The taylor series of sin x at x= π is ∑( for n=0,∞) [tex]\frac{-1^{n+1}(x-\pi )^{2n+1} }{(2n+1)! }[/tex]
the Taylor series n of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.
since the function we are given is :
sin(x), since we need to find the Taylor series of sin(x) at x=π, which can also be written as : sin(x+π)
we can find find the Taylor series of sin(x+π) at x=0
sin(x+π)=−sin(x)
= ∑( for n=0,∞) [tex]\frac{(-1)^{n}x^(2n+1) }{(2n+1)!}[/tex]
= ∑( for n=0,∞) [tex]\frac{-1^{n+1}x^{2n+1} }{(2n+1)!}[/tex]
so sin (x)= ∑( for n=0,∞) [tex]\frac{-1^{n+1}(x-\pi )^{2n+1} }{(2n+1)! }[/tex]
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find the Taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0.] f(x) = sin(x), a = π????
we want to estimate the population proportion of people in new jersey who are in favor of legalizing marijuana. a 95% confidence interval within 5% of the true value is wanted. what size sample is needed?
In order to estimate the population proportion within 5%, a sample size of at least 384 is needed.
The number of individuals or observations included in a study is referred to as the sample size. Two statistical properties are influenced by the sample size: 1) The accuracy of our estimates, and 2) The ability to draw conclusions from the study.
This can be calculated using the formula:
n = (z^2 * p * (1-p)) / (e^2)
where z is the z-score corresponding to a 95% confidence level, p is the estimated proportion of people in favor of legalizing marijuana, and e is the margin of error (5%).
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What is the value of x in the equation 3x-4y=65, when y=4?
Answer: The answer is 27
Answer:
27
Step-by-step explanation:
I hope its helpful to you.
Based on recent demand for single family homes in a growing city, it is recommended potential home buyers put 20 percent down when making an offer. A mortgage loan officer would like to test the claim that the average percent down on a single family home purchase is greater than the recommended 20 percent. To test this claim, at the 5% significance level, the mortgage loan officer collects the following data on a sample of 22 recent home purchases and records the percent down. The following is the data from this study: Sample size =22 recent home purchases Sample mean =24 percent down Sample standard deviation =9 percent down Identify the null and alternative hypothesis for this study by filling in the blanks with the correct symbol (=,≠,<, or > to represent the correct hypothesis.)
This enabled the borrower to obtain 90 percent financing while avoiding the additional cost of pmi. these loans are more commonly referred to as piggyback mortgage loans.
A loan is the lending of cash via one or more individuals, organizations, or different entities to other individuals, corporations, etc. The recipient incurs a debt and is normally susceptible to pay hobby on that debt till it is repaid as well as to repay the foremost amount borrowed.
A mortgage is a shape of debt incurred by using an character or different entity. The lender—commonly a business enterprise, economic organization, or authorities—advances a amount of money to the borrower. In return, the borrower agrees to a sure set of phrases together with any finance charges, hobby, repayment date, and different situations.
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Which graph best represents the function f(x) = (x + 1)(x − 1)(x − 4)? (4 points) Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 2, and 3. The graph intersects the y axis at a point between 10 and 15. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 2, and 3. The graph intersects the y axis at a point between 15 and 20. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 1, and 3. The graph intersects the y axis at a point between 5 and 10. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 1, 1, and 4. The graph intersects the y axis at a point between 0 and 5.
A graph which best represents the polynomial function f(x) = (x + 1)(x − 1)(x − 4) is: D. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 1, 1, and 4. The graph intersects the y axis at a point between 0 and 5.
What is a polynomial function?In Mathematics, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.
This ultimately implies that, a polynomial graph touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
In this context, we can reasonably and logically deduce that the zeros of a polynomial function are all of the values (x-intercepts) on the x-coordinate that makes this polynomial function equal to zero and these include the following on a graph:
Zeros = (-1, 0)
Zeros = (1, 0)
Zeros = (4, 0)
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data set 1 has a mean of 84 and a mad of 6. data set 2 has a mean of 78 and a mad of 8. what can be concluded about the two distributions? select each correct answer. responses the means-to-mad ratio is 1. the means-to-mad ratio is 1. the distributions are somewhat similar. the distributions are somewhat similar. the means-to-mad ratio is 0.75. the means-to-mad ratio is 0.75. the distributions are similar.
The correct answer for the question that is being presented above is this one: "D.The distributions are somewhat similar; C.The distributions are similar." Data Set 1 has a mean of 84 and a MAD of 6. Data Set 2 has a mean of 78 and a MAD of 8. You conclude about the two distributions: .The distributions are somewhat similar; The distributions are similar.
An anchor 15 3/5 m below the surface of the ocean is lowered 4 1/5 m Then it is pulled up 12 3/5 m what is the anchors new position
The new position of the anchor is 7 1/5 below the surface of the ocean
How to find the new position of the anchorInitially the anchor is located 15 3/5 m below the surface of the ocean, this is same as = -15 3/5 m
The anchor is further lowered and the position now is
= -15 3/5 m - 4 1/5 m
= -99 /5 m
Then the anchor is pulled up 12 3/5 m the new position now is
= -99 /5 m + 12 3/5 m
= -36/5
= -7 1/5
= -7.2
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Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y. (If an answer doesn't exist enter DNE.) f(x, y) = xe−x(1 + y) x ≥ 0 and y ≥ 0 0 otherwise Determine E(XY).
The value of E(XY) is equivalent or equal to -1 according to the joint pdf having function f(x, y) = xe^−x(1 + y) x ≥ 0 and y ≥ 0 0.
Given that:
f(x,y) = xe^-x(1+y), where x ≥ 0 and y ≥ 0 0.
E(XY) = ∫∞ ∫∞ xy. xe^−x(1 + y) dx dy
0 0
E(XY) = ∫∞ ∫∞ x^2y . e^−x(1 + y) dx dy
0 0
E(XY) = ∫∞ x^2 . e^−x (∫∞ y e^-xy dy) dx
0 0
E(XY) = ∫∞ x^2 . e^−x (-1/x) dx
0
E(XY) = - ∫∞ x . e^−x dx
0
E(XY) = - 1
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y are equal to i.e. E(XY) = -1.
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HELP HELP HELP FFHFJFHDHDHDHD
Answer:
y ≈ 15.9 cm
Step-by-step explanation:
using the tangent ratio in the right triangle
tan53° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{12}[/tex] ( multiply both sides by 12 )
12 × tan53° = x , that is
x ≈ 15.9 (to 1 decimal place )
choose the statement that is false.group of answer choicesa 95% confidence interval is wider than a 90% confidence intervalwhen sampling for means and thinking about the central limit theorem, the n should always be >30.when estimating the standard deviation in calculating confidence intervals, make sure you use the t tables.reducing the variation of a process will increase the width of a given confidence interval relative to that process.
Reducing the variation of a process will increase the width of a given confidence interval relative to that process.
Option C is correct .
What is a confidence interval?
In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as a confidence interval. By employing the dimensions of values used in the computation of the intervals, it is simple to establish the link between components of two confidence intervals. The width is a fundamental component in these range estimates, which are affected by sample size, etc.
Hence, reducing the variation of a process will increase the width of a given confidence interval relative to that process is false.
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To weigh your cat, you hold it while you step on the scale. By yourself, you weigh 130. 6 130. 6 pounds. Holding your cat, you weigh 142. 5 142. 5 pounds. How much does your cat weigh?.
Answer: 11.9 pounds
Step-by-step explanation:
142.5 - 130.6 = 11.9
Emma has a rain gauge on her deck to measure the amount of rain that falls in the area. After a storm with steady rain, there were 4.23 inches of water in the rain gauge. If the storm lasted 3 hours, how much water did the rain gauge collect every hour?
Answer:
1.41 inches per hour
Step-by-step explanation:
volume of water for 3 hrs=4.23 inches
v of water for 1 hours=4.23/3=1.21inches
Polygon P is dilated from the origin by a scale factor other than 1 to create polygon P′.
Determine whether each statement is true or false. Select True or False for each statement.
A. Polygon P is similar to polygo
n P′. TrueFalse
B. Polygon P is congruent to polygon P′. TrueFalse
C. The side lengths of polygon P are equal to the corresponding side lengths of polygon P′. TrueFalse
D. The angle measurements of polygon P are equal to the corresponding angle measurements of polygon P′. TrueFalse
The correct options are: Polygon P is similar to polygon P′ and The angle measurements of polygon P are equal to the corresponding angle measurements of polygon P′
What is dilation of figure?The dilation of a figure is enlargement or reduction of its original image to final image by a certain scale factor.
Given that, Polygon P is dilated from the origin by a scale factor other than 1 to create polygon P′
We know that, in dilation, both figures are similar not congruent, because they get enhanced or reduced by a certain scale factor, if scale factor is 1 then they can be congruent also.
Since, both figure are similar, therefore, their corresponding angles are congruent.
Hence, correct options are ; Polygon P is similar to polygon P′ and The angle measurements of polygon P are equal to the corresponding angle measurements of polygon P′.
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johnny is designing a rectangular poster to contain 12 in2 of printing with a 1-in margin at the top and bottom and a 3-in margin at each side. what overall dimensions will minimize the amount of paper used?
the dimensions will minimize the amount of paper used is with length 4 inch and a width 12 inch.
What is the area of the rectangle?
The area of a rectangle (A) is the product of its length 'a' and width or breadth 'b'. So, Area of Rectangle = (a × b) square units.
We have given
Johnny is designing a rectangular poster to contain 12 in² of printing with a 1-in margin at the top and bottom and a 3-in margin at each side.
Let,
l be the length and w be the width.
Area is A = l * w
Johnny is designing a rectangular poster to contain 12 in² of printing
i.e. Area of the inner printed section 12 = lw .........(1)
A 1-in margin at the top and bottom and a 3-in margin at each side.
i.e. l'=l+2 and w'=w+6
The total Area of the Poster is
A = (l+2) + (w+6) ...........(2)
Substitute the value of l from (1) in (2),
A = (12/w + 2) (w + 6)
A = 12 + 72/w + 2w + 12
A = 24 + 72/w + 2w
Differentiate w.r.t w,
A' = -72/w² + 2
For critical value put A'=0,
-72/w² + 2 = 0
2 = 72/w²
w² = 72/2
w² = 36
w = 6
Differentiate again w.r.t w,
A''(w) = 2(72/w²)
A''(6) = 2(72/(6)²)
A''(6) = 2(72/36)
A''(w) = 2*2 = 4>0
It is minimum at w=6.
Substitute in (1),
12 = lw
l = 2
The dimensions required are
l' = l + 2
= 2+2
= 4 inch
w'=w + 6
= 6 + 6
= 12 inch
Hence, the dimensions will minimize the amount of paper used is with a length 4 inch and a width 12 inch.
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logic operators are operators that compare two numbers and produce a true or false result. for example, a > b contains such an operator that compares the numbers in variables a and b if the value in a is greater than the value in b, then this operator returns a true result. otherwise, the operator returns a false result.
The operator used in the statement a > b is a comparison operator. In this case, true will be returned if the value of a is greater than the value of b, whereas false if the value of a is less than the value of b.
What are Comparison Operators?Code decisions require comparison operators. Comparison operators are used in the statement a > b. Using a and b as variables, it compares their values, returning true if a is greater than b, and false otherwise.
By comparing the values of two variables, the program can make decisions. Coders should understand how comparison operators work since they are used frequently in programming.
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MAKING AN ARGUMENT Your friend claims that given f(0) and any other value of a linear function f, you can write an
equation in slope-intercept form that represents the function. Your cousin disagrees, claiming that the two points could lie on a
vertical line. Who is correct? Explain.
O Your friend. You can write an equation in slope-intercept form even if the two points are on a vertical line.
O Your cousin. You may need more than two points to write an equation in slope-intercept form.
O Your friend. If f is a function, then the line is not vertical.
O Your cousin. If the line is vertical, it will not have a slope.
Answer:
O Your friend. If f is a function, then the line is not vertical.
Step-by-step explanation:
If you are given that the equation is a linear function, it can't have any undefined values.
Answer:
Your friend. If ƒ is a function, then the line is not vertical.
Step-by-step explanation:
I just had this question, and I solved it and got it right, see the picture
Akira is redecorating her bedroom. She misread the markings on her ruler and thought a picture frame she bought was 5.2 centimeters wide. The frame's actual width was 4.8 centimeters. What is the percent error for her measurement?
The percentage error is 8.3%
What is percentage?A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
Given that, Akira is redecorating her bedroom. She misread the markings on her ruler and thought a picture frame she bought was 5.2 centimetres wide. The frame's actual width was 4.8 centimetres.
Percentage Error = ((Estimated Number – Actual Number)/ Actual number) x 100.
= (5.2-4.8)/4.8x100 = 8.3%
Hence, The percentage error is 8.3%
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If f is continous on [a,b], then f attains an absolute maximum value f(c) and absolute minimum value f(d) at some numbers c and d in [a,b].
True
False
If f is continous on [a,b], then f attains an absolute maximum value f(c) and absolute minimum value f(d) at some numbers c and d in [a,b] then it is a true statement
What is an absolute maximum?
An absolute maximum point is a point where the function obtains its greatest possible value. Similarly, an absolute minimum point is a point where the function obtains its least possible value.
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Select the expression that have a value of 40 when x = 10.8.
The expression that has a value of 40 when x = 10.8. is (C) (x² ÷ 18) + 33.52
How to determine the expressions that fit the given category?The complete question is added at the end of this solution
From the question, we have the following expressions that can be used in our computation:
A 4,320 ÷ x
B 288/x + 16
C (x² ÷ 18) + 33.52
D (1,752 ÷ x) – 162/29
F x/12 + 36
The value of x is given as
x = 10.8
So, we evaluate the expressions at this value of x
Expression A: 4,320 ÷ x
4,320 ÷ 10.8 = 400 --- false
Expression B 288/x + 16:
288/10.8 + 16 = 42.7 --- false
Expression C (x² ÷ 18) + 33.52:
(10.8² ÷ 18) + 33.52 = 40 --- true
Expression D (1,752 ÷ x) – 162/29:
(1,752 ÷ 10.8) – 162/29 = 156.6 --- false
Expression F x/12 + 36:
10.8/12 + 36 = 36.9 --- false
Hence, the only expression is (x² ÷ 18) + 33.52
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Complete question
Select all the expressions that have a value of 40 when x = 10.8.
A 4,320 ÷ x
B 288/x + 16
C (x² ÷ 18) + 33.52
D (1,752 ÷ x) – 162/29
F x/12 + 36
Let R be an equivalence relation on a set A. Prove the following statement directly from the definitions of equivalence relation and equivalence class. For every a and b in A, if [a] = [b] then a Rb. Some of the sentences in the following scrambled list can be used to prove the statement. By definition of equivalence class, a E[b]. Let b E[a]. Then by definition of equivalence class, b Ra. Since R is symmetric, if b R a then a R b. | Thus, a Ra, and so, by definition of equivalence class, a E [a]. Since [a] = [b] and a E [a], then a E [b] by definition of set equality. | Hence, by definition of equivalence class, a Rb. By definition of equivalence relation, R is reflexive. Proof: Construct a proof by selecting appropriate sentences from the list and putting them in the correct order. 1. Suppose R is an equivalence relation on a set A, a and b are in A, and [a] = [b]. 2. ---Select--- 3. ----Select--- 4. ---Select--- 5. ---Select---
If the R is an equivalence relation then for every a and b in set R , if a = b then aRb exists.
If R is an equivalence relation on set A, a and b are in A and [a]=[b]
By the definition of the equivalence relation we can say that R is reflexive
Hence aRa and so by definition of equivalence class a ∈ [a] .
Since [a] = [b] and a ∈ [a] we can say that a ∈ [b] by the definition of set equality.
Now we will use the definition of equivalent class we can say that aRb .
An equivalence relation is a reflexive, symmetric, transitive binary link. The relationship of equipollence between line segments in geometry is one example of an equivalence relation.
Each equivalence relation separates the underlying set into distinct equivalence classes. Two items in the given set are only comparable to one another if and when they belong to the same equivalence class.
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it takes a hose 3 minutes to fill a rectangular aquarium 12 inches long, 13 inches wide, and 14 inches tall. how long will it take the same hose to fill an aquarium measuring 21 inches by 28 inches by 35 inches? minutes round your answer to the nearest minute
The hose will take 28.27 minutes to fill the second aquarium.
Given,
Rectangular Aquarium - 1
Length = 12 inches
Width = 13 inches
Height = 14 inches
Time taken by a hose to fill the aquarium = 3 minutes
Rectangular Aquarium - 2
Length = 21 inches
Width = 28 inches
Height = 35 inches
We have to find the time taken by the same hose to fill the aquarium 2.
Volume of Aquarium 1 = length × width × height
= 12 × 13 × 14 = 2184 inch³
To fill 2184 inch³, the hose will take 3 minutes.
Now,
Volume of Aquarium 2 = length × width × height
= 21 × 28 × 35 = 20580 inch³
Here,
The time taken by the hose to fill a volume of 20580 inch³;
= 3 × 20580 / 2184 = 28.27 minutes
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a test has a mean of 85 with a standard deviation of 5. which of the following scores is within one standard deviation of the mean?
A test's standard deviation is 5 and its mean is 85. scores is within one standard deviation of the mean is 25/n^12.
The square root of the variance of a random variable, sample, mean ,statistical population, data set, or probability distribution is that variable's standard deviation. Although less robust in practice, it is algebraically simpler than the average absolute deviation.The fact that the standard deviation is expressed in the same unit as the data, as opposed to the variance, is a useful characteristic of the statistic.
variance = 5^2 = 25
standard deviation of the mean = ( variance / n )^1/2
= (25/n)^1/2
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=-7x+y=-19
-2x+3y=-9
The system of equation - 7x + y = 19 and - 2x + 3y = - 9 have solution at
(-101/9, -3318/19).
What is linear system of equations?If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.
Given, A system of equations - 7x + y = 19 and - 2x + 3y = - 9.
Now, multiplying eqn(i) by 2 and eqn(ii) by 7 we get,
- 14x + 2y = 38...(iii) and - 14x + 21y = - 63...(iv)
Now, subtracting eqn(iii) from eqn(iv) we get,
(- 14x + 21y = - 63)
- (- 14x + 2y = 38)
_______________
19y = - 101.
y = - 101/19
and putting the value of y in eqn(iv) we get x = - 3318/19.
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In a test of the equality of the percent defectives from two populations when the sample sizes are large (> 30), which of the following approximation methods is appropriate?
Poisson approximation
Hypergeometric approximation
Fisher's approximation
Normal approximation
Chi-square approximation
The number of defectives follows binomial distribution with parameters (n,p) and if n>30 then binomial distribution goes to the Normal' approximation.
Given that,
We have to find which of the following approximation approaches is adequate in a test of the equality of the percent defectives from two populations when the sample sizes are big (> 30).
We know that,
What is a normal approximation?The normal curve is roughly followed by the sample distribution of averages or proportions from numerous independent experiments. The population value that corresponds to a sample proportion or average is its expectation.
Therefore, the number of defectives follows binomial distribution with parameters (n,p) and if n>30 then binomial distribution goes to the Normal' approximation.
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Help me on these please!. Thank you whoever. 13 points!!
Answer:
1. $105
2. $144
Step-by-step explanation:
For the first question:
4.20 × 25 = 105
For the second question:
4.80 × 30 = 144
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PLEASE HELPPPPPPPPP QUICKKKK
WILL MARK BRAINLEST
please look in down below all in there
Define a generic method called checkorder() that checks if four items are in ascending, neither, or descending order. The method should return -1 if the items are in ascending order, 0 if the items are unordered, and 1 if the items are in descending order. The program reads four items from input and outputs if the items are ordered. The items can be different types, including integers, strings, characters, or doubles.
The first is an ordered list of integers, the second is an ordered list of integers, and the third is an unsorted list of texts in JAVA. (Refer to the coding shown below.)
What is JAVA?In order to have as few implementation dependencies as feasible, Java is a high-level, class-based, object-oriented programming language.
Java is an object-oriented, cross-platform programming language (OOP).
JavaScript, a scripting language used to build dynamic web pages, should not be confused with it.
Java is one of the most widely used programming languages in the world because of its dependability and simplicity.
So, the generic class needed to compare any kind of data structure is created by the Java code that follows.
Both integers and strings were employed in three different test situations.
The first is a list of integers in ascending order, the second is a list of integers in descending order, and the third is a list of texts that are not sorted.
The image below that is attached shows the results.
import java.util.Scanner;
class Brainly {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
System.out.println("Order: " + checkOrder(10, 22, 51, 53));
System.out.println("Order: " + checkOrder(55, 44, 33, 22));
System.out.println("Order: " + checkOrder("John", " Gabriel", "Daniela", "Zendaya"));
}
public static <E extends Comparable<E>> int checkOrder(E var1, E var2, E var3, E var4) {
E prevVar = var1;
if (var2.compareTo(prevVar) > 0) {
prevVar = var2;
} else {
if (var3.compareTo(prevVar) < 0) {
prevVar = var3;
} else {
return 0;
}
if (var4.compareTo(prevVar) < 0) {
return 1;
} else {
return 0;
}
}
if (var3.compareTo(prevVar) > 0) {
prevVar = var3;
}
if (var4.compareTo(prevVar) > 0) {
return -1;
}
return 0;
}
}
Therefore, the first is an ordered list of integers, the second is an ordered list of integers, and the third is an unsorted list of texts in JAVA. (Refer to the coding shown below.)
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Study abroad. A survey on 1,509 high school seniors who took the SAT and who completed an optional web survey between April 25 and April 30, 2007 shows that 55% of high school seniors are fairly certain that they will participate in a study abroad program in college. 34 (a) Is this sample a representative sample from the population of all high school seniors in the US? Explain your reasoning (b) Let's suppose the conditions for inference are met. Even if your answer to part (a) indicated that this approach would not be reliable, this analysis mays be interesting to carry out (though not report). Construct a 90% confidence interval for the proportion of high school seniors (of those who took the SAT) who are fairly certain they will participate in a study abroad program in college, and interpret this interval in context (c) What does "90% confidence" mean? (d) Based on this interval, would it be appropriate to claim that the majority of high school seniors are fairly certain that they will participate in a study abroad program in college?
No, this sample is not representative of all high school seniors in the US as the sample is selected by an optional web survey, which is not a good sampling technique as non-response bias is introduced.
90% confidence interval for a population proportion.
= 0.55 ± 1.645 * √0.55(1-0, 55)/1509
= 0.55 ± 0.0211
= (0.5289, 0.5711)
We are 90% confident the true proportion of high school seniors who are fairly certain they will participate in a study abroad program in college lies between 52.89% to 57.11%b
90% confidence means if we select 100 samples, 90 of them will have their sample statistic within the 90% confidence interval. Or otherwise, we can be 90% certain that the population parameter will fall within the 90% confidence interval.
Yes, as the lower limit of the confidence interval is greater than 50%, there is strong evidence to support the claim that the majority of high school seniors are fairly certain that they will participate in a study abroad program in college.
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please help me!!!
Which number is greatest?
Answer:
It would be the third option, because the square root of 85 is 9.22, and 28/3 is 9.33 repeated.
Hope this helps, have a great day! :D
Step-by-step explanation:
if you draw square abcd and extend the sides by equal lengths to form square efgh, what must be the measure of angle heb so that the area of abcd is half the area of efgh?
The measure of angle < HEB = 60 degrees.
Given:
if you draw square abcd and extend the sides by equal lengths to form square efgh.
so that the area of abcd is half the area of efgh.
Let AB = x and HA = x
so area of square ABCD = x * x
= x^2
< HEB = 60 so < BHE = 30
EB = y
HE = 2y
HB = x + y
so x + y = [tex]\sqrt{3}[/tex] y
x = [tex]\sqrt{3}[/tex] y - y
x = ([tex]\sqrt{3}[/tex] - 1 ) y
y = x / ([tex]\sqrt{3}[/tex] - 1 )
squaring on both sides
y^2 = x^2 / ([tex]\sqrt{3}[/tex] - 1 )^2
= x^2 / 3 - 1
= x^2 / 2
Area of EFGH = (2y)^2 = 4y^2 = 2x^2 = 2 * area of ABCD.
Therefore < HEB = 60 degrees.
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a bin contains 4 items: 1 a, 1 b, 2 c and 6 d. a person randomly selects 3. how many different types of items will be selected
The 4 different types of items will be selected.
What is the combination?
Combinations are mathematical operations that count the number of possible configurations for a set of items where the order of the selection is irrelevant. In combinations, you can select the items in any order.
[tex]nCr = \frac{n!}{(n - r)! \ r!}[/tex]
This formula to find the number of combinations by using r objects from the n objects is also referred as the ncr formula.
so, we have 4 items and a person randomly selects 3.
[tex]nCr = (n, r) = (4, 3)[/tex]
[tex]= \frac{4!}{3!(4 - 3)!}[/tex]
= 4! / 3!
= 4
Hence, The 4 different types of items will be selected.
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