The general solution of the given differential equation is y(x) = C₁e^-x + 4xe^-x. The largest interval over which the general solution is defined is (-∞, ∞). There are no transient terms in the general solution.
The differential equation given can be rearranged into the form dy/dx + (x + 2)/(x + 1)y = 8xe^-x, which is a linear first order differential equation. Using the integrating factor method, an integrating factor of e^(x + 1) can be used to obtain the general solution y(x) = C₁e^-x + 4xe^-x.
The integration constant C₁ can be determined by supplying the appropriate initial conditions. As the equation is a linear first order differential equation, the general solution is valid over the entire domain of x, which is (-∞, ∞). As the equation does not involve any terms that provide a particular value for y at any point in the domain, there are no transient terms in the general solution.
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At Memorial High School, 60 of the 240 freshmen students are on an athletic team sponsored by the school. If the ratio is the same for the sophomore class, how many of the 220 sophomores are NOT athletes
Answer:
165 students or the sophomore class of 220 are not athletic.
Step-by-step explanation:
60/240 = .25 This means that 25% of the class is athletic. That would mean and .75 or 75% are not athletic.
220 x .75 = 165
May I know the answer and steps, thank you.
(3-i/1+i)³
An imaginary number is produced when we square a negative number.
The value of I is -1.
What is the Value of i?This article's introduction included a proposition. The specific measure or value of what I stands for was the subject of the statement. It is discussed in this section of the article along with an explanation of its value.
Iota is the term used to describe the imaginary portion of a complex number. The symbol "iota" or I is used to represent an imaginary number's value. An imaginary number is produced when we square a negative number.
The value of I is -1.
The concept of complex numbers is understood using this value of i.
x2 plus 1 equals zero in a quadratic equation.
x2 = -1
x = √-1
The imaginary portion is shown as -1.
I = √-1
i2 = -1
An imaginary number can be squared to get a negative value, as was previously discussed.
I = √-1
both sides being square
i2 = -1
An imaginary number plus a real number are combined to get any complex number. Iota, sometimes known as I stands for all non-real quantities.
Real numbers include 10, -20, 3, and other like values.
The integers 2i, -5, -i, etc. are examples of imaginary numbers.
Complex numbers take the form of a + ib, where I denotes the imaginary component. In addition, the number zero is complicated. Only the imaginary component of a complex number can be added to or subtracted from the imaginary part, and vice versa for the real part of the complex number.
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These tables correspond to inputs and outputs. Which of these input and output tables could represent a function rule, and which ones could not?
Table A is a function.
Table B is not a function.
Table C is a function.
Table D is not a function.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
We know a relation is a function if it is one-to-one or many-to-one.
But a relation is not a function if it is one to many.
Table A is a function and it is a many-to-one function.
Table B is not a function as input 1 leads to two different outputs 1, - 1.
Table C is a function and it is a one-to-many function.
Table D is not a function as one input leads to 3 different outputs.
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If BE=24, DF= 10, and A F= 13,
1. Find the perimeter of ΔABE
2. Find the perimeter of ΔCDF
The perimeter of ΔABE is 70 units.
The perimeter of ΔCDF is 35 units.
How to find the perimeter of a triangle?A triangle is a polygon with threes sides. The sum of angles in a triangle is 180 degrees.
Therefore, the perimeter of a triangle is the sum of the whole sides.
Triangle mid point theorem is used to find the perimeter of the triangles.
It states that the line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”
Let's find the perimeter of triangle ABE.
Hence,
perimeter of triangle ABE = AB + BE + AE
BE = 24
AE = 13 + 13 = 26
AB = 10 + 10 = 20
perimeter of triangle ABE = 24 + 26 + 20 = 70 units
perimeter of triangle CDF = DF + CD + CF
perimeter of triangle CDF = 10 + 13 + 12
perimeter of triangle CDF = 35 units
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At the candy store, Julie found a special scale that would measure the number of pounds, p, of candy and then calculate the cost, c, when you typed in the name of the candy. For her favorite candy, chocolate gummy bears, she wrote this table.
p c
0.25 1.69
0.45 3.04
0.75 5.06
1.25 11.81
Choose all of the following statements that are true.
Select one or more:
a.
A reasonable domain is [-1, 100]
b.
A reasonable domain is (0, 50] .
c.
c = 6.75p
d.
none of these
e.
A reasonable range is [0, 20].
The true statement about the function in the list of options is (d) none of these
How to determine the true statements in the list of optionsFrom the question, we have the following parameters that can be used in our computation:
p c
0.25 1.69
0.45 3.04
0.75 5.06
1.25 11.81
Where
the number of pounds of candy = p the cost of candy = cThe values in the p column represent the domain
In this case, the domain is
Domain = [0.25, 1.25]
The values in the c column represent the range
In this case, the range is
Range = [1.69, 11.81]
This means that the options (a), (b) and (e) are false
For option (c), we have
c = 6.75p
This means that
c = 6.75 * 0.25 = 1.69
c = 6.75 * 0.45 = 3.04
c = 6.75 * 0.75 = 5.06
c = 6.75 * 1.25 = 8.43 -- false
This means that the option (d) is false
Hence, none of the options is true
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What is a midpoint for zero?
The midpoint for zero is (0,0).
The midpoint can be zero. This is dependent on the value of the two points. For two points on a number line on points with values -4, and 4, the midpoint is 0. And for two points such as (-2, 5), and (2, -5), the midpoint is equal to (0, 0).
The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.
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How do you explain 2 3?
This is a coordinate pair of a point. 2 and 3 denotes X and Y coordinate respectively.
What is coordinate system?The system that is used to represent the location of points in the space is termed as coordinate system. There are two types of coordinate system such as polar and cartesian. In case system there are two reference axes which are perpendicular to each other.
In the cartesian system points are represented with respect to a vertical axis named Y axis and a horizontal axis named X axis.
How do we explain 2 3?We stated earlier that in the cartesian system a location of a point is identified by a pair of numerical terms.
So, 2, 3 indicates a pair of numerical terms. 2 denotes the X coordinate of the point and 3 denotes the Y coordinate of that point.
In the next, the distance of the point from X axis is 3 unit and distance from Y axis is 2 unit.
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Complete question is: In the point (2,3) which point denotes the y-coordinate.
Factor Completely:
-3x² + 15x - 12
Answer:
-3 (x - 4) (x - 1)
Step-by-step explanation:
a rectangular prism has dimensions of 8cm by 9cm by 10cm what is its volume?
A rectangular prism has dimensions of 8cm by 9cm by 10cm therefore the volume is 720cm³.
What is Volume?This is referred to as the measure of the space occupied within the boundaries of any three-dimensional solid.
Volume of rectangular prism = l × w × h where l is length, w is width and h is height.
Volume = 8cm × 9cm × 10cm = 720cm³.
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Rsm question please help!
The multiplication of the algebraic expressions gives x⁴ + 1.5x³ - 2x²
How to perform multiplication on algebraic expressions?An algebraic expression is an expression that consists of variables, constants, and a finite number of algebraic operations (such as addition, subtraction, multiplication, and division) e.g. 2x + 25
In order to perform the multiplication, you use expression outside the parenthesis to multiply the expressions inside the parenthesis one after the other. That is:
-0.5x²(-2x² - 3x + 4) = -2x²(-0.5x²) - 3x(-0.5x²) + 4(-0.5x²)
= 1x⁴ + 1.5x³ - 2x²
= x⁴ + 1.5x³ - 2x²
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Sandy ate 1/6 of the candy bar John ate 3/4 of it how much more of the candy bar did John eat then Sandy
Answer: 7/12
Step-by-step explanation:
Based on the given conditions, formulate: 3/4 - 1/4
Find the common denominator and write the numerators above the common denominator: 9/12 - 2/12
Calculate the product or quotient:
Write the numerators over the common denominator: 9-2
12
Calculate the sum or difference: 7/12
Answer: 7/12
lines are and s are parallel. what is m1
Answer:
30 degrees
Step-by-step explanation:
Tell whether the rate form a proportion. 4. 8 lap every 8 minute; 3. 6 lap every 6 minute
Yes, the rate 4.8 laps every 8 minutes; 3.6 laps every 6-minute form a proportion.
A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows:
1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)
4.8 lap every 8 minutes will be equal to (4.8/8) = 0.6 lap a minute.
3.6 lap every 6 minutes will be equal to (3.6/6) = 0.6 lap in a minute.
Here, as the value of the ratio of both the quantities are same so the given values are said to be in Proportion.
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Nachelle just accepted a job at a new company where she will make an annual salary of $57000. Nachelle was told that for each year she stays with the company, she will be given a salary raise of $4000. How much would Nachelle make as a salary after 4 years working for the company? What would be her salary after tt years?
a) Using the slope-intercept equation, after 4 years of working at the new company, Nachelle's salary will be $73,000 per annum.
b) After t years of working at the new company, Nachelle's salary will be $57,000 + $4,000(t).
What is the slope-intercept equation?The slope-intercept equation is in the form of y = mx + b.
The slope intercept describes the equation of a straight line, where m is the slope of the line, y and x are the y and x coordinates, and b is its y-intercept.
Initial starting salary per year = $57,000
Annual raise in salary = $4,000
Period = 4 years
Salary after 4 years = $73,000 [$57,000 + $4,000(4)]
Salary after t years = $57,000 + $4,000(t)
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Given (x – 7)2 = 36, select the values of x.
Y=6 and x=-1 parallel or perpendicular line
By plot in graph, we get Y=6 and x=-1 is perpendicular lines.
What is parallel line?Parallel lines are lines in a plane that are always the same distance apart and never intersect. They are coplanar lines that do not intersect each other, and they have the same slope.
What is perpendicular line?Perpendicular lines are lines that intersect at a right angle (90 degrees). In other words, they are lines that are at a 90-degree angle to each other. The slope of perpendicular lines are opposite reciprocals of each other, meaning that if one line has a slope of m, the other line will have a slope of -1/m.
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does the point (2, 8) satisfy the equation y = 4x?
The point satisfies the equation ! 8 = 4 × (2)
Answer:
Yes
Step-by-step explanation:
If you plug in the numbers to the equation, you should get:
8 = 4(2)
Then,
8 = 8
therefore, (2,8) does satisfy the equation y = 4x.
Work out the area of this shape. Give your answer
in cm².
3 cm
4 cm
10 cm
The area of the given shape is 46 cm²
Formulas used:
Area of the triangle = (1/2) × Base × Height
Area of rectangle = Base × Width
Here we have
The composite figure with a right-angled triangle and a rectangle
In a right-angled triangle,
The base of the triangle = 3 cm
Height of the triangle = 4 cm
Area of the triangle
= (1/2) × base × height
= (1/2) × 3 × 4
= (1) × 3 cm × 2 cm
= 6 cm²
In rectangle,
Length of the rectangle = 10 cm
Width of the rectangle = 4 cm
Area of the rectangle
= Length × Width
= 10 cm × 4 cm
= 40 cm²
By the above calculations,
Area of the given figure = Area of triangle + Area of rectangle
= 6 cm² + 40 cm² = 46 cm²
Therefore,
The area of the given shape is 46 cm²
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A consumer agency wants to determine which of two laundry detergents, A or B, cleans clothes better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale from 1–10, with 1 being the least clean to 10 being the most clean. The difference in mean ratings (A – B) was determined to be 1.5. Assuming there is no difference in the two detergents, 200 simulated differences in sample mean ratings are displayed in the dotplot.
Using the dotplot and the difference in mean ratings from the samples, is there convincing evidence that the one detergent is better than the other?
Yes, because a difference in mean rating of 1.5 or more occurred only 23 out of 200 times, meaning the difference is statistically significant and there is convincing evidence that A is more effective than B.
Yes, because a difference in mean rating of 1.5 or more occurred only 23 out of 200 times, meaning the difference is statistically significant and there is convincing evidence that B is more effective than A.
No, because a difference in mean rating of 1.5 or less occurred 167 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
No, because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
answer is D
The conclusion on if there is convincing evidence that the one detergent is better than the other is; Option D: No, because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
What is the conclusion of the sample research?We are told that, 25 pieces are randomly assigned to be cleaned with detergent A, while the remaining 25 pieces are cleaned with detergent B.
Therefore, we can say that the sample size for both detergent A and detergent B is same. We can also say that the sample is distributed randomly which means that the sample is unbiased (fair).
We are also told that the mean rating for detergent B is found to be significantly less than the mean rating for detergent A. Since we know that the mean is the average of a set of given numbers, then we can conclude that there is No evidence that the one detergent is better than the other because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
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William spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -12.2°F. Between 9am and noon, the temperature rose 16.2°F. Between noon and 3pm, the temperature dropped 9.1°F. Between 3pm and 6pm, the temperature dropped 5°F. What was the temperature at 6pm?
If William spends a winter day recording the temperature once every three hours for science class. If the temperature dropped 9.1°F. Between 3pm and 6pm, the temperature dropped 5°F. The temperature at 6pm is: -11.1°F
How to find the temperature?Between 9am and noon, the temperature rose 16.2°F, so the temperature at noon will be:
Temperature at noon = -12.2 + 16.2
Temperature at noon = 3.0°F
Between noon and 3pm, the temperature dropped 9.1°F, so the temperature at 3pm will be:
Temperature at 3pm = 3.0 - 9.1
Temperature at 3pm = -6.1°F
Between 3pm and 6pm, the temperature dropped 5°F, so the temperature at 6pm was:
Temperature at 6pm =-6.1 - 5
Temperature at 6pm = -11.1°F
Therefore the temperature at 6pm is -11.1°F.
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A hotel is offering two weekend specials. The first special is 3 nights and 4 meals for $233. The second
special is 3 nights and 3 meals for $226.50.
Part A: Write a system of equations to represent cost per night x and cost per meal y.
Part B: What is the cost per night and the cost per meal?
Answer: Part A:
To represent the cost per night x and cost per meal y in a system of equations, we can use the information provided in the question:
First Special:
3x + 4y = 233
Second Special:
3x + 3y = 226.50
Where x is the cost per night and y is the cost per meal.
Part B:
To find the cost per night and the cost per meal, we can use the information provided in the question and system of equations.
We can solve this system of equations using several methods: substitution or elimination method.
One common method to find the solution is by substitution method, where we find the value of x in terms of y from one of the equations and then substitute it into the other equation to solve for y.
x = (233 - 4y)/3
then substitute it into the other equation:
3(233 - 4y) + 3y = 226.50
now solve for y:
699 - 12y + 3y = 226.50
-9y = -472.50
y = 52.50
and we can substitute it back into the first equation:
3x + 4(52.50) = 233
3x = 80.50
x = 26.83
So the cost per night is $26.83 and the cost per meal is $52.50
Step-by-step explanation:
Given the function p(x)=6x+2, compare and contrast p(-2) and p(4). Choose the statement that is true concerning these two values.
(A) The value of p(-2) is larger then the value of p(4).
(B) The value of p(-2) is smaller then the value of p(4).
(C) The value of p(-2) is the same as the value of p(4).
(D) The values of p(-2) and p(4) cannot be compared.
Given the function p(x)=6x+2, p(-2) is -10 while p(4) is 26, this shows that value of p(-2) is smaller than the value of p(4). The correct option is B.
What is a function?A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). It is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.
p(x)=6x+2
for p(-2)
p(-2) = 6(-2) + 2
p(-2) = -12 + 2
p(-2) = -10
for p(4)
p(4) = 6(4) + 2
p(4) = 24 + 2
p(4) = 26
p(-2) < p(4)
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Answer:
(B) "The value of p(-2) is smaller then the value of p(4)" is True
Step-by-step explanation:
p(x)=6x+2
p(-2) = 6*(-2)+2
p(-2) = -12+2
p(-2) = -10
p(4) = 6*(4)+2
p(4) = 26
====
p(-2) = -10
p(4) = 26
===
(A) The value of p(-2) is larger then the value of p(4). False
(B) The value of p(-2) is smaller then the value of p(4). True
(C) The value of p(-2) is the same as the value of p(4). False
(D) The values of p(-2) and p(4) cannot be compared. False
What are the roots of the equation x² - 10x +34 = 0 in simplest
a + bi form?
What is 5c−3d−12c+d−6 written in simplest form?
To simplify the expression 5c−3d−12c+d−6, we can combine like terms:
5c − 12c + d − d − 6 = (-12c + d) + (-6)
Therefore, the expression 5c−3d−12c+d−6 can be simplified to -12c + d - 6.
Help please!! I would appreciate it
The behavior of the graph at the intervals are as follows
(0, 4} = increasing
(0, 2} = negative
{-2, 0) = decreasing
(-4, -1) = positive
How to determine the behavior of the function in the intervalsThe intervals represents some numbers and the numbers within the interval depends on the type bracket
(0, 4} = integer values from 1 2 3 4 at this interval the curve is going up hence increasing
(0, 2} = integer values from 1 2 at this interval the curve is on the negative side
{-2, 0) = integer values from -2 -1 at this interval the curve is on the decreasing
(-4, -1) = integer values from -3 -2 -1 at this interval the curve is on the on the positive side
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How is the graphed system of equations classified?
Drag and drop words into the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A Response area system has at least one solution. A Response area system has an infinite number of solutions.
A system that has no solution is classified as inconsistent.
A system that has one and only one solution is classified as independent
The system of equation graphed is consistent and independent.
How to interpret the graph of linear equations?The equations given by the graph are expressed as;
3x - 4y = 32
3x + 5y = 24
Now, if we subtract eq 1 from eq 2, we will get;
5y - (-4y) = 24 - 32
9y = -8
y = -8/9
Put 8/9 for y in eq 2 to get;
3x + 5(8/9) = 24
3x = 24 - 40/9
3x = 176/9
x = 176/27
Now, to classify solution to equations, we say that;
1) When there is no solution, it is inconsistent.
2) When there is one and only one solution, it is independent
Since we have a solution and only one solution, then we can say that the system of equation graphed is consistent and independent.
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50x4-(3 divided by 2)
198.5 is the answer
50X4-(3÷2)=198.5
Answer: 198.5
Step-by-step explanation:
= 50x4-(3 divided by 2)
= 50x4-(3/2)
= (50 x 4) - ( 3/2 )
= (200) - (3/2)
= 200 - 1.5
= 198.5
An experiment was conducted to evaluate the success of an Ebola virus vaccine. The subjects were unaware of the treatment they were given. What is this type of blinding used to prevent? Grounds for malpractice suits Subjects assigned randomly to treatments A possible source of bias Injury to the subjects The placebo effect
This type of blinding is used to prevent a potential source of bias in the experiment. By keeping the subjects unaware of the treatment they are receiving, the researchers can eliminate the possibility of any psychological effects influencing the outcome of the study. This is particularly important in cases where a treatment is being evaluated for subjective outcomes such as pain, anxiety, or depression, as the subjects' expectations and beliefs can influence their perception of the treatment's effectiveness. By keeping the subjects blinded to their treatment, researchers can ensure that the results of the study are as unbiased as possible.
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54 is 72% of what number?
Solve&Share-
The store sells boxes of adhesive
bandages. The boxes have: 12, 15, 18, 20, 25, 36, 40, 45,
50, 64, 75, or 100 bandages per box.
Which boxes have bandages that can be separated
into 2 first-aid kits with no leftover bandages?
Which boxes have bandages that can be separated into
5 first-aid kits with no leftover bandages?
Which boxes have bandages that can be separated into
10 first-aid kits with no leftover bandages?
Therefore, there are 12 bandages in 2 boxes, which is the answer to the unitary method presented problem.
What is a unitary method?The term "unitary" refers to a single or separate unit or variable . As a result, this strategy's objective is to establish values in terms of a single unit. For instance, if a car travels 44 kilometres on two litres of gas, the unitary technique can be used to determine how many kilometers it will drive on one.
Here,
Given: Each box of bandages has three packs, with two bandages in each pack.
Now, determine how many bandages there are in two boxes.
Therefore, we solve using the unitary method:
One pack contains two bandages.
In 3 packs, there are therefore = 2*2 = 6 bandages.
One box contains three packs as stated.
Consequently, we multiply 2 by 6 to obtain the bandages in 2 boxes:
=> 2 * 6 = 12
Therefore, there are 12 bandages in 2 boxes, which is the answer to the unitary method's presented problem.
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