Question 3 (Essay Worth 40 points)
(10.01, 10.09 HC)
The power series for f of x is equal to 1 over the quantity 1 minus x end quantity is defined as 1 plus x plus x squared plus x cubed plus dot dot dot equals the summation from n equals 0 to infinity of x to the nth power comma and the power series for −sinx is defined as negative x plus the quantity x cubed over 3 factorial end quantity minus the quantity x to the fifth power over 5 factorial end quantity plus x to the seventh power over 7 factorial plus dot dot dot equals the summation from n equals 0 to infinity of negative 1 to the nth power time the quantity negative x to the 2 times n minus 1 power end quantity over the quantity 2 times n minus 1 end quantity factorial period
Part A: Find the general term of the power series for g of x is equal to 4 over the quantity x squared minus 4 end quantity and evaluate the infinite sum when x = 1. Justify your solution. (15 points)
Part B: Find an upper bound for the error of the approximation sin of zero point 3 is approximately zero point 3 minus the quantity zero point 3 to the third power over 3 factorial end quantity period Round your final answer to five decimal places. (15 points)
Part C: Find a power series for h(x) = ln(1 + x) centered at x = 0 and show the work that leads to your conclusion. (10 points)
Answers
Answer:
centered at x = 0.
Step-by-step explanation:
Part A: The power series for g(x) can be obtained by using the formula for a geometric series with a first term of 1 and a common ratio of (x/2). Then we have:
g(x) = 4/((x+2)(x-2)) = 4/(4*(1 + x/2)*(1 - x/2))
= 1/(1 - x/2) - 1/(1 + x/2)
We can then use the power series for 1/(1-x) to find the power series for g(x):
g(x) = 1/(1 - x/2) - 1/(1 + x/2)
= (1/2) * (1 + x/2 + (x/2)^2 + (x/2)^3 + ...) - (1/2) * (1 - x/2 + (x/2)^2 - (x/2)^3 + ...)
= x + (3/4)*x^2 + (5/8)*x^3 + (35/64)*x^4 + ...
To evaluate the infinite sum when x = 1, we can substitute x = 1 into the power series and use the formula for an infinite geometric series:
g(1) = 1 + (3/4) + (5/8) + (35/64) + ...
= 1/(1 - 1/2) - 1/(1 + 1/2)
= 2 - 2/3
= 4/3
Therefore, the infinite sum when x = 1 is 4/3.
Part B: To find an upper bound for the error of the approximation sin(0.3) ≈ 0.3 - 0.3^3/3!, we can use the formula for the remainder term in a Taylor series:
Rn(x) = f^(n+1)(c) * (x-a)^(n+1) / (n+1)!
where f(x) = sin(x), a = 0.3, n = 3, and c is some number between a and x. We want to find an upper bound for |R3(0.3)|.
Taking the fourth derivative of f(x) = sin(x), we get:
f^(4)(x) = -sin(x)
Since |sin(c)| ≤ 1 for any c, we have:
|R3(0.3)| ≤ |f^(4)(c)| * (0.3-0)^4 / 4!
≤ 1 * 0.3^4 / 24
≤ 0.000625
Therefore, an upper bound for the error is 0.000625, rounded to five decimal places.
Part C: We can find the power series for h(x) by differentiating the power series for ln(1+x) term by term. The power series for ln(1+x) is:
ln(1+x) = x - x^2/2 + x^3/3 - x^4/4 + ...
Taking the derivative, we get:
h(x) = ln(1+x)'
= 1 - x + x^2 - x^3 + ...
which is the power series for (-1)^n x^n. Therefore, the power series for h(x) is:
h(x) = ∑(-1)^n x^n
centered at x = 0.
Related Questions
Question 5: find all of the arcs and angles
Answers
The measure of arc angle DC is 60.
The measure angle A is 45⁰.
The measure angle B is 50⁰.
The measure angle C is 45⁰.
The measure angle D is 50⁰.
What is the measure of the angles?The measure of arc angle DC is calculated as follows;
arc DC = 360 - (100 + 110 + 90) (sum of angles in a circle)
arc DC = 60
The measure angle A is calculated as follows;
m∠A = ¹/₂( arc BC ) (intersecting chord theorem)
m∠A = ¹/₂ x 90
m∠A = = 45⁰
The measure angle B is calculated as follows;
m∠B = ¹/₂( arc AD ) (intersecting chord theorem)
m∠B = ¹/₂ x 100
m∠B = 50⁰
The measure angle C is calculated as follows;
m∠C = m∠A (vertical opposite angles)
m∠C = = 45⁰
The measure angle D is calculated as follows;
m∠D = m∠B (vertical opposite angles)
m∠C = = 50⁰
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please help with full explanation!! thank you!! :))
Answers
The value of angle x is 70⁰.
What is the value of angle x?The value of angle x is calculated by applying intersecting chord theorem.
The intersecting chord theorem states that for two chords intersecting at the center of the circle, the angle formed by the intersection of the two chords is equal to the arc angle subtended at the circumference.
The value of the angle adjacent to angle x is calculated as follows;
∠QON = arc angle QN
∠QON = 110⁰
The value of angle x is calculated as;
x + ∠QON = 180
x = 180 - ∠QON
x = 180 - 110⁰
x = 70⁰
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You are given the following homogeneous Markov chain with state space {1,2,3,4,5,6,7} and transition probability matrix: P = [0.5 0.2 0.25 0.0 0.0 0.00.0 0.0 0.4 0.0 0.2 0.0 0.0 0.0 0.5 0.2 0.75 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.2 0.0 0.2 0.0 0.0 0.0 0.5 0.5 0.0 0.0 0.0 0.0 . (10 points)For the Markov chain in question 4, find the mean time spent by the Markov chain in any transient states of the chain which starts at any transient states. 6. (10 points) For the Markov chain in question 4, find the probability that the Markov chain will ever transit to one of the transient states starting from another transient state.
Answers
We can find the probabilities of ever transiting from states 4, 5, and 6 to a transient state by looking at the fourth, fifth, and sixth rows of F, respectively.
To find the mean time spent by the Markov chain in any transient states of the chain which starts at any transient state, we need to first identify the transient states. In this case, we can see that states 1, 3, and 7 are transient states since there is a non-zero probability of reaching an absorbing state (states 4, 5, and 6) from these states.
Next, we need to find the expected time spent in each of the transient states before reaching an absorbing state. We can set up a system of equations to solve for these expected times using the fact that the expected time spent in a state is equal to 1 plus the sum of the expected times spent in each possible next state, weighted by their transition probabilities.
For example, for state 1, we have:
E(T1) = 1 + 0.5E(T2) + 0.25E(T3)
where E(Ti) is the expected time spent in state i before reaching an absorbing state.
Similarly, for state 3, we have:
E(T3) = 1 + 0.4E(T2) + 0.2E(T4)
And for state 7, we have:
E(T7) = 1 + 0.2E(T5) + 0.5E(T6)
Solving these equations, we get:
E(T1) = 5
E(T3) = 5.5
E(T7) = 4
Therefore, the mean time spent by the Markov chain in any transient state is:
(E(T1) + E(T3) + E(T7))/3 = (5 + 5.5 + 4)/3 = 4.83
To find the probability that the Markov chain will ever transit to one of the transient states starting from another transient state, we can use the concept of fundamental matrix. The fundamental matrix F is defined as the matrix (I-Q)^-1, where Q is the submatrix of P consisting of the transition probabilities between transient states.
In this case, we have:
Q = [0 0.25 0.2;
0.4 0 0.2;
0.2 0.2 0]
Using a calculator or software to calculate the inverse of (I-Q), we get:
(I-Q)^-1 = [1.25 0.625 1;
0.625 1.25 1;
1 1 1.5]
The (i,j)-th entry of F represents the expected number of times the Markov chain will visit state j starting from state i before reaching an absorbing state. Therefore, the probability of ever transiting to a transient state starting from another transient state is simply the sum of the corresponding entries in F.
For example, to find the probability of ever transiting from state 2 to a transient state, we look at the second row of F:
[0.625 1.25 1]
The sum of these entries is 0.625 + 1.25 + 1 = 2.875, so the probability of ever transiting from state 2 to a transient state is 2.875.
Similarly, we can find the probabilities of ever transiting from states 4, 5, and 6 to a transient state by looking at the fourth, fifth, and sixth rows of F, respectively.
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Paula 64 grams of ground coffee beans to make 32 fluid ounces of coffee. Yesterday she made 480 fluid ounces of coffee. how many grams of ground coffee beans did paula use to make coffee
Answers
Answer:
960 grams
Step-by-step explanation:
We know from the problem that grams is proportional to fluid ounces. Therefore, if we allow g to represent the number of grams of ground coffee Paula used, we can find it using a proportion:
[tex]\frac{64}{32}=\frac{g}{480}\\\\ 32g=30720\\\\ g=960[/tex]
Can you please help me with the question!?
Answers
Answer:
Step-by-step explanation:
menu 7,1 Open table labe A , B as x y
type the numbers provided and then 4 1 and whatever problem click it\
and you will see a table again type x y and there you will get youre asnwers
Prove the quadrilateral is a square
Answers
Answer: The answer is Does it have same matching sides, is it congruent. This is how we will know if it's a square.
Step-by-step explanation: Please give Brainlist.
Hope this helps!!!!
I can answer more questions.
Help!!!!!!!!!??!!??:?3?3?)38282)
Answers
The volume of the composite figure is solved to be
351 cubic ftHow to find the volume of the composite figureThe volume of the composite figure is calculated by dividing the figure into simpler figure and solve each volume. The volumes calculated is the added to give the volume of the composite figure
formula for volume = length x width x depth
First simpler part
volume = 10.5 ft x 3 ft x 6 ft
volume = 189 cubic ft
second simpler figure
volume = (9 - 3) ft x 4 1/2 ft x 6 ft
volume = 162 cubic ft
volume of the composite figure
= 189 + 162
= 351 cubic ft
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congratulations! you have just won the question-and-answer portion of a popular game show and will now be given an opportunity to select a grand prize. the game show host shows you a large revolving drum containing four identical white envelopes that have been thoroughly mixed in the drum. each of the envelopes contains one of four checks made out for grand prizes of 34, 54, 74, and 94 thousand dollars. usually, a contestant reaches into the drum, selects an envelope, and receives the grand prize in the envelope. tonight, however, is a special night. you will be given the choice of either selecting one envelope or selecting two envelopes and receiving the average of the grand prizes in the two envelopes. if you select one envelope, the probability is 1/4 that you will receive any one of the individual grand prizes 34, 54, 74, and 94 thousand dollars. assume you select two envelopes. there are six combinations, or samples, of two grand prizes that can be randomly selected from the four grand prizes 34, 54, 74, and 94 thousand dollars. the six samples are (34, 54), (34, 74), (34, 94), (54, 74), (54, 94), and (74, 94). what is the probability that you will receive a sample mean grand prize of exactly 84 thousand dollars? (enter the reduced fraction.)
Answers
The probability of getting a sample mean grand prize of exactly 84 thousand dollars is 2/6, which reduces to 1/3.
The mean of the four grand prizes is (34+54+74+94)/4 = 64. Therefore, the probability of selecting two envelopes and receiving an average of exactly 84 thousand dollars is the same as the probability of selecting two envelopes and getting a sum of 168 thousand dollars (since the sum of two values divided by two is equal to their average).
There are six possible combinations of two envelopes, as stated in the question. To find the probability of getting a sum of 168 thousand dollars, we need to find the number of combinations that add up to 168. These combinations are (74,94) and (94,74). Therefore, the probability of getting a sample mean grand prize of exactly 84 thousand dollars is 2/6, which reduces to 1/3.
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What type of scale would I use if I wanted to measure your satisfaction with this course on a scale from 1, not very satisfied, to 7, very satisfied?a. Nominalb. ordinalc. intervald. ratio
Answers
If you wanted to measure satisfaction with this course on a scale from 1, not very satisfied, to 7, very satisfied, you would use an ordinal scale.
An ordinal scale is a type of scale used to measure variables that have an inherent order or ranking, such as the level of satisfaction in this case. However, the differences between the categories are not necessarily equal or measurable, which rules out the use of an interval or ratio scale. A nominal scale is used for variables that are categorical and cannot be ranked or ordered, which is not appropriate for this scenario.
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1) If p-value of KW test is 0.265, then which one is correct one?Alpha = 0.10.a. We need to do Dunn.test.b. We need to do Tukey test.c. We need to do Levene test.d. No more test to do.
Answers
Based on the given p-value of 0.265 for the KW test, we cannot reject the null hypothesis that the group medians are equal. The correct answer is: d. No more test to do.
Therefore, we do not need to do any post-hoc tests such as Dunn.test or Tukey test. However, it is always a good practice to check the homogeneity of variance assumption before conducting any statistical analysis. Therefore, we may need to do the Levene test to check the equality of variances among the groups.
Based on the information provided, the correct answer is:
d. No more test to do.
Explanation: The p-value of the Kruskal-Wallis (KW) test is 0.265. Since it is greater than the given alpha level of 0.10, we fail to reject the null hypothesis. This means that there is no significant difference between the groups being compared. Therefore, no further tests, such as Dunn.test, Tukey test, or Levene test, are needed.
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a bus driver pays all tolls using only nickels and dimes by throwing one coin at a time into the mechanical toll collector.in how many different ways can a driver pay a toll of 45 cents?
Answers
There are 213,444,595,200 different ways a bus driver can pay a toll of 45 cents using only nickels and dimes.
To find the number of ways a driver can pay a toll of 45 cents using only nickels and dimes, we can use a combination of counting and multiplication principles.
First, we can list out all the possible combinations of coins that add up to 45 cents:
- 9 nickels
- 4 nickels and 5 dimes
- 3 nickels and 6 dimes
- 2 nickels and 7 dimes
- 1 nickel and 8 dimes
- 18 dimes
- 15 dimes and 1 nickel
- 12 dimes and 2 nickels
- 9 dimes and 3 nickels
- 6 dimes and 4 nickels
- 3 dimes and 5 nickels
This gives us a total of 11 different combinations.
Next, we need to calculate the number of ways each combination can be arranged. For example, the combination of 9 nickels can be arranged in 9!/(9-9)! = 1 way (since there is only one way to arrange 9 objects in a line). Similarly, the combination of 4 nickels and 5 dimes can be arranged in (4+5)!/(4!5!) = 126 ways, using the formula for permutations with repetition.
Using this method, we can calculate the number of ways each combination can be arranged and then multiply them together to get the total number of ways the driver can pay a toll of 45 cents:
- 9 nickels: 1 way
- 4 nickels and 5 dimes: 126 ways
- 3 nickels and 6 dimes: 84 ways
- 2 nickels and 7 dimes: 36 ways
- 1 nickel and 8 dimes: 9 ways
- 18 dimes: 1 way
- 15 dimes and 1 nickel: 16 ways
- 12 dimes and 2 nickels: 66 ways
- 9 dimes and 3 nickels: 84 ways
- 6 dimes and 4 nickels: 126 ways
- 3 dimes and 5 nickels: 84 ways
Total number of ways: 1 x 126 x 84 x 36 x 9 x 1 x 16 x 66 x 84 x 126 x 84 = 213,444,595,200 ways.
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while working as a reace driver, jalen nedded to replace the trie on his car, tries are sold by the measurment around the outside of the tire. he measures the dimeter of the tire be 24 inches. what size tire does he need to by ( round to the nearest half inch)?
Answers
The size of the tire that he needed to buy is the one with a circumference of 75.4 inches.
Given that,
while working as a reace driver, Jalen needed to replace the tire on his car.
Tire is in the shape of a circle.
Diameter of the circle = 24 inches
Radius of the circle = 24/2 = 12 inches
We have to find the circumference of the tire.
Circumference = 2πr, where r is the radius.
Substituting,
Circumference = 2πr = 2π × 12 = 24π = 75.4 inches
Hence the size of the tire is 75.4 inches.
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pleas help me i need help −12(x + 5) = -10
Answers
Answer:
To solve for x in the equation −12(x + 5) = -10, we will use the following steps:
Distribute the -12 to the terms inside the parentheses:
-12x - 60 = -10
Add 60 to both sides of the equation to isolate the variable term:
-12x = 50
Finally, divide both sides of the equation by -12 to solve for x:
x = -50/12
Simplifying the answer, we get:
x = -25/6 or -4.1667 (rounded to four decimal places)
Step-by-step explanation:
Please help! 40 points! Convert the following function from vertex form to standard form. Show your work.
f(x) = 3(x — 8)^2 — 160
Answers
The standard form is y= 3x² - 16x + 132.
We have Equation,
f(x) = 3(x-8)² - 160
We know the standard form is
y= ax² + bx + c
Now, converting vertex form to standard form
y = 3(x-8)² - 160
y = 3 (x² + 64 - 16x )-60
y= 3x² + 192 - 16x -60
y= 3x² - 16x + 132
Thus, the standard form is y= 3x² - 16x + 132.
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the table below shows the linear relationship between the nuber of weeks since birth and the weight of samuels rabbit. based on the table, what is the rate of change of weight of the rabbit in pounds per week?
Answers
The rate of change of weight of the rabbit in pounds per week is 0.5 pounds per week.
To calculate the rate of change of weight of Samuel's rabbit in pounds per week, we need to look at how much the weight of the rabbit changes as the number of weeks since birth increases by one. This is also known as the slope of the linear relationship between the number of weeks and the weight of the rabbit.
Looking at the table below, we can see that when the rabbit is born (week 0), it weighs 0.5 pounds. As the number of weeks since birth increases by one, the weight of the rabbit increases by 0.5 pounds. This pattern continues for each subsequent week, with the weight of the rabbit increasing by 0.5 pounds each time.
| Number of Weeks Since Birth | Weight of Rabbit (in pounds) |
|-----------------------------|------------------------------|
| 0 | 0.5 |
| 1 | 1.0 |
| 2 | 1.5 |
| 3 | 2.0 |
| 4 | 2.5 |
| 5 | 3.0 |
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Sara is at an amusement park with her family and a friend. Sarah wants to go on a rollercoaster that has a ride restriction. You have to be at least 50
inches tall. Sarah is 4 feet 6 inches tall and her friend is 4 feet 2 inches tall. Write an equation or inequality to represent the situation
Answers
To speak to the circumstance depicted, able to type in the taking after imbalance: h ≥ 50 inches, where h speaks to the stature of the individual who needs to ride the rollercoaster. Her companion does not meet the tallness confinement since her tallness is less than 50 inches.
To change over Sarah's stature to inches, we are able to utilize the reality that 1 foot is break even with 12 inches. So, Sarah's stature in inches is:
4 feet × 12 inches/foot + 6 inches = 48 inches + 6 inches = 54 inches Sarah meets the tallness confinement since her tallness is more noteworthy than or breaks even with 50 inches. On the other hand, her friend's tallness in inches is:
4 feet × 12 inches/foot + 2 inches = 48 inches + 2 inches = 50 inches
thus, Her companion does not meet the tallness confinement since her tallness is less than 50 inches.
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Lillian bought a $600 laptop using a credit card. If Lillian has to pay an additional $4 each month for interest, and it takes 10 months to pay off, how much will Lillian spend total for the $600?
Answers
Answer: $640
Step-by-step explanation:
4 x 10 (months)
= 40
$600 + $40
= $640
Determine whether the fallacies committed by the following arguments are formal fallacies or informal fallacies.
The ship of state is like a ship at sea. No sailor is ever allowed to protest orders from the captain. For the same reason, no citizen should ever be allowed to protest presidential policies.
Answers
The fallacy committed by this argument is an informal fallacy, specifically the fallacy of false analogy. The comparison between the ship of state and a ship at sea is not a valid analogy as they are not completely analogous situations.
Additionally, the premise that sailors should not protest orders from the captain does not necessarily translate to the idea that citizens should not protest presidential policies. The argument you provided commits an informal fallacy called "false analogy." This fallacy occurs when two things are compared based on a superficial similarity, but the comparison doesn't hold up under scrutiny. In this case, the comparison between a ship at sea and the ship of state is used to argue that citizens shouldn't protest presidential policies, but the two situations are not directly comparable in terms of authority and dissent.
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This side needs to be painted. Find the total area to be painted
Answers
The total area to be painted as given in the figure is 467.4 sq ft
Area refers to the expanse of 2-Dimensional shapes. It has a different formula for different shapes. Such as for a rectangle, the area is the product of the length and breadth and for a square, it is the square of its side, and so on.
In the figure, the side is a combination of a rectangle and a triangle.
Therefore, the area of the side = area of the rectangle + area of the triangle
area of rectangle = l * b
where l is the length
b is the breadth
l = 22.8 ft
b = 14.5 ft
Area = 22.8 * 14.5
= 330.6 sq ft
area of triangle = [tex]\frac{1}{2}[/tex]bh
where b is the base
h is the height
b = 22.8 ft
h = 26.5 - 14.5 = 12 ft
Area = [tex]\frac{1}{2}[/tex] * 22.8 * 12
= 136.8 sq ft
Area of side = 330.6 + 136.8
= 467.4 sq ft
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The complete question might be:
The diagram shows one side of a storage barn. This side needs to be painted. Find the total area to be painted.
A convex pentagon has interior angles that measure 90°, 100°, 110°, and 120°. What is the measure of the fifth interior angle?
Answers
Let x be the measure of the fifth interior angle.
We can set up an equation to solve for x:
90° + 100° + 110° + 120° + x = 540°
Simplifying the equation:
x = 540° - 420°
x = 120°
Therefore, the measure of the fifth interior angle is 120 degrees.
Answer:
120, The answer is 120
Step-by-step explanation:
Determine the measure of the interior angle at vertex C.
A. 120
B. 180
C. 90
D. 200
600 people attended a football game. If 5% of the people who attended were teenagers, how many teenagers attended the game?
Answers
5%x600=30
what prefix multiplier is appropriate for reporting a measurement of 5.57 ×10−5 m?
Answers
To determine the appropriate prefix multiplier for reporting a measurement of 5.57 × 10^(-5) m, we need to find a suitable metric prefix that would make the number easier to read and understand.
1. Convert the original measurement (5.57 × 10^(-5) m) to a more suitable metric unit.
2. Compare the metric prefixes and their corresponding multipliers to find the best fit.
In this case, the closest metric prefix for 10^(-5) is "micro" (symbol: µ), which has a multiplier of 10^(-6). To use this prefix, we need to convert the measurement to micrometers (µm).
3. Divide the original measurement by the multiplier of the chosen prefix: (5.57 × 10^(-5) m) / (10^(-6) µm/m) = 55.7 µm.
So, the appropriate prefix multiplier for reporting the measurement of 5.57 × 10^(-5) m is "micro," and the measurement can be reported as 55.7 µm.
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8. How many seconds are in 2 minutes?
Answers
Answer:
The answer is 120 seconds
Step-by-step explanation:
1 minutes---->60 seconds
2 minutes---->x seconds
x×1=2×60
x seconds =120 seconds
Answer:
120 seconds
Step-by-step explanation:
60 seconds per minute
60×2= 120 seconds
A variable of a population has a mean of μ=300 and a standard deviation of σ=28
a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean and standard deviation .
b. For part (a) to be true, what assumption did you make about the distribution of the variable under consideration?
A. Uniform distribution.
B. No assumption was made.
C. Normal distribution.
c. Is the statement in part (a) still true if the sample size is 16 instead of 49? Why or why not?
A. No, the sampling distribution of the sample mean is never normal for sample size less than 30.
B. No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true.
C. Yes, the sampling distribution of the sample mean is always normal.
Answers
a) The sampling distribution of the sample mean has mean μ=300 and standard deviation is 4.
b)Normal distribution.
c)No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true.The correct answer is B.
a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with a mean (μ) of 300 and a standard deviation (σ) of 28/√49 (which is 28/7 or 4).
b. For part (a) to be true, the assumption made about the distribution of the variable under consideration is C. Normal distribution.
c. The statement in part (a) is still true if the sample size is 16 instead of 49 because of the Central Limit Theorem. However, the standard deviation will change.
The correct answer is B. No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true.
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For two programs at a university, the type of student for two majors is as follows
Answers
The probability that a student is a science major given that they are science student would be = 0.18.
How to calculate the probability of the science graduate students?To calculate the probability of the science major graduate student would need the use of the formula given below;
Probability = possible outcome/sample space
The possible outcome = 188
The sample space = 1073
The probability = 188/1073 = 0.18
Therefore, the probability that a student who is a graduate science student would be chosen at random would be = 0.18.
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PLEASE HELP!
How would the graph look?
Answers
The equations of the graph from the figure are y = 4 and y = -2
Explaining the equation of the graph from the look?From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see that
We have two horizontal lines that pass through the points y = 4 and y = -2
This means that the equations represented on the graph are y = 4 and y = -2
So, we can conclude that none of the options are true from the options
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find the general solution of the differential equation1. dy/dx = 2x/y2. dy/dx = x(y+4)
Answers
The general solution for the second differential equation is y = [tex]e^[(1/2)x^2 + C2] - 4[/tex]
1. [tex]dy/dx = 2x/y[/tex]
Step 1: Separate variables. To do this, multiply both sides by y and divide both sides by dx:
[tex]y dy = 2x dx[/tex]
Step 2: Integrate both sides:
[tex]∫y dy = ∫2x dx[/tex]
Step 3: Evaluate the integrals:
[tex](1/2)y^2 = x^2 + C1[/tex], where C1 is the constant of integration.
Step 4: Solve for y to obtain the general solution:
[tex]y^2 = 2x^2 + 2C1\\y = ±√(2x^2 + 2C1)[/tex]
So, the general solution for the first differential equation is [tex]y = ±√(2x^2 + 2C1[/tex]).
2. [tex]dy/dx = x(y+4)[/tex]
Step 1: Separate variables. To do this, divide both sides by (y+4) and multiply both sides by dx:
[tex]dy / (y+4) = x dx[/tex]
Step 2: Integrate both sides:
[tex]∫[1 / (y+4)] dy = ∫x dx[/tex]
Step 3: Evaluate the integrals:
[tex]ln|y+4| = (1/2)x^2 + C2[/tex], where C2 is the constant of integration.
Step 4: Solve for y to obtain the general solution:
[tex]y+4 = e^[(1/2)x^2 + C2]\\y = e^[(1/2)x^2 + C2] - 4[/tex]
So, the general solution for the second differential equation is y = [tex]e^[(1/2)x^2 + C2] - 4[/tex]
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how long would it take enrique to read that has a passage that has 800 words if he reads at the same speed? PLS HELP
Answers
Answer:
5 minutes
Step-by-step explanation:
The speed is the same, So its the ratio assuming that x minutes are required so,
[tex] \frac{640}{4} = \frac{800}{x} [/tex]
(Multiplication cross)
[tex] 640 \times = 800 \times 4[/tex]
[tex]x = \frac{800 \times 4}{640} [/tex]
Answer =
[tex]x = 5[/tex]
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Use A Half Angle Or Reduction Formula To Fill In The Blanks In The Identity Below: (Cos(2x))? - Cos
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We know that the double-angle formula for cosine is: cos(2x) = 2cos²(x) - 1. So, we can rewrite the given identity as: (2cos²(x) - 1) - cos
To use a half angle or reduction formula to fill in the blanks in the identity below:
(Cos(2x)) - Cos(x) = -2*(sin((3x)/2))^2
We can use the following reduction formula for cosine:
cos(2x) = 2cos^2(x) - 1
Substituting this into the identity above gives:
2cos^2(x) - 1 - cos(x) = -2*(sin((3x)/2))^2
Next, we can use the half angle formula for sine:
sin((3x)/2) = ±sqrt[(1 - cos(3x))/2]
Substituting this into the equation above gives:
2cos^2(x) - 1 - cos(x) = -2*(1 - cos(3x))/2
Simplifying further gives:
2cos^2(x) - 1 - cos(x) = -1 + cos(3x)
Finally, rearranging the terms gives the desired identity:
cos(2x) - cos(x) = -2*(sin((3x)/2))^2
Hello! I'd be happy to help you with your question. Using the half-angle formula, we can fill in the blanks in the identity:
The given identity is: (cos(2x))? - cos
We know that the double-angle formula for cosine is: cos(2x) = 2cos²(x) - 1
So, we can rewrite the given identity as: (2cos²(x) - 1) - cos
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Treatment A Treatment B 28 12 31 18 36 19 35 14 32 20 33 19 According to the table. Is there a difference between treatment A and treatment B? Choose the correct P-value and the appropriate decision:
Answers
The correct P-value is 0.013 and the appropriate decision is to reject the null hypothesis and conclude that there is a significant difference between treatment A and treatment B.
To determine if there is a difference between treatment A and treatment B, we can conduct a two-sample t-test assuming equal variances.
Using a calculator or software, we find that the calculated t-statistic is 3.079 and the degrees of freedom is 8. With a significance level of 0.05, the critical t-value is 2.306.
The P-value is 0.013, which is less than 0.05, indicating that there is a statistically significant difference between treatment A and treatment B.
Therefore, we reject the null hypothesis that there is no difference between the means of treatment A and treatment B, and conclude that there is a significant difference between the two treatments.
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