We have the differential equation, [tex]y''+5y'+4y=2e^{-2x}[/tex]. The question asks to find the particular solution to the DE.
To find the particular solution look at the right-hand-side and make a “guess” of what the solution could be.
Since we have [tex]2e^{-2x}[/tex] we can guess that the particular solution could be in the form [tex]Ae^{-2x}[/tex], where [tex]A[/tex] is some unknown constant.
Now finding the value of the unknown constant, [tex]A[/tex]. Lets say [tex]g(x)=Ae^{-2x}[/tex], find [tex]g'(x)[/tex] and [tex]g''(x)[/tex].
[tex]g(x)=Ae^{-2x}[/tex]
=> [tex]g'(x)=-2Ae^{-2x}[/tex]
=> [tex]g''(x)=4Ae^{-2x}[/tex]
Now plug [tex]g(x)[/tex], [tex]g'(x)\\[/tex], and [tex]g''(x)[/tex] into the given differential equation.
=> [tex]y''+5y'+4y=2e^{-2x}[/tex]
=> [tex](4Ae^{-2x})+5(-2Ae^{-2x})+4(Ae^{-2x})=2e^{-2x}[/tex]
=> [tex]4Ae^{-2x}-10Ae^{-2x}+4Ae^{-2x}=2e^{-2x}[/tex]
=> [tex]8Ae^{-2x}-10Ae^{-2x}=2e^{-2x}[/tex]
=> [tex]-2Ae^{-2x}=2e^{-2x}[/tex]
Compare the coefficients,
=>[tex]-2A=2[/tex]
=>[tex]A=-1[/tex]
So we can say our "guess" to the particular solution of the given differential equation is, [tex]y_{p} =-e^{-2x}[/tex].
What is the measure of the angle formed by Main Street and Park Street?
Answer:
90°
Step-by-step explanation:
they are forming a right angle (90°).
How would one calculate this? would appreciate more of an explanation rather than just an answer.
The man should pull rope A to lift the load more easily
How to determine the ropeFrom the question, we have the following parameters that can be used in our computation:
The diagram
To determine the rope to pull, we calculate the moment at the point
This is calculated as
Moment = Force * Perpendiculat Distance
Using the above as a guide, we have the following:
Point A = F * (6 + 2)
Point B = F * (3 + 1)
Evaluate
A = 8F
B = 4F
8F is greater than 4F
Hence, the man should pull from point A
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Given the table find f(1)
The table of linear function shows that f(1) is equal to -3
What is a linear functionA linear function is a mathematical function of the form f(x) = mx + b, where m and b are constants and x is the input variable. This function produces a straight line on a graph, with a constant slope (m) and a y-intercept (b) where the line intersects the y-axis.
The slope (m) of a linear function represents the rate of change of the function, or the steepness of the line, while the y-intercept (b) represents the value of the function when x=0.
In the function table given, we can find f(1) when we look at the table.
This shows that f(1) is equal to -3
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who knows how to solve this?
The profit was maximum when the current price raised by $2 then the profit falls in further increase of price.
What Does the axis of graph tells?The axis graph displays the point where two real number lines—one vertical and one horizontal (X axis)—intersect (Y axis). The X axis is referred to as the data set's independent variable, while the Y axis is referred to as the data set's dependent variable.
Given:
We have the Graph in which X- axis shows increase in price over the current value of Milkshake and, Y- axis shows Weekly profit Earned.
From the graph we can see that when the amount increased by $2 that gave the maximum profit.
After that it rising the money in prices leads to falls in profit.
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Rationalize the numerator
[tex]\frac{\sqrt{3} -5}{\sqrt{2} +5 }[/tex]
(Simplify your answer. Type an exact answer, using radicals as needed.)
The surd is rationalized to give √6 - 5√3 + 5√2 - 25/2 + 25
How to rationalize the fractionIt is important to note that fractions are a part of whole number or element.
The different types of fraction includes;
Simple fractionsComplex fractionsProper fractionsImproper fractions, etcGiven the expression;
√3 - 5/√2 + 5
√3 - 5/ √2 + 5 ×√2 - 5/√2 - 5
Multiply the values
√6 - 5√3 + 5√2 - 25/√4 - 5√2 + 5√2 + 25
Add the like surds and find the square roots, we get
√6 - 5√3 + 5√2 - 25/2 + 25
Hence, the expression is √6 - 5√3 + 5√2 - 25/2 + 25
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Explain how to use the distributive property to create
an expression that is equivalent to 2b + 5b.
Answer:
Step-by-step explanation:
The variable b is common to each expression.
Take the b out and put the remaining numbers in a parenthesis:
b ( 2 + 7)
b (9)
9b
paula lives 1/9/10 from school. Nate lives 1/3/4 miles from school. Cristian lives 11/8 miles from school. who lives closest to school?
The distance from the school to Cristian home is least which is 1.375 miles.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Paula lives 1 ⁹/₁₀ from school. Nate lives 1 ³/₄ miles from school. Cristian lives 11/8 miles from school.
Convert the mixed fraction and fraction number into a decimal number. Then we have
1 ⁹/₁₀ = 1.90 miles
1 ³/₄ = 1.75 miles
11/8 = 1.375 mies
The distance from the school to Cristian home is least which is 1.375 miles.
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2. A student receives test scores of 62, 83, and 91. The student's term project score is 88 and her homework score
is 76. Each test is worth 20% of the final grade, the term project is 25% of the final grade, and the homework
grade is 15% of the final grade. What is the student's mean score in the class?
3. The median for the given set of six ordered data values is 27.5. What is the missing value? ______
5 12 23 ______ 41 51
4. For the following data, approximate the mean number of emails received per day
Answer:
Step-by-step explanation:
75
You are going to a restaurant, and the subtotal
is $80.00, there is a 6.5% sales tax.
What will the total bill come to?
How much are you paying in sales tax? If you tip a 15% before tax, how much will be
the tip?
How much are you paying in total?
Answer:587
Step-by-step explanation:
Ok so it’s 587 I’m jp
let y1,y2 be independent random variables both having the uniform(0,1) distribution. re- call that the density function and distribution function of a uniform random variable y
A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function.
A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. Accordingly, the likelihood of any specific outcome of y is the same, and the likelihood of any range of outcomes is equal to the length of the range. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function. Accordingly, the length of the range multiplied by the likelihood of any specific occurrence yields the cumulative probability of any range of outcomes. Since the likelihood of any specific result in that range is 1 and the range's length is 0.5, for instance, the cumulative probability of 0 y 0.5 is 0.5. Since the likelihood of any given result within that range is still 1, but the range's length is 0.5, the cumulative probability of 0.5 y 1 is 0.75. The chance of any range of outcomes for y1 and y2 if they are independent random variables both having the uniform(0,1) distribution is just the sum of their respective cumulative probabilities.
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use newton's method to find all real roots of the equation correct to six decimal places. (enter your answers as a comma-separated list.) 4 x = 1 + x3
Using newton's method to find all real roots of the equation, 4x = 1+ x³ is
x1 = -2.11491, x2 = 0.2541, x3 = 1.86081.
We have the equation,
4x = 1+ x³
To find the real roots of equation we have,
x1 = -2.11491, x2 = 0.2541, x3 = 1.86081.
The cubic equation formula in mathematics is how the cubic equation is represented. An equation with degree three is said to be cubic. In nature, the roots of all cubic equations are either one real root and two real roots or three real roots. Cubic polynomials are the name given to three-degree polynomials.
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Pls help with this it’s due soon i need answers pls and thank you
Based on the given triangle, we can find that:
The length of PN is 11The length of GN 37The size of angle ∠GLN is 32First, we will focus on the triangle NLP. NLP is a right triangle, then we can use the formula of sinus to find the length of NP, where:
Sin ∠NLP = NP / LP
Sin 35° = NP / 20
0.57 = NP / 20
NP = 11.47
NP ≈ 11
Next, we will focus on triangle GLP. GLP is a right triangle with hypotenuse of 52 and the base of 20. Using the Phytagoras theorem we can try to find the triangle's height.
GL² = GP² + LP²
52² = GP² + 20²
2704 = GP² + 400
GP² = 2304
GP = 48
GP = GN + NP
48 = GN + 11
GN = 37
To find the size of angle ∠GLN, we have to find the size of angle ∠PGN first. We will use the Sines Law:
LP / sin ∠PGN = GL / sin ∠GPN
20 / sin ∠PGN = 52 / 1
sin ∠PGN = 20/52
∠PGN = 22.5°
∠PGN ≈ 23°
∠GLP + ∠GPL + ∠PGN = 180°
∠GLP + 90° + 23° = 180°
∠GLP = 67°
∠GLP = ∠GLN + ∠NLP
67° = ∠GLN + 35°
∠GLN = 32°
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How do you find the asymptotic complexity of a function?
To find the asymptotic complexity of a function, you need to analyze the behavior of the function as the size of the input grows. You need to determine the number of operations that are performed by the algorithm, and express this as a function of the size of the input.
What is the asymptotic complexity?
Asymptotic complexity is a measure of the growth rate of the running time of an algorithm as the size of the input grows towards infinity. It is expressed using big O notation, which provides an upper bound on the growth rate of the running time.
Here are the steps to find the asymptotic complexity of a function:
Identify the dominant operation: Identify the operation in the algorithm that takes the most time, and consider only this operation for analyzing the asymptotic complexity.Express the dominant operation as a function of the size of the input: Express the number of times the dominant operation is performed as a function of the size of the input. This function will represent the running time of the algorithm.Simplify the function: Simplify the function by ignoring lower order terms and constant factors. The goal is to express the running time in terms of a basic mathematical function that grows at the same rate as the original function.Express the simplified function using big O notation: The big O notation provides an upper bound on the growth rate of the running time. The simplified function can be expressed using the big O notation, which expresses the running time in terms of the size of the input, 'n', and a basic mathematical function.To learn more about asymptotic complexity, Visit
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A college finds that 8% of students have taken a distance learning class and that 30% of students Part (e) Are D and E mutually exclusive? Explain.are part-time students. Of the part-time students, 20% have taken a distance learning class. Let D = event that a student takes a distance learning class and E = event that a student is a part-time student. Part(a) Find P(D AND E )Part (b) Find P(EID). Part (c) Find P(D OR E). Part (d) Are D and independent?
(a) P(D and E) is equal to 0.06.
(b) P(E | D) is equal to 0.75.
(c) P(D or E) is equal to 0.32.
(d) D and E are not independent.
(e) D and E are not mutually exclusive.
The solution has been obtained using probability.
What is probability?
Probability is a mathematical concept used to determine the likelihood of an event. It merely allows us to calculate the probability or possibility that an event will occur. The range of probabilities lies between 0 and 1, where 1 signifies a certain event and 0 denotes an impossibility.
We are given the following:
No. of students that have taken a distance learning class = 8%
No. of students that are part-time students = 30%
No. of part-time students that have taken a distance learning class = 20%
Let D = event that a student takes a distance learning class and E = event that a student is a part-time student.
(a) Since, 20% of the part times students are taking distance learning classes (D and E) so,
P(D and E) = 0.3 * 0.2 = 0.06
(b) P (E | D) = P (D and E) / P (D)
P (E | D) = 0.06 / 0.08
P (E | D) = 0.75
(c) P (D or E) = 0.3 + 0.08 - 0.06 = 0.32
(d) For events to be independent, probability of D and E must be equal to P(D) x P(E).
But, P(D and E) ≠ P(D) x P(E)
So, D and E are not independent.
(e) Events are considered mutually exclusive if they do not occur at the same time.
But, D and E can occur at the same time.
So, D and E are not mutually exclusive.
Hence, the solutions have been obtained.
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if f(x) is discontinuous, determine the reason. f of x equals the quantity x squared plus 4 for x less than 1 and equals x plus 4 for x greater than 1
The two equations for f(x) are not equal at x = 1 and f(x) is therefore discontinuous at this point
f(x) is discontinuous at x = 1 because when x = 1, the two separate equations for f(x) do not have the same output. For x < 1, [tex]f(x) = x^2 + 4[/tex], so when x = 1, [tex]f(1) = 1^2 + 4 = 5. For x > 1, f(x) = x + 4[/tex] , so when x = 1, f(1) = 1 + 4 = 5. The output of f(1) is different on each side of the discontinuity. This can be seen in the following calculation:
For x < 1,
[tex]f(x) = x^2 + 4f(1) = 1^2 + 4 = 5For x > 1,f(x) = x + 4f(1) = 1 + 4 = 5[/tex]
Since f(1) is 5 for x < 1 and f(1) is also 5 for x > 1, the two equations for f(x) are not equal at x = 1 and f(x) is therefore discontinuous at this point.
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Which supplementary angles can prove
that lines L and M are parallel?
A
L-
+
M-
A. 3 and 4
B. 3 and 5
C. 7 and 8
2
3 4
5 6
78
3 and 5 supplementary angles can prove that lines L and M are parallel. The solution has been obtained by using the properties of parallel lines.
What are parallel lines?
In a plane, lines that are parallel to one another do not meet or overlap at any point. They are always parallel and equally spaced apart. Parallel lines are non-intersecting lines. Infinity is another place where parallel lines are believed to meet.
We are given a set of parallel lines and various angles are marked on the lines.
Angles 3 and 4 can not prove that the lines are parallel because they lie on the same line.
Similarly, angles 7 and 8 can also not prove.
But, angles 3 and 5 can prove this because they lie on different lines i.e. they belong to both the lines.
Hence, 3 and 5 supplementary angles can prove that lines L and M are parallel.
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Complete question:
\Which supplementary angles can prove that lines L and M are parallel?
A. 3 and 4
B. 3 and 5
C. 7 and 8
What is the weighted average length of the nails in the drawer?
A. 350 cm
B. 333 cm
C. 5.00 cm
D. 3.50 cm
(the answer is D)
^this is a reminder for me)
The weighted average length of the nails in the drawer is given as follows:
D. 3.50 cm.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
For the weighted mean, each observation is multiplied by it's weight.
Considering the percentages as the weights, the weighted average length of the nails in the drawer is obtained as follows:
0.705 x 2.5 + 0.19 x 5 + 0.105 x 7.5 = 3.5.
Meaning that option D is the correct option for this problem.
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Margaret made 15 pullovers during the year.her teacher said 9 of them were very good. What percentage was this
Answer:
60%
Step-by-step explanation:
9/15 converted = 0.6 = 60%
Let AA be the event that a randomly selected IRSC student is an Associate of Arts student and
P(AA) = 0.41. Let the event PM be the event that a randomly selected IRSC student is on the pre-med
degree track and P(PM) = 0.38. Finally, the probability that a randomly selected IRSC student is an AA degree seeker and on the pre-med degree track is 0.05. Use this information to calculate the following
probability.
Answer:
P(AA) = 0.41
P(PM) = 0.38
P(AA and PM) = 0.05
As you are finding P(AA or PM), you can apply the formula:
P(A U B) = P(A) + P(B) - P( A ∩ B)
U = Union P( A U B) = P (A or B)
∩ = And
From the formula, you can find out the answer:
P(AA or PM) = P(AA) + P(PM) - P(AA and PM)
= 0.41+0.38-0.05
= 0.74
hope this helps!!!!
Step by step please, need help. Good luck and thank you for your help
Answer:
B) Linear Pair
D) Adjacent
E) Supplementary
Step-by-step explanation:
Because the sum of the two angles is 180°, we conclude that the correct options are:
B, D, and E.
Which is the relationship between the two angles?We want to find the relationship between angles a and b.
Notice that if we would add these two angles, we would get a plane angle, then we could write:
∠a + ∠b = 180°.
That means 3 things:
The angles are adjacent because share a vertex and a common side, and the angles are supplementary because their sum is equal to 180°, and also are a linear pair, because their sum is equal to 180°.
Then the correct options are:
B, D, and E.
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please help, urgent!!!!!
Answer:
[tex]\frac{6}{15} - \frac{5}{15} = \frac{1}{15}[/tex]
Step-by-step explanation:
Simplify-(-5) and -|-2|
(I don’t understand the steps)
Answer: -(-5) =5
-|-2| = -2
Step-by-step explanation:
Two negatives = positives
Glad to help do you mind clicking the crown for me it would really help please and thank you have a blessed day!
kenia wants to buy a $75.00 skateboard. She has 25.00 saved so far. she mows lawns to make extra money and earns 20.00 for each lawn she mows. Which inequality can be used to determine the number of lawns, x, she needs to mow to have enough money to buy the skateboard
Step-by-step explanation:
75.00 - 25.00 = 50.00
50.00 / 20.00 = 2.50
So, she needs to mow 2.5 lawns or more to have enough money to buy the skateboard.
The inequality can be expressed as:
20.00 * x >= 50.00
x >= 2.50
So, the inequality "x >= 2.50" can be used to determine the number of lawns she needs to mow to have enough money to buy the skateboard.
Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that enclose his front yard. The length is five feet less than three times the width. Find the length and width of the fencing.
The length and the width of the fencing are 85 feet and 30 feet respectively.
What is a rectangular perimeter?The whole distance that a rectangle's borders, or its sides, the cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.
Given:
Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that encloses his rectangular front yard.
The length is five feet less than three times the width.
Let w be the width.
Then, 3w - 5 is the length.
So, the perimeter of the rectangular fence = 200 + w.
Now, 2(3w - 5 + w) = 200 + w
6w - 10 + 2w = 200 + w
7w = 210
w = 30
Then length = 85
Therefore, length = 85 feet and width = 30 feet.
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Determine for each of the following which of the figures
labeled (1) through (10) can be classified under the given term:
As per the given triangles given in the question, the corresponding names are mentioned accordingly in the answer.
How do triangles work?A triangle is a basic polygonal geometry with three sides and three interior angles. This is a fundamental geometric shape that is particularly related. Its three vertices are joined together. Depending on their sides and angles, triangles can be classified into a wide range of groups.
In geometry, there are six different kinds of triangles. There are two categories into which they can be divided. The three triangles are categorized as equilateral triangles, isosceles triangles, and scalene triangles based on their sides. Triangles can be classified as acute, obtuse, or right-angled depending on the angle at which they are formed. There are so six different kinds of triangles in geometry.
As per the given information in the question,
a. 1, 2
b. 1
c. 2
d. 6
e. 5, 6, 7
f. 7
g. 6
h. 6
i. 4, 6
j. 4, 6
k. 4, 8
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Complete question -
100 points!!!
There is a pic if you click on it
Here is a graph that shows the water height of the ocean between September 22 and September 24, 2016 in Bodega Bay, CA.
1. The water's height at 12 pm on September 22 was given as follows: 3.5 feet.
2. The number of times that the water's height was of 5 feet is of: 4 times.
3. The lowest rate the water got during this time period was of: 0.5 feet at 12 pm on 09/24.
4. The water never reaches a height of 6 feet.
How to make the estimates?The estimates are made considering the graph of the function.
The input and the output of the graph are given as follows:
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In this polygon, all angles are right angles.
What is the area of this polygon?
Enter your answer in the box.
ft²
Polygon in the shape of a letter L, which could be formed by a horizontal rectangle attached along the bottom part of a vertical rectangle. The left side of the figure is 18 ft, the bottom side of the figure is 21 ft, the right side of the figure is 8 ft, and the top part of the horizontal rectangle to the right of the vertical rectangle is 12 ft.
On solving the provided question, we can say that the area of the rectangle polygon is 474 ft².
What is rectangle?A rectangle in Euclidean geometry is a parallelogram with four slight angle. It may alternatively be described as a hexagon that is basic rule, or one in which all of the angles are equal. A straight angle is another another option for the parallelogram. In a square, four of the vertices are the same length. A quadrilateral with a rectangle-shaped cross section has four 90 ° angle vertices + equal parallel sides. As a result, it is sometimes referred to as a "equirectangular rectangle". Due to such equal and parallel dimensions of its two sides, a rectangle is occasionally referred to as parallelogram.
The left rectangle has a height of 18 ft and a width of 21 ft, so its area is:
[tex]18 ft x 21 ft = 378[/tex] ft²
The right rectangle has a height of 12 ft and a width of 8 ft, so its area is:
[tex]12 ft x 8 ft = 96[/tex] ft²
Therefore, the total area of the polygon is:
378 ft² + 96 ft² = 474 ft²
So the area of the polygon is 474 ft².
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If the size of one object is 8.5*10^-4 meters and the size of a second object is 3.7*10^6, how many times bigger is the second object compared to the first object?
The second object is approximately 4.4 * 10^9 times bigger than the first object.
Division of numbers involving Scientific Notation.The division of the value of the second scientific notation from the first scientific notation is the precise and accurate way with which we can determine many many times bigger is the second object compared to the first object.
To do so, group coefficients together and exponents together to divide numbers in scientific notation. i.e.
= (3.7/8.5) * ((10^6)/(10^−4))
= 0.43529411 × ((10^6)/(10^−4))
Subtract the exponent from the denominator from the exponent of the numerator for the same base 0.43529411 ⋅ 10^(6 −4*−1)
= 0.43529411 × ((10^6+4)
= 0.43529411 × 10^10
= 4.3529411 × 10^9
≅ 4.4 × 10^9
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Determine whether each statement is always true, sometimes true, or
never true.
1. Every square is a rhombus.
2. Every rhombus is a parallelogram.
3. Every rectangle is a parallelogram.
4. The diagonals of a square are perpendicular.
5. If the diagonals of a quadrilateral bisect each other, then the
quadrilateral is a square.
6. If the diagonals of a quadrilateral are perpendicular, then the
quadrilateral is a rhombus.
7. The diagonals of a rectangle are congruent.
8. The diagonals of a rhombus bisect the vertex angles.
9. Some rectangles are rhombi.
10. Some rhombi are squares.
Here the statements 1, 2, 3, 4, 5, 7, 8, 10 are correct according to the rules of the shapes.
1: A rhombus is a quadrilateral with four equally sized sides. Each square is a rhombus since they all have four sides that are the same length. 2: Due to the parallel alignment of its opposing sides, every rhombus is a parallelogram. 3: It is true that all rectangles are parallelograms since they have two sets of parallel sides and two pairs of equal opposing sides. 4: The other is split into two equal halves by each bisector. 5: If a quadrilateral's diagonals are equal and bisect one another at right angles, it is a square. 7: Since the diagonals themselves are congruent, each bisected line segment is also congruent. 8: The diagonals split a rhombus's vertex angles into equal halves. The diagonals of a rhombus are at right angles to one another. 10: A square is a rhombus. Sometimes, this is accurate. When a rhombus has four right angles, it is true. So the statements 1,2,3,4,5,7,8,10 are correct.
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There will be 1,825 campers at a state summer camp this year. If each cabin has 2 counselors for every 25 campers, what prediction can you make about the number of counselors who will be at the state camp?
A There will be about 23 counselors there.
B There will be about 146 counselors there.
C There will be about 900 counselors there.
D There will be about 913 counselors there.
Answer: B
Step-by-step explanation:
1825/25=73
73*2=146
146