The improper integral converges.
Does the improper integral converge or diverge?To determine whether the improper integral converges or diverges, we need to analyze its behavior as the upper limit approaches infinity. The given integral is:
[tex]\int _0^ \infty (e^2x + e^{(-2x)}) dx[/tex]
First, we evaluate the integral limits independently. Let's start with the term [tex]e^{2x}[/tex]:
[tex]\int _0^\infty e^2x dx[/tex]
This integral converges since the exponential function grows rapidly as x increases. Similarly, for the term [tex]e^{(-2x)}[/tex]:
[tex]\int _0^\infty e^{(-2x)} dx[/tex]
This integral also converges as the exponential function approaches zero as x approaches infinity. Since both terms converge, the sum of the integrals converges as well.
Therefore, the improper integral converges.
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Quick algebra 1 assignment for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
Oh by the way this is just a section of the real assignment, the assignment calls for you to make an app that people can play to learn inverse variation & direct variation and stuff.
Hope that helps solve this! :)
The example on direct variation is illustrated below based on the information given.
How to illustrate the direct variation?An example will be:
When x = 2, y = 10. Find the value of y when x is 6.
In this case, this will be calculated thus:
y = kx
10 = 2k
k = 10/2
k = 5
Since y = kx.
y = 5 × 6
y = 30
The value of y is 30.
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On a coordinate plane, a line goes through (0, 1) and (5, 0). what is the equation of the line that is perpendicular to and has the same y-intercept as the given line? y = one-fifthx 1 y = one-fifthx 5 y = 5x 1 y = 5x 5
Answer: [tex]y=5x+1[/tex]
Step-by-step explanation:
The slope of the given line is
[tex]\frac{1-0}{0-5}=-\frac{1}{5}[/tex]
Since perpendicular lines have slopes that are negative reciprocals, the slope of the line we want to find is 5.
Since the y-intercept is (0,1), the equation is [tex]y=5x+1[/tex].
Answer: the answer is c
Point A is at (3, -8) and point B is at (7, 3). Point M is the midpoint of point A and point B.
The midpoint of point A and point B is (5, -2.5)
How to determine the midpoint?The coordinates are given as:
A = (3, -8)
B = (7, -3)
The midpoint is calculated as:
(x, y) = 0.5 * (x1 + x2, y1 + y2)
So, we have:
(x, y) = 0.5 * (3 + 7, -8 + 3)
This gives
(x, y) = 0.5 * (10, -5)
Evaluate
(x, y) = (5, -2.5)
Hence, the midpoint of point A and point B is (5, -2.5)
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answer the given questions please!
then he started to prepare the games for this 4 friends. if each game takes 5 minutes to prepare and he prepared a total of 5 games. how many minutes did it take for andrew to prepare all the games
Answer:
25 minutes
Step-by-step explanation:
If it takes 5 minutes to prepare one game we need to multiply 5 games by 5 minutes: 5*5 = 25 minutes
PLEASE HELP IM STUCK
Hello, the solution of the problem is in this photo.
If the graph of the line falls from left to right, then the slope is negative.
Under his cell phone plan, Liam pays a flat cost of $69.50 per month and $5 per gigabyte. He wants to keep his bill under $90 per month. Write and solve an inequality which can be used to determine x, the number of gigabytes Liam can use while staying within his budget.
Using a linear function, the inequality is given by: 69.5 + 5x < 90.
The solution is: x < 4.1.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we have that:
The y-intercept is the flat cost of $69.50.The slope is the cost per gigabyte of $5.Hence the cost of using x gigabytes is:
C(x) = 69.5 + 5x.
The cost has to be under 90, hence the inequality is:
C(x) < 90
69.5 + 5x < 90.
Then the solution is:
5x < 90 - 69.5.
x < 20.5/5
x < 4.1.
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Answer:
Inequality: 5x+35<50
Answer: x<3
Step-by-step explanation:
Which graph represents the solution
8 - 3x ≥ -4
Answer:
3rd option
Step-by-step explanation:
8 - 3x ≥ - 4 ( subtract 8 from both sides )
- 3x ≥ - 12
divide both sides by - 3 , reversing the symbol as a result of dividing by a negative quantity.
x ≤ 4
since ≤ the circle on number line is solid ( not open )
since less than 4 then arrow points left away from 4
the solution is shown on the third graph
he function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours. Which times and distances are represented by the function? Select three options. The starting distance, at 0 hours, is 300 miles. At 2 hours, the traveler is 725 miles from home. At 2.5 hours, the traveler is still moving farther from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.
The true statements are (b), (d) and (e)
At 2 hours, the traveler is 725 miles from home.At 3 hours, the distance is constant, at 875 miles.The total distance from home after 6 hours is 1,062.5 miles.How to determine the times and distances are represented by the function?From the function, we have the following piecewise function and the domains
D(t) = 300t + 125, 0 ≤ t < 2.5
D(t) = 875, 2.5 ≤ t ≤ 3.5
D(t) = 75t + 612.5, 3.5 < t ≤ 6
When t = 2, we use the domain 0 ≤ t < 2.5
So, we have
D(2) = 300 * 2 + 125
Evaluate the product
D(2) = 600 + 125
Evaluate the sum
D(2) = 725 --- this is true
When t = 3, we use the domain 2.5 ≤ t ≤ 3.5
So, we have
D(t) = 875
This gives
D(3) = 875 -- this is true
When t = 6, we use the domain 3.5 < t ≤ 6
So, we have
D(t) = 75t + 612.5
This gives
D(6) = 75* 6 + 612.5
Evaluate the product
D(6) = 450 + 612.5
Evaluate the sum
D(6) = 1062.5 --- this is true
Hence, the true statements are (b), (d) and (e)
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Complete question
Select three options. The starting distance, at 0 hours, is 300 miles. At 2 hours, the traveler is 725 miles from home. At 2.5 hours, the traveler is still moving farther from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.
Answer:
At 2 hours, the traveler is 725 miles from home.
At 3 hours, the distance is constant, at 875 miles.
The total distance from home after 6 hours is 1,062.5 miles.
Step-by-step explanation:
Amadou has a points card for a movie theater.
He receives 30 rewards points just for signing up.
He earns 8.5 points for each visit to the movie theater.
He needs 115 points for a free movie ticket.
Write and solve an equation which can be used to determine vvv, the number of visits Amadou must make to earn a free movie ticket.
He needs to do 10 visits to earn a free ticket.
How many visits Amadou must do to earn a free ticket?
We know that he gets 30 points just for signing up, and he gets 8.5 points for each visit, then the amount of points as a function of v, the number of visits, is:
P(v) = 30 + 8.5*v
He will get a free movie ticket when he gets 115 points, then we need to solve the linear equation:
P(v) = 115 = 30 + 8.5*v
Solving for v:
v = (115 - 30)/8.5 = 10
He needs to do 10 visits to earn a free ticket.
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ASAAP PLEASE PLEASEPLEASE PLEASE
2b^3 -5 b^2 +b+2. R 9/ b-4
Use synthetic division
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
[tex]Answer: \displaystyle\left {{x^2+(y-3)^2=36} \atop {x^2+(y+8)^2=36}} \right. .[/tex]
Step-by-step explanation:
[tex]D=12\ \ \ \ O(0;b)\\\displaystyle\\R=\frac{D}{2}\\R=\frac{12}{2} \\ R=6.\\Circle \ equation\ is:\\(x-a)^2+(y-b)^2=R^2.\\a=0\ \ \ \ \ R=6\\x^2+(y-b)^2=6^2\\x^2+(y-b)^2=36\\Henese:\\\displaystyle\\\left {{x^2+(y-3)^2=36} \atop {x^2+(y+8)^2=36}} \right. .[/tex]
The stem-and-leaf plot shows the points scored by Jason in nine basketball games.
Stem Leaves
1: 0 2 9
2: 3 6 6 7
3: 4
4: 0
What is the outlier of the data set?
A - 40
B - 26
C - 23
D - 10
Considering the given stem-and-leaf plot, the outlier is given by:
A - 40
What is an stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
Outliers are usually the lowest or the highest value in the data-set. In this problem:
The lowest value is 10, but the second lowest is 12, which is close to 10.The highest value is 40, but the second lowest is 34, which is farther to 40 than 12 is to 10, hence 40 is an outlier.More can be learned about stem-and-leaf plots at https://brainly.com/question/27683035
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HURRY PLS ANSWER NOW!!
What is the area of the trapezoid?
33 in2
52.5 in2
82.5 in2
91 in2
Answer:
91 in2
Step-by-step explanation:
11+15 over 2 , times by 7 equals 91 ??
What is the simplified form of startroot 100 x superscript 36 baseline endroot ?
The simplified form of the expression is [tex]10 x^{18}[/tex].
What are indices in maths?
An index, or a power, is the small floating number that goes next to a number or letter.The plural of index is indices. Indices show how many times a number or letter has been multiplied by itself.The given expression is [tex]\sqrt{100x^{36} }[/tex]
Applying the rule, [tex]\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}[/tex]
Now, [tex]\sqrt{100} \sqrt{x^{36} }[/tex]
Simplifying, we get;
[tex]10\sqrt{x^{36} }[/tex]
Applying the exponent rule, [tex]a^{bc} = (a^{b} )^{c}[/tex]
We get
[tex]10 \sqrt{(x^{18} })^{2}[/tex]
[tex]10 x^{18}[/tex]
Therefore, the simplified form of the expression is [tex]10 x^{18}[/tex].
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Answer:
10 x 18
Step-by-step explanation:
How many significant digits are there in the number 1.00250? A.7 B. 6 C. 5 D. 4
Answer:
B.6 is the significant digits of number 1.00250
I HOPE IT HELP YOU
The number of significant figures that are available in 1.00250 are; B: 6
What is the significant figure?
Significant figures are defined as the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value.
Now, in the question we are given the decimal number 1.00250.
Now, it should be noted that when dealing with significant numbers as regards decimals, any zero digit to the left of the decimal is a non-significant figure while any zero digit to the right of the decimal is a significant figure.
Thus, the significant figures in the question are all the numbers which are 6 in number.
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5/8 of the students in siena's class have brown eyes. 2/3 of the students with brown eyes are girl. what fraction of the students in siena's class are girls with brown eyes? *
The fraction of the students in Siena's class are girls with brown eyes is 5/12.
Let the fraction of students in Siena's class with brown eyes be a=5/8.
And the fraction of students in Siena's class with brown eyes are girls be b=2/3.
Then, the fraction of students in Siena's class are girls with brown eyes be z=a×b
Therefore, by substituting the fraction values, we get
z=(5/8)×(2/3)
z=5/12.
Hence, 5/8 of the students in Siena's class have brown eyes. 2/3 of the students with brown eyes are girl. Then, the fraction of students in Siena's class are girls with brown eyes is 5/12.
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Warm-Up
Consider the graph of function f.
Determine which equation matches each described transformation of function f.
Drag the tiles to the correct boxes to complete the pairs.
If this is the one you are talking about then:
horizontal translation of 3 units is: y= f(x-3)
vertical stretch by a scale factor of 3 is: y= 3f(x)
reflection over the x-axis is: y= -f(x)
vertical translation of 3 units is: y= f(x)+3
Step-by-step explanation:
Adding a value to f(x) translates the graph of f vertically. So, the equation that shows a vertical translation of 3 units is y = f(x) + 3.
Adding a value to the input, x, of f(x) translates the graph of f horizontally. So, the equation that shows a horizontal translation of 3 units is y = f(x − 3).
Multiplying f(x) by a negative value reflects the graph of f over the x-axis. So, the equation that shows a reflection over the x-axis is y = -f(x).
Multiplying f(x) by a constant, k, vertically stretches the graph of f by a scale factor of k. So, the equation that shows a vertical stretch by a scale factor of 3 is y = 3f(x).
In a class of 48 students, one fourth of them regularly watch a particular tv programme. how many of the students do not regularly watch the programme?
36 students does not watch regularly the programme.
Lets simplify the problem,
Total students = 48
Regular students 1//4*48
=> 12 students
Through Simple Subtraction method,
Irregular students = Total students - regular students
Irregular students = 48-12
=36
Hence 36 students does not watch regularly the programme.
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The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the _____. Group of answer choices constant term error term residual model parameter
The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the Residual model.
What is regression?Regression is the process used to predict the variation in one variable based on another variable.
What are the dependent variable and the independent variable?The variable that is to be predicted by the regression is called the dependent variable or response variable since it depends on another variable.The variable that is used to predict the dependent variable is called the independent variable or explanatory variable since it explains the variation in the required variable.The dependent values belong to the y-axis and the explanatory values belong to the x-axis. What is a residual model?The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the residual model.
This value s predicted by the regression line.
Residual = Observed value - predicted value
Therefore, the difference is known as residual.
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PLEASE HELP!!! the photo has the question and options please help
The equation which expresses the number of bacteria, P, present at any time, t is P(t) = 4(2)^t
EquationNumber of bacteria = PTime = tCheck all options
When t = 1
P(t) = 8(4)^t
= 8(4)¹
= 8(4)
P(t) = 32
Not true
P(t) = 4(2)^t
= 4(2)¹
= 4(2)
= 8
True
P(t) = (2)^t
= (2)¹
= 2
Not true
P(t) = 8(2)^t
= 8(2)¹
= 8(2)
= 16
Not true
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Y=5-2x 4x+2y=10 please help me
Answer:
Infinite solutions.
Step-by-step explanation:
y = 5 - 2x
2x + y = 5 ---------(I)
a₁ = 2 ; b₁ = 1 and c = 5
4x + 2y = 10
a₂ = 4 ; b₂ = 2 and c₂ = 10
[tex]\sf \dfrac{a_1}{a_2}=\dfrac{2}{4}=\dfrac{1}{2}\\\\\dfrac{b_1}{b_2}=\dfrac{1}{2}\\\\\dfrac{c_1}{c_2}=\dfrac{5}{10}=\dfrac{1}{2}[/tex]
⇒ [tex]\sf \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}=\dfrac{1}{2}[/tex]
So, the line are coincident and has infinite solutions.
The total mass of 4 identical pencil boxes and a notebook is 700 g. each pencil box has a mass of 140 g. what is mass of the notebook?
Answer:
140g
Step-by-step explanation:
One pencil box has a mass of 140g, to find out the weight of 4 pencil boxes we multiply 140 by 4: 140*4 = 560g
Let the mass of the notebook be x: 560+x = 700
560+x = 700
x = 140g
3/4 + 1/2 + 1/3 + 2/9 + ....... = 9/4 es verdadero oh falso y como se resuelve ?
The missing fraction is 7/9
Finding missing values in an addition equationThe given equation is:
[tex]\frac{3}{4}+\frac{1}{2}+\frac{2}{9}+x=\frac{9}{4}[/tex]
This can be simplified as:
[tex]\frac{27+18+8+36x}{36} =\frac{9}{4} \\\\\frac{53+36x}{36} =\frac{9}{4}[/tex]
Cross multiply
[tex]9(36)=4(53+36x)\\\\324=212+144x\\\\144x=324-212\\\\144x=112\\\\x=\frac{112}{144} \\\\x=\frac{7}{9}[/tex]
Therefore, the missing value is [tex]\frac{7}{9}[/tex]
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Gloria says the two expressions 1/4 (12x + 24) -9x and -6(x + 1) are equivalent. is she correct? Explain how you know
Answer:
No
Step-by-step explanation:
Lets simplify both expressions:
We will start with Gloria's first expression:
[tex]1/4 (12x + 24) -9x[/tex]
Apply distributive property:
[tex](3x + 6) -9x[/tex]
Combine like terms, we are then left with:
[tex]6-6x[/tex]
Now lets simplify the second expression
[tex]-6(x+1)[/tex]
Apply distributive property
[tex]-6x-6[/tex]
Rearrange:
[tex]-6-6x[/tex]
Now we can see that the two equations are not equal, as the first is 12 greater than the second. Another way we could have tested this was plugging in a value for x and then solving.
Which statement can you use to conclude that quadrilateral xyzw is a parallelogram
Answer: Option (4)
Step-by-step explanation:
A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.
What’s 2 + 2 + 5 + 69 + 89. This will definitely help me out.
Answer:
167
Hope this helps you out
Answer:
167
Step-by-step explanation:
Break it into steps.
2+2+5 = 9
69 + 9 = 78
78 + 89 = 167
Hope this helps.
The number 21 is the sum of two consecutive integers 10 and 11. What is the largest number of positive, consecutive integers whose sum is 21
Answer:
11
Step-by-step explanation:
What elements does a strong body paragraph in a literary analysis always contain? Select three options.
The elements which must be contain in a body paragraph of a literary analysis are;
An introduction to a text.Reasons that support a viewpoint.Supporting evidence and commentary.What elements does a strong body paragraph in a literary analysis always contain?A strong body paragraph basically is characterized as a medium of stating facts regarding a viewpoint and these statements must be accompanied by supporting evidence and commentary.
On this note, the three elements which should be contained in a strong body paragraph are;
An introduction to a text.Reasons that support a viewpoint.Supporting evidence and commentary.Remarks:
an introduction to a text
reasons that support a viewpoint
O a thesis statement
supporting evidence and commentary
Da summary of the main points
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Polynomial Question
Find the roots if one of the roots is the product of the other two
Step-by-step explanation:
x³ - x² - 24x - 36
factors of -36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and negative equivalents.
1 - 1 - 24 - 36 != 0
8 - 4 - 48 - 36 != 0
27 - 9 - 72 - 36 != 0
64 - 16 - 96 - 36 != 0
216 - 36 - 144 - 36 = 0
So one factor is 6
x = 6
(x - 6) = 0
x²(x - 6) = x³ - 6x²
5x(x - 6) = 5x² - 30x
6(x - 6) = 6x - 36
x³ - 6x² + 5x² - 30x + 6x - 36
(x - 6)(x² + 5x + 6)
(x - 6)(x² + 3x + 2x + 6)
(x - 6)(x(x + 3) + 2(x + 3))
(x - 6)(x + 3)(x + 2)
x - 6 = 0
x = 6
x + 3 = 0
x = -3
x + 2 = 0
x = -2
x = -2, -3, 6.
One is the product of the other 2 as -2 x -3 = 6.
Graphic proof is shown above or below in the image