That 16 meters of electric wire costs 3214, one meter of electric wire costs 3214/16 = 200.6875.
To find the expense of 11 meters of wire, increase the expense per meter by 11:
Cost of 11 meters of wire = 11 * 200.6875 = 2,207.5625
Thus, Jermaine's dad will burn through 2,207.5625 for 11 meters of wire.
The expense of 16 meters of electric wire is 3214, so the expense per meter can be determined by separating the complete expense by the quantity of meters: 3214/16 = 200.6875. To find the expense of 11 meters of wire, we increase the expense per meter by 11: 200.6875 * 11 = 2,207.5625. This implies that Jermaine's dad will burn through 2,207.5625 for 11 meters of wire. This computation gives the expense of the wire in view of a known cost for every meter, permitting us to effortlessly gauge the expense of various lengths of wire.
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The complete question is :
16 m of electric wire costs 3214, how much will jermaine's father spend for the 11 m of wire cost?
ten people are sitting in a row of ten chairs, chewing gum. each person spits out their gum and places it either under their own chair or under an immediately adjacent chair. how many ways can this happen such that every chair ends up with exactly one piece of gum under it?
There are 512 ways that every chair can end up with exactly one piece of gum under it.
This problem can be solved using the Principle of Inclusion-Exclusion.
Let's call the number of ways that gum is placed under a chair i "Ai". Then we have:
A1 = 1
A2 = 2
A3 = 4
...
A10 = 1024
Now, we want to calculate the number of ways that gum is placed under every chair such that exactly one piece of gum is placed under each chair. To do this, we need to subtract the number of ways that gum is placed under two chairs and add the number of ways gum is placed under three chairs, and so on.
The number of ways that gum is placed under two chairs can be calculated as:
C(10, 2) * 2^8 = 45 * 256 = 11520
The number of ways that gum is placed under three chairs can be calculated as:
C(10, 3) * 2^7 = 120 * 128 = 15360
Continuing this process, we have:
A = 1024 - 11520 + 15360 - 14336 + 8192 - 2048 + 256 - 16 + 1 = 512
So there are 512 ways that every chair can end up with exactly one piece of gum under it.
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There are 512 ways that every chair can end up with exactly one piece of gum under it.
This problem can be solved using the Principle of Inclusion-Exclusion.
Let's call the number of ways that gum is placed under a chair i "Ai". Then we have:
A1 = 1
A2 = 2
A3 = 4
...
A10 = 1024
Now, we want to calculate the number of ways that gum is placed under every chair such that exactly one piece of gum is placed under each chair. To do this, we need to subtract the number of ways that gum is placed under two chairs and add the number of ways gum is placed under three chairs, and so on.
The number of ways that gum is placed under two chairs can be calculated as:
C(10, 2) * 2^8 = 45 * 256 = 11520
The number of ways that gum is placed under three chairs can be calculated as:
C(10, 3) * 2^7 = 120 * 128 = 15360
Continuing this process, we have:
A = 1024 - 11520 + 15360 - 14336 + 8192 - 2048 + 256 - 16 + 1 = 512
So there are 512 ways that every chair can end up with exactly one piece of gum under it.
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the position of the particle as a function of time is given by x(t) = e-(t - 3)2, where x is in meters and t is in seconds. what is the velocity of the particle, in meters per second, at t = 2.9 s?
For a particle having a position of function e^-(t - 3)², the velocity at 2.9s is obtained as 0.198008 m/s.
What is velocity?
The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.
The position of a particle is denoted by a function x(t) = e^-(t - 3)², where x is the distance and t is the time.
Differentiate the function -
v(x) = d/dt(x) = d/dt[e^-(t - 3)²]
v(x) = e^-(t - 3)²[-2(t - 3)]
Now, substitute the value of t = 2.9 in the equation -
v(2.9) = e^-(2.9 - 3)²[-2(2.9 - 3)]
v(2.9) = e^-(-0.1)²[-2(-0.1)]
Use the exponent formula a^-b = 1/a^b -
v(2.9) = 1/e^(-0.1)²[0.2]
Square the digit (0.1) -
v(2.9) = 1/e^(0.01)[0.2]
Substitute the value ofe^0.01 = 1.01005 -
v(2.9) = (1/1.01005)[0.2]
Use the arithmetic operation of division -
v(2.9) = (0.99004)[0.2]
v(2.9) = 0.198008
Therefore, the velocity of the particle is 0.198008 m/s.
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112 is what percent of 320?
Answer:
Step-by-step explanation:
It is 35%
First turn the question into a fraction which is 112/320, and now since it is asking for percentage we multiply the whole fraction by 100 which will look like this:
112/320 X 100.
If you put that into the calculator you will get 35. But you can also do it mentally.
If you choose to do it mentally, we go left to right so 112 X 100 = 11200 and then divide 11200 by 320 and you get 35.
Neil rents a bike that costs $12 for 4 hours and $18 for 7 hours. Whats the slope?
Answer: 2
Step-by-step explanation:The slope of a line is the ratio of the change in y-values to the change in x-values between two points on the line.
To find the slope, we first need to find two points on the line, for example (4,12) and (7,18).
Then, the slope can be calculated as:
(18 - 12) / (7 - 4) = 6 / 3 = 2.
The slope is 2.
Name the seven types of quadrilaterals?
Different Quadrilateral Types
Trapezium.Parallelogram.Rectangle.Rhombus.Square.Kite.What is meant by quadrilateral?A polygon with four sides, four vertices, and four angles is called a closed quadrilateral. A polygon with four sides, such as a square, rectangle, or rhombus, is referred to as a quadrilateral.You are most likely currently staring at a computer screen that resembles a quadrilateral. Geometry lessons cover the quadrilateral as a geometrical shape.A polygon with four sides exactly is referred to as a quadrilateral. The fact that a quadrilateral has exactly four vertices and four angles is also implied by this. When discussing 2-D figures, it's common to talk about both the inside and the boundary (the line segments that make up the figure's edges).To learn more about quadrilaterals, refer to:
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Please help me outtt
Hey there!
|2x + 1| < -4
Since you have an absolute value that is LESS than 0, we can say that it doesn’t have any solutions.
Thus, your answer should be:
NO SOLUTIONS
REMEMBER: If your absolute value is smaller/less than 0, you would NOT have any solutions to the particular equation (like this one you have provided just now)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A restaurant has 50 tables. 40% of the tables have 2 chairs at each table. The remaining 60% of the tables have 4 chairs at each table. How many tables have 2 chairs?
Answer:
There are 20 tables with 2 chairs and 30 tables with 4 chairs in the restaurant. To calculate this, you can use the following formula: 40% of 50 tables = 50 x 0.4 = 20 tables with 2 chairs. The remaining 60% of 50 tables = 30 tables with 4 chairs.
The function h(x) = -x +34 models the height of the roof of a house, where x is the horizontal distance from the center of the house. If a raindrop
falls from the end of the roof, how far from the center of the base does it land? Explain your solution.
The horizontal distance of a raindrop that falls from the end of the roof to the center of the base of the house, obtained from the linear equation for the height of the roof is; x = 18 feet
What is a linear equation?A linear equation is an equation that has one as the highest index, and which when graphed, forms a straight line.
The linear function for the height of the roof is, h(x) = -|x| + 34
Where;
h(x) = The height of the roof
x = The horizontal distance from the center of the roof
The minimum height of the roof, obtained from the diagram = 16 feet
Therefore, we get, when h(x) 16, substituting the value h(x) = 16, in the function for the height of the roof, we get;
h(x) = -|x| + 34
h(x) = 16
Therefore, 16 = -|x| + 34 (substitution property)
|x| = 34 - 16 = 18
The distance from the center of the house, which corresponds to the least height of the roof, which is the end of the roof and the location at which the raindrop falls is; x = 18 feet
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What does it mean when a histogram is skewed left?
The mean is frequently less than the median when the distribution of the data is skewed to the left. The mean is frequently higher than the median when the distribution is skewed to the right.
What is a histogram?
A histogram is a representation of statistical data that makes use of rectangles to display the frequency of data items in a series of equal-sized numerical intervals. The independent variable is plotted along the horizontal axis and the dependent variable is plotted along the vertical axis in the most popular type of histogram.
Left-skewing histograms: As seen in the example below, some histograms will have a left-skewing distribution. Negatively skewed refers to a distribution that is skewed to the left. There are many instances of this type of distribution on the right side's upper-value cells, while there are few instances on the left side's lower-value cells (left side). When information is gathered from a system with a boundary, such as 100, a skewed distribution, such as 100, can result. In other words, none of the data that was gathered has values greater than 100.
Some histograms will display a distribution that is skewed to the right, as shown below. Positive skewness refers to a distribution that is skewed to the right. Large numbers of occurrences in the lower-value cells (left side) and few in the upper-value cells characterize this type of distribution (right side). When information is gathered from a system with a boundary like zero, the distribution may become skewed. In other words, all the data that was gathered has values that are greater than 0.
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The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system. [1 0 0 -2 1 0 0 0 -3 1 0 0 0 -1 1 4 -5 4 3] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The solution has infinitely many elements.
O B. The solution set is empty.
The solution set contains one solution:
The solution to the original system is:x1 = 0, x2 = 0, x3 = -1, x4 = -3, x5 = 1
How to find the solution to the original system?The given matrix is in row echelon form, meaning that the leading entry of each non-zero row is to the right of the leading entry of the previous row. In this form, the solution to the linear system can be found by back substitution.
Starting from the bottom row, we have the equation:
-1 * x4 + 4 * x5 = -1
Solving for x4, we have:
x4 = -4 * x5 + 1
Moving up to the next row, we have:
0 * x1 + 0 * x2 + 3 * x5 = 3
Solving for x5, we have:
x5 = 1
So, x4 = -4 * 1 + 1 = -3.
Next, the third row gives us:
0 * x1 + 0 * x2 - 3 * x3 + 4 * x4 = 4
Substituting the value of x4, we have:
0 * x1 + 0 * x2 - 3 * x3 + 4 * (-3) = 4
Solving for x3, we have:
x3 = -1
Since there are no more non-zero rows in the matrix, we have found a complete solution for the linear system.
The solution set of the original system is the set of all possible values of (x1, x2, x3, x4, x5) that satisfy the system of equations represented by the matrix. Since the given matrix is in row echelon form, this solution set is unique and consists of a single point in the 5-dimensional space.
The solution to the original system is:
x1 = 0, x2 = 0, x3 = -1, x4 = -3, x5 = 1
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5. what is the average for the following set of numbers: 10.2, 12.5, 13.3, 15.5, 9.6, 10.7
The average of the set of numbers 10.2, 12.5, 13.3, 15.5, 9.6, 10.7, is 11.9[tex]\overline{6}[/tex]
What is an average value?An average is the sum of a set of values divided by the number of values sin the set. The average value, which is also known as the mean, value in descriptive statistics, is a measure of central tendency, which helps describes the values within a set of data.
Therefore, the average of the set of numbers can be found by adding the numbers together, and dividing the result by the count of the numbers as follows;
The sum of the numbers, ∑ = 10.2 + 12.5 + 13.3 + 15.5+ 9.6 + 10.7 = 71.8
The count of the set of numbers, n = 6
The average = ∑/nTherefore, the average = 71.8/6 = 11 29/30 = 11.9[tex]\overline{6}[/tex]
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What are the patterns?
(Please help I have no idea)
Line 1:
Line 2:
Line 3:
The patterns are:
Line 1: T A C G T T T A A T G A G G C C C T A G T G
Line 2: T C C C C T A G T C G T G G C C T A A A G T C
Line 3: A C T G C T A G C T A C G T T A T C G T C C G
What is base pairing?Base pairing rule refers to the specific pairing of nitrogenous bases in DNA. According to this rule, adenine (A) pairs with thymine (T) and cytosine (C) pairs with guanine (G) through hydrogen bonds. This base pairing results in a complementary sequence of nucleotides on the two strands of DNA, forming a stable double helix structure.
The base pairing rule ensures the accurate replication and transmission of genetic information from one generation to the next. The DNA strands become:
a. Original: A T G C A A A T T A C T C A C C G G G A T C A C
Complementary: T A C G T T T A A T G A G G C C C T A G T G
b. Original: A G G G G A T C A G C A C C G G A T T T C A T G
Complementary: T C C C C T A G T C G T G G C C T A A A G T C
c. Original: T G A C G A T C G A T G C A C A T G C A T G G C
Complementary: A C T G C T A G C T A C G T T A T C G T C C G.
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a rectangular bin with a square base, an open top, and a volume of 62,500 cm3 is to be made. what is the minimum surface area for the bin? enter only the minimum surface area, and do not include units in your answer.
Minimum surface area of rectangular bin with 62,500 cm^3 volume and square base is 31250 cm^2.
What is rectangle ?
A rectangle is a two - dimensional shape with four sides, where each pair of opposite sides are equal in length and parallel to each other
Let's say the length, width and height of the rectangular bin are l, w and h respectively. The volume of the bin can be expressed as:
V = l * w * h = 62500 cm^3 (Given)
Since the base is a square, have w = l. Therefore,
V = l^2 * h
h = V / l^2 = 62500 / l^2
The surface area of the bin can be expressed as:
A = 2lw + 2lh + 2wh
Substituting the value of w = l and h = V / l^2, get:
A = 2l^2 + 2l * (V / l^2) + 2l * l = 2l^2 + 2V / l + 2l^2 = 4l^2 + 2V / l
To minimize the surface area, differentiate A with respect to l and set it to zero:
dA/dl = 8l + 2V / l^2 = 0
4l^3 = V
l^3 = V / 4
Taking the cube root of both sides,
l = (V / 4)^(1/3)
Substituting the value of V,
l = (62500 / 4)^(1/3) = (15625)^(1/3) = 125 cm
Since w = l,
w = 125 cm
h = V / l^2 = 62500 / (125)^2 = 250 cm
The minimum surface area is then given by,
A = 2lw + 2lh + 2wh = 2 * 125 * 125 + 2 * 125 * 250 + 2 * 125 * 125 = 31250 cm^2
Minimum surface area of rectangular bin with 62,500 cm^3 volume and square base is 31250 cm^2.
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Minimum surface area of rectangular bin with 62,500 cm³ volume and square base is 31250 cm^2.
A rectangle is a two - dimensional shape with four sides, where each pair of opposite sides are equal in length and parallel to each other
Let's say the length, width and height of the rectangular bin are l, w and h respectively. The volume of the bin can be expressed as:
V = l * w * h = 62500 cm³ (Given)
Since the base is a square, have w = l. Therefore,
V = l² * h
h = V / l² = 62500 / l²
The surface area of the bin can be expressed as:
A = 2lw + 2lh + 2wh
Substituting the value of w = l and h = V / l^2, get:
A = 2l² + 2l * (V / l²) + 2l * l = 2l²+ 2V / l + 2l² = 4l² + 2V / l
To minimize the surface area, differentiate A with respect to l and set it to zero:
dA/dl = 8l + 2V / l² = 0
4l³ = V
l³ = V / 4
Taking the cube root of both sides,
l = (V / 4)^(1/3)
Substituting the value of V,
l = (62500 / 4)^(1/3) = (15625)^(1/3) = 125 cm
Since w = l,
w = 125 cm
h = V / l² = 62500 / (125)²= 250 cm
The minimum surface area is then given by,
A = 2lw + 2lh + 2wh = 2 * 125 * 125 + 2 * 125 * 250 + 2 * 125 * 125 = 31250 cm²
Minimum surface area of rectangular bin with 62,500 cm^3 volume and square base is 31250 cm².
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What can you infer about non-Euclidean geometry
Non-Euclidean geometries provide a different and more general view of geometry that can help better understand the nature of space and the relationships between objects in the world .
What is Non-Euclidean geometry ?Non-Euclidean geometry is a branch of mathematics that studies the properties and characteristics of geometries that are different from Euclidean geometry, which is the traditional study of geometry and the one most people are familiar with .
Non-Euclidean geometries differ from Euclidean geometry in that they have different postulates , or basic assumptions , about the relationships between points, lines, and angles .
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the distribution of prices for a certain car model is approximately normal with mean $21,800 and standard deviation $400. a random sample of 4 cars of the model will be selected. what is the correct unit of measure for the mean of the sampling distribution of x¯ ?
The required unit of the measure of the mean is given in Dollars. Option A is correct.
Given that:
The distribution of prices for a certain car model is approximately normal with a mean of $21,800 and a standard deviation of $400. A random sample of 4 cars of the model will be selected.
The correct unit of measure for the mean of the sampling distribution of the price of the car is to be determined,
The mean of the values is the ratio of the total sum of values to the number of values.
Since the given data is of price in dollars so the measure of the mean will also be taken in Dollars because the mean is defined as the sum of all the values in a particular unit divided by the total number of different quantities.
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What is the percent of increase from 40 to 48
how to reccepts 10 integers from the user using an array and a loop. the user will type the input on the console.
The reaccepts 10 integers from the user using an array and a loop is explained below.
To start, you need to declare an array variable that can store 10 integers. For example, you can declare an array variable called "numbers" as follows:
int numbers[10];
Next, you will use a loop to repeatedly ask the user to input an integer. The loop will run 10 times to receive 10 integers. You can use the for loop for this purpose.
Here is an example:
for (int i = 0; i < 10; i++) {
printf("Enter integer %d: ", i + 1);
scanf("%d", &numbers[i]);
}
In this code, the for loop starts with the value of i being 0. It runs until i is less than 10. After each iteration, i is incremented by 1.
After the loop finishes, all 10 integers received from the user are stored in the numbers array. You can access them using the index of the array.
In conclusion, to receive 10 integers from the user using an array and a loop, you need to declare an array variable, use a for loop to repeatedly ask the user for input, and store the input in the array using the scanf function.
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What is the sum?
(9c-8) + (2c-6)
Answer:
The sum is 11c - 14.
I need help seeing if I’m correct with my answers .please and thank you
Answer:
Step-by-step explanation:
13) 5.38 Slightly off
14) 10.4 Correct
15) Can't read the numbers
16) 11.7 slightly off
17) Can't read (be careful with which side goes where in the Pythagorean Theorem calculation. a^2 + b^2 = c^2 where a and b are the two sides and c is the hypotenuse (across from the right angle).
18) 16.46
19) 10.57
20) 7.04
21) 4.87 It seems that the hypotenuse is given as 7.2, so the equation should be 5.3^2 + x^2 = 7.2^2
22) Same as in 21: 2.7^2 + x^2 = 6.5^2 x = 5.91
[But I'm having difficulty reading the problems due to fuzziness]
−4( w + 1) = −24
Thanku
Christopher plans to repaint some classroom bookcases. He has 8 gallons of paint. All of the bookcases are the same size and and each book requires 2/5 gallons of paint. How many bookcases will he be able to paint?
The number of bookcases that Christopher will be able to paint. given the amount of paint he has, is
How to find the number of bookcases ?Each bookcase would require 2 / 5 gallons of paint and Christopher has 8 gallons of paint to spare.
This means that the number of bookcases that can be painted would be :
= Gallons of paint available / Requirement for each book
Gallons of paint available = 8 gallons
Requirement for each book = 2 / 5 gallons
The number of bookcases is:
= 8 ÷ 2 / 5
= 8 x 5 / 2
= 20 bookcases
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how many faces edges and vertices does a rectangular prism have
A rectangular prism has 6 faces, 8 vertices and 12 edges.
What is rectangular prism?
A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid. A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.
If all the faces of the prism are squares then the rectangular prism is a cube. The volume of a rectangular prism is a measure of the space inside the prism.
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plot y = sin(x), x = 0...720 deg, where only the positive values of y are shown on the plot. use loops (for, while) to generate the x and y data, using 1 degree increments of x.
We convert the x value from degrees to radians using math.radians. If the sine value is positive, we append it to the y_values list. If the sine value is negative, we append 0 to the y_values list instead.
Here's a code snippet in Python that generates the x and y data for the sine function with a 1 degree increment of x from 0 to 720 degrees:
import math
x_values = []
y_values = []
for x in range(0, 721, 1):
x_values.append(x)
y = math.sin(math.radians(x))
if y >= 0:
y_values.append(y)
else:
y_values.append(0)
In this code, we use the math.sin function to calculate the sine value for a given x in radians. We convert the x value from degrees to radians using math.radians. If the sine value is positive, we append it to the y_values list. If the sine value is negative, we append 0 to the y_values list instead.
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A cup of coffee contains approximately 95 mg of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how long will it take for half of the caffeine to be eliminated from a person’s body?
Please help! Ordering angles least to greatest as well as side lengths
As side EG is the largest side at 15, and the greatest angle is the opposite side's angle, ∠F.
what is triangle ?Given that it consists of sides and three vertices, a triangle qualifies as a polygon. It connects to the fundamental geometric shapes. Triangle ABC is the term used to refer to such a triangle with the points A, B, and C. When the three points are not collinear, a unique plane and triangle in Geometric forms are discovered. Triangles are polygons because they have three sections and three corners. The points where the four structures of the triangle converge are referenced to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.
given
Find the smallest angle by finding the angle opposite the smallest side, then the medium-sized angle by finding the angle opposite the medium-sized side .
Then the greatest angle by finding the angle opposite the largest side when there are three side lengths available.
As side FG is the smallest side at 7, and the smallest angle is the one across from it, ∠ E.
The opposing angle, ∠G, is the medium-sized angle, just as side EF is a medium-sized side as measured by 12.39.
As side EG is the largest side at 15, and the greatest angle is the opposite side's angle, ∠F.
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The complete question is :-
a) Order the angle measures m∠E , m∠F and m∠EGF from least to greatest ad well as side length .
4. Joy earned 20,000 bonus points on her computer assignment. This is 10 times as many bonus points as she earned last week. How many bonus points did Joy earn last week? Explain your thinking.
PLS I NEED THE ANSWER
Answer: Joy earned 2000 bonus points
Step-by-step explanation: Since Joy earned 20000 bonus points last week and the bonus points she earned this week is ten times less than what she earned last week, the full equation would be 20000/10 which would equal 2000.
-1+p<15 what is the value of p?
Answer:
-1+p<15
=-1+1+p<15+1
=p<16
A rectangular field, 400 m long, has an area of 6 hectares. Calculate the perimeter of the field [ 1 hectare=10000m2] What's the answer to this question and what is the way to solve it!
The perimeter of this rectangular field is equal to 1,100 meters.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width of a rectangle.L represents the length of a rectangle.Note: Area = 6 × 10,000 = 60,000 m^2.
Next, we would determine the width of this rectangle:
60,000 = 400W
W = 60,000 /400
Width, W = 150 m.
Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;
Perimeter of a rectangle = 2(L + W)
Perimeter of a rectangle = 2(400 + 150)
Perimeter of a rectangle = 2(550)
Perimeter of a rectangle = 1,100 meters.
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The perimeter of the rectangular field with an area of 6 hectares and length of 400m is 1100 meters.
What is the perimeter of the field?The perimeter of a rectangle is expressed as;
P = 2( length + width )
Given the data in the question;
Length of the field = 400m Area of the field = 60,000m²Width of the field = ?First, we determine the width of the field using the area formula.
Area = Length × width
Plug in the values and solve for width
60,000m² = 400m × width
60,000m² / 400m = Width
Width = 150m
Now, the perimeter will be;
P = 2( 400 + 150 )
P = 2( 550 )
P = 1100 meters.
Therefore, the perimeter is 1100 meters.
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A rectangle has sides measuring (3x + 5) units and (6x + 11) units. Part a: what is the expression that represents the area of the rectangle? show your work to receive full credit. Part b: what are the degree and classification of the expression obtained in part a? part c: how does part a demonstrate the closure property for polynomials?.
Part a: The expression that represents the area of the rectangle is A = (3x + 5)(6x + 11). To calculate the area, we must multiply the two sides of the rectangle together. The length of the rectangle is 3x + 5 units and the width of the rectangle is 6x + 11 units. Therefore, the area is (3x + 5)(6x + 11).
Part b: The degree of the expression obtained in part a is 2 and the classification is a binomial.
Part c: The closure property for polynomials states that the result of combining two polynomials is also a polynomial. In part a, we combined two polynomials, 3x + 5 and 6x + 11, to form the expression (3x + 5)(6x + 11). This expression is also a polynomial, demonstrating the closure property for polynomials. The closure property for polynomials allows us to combine two polynomials and still have a polynomial as the result. This is important in mathematics because it allows us to simplify equations and solve problems more quickly and efficiently.
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Inverse Variation
Independent Practice
Suppose a camper took 2 h to ride around a resevoir at 10 mi/h at the beginning of the summer. By the end of the summer, she can ride around the resevoir in 1
h. What is her rate at the end of the summer?
A. 30 mi/h
B. 0.35 mi/h
C. 13.3 mi/h
D. 9.5 mi/h
Her rate at the end of the summer is 20 miles per hour.
What is her rate at the end of the summer?We can define the rate in this case as the change in position as a function of the time.
So, the rate would be something like a speed (exactly a speed, actually).
Initially, the camper travles at a rate of 10mi/h in 2 hours, so the total distance is:
d = (10mi/h)*2h = 20mi
And at the end of the sumer, the camper travels that distance in one hour, so the rate at the end of the summer is:
R = 20mi/1h = 20mi/h
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