Simpson's rule, the estimated distance the runner covered during the first 5 seconds of the race is approximately 17.9625 meters
To estimate the distance the runner covered during the first 5 seconds of the race using Simpson's rule, we need to use the given data points and apply the formula for Simpson's rule:
Distance ≈ h/3 * [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + ... + 2f(xn-2) + 4f(xn-1) + f(xn)]
where h is the step size (time interval) between consecutive data points and f(xi) represents the velocity at each time point.
Given the data points:
t(s): 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5
v(m/s): 0, 2.25, 4.7, 4.9, 5.8, 7.95, 8.9, 10.3, 10.75, 10.85, 10.85
The step size (h) is 0.5 seconds, and we have 11 data points.
Using Simpson's rule, we can calculate the distance as follows:
Distance ≈ (0.5/3) * [0 + 4(2.25) + 2(4.7) + 4(4.9) + 2(5.8) + 4(7.95) + 2(8.9) + 4(10.3) + 2(10.75) + 4(10.85) + 10.85]
Distance ≈ (0.5/3) * [0 + 9 + 9.4 + 19.6 + 11.6 + 31.8 + 17.8 + 41.2 + 21.5 + 43.4 + 10.85]
Distance ≈ (0.5/3) * 215.55
Distance ≈ 17.9625 meters
Therefore, using Simpson's rule, the estimated distance the runner covered during the first 5 seconds of the race is approximately 17.9625 meters
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To estimate the distance the runner covered during the first 5 seconds of the race using Simpson's rule, we first need to calculate the area under the curve of the velocity vs. time graph.
Simpson's rule involves approximating the area using quadratic polynomials, which means we need to split the interval [0,5] into subintervals of equal width. In this case, we have 10 data points, so we can split the interval into 5 subintervals of width 1. We then apply Simpson's rule to each subinterval and sum up the results to get the total estimated area. Once we have the estimated area, we can multiply it by the runner's average speed during the first 5 seconds (which we can calculate by taking the mean of the velocity data) to get the estimated distance covered.
To estimate the distance using Simpson's Rule, follow these steps:
1. Divide the time interval into even subintervals: 0, 0.5, 1, ..., 5 (10 subintervals, h = 0.5).
2. Apply Simpson's Rule formula: (h/3) * (f(a) + 4∑(odd intervals) + 2∑(even intervals) + f(b)).
3. Plug in given velocities for f(a), f(b), and at each subinterval.
4. Calculate the sum: (0.5/3) * (0 + 4*(2.25+4.9+7.95+10.3+10.85) + 2*(4.7+5.8+8.9+10.75) + 10.85).
5. Solve the equation: (0.5/3) * (135.4) ≈ 11.283 m.
The runner covered approximately 11.283 meters during the first 5 seconds of the race.
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Solving systems of equations by substitution worksheet
1. y = 6x-11
-2x-3y = -7
2. 2x-3y = -1
y = x-1
1. steps to find the value of x
The first step is to equalize the form of the equation.
y = 6x-11 = -6x+y= -11
-2x-3y = -7
thus becoming:
-6x+y= -11
-2x-3y = -7
Then eliminate y:
-6x+y= -11 | times -3| becomes 18x-3y=33
18x-3y=33
-2x-3y = -7
y in the equation can be eliminated to become:
20x=40
x=40/20
x=2
steps to find the value of y:
The first step is to equalize the form of the equation.
y = 6x-11 = -6x+y= -11
-2x-3y = -7
thus becoming:
-6x+y= -11
-2x-3y = -7
Then eliminate x:
-2x-3y = -7 | multiplied by 3| becomes -6x-9y=-21
-6x+y= -11
-6x-9y=-21
x in the equation can be eliminated to become:
10y=10
y=-10/10
y=1
2.
1. steps to find the value of x
The first step is to equalize the form of the equation.
2x-3y = -1
y = x-1 becomes -x+y=-1
thus becoming:
-2x-3y = -1
-x+y=-1
Then eliminate y:
-x+y=-1| times -3| to 3x-3y=3
-2x-3y = -1
3x-3y=3
y in the equation can be eliminated to become:
-5x=-4
x=4/5
Steps to find the value of y:
The first step is to equalize the form of the equation.
2x-3y = -1
y = x-1 becomes -x+y=-1
thus becoming:
-2x-3y = -1
-x+y=-1
Then eliminate x:
-x+y=-1| multiplied by 2| becomes -2x+2y=-2
-2x-3y = -1
-2x+2y=-2
x in the equation can be eliminated to become:
-5y=1
y=-1/5
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What is the difference between factor theorem and remainder theorem Class 9?
The remainder theorem states that the value of f(a) is equal to the remainder for any polynomial f(x) when divided by the binomial xa. The factor theorem states that (xa) is a factor of f(x) and vice versa if an is a zero of a polynomial f(x).
A special example of the polynomial remainder theorem is the Factor theorem. So, according to the factor theorem, a polynomial has a factor if and only if: If and only if f (M) = 0, the polynomial x-M is a factor of the polynomial f(x). According to the Remainder Theorem, the remainder will be if a polynomial (x) is divided by a linear binomial of the kind (x - a) (a).
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How do you write 8x8x8x8 in exponential form?
The exponential form of given expression "[tex]8 \times 8 \times 8 \times 8[/tex]" is [tex]8^{4}[/tex] , and the value of this exponential expression is 4096 .
The exponential expression is given as : [tex]8 \times 8 \times 8 \times 8[/tex] ;
we have to represent the given expression in exponential Form ,
The Law Of Exponents states that , when multiplying the numbers having same base and different exponents , then the base is kept same and the exponents are added ,
So , According to Law Of Exponents ,
the given expression can be written in exponential form as :
⇒ [tex]8 \times 8 \times 8 \times 8[/tex] ;
⇒[tex]8^{1+1+1+1}[/tex]
⇒ [tex]8^{4}[/tex] .
So , the exponential form is [tex]8^{4}[/tex] .
and the value of this expression is = 4096 .
Therefore , the exponential form of [tex]8 \times 8 \times 8 \times 8[/tex] is 8⁴ .
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In LMN MN=15cm, LP is perpendicular to MN, LP=100 angle PLN=PNL. Calculate the length of LN
The length of LN is approximately 101.12 cm.
What is the length of the hypotenuse?
In a right triangle, the hypotenuse is the side opposite to the right angle and it is the longest side of the triangle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In a right triangle, the length of the hypotenuse is given by the Pythagorean theorem: c^2 = a^2 + b^2.
In this case, we are given that LN is the hypotenuse, and LP and MN are the other two sides.
We are also given that LP = 100 and MN = 15, and that angle PLN = PNL which means that the triangle is a right triangle.
We can use the Pythagorean theorem to find the length of LN:
LN^2 = LP^2 + MN^2
LN^2 = 100^2 + 15^2
LN^2 = 10000 + 225
LN^2 = 10225
LN = √10225
LN ≈ 101.12 cm
So the length of LN is approximately 101.12 cm.
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How do you find the midpoint between any two points using only their coordinates?
To find the midpoint between any two points in a plane using only their coordinates, you can use the midpoint formula. The midpoint formula is:
(x,y) = ((x1 + x2) / 2, (y1 + y2) / 2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points, and (x,y) are the coordinates of the midpoint.
For example, if we have two points (-2,8) and (4,10)
(x,y) = ((-2 + 4) / 2, (8 + 10) / 2)
(x,y) = (1,9)
The midpoint of the given points (-2,8) and (4,10) is (1,9).
It's worth noting that this formula can be adapted for three-dimensional points, where the midpoint formula would be
((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)
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Which graph shows a system of equations with the solution (5, -3)?
Right-hand bottom graph shows a system of equations with the solution (5, -3).
What is Graph?A diagram that depicts the connection between two values, measures, or other objects as a line or curve.
According to the inquiry,
Due to the fact that the two lines meet at the position where they do, the graph on the bottom right depicts a system of equations with the answers (5, -3) (5, -3).
Therefore, the proper answers to the problem are represented by the bottom right.
Right-hand bottom graph has the proper equations and their answers (5,-3).
Right-hand bottom graph shows a system of equations with the solution (5, -3).
The complete question is
Which graph shows a system of equations with the solution (5, -3)?
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Suppose one friend decided to pay for a bag of pretzels
and a drink for all 4 of them.
If x equals the cost of the pretzels and y equals the cost of
the drink, what expression represents the total cost?
A 4+x+y
B 4(x+y)
c 4x+y
D x+4y
Answer:
C
Step-by-step explanation:
4x is really just 4 times the cost of the drinks +the cost of the pretzel bag so ita 4x+y
Solving a Mixed-Degree
Consider the following system of equations:
10 + y = 5x + x2
5x + y = 1
The first equation is an equation of a
The second equation is an equation of a
What are the solutions of the system?
Answer:
The solutions are:
(1,-4), and (-11,56)
Step-by-step explanation:
10 + y = 5x + x^2
5x + y = 1
Rearrange both equations to isolate y:
y = x^2 + 5x - 10
y = -5x+1
Since y=y, we set set the right sides of both equations equal to each other:
-5x+1 = x^2 + 5x - 10
Rearrange
-x^2 - 10x + 11 = 0
x^2 +10x - 11 = 0
Factor
(x+11)(x-1) = 0
x = -11 and 1
Use these two values of x to find y. We'll use the simpler equation of
y = -5x+1.
x _y
1 -4 (1,-4)
-11 56 (-11,56)
See the attached graph for proof.
2x+3y=3,2y+3z=4,2x+2z=8
Answer:
x=6/5
y=1/5
z=14/5
i think i not 100% sure
In your own words define energy transformation
Which statements are true about the volume of the triangular pyramid shown? Select two choices. (Recall the formula V = one-third B h.)
A triangular pyramid. The base has a base of 8 feet and height of 2 feet. The pyramid has a height of 6 feet.
[Not drawn to scale]
The value of h in the formula V = one-third B h is 2 ft.
The area of the base, B, is 8 feet squared.
The sum of the areas of the faces can find the volume.
The volume is 16 feet squared.
The expression One-third (8) (2) (6) can be used to find the volume of the pyramid.
The correct statements are,
The area of the base, B, is 8 feet squared.
The expression one-third (8) (2) (6) can be used to find the volume of the pyramid.
What is a triangular pyramid?A tetrahedron is a polyhedron in geometry that has four triangular faces, six straight edges, and four vertex corners. It is often referred to as a triangle pyramid. The tetrahedron is the simplest and only regular convex polyhedron with less than five faces.
Given that a triangular pyramid. The base has a base of 8 feet and a height of 2 feet. The pyramid has a height of 6 feet. The volume of the triangle is calculated as,
The area of the base,
A = 1/2 x b x h
A = 1/2 x 8 x 2
A = 8 feet
The volume will be calculated by the formula,
Volume = 1 / 3 x Base are x h
Volume = 1 / 3 x 8 x 2 x 6
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which of the following is the graph of the piecewise function
Step-by-step explanation:
[tex]\displaystyle\\f(x)=\left\{\begin{array}{ccc}\sqrt{-x-1}\ \ \ if}\ \ \ x\leq -1 \\\frac{x}{x^2-x-2}\ \ \ if\ \ \ -1 < x < 2 \\log_2(x-1)\ \ \ if\ \ \ x\geq 2\end{array}\right[/tex]
Answer:
The equation and the tables represent two different functions. Use the equation b = 6a - 10 and the table to answer the questions. This table represents c as a function of a.
Answer:
[tex]A. \;\;b \;is \;greater[/tex]
[tex]B.\;\;a = 1, b = -4[/tex]
[tex]C.\;\;a = 6, c = 20[/tex]
Step-by-step explanation:
Part A
We have the relationship
[tex]b = 6a - 10[/tex]
When [tex]a[/tex] is [tex]-2[/tex], the value of [tex]b[/tex] is
[tex]b = 6(-2) -10 = -12 -10 = -22[/tex]
The corresponding value of [tex]c[/tex] for [tex]a = - 2[/tex] is -[tex]21[/tex]
[tex]-21[/tex] is greater than [tex]-22[/tex] so answer is : [tex]b[/tex] is greater
Part B
When [tex]c[/tex] is [tex]6[/tex], we see that the value of [tex]a[/tex] from the table is [tex]1[/tex]
The corresponding value of b is:
[tex]b = 6(1) - 10 = 6 - 10 = -4[/tex]
Part C
When [tex]b = 26[/tex], plugging this into the equation[tex]b = 6a - 10[/tex] we get
[tex]26 = 6a - 10\\\\26 + 10 = 6a\\\\36 = 6a\\\\[/tex]
or
[tex]6a = 36[/tex] giving [tex]a = 36/6 = 6[/tex]
For [tex]a = 6[/tex], from the table we see that the corresponding value of [tex]c = 20[/tex](ANS)
Let f(x) = |x| + 2
The graph of f(x) is transformed into the graph of g(x) by a translation of 3 units right and 1 unit up.
What is the equation for g(x)?
45 points!!!
The required function after the trasformation of 3 units right and 1 unit up is given as g(x) = |x - 3| + 3.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given equation of function f(x) = |x| + 2
The above function is an aboslute function, so in order to translate the function right, the function after transformation will be as |x - 3| + 2, we subtract 3 from x to translate in the horizontal x-axis.
Now,
Add + 1 to the function to translate it 1 unit up,
The function becomes,
g(x) = |x - 3| + 3
Thus, the required function after the trasformation of 3 units right and 1 unit up is given as g(x) = |x - 3| + 3.
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e.
d.
C.
b.
a.
12
Original
Fractions
47 35 59 23 14207956 5238
Common
Denominator
35
Equivalent Fractions
> or <
+11
4
7
9
5
12
3.5
름
5
6
3.8
ble to help you rewrite the problems with common denominators. Then solve.
The fractions with the common denominators are given as follows:
4/7 = 36/63.5/9 = 35/63.The inequality relating the fractions is given as follows:
4/7 > 5/9.
What is a fraction?A fraction is a numerical representation of the division of the two terms x and y, as follows:
Fraction = x/y.
The terms are classified as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.The fractions for this problem are given as follows:
4/7.5/9.The denominators are given as follows:
7 and 9.
The least common multiple of 7 and 9 is given as follows:
7 x 9 = 63.
Hence the equivalent fractions are given as follows:
4/7 = 36/63. (63/7 = 9, hence both the numerator and denominator are multiplied by 9).5/9 = 35/63 (63/9 = 7, hence both the numerator and denominator are multiplied by 7).The equivalent fractions have the same denominator, while the equivalent fraction to 4/7 has the greater numerator, hence the inequality is given as follows:
4/7 > 5/9.
Missing InformationThe problem is given by the image presented at the end of the answer.
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A cubical tank full of water is emptied in a cylindrical tank. If the edge of cubical tank is 77cm, find the height to which the water rises in the cylinder whose bbase diameter 1.4m.
Answer:
Step-by-step explanation:
H=456,533/pier^2
H=456533×7/22×7×7*. Here 7 as radius
H=29.645cm
Find the sales tax selling price 20$ rate of sales tax 3%
10 packages of bacon cost $20.50 at the grocery store. How much will 1 pack of bacon cost?
A.$2.05
B.$2.25
C.$2.00
D.$2.10
Answer: $2.05
[tex]$20.50/10=2.05[/tex]
How do you write 10x10x10x10 in exponential form?
Answer:
10^4
Step-by-step explanation:
10= 10^1
10x10 = 10^2 (2 10s)
10x10x10=10^3 (3 10s)
10x10x10x10=10^4 (4 10s)
basically the number of 10s you are multiplying will be the number of exponents you will use in this case.
Lindsay earned a 98 on her final exam for biology. The mean score was 78.2 and the standard deviation was 8.4. What was Lindsay’s z-score?
Lindsay's z - score, given the mean score, the standard deviation, and her score, is 2. 35.
How to find the z - score ?To calculate a z-score, you subtract the mean from the individual score and then divide by the standard deviation.
The formula is:
z = (x - μ) / σ
Where
x is the individual score
μ is the mean
σ is the standard deviation.
So, to find Lindsay's z-score:
z = (98 - 78.2) / 8.4
z = 19.8 / 8.4
z = 2.35
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The boatbill is present in a density of at least one pair per 20 acres at the same time that two different types of plants are dominant. What are these plants?.
The two types that the boatbill will dominate are grasses and shrubs according to the attached table.
What is density?The density of an item is defined as its mass divided by its volume. Density is commonly expressed in grams per cubic centimeter (g/cm3). Remember that grams are a unit of mass and cubic centimeters are a unit of volume (the same volume as 1 milliliter). “Density = mass divided by volume.” Density is a compound metric that tells us about an object's mass in proportion to its volume. The density of a substance is the measure of how densely it is packed together. It is expressed as mass per unit volume. Density Symbol: D or ρ Density Formula: = m/V, where is the density, m is the object's mass, and V is its volume.
Here,
According to the accompanying data, the boatbill will predominate among grasses and bushes.
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11
1 point
Which is the slope of the proportional relationship?
3/4
2
1/2
4/3
X3456
Y
3 6
69
8
5 10
6 12
Answer:
The number line that represents the inequality 6x - 12 > -6 is (D)
How to determine the number line?
The inequality is given as:
6x - 12 > -6
Add 12 to both sides
6x > 12 - 6
Evaluate the difference
6x > 6
Divide both sides by 6
x > 1
The number line that represents the above inequality is (D)
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How many square meters are in 280 square centimeters
We can perform a change of units to see that 280 square centimeters is equivalent to 0.028 square meters.
How many square meters are in 280 square centimeters?We want to perform a change of units between square centimeters and meters.
Remember the relation:
100cm = 1m
Now we can square both sides of that equation, then we will get:
(100 cm)^2 = (1m)^2
10,000 cm^2 = 1m^2
Then if we have a measure in square centimeters, to transform it into square meters we need to divide that measure by 10,000.
Then:
280 cm^2 = (280/10,000) m^2 = 0.028 m^2
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True or False? If false, state the correct solution.
Answer:
TRUE
Step-by-step explanation:
(2x^2-5x-3)/(x-3) = (2x+1)
(2x^2)/(x-3) - (5x)/(x-3) - 3/(x-3) = (2x+1)
[separated each term on the left side]
(2x^2)- (5x) - 3 = (2x+1)(x-3)
2x^2- 5x - 3 = (2x+1)(x-3)
(2x+1)*(x-3) = (2x+1)(x-3)
Both sides are the same. The equation is TRUE.
A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 7 grams and the amount of gold in each necklace is 18 grams. The jeweler made a total of 7 bracelets and necklaces using 82 grams of gold. Determine the number of bracelets made and the number of necklaces made.
The number of bracelets made is 4 and number of necklaces made is 3.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Let x be the number of bracelets made and y be the number of bracelets made.
There are total of 7 bracelets and necklaces.
x + y = 7
Amount of gold in each bracelet = 7 grams
Amount of gold in x bracelets = 7x grams
Amount of gold in each necklace = 18 grams
Amount of gold in y necklaces = 18y grams
Total gold used is 82 grams.
7x + 18y = 82
We have two linear equations :
x + y = 7 ⇒ x = 7 - y
7x + 18y = 82
Substituting x = 7 - y in second equation,
7 (7 - y) + 18y = 82
49 - 7y + 18y = 82
11y = 82 - 49
11y = 33
y = 33/11
y = 3
x = 7 - y = 7 - 3 = 4
Hence the number of bracelets and necklaces are 4 and 3 respectively.
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Rewrite 5 square root 3^4 as an expression with a rational exponent. Then mark this number on the graph of f (x) = 3^x. Explain how you know where to place it.
Step-by-step explanation:
the nth root of something can be expressed as 1/n as exponent.
e.g. sqrt(2) = 2^(1/2).
so, the 5th root of 3⁴ = 3^(4/5)
for f(x) = 3^x
that means that x = 4/5 = 0.8.
so, I go on the x-axis to the right to 0.8, and from there straight up to the actual curve.
that is the desired point.
What is section formula and midpoint formula?
The section formula helps to find out the coordinates of points that divide the line in the m:n ratio whereas the midpoint formula helps us to find the midpoint of a line.
The section formula is used in geometry to find out centroid, incenters, etc. It is of two types: Internal division and external division. These types depend on the position of point P.For a point P(x,y) dividing line a(a,b) and B(c,d) in ratio m:n, The
Internal division section formulae is- P(x)=(c.m +a.n)/m+n , P(y)=(d.m+b.n)/m+nExternal division section formulae is- P(x)=(c.m - a.n)/m-n , P(y)=(d.m-b.n)/m-nThe midpoint formula is used to find the center of a line or a figure. It is a mathematical equation used in geometry and economics. On a line from point (x1,y1) to (x2,y2) the midpoint P= (x1+y1)/2 , (x2+y2)/2. It divides the line in 1:1 ratio.
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What is the measure of 23 if clld?
Answer:
i tink im doing this complete wrong but 1.380649×10−23 J
Step-by-step explanation:
Unit 11: Volume & Surface Area
Homework 2: Area of Sectors
Need help with 9 an 10
The area of sector in question 9 is 141.87 ft² and the area of sector in question 10 is 107.70 m².
What is the area of sector in circle?A circle is a collection of points that are all equally distance from the circle's centre. The radius is the usual distance a circle travels from its centre to its point. The circle's centre (o) and radius (r) serve as its definition (r).
A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends.
Given in question 9, r = HK = 25 ft
angle of sector = 26°
so the area of sector A₉ = (26°/360°)π*r²
⇒ A₉ = (26°/360°)* 22/7 * (25)²
⇒ A₉ = (26°/360°)* (22 * 625)/7
⇒ A₉ = 357,500/2520
⇒ A₉ = 141.87 ft²
Given in question 10, SR = 26 m
⇒ r = ST = SR/2
⇒ r = 26/2 = 13 m
angle of sector = 73°
so the area of sector A₁₀ = (73°/360°)π*r²
⇒ A₁₀ = (73°/360°)* 22/7 * (13)²
⇒ A₁₀ = (73°/360°)* (22 * 169)/7
⇒ A₁₀ = 271,414/2520
⇒ A₁₀ = 107.70 m²
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why is there a limit
Term limits have been approved almost everywhere they’ve been on the ballot.
Are term limits helpful?
However, the evidence suggests that at the margin, term limits are helpful to the cause of individual liberty. Elhauge’s report showed that term limits lessen the influence of seniority. His research demonstrated that long-term lawmakers from both major parties vote for more bureaucracy than do lawmakers who have been in office for shorter times.
Therefore, term limits have been approved almost everywhere they’ve been on the ballot
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