If 4 in has a force of 50 applied. The pressure is 12.5N/m².
How to find the pressure?Using this formula to find the pressure
Pressure = Force /Area
Where:
Force = 50
Area =4
Let plug in the formula
Pressure = 50/4
Pressure = 12.5 N/m²
Therefore the pressure is 12.5 N/m².
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A student stand 8meters away from a tree which is a metre tall. the student look at the top of the tree on a fruit. how far away is the student from the fruit?
Answer:
8.06 m
Step-by-step explanation:
Assuming the tree forms a right angle with the ground, the distance from the student to the tree represents the hypotenuse of a right triangle.
The hypotenuse can be found using the Pythagorean Theorem.
[tex]a^2+b^2=c^2\\a=8m\\b=1m\\c^2=(8m)^2+(1m)^2\\c^2=65m^2\\c=\sqrt65m^2\\c=8.06m[/tex]
The time it takes NFL running backs to run the 40-yard dash follows a normal distribution with a mean time of 4.59 seconds and a standard deviation of 0.12 second. Let x = the time it takes an NFL running back to run the 40-yard dash. (Use the Empirical Rule. Write your answers as a percent.) (a) P(x < 4.23)
The Empirical Rule given helps in determining Let x = the time it takes an NFL running back to run the 40-yard dash and that P(x < 4.23) is =95%.
In Football, every play is made from both yardage benefit or yardage loss that is a calculation of a poor or advantageous number. With every byskip or run that the offense attempts, you need to upload the yardage that they made collectively to apprehend wherein they've superior to at the field.
Here we have that,
NFL= 40 yard run
x = the time it takes an NFL running back
[tex]mu=4.59 \\sigma= 0.12[/tex]
Using Empirical rule,
[tex](A)P(X)P(4.35 < x > = P( -2 < Z > = P\\\\(Zthe usage of empirical rule=95%/2 + 95%/2=47.5%+47.5%=95 %[/tex]\
Thus the P(x < 4.23) = 95%.
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A law firm is going to designate associates and partners to a big new case. The
daily rate charged to the client for each associate is $400 and the daily rate
for each partner is $900. The law firm designated twice as many partners as
associates to the case and was able to charge the client $4400 per day for
these lawyers' services. Determine the number of associates assigned to the
case and the number of partners assigned to the case.
The required number of associates is 2 and the number of partners is 4.
What is arithmetic?
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Main body:
daily rate charged to the client for each associate = $400
daily rate charged to the client for each partner = $900
According to question :
The law firm designated twice as many partners as associates , that means
P=2A ---(1)
900*P +400A =4400 ---(2)
substitute the value of eqn (1) in (2).
900 *2A +400A = 4400
1800 A+400 A =4400
2200A =4400
A= 2
therefore P = 4.
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Is linear and quadratic function the same?.
No. Linear functions and quadratic functions are not the same.
Given,
Linear function;-A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane. This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).
Quadratic function;-A polynomial function of degree 2 known as a quadratic function is expressed in the generic form f(x)=ax2+bx+c. Where a0, real numbers a, b, and c are used. The graph of the quadratic function f(x)=x2 that squares an input value is shown below.
Difference between linear and quadratic function;When we graph a linear function, we get a straight line, however with a quadratic function, we get a parabola. In contrast to the slope of a linear polynomial, the slope of a quadratic polynomial is dynamic.
That is,
Linear functions and quadratic functions are not the same.
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suppose and . what does the tangent line approximation give as an approximation for ? 29.2 what does the tangent line approximation give as an approximation for ? (4*.1)/.1
Using tangent line approximation formula,
the tangent line approximation at x= 29.2 is
L(x) = 2x - 1 or L(29.2) = 57.4
Given a function f differentiable at tangent
x=a, we can find that the slope of the tangent of y=f(x) at (a,f(a)) can be found by writing . ). The resulting tangent line through (a,f(a)) and the gradient m=f'(a) is the point-gradient given by
y−f(a)=f'(a)(x−a) has an equation of the form This can also be expressed as y=f'(a)(x−a)+f(a).
Replacing the variable y by the expression L(x) yields
points (a, f( a)) called L(x)=f′(a)(x−a)+f(a). , L(x) is just the new name for the tangent, and
f(x)≈L(x) for x near a.
For example, suppose the function y=f(x) is known to have a tangent approximation at the point (1, 3) given by L(x)=3−2(x−1), but the function Other things about f.
we have given that,
f(x) = 2x - 1
x= 29.0 near to 29.2
f(29.0) = 58 - 1 = 57
f'(x) = 2
so, the point is (29.0, 57) and slope of tangent is 2 .
tangent line , 57 = 2(29) + b
=> b = -1
then equation is 2x - 1 = y
we to calculate tangent line approximation give as an approximation for at x = 29.2
tangent line approximation,
y = 2 (29.2) - 1 = 57.4
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Complete question:
suppose and f (x) = 2x - 1 , what does the tangent line approximation give as an approximation for x= 29.2??
a courier company charges $15 plus $1.60 per pound to deliver packages. identify the independent and dependent variables, and write a rule in function notation for the given situation.
The rule in function notation for the courier company charge on delivery is
C = 15 + 1.6x
Independent variables are the ones that you include in the model to explain or predict changes in the dependent variable.
The dependent variable is what you want to use the model to explain or predict. The values of this variable depend on other variables. It is the outcome that you’re studying. It’s also known as the response variable, outcome variable, and left-hand variable.
Given in the question,
A courier company charges $15 plus $1.60 per pound to deliver packages
Here , the dependent variable is cost of delivery because it is depending on how much a packages is weighting
The independent variable here is the weight of package because it doesn't depend on anything.
Let the cost of delivery be C and weight of package be x
The function for the charge will be :
C = 15 + 1.6x
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Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.
The proof for the difference between the squares of any two consecutive integers is equal to the sum of these two integers is done.
Define the term consecutive integers?Numbers that follow one another sequentially are known as consecutive numbers. Every time there are two numbers, there is a 1 difference. The mean and median of a sequence of numbers are equal. If n is just a number, then it follows that n, n+1, and n+2 are also numbers.Let x stand in for any integer.
The next integer (the one that comes after) should then be x+1.
The assertion calls for proof;
(x+1)² - x² = x+(x+1)
Address the left side;
= x² + x + x + 1² - x²
= 2x+1 (Left Hand Side Solution)
Now, work on the right side.
= x + (x + 1)
= 2x + 1
Since, the LHS=RHS (left hand side=right hand side) is obvious, subtracting the difference between two successive squared numbers equals adding the two integers.
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a single card is drawn from a standard deck of 52 cards. what are the odds against drawing an odd numbered card?
Answer:26%
Step-by-step explanation:
Fwam took a taxi from his house to the airport. The taxi company charged a pick-up fee of $3. 80 plus $2. 25 per mile. The total fare was $33. 05, not including the tip. Write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.
The taxi company charged a pick-up fee of $3. 80 plus $2. 25 per mile. So, the number of miles in the taxi ride with the total fare $33. 05 is 13 miles.
How to determine the number of miles in the taxi ride?Write and solve an equation
Supppse, the number of miles = x
Total fare = a pick-up fee + fare per mile × the number of miles
Total fare = 3.80 + 2.25 x
Determine the number of miles
Total fare = 3.80 + 2.25 x
33.05 = 3.80 + 2.25 x
2.25 x = 33.05 - 3.80
2.25 x = 29.25
x = 29.25/2.25
x = 13
The number of miles in the taxi ride is 13 miles.
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what is the distance from amelia to the top of the tower? type your answer in the box. use numerals instead of words. the distance from amelia to the top of the tower is feet.
The distance from Amelia to the top of the tower is 100 feet.
Define trigonometric identities.Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry.
Given,
Considering the query;
The tower has a 50-foot height.
Amelia's position and the top of the tower form a 30° angle.
Trigonometric identities, therefore;
Thus,
x = 50/sin30°
sin 30° = 50/x.
x = 50/0.5
x = 100 ft.
The distance from Amelia to the top of the tower is 100 feet.
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I will give brainlest to first person to answer correctly!
Answer:
R = 1
Step-by-step explanation:
R = y/x
Substitute the x and y values, for example, the first row
5.8/5.8 = 1
Therefore the answer is 1
For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment.
The maximum absolute values of the shear and bending moment is 2P and 3Pₐ respectively.
(a) Diagram is shown in image.
From A to B:
+∑Fy = 0: V = -P
+∑M₁ = 0: M = -P
From B to C:
+∑Fy = 0:
-P-P-V = 0
⇒ V = -2P
+∑M₂ = 0:
Pₓ+P(x - a)+M =0
⇒
M = -2Pₓ + Pₐ
(b) The maximum bending moment occurs in a beam, when the shear force at the section is zero or changes the sign because at point of contra fixture the bending moment is zero.
Therefore
|V|max = 2P
|M|max = 3Pₐ
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Suppose A is an invertible n×n matrix and v is an eigenvector of A with associated eigenvalue 4. Convince yourself that v is an eigenvector of the following matrices, and find the associated eigenvalues:
A4, eigenvalue = ?
A−1, eigenvalue = ?
A+4In, eigenvalue = ?
2A, eigenvalue = ?
The eigenvector of matrix A4 is 4096.
The eigenvalue of the matrix A-1 is 1/8.
(A+4I) has an eigenvalue of 12.
40 is the eigenvalue of 5Av.
The collection of scalar values known as the eigenvalues of a matrix are connected to the set of linear equations that are most likely contained within the matrix equations.
The eigenvectors are also known as the characteristic roots.
If the matrix A's eigen vector v is linked to an eigen value.
Av then equals lamda v.
The fact that v is an eigen vector of A with the value eight is assumed.
hence, Av = 8v.
We must determine the eigenvalue of A4.
A4*v equals A3(8v) = 84*v equals 4096v.
As a result, the eigenvalue of A4 is 4096.
Suppose A has an eigenvalue of 8. The eigenvalue of A-1 is thus 1/8.
It is calculated that the eigenvalue of (A+4I) is (A +4In)v = Av + 4v = 8v + 4v =12v.
(A+4I) has an eigenvalue of 12.
The value of 5Av's eigenvalue is 5Av = 5*8v = 40v.
40 is the eigenvalue of 5Av.
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A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries negative 10, 0, 0, negative 4, negative 6, 0. Which is a y-intercept of the continuous function in the table? Group of answer choices (0, –6) (–2, 0) (–6, 0) (0, –2)
A y-intercept of the continuous function in the table is; (0, –6)
What is the y-intercept of the given function table?The y-intercept of a function is defined as the point where the graph intersects the y-axis. This means the point where the x-value is zero.
Now, from the function table given, we can see the coordinates of the function are given as;
(-4, 10)
(-3, 0)
(-2, 0)
(-1, -4)
(0, -6)
(1, 0)
Now, from the coordinates above , we can see that the only coordinate that has the x-value as zero is the one (0, -6) and as such by definition, it is the y-intercept.
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Line m is parallel to the y-axis, and its slope is _____. negative undefined positive 0
Answer:
undefined slope
Step-by-step explanation:
a vertical line parallel to the y- axis has an undefined slope
g(x) = 3x^2+ 5
f(x) = x - 2
Find | g
The value of (gof)(x) is [tex]3x^2[/tex] - 12x + 17
The first function is
g(x) = [tex]3x^2[/tex] + 5
The second function is
f(x) = x - 2
The function is the mathematical statement that shows the relationship between one variable and another variable. If one variable is independent variable and another variable is dependent variable. The function consist of the different variable, numbers and mathematical operators
Then the value of (gof)(x) is
g(f(x) = g(x-2)
Then,
g(x - 2) = 3 × [tex](x-2)^2[/tex] + 5
Expand the terms
g(x - 2) = 3 × ([tex]x^2[/tex] - 4x + 4) +5
g(x - 2) = [tex]3x^2[/tex] - 12x + 12 +5
Add the terms
g(x - 2) = [tex]3x^2[/tex] - 12x + 17
Hence, the value of (gof)(x) is [tex]3x^2[/tex] - 12x + 17
The complete question is
If g(x) = 3x^2+ 5
f(x) = x - 2
Find the value of (gof)(x)
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in a manufacturing process, a random sample of 36 manufactured bolts has a mean length of 3 inches with a standard deviation of .3 inches. what is the 99 percent confidence interval for the true mean length of the manufactured bolt?
The 99% confidence interval for the true mean length of the manufactured bolt is (2.9177, 3.0823)
Here, we need to construct a 99% confidence interval for population mean (μ) is given by
μ = x + Zα/2 * σ/√n or μ = x - Zα/2 * σ/√n
where, μ = population mean
x = sample mean
= 3 inches
σ = population standard deviation
= 0.3 inches
Zα/2= z score for a two tailed test at level of significance α = 2.576( for a 99% confidence level)
So, the upper limit would be,
μ = 3 + 1.645 * (0.3/√36)
μ = 3 + 1.646 * (0.3/6)
μ = 3.0823
And the lower limit would be,
μ = 3 - 1.645 * (0.3/√36)
μ = 3 - 1.646 * (0.3/6)
μ = 2.9177
Hence, the 99% confidence interval is (2.9177, 3.0823)
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the michner corporation is trying to choose between the following two mutually exclusive design projects: table Picture
If the required return is 10 percent then the profitability index for project 1 is 1.140 and project 2 is 1.284. If the company applies the profitability index decision rule, then project 2 should the firm accept.
In the given question, the michner corporation is trying to choose between the following two mutually exclusive design projects.
A1. Profitability index
Profitability index = present value of cash flow/initial investment
Project 1
Present value of future cash flows = 37600/(1+0.1)³
Present value of future cash flows = 93,505.634
Initial investment = 82,000
Now substitute values in formula
Profitability index = 93,505.634/82,000
Profitability index = 1.140.
Project 2
Present value of future cash flows = 11,200/(1+0.1)³
Present value of future cash flows = 27,852.742
Initial investment = 21,700
Now substitute values in formula
Profitability index = 27,852.742/21,700
Profitability index = 1.284
A2. Multiple choice.
The project with higher probability index should be accepted, therefore Project 2 should be accepted.
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What is a prime multiple?.
Prime multiples are numbers that add to make a prime. The sum of the factors 1 and 7 is 7. Consequently, 1 and 7 are the prime multiples of 7.
In the given question we have to explian about the prime multiple.
The numbers that result from multiplying the original number by any whole number are the multiples of that number. Prime multiples are hence numbers that add to make a prime. The sum of the factors 1 and 7 is 7. Consequently, 1 and 7 are the prime multiples of 7.
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A box contain 576 marble of 6 different color. If there are 254 boxe how many marble are in all the boxe
Answer:
146304 marbles
Step-by-step explanation:
We do not need to worry about the color part, at least right now
One box contains 576 marbles
To find how many are in 2 boxes we would do 576 * 2
To find 254, we would do 576 * 254
Now, I would suggest using lattice multiplication here. If you do not know how to do that, long multiplication works fine.
I can't show that here, but I can show the answer:
576 * 254 = 146304
So, there are 146304 marbles is 254 boxes
find two positive numbers that satisfy that the product is 147 and the sum of the first number plus three times the second number is a minimum.
Two positive numbers that satisfy x=21 and y=7
XY = 147
x +3y = x + 3(147/x) = (x²+ 441)/x = f(x)
0= f'(x) = (x ( 2x) - x² - 441)/x²
= 2x² - x² -441)/x²
= (x² - 441)/x²
So then x² - 441 = 0
x = 21 , as x>0
x=21 and y=7,
the max sum is 21 +3(7) = 42
Related to best a regular and a primary-order (linear) time period, in which m is the slope and b is the y-intercept. every so often, the above is referred to as a "linear equation of variables," where y and x are the variables. a linear feature is defined as a feature that has both one or two variables without exponents. it is a function that graphs to the direct line.
A linear equation in two variables is of the shape Ax + by way of + C = zero, in which A and B are the coefficients, C is a consistent term, and x and y are the two variables. Linear functions are those whose graph is an instant line. A linear feature has the subsequent shape. y = f(x) = a + bx. A linear characteristic has one impartial variable and one based variable. The independent variable is x and the base variable is y.
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The y-intercept of f(x)=3(1/2)x is ____________________ the y-intercept of the function in the graph:
The y-intercept of f(x) = 3(1/2)x is less than the y-intercept of the graphed function.
What is the Y-intercept of a Function?The y-intercept of function, y = mx + b, is the value of b, which is the point on the graph where the line intersects the y-axis.
Given the function, f(x) = 3(1/2)x, the y-intercept is 0 because if we examine the equation given in slope-intercept form as y = mx + b, there is no value of b, or rather, the value of b is equal to 0.
In the given graph above, the line of the function intercepts the y-axis at 4. This implies that the y-intercept of the function on the graph is 4.
Therefore, f(x) = 3(1/2)x has a y-intercept that is less than that of the function in the given graph.
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Which number line represents the solution set for the inequality 4 x 3 ≤ 2 2x?.
The number line which represents the solution set for the inequality is
x ≤ -5.
What is number line?
In elementary mathematics, a number line may be a image of a graduated line that is visual illustration of the important numbers. each purpose of variety|variety} line is assumed to correspond to a true number, and each real to a degree.
Main body:
[Given]=
-4(x + 3) ≤ -2 - 2x
Using the distributive property of multiplication on LHS
-4x-12 ≤ -2 - 2x
By transposing the terms with variables on one side and the constant on the other side
- 4x + 2x ≤ –2 + 12
By further calculation
- 2x ≤ 10
Divide both sides by -2
x ≤ -5
Therefore, x ≤ -5 represents the solution set.
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What kind of equation of a line is Y y1 M x x1 )?.
Slope intercept form of equation of a line is described by y - y1 = m(x - x1)
The are three kinds of equation of a line
a) point intercept form
b) slope point form
c) point point form
The formula y - y1 = m(x - x1) is usually described as the 'point-slope form' for the equation of a line.
where m represents the slope of the line and x1 and y1 is the point given through which the line passes.
It is useful when one point on a certain line and the slope of that certain line is known, then the equation of the line can be structured using this form.
Thus, the slope intercept form of equation of a line is described by y - y1 = m(x - x1)
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find the area of the shape either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal
The area of a sector from the given figure is 50.24 square units.
From the given figure, radius of sector =8 units and the central angle =90°.
What is area of a sector?The area of a sector is the space inside the section of the circle created by two radii and an arc. It is a fraction of the area of the entire circle.
The formula to find the area of a sector = [tex]\frac{\theta}{360^o} \times\pi r^2[/tex].
Here, r=8 units and θ=90°
Using the area of a sector formula, we get
90°/360° ×3.14×8²
= 0.25×3.14×64
= 50.24 square units
Therefore, the area of a sector from the given figure is 50.24 square units.
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The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84? (a) 0.683 (b) 0.954 (c) 0.271 (d) 0.340
The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .
In the question ,
it is given that ,
The random variable X is said to be normally distributed ,
the mean is given as , μ = 70 , and
standard deviation of normal distribution is (σ) = 10
probability that X is between 72 and 84 is written as P(72 < X < 84)
= P((72 - 70)/10 [tex]<[/tex] Z [tex]<[/tex] (84 - 70)/10)
= P(0.2 < Z < 1.4)
= P(0 [tex]<[/tex] Z [tex]<[/tex] 1.4) – P(0 [tex]<[/tex] Z [tex]<[/tex] 0.2)
From the z table , we get the values as
= 0.4192 – 0.0793
= 0.3399
≈ 0.340
Therefore , The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .
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If an experiment is selecting a card from a deck of cards, then the sample space is.
The sample space is all the cards in the deck if an experiment involves choosing one card from a deck of playing cards.
Given statement,
If an experiment is selecting a card from a deck of cards, then the sample space is,
For the given case,
The sample space in this case is " all the cards in the deck "
Therefore, If an experiment is selecting a card from a deck of cards, then the sample space is all the cards in the deck.
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the least squares regression line is the line which minimizes the sum of the squared residuals for all the points in the scatterplot. the vertical distance between a point in the scatterplot and the predicted value on the regression line is the residual for the point. least square estimates from simple linear regression are the slope b1 estimates, on average, the change in the y variable associated with one unit increase in x variable.
The correct statements for least square estimates is the 3rd and 4th statements.
What is least square estimates?Least square estimates is method to predicted the observed Y value with minimized the sum of squared errors when using the fitted line.
The first and second statements is about simple linear regression. Simple linear regression is refers to linear line as parameter for fitting a model.
All statements are correct, but since the question asks for which statement is correct for least squares estimation, only the third and fourth statements are correct.
Thus, the 3rd and 4th statements is correct for least square estimates.
Your question is incomplete, but most probably your full question was (image attached)
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What is the image point of (-9, -5) after the transformation T -5,0 of D2?
(-14, -5) is the image point of (-9, -5) after the transformation T(-5,0)
How to find the image of a point after transformation?Transformation is defined as the change in the position of a point, a line or a geometric figure
Given: point (-9, -5) with transformation T (-5,0)
This implies there is a change in the position of the original point by (-5, 0). Thus, the image point can be determined as follows:
image point = (-9, -5) + (-5,0)
= (-9+(-5), -5+0)
= (-14, -5)
Therefore, the image point is (-14, -5)
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What are the reasons for the increase in the number of interest groups ?.
Over the past forty years, there has been a sharp rise in the quantity and variety of interest groups. .
What exactly are state and federal jurisdictions?In general, federal courts handle cases involving federal law, while state courts hear cases involving state law. Because most crimes are violations of local or state law, state courts typically hear criminal cases.
What are the three categories of federal authority?The 94 District Courts (trial courts), 13 Courts of Appeals (intermediate appellate courts), and the United States Supreme Court are the three main categories of federal courts within the federal system (the court of final review).
The three main causes of this surge are the "New Politics" movement, the increase of the role of government, and grassroots conservative action. Federal jurisdiction over a wide variety of public policy problems was expanded throughout the 1960s and 1970s, and there was a matching rise in the number of interest organizations that could exert pressure on elected officials
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