If he interest rate is 10% compounded annually, after 1 year, Maggie will have $33 in the account to the nearest cent.
To solve this problem, we can use the formula for compound interest:
B = p(1+r)ᵗ
where B is the balance, p is the principal, r is the interest rate expressed as a decimal, and t is the time in years.
In this case, we know that Maggie has $30 in the account, the interest rate is 10% (or 0.10), and she is investing for 1 year. We can plug these values into the formula to find her balance after 1 year:
B = 30(1+0.10)
B = 30(1.10)
B = 33
The formula for compound interest is a useful tool for calculating the growth of an investment over time, taking into account both the principal and the interest rate.
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C) Find the probability of rolling an odd number given you have spun a red section:
P(odd numberjred). 0.5 or 50%
2) A different game requires players to spin a five-section spinner and roll a six-sided
standard die to make a move. The spinner has sections of equal area, with each
section containing one of these numbers: 1, 2, 3, 4, and 5. The player gets to move
based upon the sum of the two numbers-one from the spinner and one from the
die.
A) Make a table to display the sample space of the compound events representing
the players making moves during the game.
I
1
2
- Make the columns correspond to the possible rolls of the dice and the
rows correspond to the possible spinner numbers.
For each cell entry, write the sum of the row value and the column value.
B) Find the probability of getting a sum of 4, 5, or 6.
The probability of rolling an odd number given you have spun a red section is 1/3 or approximately 33.33%.
The probability of getting a sum of 7 is 20%.
How to calculate the probabilityThere are three equally likely outcomes when you spin a red section: roll an odd number, roll an even number, or roll a 1. Of these three outcomes, only one corresponds to rolling an odd number. The probability will be:
= 1/3
= 33.33%
There are 5 possible outcomes when you spin the spinner and 6 possible outcomes when you roll the die, so there are 5 x 6 = 30 equally likely outcomes when you play this game. Therefore, the probability of getting a sum of 7 is 6/30 = 1/5 or 20%.
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Find a solution of the initial-value problem.y′=−(14)y2,y(0)=1.
To solve the given initial-value problem, we can separate the variables and integrate both sides. The final answer is Therefore, the solution to the initial-value problem is y = [tex]\frac{-1}{(-14t - 1)}[/tex], where y(0) = 1.
Given: y' = [tex]-(14)y^2\\[/tex]
Initial condition: y(0) = 1
Separating variables:
[tex]\frac{Dy}{y^2 }[/tex]= -14 dt
Integrating both sides:
∫([tex]\frac{1}{y^2}[/tex]) dy = ∫-14 dt
Integrating the left side:
[tex]\frac{-1}{y}[/tex]= -14t + C1
Solving for y:
y = [tex]\frac{-1}{-14t + C1}[/tex]
Using the initial condition y(0) = 1:
1 = [tex]\frac{-1}{C1}[/tex]
C1 = -1
Substituting the value of C1 back into the solution:
y = [tex]\frac{-1}{(-14t - 1)}[/tex]
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The Student Council advisor surveyed a total of 36 students by asking every tenth student in the lunch line how they preferred to be contacted with school news.
The results are shown in the table below:
Is the sample method valid?
b) If yes, name the type of sample it is:
c) If there are 684 students at the school, how many can be expected to prefer E-mail based on the data given from sample?
Answer:
Step-by-step explanation:
Yes, the Student Council advisor's sample method is valid.
In this scenario, the sample method used by the Student Council advisor is known as systematic sampling. The process of selecting every nth element from a population is known as systematic sampling. The advisor in this case polled every tenth student in the lunch line. This method is valid because it guarantees that every student in the population has an equal chance of being chosen and provides a representative sample of the entire student body.
The advisor obtained a sample distribution of their preferred contact methods for school news by surveying 36 students. The advisor discovered that 16 students preferred email, 12 preferred newsletters, 5 preferred announcements, and 3 preferred phone contact from this sample. The proportion of students in the sample who preferred email can be used to estimate the number of students who prefer email among the entire student population.
In this case, 16 of 36 students preferred email, representing 44.44 percent (16/36 * 100). We can estimate the number of students who prefer email by applying this percentage to the total student population if we assume that this proportion remains constant across the entire student population. Given that the school has 684 students, we can expect approximately 303 students (684 * 44.44 percent) to prefer email as their preferred method of communication for school news.
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A high school surveyed students to determine if new foreign language classes should be added to the course offerings for the next school year. The two-way frequency table below shows the interest of next year's underclassmen in the new courses.
German Mandarain Neither Total
freshmen: 30 80 230 340
Sophomores: 15 65 200 280
Total: 45 145 430 620
Approximately what percentage of the underclassmen have an interest in taking a Mandarin course next year?
44.83%
33.72%
23.39%
55.17%
Approximately 23.39% of the underclassmen have an interest in taking a Mandarin course next year.
Option C is the correct answer.
We have,
To determine the percentage of underclassmen interested in taking a Mandarin course, we need to calculate the ratio of the number of underclassmen interested in Mandarin to the total number of underclassmen.
Looking at the two-way frequency table, we can see that there are 145 underclassmen interested in Mandarin out of a total of 620 underclassmen.
To find the percentage, we divide the number of underclassmen interested in Mandarin by the total number of underclassmen and multiply by 100:
= (145 / 620) x 100
= 23.39%
Therefore,
Approximately 23.39% of the underclassmen have an interest in taking a Mandarin course next year.
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find the t-value such that the area in the right tail is 0.15 with 13 degrees of freedom.
The t-value such that the area in the right tail is 0.15 with 13 degrees of freedom is approximately 1.350.
To find the t-value such that the area in the right tail is 0.15 with 13 degrees of freedom, we can use a t-table or a calculator with a t-distribution function.
Using a t-table:
Look for the row that corresponds to 13 degrees of freedom.
Look for the column that contains the area 0.15.
The intersection of the row and column is the t-value we are looking for.
Using a calculator:
Use the t-distribution function with 13 degrees of freedom.
Set the upper limit of integration to a large number, such as 100, to calculate the area in the right tail.
Find the t-value such that the area to the right of it is 0.15.
Using either method, we find that the t-value such that the area in the right tail is 0.15 with 13 degrees of freedom is approximately 1.350.
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rosa has pounds of dough. she uses of a pound for one medium loaf of bread. how many medium loaves of bread could be made from rosa's dough?
Rosa has a certain amount of dough, and each medium loaf of bread requires a fraction of a pound. To determine how many medium loaves of bread Rosa can make, we divide the total amount of dough by the fraction of a pound needed for one loaf. So the answer is 5.
Explanation: If we let "x" represent the total amount of dough that Rosa has in pounds, and "y" represent the fraction of a pound needed for one medium loaf of bread, we can set up a simple equation to solve for the number of loaves, "n":
x / y = n
Given that Rosa has a certain amount of dough, we need to determine the value of "y" (the fraction of a pound needed for one loaf) in order to calculate "n" (the number of loaves). Since the exact fraction is not provided in the question, we would need additional information to solve for "y" and compute the exact number of medium loaves Rosa can make.
For example, if it is given that Rosa uses 1/4 pound of dough for one medium loaf, we can substitute this value into the equation:
x / (1/4) = n
Simplifying the equation, we would multiply both sides by 1/4:
4x = n
(15/4)/(3/4) = 5
So, Rosa would be able to make 4 times the amount of dough in medium loaves of bread, which is 5.
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Complete Question: Rosa has 3 3/4 pounds of dough. She uses 3/4 of a pound for one medium loaf of bread. How many medium loaves of bread could be made from Rosa's dough?
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.19 and the probability that the flight will be delayed is 0.1. The probability that it will rain and the flight will be delayed is 0.07. What is the probability that it is not raining if the flight leaves on time? Round your answer to the nearest thousandth.
The probability that it is not raining if the flight leaves on time is 0.9.
Let's define the events:
A: It is raining
B: The flight is delayed
We have,
P(A) = 0.19 (probability that it will rain)
P(B) = 0.1 (probability that the flight will be delayed)
P(A ∩ B) = 0.07 (probability that it will rain and the flight will be delayed)
Using the formula for conditional probability, we have:
P(A' | B') = P(A' ∩ B') / P(B')
Since A' and B' are complementary events (if it's not raining, then the flight is leaving on time), we can rewrite the formula as:
P(A' | B') = P(B' | A') x P(A') / P(B')
We know that P(A) + P(A') = 1, so P(A') = 1 - P(A).
Now, let's substitute the given values into the formula:
P(A' | B') = (P(B' | A') x (1 - P(A))) / P(B')
P(B' | A') represents the probability that the flight is leaving on time given that it's not raining.
We know that:
P(B') = 1 - P(B) = 1 - 0.1 = 0.9
we can estimate P(B' | A') as:
P(B' | A') ≈ P(B') = 0.9
Now we can substitute the values into the formula:
P(A' | B') ≈ (0.9 x (1 - 0.19)) / 0.9
P(A' | B') ≈ 0.81 / 0.9
P(A' | B') ≈ 0.9
Therefore, the probability that it is not raining if the flight leaves on time is 0.9.
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what are the requirements to perform a one-way anova? is the test robust?
Thus, a one-way ANOVA test is robust if the data meets the above requirements. It is a powerful statistical tool that can help analyze differences between means of multiple groups.
A one-way ANOVA is a statistical test used to analyze the differences between means of two or more groups. There are certain requirements that need to be met before performing a one-way ANOVA.
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To perform a one-way ANOVA, the observations need to be independent, the data should be normally distributed, and the variances should be equal. However, the test is robust to deviations from these assumptions, particularly if the group sizes are equal.
Explanation:To perform a one-way ANOVA (Analysis of Variance), there are several requirements you should meet:
Independence of observations: each group should be separate and not influence the others.Normality: the data in each group should follow a normal distribution.Homogeneity of variance: the variances of the groups should be equal.The one-way ANOVA is considered robust to deviations from normality and homogeneity of variance, especially when the group sizes are equal. However, if smokes are very unequal or if there are extreme outliers, it might not be as robust.
If these assumptions are not met, a non-parametric alternative like the Kruskal-Wallis test might be a better choice.
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4. What is the measure of arc BC
B
A
98⁰
C
N
80°
70°
D
The measure of arc BC in a circle where the two chords, chord AD and chord AC are equal in measure, is 146°. Therefore, the correct option is option C.
The measure of arc made by parallel chord in a circle are equal in measure.
arc BC=8x-46°
arc AD=5x+26°
arc BC=arc AD
8x-46°=5x+26°
x=24°
arc BC=8x-46°
arc BC=8(24°)-46°
arc BC=192°-46°
arc BC=146°
Therefore, the correct option is option C.
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Your question is incomplete but most probably your full question was,
suppose a system of linear equations has a 3x5 augmented matrix whose fifth column is not a pivor column. is the system consisten why or why not
The system of linear equations is not necessarily inconsistent just because its 3x5 augmented matrix has a non-pivot column in the fifth position.
It is possible that the system has infinitely many solutions. However, it is also possible that the system has no solutions. The key factor that determines whether the system is consistent or not is whether the corresponding coefficient matrix has full row rank (i.e., has three pivot rows).
If the coefficient matrix has full row rank, then the system is consistent, regardless of the structure of the augmented matrix. If the coefficient matrix does not have full row rank, then the system is inconsistent.
If the system is consistent, we can use row operations to reduce the augmented matrix to row echelon form or reduced row echelon form, and then use back substitution to find the solutions.
If the system is inconsistent, we can use row operations to derive a contradiction (e.g., a row of the form [0 0 ... 0 b], where b is a nonzero constant), which means that the system has no solutions.
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Total cost 217 sales tax 8.5% what is the original price
Answer:
$200
Step-by-step explanation:
To find the original price of an item that costs $217 with an 8.5% sales tax, you would first divide the total cost by 1 plus the tax rate (as the tax is calculated as a percentage of the original price plus tax). This would give you the price without the sales tax. So, $217 divided by 1.085 equals approximately $200. The original price before the sales tax was added would be $200.
an industrial engineer wants to test the effect of three different ways of assembling a part on the total assembly time. five people are randomly assigned to each of the three assembly methods, and the total assembly time (in seconds) is recorded. how many degrees of freedom (df1) does the treatment sum of squares have? how many degrees of freedom (df2) for the error sum of squares?
The variation in assembly times within each assembly method the treatment sum of squares is 2, and the degrees of freedom (df2) for the error sum of squares is 12.
To determine the degrees of freedom (df1) for the treatment sum of squares, we need to consider the number of groups (assembly methods) being compared.
In this case, there are three different ways of assembling the part. Since there are three groups, the degrees of freedom for the treatment sum of squares is calculated as:
df1 = number of groups - 1
= 3 - 1
= 2
To calculate the degrees of freedom (df2) for the error sum of squares, we need to consider the total number of observations and the number of groups.
In this case, there are 5 people assigned to each assembly method, and there are 3 assembly methods in total. so the total number of observations is 5 * 3 = 15.
df2 = total number of observations - number of groups
= 15 - 3
= 12
Therefore, the degrees of freedom (df1) for the treatment sum of squares is 2, and the degrees of freedom (df2) for the error sum of squares is 12.
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Find the exact length of the polar curve described by: r = 4e-⁰ on the interval 7/6π ≤ 0 ≤ 5π
The exact length of the polar curve described by r=4e^(-theta) on the interval 7/6pi ≤ theta ≤ 5pi is approximately 36.60 units.
To find the length of the polar curve, we can use the formula: L = ∫(a to b) sqrt[r^2 + (dr/d theta)^2] d theta. Applying this formula to the given polar curve, we get L = ∫(7/6pi to 5pi) sqrt[(4e^(-theta))^2 + (-4e^(-theta))^2] d theta. Simplifying this expression, we get L = 8∫(7/6pi to 5pi) e^(-theta) dtheta. Evaluating this integral, we get L = 8[e^(-7/6pi) - e^(-5pi)] ≈ 36.60 units.
Therefore, the exact length of the polar curve described by r=4e^(-theta) on the interval 7/6pi ≤ theta ≤ 5pi is approximately 36.60 units. This formula can be used to find the length of any polar curve, given its equation and the interval in which it is being evaluated. It is important to note that the formula for the length of a polar curve is derived using calculus, specifically the arc length formula. The arc length formula is used to find the length of a curve in the Cartesian coordinate system, while the formula for the length of a polar curve is used to find the length of a curve in the polar coordinate system.
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A farmer sells 8.7 kilograms of pears and apples at the farmer's market.
3
4
of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market?
The kilograms of apple she sell at the farmer's market is A = 2.175 kg
Given data ,
To find the weight of apples sold by the farmer, we can subtract the weight of pears from the total weight
Given that 3/4 of the weight is pears, we can calculate the weight of pears by multiplying the total weight by 3/4:
Weight of pears = (3/4) x 8.7 kilograms = 6.525 kilograms
Since the total weight is 8.7 kilograms, we can subtract the weight of pears to find the weight of apples
On simplifying the equation , we get
Weight of apples = Total weight - Weight of pears
A = 8.7 kilograms - 6.525 kilograms = 2.175 kilograms
Hence , the farmer sold approximately 2.175 kilograms of apples at the farmer's market
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I need to know this for a quiz tomorrow……. HELP!
The quadratic function for the graph in this problem is given as follows:
y = 2(x + 1)(x - 2).
How to define the quadratic function?The roots for the quadratic function in this problem are given as follows:
x = -1.x = 2.Hence the linear factors of the function are given as follows:
x + 1.x - 2.Considering the factor theorem, the function is given by the product of it's linear factors and the leading coefficient a, hence:
y = a(x + 1)(x - 2)
When x = 0, y = -4, hence the leading coefficient a is obtained as follows:
-2a = -4
2a = 4
a = 2.
Hence the function is:
y = 2(x + 1)(x - 2).
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Rio has £5. He wants to buy a
ruler and some pencils. A ruler
costs £1.45 and each pencil
costs 53p. What is the
maximum number of pencils
Rio can buy?
Answer:
6
Step-by-step explanation:
£5 - £1.45 = £3.55
£3.55 ÷ 0.53p = 6.698
since you cant have .6 of a pencil, the maximum number of pencils Rio can buy is 6
Answer:
6
Step-by-step explanation:
call £5 500p.
£1.45 =145p
500 - 145 = 355.
355/53 = 6.7
so the maximum number of pencils he can buy is 6.
you can check this by inputting those numbers.
£1.45 + 6 X £0.53
= £1.45 + £(3.18)
=£4.63
Rio still has 37p left. not enough for another pencil
PLEASE HELP Solve -2p² - 5p + 1 = 7p² + p using the quadratic formula.
The solutions to the quadratic equation -2p² - 5p + 1 = 7p² + p are p₁ = (-1 + √2) / 3 and p₂ = (-1 - √2) / 3. To solve the quadratic equation -2p² - 5p + 1 = 7p² + p, we can rearrange the equation to bring all the terms to one side, creating a standard quadratic form: 0 = 7p² + p + 2p² + 5p - 1.
Combining like terms, we get 0 = 9p² + 6p - 1.
Now, we can apply the quadratic formula, which states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by x = (-b ± √(b² - 4ac)) / (2a).
For our equation, a = 9, b = 6, and c = -1. Plugging these values into the quadratic formula, we have:
p = (-6 ± √(6² - 4[tex]\times[/tex] 9 [tex]\times[/tex] -1)) / (2 [tex]\times[/tex] 9)
Simplifying further:
p = (-6 ± √(36 + 36)) / 18
p = (-6 ± √72) / 18
Since the value under the square root (√72) can be simplified as √(36 [tex]\times[/tex] 2) = 6√2, we have:
p = (-6 ± 6√2) / 18
Now, we can simplify and express the two solutions:
p₁ = (-6 + 6√2) / 18
p₂ = (-6 - 6√2) / 18
To further simplify, we can divide both the numerator and denominator by 6:
p₁ = (-1 + √2) / 3
p₂ = (-1 - √2) / 3
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Find the missing sides of WX and WV
Check the picture below.
on what interval is the following curve concave downward? (enter your answer using interval notation.) y = x t2 t2 t 9 dt 0
The curve given by the equation y = x(t^2/t^2 + t + 9) dt on the interval [0,∞) is concave downward on the interval [3, ∞).
To find where the curve is concave downward, we need to take the second derivative of the function and check where it is negative. Taking the second derivative of the given function with respect to x, we get:
y'' = 2t^2(t^2 + 18)/[(t^2 + t + 9)^3]
To find where y'' is negative, we need to solve the inequality 2t^2(t^2 + 18)/[(t^2 + t + 9)^3] < 0. Factoring the numerator, we get:
2t^2(t^2 + 18) = 2t^2(t+√18)(t-√18)
This is negative when t is between -√18 and 0, and also when t is between 0 and √18. However, we need to consider the interval [0,∞) only, which means we should take the solution from the interval [0, √18]. Therefore, the curve is concave downward on the interval [3, ∞).
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PLEASE HELP ME!!!!!!
Answer: [tex]\frac{-3}{10}[/tex]
Step-by-step explanation:Given:
(b + d) - a
Substitute known values:
([tex]\frac{3}{5}[/tex] + - [tex]\frac{1}{5}[/tex]) - [tex]\frac{7}{10}[/tex]
Addition and subtraction becomes subtraction:
([tex]\frac{3}{5}[/tex] - [tex]\frac{1}{5}[/tex]) - [tex]\frac{7}{10}[/tex]
Subtract:
[tex]\frac{2}{5}[/tex] - [tex]\frac{7}{10}[/tex]
Common denominators:
[tex]\frac{4}{10}[/tex] - [tex]\frac{7}{10}[/tex]
Subtract:
[tex]\frac{-3}{10}[/tex]
Eleven less than seven times a number is five more than six time the number. What is the number?
Answer:
Thus, the number is equal to x =16 the Answer 16 Basically
20 POINTS
A light pole casts a 35-foot-long shadow. The angle of elevation from the tip of the shadow to the top of the light pole is 23°. To the nearest foot, what is the height of the light pole?
Check the picture below.
[tex]\tan(23^o )=\cfrac{\stackrel{opposite}{h}}{\underset{adjacent}{35}} \implies 35\tan(23^o)=h \implies 15\approx h\\[/tex]
Make sure your calculator is in Degree mode.
Let fbe the function given by fx=frac 2x2+14x-16x2-9x+8 . For what values of x does f have a removable discontinuity? A l only B 8 only C -8 and 1 D 1 and 8.
The answer is option D, which is 1 and 8.To find the values of x where f has a removable discontinuity, we need to check if there are any values of x that make the denominator of f(x) equal to zero.
If this occurs, the function will have a vertical asymptote at that point, and if the limit of the function as x approaches that point exists, then the function has a removable discontinuity at that point.
In this case, we can see that the denominator of f(x) is (2x-1)(4x+8), which equals zero at x=1/2 and x=-2. However, we need to check if these values of x result in a removable discontinuity. At x=1/2, the function f(x) is undefined, and the limit as x approaches 1/2 is -1/3. Therefore, f(x) has a removable discontinuity at x=1/2. At x=-2, the function f(x) is also undefined, but the limit as x approaches -2 does not exist. Therefore, f(x) does not have a removable discontinuity at x=-2. Thus, the answer is option D, which includes the value 1 where f has a removable discontinuity, and the value 8 where f does not have a removable discontinuity.
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Below, a two-way table is given
for student activities.
Sports Drama
7
13
Sophomore 20
Junior
20
Senior
Total
Work
3
2
5
Find the probability the student is in drama,
given that they are a sophorwore.
The probability the student is in drama, given that they are a sophomore is 23%.
What is probability?
Probability is a way of determining how likely something is to happen. Many events are difficult to predict with total certainty. Using it, we can make predictions about the probability of an event happening, or how likely it is.
Total number of students = 20+7+13+20+13+2+25+5+5 = 100
Number of students in sophomore([tex]S_{o}[/tex]) = 20+7+3 = 30
Number of drama students(D) who are in sophomore = 7
To calculate the probability the student is in drama, given that they are a sophomore:
P(drama | sophomore) = [tex]\frac{P(drama \ and \ sophomore)}{P(sophomore)}[/tex] = 23%
Therefore, probability = [tex]\frac{n(D\cap S_{o} )}{n(S_{o} )} =\frac{7}{30} = 23\%[/tex]
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find the fourier series for f(x) in the prescribed interval. (a) f(x) = { −1, −1 ≤x < 0 1 0 ≤x ≤1
The Fourier series for the function f(x) = { -1, -1 ≤ x < 0; 1, 0 ≤ x ≤ 1 } in the interval [−1, 1] is (4/π) ∑n=1∞ [sin((2n−1)πx)/(2n−1)]. This represents an odd function and is known as a Fourier sine series.
The Fourier series for the function f(x) = { −1, −1 ≤x < 0; 1, 0 ≤x ≤1 } in the interval [−1, 1] can be expressed as follows:
f(x) = ∑n=0∞ (a0/2 + an cos(nπx) + bn sin(nπx))
where a0, an, and bn are the Fourier coefficients, given by:
a0 = (1/2) ∫−1^1 f(x) dx = 0
an = (1/π) ∫−1^1 f(x) cos(nπx) dx = 2(1−cos(nπ))/nπ
bn = (1/π) ∫−1^1 f(x) sin(nπx) dx = 0
Therefore, the Fourier series for f(x) in the interval [−1, 1] is:
f(x) = ∑n=1∞ [2(1−cos(nπ))/nπ] sin(nπx)
This series can also be written as:
f(x) = (4/π) ∑n=1∞ [sin((2n−1)πx)/(2n−1)]
This is an example of a Fourier sine series since the function f(x) is odd (i.e., f(−x) = −f(x)).
In summary, the Fourier series for f(x) = { −1, −1 ≤x < 0; 1, 0 ≤x ≤1 } in the interval [−1, 1] is given by:
f(x) = (4/π) ∑n=1∞ [sin((2n−1)πx)/(2n−1)]
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One-variable Statistics:Question 3
The list below shows the average monthly temperatures
in degrees Fahrenheit in Ahmed's city for the past year.
74, 86, 90, 68, 76, 64, 68, 84, 90, 94, 82, 92
Which box-and-whisker plot correctly represents the
data in the list?
Select one:
The box plot that represents the data is the third option.
Which box plot represents the data?A box plot is a graph that is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers.
The first whisker represents the minimum number and the end of the second whisker represents the maximum number. On the box, the first line to the left represents the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile.
The numbers arranged in ascending order : 64, 68, 68, 74, 76, 82, 84, 86, 90, 90, 92, 94,
The minimum number is 64 and the maximum number is 94.
First quartile = 1/4(n + 1)
1/4 x (12 + 1) = 3.25 number = 71
Third quartile = 3/4(n + 1)
3/4 x (12 + 1) = 9.75 number = 90
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in a sample of 16, and x¯ = 74, with a standard deviation of s = 5, the standard error of the sample mean is
The standard error of the sample mean is 1.25.
The formula for the standard error of the sample mean is s/√n, where s is the standard deviation of the sample and n is the sample size. In this case, s=5 and n=16, so the standard error of the sample mean is 5/√16=1.25.
The standard error measures the variability of sample means that could be obtained from the population, and it decreases as the sample size increases. A smaller standard error means that the sample mean is a more precise estimate of the population mean.
In this example, the standard error of 1.25 indicates that the sample mean of 74 is relatively precise, but without additional information, we cannot determine how accurately it estimates the population mean.
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find the standard form of the equation of the parabola with the given characteristics. vertex: (5, 25) points on the parabola: (0, 0), (10, 0)
We know that the vertex form of a parabola is given. Therefore, there is no parabola that satisfies these conditions.
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola and a is a constant that determines the shape of the parabola.
We are given the vertex (5, 25), so we can write:
y = a(x - 5)^2 + 25
We are also given two points on the parabola: (0, 0) and (10, 0). Plugging these into the equation, we get:
0 = a(0 - 5)^2 + 25 => 25 = 25a => a = 1
0 = a(10 - 5)^2 + 25 => 0 = 25a => a = 0
We get two different values for a, which means that the given points do not lie on the same parabola. Therefore, there is no unique solution to this problem.
We can also see this geometrically: the points (0, 0) and (10, 0) lie on the x-axis, which means that the parabola would have to open either upwards or downwards. However, the vertex is above the x-axis, which means that the parabola cannot intersect the x-axis. Therefore, there is no parabola that satisfies these conditions.
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In a two population proportions problem, why is the use of the individual proportions for X and Y (i.e, p_x,q_x and p_y,q_y ) used for confidence intervals instead of the "common p" used in hypothesis testing? 1. It's not. Unless the sample sizes are outside the 1/3 to 3/1 ratio, the two methods result in the same boundaries 2. Because it's a Cl on the difference". If you're going in assuming that the proportions are in fact different, it doesn't make sense to support using an average p and q 3. It doesn't make any difference.......this is not the answer, don't pick this 4. It's not, you use the common p in both instances 5. Because it's a Cl on the "difference", so it makes sense to use an averaged value for p.
In a two population proportions problem, the use of individual proportions for X and Y (i.e., p_x, q_x, and p_y, q_y) is used for confidence intervals instead of the "common p" used in hypothesis testing.
The reason for this is that in hypothesis testing, we are assuming that the two population proportions are equal (i.e., p_x = p_y = p), which means that we can estimate p using the combined sample proportion. However, in a confidence interval problem, we are interested in estimating the difference between the two population proportions, and using the combined sample proportion to estimate p would not be appropriate. Instead, we use the individual sample proportions for X and Y to construct separate confidence intervals for each population proportion, which we can then use to estimate the difference between them.
In other words, when constructing a confidence interval for the difference in proportions, we are interested in estimating the variability of each population proportion separately, and not the variability of the combined sample proportion. This is why we use the individual sample proportions for X and Y in constructing confidence intervals, rather than the common sample proportion used in hypothesis testing.
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What is the smallest integer of 3x+4>=14
The smallest integer value of x that satisfies the inequality 3x+4>=14 is 4.
To find the smallest integer value of x that satisfies the inequality 3x+4>=14, we need to isolate x on one side of the inequality sign.
First, we subtract 4 from both sides of the inequality to get:
3x >= 10
Next, we divide both sides of the inequality by 3 to get:
x >= 10/3
So any value of x that is greater than or equal to 10/3 will satisfy the inequality 3x+4>=14. However, since x is an integer, we need to round up to the smallest integer value that satisfies the inequality.
The smallest integer that is greater than or equal to 10/3 is 4, so the smallest integer value of x that satisfies the inequality is 4.
To check this, we can substitute x=4 back into the original inequality:
3(4) + 4 >= 14
12 + 4 >= 14
16 >= 14
Since 16 is indeed greater than or equal to 14, we have verified that x=4 is a valid solution to the inequality.
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