determine the area (in units2) of the region between the two curves by integrating over the y-axis. x
Answers
The area of the region between the two curves by integrating over the y-axis, x = y² and x = 9 is 18 square units.
Total Area inclosed between line and Curve:The area where the "area under the curve" is common to both the straight line and the given curve is called the bounding area. Therefore, the area common to both can be found by subtracting the area under line T from the area under curve C. The x constraint for computing the area under the curve can be found by solving the system of equations for the coordinates of the intersection of the line and the curve.
We have given the curve , x = y² and line x = 9 and bounded region is A in above graph of x = y² and line x = 9.
Now, we determine the intersection points of curve and line,
put x = 9 in curve equation we get,
y² = 9 => y = +-√9
= + 3 or -3
Total area bounded by curve and line, A = integration of curve over y from y = -3 to y= 3
= ₋₃∫³x dy = ₋₃∫³y² dy = ₋₃[ y³/3]³
= [ (3)³/3 - (-3)³/3]
= 9 + 9 = 18
Hence, the required area is 18 square unit.
Complete question:
determine the area (in units2) of the region between the two curves by integrating over the y-axis. x = y² , x = 9
Related Questions
Solve: 2x - 3= 2x - 5
A infinitely many solutions
B no solution
C 5/3
D 0
E -2
Answers
Therefore it’s false
Option B [no solution]
I do not understand what is going on for this question
Answers
(x,y,z)=(19,14,3)
What is equation matrix and vector?This means that by dividing the inverse of the A matrix by the B matrix, we may calculate the values of x, y, and z (the X matrix).An arrangement of numbers, occasionally expressions and symbols, in rows and columns is called a matrix. Quantum mechanics, optics, mathematics, and other mathematical functions are all solved using matrix formulas.It's not nearly as difficult as it sounds; all you have to do is multiply the rows by the columns and add up the components.In geology, seismic surveys are carried out using matrix technology. They are employed in the production of graphs, statistics, calculations, and scientific investigations and research in a range of fields.A matrix is a collection of numbers, while a vector is a list of numbers that can be in either a row or a column (one or more rows, one or more columns).To learn more about equation matrix refer to:
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Given f(x) = -x - 5 find f (0)
Answers
Answer: f(0)=-5
Step-by-step explanation:
f(0) means that x = 0
sub in 0 into the equation
f(0)=-0-5
f(0)=-5
Answer:
f(0) = -5
Step-by-step explanation:
Given f(x) = -x - 5
In order to find f(0), you need to replace x with 0
so f(0) = -(0) - 5
f(0) = -5
John started a home delivery service from several local restaurants. He charges a $5 tip on the delivery, plus $0.75 for every mile he travels.
Write an equation for the function that relates the total cost of a trip to the distance.
Answers
Answer:
y = total cost
x = mile
y = 5 + 0.75xStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Answer: y = 5 + 0.75x
Step-by-step explanation:
At 2 p.m., two cars leave Eagle River, WI, one headed north and one headed south. If the car headed north averages 45 mph and the car headed south averages 40 mph, when will the cars be 170 miles apart?
Answers
The time at which the two cars will be 170 miles apart is; 1.619 hours
How to solve Algebra Word Problems?Let us write an equation for each car as;
d₁ = r₁*t₁ (northbound)
d₂ = r₂*t₂ (southbound)
They both start at the same time, and will stop them both when they are 170 miles apart. Thus;
t = d₁/r₁
t = d₂/r₂
Thus, the equation to find their times is;
d₁/r₁ = d₂/r₂
d₁ = d₂r₁ /r₂
Thus;
d₁ + d₂ = 170
d₁ = 170 - d₂
Similarly, r₁ = 45 mph and r₂ = 40 mph
170 - d₂ = d₂(45/60)
4(170 - d₂) =3d₂
7d₂ = 680
d₂ = 680/7
d₂ = 97.143 miles
d₁ = 170 - 97.143
d₁ = 72.857 miles
t₁ = d₁/r₁ = 72.857/45 = 1.619 hours
This represents the time that they will be 170 miles apart
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Original: 2.4
New: 0.8
Answers
Answer:
Divide by 3
Step-by-step explanation:
If you know your multiplication tables, you will know that 8·3 = 24. In reverse, that is 24 / 8 = 3. If you move the decimal point—the dot used for decimals always behind the last digit of a whole number—to the left or right, the answer will stay the same. This is why:
8 · 3 = 24, 80 · 3 = 240, 800 · 3 = 2,400, and so on.
Applying this but the decimal moving to the left results in:
0.8 · 3 = 2.4
I hope you understand!
(If you haven't already, learn your multiplication tables. Just some advice)
What’s 9.1k in numbers?
Answers
Answer:
9,100
Step-by-step explanation:
"9.1k" is a shortened notation for 9,100, where "k" stands for "kilo," which means thousand.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
The "k" stands for "kilo," which means thousand. Therefore, when you see a number followed by "k," you can assume that the actual number is 1,000 times greater than what is shown.
In this case, "9.1k" means 9.1 times 1,000, which equals 9,100.
This notation is often used in contexts where brevity is important, such as in social media posts or online comments, where character limits may apply.
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Calculate the standard deviation of the following set of numbers. Use the formula for the standard deviation (s) shown, where x represents the values, n is the number of values, and is the summation symbol, which indicates that you should add the values. S = mon-1) (* {x? - (Ex)}) values: Xı = 13,X2 = 16, x3 = 10 Do not round your answers. Step 1. Calculate the square of each data value. Step 2. Determine n times the sum of squares of the three values. 1 Step 3. Calculate the sum of the three values. Step 4. Calculate the square of the sum of the three values. ηΣ x2 = Step 3. Calculate the sum of the three values. Σx= Step 4. Calculate the square of the sum of the three values. Step 5. Calculate the variance. (n-1) (»« - (Ex)")= Step 6. Calculate the standard deviation. 1 nin – 1) (»Ex2 - (2 x)") =
Answers
The standard deviation is 3.
What is standard deviation?Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.
Given, formula for the standard deviation
s = √[1/n(n-1)](n∑x²-(∑x)²)
values: x₁ = 13, x₂ = 16, x₃ = 10
step1: Calculate the square of each data value.
x₁² = 13² = 169
x₂² = 16² = 256
x₃²= 10² = 100
step2: Determine n times the sum of squares of the three values.
n∑x² = n(x₁²+x₂²+x₃²)
=3(169+256+100) = 1575
step3: Calculate the sum of the three values.
∑x = x₁+x₂+x₃
= 13+16+10 =39
step4: Calculate the square of the sum of the three values.
(∑x)² = 1521
step5: Calculate the variance.
[1/n(n-1)](n∑x²-(∑x)²)
=[1/3(3-1)](1575-1521)
=54/6
=9
step6: Calculate the standard deviation.
√[1/n(n-1)](n∑x²-(∑x)²)
= √9
=3
Hence, The standard deviation using the given formula for x₁=13, x₂=16 and x₃=10 is 3.
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How can you find 50% of a number quickly in your head?
Answers
Answer:
Divide by 2
Step-by-step explanation:
Write 0.006655 in scientific notation
Answers
Answer: 6.655 * 10^-3
Step-by-step explanation:
0.006655 in scientific notation
6.655 × 10³
Please Help!!
Jamie and Hudson took a road trip to the beach. Their total distance traveled after getting on the highway can be found using the function d(h)=55h+10, where h is the number of hours they have been driving on the highway.
1) Explain why the relationship between total distance and hours is a function.
2) Is this function continuous or discrete? Explain how you know.
3) If the girls can drive a maximum of 8 hours, what is the domain for the function? Explain your answer.
4) If the girls can drive a maximum of 8 hours, what is the range for the function? Explain your answer.
5) Create a graph that models this function. Be sure to include a title and to label your x- and y-axis with the variable names, not just x and y.
6) What is the slope of the function? What does it represent?
7) What is the y-intercept? What does it represent?
Answers
The total distance is an illustration of a linear function.
(1) Why the relationship is a function
The relationship is a function because all input values of h, have exactly one corresponding output value of d
(2) The function type
The function is a discrete function, because the number of hours is an integer, and it cannot take decimal values (in this case)
(3) The domain for a drive of 8 hours
The domain is the set of time the girls drive.
So, the domain is: [0,8]
(4) The range
The function is given as:
d= 55h + 10
When h = 0,
d = 55(0) + 10 = 10
When h = 8,
d = 55(8) + 10 = 450
So, the range is: [10,450]
(5) The graph
Sorry
(6) The slope
A linear function is represented as:
y = mx + c
Where:
m represents the slope.
So, by comparison:
Slope = 55
The slope in this case represents the distance travelled per hour
(7) The y-intercept
In (6) above, c represents the y-intercept.
So, by comparison:
c = 10
The y-intercept in this case represents the initial distance
The trip to Australia is in six months how much does she need to save each month to make her go of $2,370.00?
Answers
Answer:
2 370 / 6 = 395
She need to save $395 per monthStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Suppose that a random sample of 41 state college students is asked to measure the length of their right foot in centimeters. A 95% confidence interval constructed using the data is (21.709, 25.091). Which is a correct interpretation for the confidence interval?
a. 95% of the time the sample mean foot length is between (21.709, 25.091).
b. 95% of the foot lengths are between (21.709, 25.091).
c. 95% of the time the population mean foot length is between (21.709, 25.091)
d. All of the above.
e. None of the above.
Answers
The correct interpretation for the confidence interval for the given random sample of 41 state college students is option e (i.e. none of the above).
What is Confidence Interval ?
Confidence interval gives a range of estimated value of population parameter. The value that does not lie within the confidence interval tend to not represent the population parameter whereas , if the value lie inside the confidence interval it represent the population parameter with a certain confidence level.
What are random samples ?
A simple random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected, minimising the risk of selection bias.
According to the question , A 95% confidence interval constructed using the data is (21.709, 25.091)
95 % confidence interval is (21.709, 25.091).
Sample size is 41 state college students
Hence , The correct option is E as the confidence interval tend to reflect the population parameter. And also it show that there is certain confidence level that population parameter will lie within the confidence interval. Suppose we take out 100 sample at random that 95% of this will have population foot length mean between 21.709 and 25.091.
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Suppose you took a large number of random samples of size n from a large population and calculated the mean of each sample. Then suppose you plotted the distribution of your sample means in a histogram. Now consider the following possible attributes of your collected data and the population from which they were sampled. For which of the following sets of attributes would you not expect your histogram of your sample means to follow a nearly normal distribution?
A) n = 10. The population distribution is unknown, but the distribution of data in each sample is heavily skewed.
B) n = 120. The population distribution is slightly skewed.
C) n = 20. The population distribution is nearly normal.
D) n = 120. The population distribution is unknown, but the distribution of data in each sample is slightly skewed.
Answers
No, because with a sample size of 10, the heavily skewed population distribution will not allow for a nearly normal distribution of sample means.
With a sample size of 10, the heavily skewed population distribution will not allow for a nearly normal distribution of sample means. This is because the sample size is too small and the skewed population distribution will not have enough data to accurately represent the overall population. With a sample size of 10, the sample means will be heavily influenced by outliers and extreme values, which will lead to a histogram that is skewed and not nearly normal. Therefore, no matter how slightly skewed the population distribution is, a sample size of 10 is not large enough to create a normal distribution of sample means.
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A random sample of 55 standard hotel rooms in the Philadelphia area has a mean nightly cost of $154.17. From previous studies, it has been found that the standard deviation of the price of all hotel rooms in Philadelphia is $38.60. Construct a 99% confidence interval for the population mean cost . Round to the nearest penny. Show work below . (5 points )
Answers
The 99% confidence interval for the population mean cost is 38.37 to 269.97.
What is confidence interval?
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
Given that the standard hotel rooms in the Philadelphia area has a mean nightly cost of $154.17.
The standard deviation of the price of all hotel rooms in Philadelphia is $38.60.
According to the empirical rule,
P(μ - 3σ ≤ X ≤ μ - 3σ) = 99%.
Here μ = 154.17 and σ = 38.60.
Calculating the confidence interval:
154.17 - (3 × 38.60) ≤ X ≤ 154.17 + (3 × 38.60)
38.37 ≤ X ≤ 269.97
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A fisherman is measuring the amount of bait he has remaining, y, in his bucket he puts 20 peices of bait in his bucket at the beginning of his fishing trip and uses 2 pieces every hour, x.
What is the slope for this linear relationship and what does it mean in this situation?
A. -2; the amount of bait decreases by 2 pieces each hour
B. 2; the amount of bait increases by 2 pieces each hour
C. -20; the amount of bait in the bucket when the fishing trip began
D. 20; the amount of bait in the bucket when the fishing trip began
Answers
Answer:
A
Step-by-step explanation:
bait left = 20 - 2x where x = hours slope = -2 answer A
What is the common ratio of the geometric sequence?
Number graph ranging from zero to ten on the x axis and zero to twenty-eight on the y axis. Points are plotted on the graph at (one, eight), (two, twelve), (three, eighteen) and (four, twenty-six point five). The points form a general positive trend.
Answers
A geometric series is one in which there is a constant between two successive numbers in the series.
What is geometric progression?When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.
The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression
Suppose the series is given as
2,4,8,16,32,64.........
The common difference is defined as the ratio of the next term to the previous term.
From the above series, the common ratio is calculated as,
Common ratio = 4 / 2
Common ratio = 2
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Find the measure of triangle ABD from given figure
Answers
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answers
For the following right triangle, find the side length x , round to the nearest hundredth.
Answers
Answer: 14.9
Step-by-step explanation:
Pythagoras Theorem States that for any right angled triangle.
a ^ 2 + b^2 = c ^2.
a = 10
b = 11
x = unknown
x^2 = a ^ 2 + b^2
x^2 = (10 * 10) + (11 * 11)
x = sqrt(100 + 121)
x = sqrt(221)
x = 14.9
What is the product of (-4)(16) (-7)
A-108
B -71
C 57
D 448
Answers
Answer:
D 448
multiply -4×16×-7
= 448
Mary, Keith, and David sent a total of 149 text messages over their cell phones during the weekend. Keith sent 4 times as many messages as David. David sent 5 fewer messages than Mary. How many messages did they each send?
Answers
The messages sent by each person will be:
David sent 24 message
Keith sent 96 messages
Mary sent 29 messages.
How many messages did they each send?Let David be represented as x.
Keith sent 4 times as many messages as David. This will be 4x.
David sent 5 fewer messages than Mary. Mary has x + 5.
The equation will be:
David + Keith + Mary = 149
x + 4x + x + 5 = 149
6x + 5 = 149
Collect like terms
6x = 149 - 5
6x = 144
Divide
x = 144 / 6
x = 24
David sent 24 message
Keith = 4x
= 4 × 24
= 96 messages
Mary = x + 5
= 24 + 5
= 29 messages.
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In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by A. Delta y = f(x_1 + x_1, x_2, ....., x_k) - f(x_1, x_2, ... x_k). B. Delta Y = f(x_1 + Delta x_1, x_2, ...., x_k) - f(x_1, x_2, .... x_k). C. Delta Y = f(x_1 + Delta x_1, x_2 + Delta x_2, ...., x_k + Delta x_k) - f(x_1, x_2, ...., x_k). D. Delta Y = f(x_1 + x_1, x_1, .... x_k).
Answers
The expected change in the dependent variable for a change in one of the explanatory variables in a nonlinear model is given by Delta Y = f(x_1 + Delta x_1, x_2, ...., x_k) - f(x_1, x_2, .... x_k).
Any attribute that can have different values, such as height, age, temperature, or test results, is referred to as a variable in research.
To assess the causality of relationships, researchers frequently modify or measure independent and dependent variables in studies.
The cause is the independent variable. Its value is unaffected by the other study variables.
The effect is the dependent variable. Changes in the independent variable affect its value.
A dependent variable is one that is altered as a result of the modification of an independent variable. Your independent variable "depends" on the outcome you're interested in measuring.
Dependent variables are also referred to as:
.response elements (they respond to a change in another variable)
.outcome factors (they represent the outcome you want to measure)
.Left-side parameters
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The expected change in the dependent variable for a change in one of the explanatory variables in a nonlinear model is given by Delta Y = f(x_1 + Delta x_1, x_2, ...., x_k) - f(x_1, x_2, .... x_k).
Any attribute that can have different values, such as height, age, temperature, or test results, is referred to as a variable in research.
To assess the causality of relationships, researchers frequently modify or measure independent and dependent variables in studies.
The cause is the independent variable. Its value is unaffected by the other study variables.
Effect is the dependent variable. Changes in the independent variable affect its value.
A dependent variable is one that is altered as a result of the modification of an independent variable. Your independent variable "depends" on the outcome you're interested in measuring.
Dependent variables are also referred to as:
.response elements (they respond to a change in another variable)
.outcome factors (they represent the outcome you want to measure)
.Left-side parameters
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A rental car agency charges $15 per day plus 11 cents per mile to rent a certain car. Another agency charges $18 per day plus 8 cents per mile to rent the same car. How many miles will have to be driven for the cost of the car from the first agency to equal the cost of a car from the second agency?
Answers
If a rental car agency charges $15 per day plus 11 cents per mile to rent a certain car. The number of miles you have to be driven for the cost of the car from the first agency to equal the cost of a car from the second agency is 100 miles.
How to find the number of miles:First step is to set the equation that will be used to find the number of miles
Equation
15+.11x=18+.08x
So,
Number of miles
15+.11x=18+.08x
Collect like terms
.03x=3
Divide both side by 0.03
x=3/.03
x =100 miles
Therefore we can conclude that the number of miles is 100 miles.
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-\sqrt(16x^(2)) if x<0
Answers
Therefore , [tex]-4|x|[/tex] is the square root of [tex]-\sqrt{16x^{2} }[/tex]
what is square root?When a number is multiplied by itself, the result is known as the square root of the number. To represent the square root, use the radical symbol. For illustration, [tex]\sqrt[/tex]16 = 4. Another name for the radical sign is the root symbol or surds.
given
- [tex]\sqrt{16x^{2}[/tex] when [tex]x[/tex] < 0,
In order to solve the given expression we will take the square root of the term inside the root.
Perfect squares (squares of integers) make up the word in the square root, thus we can express it as a square of the numbers.
⇒ [tex]-\sqrt{(4x)^{2} }[/tex] [ as [tex](4x)^{2}[/tex] = [tex]16x^{2}[/tex]]
On taking square root the square gets removed. So, we have,
[tex]-|4x|[/tex] =[tex]-4|x|[/tex]
Since , so the value would be negative.
Therefore , [tex]-4|x|[/tex] is the square root of [tex]-\sqrt{16x^{2} }[/tex]
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NO LINKS!!
You are offered two jobs selling textbooks. One company offers an annual salary of $42000 plus a year-end bonus of 1% of your total sales. The other company offers an annual salary of $30000 plus a year-end bonus of 2.5% of your total sales. How much would you have to sell in a year (in dollars) to make the second offer the better offer?
Total sales would need to be greater than $
Answers
Answer:
At $800,000 of sales the offers are equal. Anything over 800,000 makes the second deal a better deal.
Step-by-step explanation:
Let y equal the total money earned.
Let x equal the total sales.
y = .01x + 42000
y = .025x + 30000 Set these two equations equal to each other.
.01x + 42000 = .025x + 30000 Subtract .01x from both sides
.01x -.01x + 42000 = .025x - .01x + 30000
42000 = .015x + 30000 Subtract 30000 from both sides
12000 = .015x Divide both sides by .015
[tex]\frac{12000}{.015}[/tex] = [tex]\frac{.015x}{.015}[/tex]
800,000 = x
Answer:
job 1 , y = 42 000 + 0.01x
job 2 , y = 30 000 + 0.025x
42 000 + 0.01x < 30 000 + 0.025x
42 000 - 30 000 < 0.025x - 0.01x
12 000 < 0.015x
x < 800 000
You need to make total sales of more than $800 000 to make the second offer better.example of u get 900 000 total sales
42 000 + 0.01(900 000) < 30 000 + 0.025(900 000)
42 000 + 9000 < 30 000 + 22 250
51 000 < 52 500
Therefore, you need to make a total sales of more than $800 000.Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Please show me how to solve this problem?
Answers
Answer:
I think you forgot to show us the problem
The two graphs shown below detail the results of two independent response polls studying favorite movie genres.
Which genre had the same number of votes in each study?
a. action
b. horror
c. mystery
d. not enough information
Please select the best answer from the choices provided
• A
• B
• C
• D
Answers
The genre which had the same number of votes in each study is: B. horror.
What are the types of graph?In Mathematics, there are different types of graph and these include the following:
Box and whisker plotScatter plotBar graphDot graphLine graphHistogramPie chartWhat is a pie chart?A pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors.
From the bar chart, the number of votes for horror movie is equal to 40 votes. Next, we would calculate the number of votes for horror movie in the pie chart as follows;
Number of votes = 16/100 × 250
Number of votes = 0.16 × 250
Number of votes = 40 votes.
In conclusion, we can logically deduce that horror is a movie genre that has the same number of votes in each independent study.
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If a random variable that is normally distributed has a mean of 25 and a standard deviation of
3, convert the given value to a z-score.
a. x = 23
b. x = 33
c. x = 19
d. x = 45
Answers
Answer:
Step-by-step explanation:
To convert a value to a z-score, you need to subtract the mean and divide by the standard deviation. Here is how to convert each value to a z-score:
a. x = 23: (23 - 25) / 3 = -0.67
b. x = 33: (33 - 25) / 3 = 2.33
c. x = 19: (19 - 25) / 3 = -1.67
d. x = 45: (45 - 25) / 3 = 6.67
Therefore, the z-scores are -0.67, 2.33, -1.67, and 6.67 for values a, b, c, and d respectively.
A new cure has been developed for a certain type of cement that should change the mean compressive strength.It is known that a standard deviation is 130 kg/cm2and we may assume normal distribution. 9 pieces of cementhave been tested and the observed sample mean is ¯X= 4970. Find the 95% confidence interval for the mean.
(a) [4858.37,5081.63] (b) [4885.07,5054.93] (c) [4858.37,5054.93]
(d) [4944.52,4995.48] (e) [4858.37,5054.93]
Answers
(a) The 95% confidence interval for the mean of the compressive strength is 4885.1 < μ < 5054.9.
(b) The 95% confidence interval for the mean of compressive strength is 4975.2 < μ < 5012.4.
a) We have to find the 95% confidence interval for the mean of the compressive strength.
we are given
x = sample mean = 4970
n = sample size = 9
σ = population standard deviation = 130
The 95% confidence interval for population mean is
x - Za/2*(σ/√n) < μ < x + Za/2*(σ/√n)
For a = 0.05 Za/2 = Z0.025 = 1.96
4970 - 1.96*(130/√9) < μ < 4970 + 1.96*(130/√9)
4885.1 < μ < 5054.9
Hence, the 95% confidence interval for the mean of the compressive strength is 4885.1 < μ < 5054.9.
b) We have to find the 95% confidence interval for the mean of the compressive strength.
Since the population's standard deviation is unknown in this instance, the population mean's t confidence interval is used.
From the data n = 9
X = sample mean = 4993.8
s = sample standard deviation = 24.2
For a= 0.05 and degree of freedom = n -1 = 8
ta/2 , n-1 = t0.025,8 = 2.306
x - ta/2*(s/√n) < μ < x + ta/2*(s/√n)
4993.8 - 2.306*(24.2/√9) < μ < 4993.8 + 2.306*(24.2/√9)
4975.2 < μ < 5012.4
Hence, the 95% confidence interval for the mean of compressive strength is 4975.2 < μ < 5012.4.
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The complete question is:
A new cure has been developed for a certain type of cement that should change its mean compressive strength.
a) It is known that the standard deviation of the compressive strength is 130 kg/cm^2 and that we may assume that it follows a normal distribution. 9 chunks of cement have been tested and the observed sample mean is X = 4970. Find the 95% confidence interval for the mean of the compressive strength.
b) Now, assume that we do not know the standard deviation of the normal distribution. 9 chunks of cement have been tested, and the measurements are 5001, 4945, 5008, 5018, 4991, 4990, 4968, 5020, 5003. Find the 95% confidence interval for the mean of the compressive strength.