Answer:
There are 14 $10 bills and 16 $20 bills.
Step-by-step explanation:
Let
x = number of $10 bills
y = number of $20 bills
The sum of the value of x and y is $460.
10 x + 20 y = 460 [1]
The sum of x and y is equal to the total number of bills.
x + y = 30
y = 30 - x [2]
We replace [2] in [1],
10 x + 20 (30 - x) = 460
10 x + 600 - 20 x = 460
-10 x = -140
x = 14
We can get y if we replace this value of x in [2].
y = 30 - 14 = 16
Evaluate the integral i = z s f ds when f(x, y, z) = z 2 + 3xy and s is the portion of the plane x + 2y + 2z = 0 above the unit disk x 2 + y 2 ≤ 1 in the xy-plan
To solve the surface integral of a scalar field as given, parametrize the surface S, compute the gradient of the scalar field f, and setup the integral related to the given plane equation and limits of the unit disk. Details of the setup and a specific numerical solution are not provided.
Explanation:The problem you've asked about, i.e., evaluating the integral i = z s f ds when f(x, y, z) = z 2 + 3xy and s is the portion of the plane x + 2y + 2z = 0 above the unit disk x 2 + y 2 ≤ 1 in the xy-plan, falls under the subject of vectors and calculus, particularly triple integrals. It includes a surface integral of a scalar field.
In general, to evaluate a surface integral of a scalar field, first, you should parametrize the surface S with vector function r(u, v). Then you calculate the cross product of partial derivatives of r with respect to u and v to find the surface element dS. In other words, you compute the gradient of the scalar field f.
In this case, you would need to set up the integral with f(x, y, z) and ds related to the given plane equation x + 2y + 2z = 0 and the limits to the unit disk. Solve this integral by any standard method (like substitution or by parts) as needed depending on the complexity of f.
Note: Since the specific setup and solution to this integral could be complex and calculation heavy, a detailed step by step solution is not provided in this formatted answer.
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225/400 in simplest form
The simplified expression of 225/400 is 9/16
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
225/400
Divide 225 and 400 by 25
so, we have the following representation
225/400 = 9/16
This cannot be further simplified
Hence, the simplified expression is 9/16
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The length of a rectangle is 4 meters less than twice the width. If the area of the rectangle is 286 square meters, find the dimensions.
The dimensions of the rectangle are length = 22 meters and width = 13 meters
What is area of rectangle?[tex]A=l\times w[/tex], where 'l' is the length and 'w' is the width of the rectangle.
For given question,
Suppose 'l' is the length and 'w' is the width of the rectangle.
The length of a rectangle is 4 meters less than twice the width.
So, we get an equation,
⇒ l = 2w - 4
The area of the rectangle is 286 square meters.
⇒ A = 286 sq. m.
Using the formula for the area of the rectangle,
[tex]\Rightarrow A=l\times w\\\\\Rightarrow 286=(2w-4)\times w\\\\\Rightarrow 286=2w^2-4w\\\\\Rightarrow 2w^2-4w-286=0[/tex]
Now, we solve the quadratic equation [tex]2w^2-4w-286=0[/tex]
[tex]\Rightarrow 2w^2-4w-286=0\\\\\Rightarrow w^2-2w-143=0\\\\\Rightarrow (w-13)(w+11)=0\\\\\Rightarrow w-13=0~~~or~~~w+11=0\\\\\Rightarrow w=13~~~or~~~w=-11[/tex]
w = -11 is not possible.
So, the width of the rectangle is 13 meters.
And the length of the rectangle would be,
[tex]\Rightarrow l \\= 2w - 4\\=(2\times 13)-4\\=22[/tex]
Therefore, the dimensions of the rectangle are length = 22 meters and width = 13 meters
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The spread of data set X is greater than the spread of data set Y, and the data sets are normally distributed. Which statement is true? The mean of data set X is greater than the mean of data set Y. The median of data set X is less than the median of data set Y. The standard deviation of data set X is greater than the standard deviation of data set Y. The range of data set X is less than the range of data set Y. The mode of data set X is greater than the mode of data set Y.
Answer:
The answer is option C on plato :)
Step-by-step explanation:
In one year, Michael earned $6300 as a work study in college. He invested part of the money at 9% and the rest at 7%. If he received a total of $493 in interest at the end of the year, how much was invested at 7%? How much was invested 9%?
Graph the line for y+1=−35(x−4) on the coordinate plane. What are the coordinates that's all I need to know
which of the fallowing functions has a slope 3/2 and contains the midpoint segment between (6, 3) and (-2, 11)?
on the blueprint of the house 44 millimeters represents 8 meters. the length of the living room is 33 millimeters on the blueprint. what is the actual length of the living room?
The actual length of the living room is 6 meters.
What is unit conversion?
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
Here the unit of lengths, millimeter is converted to meter based on the given scale
For the given situation,
In blue print the house is represented as follows,
44 millimeters = 8 meters
⇒ [tex]1 millimeter = \frac{8}{44} meters[/tex]
⇒ [tex]1 millimeter = 0.18 meters[/tex]
The length of the living room = 33 millimeters
The actual length of the living room in meters = [tex]33(0.18)[/tex]
⇒ [tex]5.94[/tex] ≈ [tex]6 meters[/tex]
Hence we can conclude that the actual length of the living room is 6 meters.
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please please answer these two (16-17) questions
[tex]F(x)=(6 \sqrt{x} -2)(5 \sqrt{x} +7)[/tex]
Sets A and B, shown in the Venn diagram, are such that the total number of elements in set A is twice the total number of elements in set B. Altogether, there are 3011 elements in the union of A and B, and their intersection has 1000 elements. What is the total number of elements in set A?
Ms. Rios buys 453 grams of strawberries she has 23 grams left after making smoothies how many grams of strawberries did she use
Ms. Rios used 430 grams of strawberries to make her smoothies. This is calculated by subtracting the amount left (23 grams) from the total amount purchased (453 grams).
Explanation:To determine how many grams of strawberries Ms. Rios used for making smoothies, we can subtract the quantity of strawberries left unprocessed from the total quantity she originally purchased. In this case, Ms. Rios bought 453 grams of strawberries and had 23 grams left after making smoothies.
The formula to determine the solution would be: Total amassed quantity - Remaining quantity = Used quantity
By filling the above formula with our values, the solution will be as follows: 453 grams (total) - 23 grams (remaining) = 430 grams (used).
Thus, Ms. Rios used 430 grams of strawberries for making smoothies.
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Yearbook sales this year increased 120% over last years yearbook sales. If 465 yearbooks were sold last year, how many were sold this year?
Answer:
This year 1,023 books were sold.
Step-by-step explanation:
Last year the number of yearbooks were sold = 465
This year sales are increased 120% over last years sales.
this year sale = 465 + (120% of 465)
= 465 + ([tex]\frac{120}{100}[/tex] × 465)
= 465 + (1.2 × 465)
= 465 + 558
= 1,023 books
This year 1,023 books were sold.
Suppose there is a strong positive correlation between v and w. Which of the following must be true?
A farmer has 260 feet of fencing to make a rectangular corral. What dimensions will make a corral with the maximum area? What is the maximum area possible?
if it is a square is it a quadrilateral
Out of 6 women would consider themselves baseball fans, with a standard deviation of
The intelligence quotient (iq) test scores are normally distributed with a mean of 100 and a standard deviation of 15. what is the probability that a person would score 130 or more on the test?
The sat scores have an average of 1200 with a standard deviation of 60. a sample of 36 scores is selected. what is the probability that the sample mean will be larger than 1224? round your answer to three decimal places.
Final answer:
The probability that the sample mean of SAT scores will be larger than 1224 is 0.008. This is calculated using the z-score, which in this case is 2.4 after determining the standard error of the sampling distribution.
Explanation:
To find the probability that the sample mean will be larger than 1224, we will use the concept of the sampling distribution of the sample mean. Given the population mean (μ) is 1200 and standard deviation (σ) is 60, and that the sample size (n) is 36, the standard deviation of the sampling distribution, known as the standard error (SE), is
σ/√n = 60/√36 = 10.
We calculate the z-score for the sample mean of 1224 using the formula
z = (X - μ)/SE = (1224 - 1200)/10 = 2.4
A z-score of 2.4 indicates that the sample mean is 2.4 standard errors above the population mean.
To find the probability associated with this z-score, we refer to the normal distribution table or use a calculator. The probability to the left of z = 2.4 is 0.9918. Therefore, the probability that the sample mean is greater than 1224 is
1 - 0.9918 = 0.0082
which can be rounded to three decimal places as 0.008.
Which numbers are a distance of 4 units from 7 on the number line? A number line ranging from negative 3 to 15. Select each correct answer.
3
11
7
15
4
−3
Answer: 3, 11
Step-by-step explanation:
As u see in this screen shot there is wrongs and rights
Simplify the expression where possible. (r 3) -2
Find the unit rate by using WKU. David drove 135 miles in 3 hours.
solve each equation over [0,2pi)
4cos^4x-13cos^2x+3=0
The length of a rectangle is twice its width. The perimeter is 60 ft. Find its area.
Answer:
200 feet squared
Step-by-step explanation:
W=Width
2W=Length
Perimeter = 2*Length + 2*Width
Now use substitution for the Length
60 = 2(2W) + 2(W)
60=4W + 2W = 6W divide both sides by 6
60/6 = 6W/6
10 = W
Width = 10 and Length is twice as long so it is 20. 10+10+20+20=60
The area is Length * Width = 20*10=200
Find the value of kk for which the constant function x(t)=kx(t)=k is a solution of the differential equation 3t3dxdt+5x−3=03t3dxdt+5x−3=0.
Write the following comparison as ratio reduced to lowest terms 194 inches to 17 feet
If the apy of a savings account is 3.7%, and if the principal in the savings account were $3600 for an entire year, what will be the balance of the savings account after all the interest is paid for the year?
Two trains arrived at a station at 2:55 P.M., with one arriving on Track A, and the other arriving on Track B. Trains arrive on Track A every 16 minutes, and they arrive on Track B every 18 minutes. At what time will trains next arrive at the same time on both tracks? A) 4:07 P.M. B) 5:19 P.M. C) 6:31 P.M. D) 7:43 P.M.
For each of the following functions, find the maximum and minimum values of the function on the circular disk: x^2+y^2≤1. Do this by looking at the level curves and gradients.
f(x,y)=x+y+4
maximum value =
To find the maximum and minimum values of the function f(x, y) = x + y + 4 on the circular disk x^2 + y^2 ≤ 1, evaluate the function at the boundary of the disk.
Explanation:To find the maximum and minimum values of the function f(x, y) = x + y + 4 on the circular disk x^2 + y^2 ≤ 1, we can use the method of level curves and gradients.
First, find the gradient of the function f(x, y) using partial derivatives.Next, find the critical points of the function by setting the gradient equal to zero and solving for x and y.Finally, evaluate the function at the critical points and the boundary of the circular disk to find the maximum and minimum values.In this case, since the function f(x, y) = x + y + 4 is linear, it does not have any critical points. Therefore, the maximum and minimum values of the function on the circular disk x^2 + y^2 ≤ 1 are obtained by evaluating the function at the boundary of the disk.
When x^2 + y^2 = 1, the function value is largest at the point (x, y) = (-1, 0), giving a maximum value of -1 + 0 + 4 = 3. The function value is smallest at the point (x, y) = (1, 0), giving a minimum value of 1 + 0 + 4 = 5.
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Beyond Euclidean Geometry.
Many airlines use maps to show the travel paths of all their flights, which are called route maps. For instance, K12Air has a route map that describes all the possible routes to and from Samsville, Shiloh, Camden, Chelsea, Jamestown, and Lorretta.
You have been provided a route map for K12Air. Write a question about this map that involves Hamiltonian or Euler circuits or paths.
Help me come up with a question?
A suitable question to ask about the K12Air route map in the context of Hamiltonian or Euler circuits or paths could be:
Is it possible to find a Hamiltonian circuit on the K12Air route map that allows a plane to travel through each city exactly once before returning to the starting city?
To formulate a question involving Hamiltonian or Euler circuits or paths, one must understand the difference between these concepts:
- A Hamiltonian path is a path in an undirected or directed graph that visits each vertex exactly once. If this path returns to the starting vertex, it is called a Hamiltonian circuit.
- An Euler path is a path in a graph that visits every edge exactly once. If this path starts and ends at the same vertex, it is called an Euler circuit.
Given the context of the K12Air route map, which describes all the possible routes to and from various cities, the question should focus on whether it's possible to traverse the graph representing the route map in a way that satisfies the conditions of either a Hamiltonian or an Euler circuit/
For the Hamiltonian circuit, the question is whether there exists a sequence of flights that allows a plane to start at one city, visit every other city exactly once, and return to the starting city without repeating any city. This would require the route map to have a Hamiltonian circuit, which is a more stringent condition than an Euler circuit because it involves visiting all vertices exactly once.
For an Euler circuit, the question would be whether there exists a sequence of flights that allows a plane to traverse every possible route exactly once before returning to the starting point. This would require the route map to have an Euler circuit, meaning every edge (route) is used exactly once.
In the case of K12Air, the question about the Hamiltonian circuit is particularly interesting because it tests the connectivity of the route map and the possibility of a round trip that covers all cities without repetition. This could be relevant for planning efficient travel itineraries or for optimizing the use of airline resources. If the route map does not allow for a Hamiltonian circuit, one might then ask if a Hamiltonian path exists, which would not require returning to the starting city.
To answer such a question, one would need to analyze the connectivity of the graph represented by the route map, possibly using theorems related to Hamiltonian graphs, such as Dirac's theorem or Ore's theorem, which provide sufficient conditions for a graph to contain a Hamiltonian circuit.