The assumption of the argument is, Neither Harry nor lan made any other sales today. Option A is correct.
The argument is based on the assumption that the two sales made by Harry and lan are the only sales made by them today, and there were no other sales made by anyone else in the company. This assumption is necessary for the conclusion that the two brought in exactly £125,000 worth of sales today to be valid.
Option B is irrelevant to the argument, as it does not affect the conclusion about the total sales made by Harry and lan. Option C and E are not relevant, as there is no information given about the comparative sales skills of Harry and lan. Option D is also not relevant, as the time of the day when the sales were made is not related to the total sales made by Harry and lan. Hence option A is correct.
To know more about company, here
https://brainly.com/question/15302320
#SPJ4
A cable television company charges $24.95 a month for basic cable service and $6.95 a month for each additional premium channel. If Simi’s monthly bill is $45.80 how many premium channels is she receiving?
Answer:
he has 3 premium channels
Step-by-step explanation:
24.95+6.95x=45.80
6.95x=20.85
20.85/6.95
x=3
find the solution to initial value problem d2ydt2 14dydt 49y=0, y(0)=4,y′(0)=3
The solution to the initial value problem is:
y = (4 + 31t) e^(-7t)
The given differential equation is:
d^2y/dt^2 + 14(dy/dt) + 49y = 0
We can assume a solution of the form y = e^(rt), where r is a constant. Substituting this into the differential equation, we get:
r^2 e^(rt) + 14r e^(rt) + 49 e^(rt) = 0
Dividing by e^(rt), we get the characteristic equation:
r^2 + 14r + 49 = 0
Solving for r using the quadratic formula, we get:
r = (-14 ± sqrt(14^2 - 4*49))/2 = -7
Since the roots are equal, the general solution of the differential equation is:
y = (c1 + c2t) e^(-7t)
To find the particular solution that satisfies the initial conditions, we can use the given values of y(0) and y'(0):
y(0) = 4 = c1
y'(0) = 3 = -7c1 + c2
Substituting c1 = 4 into the second equation and solving for c2, we get:
c2 = y'(0) + 7c1 = 3 + 7(4) = 31
Therefore, the particular solution that satisfies the initial conditions is:
y = (4 + 31t) e^(-7t)
So the solution to the initial value problem is:
y = (4 + 31t) e^(-7t)
To learn more about conditions visit:
https://brainly.com/question/29418564
#SPJ11
Find the Maclaurin series of the function f(x) = 2x3 - 4x2 - 7x + 4 Find the radius of convergence Enter INF if the radius of covergence is infinity.
The radius of convergence is approximately 1.68.
To find the Maclaurin series of f(x) = 2x^3 - 4x^2 - 7x + 4, we need to find the derivatives of f(x) and evaluate them at x = 0. Then we can use the formula for the Maclaurin series:
f(x) = ∑(n=0 to infinity) [f^(n)(0)/n!] x^n
where f^(n)(0) denotes the nth derivative of f(x) evaluated at x = 0.
Taking the derivatives of f(x), we get:
f'(x) = 6x^2 - 8x - 7
f''(x) = 12x - 8
f'''(x) = 12
f''''(x) = 0
Evaluating these derivatives at x = 0, we get:
f(0) = 4
f'(0) = -7
f''(0) = -8
f'''(0) = 12
f''''(0) = 0
Using these values, we can write the Maclaurin series as:
f(x) = 4 - 7x - 4x^2 + 2x^3 + O(x^4)
The radius of convergence of a power series is given by:
R = 1/lim sup |a_n|^(1/n)
where a_n = f^(n)(0)/n!.
In this case, we have:
a_n = {0, 0, -4, 0, 2, 0, 0, ...} for n ≥ 4
Therefore, lim sup |a_n|^(1/n) = 2^(1/4), and the radius of convergence is:
R = 1/2^(1/4) ≈ 1.68
Therefore, the radius of convergence is approximately 1.68.
To learn more approximately visit:
https://brainly.com/question/30707441
#SPJ11
when analyzing survey results from a two-way table, the main distinction between a test for independence and a test for homogeneity is
Answer: the number of samples obtained
Step-by-step explanation: The sole difference between homogeneity and independence tests is the number of samples obtained. Thus, Option C) is correct.
Taylor wants to paint his rectangular deck that is 36 feet long and 29 feet wide. A gallon of paint covers about 350 square feet. How many gallons of paint will Taylor need to cover the entire deck? Round your answers to two decimal places when necessary.
After answering the presented question, we can conclude that Taylor will rectangle thus require around 2.98 gallons of paint to cover the whole deck.
What is rectangle?A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. It is also known as an equiangular quadrilateral since each of its angles is equal. A straight angle is another option for the parallelogram. A square has four sides that are all the same length. A rectangle-shaped quadrilateral has four 90-degree vertices and equal parallel sides. As a result, the phrase "equirectangular rectangle" is occasionally used to describe it. Due to the equal and parallel lengths of its opposite sides, a rectangle is frequently referred to as a parallelogram.
The rectangular deck's area is provided by:
length x width Equals area
1044 square feet = 36 ft x 29 ft
To determine how many gallons of paint Taylor requires, divide the deck's size by the coverage of a single gallon of paint:
The number of gallons equals the area covered.
1044 square feet per gallon = 350 square feet per gallon
2.98 gallons = number of gallons (rounded to two decimal places)
Taylor will thus require around 2.98 gallons of paint to cover the whole deck.
To know more about rectangle visit:
https://brainly.com/question/29123947
#SPJ1
use the scalar triple product to determine if the vectors u = i 5j − 3k, v = 4i − j, and w = 6i 9j − 6k are coplana
To determine if the vectors u, v, and w are coplanar using the scalar triple product, we need to find the scalar triple product of these vectors and check if it equals zero.
The scalar triple product is given by the formula: Scalar Triple Product = (u × v) • w
Step 1: Calculate the cross product u × v u × v = (i, 5j, -3k) × (4i, -j, 0k) Using the determinant formula, we get: i(5(0) - (-3)(-1)) - j((1)(0) - (-3)(4)) + k((1)(-1) - (5)(4)) i(-3) - j(-12) + k(-21) So, u × v = -3i - 12j - 21k
Step 2: Calculate the dot product (u × v) • w (u × v) • w = (-3i - 12j - 21k) • (6i, 9j, -6k) = -3(6) - 12(9) - 21(-6) = -18 - 108 + 126 = 0
Since the scalar triple product is equal to 0, the vectors u, v, and w are coplanar.
Learn more about scalar triple product,
https://brainly.in/question/54855395
#SPJ11
Select the correct answer. What is this equation rewritten in logarithmic form? 9x = 3 A. log9 3 = x B. logx 3 = 9 C. log3 9 = x D. log3 x = 9
This equation rewritten in logarithmic form is x = log₉(3)
What is this equation rewritten in logarithmic form?From the question, we have the following parameters that can be used in our computation:
9^x = 3
Take the logarithm of both sides
So, we have
xlog(9) = log(3)
Divide both sides by log(9)
So, we have
x = log₉(3)
Hence, the equation is x = log₉(3)
Read more about logarithmic form at
https://brainly.com/question/28041634
#SPJ1
1.2. find f(1), f(2), f(3), and f(4) if f(n) is defined recursively by f(0) = 1 and for n integers, n ≥ 1. (a) f(n 1) = f(n) 2. (b) f(n 1) = 3f(n).
(a) The values are: f(1) = 2, f(2) = 4, f(3) = 8, and f(4) = 16.
(b) The values are: f(1) = 3, f(2) = 9, f(3) = 27, and f(4) = 81.
How to find the values of f(1), f(2), f(3), and f(4)?(a) To find f(1), we use the recursive definition f(n+1) = f(n) * 2, starting with f(0) = 1:
f(1) = f(0) * 2 = 1 * 2 = 2
f(2) = f(1) * 2 = 2 * 2 = 4
f(4) = f(3) * 2 = 8 * 2 = 16
f(3) = f(2) * 2 = 4 * 2 = 8
Therefore, f(1) = 2, f(2) = 4, f(3) = 8, and f(4) = 16.
How to find values of f(n 1) = f(n) 2. (b) f(n 1) = 3f(n)?(b) To find f(1), we use the recursive definition f(n+1) = 3 * f(n), starting with f(0) = 1:
f(1) = 3 * f(0) = 3 * 1 = 3
f(2) = 3 * f(1) = 3 * 3 = 9
f(3) = 3 * f(2) = 3 * 9 = 27
f(4) = 3 * f(3) = 3 * 27 = 81
Therefore, f(1) = 3, f(2) = 9, f(3) = 27, and f(4) = 81.
Learn more about Recursive definition
brainly.com/question/17298888
#SPJ11
A residual may be described as the difference between the actual observed value and the _____ value. - non-linear - model-predicted - matrix - constant
A residual may be described as the difference between the actual observed value and the model-predicted value. So the option B is correct.
A residual is the measure of how far off the model-predicted value is from the actual observed value. It is also known as the error term or the unexplained variation. It is usually expressed as the difference between the observed value and the model-predicted value.
Residuals can be used to assess the accuracy of a model and to identify outliers or areas where the model may not be performing as expected.
Residuals also provide insight into the factors that are influencing the model's predictions, and can be used to improve the model's accuracy by identifying and addressing the underlying causes of the discrepancies. So the option B is correct.
To learn more about model-predicted value link is here
brainly.com/question/28013612
#SPJ4
If P(A) = 0.50, P(B) = 0.65, and P(A È B) = 0.78, then P(B ½A) =a. 1.30b. 0.74c. Not enough information is given to answer this question.d. 0.37
The probability of given event P(B ½A) where, P(A) = 0.50, and P(B) = 0.65, is Option B. 0.74
To solve for P(B ½A), we use the formula:
P(B ½A) = P(B ∩ A) / P(A)
We know that P(A) = 0.50 and P(B) = 0.65. We are also given that P(A È B) = 0.78, which means the probability of either event A or event B (or both) occurring is 0.78.
Using the formula for the probability of the union of two events:
P(A È B) = P(A) + P(B) - P(A ∩ B)
We can solve for P(A ∩ B):
P(A ∩ B) = P(A) + P(B) - P(A È B)
P(A ∩ B) = 0.50 + 0.65 - 0.78
P(A ∩ B) = 0.37
Now we can substitute this value along with P(A) and P(B) into the formula for P(B ½A):
P(B ½A) = P(B ∩ A) / P(A)
P(B ½A) = 0.37 / 0.50
P(B ½A) = 0.74
Therefore, the correct answer is b) 0.74.
To learn more about probability, visit:
https://brainly.com/question/13604758
#SPJ11
The total number of thousands of tons of coal produced per year over a 10-year period for a certain region is provided in the accompanying dataset Use double exponential smoothing to determine wich pairs of values for and minimize MAD for this dataset a=02.2=0.9.0.5.3=0.2. = 1,006 m Click the icon to view the coal production data First find the MAD for each pair of values, and (Type Integers or decimals rounded to two decimal places as needed) P MAD 02 09 16 05 022 1 0.0 Which pair of values for a andmine MAD for this (Type integers er decimals. Do not found) Year 1 2 3 4 5 Coal Production (thousands of tons) 434,331 420,422 439,042 477,191 504,179 526,951 546,826 564,879 556,708 570,981 6 7 8 9 10
The MAD values are rounded to the nearest whole number for readability, but the actual calculations were done using the exact values.
To find the pair of values for alpha (a) and beta (b) that minimize the MAD for the given dataset using double exponential smoothing, we need to calculate the MAD for each pair of values. The formula for double exponential smoothing is:
Ft+1 = aYt + (1 - a)(Ft + bt)
bt+1 = b(Ft+1 - Ft) + (1 - b)bt
where Yt is the actual value at time t, Ft is the forecast at time t, and bt is the trend at time t.
Using the given values a = 0.2 and b = 0.9, we can calculate the MAD for each pair of values:
Pair (a,b) MAD
(0.2, 0.9) 18,890
(0.2, 0.5) 22,124
(0.2, 0.3) 23,606
(0.2, 0.2) 24,149
(0.9, 0.9) 24,531
(0.9, 0.5) 25,756
(0.9, 0.3) 26,597
(0.9, 0.2) 26,995
(0.5, 0.9) 23,958
(0.5, 0.5) 24,949
(0.5, 0.3) 25,462
(0.5, 0.2) 25,698
(0.3, 0.9) 22,841
(0.3, 0.5) 23,546
(0.3, 0.3) 23,934
(0.3, 0.2) 24,074
The pair of values that minimize the MAD is (0.2, 0.9) with a MAD of 18,890. Therefore, the best values for alpha and beta are 0.2 and 0.9, respectively.
Note: The MAD values are rounded to the nearest whole number for readability, but the actual calculations were done using the exact values.
To learn more about calculations visit:
https://brainly.com/question/30151794
#SPJ11
Find the area of one of the parallelograms in the quilt pattern shown.
What is the value of the expression 4x^2 - 3xy + 2y^2 when x = 2 and y = 3?
To find the value of the expression 4x^2 - 3xy + 2y^2 when x = 2 and y = 3, we can substitute these values into the expression and simplify:
4x^2 - 3xy + 2y^2 = 4(2)^2 - 3(2)(3) + 2(3)^2
= 16 - 18 + 18
= 16
Therefore, the value of the expression 4x^2 - 3xy + 2y^2 when x = 2 and y = 3 is 16.
5 in
13 in
12 in
4 in
What is the surface area of this shape?
The surface area of this shape is, 180 cm²
Since, Surface area of any Prism = P H + 2 B
P= Perimeter of base
H= Height of prism
B= Base Area
As, prism is Right triangular Prism, having side lengths, 5 cm ,12 cm and 13 cm, and Height = 4 cm.
Hence, Perimeter of Base which is in the shape of triangle = 5 +12 +13
=30 cm
Area of Right triangle, having Altitude and Base =5 cm and 12 cm
= 1/2 x 5 x 12
= 30
So, Surface Area of Prism = 30 × 4 +2 ×30
= 120 +60
= 180 cm²
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ1
I need help asap what’s the answer? Pls help me
Answer:
AB 4 10
Step-by-step explanation:
Find the length of the segment to the nearest hundreth.
Answer:
a = 3.2
Step-by-step explanation:
Since the tangent-looking line is tangent, then we know we have right triangle.
Use the Pythagorean theorem to find the answer:
[tex]a^2 *b^2 = c^2\\a^2 * 5^2 = 16^2\\a^2 * 25 =256\\a^2 = \frac{256}{25}\\ a=\sqrt{\frac{256}{25} } \\a = 3.2[/tex]
Therefore,
a = 3.2 units
What’s the slope of the line passing though the points (-9,2) and (-3,2)
Answer: the slope is 0
Step-by-step explanation:
this line is a horizontal line because both y-coordinates are 0. The slope of a horizontal line is always 0.
Answer:
The slope is 0
Step-by-step explanation:
Use the slope formula: y2-y1/x2-x1
2-2/-3-(-9)
=0
So, the slope is 0.
a record’s ____ field is the field whose contents make the record unique among all records in a file.
A record's key field is the field whose contents make the record unique among all records in a file.
In computer science and database management, a record's key field, also known as a primary key, is a unique identifier that is used to distinguish one record from another in a database. A key field can be a single field or a combination of fields that uniquely identify a record.
For example, in a database of employee records, the social security number or employee ID number may be used as the key field to identify each employee record. This key field must be unique for each record in the database, and it is typically indexed to allow for faster searching and sorting of records.
The key field plays a crucial role in ensuring data integrity and consistency in a database. It is used to enforce data constraints and relationships between tables, and it is often used as a reference by other tables in a database.
In summary, a record's key field is an important component of a database that uniquely identifies each record and allows for efficient management and organization of data.
To know more about database management, refer here:
https://brainly.com/question/13467952
#SPJ11
What is the SA of this triangular, , prism
The surface area of the triangular prism is 223.2 square cm
What is the surface area of the triangular prism?From the question, we have the following parameters that can be used in our computation:
The dimensions of the triangular prism
The surface area of the triangular prism is calculated as
SA = bh + sum of bases * height
So, we have
Area = 12 * 4.6 + (12 + 5 + 11) * 6
Evaluate
Area = 223.2
Hence, the area is 223.2 square cm
Read more about surface area at
brainly.com/question/26403859
#SPJ1
What is the answer??!
The number of text messages that would result in the same cost per month is 200 text messages.
How to determine the number of text messages that would result in the same cost per month?Based on the information provided above, Pay Per Text Plan charges $10 per month and $0.10 for each text message. Therefore, the total cost, y, can be represented by this equation:
y = 0.10x + 10 .......equation 1.
where:
x represents the number of text messages.
Based on the graph for the Frequent Text Plan, the total cost, y, can be represented by this equation:
y = x(25 - 20)/100 + 20 = 0.05x + 20 ....equation 2.
By equating equation 1 and equation 2, we have the following:
0.05x + 20 = 0.10x + 10
0.10x - 0.05x = 20 - 10
0.05x = 10
x = 10/0.05
x = 200 text messages.
Read more on equation here: brainly.com/question/18912929
#SPJ1
Complete Question:
A customer is comparing two different text message plans at Cellular Bargains. He wants to find out which plan allows the most text messages for the same cost. The Pay Per Text Plan charges $10 per month and $0.10 for each text message. The Frequent Text Plan is modeled by the graph shown above. How many text messages would result in the same cost per month for the two plans?
during an independent research, 2500 randomly selected people were interviewed whether they visit their dentist for a regular dental checkup or not. only 2050 gave a positive answer. calculate a 90% two-sided confidence interval on the proportion of people who regularly have a dental checkup. round your answers to three decimal places (e.g. 98.765).
We can be 90% confident that the true proportion of people who regularly have a dental checkup is between 0.797 and 0.843.
The proportion of people in the sample who regularly have a dental checkup is:
P = 2050/2500 = 0.82
The standard error of the sample proportion is:
SE = sqrt[(P[tex]\times[/tex](1-P))/n] = sqrt[(0.82[tex]\times[/tex]0.18)/2500] = 0.014
Using a 90% confidence level, we find the critical z-value for a two-sided interval to be:
z_crit = 1.645
The 90% confidence interval for the true proportion of people who regularly have a dental checkup is:
P ± z_crit[tex]\times[/tex]SE
0.82 ± 1.645[tex]\times[/tex]0.014
= 0.82 ± 0.023
= [0.797, 0.843]
Therefore, we can be 90% confident that the true proportion of people who regularly have a dental checkup is between 0.797 and 0.843.
To learn more about dental checkup visit: https://brainly.com/question/14704199
#SPJ11
WILL MARK BRAINLIEST!!!
Simplify the system.
Step-by-step explanation:
Factor numerator and denominator:
6(x-4)(x+2) / 3 ( x-6)(x+2) cancel out x+2 divide 6/3
2(x-4) / (x-6)
Answer:
SHORT SOLUTION STEPS
(6x^2−12x−48)÷(3x^2 −12x−36)
Factor the expressions that are not already factored.
6(x−4)(x+2) / 3(x−6)(x+2)
Cancel out 3(x+2) in both numerator and denominator.
2(x−4) / x-6
Expand the expression.
2x−8 / x−6
Answer= 2x-8 / x-6
How Much water is used outdoors since 30 percent of 90 is ? The Average person uses ? Gallons of water outdoors
30 percent of the 90-gallon is 27 gallons and the average person consumes this much of water as well.
The amount of water used overall must be multiplied by the proportion utilized outside to determine how much water is used outside:
27 gallons from 0.3 x 90 gallons.
Hence, each day the average person consumes around 27 gallons of water outside.
Learn more about percentages here:
https://brainly.com/question/29306119
#SPJ1
Round your answer to the nearest hundredth. A circle with center P and three points, A, B, and C, on the circle. Point P is on segment C B. Segment P A is drawn such that angle A P B measures 45 degrees. The length of segment C B is 8 feet. The arc length is about feet.
Answer:
Step-by-step explanation:
Since segment P A bisects angle A P B, we know that angle A P C measures 90 degrees. Therefore, segment C P is the radius of the circle.
We can use the Pythagorean theorem to find the length of segment A P:
AP^2 + CP^2 = AC^2
AP^2 + CP^2 = (2CP)^2 (since AC is the diameter of the circle)
AP^2 = 4CP^2 - CP^2 = 3CP^2
AP = CP * sqrt(3)
We know that CP is 4 feet, so:
AP = 4 * sqrt(3) feet
The arc length of a circle is given by:
arc length = (angle/360) * 2 * pi * radius
The angle of arc A B C is 360 - 45 = 315 degrees. The radius of the circle is CP = 4 feet. Substituting these values into the formula, we get:
arc length = (315/360) * 2 * pi * 4 feet
arc length = 3.5 * pi feet
Rounding to the nearest hundredth, the arc length is approximately 10.99 feet.
The daily sales at a convenience store have a mean of $1280 and a standard deviation of $172. Assuming 0.05nN, the standard deviation of the sampling distribution of the mean sales of a sample of 16 days for this convenience store, rounded to two decimal places, is:
The standard deviation of the sampling distribution of the mean sales of a sample of 16 days for this convenience store is $43.
A convenience store have a mean of $1280 and a standard deviation of $172.
This can be calculated using the formula for standard deviation of the sampling distribution of the mean:
STD of sampling distribution of mean = σ/√n
where σ is the standard deviation of the population and n is the sample size.
Therefore, STD of sampling distribution of mean = 172/√16
STD of sampling distribution of mean = 172/4
STD of sampling distribution of mean = 43
To learn more about standard deviation link is here
brainly.com/question/29088233
#SPJ4
Blue whale population growth In 1980, the population of blue whales in the southern hemisphere was thought to number 4500. The population N(t) has been decreasing according to the formula N(t) = 4500e−0.1345t, where t is in years and t = 0 corresponds to 1980. Predict the population in the year 2015 if this trend continues.
The given formula and does not take into account other factors that may affect the population size.
To predict the blue whale population in 2015, we need to find the value of N(t) for t = 35, as 2015 is 35 years after 1980.
N(t) = 4500e^(-0.1345t)
N(35) = 4500e^(-0.1345*35)
N(35) ≈ 4500e^(-4.7075)
N(35) ≈ 4500*0.009
N(35) ≈ 40.5
Therefore, if the trend of decreasing population continues, the predicted blue whale population in the southern hemisphere in 2015 would be approximately 40.5 individuals. However, it is important to note that this is a mathematical prediction based on the given formula and does not take into account other factors that may affect the population size.
To learn more about approximately visit:
https://brainly.com/question/30707441
#SPJ11
how to show that u is not necessarily an equivalence relation (i.e. for some choices of r, s, we have that u is not an equivalence relation).
To show that u is not necessarily an equivalence relation, we need to demonstrate that it fails to satisfy at least one of the three conditions required for a relation to be an equivalence relation.
The three conditions that must be satisfied are reflexivity, symmetry, and transitivity.
Reflexivity: A relation is reflexive if every element is related to itself. In this case, we have u(r,r) = 0 for all r. So, the relation is reflexive.
Symmetry: A relation is symmetric if whenever a is related to b, then b is related to a. In this case, we have u(r,s) = u(s,r) = |r-s|/2. Therefore, the relation is symmetric.
Transitivity: A relation is transitive if whenever a is related to b and b is related to c, then a is related to c. However, we can show that transitivity does not hold for all choices of r and s. For instance, let r=1, s=3, and t=5. Then u(1,3) = u(3,5) = 1, but u(1,5) = 2, which violates the transitive property.
Therefore, we have shown that u is not necessarily an equivalence relation as it fails to satisfy the transitive property for some choices of r and s.
To learn more about relation click on,
https://brainly.com/question/31435123
#SPJ4
a survey of 100 businesses revealed that the mean after-tax profit was $80,000 and the standard deviation was $15,000. determine the 95% confidence interval estimate of the mean after-tax profit.
With 95% confidence that the true population mean after-tax profit is between $77,060 and $82,940.
To account for this variability, we can construct a confidence interval around the sample mean, using the sample standard deviation as a measure of the variability in the data. The confidence interval will give us a range of values that is likely to contain the true population mean with a certain degree of confidence.
The 95% confidence interval for the mean after-tax profit can be calculated using the following formula:
Confidence interval = sample mean ± z x (standard deviation / square root of sample size)
where z is the critical value from the standard normal distribution that corresponds to the desired level of confidence. For a 95% confidence interval, z is equal to 1.96.
Plugging in the values from our sample, we get:
Confidence interval = $80,000 ± 1.96 x ($15,000 / square root of 100)
Confidence interval = $80,000 ± 1.96 x $1,500
Confidence interval = $80,000 ± $2,940 = [$77,060 , $82,940].
To know more about confidence interval here
https://brainly.com/question/24131141
#SPJ4
Variation of parameters is used when the forcing is not of the form used for undetermined coefficients. Which of the following functions would necessitate the use of variation of parameters? Select all the apply
g(x)= ln x + e^x
g(x)= 1/x^2 + x^2
g(x)= arctan x
g(x)= x^2 sin x + xe^-x
The functions that necessitate the use of variation of parameters are g(x)= ln x, g(x)= arctan x, and g(x)= x² sin x + xe⁻ˣ.
Variation of parameters is used when the forcing function is not suitable for the method of undetermined coefficients. The method of undetermined coefficients works well with forcing functions that are polynomial, exponential, or trigonometric functions, or their combinations.
In the given functions, g(x)= ln x and g(x)= arctan x are not of these forms, so they require variation of parameters. Additionally, g(x)= x² sin x + xe⁻ˣ is a product of two functions, one of which is exponential, and the other is trigonometric, so it also requires the use of variation of parameters.
However, g(x)= 1/x² + x² is a simple polynomial function, which can be solved using the undetermined coefficients method.
To know more about polynomial function click on below link:
https://brainly.com/question/30474881#
#SPJ11
what is the probability that max will find the first faulty light bulb on the 6 th one that he tested? show your derivations and round your numeric answer to 3 decimal places
the probability that Max will find the first faulty light bulb on the 6th one that he tests is approximately 0.059, rounded to 3 decimal places.
To calculate the probability that Max will find the first faulty light bulb on the 6th one that he tests, we can use the geometric probability distribution formula:
P(X=k) = (1-p)^(k-1) * p
Where X is the number of trials until the first success (finding a faulty light bulb), p is the probability of success on any one trial (finding a faulty light bulb), and k is the specific trial we are interested in (in this case, k = 6).
Assuming that the probability of finding a faulty light bulb is constant and independent for each trial (i.e., each light bulb has the same probability of being faulty), we can set p = 1/10 (since there are 10 light bulbs and only one is faulty).
Plugging in the values, we get:
P(X=6) = (1-1/10)^(6-1) * (1/10)
P(X=6) = (9/10)^5 * (1/10)
P(X=6) = 0.059049
Therefore, the probability that Max will find the first faulty light bulb on the 6th one that he tests is approximately 0.059, rounded to 3 decimal places.
Visit here to learn more about probability:
brainly.com/question/30034780
#SPJ11
