a company want to find out if there is a linear relationship between indirect labor expense (ile), in dollars, and direct labor hours (dlh). data for direct labor hours and indirect labor expense for 25 months are given. approximately what percentage of the variation in indirect labor expenses is explained by the regression model you derived? place your answer, rounded to 2 decimal places, in the blank. do not use any stray punctuation marks or a percentage sign. for example, 78.91 would be a legitimate entry.
DLH(X) 20 25 22 23 20 19 24 28 26 29 22 26 ILE(Y) 361 355 376 384 374 311 427.2 387.5 450.8 475.2 462.6 333.3 389.9 445 511 501.1 544.9 423.8 574.1 535.4 444.7 578.4 399.6 355 313 25 28 32 33 34 30 36 37 31 20
Answers
For the data given above, the Coefficient of determination r² obtained using the Coefficient of determination calculator is 0.45; which means that (0.45 * 100%) about 45% of the variation in indirect labor expense is explained by the regression line while 55% is due to other factors.
For mean:
Mean of x = ∑xi/n = 689/25 = 27.56 (where n = 25)
V (X) = ∑(xi^2)/n - Mean of x^2
V (X) = 19763/25 - 27.56^2
V (X) = 790.52 - 759.5536
V (X) = 30.9664
Similarly, Mean of y = ∑yi/n = 10713.5/25 = 428.54
V (Y) = ∑(yi^2)/n - Mean of y^2
V (Y) = 4739568.87/25 - 428.54^2
V (Y) = 189582.7548 - 183646.5316
V (Y) = 5936.2232
Variance of x = 30.9664
Variance of y = 5936.223
Covariance(X, Y) = 1/n∑xy - mean of x. mean of y
Covariance(X, Y) = (1/25 x 302477.1) - (27.56 x 428.54)
Covariance(X, Y) = 12099.084 - 11810.5624
Covariance(X, Y) = 288.5216
Coefficient of covariance (r) = COV(X,Y)/\(\sqrt{VARX} . \sqrt{VARY}\)
Coefficient of covariance (r) = 288.5216/\((\sqrt{30.9664} . \sqrt{5936.223})\)
Coefficient of covariance (r) = 288.5216/ (5.564746176 x 77.04688832)
Coefficient of covariance (r) = 288.5216/ 428.7463771
Coefficient of covariance (r) = 0.672942363
Therefore,
r= 0.672942
r^2= 0.452851
From the excel sheet and the values given above by calculating, we can see that r = 0.67 which indicates a weak linear relationship between X and Y.
r^2=.45 which indicates that 45% of the variation in indirect labor expenses could be explained by the regression model.
The coefficient of determination, r² gives the proportion of explained variance due to the regression line.
To learn more about the variance visit: https://brainly.com/question/29365746
#SPJ4
Related Questions
A student mows lawns on the weekends. It takes him 140 minutes to mow 4 lawns. What prediction can you make about the time he will spend this weekend if he has 12 lawns to mow?
It will take him 12 hours to mow 12 lawns.
It will take him 10 hours to mow 12 lawns.
It will take him 7 hours to mow 12 lawns.
It will take him 3 hours to mow 12 lawns.
Answers
Answer:
C. It will take him 7 hours to mow 12 lawns
Step-by-step explanation:
140 mins = 4 lawns
12 lawns = 4 x 3
140 x 3 = 420 minutes (12 lawns)
420 ÷ 60 = 7 hours
What is the midpoint of (-4,8) and (6,-5)
Answers
Answer:
(1,3/2)
Step-by-step explanation: x=(-4+6)/2=1
Y=(8-5)/2=3/2
A matinee movie ticket costs $7.35.A regular movie ticket costs $12.25.What percent discount of the regular
price is the matinee movie ticket?
Answers
Answer:
The percent will be 490%
Step-by-step explanation:
If you subtract 7.35 for 12.25 you get a 4.9 and 4.9 as a percent is 490%(:
determine whether the sequence converges or diverges. if the sequence converges, find its limit. fn = n2022
Answers
The sequence fn = n^2022 diverges. This is because the exponent 2022 is an even number and as n approaches infinity, the sequence grows infinitely large without bound. Therefore, there is no limit to the sequence.
To determine whether the sequence converges or diverges, and if it converges, find its limit for the sequence f(n) = n^2022, follow these steps:
Step 1: Identify the sequence's terms
The sequence is given as f(n) = n^2022, where n is a positive integer.
Step 2: Check for convergence or divergence
To check if the sequence converges or diverges, we need to find the limit as n approaches infinity. In this case, we have:
lim (n → ∞) n^2022
Step 3: Evaluate the limit
As n approaches infinity, n^2022 will also approach infinity, because the power (2022) is a positive integer, and raising a positive integer to a positive power will only increase its value.
Thus, lim (n → ∞) n^2022 = ∞.
Step 4: Determine convergence or divergence
Since the limit as n approaches infinity is infinity, the sequence does not have a finite limit. Therefore, the sequence diverges.
Know more about sequence here:
https://brainly.com/question/28169281
#SPJ11
A rectangular sheet of tin measures 20 inches by 12 inches. suppose you cut a square out of each corner and fold up the sides to make an open-topped box. what size square should you cut out in order to maximize the volume of the box? please show your work/justify your answer.
Answers
Therefore, to maximize the volume of the box, a square with a side length of 5 inches should be cut out.
To determine the size of the square that should be cut out to maximize the volume of the box, we can follow these steps:
1. Let's assume that the side length of the square to be cut out is 'x' inches.
2. After cutting out the squares, the resulting box will have dimensions of length (20 - 2x) inches, width (12 - 2x) inches, and height 'x' inches.
3. The volume of the box can be calculated by multiplying these dimensions: V = (20 - 2x)(12 - 2x)x.
4. Simplifying the expression, we get \(V = 4x^3 - 64x^2 + 240x\).
5. To maximize the volume, we need to find the value of 'x' that maximizes the volume function V.
To find the maximum volume, we can take the derivative of V with respect to 'x' and set it equal to zero, then solve for 'x':
\(dV/dx = 12x^2 - 128x + 240\)
Setting dV/dx = 0:
\(12x^2 - 128x + 240 = 0\)
Factoring the quadratic equation: 12(x - 5)(x - 4) = 0
Solving for 'x', we find two possible values: x = 4 and x = 5.
To determine which value of 'x' maximizes the volume, we can compare the values of V at these points. Evaluating V for x = 4 and x = 5:
\(V(x=4) = 4(4)^3 - 64(4)^2 + 240(4) = 256\)cubic inches
\(V(x=5) = 4(5)^3 - 64(5)^2 + 240(5) = 300\) cubic inches
Comparing the volumes, we see that V(x=5) = 300 cubic inches is greater than V(x=4) = 256 cubic inches.
To learn more about quadratic click here: https://brainly.com/question/30098550
#SPJ11
Alana sold 6 oranges for $3. Write the equation that represents the price for any number of oranges.
Answers
Answer:
50 cents ($0.50)
Step-by-step explanation:
We need to find the price for one orange. To get one orange, you have to divide 6 by 6. Anything you do to one side of the equation must be done to the other side. You have to divide 3 by 6. If you do this, you get .5, or 1/2. In money, that translates to 50 cents.
Hope this helps!
Step-by-step explanation:
the price of one orange is indeed 3/6 = 1/2 = $0.50.
the equation residential the price for any number of oranges contains then a variable, say x, to stand for the number of purchased oranges :
p(x) = 0.5x
meaning that the price of x oranges is 0.5×x.
\[ s=-\frac{17 \pi}{3} \] Use the wrapping function to find the terminal point \( W(s)=(x, y) \) of the string of length \( |s| \) with initial point at \( (1,0) \). \( W\left(-\frac{17 \pi}{3}\right)
Answers
The terminal point \((x, y)\) of the string with a length of \(|\frac{17 \pi}{3}|\) and an initial point at \((1, 0)\) is approximately \((-0.5, -\frac{\sqrt{3}}{2})\).
To find the terminal point of the string, we use the wrapping function, which maps the real number line to the unit circle. The wrapping function is defined as \(W(s) = (\cos s, \sin s)\).
Given \(s = -\frac{17 \pi}{3}\), we can evaluate the wrapping function as follows:
\[
W\left(-\frac{17 \pi}{3}\right) = \left(\cos \left(-\frac{17 \pi}{3}\right), \sin \left(-\frac{17 \pi}{3}\right)\right)
\]
Using the unit circle trigonometric values, we know that \(\cos \left(-\frac{17 \pi}{3}\right) = -\frac{1}{2}\) and \(\sin \left(-\frac{17 \pi}{3}\right) = -\frac{\sqrt{3}}{2}\).
Therefore, the terminal point of the string is approximately \((-0.5, -\frac{\sqrt{3}}{2})\).
To learn more about trigonometric values Click Here: brainly.com/question/31135215
#SPJ11
Ashley had 4/ 5 of a spool of yarn. She used 2/5 of it for her project. What fraction of the spool was used for her project? Write your answer in simplest form
Answers
Ashley used 8/25 of the spool for her project.
To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):
(4/5) * (2/5) = 8/25
Know more about fraction here:
https://brainly.com/question/10354322
#SPJ11
One of the factors of 6x3 − 864x is 4 x2 x + 12 x − 8
Answers
Your answer is x + 12
Hope this helped!
Answer:
x+12
Step-by-step explanation:
Correct on test
Solve the following equation for all radian solutions and if 0 ≤ t < 2π. Give all answers as exact values in radians. Do not use a calculator. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
1. 9 cos t -root3=7cost
a) all radian solutions (Let k be any integer.) t= ______rad
b) 0 ≤ t < 2π. t= ______rad
2.3 cos t = 9 cos t − 3 root3
a) all radian solutions (Let k be any integer.) t= ______rad
b) 0 ≤ t < 2π. t= ______rad
3.5 sin t + 8 = −3 sin t
a) all radian solutions (Let k be any integer.) t= ______rad
b) 0 ≤ t < 2π. t= ______rad
Answers
In this problem set, we will be solving three different equations involving trigonometric functions. Within the interval 0 ≤ t < 2π, the solutions are t = π/6 and t = 11π/6. Within the interval 0 ≤ t < 2π, the solutions are t = π/3 and t = 5π/3. And for the third equation, there is no solution.
When solving these equations, we will be looking for all radian solutions, as well as solutions within the interval 0 ≤ t < 2π.
It's important to remember that an equation is simply a mathematical statement that shows that two expressions are equal. In order to solve the equation, we need to manipulate the expressions in such a way that we can isolate the variable we are solving for.
For the first equation, we are given 9 cos t - root3 = 7 cos t. To solve for t, we want to isolate the cosine term on one side of the equation. We can do this by subtracting 7 cos t from both sides, which gives us 2 cos t - root3 = 0. Next, we can divide both sides by 2 to get cos t = root3/2. We recognize that this is a special angle for cosine, which occurs at π/6 and 11π/6 radians. Therefore, the solutions for all radian values of t are t = π/6 + 2kπ and t = 11π/6 + 2kπ, where k is any integer. Within the interval 0 ≤ t < 2π, the solutions are t = π/6 and t = 11π/6.
For the second equation, we have 3 cos t = 9 cos t - 3 root3. Similar to the first equation, we want to isolate the cosine term on one side, so we can subtract 9 cos t from both sides, which gives us -6 cos t = -3 root3. Dividing both sides by -6, we get cos t = 1/2 root3. Again, this is a special angle for cosine, which occurs at π/3 and 5π/3 radians. Therefore, the solutions for all radian values of t are t = π/3 + 2kπ and t = 5π/3 + 2kπ, where k is any integer. Within the interval 0 ≤ t < 2π, the solutions are t = π/3 and t = 5π/3.
For the third equation, we have 5 sin t + 8 = -3 sin t. To isolate the sine term, we can add 3 sin t to both sides, which gives us 8 = -2 sin t. Dividing both sides by -2, we get sin t = -4. This is not a valid solution, as the range of the sine function is between -1 and 1. Therefore, there is no solution to this equation.
For more such questions on Solutions.
https://brainly.com/question/29016480#
#SPJ11
Verify that (0, 0) is a critical point, show that the system is locally linear, and discuss the type and stability of the critical point (0, 0) by examining the corresponding linear system. dx/dt = -x + y + 2xy dy/dt = -4x - y + x^2 - y^2
Answers
The critical point (0, 0) is not valid as it is not a critical point.
What is the derivative of ln(x^2 + 1)?To determine whether (0, 0) is a critical point, we need to check if the system's derivative with respect to time is equal to zero at that point.
Given the system of equations:
dx/dt = -x + y + 2xy
dy/dt = -4x - y + x^2 - y^2
We can evaluate the derivatives at (0, 0):
d/dt(dx/dt) = d/dt(-x + y + 2xy) = -1 + 0 + 2(0)(0) = -1
d/dt(dy/dt) = d/dt(-4x - y + x^2 - y^2) = -4 + 0 + 0 - 0 = -4
Since both derivatives are nonzero at (0, 0), it is not a critical point.
Now, let's analyze the linearization of the system around the critical point (0, 0) to determine its stability.
The linearization involves finding the Jacobian matrix evaluated at (0, 0):
J = | d(dx/dt)/dx d(dx/dt)/dy |
| d(dy/dt)/dx d(dy/dt)/dy |
Taking the partial derivatives:
d(dx/dt)/dx = -1
d(dx/dt)/dy = 1 + 2x
d(dy/dt)/dx = -4 + 2x
d(dy/dt)/dy = -1 - 2y
Evaluating these derivatives at (0, 0), we have:
d(dx/dt)/dx = -1
d(dx/dt)/dy = 1
d(dy/dt)/dx = -4
d(dy/dt)/dy = -1
So the Jacobian matrix J at (0, 0) becomes:
J = | -1 1 |
| -4 -1 |
The eigenvalues of this matrix can help determine the stability of the critical point (0, 0). We calculate the eigenvalues by solving the characteristic equation:
det(J - λI) = 0
where λ is the eigenvalue and I is the identity matrix. Substituting the values into the equation, we get:
| -1-λ 1 | = (λ+1)(λ+1) - 4
| -4 -1-λ | = λ^2 + 2λ - 3
Expanding and simplifying:
λ^2 + 2λ - 3 = 0
Factoring the equation:
(λ + 3)(λ - 1) = 0
The eigenvalues are λ = -3 and λ = 1.
The stability of the critical point (0, 0) can be determined based on the sign of the real parts of the eigenvalues:
1. If both eigenvalues have negative real parts, the critical point is a stable node.
2. If both eigenvalues have positive real parts, the critical point is an unstable node.
3. If one eigenvalue has a positive real part and the other has a negative real part, the critical point is a saddle point.
In this case, we have one eigenvalue with a positive real part (λ = 1) and one eigenvalue with a negative real part (λ = -3). Therefore, the critical point (0, 0) is a saddle point.
To summarize:
- (0, 0) is not a critical point.
- The linearization of the system around (0, 0) yields a Jacobian matrix J = |-1 1| and |-4 -1|.
- The eigenvalues of J are λ = -3 and λ = 1.
- Thus, the critical point (0, 0) is a saddle point.
Learn more about eigenvalues
brainly.com/question/29861415
#SPJ11
PLEASE HELP !!
Given that p II q, fill in the reasons why each statement is true.
Answers
Answer:
1. Given
2. Def of Vertical Angles
3. Alternate Interior Angles
4. Def of Vertical angles
5. Opposite exterior angles
Step-by-step explanation:
URGENT
A triangle has a perimeter of 165 cm. The first side is 65 cm less than twice the second side. The third side is 10 cm less than the second side. Find the length of each side of the triangle.
What equation represents the length of the third side if the second side is length s?
s - 10
s + 10
2s - 10
2s + 10
Answers
Answer:
Step-by-step explanation:
Perimeter 165 cm
1st. 65 cm < 2s
3rd. 10 cm < s
The 2nd side is twice than the first side but 10cm longer than the
3rd side, so it'll be
2nd. 2s + 10
a triangle has a perimeter of 165 cm. the first side is 65cm less than twice the second side. the third side is 10cm less than the second side. write and solve an equation to find the length of each side of the triangle
FIRST, we need variables. Once we define variables, it's much easier to turn this word problem into a math problem.
Let a = first side
Let b = second side
Let c = third side
NOW, we can turn the words into equations:
"a triangle has a perimeter of 165 cm."
a + b + c = 165
"the first side is 65cm less than twice the second side."
a = 2b - 65
"the third side is 10cm less than the second side."
c = b - 10
Before we finish, I have to ask: Who writes problems like this??? Pointless problems like these are why kids don't like math! Ugh. Drives me crazy. It's a shame, because solving math problems really does have a certain satisfaction, once you learn how. [Okay. I'm done. Back to the problem.]
If we could get this to have only one variable, we could solve it. Substitution to the rescue!
a + b + c = 165 (rewrote equation from above)
(2b - 65) + b + (b - 10) = 165 (substituted "a" and "c" from equations above)
See how that works? Let's solve it.
2b - 65 + b + b - 10 = 165 (dropped the parentheses, because there was nothing to distribute, not even a minus sign)
4b - 75 = 165 (combined like terms)
4b = 240 (added 75 to both sides)
b = 60 (divided both sides by 4)
We found the second side! We can find the first and third sides using those equations from above:
a = 2b - 65
a = 2*60 - 65
a = 120 - 65
a = 55
c = b - 10
c = 60 - 10
c = 50
All done.
PLEASE help me with this math problem..
Answers
Answer:
6
Step-by-step explanation:
25 / 10 = 2.5
15 / 2.5 = 6
What is an equation of the line that passes through the points (-4, 2) and
(-8, -3)?
Answers
Answer:
The equation of line 65 and the sum is 80
One pygmy shrew weighs 3 3/18 ounces, and another weighs 4 4/7 ounces. Estimate the total weight.
O about 8 1/2
O about 7 1/2
O about 9 ounces
O about 7 ounces
Answers
==============================================
Reason:
It might help to draw a number line for this.
3/18 is closer to 0 than it is to 1/2 = 9/18, so the mixed number 3 & 3/18 rounds to 3 when rounding to the nearest half.
4/7 is closer to 1/2 = 4/8 than it is to either 0 or 1, so 4 & 4/7 rounds to 4 & 1/2 when rounding to the nearest half.
Adding 3 to 4 & 1/2 gets 7 & 1/2 since we add the whole parts 3+4 = 7, and the fractional part stays as it is.
-----------
Check:
(3 + 3/18) + (4 + 4/7) = 7.738 approximately
7 + 1/2 = 7.5 exactly
The two results aren't too far off. The estimate of 7 & 1/2 is an underestimate.
Answer:
About 7 1/2 ounces
Step-by-step explanation:
Add your whole numbers first, 3 + 4 = 7
Now the fractions:
3/18 = 1/6
Estimate 4/7 + 1/6, the answer is somewhere between 1/2 and 1 whole. Therefore the answer is about 7 1/2
Check:
3/18 × 7/7 = 21/126
4/7 × 18/18 = 72/126
21/126 + 72/126 = 93/126
The actual answer is 7 31/42, so the closest answer is 7 1/2
60 points and branilest if you answer
It takes 3 ½ spoons of chocolate syrup to make 3 ⅗ gallons of chocolate milk. How many spoons of chocolate syrup would it take to make 6 gallons of chocolate milk ?
Answers
Answer: 4 gallons require 5 5/39 spoons of syrup
Step-by-step explanation:
Given it takes 3 2/6 spoons to make 2 3/5 gallons of chocolate milk
i.e. 20/6 spoons make up 13/5 gallons of milk
⇒1 gallon require 20/6/13/5 spoons of milk
⇒ 20 x 5/6 x 13 spoons of milk
⇒ 100/78 spoons of milk
Therefore 4 gallons require 4 x 100/78 spoons
⇒ 400/78 spoons
⇒ 200/39 spoons
⇒ 5 5/39 spoons
Answer:
5 5/6 spoons
Step-by-step explanation:
We can use ratios to solve
3 1/2 spoons x spoons
-------------- = ------------------
3 3/5 gallons 6 gallons
Using cross products
3 1/2 *6 = 3 3/5x
Changing to an improper fraction
7/2*6= 18/5*x
21 = 18/5x
Multiply by 5/18
21 * 5/18 = 18/5 x*5/18
21/18 *5 =x
7/6 *5 =x
35/6=x
Changing to a mixed number
5 5/6 spoons
Mary Seitz invested a certain amount of money in a savings account paying 3% simple interest per year. When she withdrew her money at the end of 3 years, she received in $3900 interest. How much money did Mary place in the savings account?
Answers
Answer:
351
Step-by-step explanation:
3%=0.03
3900*0.03*3=351
We say that a point estimator is unbiased if (choose one):its sampling distribution is centered exactly at the parameter it estimates. The standard deviation of its sampling distribution decreases as the sample size increases. Its sampling distribution is normal. Its value is always equal to the parameter it estimates. Choices (A), (B), and (C) are all true. The next four questions refer to the following information:A study was conducted in order to estimate ?, the mean number of weekly hours that U. S. Adults use computers at home. Suppose a random sample of 81 U. S. Adults gives a mean weekly computer usage time of 8. 5 hours and that from prior studies, the population standard deviation is assumed to be ? = 3. 6 hours
Answers
The correct answer is (A): "its sampling distribution is centered exactly at the parameter it estimates."
An estimator is a statistic that is used to estimate an unknown parameter in a population. A point estimator is a single value that is used to estimate the population parameter. The goal of a point estimator is to provide an estimate that is as close to the true value of the parameter as possible.
One way to evaluate the quality of a point estimator is to look at its bias, which is the difference between the expected value of the estimator and the true value of the parameter it is estimating. An estimator is unbiased if its expected value is equal to the true value of the parameter it estimates. In other words, an unbiased estimator is centered exactly at the parameter it estimates.
In the context of the given problem, the sample mean of weekly computer usage time (8.5 hours) is a point estimator for the population mean weekly computer usage time. To evaluate whether this estimator is unbiased, we would need to look at its sampling distribution and check whether its expected value (i.e., the mean of the sampling distribution) is equal to the true population mean.
Learn more about statistics here: brainly.com/question/15525560
#SPJ4
Based on what you see here, what is the domain of this function?*
Your answer
This is a required question
Answers
Answer:
Domain seems to be all real numbers.
Step-by-step explanation:
To convert the number below to scientific notation, where should you move
the decimal point?
2,000
O A. Three places to the right
O B. Three places to the left
C. Four places to the right
O D. Four places to the left
Answers
Answer:
B. Three places to the left
Step-by-step explanation:
2000.
Move three to the left
2.000
Answer:
B
Step-by-step explanation:
bc I've done it before that and the other ones don't make sense
What happens if simultaneous Equations have two of the same variable like below? How would I solve it?
6A + 4B + 5C = 390
6A + 4B + 5.75C = 405
Answers
Answer:
C = 20
Step-by-step explanation:
What happens if simultaneous Equations have two of the same variable like below? How would I solve it?
6A + 4B + 5C = 390
6A + 4B + 5.75C = 405
Step 1
We solve for C first
6A + 4B + 5C = 390....Equation 1
6A + 4B + 5.75C = 405... Equation 2
We substract Equation 1 from Equation 2
0.75C = 15
C = 15/0.75
C = 20
Use a graphing utility to approximate the real solutions, if any, of the following equation. All solutions lie between - 10 and 10. x4 - 2x +5x - 2=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is { } (Round to two decimal places as needed. Use a comma to separate answers as needed.) O B. There is no real solution.
Answers
To approximate the real solutions of the equation x^4 - 2x + 5x - 2 = 0 using a graphing utility, we can plot the equation on a graph and observe where it intersects the x-axis. By doing so, we can determine the x-values that correspond to the real solutions.
Using a graphing utility, we input the equation and set the x-axis limits between -10 and 10. After plotting the graph, we observe the points where the curve intersects the x-axis. These x-values are the approximate real solutions of the equation.
Upon analyzing the graph, if there are any points where the curve intersects the x-axis, we can note those x-values as the approximate real solutions. If there are no intersections, then there are no real solutions
Therefore, we select the answer choice that corresponds to the x-values where the curve intersects the x-axis. If there are no intersections, we select the answer choice stating that there are no real solutions.
In this case, since we don't have the graph or its details, I am unable to determine the real solutions or whether they exist. Please input the specific x-values obtained from the graphing utility, and I will be happy to assist you further.
To know more about Newton's method visit:
https://brainly.com/question/32559514
#SPJ11
Explain why 10 x 2 is equivalent to 10 ÷ 1/2??
Answers
Answer: Because multiplying or dividing by the reciprocal is the same.
pls helpppppppppppppp
Answers
Answer:
-1/36
Step-by-step explanation:
-5/18 - ( -1/4)
Subtracting a negative is like adding
-5/18 + 1/4
Getting a common denominator of 36
-5/18 *2/2 + 1/4 *9/9
-10/36 + 9/36
-1/36
A rental car agency charges $220.00 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $380.00?
Answers
40 miles per week
Step-by-step explanation:
380-220 = 160÷4 = 40
You can travel 320 miles in one week for $320 miles.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
A rental car agency charges $220.00 per week plus $0.25 per mile to rent a car.
If the amount is $380.
Then, 380 - 220 = 160
And 160 divided by 0.5,
= 160/0.5
= 320 miles.
Therefore, the required distance is 320 miles.
To learn more about the division;
https://brainly.com/question/13263114
#SPJ2
Which statement is true regarding the functions on the
graph?
A. f(-3) = g(-4)
B. f(-4) = g(-3)
C. f(-3) = g(-3)
D. f(-4) = g(-4)
Answers
Answer:
C. f(-3) = g(-3)
Step-by-step explanation:
Let's look at each option to which one is true with regard to the given functions on the graph.
The option that is correct is the option that shows where the graph of f(x) and g(x) intercepts or cut across each other.
Now, take a look at the graph, the line of both functions intercepts at x = -3. At this point, the value of f(-3) and g(-3) is equal to -4.
Therefore: f(-3) = g(-3)
HELP ME PLEASE!!!!!!
Answers
Answer:
53 people
Step-by-step explanation:
\(\frac{2}{5}\) × 120 = = 48
48 + 5 = 53 people
____
You've made your grade level high school, lower it to Grade 4. Thank you!
Find the derivative of the given function. y = 6x2(1 - 5x) dy dx
Answers
Applying the product rule and the chain rule will allow us to determine the derivative of the given function, "y = 6x2(1 - 5x)".
Let's first give the two elements their formal names: (u = 6x2) and (v = 1 - 5x).
The derivative of (y) with respect to (x) is obtained by (y' = u'v + uv') using the product rule.
Both the derivatives of (u) and (v) with respect to (x) are (u' = 12x) and (v' = -5), respectively.
When these values are substituted, we get:
\(y' = (12x)(1 - 5x) + (6x^2)(-5)\)
Simplifying even more
\(y' = 12x - 60x^2 - 30x^2\)
combining comparable phrases
\(y' = 12x - 90x^2\)
As a result, y' = 12x - 90x2 is the derivative of the function (y = 6x2(1 - 5x)) with respect to (x).
learn more about product here :
https://brainly.com/question/31815585
#SPJ11
Use a taylor series to approximate the following definite integral. retain as many terms as needed to ensure the error is less than 10^-3
0.51
∫ In (1+x^2)dx
0
0.51
∫ In (1+x^2)dx ≈ ___
0
(Type an integer or decimal rounded to three decimal places as needed.)
Answers
The definite integral can be approximated as:0.51
∫ ln(1+x^2) dx ≈ 2[(0.51^3)/3 - (0.51^7)/(73) + (0.51^11)/(113*5)]≈ 0.335 (rounded to three decimal places).
We can use a Taylor series expansion of ln(1+x^2) to approximate the definite integral:
ln(1+x^2) = 2∑(-1)^n (x^2)^(2n+1) / (2n+1)
Integrating both sides from 0 to 0.51, we get:
∫ ln(1+x^2) dx = 2∑(-1)^n ∫ x^(4n+2) / (2n+1) dx
Evaluating the integral and plugging in the limits of integration, we get:
∫ ln(1+x^2) dx ≈ 2∑(-1)^n (0.51)^(4n+3) / [(2n+1)(4n+3)]
To ensure that the error is less than 10^-3, we need to determine how many terms we need to include in the series. We can use the remainder term of the Taylor series to estimate the error:
Rn(x) = ln(1+x^2) - 2∑(-1)^n x^(4n+2) / (2n+1)
The remainder term can be bounded by:
|Rn(0.51)| ≤ M * (0.51)^(4n+3+1) / (4n+4)!
where M is a constant upper bound for the (4n+4)th derivative of ln(1+x^2) on the interval [0, 0.51]. We can use a computer algebra system or calculator to find that M ≈ 12.8.To ensure that |Rn(0.51)| < 10^-3, we can solve the inequality:
M * (0.51)^(4n+4) / (4n+4)! < 10^-3
Using trial and error or a calculator, we find that n = 2 gives a sufficiently small error.
For such more questions on Definite integral:
https://brainly.com/question/31344244
#SPJ11
The approximate value of the definite integral is 0.186, accurate to within 10^-3.
We can start by finding the Taylor series for ln(1+x^2) about x=0:
ln(1+x^2) = 0 + 1x^2 - 1/2x^4 + 1/3x^6 - 1/4x^8 + ...
Integrating this series term by term, we get:
∫ ln(1+x^2) dx = C + 1/3 x^3 - 1/10 x^5 + 1/21 x^7 - 1/36 x^9 + ...
where C is the constant of integration.
To ensure that the error is less than 10^-3, we need to bound the remainder term Rn(x) = |f(x) - Tn(x)| by 10^-3, where Tn(x) is the nth-degree Taylor polynomial for ln(1+x^2) centered at x=0.
Using the Lagrange form of the remainder term, we have:
|Rn(x)| ≤ (M/[(n+1)!]) |x-a|^(n+1)
where M is an upper bound on the absolute value of the (n+1)th derivative of ln(1+x^2) on the interval [0,0.51].
Since the (n+1)th derivative of ln(1+x^2) is:
(-1)^n (2^n-1)! / (x^2+1)^n+1
we can see that the absolute value of this derivative is maximized at x=0.51 when n=3. Therefore, we have:
M = |fⁿ⁺¹(ξ)| = 39.0625
where ξ is some point in the interval [0,0.51].
Thus, we need to find the minimum value of n such that:
(39.0625/(n+1)!) (0.51)^(n+1) ≤ 10^-3
We can solve this inequality numerically or by trial and error to find that n=3 is sufficient. Therefore, the fourth-degree Taylor polynomial for ln(1+x^2) is accurate to within 10^-3 on the interval [0,0.51].
Using this polynomial, we have:
∫ ln(1+x^2) dx ≈ C + 1/3 x^3 - 1/10 x^5 + 1/21 x^7
Evaluating this integral from 0 to 0.51 and solving for C using the fact that ln(1+0) = 0, we get:
C = 0
∫0.51 ln(1+x^2) dx ≈ 0 + 1/3 (0.51)^3 - 1/10 (0.51)^5 + 1/21 (0.51)^7
≈ 0.186
Know more about definite integral here:
https://brainly.com/question/29974649
#SPJ11