 240 months.
PMT = [tex](0.005625 * $886875) / (1 - (1 +0.005625)^{240} )[/tex]
PMT = $7,351.98
Therefore, we can conclude that the annual payment is approximately $7,351.98
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Suppose that we want to estimate what proportions of all drivers exceed the legal speed limit on a certain stretch of road between Los Angeles and Bakersfield. Use the formula of the earlier exercise to determine how large a sample we will need to be at least 99 % confident that the resulting estimate, the sample proportion, is off by less than 0.04.
We need a sample size of at least 665 drivers to estimate the proportion of all drivers exceeding the legal speed limit on the certain stretch of road between Los Angeles and Bakersfield with a margin of error of 0.04 and a 99% confidence level.
To estimate the proportion of all drivers exceeding the legal speed limit on a certain stretch of road between Los Angeles and Bakersfield with a margin of error of 0.04 and a 99% confidence level, we need to use the following formula:
[tex]n = (Z^2 * p * (1 - p)) / E^2[/tex]
where n is the sample size, Z is the Z-score for the desired confidence level (2.576 for 99% confidence level), p is the estimated proportion of drivers exceeding the speed limit (we don't have an estimate, so we'll use 0.5 for maximum variability), and E is the margin of error we want (0.04).
Plugging in the values, we get:
[tex]n = (2.576^2 * 0.5 * (1 - 0.5)) / 0.04^2[/tex]
n = 664.92
Therefore, we need a sample size of at least 665 drivers to estimate the proportion of all drivers exceeding the legal speed limit on the certain stretch of road between Los Angeles and Bakersfield with a margin of error of 0.04 and a 99% confidence level.
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Find the 8th term of the geometric sequence 4,-12,36
The 8th term of the geometric sequence [tex]4,-12, 36[/tex] is [tex]-8748[/tex].
How to find the 8th term of the geometric sequence?We must find common ratio by dividing the term by its preceding term. By dividing second term (-12) by the first term (4), this gives us:
= -12 / 4
= -3
So, the common ratio is -3.
The formula for the nth term of geometric sequence to find the 8th term is : an = a1 * r^(n-1) where an = nth term, a1 = first term, r = common ratio and n = term number
a8 = 4 * (-3)^(8-1)
a8 = 4 * (-3)^7
a8 = 4 * (-2187)
a8 = -8748.
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Find the gradient of a line perpendicular to the longest side of the triangle formed by A(-3,4),B(5,2) and C(0,-3)
The gradient of the line is 2
How to solve for the gradient[tex]Distance AB = \sqrt{[(5-(-3))^2 + (2-4)^2]}= \sqrt{68} \\Distance AC = \sqrt{[(-3-0)^2 + (4-(-3))^2]} = \sqrt{58} \\Distance BC = \sqrt{[(5-0)^2 + (2-(-3))^2]}= \sqrt{50}[/tex]
mAB = (2 - 4) / (5 - (-3)) = -1/2
This is the slope of AB
-1 / (-1/2) = 2
we have to find the point that is perpendicular to AB
(-3 + 5) / 2 = 1
(4 + 2) / 2 = 3
1 , 3 are perpendicular to AB
y - 3 = 2(x - 1)
y - 3 = 2x - 2
y = 2x + 1
There fore the gradient of the line is 2
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