Mathematical induction, .∴ Pn+1 follows if Pn is true. For all positive integers of n, Pn holds true because P1 is true.
To prove mathematical induction?Assume that Pn is 4 + 9 + 14 +... + (n/2)(5n + 3)=(5n -1).
First, establish that P1 is accurate when n equals 1.
LHS= 4
RHS
= 1/2(5 + 3)
= 1/2(8)
= 4
= LHS
Is P1 true.
2) Assume Pn to be accurate, i.e., 4 + 9 + 14 +... + ( 5n -1)= (n/2)(5n +3)
3) Establish Pn+1 as true in the induction stage.
Replace (n+1) on both sides of n to obtain Pn+1.
Pₙ₊₁: 4 +9 +14 +...+(5n -1)+ [5(n+1) -1]=
Establish the RHS and LHS's parity.
LHS = 4 +9 +14 +...+(5n -1)+ [5n +5-1]
Bold expression in (2) should be replaced with the value of Pn:
.∴ Pn+1 follows if Pn is true. For all positive integers of n, Pn holds true because P1 is true.
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Two 3 x 4 rectangles overlap, as shown below. Find the area of the overlapping region (which is shaded).
Rectangles
The Area of a Rectangle
In geometry, a figure is defined as a rectangle if it is a quadrilateral and it has four right angles and two pairs of parallel sided. The area of such a figure is calculated as A=l w, where l represents the length and w represents the width.
719/64 unit² is the area of the overlapping region (which is shaded)
Rectangles .
What is a rectangle, exactly?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral.
Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
the Pythagorean theorem as follows to calculate the value of x .
( 4 - x )² = 3² + x ²
16 - 8x + x² = 9 + x²
16 - 8x = 9
16 - 9 = 8x
7/8 = x
Thus, the area of the shaded region will be equal to the area of rectangle ABDC minus the area of the two triangles on the same rectangle. The area of rectangle ABDC is equal to
A = l * w
= 4 * 3
A = 12
The area of each of the two triangles is equal to
A = 1/2bh
= 1/2 ( 7/8) ( 7/8 )
= 49/128
The area of the two triangles is equal to
A = 2 * 49/128
A = 49/64
Therefore, the area of the shaded region is equal to
12 - 49/64 = 719/64 unit²
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students want to verify that the centripetal acceleration of an object undergoing uniform circular motion with tangential speed vv and radius rr can be described by the equation ac
Yes, this is correct. The centripetal acceleration of an object undergoing uniform circular motion with tangential speed v and radius r can be described by the equation a_c = v^2/r.
The centripetal acceleration of an object undergoing uniform circular motion with tangential speed v and radius r can be calculated using the equation a_c = v^2/r.
The centripetal acceleration of an object undergoing uniform circular motion with tangential speed v and radius r can be described by the equation a_c = v^2/r. This equation shows that the acceleration of an object in uniform circular motion is proportional to the square of the velocity and inversely proportional to the radius of the circle. This equation is a result of Newton's second law, which states that the sum of the forces acting on an object is equal to the mass of the object multiplied by its acceleration. The centripetal acceleration is the acceleration of an object towards the center of the circle and is perpendicular to the direction of motion. In order to calculate the centripetal acceleration of an object, the velocity and radius of the circle must be known. The equation a_c = v^2/r can then be used to calculate the centripetal acceleration of the object.
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In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points is in the same quadrant as the fourth vertex of the square?A. (-5, -3)B. (-5, 3)C. (5, -3)D. (3, -5)E. (3, 5)
The point (-5,3) is in the same quadrant as the fourth vertex of the square.
The given points are representing the points in the quadrant of the cartesian coordinate system. According to this any location on a 2-D plane is represented by 2 numbers, x and y, where x represents the horizontal displacement from the origin of the plane and y represents the vertical displacement from the origin.
Since the given points are the vertices of a square they must be in the form (c, d), (c, -d), (-c, -d), and (-c,d). So, from the given points only the B (-5,3) satisfies the given condition and forms the square.
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HELP ASAP!!!! NO LINKS OR SPAM
Willa earns a bi-weekly gross income of $2,417.00 and has total monthly debt payments of $1,623.00. Determine Willa's current debt-to-income ratio. Round the final answer to the nearest whole percent. (2 points)
28%
31%
34%
35%
Willa's debt to income ratio is 34%.
What is Debt to Income Ratio?Debt to income ratio is usually calculated as a percentage of the gross monthly debt payments divided by the gross monthly income.
Given that,
Willa earns a bi-weekly gross income of $2,417.00
Monthly gross income = 2 × $2,417.00 = $4834
Monthly debt payments = $1,623.00
Debt to income ratio = $1,623.00 / $4834.00
= 0.3357
= 33.57%
= 34%
Hence the debt to income ratio of Willa is 34%.
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1.
If
z
y
=
x
, which of the following statements is true?
z - x = y
z - y = x
x · y = z
Answer:b
Step-by-step explanation:
1 point 8 divided by 0 point 6
Answer:
3 is the answer
Step-by-step explanation:
1.8/0.6
example: see the image and follow how to do it
perpendicular to line y=1/2x-8 passes through (7,-6) point slope form
The equation of line is y = -2x + 8 and the slope is m = -2
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
The equation of line perpendicular to the line is y = ( 1/2 )x - 8
Now , the slope of the line m₁ = 1/2
For perpendicular lines , the product of the slopes is -1
So , m₁ x m₂ = -1
So , the value of Slope m₂ = -2
And , the line passes through the point P ( 7 , -6 )
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - ( -6 ) = ( -2 ) ( x - 7 )
On simplifying the equation , we get
y + 6 = -2x + 14
Subtracting 6 on both sides of the equation , we get
y = -2x + 8
Hence , the equation of line is y = -2x + 8
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Find the volume of a cone that has a radius of 8 inches and a slant height of 10 inches. Round your answer to the nearest tenth of a cubic inch.
Answer:
401.9 in³------------------------------------
Volume of the cone:
V = πr²h/3We have a slant height and radius. They represent a hypotenuse and one of the legs of the right triangle.
Use Pythagorean to find the other leg, the height h of the cone:
[tex]h = \sqrt{10^2-8^2}=\sqrt{100-64} =\sqrt{36}=6\ in[/tex]Find the volume:
V = 3.14*8²*6/3 = 401.92 ≈ 401.9 in³The volume of the cone is calculated as: 671.0 cubic inches.
How to Find the Volume of a Cone?The volume of a cone can be found using the formula:
V = (1/3) * pi * r^2 * h
Where V is the volume, pi is approximately 3.14, r is the radius of the base, and h is the height (or slant height) of the cone.
In this case, the radius of the base is 8 inches and the slant height is 10 inches. So, the volume of the cone can be found by:
V = (1/3) * pi * 8^2 * 10
V = (1/3) * 3.14 * 64 * 10
V = (1/3) * 201.12 * 10
V = 671.04 cubic inches
Rounding the answer to the nearest tenth of a cubic inch, the volume of the cone is approximately 671.0 cubic inches.
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What is 2015 in Roman numeral
Answer:
MMXV
Step-by-step explanation:
(◕ᴗ◕✿)(◕ᴗ◕✿)(◕ᴗ◕✿)
Kazuko says the expressions 5x and 6 - x are equivalent expressions, because you
can substitute 1 for x in both expressions and get the same result. Is Kazuko's
reasoning correct? Explain.
Yes Kazuko's reasoning is correct the expressions 5x and 6 - x are equivalent expressions
How do you determine whether two phrases are equal?When two expressions can be reduced to a single third expression or when one of the expressions can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.
X-terms and constants should be combined with any other like terms on either side of the equation. Put the terms in the same sequence, with the x-term generally coming before the constants. The two phrases are equal if and only if each of their terms is the same.
5x and 6 - x
5x + 6 - x
2 (2 x + 3)
4 x + 6
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which point represents the center of the circle shown below?
O A Point M
• B. Point K
• C. Point R
• D. Point T
Point K is the point that marks the centre of the circle depicted below. This is due to the fact that the centre of a circle is the place from which all of its points are equally far. As a result, Point K is the circle's midpoint and consequently its centre.
What is a Circle?To put it simply, a circle is a spherical shape without any edges or line segments. In geometry, it has the shape of a closed curve. The circle's points are set apart from the center by a specified amount.
A circle is a closed, two-dimensional object in which all points in the plane are equally spaced apart from the center. The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric about the center for all angles.
A circle is a figure with a round shape, all of its points lying on the same plane and all of its points being equally spaced from the circle's center.
The center of the circle can be found by finding the midpoint of the diameter, which passes through points K and T.
The midpoint of the diameter can be found by taking the average of the x and y coordinates of points K and T.
Midpoint of AB = (x1+x2/2 , y1+y2/2)
Midpoint of K and T = ((-2 + 4)/2 , (1 + 7)/2)
Midpoint of K and T = (1 , 4)
Therefore, the center of the circle is point K.
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The radioactive substance cesium-137 has a half-life of 30 years. The amount A(t) (in grams) of a sample of cesium-137 remaining after t years is given by the following exponential function.
A(t)=458(1/2 (is written as a fraction) t/3) also written as a fraction
Find the initial amount in the sample and the amount remaining after 50 years.
Round your answers to the nearest gram as necessary.
Answer:
1818886278282871728282882
The average temperature during the winter in three states is given.
• Maine: 8.4°C below zero
• Minnesota: 10.9°C below zero •Georgia: 8.8°C
Part A Order these temperatures from least to greatest. Select your answers from the drop-down lists. Least to Greatest:
Part B Explain how you determined the order of the temperatures.
Answer:
10.9 8.4 8.8
Step-by-step explanation:
Both 10.9C and 8.4C are below zero. We can identify both are in negative temperatures. 8.8C was not labeled as below zero, which indicates a positive unit.
Find the correct representation for the slope of the tangent line to the curve cosxy + 3sin2x + 2y.
a. sin xy (dx/dy +y) + 6 cos x+2
b. -sin xy (dx/dy +y) + 6 sin x cos x+ (2dy/dx)
c. -sin (xy) (x dy/dx) + 6 sin x + 2
d. sin (xy dy/dx +y) + 6cos x+ 2 dy/dx
The slope of the tangent line to the curve cos(xy) + 3sin^2(x) + 2y at a point (x,y) is -sin(xy) ( x * dy/dx + y) + 6*sin(x)*cos(x) + 2dy/dx.
So the option b is the correct representation for the slope of the tangent line to the curve.
The correct representation for the slope of the tangent line to the curve cos(xy) + 3sin^2(x) + 2y is c. -sin (xy) (x dy/dx) + 6 sin x + 2.
The slope of a tangent line to a curve at a point (x,y) is given by the derivative of the function with respect to x, evaluated at that point.
So to find the slope of the tangent line to the curve cos(xy) + 3sin^2(x) + 2y, we need to find the derivative of the function with respect to x.
The derivative of cos(xy) with respect to x is
-sin(xy) ( x * dy/dx + y)
The derivative of sin^2(x) with respect to x is
2*sin(x)*cos(x)
The derivative of y with respect to x is
dy/dx
So the derivative of the function with respect to x is:
-sin(xy) ( x * dy/dx + y) + 6*sin(x)*cos(x) + 2dy/dx
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Which of these classes do the matrices A and B belong to (more than one answer is possible for each matrix: invertible; orthogonal; projection; permutation; diagonalizable; Markov.A = [0 0 1]0 1 01 0 0B = 1/3[1 1 1]1 1 11 1 1
Matrix A belongs to the permutation and Markov classes. A permutation matrix is a square matrix with exactly one 1 in each row and each column, and 0s everywhere else.
This is the case for matrix A, as it has one 1 in each row and column and 0s everywhere else. Matrix A is also a Markov matrix, which means that all the entries are non-negative and the sum of each row is equal to 1. This can be seen by summing each row, which yields 1+0+0 = 1, 0+1+0 = 1, and 1+0+0 = 1.
Matrix B belongs to the orthogonal, projection, and diagonalizable classes. Matrix B is orthogonal, which means that it is a square matrix whose columns and rows are orthonormal unit vectors (i.e. the dot product of any two columns or rows is 0). This is the case for matrix B, as the dot product of any two columns or rows yields 0. Matrix B is also a projection matrix, which means that it is a square matrix whose columns are all of unit length (i.e. the dot product of any two columns or rows is 1). This can be seen by taking the dot product of any two columns or rows, which yields 1. Finally, matrix B is diagonalizable, which means that it can be transformed into a diagonal matrix using a similarity transformation. This can be seen by calculating the eigenvalues and eigenvectors of matrix B, which yields the same diagonal matrix.
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Find the number of ways 66 identical coins can be separated into three nonempty piles so that there are fewer coins in the first pile than in the second pile and fewer coins in the second pile than in the third pile.
There are 331 ways when 66 identical coins can be separated into three nonempty piles
Let the piles have a, b and c coins, with 0<a <b <c. Then, let b=a+k₁, and
c=b+k₂, such that each ki≥1.
The sum is then a+a+k₁+a+k₁+k₂= 66 ⇒ 3a+2k₁+k₂ = 66.
This is simply the number of positive solutions to the equation
3x+2y+z = 66.
If a = 1, then 2k₁ + k₂ = 63⇒ 1≤k₁ ≤31. Each value of k₁ corresponds to a unique value of k₂, so there are 31 solutions in this case.
Similarly, if a = 2, then 2k₁+k₂= 60⇒ 1≤k₁ ≤29, for a total of 29 solutions in this case.
If a = 3, then 2k₁+ k₁= 57 ⇒ 1 ≤ k₁ ≤28, for a total of 28 solutions.
In general, the number of solutions is just all the numbers that aren't a multiple of 3, that are less than or equal to 31.
We then add our cases to get
=1+2+4+....31=1+2+3+...31-3(1+2+3+...10)
=31*(32)/2-3(55)
=31*16-165
=496-165
=331
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using the definitions and diagram, determine which sets each number belongs to. circle the symbol if the number belongs to that set. the first one has been done for you as an example. g
The number 9 does not belong to the set g, so it does not get circled. The number 9 belongs to the set A, so it should be circled.
The number 9 does not belong to the set g, so it does not get circled. The number 9 belongs to the set A, so it should be circled.
g = {2, 4, 6, 8}
9
A: A
The number 9 does not belong to the set g, so it does not get circled. The number 9 belongs to the set A, so it should be circled.
The number 9 does not belong to the set g, which consists of the numbers 2, 4, 6, and 8. Instead, the number 9 belongs to the set A, so the symbol should be circled to indicate this. The set A includes all the numbers from 1 to 10, so the number 9 is included. This means that the circle should be placed around the symbol for set A to indicate that 9 belongs to this set.
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8. ABC has vertices A(0, 0), B(0, -2), and C(-3, 0). What are the coordinates
of the orthocenter of ABC?
Answer:
(-1,-1)
Step-by-step explanation:
join the mid points of AB, BC & AC ...
you got the orthocenter point, then we can read the coordinates from X-axis and Y-axis.
Assignment Scoring
Your best submission for each question part is used for your score.
4.
DETAILS AUFEXC4 10.4.025. 28/100 Submissions Used
Find the minimum or maximum value of the quadratic function.
f(x) = x² - 6x + 9
(-2,11)
x Your answer cannot be understood or graded. More Information
State whether the value is a minimum or a maximum.
minimum
O maximum
Submit Answer
The quadratic function f(x) = x² - 6x + 9 has a minimum at point (3,0).
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The given quadratic function is - f(x) = x² - 6x + 9.
Find the differentiation of f(x) -
dy/dx = d/dx (x² - 6x + 9)
d/dx (x²) - d/dx (6x) + d/dx (9)
2x - 6 + 0
2x - 6 = 0
For stationary values, dy/dx = 0
2x - 6 = 0
2x = 6
x = 6/2
x = 3
At x = 3 we get stationary values.
Now, d²y/dx² = 2x - 6
d/dx (2x - 6)
d/dx (2x) - d/dx (6)
2 - 0 = 0
2 = 0
(d²y/dx²) x=3 = 2 (positive)
Therefore, at x = 3 the function is minimum.
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Repeated addition:
1 3 + 1 3 + 1 3= a b
a =
b =
Answer:
[tex]\frac{1}{3} + \frac{1}{3} + \frac{1}{3} = \frac{3}{3} = 1[/tex]
a=3
b=3
Third part
Commutative property
Fourth part
Inverse property
Fifth part
Identity property
Step-by-step explanation:
Answer:
1st part is a= 3
b= 9
Second part
x=16
y= -24
Third part
Commutative property
Fourth part
Inverse property
Fifth part
Identity property
Step-by-step explanation:
Determine whether the following system of linear equations have no solution, infinitely many solution or unique solutions.x+2y=3,2x+4y=15A.No solutionB.Infinitely many solutionC.Unique solutionD.Cannot be determined
C. Unique solution. The system of linear equations have a unique solution because the equations are consistent and have the same number of variables and equations.
The given system of linear equations is x+2y=3 and 2x+4y=15. To determine whether the system of linear equations have no solution, infinitely many solution or unique solutions, we need to solve the system of equations. Firstly, we expand and simplify both equations to get x+2y=3 and 2x+4y=15. Then, we compare the coefficients of the equations to determine if the system of equations is consistent, inconsistent or dependent. Since the equations are consistent and have the same number of variables and equations, we can solve the system of equations. By isolating the variables and using the substitution method, we can solve the system of equations to get x=3 and y=3. This means that the system of linear equations have a unique solution.
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1.in a multivariate regression, which of the following is a true statement concerning the f-statistic?
In multiple regression,
a. The F statistic is only appropriate if errors are homoskedastic.b. The F statistic can never be negative.d. The F statistic has approximately an X² distribution in large samplesThus, option (a), (b), and (d) is correct.
What is F-Test?The F-test is done to check for the equality of variances for the samples given whereas the F-distribution is a positively skewed distribution involving the numerator and the denominators degrees of freedom
a. The F statistic is only appropriate if errors are homoskedastic.
b. The F statistic can never be negative.
c. The F statistic has approximately a normal distribution in large samples.
d. The F statistic has approximately an X² distribution in large samples
In the given question, parts (a), (b), and (d) are true.
As the F-distribution is always positively skewed and is the ratio of the mean squares of between and within errors, it can never be negative and the assumptions of the samples having equal variances need to be fulfilled before proceeding with the test
Hence, in multiple regression,
a. The F statistic is only appropriate if errors are homoskedastic.
b. The F statistic can never be negative.
d. The F statistic has approximately an X² distribution in large samples
option (a), (b), and (d) is correct.
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Full question:
Which of the following is true about the F statistic in the multiple regression model? (Select all that apply.)
a. The F statistic is only appropriate if errors are homoskedastic.
b. The F statistic can never be negative.
c. The F statistic has approximately a normal distribution in large samples.
d. The F statistic has approximately a χ² distribution in large samples.
find the distance between dallas, texas, whose latitude is n, and omaha, nebraska, whose latitude is n. assume that earth is a sphere of radius 4000 miles and that the cities are on the same longitude (omaha is due north of dallas). City Latitude
Dallas, Texas 32° 47' 39'' N.
Omaha, Nebraska 41° 15' 50'' N.
The distance between Dallas, Texas and Omaha, Nebraska is 631.4 miles.
The distance between Dallas, Texas and Omaha, Nebraska can be calculated using the Haversine Formula. This formula calculates the great circle distance between two points on a sphere, taking into account the curvature of the Earth. The formula is as follows:
d = 2r arcsin( sqrt[ sin^2((lat2 - lat1)/2) + cos(lat1)cos(lat2)sin^2((lon2 - lon1)/2)] )
In this case, the latitude of Dallas, Texas is 32° 47' 39'' N and the latitude of Omaha, Nebraska is 41° 15' 50'' N. Since the two cities are on the same longitude, we can assume that the longitude for both cities is 0°.
Plugging these values into the formula, we get:
d = 2(4000 miles) arcsin[ sqrt[ sin^2((41° 15' 50'' N - 32° 47' 39'' N)/2) + cos(32° 47' 39'' N)cos(41° 15' 50'' N)sin^2((0° - 0°)/2)] ]
d = 631.4 miles
Therefore, the distance between Dallas, Texas and Omaha, Nebraska is 631.4 miles.
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Square ABCD has a diagonal AC with the given vertices. Find the coordinates of the remaining vertices.
A(2, 2) and C(6, - 2)
The coordinates are (_,_) and (_,_)
Square ABCD has a diagonal AC with the given vertices. Find the coordinates of the remaining vertices. A(2, 2) and C(6, - 2)
The coordinates are B(4,-2,) and (4,0)
What do you mean by coordinates?Coordinates are two numbers (Cartesian coordinates), or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane. A coordinate plane has four quadrants and two axes: the x axis (horizontal) and y axis (vertical). (One way of helping children to remember which of these is which is to tell them that the x axis goes across because ‘x’ is a cross.)
The Cartesian Coordinate System is the name of the two-dimensional plane that is used in math to calculate points using a set of perpendicular lines and basing the points on the place where the line meet. The plane is called a Cartesian plane and Perpendicular lines are lines that intersect at exactly 90 degrees, which makes a right angle.
If A(2,2) and C(6,-2) are the coordinates of two opposite vertices of the square, then the square is a rectangle with a diagonal AC. The remaining vertices of the square can be determined by using the fact that opposite sides of a square are parallel and congruent.
If A(2,2) is one vertex of the square, then the vertex opposite it is C(6,-2)
If C(6,-2) is one vertex of the square, then the vertex opposite it is A(2,2)
The vertex B(x,y) can be found by moving 2 units left from C(6,-2)
x = 6 - 2 = 4
y = -2
so B(4,-2)
The vertex D(x,y) can be found by moving 2 units up from B(4,-2)
x = 4
y = -2+ 2 = 0
so D(4,0)
Therefore, the coordinates of the remaining vertices of the square are B(4,-2) and D(4,0)
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Pls help please pls please
Answer:
x=5/3 0r 1 2/3
4. Alfonso surveyed several students in his school. He asked them to give the grade that they are in and the number of pets they have at home. The results are shown in the table below.
Survey Results
Grade
5
6
2
1
4
2
4
1
4
3
5
Number of
Pets
0
4
2
3
5
1
2
2
0
5
2
Find the correlation coefficient for the data. Round to the nearest hundredth
EDIT: IT ISNT 0.35 , 0.36 nor 0.37 SOOO PLEASE REFRAIN FROM GIVING ME THISE ANSWERS!!!
Answer: sorry would help ya but i can't because i have no clue what the question is asking me to round...
There are three boxes one of them contains gold. In each box, there is amessage
Answer:
Gold is in Box 1
Step-by-step explanation:
There are 3 boxes. One of them contains gold
In each box, there is a message, and one of them is true.
Box 1: "The gold is not in Box 2".
Box 2: "The gold is in this box"
Box 3: "The gold is not in this box".
Which box has the gold?
Answer:
O Box 1
O Box 3
O Box 2
There's not enough info
Assume each statement to be true at a time, and check for contradictions.
Box 1: "The gold is not in Box 2".
Assume True. Gold in 1 or 2.
Box 2: "The gold is in this box"
False. Gold not in 2.
Box 3: "The gold is not in this box".
False. Gold in 3
Contradiction between box1 and box 3 message.
Box 2: "The gold is in this box"
Assume true. Gold in 2.
Box 1: "The gold is not in Box 2".
False. Gold in 2.
Box 3: "The gold is not in this box".
False. Gold in 3.
Contradiction between boxes 2 and 3. Box 2 message cannot be true.
Box 3: "The gold is not in this box".
Assume true. Gold in 1 or 2.
Box 1: "The gold is not in Box 2".
False. Gold in 2.
Box 2: "The gold is in this box"
False. Gold not in 2.
No contradictions.
Gold must be in 1.
Answer: Gold is in Box 1
Differentiation stationary points please help
A stationary point can be found by solving d y d x = 0 , i.e. finding the x coordinate where the gradient is 0.
How do you find the coordinates of a stationary point of a curve?When the derivative of a function, f(x), equals 0, it is said to be stationary. Because the function is neither increasing nor decreasing at these locations, they are referred to be "stationary" points.
This graphically correlates to locations on the graph of f(x) where the horizontal line that forms the tangent to the curve is present.When the derivative of a function, f(x), equals 0, it is said to be stationary. Because the function is neither increasing nor decreasing at these locations, they are referred to be "stationary" points.
Stationary Points Defined. Remember that a stationary point is a value of x0 for x at which f′(x0)=0 f ′ (x 0) = 0 for a univariate function y=f(x) y = f (x).
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2x+y=30
x+3y=36
by elmination methods
The solution to the system of equations 2x + y = 30 and 2x + 6y = 72 is (10.8, 8.4)
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Given the equations:
2x + y = 30 (1)
x + 3y = 36; multiplying by 2 gives:
2x + 6y = 72 (2)
To solve by elimination method, subtract equation 2 from 1, hence:
-5y = -42
Dividing by -5:
y = 8.4
Put y = 8.4 in equation 2:
2x + 6(8.4) = 72
2x = 21.6
x = 10.8
The solution is (10.8, 8.4)
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Suppose that f(x) and g(x) are polynomials of degree 4 and 5 respectively. What is the degree of f(x^3) g(X^2)?
The degree of a polynomial is the highest exponent of its terms. Since f(x) and g(x) are both polynomials of degree 4 and 5 respectively, the degrees of f(x) and g(x) are 4 and 5 respectively.
The degree of f(x^3) g(X^2) is 14.
The degree of a polynomial is the highest exponent of its terms. Since f(x) and g(x) are both polynomials of degree 4 and 5 respectively, the degrees of f(x) and g(x) are 4 and 5 respectively. When we substitute x^3 for x in f(x) and x^2 for x in g(x), the highest exponent of the terms of f(x^3)g(x^2) is 3*4 + 2*5 = 14. Therefore, the degree of f(x^3) g(x^2) is 14.
The degree of f(x^3) g(x^2) is 14, which is calculated by multiplying the degree of f(x) and g(x) with the exponent of their respective terms. The degree of a polynomial is the highest exponent of its terms. Since f(x) and g(x) are both polynomials of degree 4 and 5 respectively, the degrees of f(x) and g(x) are 4 and 5 respectively.
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