find the taylor series for f centered at 4 if f (n)(4) = (−1)nn! 3n(n 1) . [infinity] n = 0 what is the radius of convergence r of the taylor series?
Answers
Answer:
The radius of convergence (r) is 1/6.
Step-by-step explanation:
To determine the Taylor series for the function f centered at 4, we need to get its derivatives and evaluate them at x = 4
.Let's start by finding the derivatives of f:
f'(x) = (-1)^1 * 1! * 3(1)(1 - 1) = 0f''(x)
= (-1)^2 * 2! * 3(2)(2 - 1)
= 12f'''(x)
= (-1)^3 * 3! * 3(3)(3 - 1)
= -108f''''(x)
= (-1)^4 * 4! * 3(4)(4 - 1)
= 432
Continuing this pattern, we can get the nth derivative:f^(n)(x) = (-1)^n * n! * 3n(n - 1).
Now, let's evaluate these derivatives at x = 4:
f(4) = f^(0)(4)
= (-1)^0 * 0! * 3(0)(0 - 1)
= 0f'(4)
= f^(1)(4)
= 0f''(4)
= f^(2)(4)
= 12f'''(4)
= f^(3)(4)
= -108f''''(4)
= f^(4)(4)
= 432
We can see that all the odd derivatives evaluate to zero at x = 4.
Next, we can express the Taylor series for f centered at 4 as follows:
f(x) = f(4) + f'(4)(x - 4)^1 + f''(4)(x - 4)^2 + f'''(4)(x - 4)^3 + ...
Since all the odd derivatives evaluate to zero at x = 4, we can simplify the Taylor series as:
f(x) = 0 + 0 + 12(x - 4)^2 + 0 + 432(x - 4)^4 + ...
Simplifying further, we have:
f(x) = 12(x - 4)^2 + 432(x - 4)^4 + ...
The radius of convergence (r) of the Taylor series can be determined using the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is L, then the series converges if L < 1 and diverges if L > 1.
In our case, the ratio of consecutive terms is:
L = lim(n->∞) |a(n+1) / a(n)|
For the Taylor series of f, the terms are:
a(n) = 12(x - 4)^2 for even values of na(n) = 432(x - 4)^4 for even values of n
Taking the absolute value of the ratio of consecutive terms and simplifying, we have:
L = lim(n->∞) |432(x - 4)^4 / 12(x - 4)^2|L
= lim(n->∞) |36(x - 4)^2|
The limit depends on the value of (x - 4)^2.
For the series to converge, we need |36(x - 4)^2| < 1. This means that the absolute value of (x - 4)^2 must be less than 1/36.
Therefore, the radius of convergence (r) is 1/6.The Taylor series for f centered at 4 is:f(x) = 12(x - 4)^2 + 432(x - 4)^
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Related Questions
ITEM 14 - from the lesson Modeling with Linear Inequalities
Catherine is practicing math and science questions to prepare for her upcoming exams. It takes her 12 minutes to do a math question and 5 minutes to answer a science question.
Among the following options, which one should she choose if she wants to spend less than an hour practicing?
Hint: Set up an equation to represent the scenario. Here is how you should set your equation up.
A. 3 math questions and 5 science questions
B. 2 math questions and 7 science questions
C.5 math questions and 1 science question
D.4 math questions and 3 science questions
Answers
The option she should choose based on the given condition is Option B 2 math questions and 7 science questions.
What are linear inequalities?
When two linear expressions are compared using the inequality symbols, that is an expression of a linear inequality.
Given, Time is taken for solving single math question = 12 minutes
Time is taken for solving single science question = 5 minutes
Let 'x' be the total number of math questions and 'y' be the total number of science questions.
Then,
The total time taken for 'x' math questions = 12x minutes
The total time taken for 'y' science questions = 5y minutes
So, as defined in the question, we get
Total time she wants to spend practicing < 60 minutes
i. e. 12x + 5y < 60 .................... (i)
Now, we check this condition for each answer choice
A) x = 3 and y = 5, substituting values in equation (i)
So, 12*3 + 5*5 < 60
or, 36+25 < 60
or, 61 < 60 (Not valid)
B) x = 2 and y = 7, substituting values in equation (i)
So, 12*2 + 5*7 < 60
or, 24+35 < 60
or, 59 < 60 (Valid)
So, Option B is valid.
Hence, the required answer of choice is Option B i.e. 2 math questions and 7 science questions.
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(y^11)(y^2)^8 + y^x what is the value of x?
Answers
Using derivatives+optimization, find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side 12.
Answers
Check the picture below atop.
we know is an equilateral triangle, meaning that all its interior angles are 60°, and thus if we run a line from the top vertex as you see there, we end up with a 30-60-90 triangle, either way there's an equation to get its height, and anyhow the altitude of it is 6√3.
As the rectangle moves up and down the triangle, with the rectangle having a width of "w" and a length of "L", the triangle that it forms above itself is a triangle, always with a base of "L" and a height of 6√3 - w.
BTW we laid the rectangle as you see on the bottom side, but laying it anywhere else it'd have ended up in the same arrangement.
well, with the bottom of the rectangle beign parallel to that of the side of the circumscribing triangle, the small upper triangle is similar to the containing triangle by AAA, and since we have similar triangles, we can say that.
\(\cfrac{6\sqrt{3}}{12}=\cfrac{6\sqrt{3}-w}{L}\implies \cfrac{\sqrt{3}}{2}=\cfrac{6\sqrt{3}-w}{L}\implies L\sqrt{3}=12\sqrt{3}-2w \\\\\\ L=\cfrac{12\sqrt{3}-2w}{\sqrt{3}}\implies L=12-\cfrac{2w}{\sqrt{3}}\implies L=2\left(6-\cfrac{w}{\sqrt{3}} \right) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Area of the rectangle}}{A=wL\implies A(w)=w\cdot 2\left(6-\cfrac{w}{\sqrt{3}} \right)}\implies A(w)=2\left(6w-\cfrac{w^2}{\sqrt{3}} \right)\)
\(\cfrac{dA}{dw}=2\left(6-\cfrac{2w}{\sqrt{3}} \right)\implies \cfrac{dA}{dw}=4\left(3-\cfrac{w}{\sqrt{3}} \right) \\\\[-0.35em] ~\dotfill\\\\ 0=4\left(3-\cfrac{w}{\sqrt{3}} \right)\implies \boxed{w=3\sqrt{3}}\)
hmmm the way I usually run a 1st derivative test is, by using the critical point and slicing from it just a tiny bit, like say 3√3 - 0.000000001 to check the region on the left and then 3√3 + 0.000000001 to check the region on the right.
Check the picture at the bottom, the 1st derivative test more or less gives us those values, positive on the left-side and negative on the right-side, meaning as you can see in the arrows, is a maximum at that point.
\(\stackrel{\textit{we know that}}{L=2\left(6-\cfrac{w}{\sqrt{3}} \right)}\implies L=2\left(6-\cfrac{3\sqrt{3}}{\sqrt{3}} \right)\implies \boxed{L=6}\)
3. XY has an equation of x = 8. What is the equation, in point-slope form, of a line that is
perpendicular to XY and passes through (6, 9)?
(i'm looking for an explanation)
Answers
Answer: y=9
Step-by-step explanation:
Plug in (6,9) into the slope intercept form equation:
9=0(6) +b
Then get
9=b
When you make the equation you would end up with:
y=0x+9
which simplifies to y=9
To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?
Answers
Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.
Identify the linear equation?Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12
We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.
Take the provided linear equation system into consideration.
3x - 2y = 4 ................(1)
9x - 6y = 12 ..................(2)
Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12
The slopes of the provided equations are also same.
Difference with regard to x for equation (1) yields,
additional to equation (2),
With regard to x, we can differentiate to get,
The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.
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answer the questions below about the following function
what is the domain of f(x)
what is the range of f(x)
what is the x-intercept of f(x)? enter your answer as an ordered pair. if no x-intercept exists, enter none
what it the equation of the vertical asymptote
Answers
Domain of the function is, (0, ∞).
Range of the function is, (-∞, ∞).
x - intercept of the function is, (1, 0).
Vertical asymptote of the function is, None.
What is domain and range?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
First to find the domain of the function,
Since, all input values shown on the x-axis make up a graph's domain.
We can see that values of x values are from 0 to ∞.
Hence, the domain is (0, ∞).
Now to find the range.
Since, the y-axis on a graph represents the possible output values, or range.
The y - axis having the values from -∞ to ∞.
Hence, the range of the function is, (-∞, ∞).
x - intercept is the point where function crosses the x - axis.
Here function crosses x - axis at (1, 0).
Hence, the x - intercept is (1, 0).
A graph's vertical asymptote is the vertical line at x = a where the graph trends toward positive or negative infinity as the inputs go closer to a.
So, the vertical asymptote is x = 0.
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how are we supposed to do this?
Answers
make a plotting graph and use the x and y axis and make little point :) hope this helps
Answer:
What math class is this?
Step-by-step explanation:
for each of the following systems, find the fixed points, classify them, sketch the neighboring trajectories, and try to fill in the rest of the phase portrai
Answers
Finding the fixed points, classifying them, sketching the neighboring trajectories, and filling in the rest of the phase portrait can help us understand the behavior of a dynamical system and make predictions.
To find the fixed points of a system, we need to solve for the values of the variables that make the derivatives equal to zero. Once we have found the fixed points, we can classify them by analyzing the sign of the derivatives near each point. If the derivatives are positive on one side and negative on the other, then the fixed point is unstable, meaning nearby trajectories will move away from it. If the derivatives are negative on both sides, then the fixed point is stable, meaning nearby trajectories will move towards it. If the derivatives are zero on one side and positive or negative on the other, then the fixed point is semi-stable or semi-unstable, respectively.
Once we have classified the fixed points, we can sketch the neighboring trajectories by analyzing the sign of the derivatives along those trajectories. If the derivatives are positive, then the trajectory will move in the positive direction, and if they are negative, then it will move in the negative direction. By sketching the neighboring trajectories, we can get a sense of how the system behaves in different regions of the phase space.
Finally, we can try to fill in the rest of the phase portrait by looking for other features such as limit cycles, separatrices, or regions of phase space where trajectories diverge or converge.
Overall, finding the fixed points, classifying them, sketching the neighboring trajectories, and filling in the rest of the phase portrait can help us understand the behavior of a dynamical system and make predictions about its future evolution.
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write the sum 16 25 36 49 64 81 100 12116 25 36 49 64 81 100 121 using sigma notation. the form of your answer will depend on your choice of the lower limit of summation.
Answers
We can write the terms in sigma notation as follows; ∑n=4¹¹n²I.
Given terms are 16, 25, 36, 49, 64, 81, 100, 121. We can write these terms in sigma notation as follows; ∑n=4¹⁵⁰n² - 16 25 36 49 64 81 100 121.
We can observe that the above terms are square of natural numbers starting from 4 to 11.Thus, we can write the terms in sigma notation as follows; ∑n=4¹¹n²I
Sigma notation, also known as summation notation, is a concise way to represent the sum of a sequence of terms. It uses the Greek letter sigma (∑) to denote the sum and provides a compact form for writing mathematical series.
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Marian Plunket owns her own business and is considering an investment. if she undertakes the investment, it will pay $28,000 at the end of each of the new 3 years. the opportunity requires an initial investment of $7,000 plus an additional investment at the end of the second year of $35,000. what is the NPV of this opportunity if the interest rate is 8% per year? Should Marian take it?
Answers
The NPV is positive, it is worth taking the Investment.
Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.
This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:
NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.
The given problem can be solved by using the following steps:
Calculate the present value (PV) of the expected cash inflows:
Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82
Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39
Since the NPV is positive, it is worth taking the investment.
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what is the value of s?
____ units
Answers
Answer:
s = 17
Step-by-step explanation:
a^2+b^2=c^2
a=8, b=15, c=s
64+225=c^2
289 =c^2
c= 17
Answer:
What are the choices
Step-by-step explanation:
American ladybugs have an average adult length of 1 cm with a known standard deviation of 0.2 cm. The population of American ladybugs in Raleigh was around 440000 last spring. Assume a normal distribution for the lengths of adult American ladybugs. Your niece asks you what's the probability of a random ladybug in Raleigh being bigger than 1.5 cm. Is it appropriate to calculate this probability? Select one:
a. No, because the population distribution is skewed. b. No, because the sample size is less than 30. c. No, because the empirical rule is violated.
Answers
Therefore, probability solution is estimating this likelihood without additional data or analysis is inappropriate correct response is option a.
What exactly does the probability entail?The main goal of the mathematical branch known as statistical inference is to estimate the likelihood that a statement is accurate or that a particular event will take place. Any number among 0 and 1, where 1 typically denotes confidence and 0 typically denotes possibility, can be used to symbolise chance. A probability diagram illustrates the likelihood that a particular occurrence will take place.
Here,
Because of the skewed demographic distribution, the right response is (a).
We could use the normally distributed to compute probabilities because the length of adult American ladybirds is distributed normally with a known standard deviation. The normal distribution may not, however, correctly depict the distribution of ladybird lengths in the population due to the skewed population distribution.
Furthermore, even if the difference between the actual community mean and the assumed mean of 1 cm is tiny, the given size of the population of 440000 could result in a statistically significant outcome.
However, because the assumption of normality may not hold true, this does not imply that we can accurately determine the likelihood of a random ladybird in Raleigh being larger than 1.5 centimetres.
Therefore, estimating this likelihood without additional data or analysis is inappropriate.
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Vivienne noticed a metal object lying by the railroad tracks. She believes the object may have originally been a copper penny that was run over by a train. What information about the metal object would be most useful in determining if her hypothesis is correct
Answers
The information about the metal object that would be most useful in determining if Vivienne's hypothesis is correct is its density. Therefore, the correct option is D.
This is because density is a measure of an object's mass relative to its volume. Since density is an intrinsic property of the material from which the object is made, it can help determine what type of metal the object is. Furthermore, since copper has a relatively high density, knowing the density of the metal object can help determine whether or not it is made of copper.
Density is a physical property that describes the mass per unit volume of a substance. The term density is used to describe the mass of an object per unit volume. The formula for calculating density is:
Density = mass/volume
Therefore, to determine whether the object is a copper penny that was run over by a train, we need to determine its density. Hence, the correct answer is option D.
Note: The question is incomplete. The complete question probably is: Vivienne noticed a metal object lying by the railroad tracks. She believes the object may have originally been a copper penny that was run over by a train. What information about the metal object would be most useful in determining if her hypothesis is correct? A. its mass B. its texture C. its volume D. its density.
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Nikki works at a store that sells consumer electronics. She earns $12 per hour, plus a commission of 5% of her total sales amount each day. Nikki worked 8 hours on Saturday. Including her commission, Nikki earned a total of $139 on Saturday. Which equation can be solved for x, Nikki’s total sales amount in dollars on Saturday?
Answers
Answer:
See below.
Step-by-step explanation:
So, Nikki earns $12 per hour.
And she also earns a 5% or 0.05 commission of her total sales each day.
On Saturday, she worked eight hours and she earned $139. In other words, she earned 8(12) or $96 from working her hours and another $43 (139-96) from her commission.
Thus:
\(139=96+0.05x\)
Where x represents Nikki's total sales on Saturday.
Further notes:
To solve, subtract 96 from both sides and divide by 0.05:
\(139=96+0.05x\\43=0.05x\\x=\$860\)
Thus, her total sales that day were $860.
time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 8 min and standard deviation 4 min. if five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min?
Answers
The probability that the sample average amount of time taken on each day is at most 11 min is 0.210.
Given data,
The time it takes a randomly chosen mortgage applicant to complete a certain form has a normal distribution with a mean value of 8 minutes and a standard deviation of 4 minutes. What is the likelihood that the sample average time taken on each day is at most 11 minutes if five people complete out a form on one day and six on another?
The normal distribution is a continuous distribution of data that has a bell-shaped curve. The normally distributed random variable x has to mean μ and standard deviation σ.
Also, the standard normal distribution represents a normal curve with a mean of 0 and a standard deviation of 1. Thus, the parameters involved in a normal distribution are mean μ and standard deviation σ.
Standardized z-score:
The standardized z-score represents the number of standard deviations the data point is away from the mean.
→ If the z-score takes a positive value when it is above the mean (0).
→ If the z-score takes a negative value when it is below the mean (0).
Let,
X ~ N = [x,σ/√n]
z = X - μ/ σ/√n
The probability that the sample average amount of time taken on each day is at most 11 min is obtained below,
From the given information, the sample size for the first day is 5 and the sample size for the second day is 6.
P(X ≤ 11 and Y ≤ 11) = P(X ≤ 11) * P(Y ≤ 11)
= P(z ≤ 1.67) * P(z ≤ 1.83)
= 0.452 * 0.466
= 0.210
Hence, the probability that the sample average amount of time taken on each day is at most 11 min is 0.210.
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Solve the question below.
Answers
The feet that he descended in 8 hours will be 135168 feet.
How to calculate the value?From the information, it was stated that the the hiker hikes at a rate of 3.2 miles per hour.
Therefore, the number of miles after 8 hours will be:
= 8 × 3.2
= 25.6 miles
It should be noted that 1 mile = 5280 foot
Therefore, this will be:
= 25.6 × 5280
= 135168 feet
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wht is 700000x4864493-490
Answers
Answer:
3.4051451e+12
Step-by-step explanation:
:/
Answer:
3.40515e12
Step-by-step explanation:
Given P(A) = 0.2, P(B) = 0.7, P(A | B) = 0.5, do the following.
(a) Compute P(A and B).
(b) Compute P(A or B).
Answers
(a) The probability of both events A and B occurring simultaneously, P(A and B), is 0.35.
(b) The probability of either event A or event B occurring, P(A or B), is 0.55.
(a) To compute P(A and B), we need to find the probability of both events A and B occurring simultaneously. We are given P(A | B) = 0.5, which represents the probability of event A occurring given that event B has occurred. This information indicates that there is a 50% chance of event A happening when event B has already occurred.
We are also given P(B) = 0.7, which represents the probability of event B occurring. Combining this with the conditional probability, we can calculate P(A and B) using the formula: P(A and B) = P(A | B) * P(B).
Substituting the given values, we have P(A and B) = 0.5 * 0.7 = 0.35. Therefore, the probability of both events A and B occurring simultaneously is 0.35.
(b) To compute P(A or B), we need to find the probability of either event A or event B occurring. We already know P(A) = 0.2 and P(B) = 0.7.
However, we need to be careful not to double-count the intersection of A and B. To avoid this, we subtract the probability of the intersection (P(A and B)) from the sum of the individual probabilities. The formula to calculate P(A or B) is: P(A or B) = P(A) + P(B) - P(A and B).
Substituting the given values, we have P(A or B) = 0.2 + 0.7 - 0.35 = 0.55. Therefore, the probability of either event A or event B occurring is 0.55.
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Arrange the following lines to make a program that determines when the number of people in a restaurant equals or exceeds 10 occupants. The program continually gets the number of people entering or leaving the restaurant. Ex: 2 means two people entered, and -3 means three people left. After each input, the program outputs the number of people in the restaurant. Once the number of people in the restaurant equals or exceeds 10, the program exits. If an InputMismatchException exception occurs, the program should get and discard a single string from input. Ex: The input "2 abc 8" should result in 10 occupants. Not all lines are used in the solution.
Answers
Here is a possible program that meets the requirements: import java.util.Scanne imporjava.util.InputMismatchException; public class RestaurantOccupancy {
public static void main(String[] args) {
Scanner input = new Scanner(System.in);
int occupancy = 0;
The program starts by importing the Scanner and InputMismatchException classes from the java.util package.
In the main method, we declare a Scanner object named input and an integer variable named occupancy initialized to 0.
The program enters a while loop that continues as long as the occupancy is less than 10. Inside the loop, we prompt the user to enter the number of people entering or leaving the restaurant, read the input as an integer using input.nextInt(), and store it in a variable named delta.
We then add delta to the occupancy variable to update the current occupancy, and print it to the console using System.out.println(). If an InputMismatchException is thrown (i.e., the user enters a non-integer value), we catch the exception, read the next token as a string using input.next(), and print an error message to the console.
Once the occupancy reaches or exceeds 10, the while loop exits, and we print a message indicating that the occupancy limit has been reached and the program is exiting.
Here is a step-by-step explanation for a program that meets the described requirements:
1. Import the necessary libraries:
```java
import java.util.Scanner;
import java.util.InputMismatchException;
```
2. Create a class and the main method:
```java
public class RestaurantOccupancy {
public static void main(String[] args) {
```
3. Initialize the required variables and create a Scanner object for reading input:
```java
int occupants = 0;
int change;
Scanner input = new Scanner(System.in);
```
4. Create a loop that continues until the number of occupants equals or exceeds 10:
```java
while (occupants < 10) {
```
5. Use a try-catch block to handle the `InputMismatchException` exception:
```java
try {
change = input.nextInt();
occupants += change;
System.out.println("Number of people in the restaurant: " + occupants);
} catch (InputMismatchException e) {
input.next(); // Discard the invalid input
}
```
6. Close the while loop, Scanner object, and the main method:
```java
}
input.close();
}
}
```
while (occupants < 10) {
try {
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the two internal dimensions represented on the axes of the space matrix are
Answers
The space matrix is a strategic management tool that helps organizations analyze their internal dimensions by plotting their financial strength and competitive advantage on the axes. This analysis enables decision-makers to determine appropriate growth strategies and allocate resources effectively.
The two internal dimensions represented on the axes of the space matrix are technology and market diversity. This is determined by plotting the company's position on each dimension using a scale of one to six, with one being low and six being high. The space matrix then combines these two dimensions with two external dimensions (industry attractiveness and business strength) to create a visual representation of the company's position in the market. In summary, the space matrix assesses a company's competitive position and strategic choices by evaluating these four dimensions in a three-by-three matrix.
Financial Strength (FS): This axis represents the organization's financial position, which can include factors like revenue, profitability, and access to capital. A strong financial position allows a company to invest in new projects and face competition effectively. Competitive Advantage (CA): This axis represents the unique capabilities, resources, or attributes that give an organization an edge over its competitors. These can include aspects like superior products, strong brand recognition, and efficient supply chain management. A sustainable competitive advantage enables a company to maintain or improve its market position.
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In ΔRST, the measure of ∠T=90°, ST = 71 feet, and RS = 94 feet. Find the measure of ∠S to the nearest tenth of a degree.
Answers
Answer:
40.9
Step-by-step explanation:
In ΔRST, the measure of ∠T=90°, ST = 71 feet, and RS = 94 feet. Find the measure of ∠S to the nearest tenth of a degree.
What is the equation of this line?
A.) y=1/2x-2
B.) y=2x-2
C.) y=-1/2-2
D.) y=-2x-2
Answers
Plug the x and y values to get it
Answer:
Plug the x and y values to get it
Step-by-step explanation:
PLEASE HELP!!
Find the value of x and identify the type of polynomial.
A. X = 60; regular pentagon
B. x = 60; regular quadrilateral
C. x= 100; pentagon
D. x= 100; quadrilateral
E. X=85; regular quadrilateral
Answers
Answer:answer is 100; quadrilateral
Step-by-step explanation:
Give a 98% confidence interval for one population mean, given asample of 28 data points with sample mean 30.0 and sample standarddeviation s = 2.40.
Answers
We have a sample of 28 data points. The sample mean is 30.0 and the sample standard deviation is 2.40. The confidence level required is 98%. Then, we calculate α by:
\(\begin{gathered} 1-\alpha=0.98 \\ \alpha=0.02 \end{gathered}\)The confidence interval for the population mean, given the sample mean μ and the sample standard deviation σ, can be calculated as:
\(CI(\mu)=\lbrack x-Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}},x+Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}}\rbrack\)Where n is the sample size, and Z is the z-score for 1 - α/2. Using the known values:
\(CI(\mu)=\lbrack30.0-Z_{0.99}\cdot\frac{2.40}{\sqrt[]{28}},30.0+Z_{0.99}\cdot\frac{2.40}{\sqrt[]{28}}\rbrack\)Where (from tables):
\(Z_{0.99}=2.33\)Finally, the interval at 98% confidence level is:
\(CI(\mu)=\lbrack28.94,31.06\rbrack\)true or false? the closer together the numbers being compared the more decimal places you need to use.
Answers
Answer:
False
Step-by-step explanation:
CD has endpoints C(-3, 4) and D(1, -2). Find the coordinates
of its midpoint.
Answers
Answer:
Midpoint (-1 , 1)
Step-by-step explanation:
Formula: (midpoint)
Let the point A(x , y) be the midpoint of CD.
\(x=\frac{x_c+x_D}{2} =\frac{-3+1}{2} =\frac{-2}{2} =-1\)
\(y=\frac{x_C + y_D}{2} =\frac{4+(-2)}{2} =\frac{2}{2} =1\)
Then
A(-1 , 1)
Answer: (-1;1)
Step-by-step explanation:
x =(-3+1)/2
Y=(4-2)/2
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BC = 3
and DC = 1, what is the length of AC?
B.
3
A
D 1 C
Answers
Answer:
AC = 9
Step-by-step explanation:
\( \frac{3}{1} = \frac{ac}{3} \\ ac = 3 \times 3 \\ 9\)
Given cos 0 = 3/5 and 0 is in Quadrant I, what is the value of tan 0 ?
Answers
Answer:
4 / 3
Step-by-step explanation:
cos θ = 3 / 5
cos 53 = 3 / 5
θ = 53
tan θ = sin θ / cos θ
sin 53 = 4 / 5
tan 53 = sin 53 / cos 53
= ( 4 / 5 ) / ( 3 / 5 )
= ( 4 / 5 ) x ( 5 / 3 )
= ( 4 x 5 ) / ( 5 x 3 )
tan 53 = 4 / 3
A subset of a population selected to represent the population is
Group of answer choices
a subset
a sample
a small population
a parameter
Answers
A subset of a population selected to represent the population is a sample.
A sample is a subset of a population that is selected to represent the larger population as a whole. It is important to select a representative sample so that the results of the analysis are accurate and reliable.
What is a population?A population can be defined as a group of individuals, objects, or subjects that share common observable characteristics or traits. A population is a group of things that share something in common, and it can be any size.
What is a sample?A sample is a smaller group of individuals, objects, or subjects that are taken from the population to perform research or statistical analysis. Samples are typically used in research to estimate what is happening in the population as a whole.
What is a subset?A subset is a subset of a larger group.
In other words, it is a smaller set that is part of a larger set. A subset can contain any number of elements or members, and it can be of any size.
Hence, the "a sample" is correct.
To know more about the "subset": https://brainly.com/question/30802975
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A computer company will sell its new tablet
computer for six hundred forty dollars and
sixty-five cents. How is this number written in
expanded notation?
Answers
Explanation: J is equivalent to $640.65
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