The left Riemann Sum approximation for the integral of 20(4x² - 2x)dx over the interval [0, 20] with four equal subintervals is 165250.
In calculus, the integral is a mathematical tool that allows us to find the area under a curve. It is an important concept that is used in many fields of science and engineering. One way to estimate the value of an integral is by using a Riemann Sum, which involves dividing the region under the curve into small rectangles and adding up their areas.
In this case, we will be using a left Riemann Sum with four equal subintervals to estimate the integral of 20(4x² - 2x)dx.
To use a left Riemann Sum, we need to first divide the interval of integration into equal subintervals. In this case, we have four subintervals of width
=> (b - a)/n = (20 - 0)/4 = 5.
The left endpoint of each subinterval will be used as the height of the rectangle that represents the area under the curve in that subinterval.
Next, we need to evaluate the function 20(4x² - 2x) at the left endpoints of each subinterval. These values will be used as the heights of the rectangles. The left endpoints are 0, 5, 10, and 15, so we have:
f(0) = 20(4(0)² - 2(0)) = 0
f(5) = 20(4(5)² - 2(5)) = 1900
f(10) = 20(4(10)² - 2(10)) = 7200
f(15) = 20(4(15)² - 2(15)) = 15150
We can now find the area of each rectangle by multiplying its height by its width (5). The total area is the sum of these areas:
(0)(5) + (1900)(5) + (7200)(5) + (15150)(5) = 165250
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y=3x+2
-4x+2y=8
elimination method
The solution of the equations y = 3x + 2 and - 4x + 2y = 8 by elimination method will be (2, 8).
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
The equations are given below.
y = 3x + 2
2y = 6x + 4
6x - 2y = - 4 ...1
- 4x + 2y = 8 ...2
Add both equations, then we have
6x - 4x = - 4 + 8
2x = 4
x = 2
Then the value of 'y' is given as,
y = 3(2) + 2
y = 6 + 2
y = 8
The solution of the equations y = 3x + 2 and - 4x + 2y = 8 by elimination method will be (2, 8).
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What is the inverse of a function f(x)=2x +1 ?
A•H(x)=1/2x-1/2
B•H(x)=1/2x+1/2
C•H(x)=1/2x-2
D• H(x)=1/2x+2
The inverse of a function f(x)=2x + 1 include the following: A. H(x) = 1/2x - 1/2
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
f(x) = y = 2x + 1
x = 2y + 1
By rearranging the equation, we have the following:
2y = x - 1
y = (x - 1)/2
H(x) = 1/2(x) - 1/2.
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someone help please asap and thank you
Step-by-step explanation:
fund the slope then use the two point form
The points A B C D and E lie on the circle PAQ is a tangent to the circle at A and EC=EB Angle ECB=80° and angle ABE = 40° Find the values of v w x y and z
The values of v w x y and z are given below:
v= 40°w= 80°x= 40°y= 80°z= 80°How to solve these<EDA= <EBA= 40°
==> x= 40°
This is because the circumferential arc of the same arc is equal.
<PAE= <ADE= 40°
=>v= 40°
This is based on the alternate segment theorem.
Because EC= EB, <ECB= <EBC= 80°
=> w= 80°
This is based on the properties of an isosceles triangle.
<ECB = <EAB = 80°
=> y= 80°
This is because the circumferential angle of the same arc are equal
Because <EBC = <ECB= 80°
=> <BEC = 180° -(80 x2)
= 20°
This is because the sum of the interior angles of the triangle is 180°
<AEB = 180°-y - <ABE
= 60°.
<AEC = <AEB + <BEC= 60° + 20°
=80°.
So <ADC = <AEC = 80°
=> = 80°
This is because the circumferential angle of the same arc are equal
Therefore,
v= 40°w= 80°x= 40°y= 80°z= 80°Read more about geometry here:
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A system of linear equations is shown in the graph. How many solutions does the system have?br /> One solution at (0, 4) One solution at (−3, 0) Infinitely many solutions No solution
There are two solutions to the system of linear equations depicted in the graph: one at (0,4) and one at (-3,0). There is only one distinct solution to the system of equations where the two lines intersect at the points (-3,0) and (0,4).
How can the number of solutions to a system of linear equations be determined?If the slopes are the same but the y-intercepts vary, the system has no solution. If the slopes are different, the system only has one solution. The system has an endless number of solutions if the slopes and y-intercepts match.
How many possible solutions can there be for a system of two linear equations?There are therefore countless possible answers. A different kind of linear equation system is a system with two parallel lines represented by the equations is referred to be an inconsistent system. The lines have distinct y-intercepts but the same slope.
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What happens if the residual is negative?
When the residual is negative it represents the predicted value is very much high.
A residual represents the measure of how well a line fits for the given individual data points which were plotted on the graph. Residual plot is representation on the graph which shows the residuals on the vertical axis also independent variable on the horizontal axis of the graph.If the residual value is positive it represents the predicted value is very low on the regression line.If the residual value is negative it represents the predicted value is very high on the regression line.Therefore, the negative residual value on the regression line represents the predicted value is very much high.
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If £31 = 500 rubles how many £ are in 992 rubles ? Give answer to 2 dp
Answer:
61.504
Step-by-step explanation:
Answer:
There are £61.50 in 992
Step-by-step explanation:
Here, we shall be doing some currency conversions.Now, £31 = 500 rublesThen;£x = 992 rubles To get c, what we do is simply cross multiply £x * 500 rubles = £31 * 992 rubles £x = (£31 * 992 rubles)/500 rubles £x = £61.504which is £61.50 to two decimal places
hope this helps!!
The atmosphere of a certain planet is made up of many elements. What part of the atmosphere is made up of Element 2? That's the question its asking my, please help, I am so bad at math! ASAP!!!!!
The percentage of the atmosphere made up of element 2 is 17%.
What is the percentage?According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.
Given that in the pie chart, the atmosphere is distributed in different parts by which it is made.
The data is,
Element 1 = 76%
Element 2 = 17%
Other = 76%
The amount of element 2 in the atmosphere is 17%.
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Parallelogram CALM is multiplied by a scale factor to create Parallelogram
C'A'LM'. Parallelogram C'A'L'M' has an area of 485.64 square feet. What is the
scale factor for the area of the pre-image to get the image?
The scale factor for the area of the pre-image to get the image is 2.
What is scale factor?Suppose a figure (pre image) is dilated (dilated image) by scale factor of k. So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:
L = k × M
where 'k' will be called as scale factor.
The linear things grow linearly like length, height etc.
The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.
So area of first figure = k² × area of second figure
Given that Parallelogram CALM is multiplied by a scale factor to create Parallelogram C'A'LM'. Parallelogram C'A'L'M' has an area of 485.64 square feet. Also, the area of the parallelogram CALM is 121.41 square feet.
Therefore, we can write,
Final Area / Initial Area = (Scale Factor)²
485.64 square feet / 121.41 square feet = (Scale Factor)²
4 = (Scale Factor)²
(Scale Factor) = √4
Scale Factor = 2
Hence, Scale Factor = 2
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The complete question is:
The area of Parallelogram CALM is 121.41 square feet. Parallelogram CALM is multiplied by a scale factor to create Parallelogram C'A'LM'. Parallelogram C'A'L'M' has an area of 485.64 square feet. What is the scale factor for the area of the pre-image to get the image?
An apple pie is cut into six equal slices. If the diameter of the pie is ten inches, what is the approximate arc length of one slice of pie?
A 1.67 in.
B 3.14 in.
C 5.24 in.
D 13.08 in.
The approximate arc length of one slice of apple pie, when the diameter of the pie is ten inches, is option (c) - 5.24 inches.
We know that the apple pie is cut into 6 equal slices,
therefore, Θ = 360/6 = 60° (for each slice of the apple pie)
then the diameter of the apple pie is, d = 10 inches
from the diameter we can find the radius, r = 10/2 inches = 5 inches
arc length = 0/360 × 2[tex]\pi[/tex]r
we put the values of r and [tex]\pi[/tex] into the equation, we get the following:
= 60/360 × [tex]2\pi[/tex] × 5
= 5.24 inches.
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Amy used her first 2 tokens at Glimmer Arcade to play a game of Roll-and-Score. Then she
played her favorite game, Balloon Bouncer, over and over until she ran out of tokens. Balloon
Bouncer costs 3 tokens per game, and Amy started with a bucket of 35 game tokens.
Which equation can Amy use to find how many games of Balloon Bouncer,
she played
Answer:
11
Step-by-step explanation:
Let's call the number of games of Balloon Bouncer that Amy played as "x".
Amy started with 35 tokens and used 2 for Roll-and-Score, so she had 35 - 2 = 33 tokens left.
Each game of Balloon Bouncer costs 3 tokens, so the total number of tokens used for Balloon Bouncer games is 3x.
Therefore, the equation to find the number of games Amy played is:
33 = 3x
Solving for x, we get:
x = 11
So Amy played 11 games of Balloon Bouncer.
Answer: 3g + 3 = 35
Step-by-step explanation:
If angle AOB = 4x - 2 and BOC = 5x + 10 and COD = 2x + 14. What is x?
We need the angle AOD to find the x value
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Missed data: ABCD is a QUADRILATERAL
'O' is a point in the middle joining OA,OB,OC and OD , find the angle AOD which is x here
Adding 3 angles we get 11x+22,
Equation is :
11x+22 + AOD = 360
=> AOD = 360 - 22- 11x
AOD= 338- 11x
We need the angle AOD to find the x value
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how to solve this 7c-3+2c=15
The correct expression for 7c-3+2c=15 is c = -1
What is expression?An expression is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division. The structure of an expression is: Expression = (Number, Math Operator, Number) For example, = 7 + 9 = 23 × 4 = 37 – 6 = 25 + 9 – 4 ÷ 2
Move all terms containing c to the left side of the equation.
Subtract 3c from both sides of the equation:
[tex]= > 7c+6-3c=2[/tex]
Subtract 3c from 7c:
[tex]= > 4c+6=2[/tex]
Move all terms not containing c to the right side of the equation.
Subtract 6 from both sides of the equation:
[tex]= > 4c=2-6[/tex]
Subtract 6 from 2:
[tex]4c=-4[/tex]
Divide each term in [tex]4c=-4[/tex] by [tex]4[/tex] and simplify.
Divide each term in [tex]4c=-4[/tex] by [tex]4[/tex]:
[tex]\frac{4c}{4} =\frac{-4}{4}[/tex]
Simplify the left side:
Cancel the common factor of [tex]4[/tex]:
[tex]c=\frac{-4}{4}[/tex]
Simplify the right side.
Divide [tex]-4[/tex] by [tex]4[/tex]:
[tex]c=-1[/tex]
Therefore, the correct expression for 7c-3+2c=15 is c = -1
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The question is:
How to solve this 7c-3+2c=15
Which equations are true for the values of x, y, and z?
The equations that are true for the values of x, y and z are :
x degrees + 65 degrees = 180 degreesx degrees = z degreesy degrees = 65 degreesWhat are the equations for x, y, and z ?The equations can be found based on the relationships between the variables as angles.
x and z are opposite each other which makes them congruent angles which means that they are the same value.
y and 65 degrees are also opposite each other which makes them congruent.
x and 65 degrees are on a straight line and so will add up to 180 degrees which is why the correct equation would be :
x degrees + 65 degrees = 180 degrees
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Options include:
x degrees + 65 degrees = 180 degreesx degrees = z degreesy degrees = 65 degreesx degrees= 65 degreesx degrees + y degrees + z degrees = 115 degreesSimplify the algebraic expression by using the Distributive Property first and then combining like terms.
Explain your answer or show your work.
12x-18y/6 +4y
The value of the equation is A = ( 6x - 9y ) / ( 3 + 2y )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = ( 12x - 18y ) / ( 6 + 4y )
On simplifying the equation , we get
Taking the common factor as 6 in the numerator , we get
A = 6 ( 2x - 3y ) / ( 6 + 4y )
Taking the common factor as 2 in the denominator , we get
A = ( 6/2 ) ( 2x - 3y ) / ( 3 + 2y )
On further simplification , we get
A = 3 ( 2x - 3y ) / ( 3 + 2y )
A = ( 6x - 9y ) / ( 3 + 2y )
Hence , the equation is A = ( 6x - 9y ) / ( 3 + 2y )
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is 1/2 solution to the equation 8 - 2z = 10z+3? Select your answers from the drop-down lists.
Answer: 2.4
Step-by-step explanation:
8-2z=10z+3
First, take variables to one side
Don’t forget to change symbols when switch
-2z -10z= -8+3
Now solve, simplify
-12z=-5
The negatives cancel out, so divide both sides by 12
Z= 2.4
And i dont get this aswell
Answer:5
Step-by-step explanation:
This is a variation question.
When m is inversely proportional to n,
m ∝ 1/n
Now, there is a constant of 100.
So the formula connecting m and n is
m=k/n where k is the constant
=>m=100/n
Now, n= 20 ( 20 printers)
Thus, m=
100/20=5 minutes.
Hope this helps :)
Bella has volunteered to feed the dogs at a shelter. The table shows the number of cups of dog food that each dog should be fed each day. What does the number of observations in this data set signify
It signifies the number of dogs that Bella feeds. The number of observations in dataset is an important characteristic that helps to determine the size of data and potential variability of data.
The table of the number of cups of dog food that each dog should be fed each day is a dataset that contains multiple observations. Each row in the table represents one observation for one dog, with information about the number of cups of dog food that the dog should be fed each day.
The number of observations in this data set is equal to the number of dogs that Bella will be feeding at the shelter. Each observation in the dataset represents a single unit of information, in this case, the number of cups of dog food that a particular dog should be fed.
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Alexandria forgets to bring her lunch to school 15 of the time, or about once a week. When she does, she buys a school lunch for an average cost of $4.75. If there are 180 days of school, about how much money can Alexandria expect to spend on school lunches for the year?
Alexandria can expect to spend about $128.25 on school lunches for the year if she forgets to bring her lunch about once a week.
If Alexandria forgets to bring her lunch 15% of the time, then she will need to buy a school lunch on 15% of the 180 school days:
15% of 180 = 0.15 × 180 = 27 school days
So, Alexandria will buy a school lunch 27 times during the school year.
The average cost of a school lunch is $4.75.
So the total cost of buying school lunches for the year will be:
27 × $4.75 = $128.25
Therefore, Alexandria can expect to spend about $128.25
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What is the area of this compound figure?
Answer:
99 square millimeters
Answer given by the other user is correct. Merely giving the steps required to solve such a problem
Step-by-step explanation:
Break up the figure into 3 rectangles as shown in the attached image
The area of the top rectangle with size 11 x 3 = 33 square millimeters
The area of the small rectangle is 2 x 5 = 10 square millimeters
The area of the vertical rectangle is 4 x 14 = 56 square millimeters
Total area = 33 + 10 + 56
= 99 square millimeters
HEYOOO 60 POINTS
just answer this very complicated math question to get some easy points
*brailiest for most pizzazz* :
1 + 1 = ?
Answer:
1 + 1 = 2
Step-by-step explanation:
you add one and add another one and together thetr is two. so you would have two left.
A repeated-measures research study and a separate independent-measures research study both produced a t statistic with df = 10. How many individuals participated in each research study?
Group of answer choices
a.)n = 12 for a repeated-measures research study and n = 11 for an independent-measures research study
b.)n = 12 for a repeated-measures research study and n = 12 for an independent-measures research study
c.)n = 11 for a repeated-measures research study and n = 11 for an independent-measures research study
d.)n = 11 for a repeated-measures research study and n = 12 for an independent-measures research study
By applying repeated and independent measures concepts, it can be concluded that there are 11 individuals participated in the repeated-measures research study and 12 individuals participated in the independent-measures research study (option D).
In a repeated-measures research study, the degree of freedom (df) is calculated by subtracting 1 from the number of individuals in the study (n). Therefore, if df = 10, then the number of individuals in the study is 10 + 1 = 11.
Whilst, in an independent-measures research study, the degree of freedom (df) is calculated by subtracting 2 from the number of individuals in the study (n). Therefore, if df = 10, then the number of individuals in the study is 10 + 2 = 12.
Therefore, it can be concluded that there are 11 individuals participated in the repeated-measures research study and 12 individuals participated in the independent-measures research study (option D).
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the t-value changes depending on the number of data points collected.
Yes, that is correct. The t-value is used to calculate the significance of the difference between two sample means.
It is used in a t-test, which is a type of hypothesis test that is commonly used in statistical analysis. The t-value changes depending on the number of data points (sample size) collected, as well as the level of confidence desired and the standard deviation of the population. A larger sample size typically results in a smaller t-value, which means that the difference between the two sample means is more significant. On the other hand, a smaller sample size leads to a larger t-value, which means that the difference between the two sample means is less significant. Yes, that is correct. The t-value is used to calculate the significance of the difference between two sample means.
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If today is saturday , what day of week will it be 150 days from today ??
what is the interest rate on an investment of $470 at for seven years with an ending balance of 683.85
Answer:
Step-by-step explanation:
To find the interest rate on an investment of $470 for seven years with an ending balance of $683.85, you can use the formula for simple interest:
I = P * r * t
Where I is the interest earned, P is the principal amount ($470), r is the interest rate, and t is the number of years (7).
Rearranging the formula to solve for r:
r = I / (P * t)
Substituting the given values:
r = (683.85 - 470) / (470 * 7)
r = 213.85 / 3290
r = 0.0649 or 6.49%
So, the interest rate on the investment of $470 for seven years with an ending balance of $683.85 is 6.49%.
how many times does 4 go in 5
Answer:
Step-by-step explanation:
9 times
6,7,8,9 (4 times starting at 5)
Answer: 1.25
Step-by-step explanation:
you divide/combine 5 and 4 to get Ur anwser 1.25. Yet it's the same thing as asking ,"How much is 5 divided by 4?" just think of it to yourself as how many times you can fit 4 into 5. One tip you can use is 4(x) = 5 and x will equal 1.25.
Use the table to make a function
The quadratic equation that represents the parabola is y - 2 = - x².
How to determine and check a quadratic equation
In this problem we find a table representing a quadratic equation, whose definition can be found by using two points and the vertex form of the parabola equation:
Vertex form
y - k = C · (x - h)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constantFirst, determine the coordinates of the vertex of the parabola by table:
(h, k) = (0, 2)
Second, find the vertex constant:
C = (y - k) / (x - h)²
C = (1 - 2) / (1 - 0)²
C = - 1
Third, write the equation of the parabola:
y - 2 = - x²
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Use the given scale factor and the side lengths of the scale drawing determine the side lengths of the real object.
Side a is 2.5 inches long, side b is 5 inches long and side c is 6.5 inches long. Therefore, option C is the correct answer.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, scale factor =2:1
Scale drawing to object the scale factor is 2:1.
Now,
a=1/2 *5 =2.5 inches
b= 1/2 *10 = 5 inches
c= 1/2 * 13 = 6.5 inches
Therefore, option C is the correct answer.
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2v+12≥16 need help pls give 30 points
The method for addressing inequality 2v + 12 ≥ 16 is v ≥ 2. This indicates that any value of v larger than or equal to 2 will fulfil the inequality.
What is meant by inequality?The idea of inequality—the state of not being equal, particularly in status, rights, and opportunities1—is one that is central to social justice theories. However, because it frequently has diverse meanings to different people, it can become confusing in public discourse.
What kind of mathematical inequality is this, specifically?The equation-like appearance of the phrase 5x 4 > 2x + 3 is altered by the arrowhead in place of the equals sign. It serves as an illustration of inequity. This shows that the section on the left, 5x 4, is bigger than the part on the right.
Subtract 12 from both sides of the inequality:
2v + 12 - 12 ≥ 16 - 12
Simplifying, we get:
2v ≥ 4
Divide both sides of the inequality by 2:
2v/2 ≥ 4/2
Simplifying, we get:
v ≥ 2.
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O DATA ANALYSIS AND PROBABILITY
Range of a data set
Ann is recording the percentages she earned on each quiz in her math class. Here are her results for the last 7 quizzes.
74, 64, 90, 74, 92, 68, 71
Find the range of the data set.
a
X
5
The range of the data set is, 28
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The data set is,
74, 64, 90, 74, 92, 68, 71
Now, We know that;
Range of data set is calculating by subtracting the lowest value from highest value.
Hence, The range is,
⇒ Highest value - Lowest value
⇒ 92 - 64
⇒ 28
Thus, The value of range = 28
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