The coefficient of determination, denoted as R², is a statistic that measures the proportion of the variance in the dependent variable that is explained by the independent variables in a regression model.
The coefficient of determination, R², measures the goodness of fit of a regression model. It ranges from 0 to 1, with a higher value indicating a better fit. The calculation of R² involves comparing the variation in the dependent variable (represented by the total sum of squares, TSS) to the variation explained by the regression model (represented by the regression sum of squares, SSR). The formula for R² is SSR/TSS.
R² can be interpreted as the proportion of the total variation in the dependent variable that is accounted for by the independent variables included in the model. In other words, it tells us the percentage of the response variable's variability that can be explained by the regression model.
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What is the 3 4 5 Triangle rule in construction?
I've discovered that using the 3:4:5 triangle is the simplest way to determine for sure if an angle is 90 degrees. According to this rule, a triangle is a right triangle if the diagonal between its two points measures 5, even though one of its sides measures 3 and the other measures 4.
Aim for a measuring ratio of 3:4:5, to create an absolutely square corner. To put it another way, you need a length of three feet on the straight line, four feet on the perpendicular line, and five feet crosswise. You will get a corner that is exactly square if all three measurements are accurate.
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Will E. Wait works at Willy Wonka's Chocolate Factory. His annual salary is $58,500.
He is paid biweekly. What is Will's biweekly gross salary?
Your answer
Answer: 562.50
Step-by-step explanation:
- Hair grows at a rate of 1/64 inch per day. Write this number using negative exponents.
Answer:
[tex]4^{-3}[/tex]
Step-by-step explanation:
[tex]4^{3}[/tex] = 64
Take the reciprocal of both sides.
1/64 = [tex]4^{-3[/tex]
Please help!! i included a picture as well not sure if it would help !Write the equation of a quadratic function given the transformations given below:
• Opens upwards
●
A = ½
● Horizontal shift right 5
• Vertical shift down 2
The parent function of the quadratic family is f(x) = x2. A transformation of the graph of the parent function is represented by the function g(x) = a(x − h)2 + k, where a ≠ 0.
What is quadratic function?A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.
A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form. The three graphs in the image below are all parabolas.
Regarding a line known as the axis of symmetry, all parabolas are symmetric. The vertex of a parabola is the location where the axis of symmetry of the curve crosses.You are aware that a line is defined by two points. This implies that there is only one line that contains both points if you are given any two points in the plane. Points and quadratic functions both fit this description.There is only one quadratic function f whose graph contains all three points when there are three points in the plane with distinct first coordinates and that are not on a line. This fact is demonstrated by the applet below. Three spots are shown on the graph, and a parabola passes through them all.The text box behind the graph displays the associated function. The function and parabola are updated if any of the points are moved.Using the methods of stretching/shrinking and moving (translation) the parabola y = x2 several quadratic functions can be graphed easily by hand.How do you determine if quadratic equation opens up or down?A quadratic function's graph takes the form of a parabola. The parabola will open upward if the value of the "a" term is positive, and downward if the value is negative
How to shift a function upwards?.A function can be raised by adding outside of it: f (x) + b raises f (x) by b units. The same principles apply for moving a function down, except instead of subtracting a positive integer, f (x) b represents f (x) moved down b units.
Shift Up and Down by Changing the Value of kYou can represent a vertical (up, down) shift of the graph of f(x)=x2 by adding or subtracting a constant, k.
f(x)=x2+k
Right- and down-shift of a functionBy increasing or decreasing the output or the input, you can change the direction of the function's graph to the right, left, up, or down. A function's output can be increased to move the graph up. The graph is shifted downward when a function's output is subtracted from.
Horizontal and vertical shift of a functionThe output has a constant added to it, which causes the vertical shift. For a positive constant, move the graph upward; for a negative constant, move it below. A constant supplied to the input causes a horizontal shift. For a positive constant, move the graph to the left; for a negative one, move it to the right.
Shift left and right by changing the value of hYou can represent a horizontal (left, right) shift of the graph of f(x)=x2 by adding or subtracting a constant, h, to the variable x, before squaring.
f(x)=(x−h)2
If h>0, the graph shifts toward the right and if h<0 , the graph shifts to the left.
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56 unit needed, 6 unit per cae what i the number of cae and the number of additional unit?
As per the unitary method, the number of care is 9 and the number of additional method is 2.
The term unitary in set theory is defined as the way to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.
Here we have given that the total number of units is 56.
And here we also know that the number of units in each care is 6.
Now, we have to find the total number of care, that can be obtained by dividing the total care by the units in each care,
then it can be written as,
=> 56/6
When we divide the term then we get the quotient as 9 and the remainder as 2.
Therefore, while looking into these we have identified that there are 9 cares and 2 additional units are in the group.
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9+ a/6=8
show work
solve a
Answer:
a = -6
Step-by-step explanation:
9+a/6=8 1. -9 both sides
(6)a/6= -1(6) 2. multiply 6 on both sides
a = -6
How many children can you predict a family has if the amount spent on groceries per week is $169.47?
Answer: Well for a family of 6 we spend around 200-300$, so a family of 4-5 if older like teens, or 6-7 for young toddlers.
Which of the following is a factor of p x x 2 − 4x − 5?(x+5)(x - 1)(x+5)(x + 1)(x + 1)(x - 5)(x - 1)(x - 5)
(x+5)(x - 1) is a factor of p(x) = x² - 4x - 5
We can see that by applying polynomial long division or by applying synthetic division, both of these methods will give the same result.
x² - 4x - 5 = (x + 5)(x - 1)q(x) + r(x)
where q(x) and r(x) are the quotient and remainder of the polynomial division respectively. Since r(x) = 0, it means (x + 5)(x - 1) is a factor of p(x) = x² - 4x - 5.
I really need help with this worksheettt please
Answer:
2x² + x + 3
Step-by-step explanation:
2x² + x + 3
2x² + (5/2)x + 3
Is 3 2 an ordered pair?
Yes, (3, 2) is an ordered pair.
The combination of the x coordinate (abscissa) and the y coordinate (ordinate) is called an ordered pair, which has two values written in a fixed order within parentheses.
It can help us to locate a point on the cartesian plane for better visual understanding. The numerical values in an ordered pair can be both integers or fractions.
In the Cartesian plane, we can define a two-dimensional space with two perpendicular reference lines, the x-axis and the y-axis. The point where the two lines meet is the origin (O).
For example plot the point Q with the coordinates (3, 2)
According to the definition of ordered pair, the point Q will be written as:
Q = (3, 2)
The left number in the ordered pair shows the distance from the “x” axis which is 3
The right number shows the distance from the “y” axis which is 2.
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When graphing polynomials we can determine the end behavior by the?
When graphing polynomials, we can determine the end behavior by the degree of the polynomial and the coefficient of the leading term.
The degree of a polynomial is the highest exponent of the variable found in the equation. The coefficient of the leading term is the number that is multiplied by the variable in the leading term. The end behavior of a polynomial can be determined by examining the sign of the coefficient and the degree of the polynomial.
For example, let's consider the polynomial equation y = x^3 - 2x^2 + 5x + 7. The degree of this polynomial is 3, and the coefficient of the leading term is 1. This means that the end behavior of this polynomial equation will be increasing, since the coefficient and degree are both positive. To confirm this, we can calculate the limit of the polynomial as x approaches positive and negative infinity. As x approaches positive infinity, the limit of y is positive infinity (∞), and as x approaches negative infinity, the limit of y is also positive infinity (∞). This confirms that the end behavior of this polynomial equation is increasing.
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help pleaseee i can’t get it right
The compositions between functions f(x) = 3 · x - 2 and g(x) = x + 1 are f[g(x)] = 3 · x + 1 and g[f(x)] = 3 · x - 1, respectively.
How to use composition between two functions
Let be f(x) and g(x) functions, there is a composition of the form f[g(x)], when the independent variable of function f is substituted by function g. That is to say:
f ° g(x) = f [g(x)]
First, define functions f(x) and g(x):
f(x) = 3 · x - 2
g(x) = x + 1
Second, perform the required compositions and simplify the expressions:
f[g(x)] = 3 · (x + 1) - 2
f[g(x)] = 3 · x + 1
g[f(x)] = (3 · x - 2) + 1
g[f(x)] = 3 · x - 1
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The price of strawberries at Fine Foods is shown in the graph. At best Market, the price y for x pounds of strawberries is given by y=2.90x. Which store sells strawberries at a cheaper unit price?
The store that sells strawberries at a cheaper unit price is Fine Foods.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x represents the number of pounds of strawberries.y represents the price in dollars.k represents the constant of proportionality.In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.
Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 2/1 = 6/3 = 10/5 = 14/7
Constant of proportionality (k) = 2.
Therefore, an equation for the price of strawberries at Fine Foods is y = 2x and as such, it sells strawberries at a cheaper unit price.
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Which trigonometric ratio is used to find the cosine of a right triangle?
Answer: Cosine ratios are exactly the same idea of sine ratios or tangent ratios. The only difference between it and the other two trigonometric ratios is that it is the ratio of the adjacent side to the hypotenuse of a right triangle.
Why do we use the midpoint method?
The midpoint method is a numerical integration technique used to approximate the definite integral of a function over a given interval. It is a Riemann sum method.
What does the midway in math mean?The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places. When we know the coordinates of two points, we can apply the midpoint formula to get the midpoint between them.
Here,
The midpoint method is used for a few reasons:
Simplicity: The midpoint method is relatively easy to understand and implement, compared to other numerical integration techniques.
Accuracy: The midpoint method is more accurate than some other Riemann sum methods like the left-hand rule or right-hand rule, which evaluate the function at the endpoints of each subinterval.
Efficiency: The midpoint method is more efficient than some other numerical integration techniques, especially for functions that are not smooth or have sharp changes.
Flexibility: The midpoint method can be used for both definite and indefinite integrals, and for functions that are not well-behaved.
Overall, the midpoint method is a simple, accurate, efficient and flexible numerical integration method that can be used to approximate the definite integral of a function over a given interval.
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evaluate the expression
If the length of a rectangle increases 2 times and the width decreses 3 times, then its area decreased by :
a) 66.6%
b) 66.(6)%
c) 33.(3)%
d) 33.3%
e) 30%
The statement which is correct about the Area of the rectangle in discuss as required is that the area decreased by; Choice C; 33.(3)%.
By what percent does the area of the rectangle decrease?As evident in the task content; the length of a rectangle increases 2 times and the width decreses 3 times;
Since the initial length can be said to be; l and the initial width can be said to be; w and Area A = l × w.
However, when the length and width change as described; the area of the rectangle is;
Area = 2l × ( w / 3 )
Area = ( 2/3 ) × lw
On this note, the new Area of the rectangle is two-third the initial area.
On this note, the area of the rectangle has decreased by one-third which is equivalent to; Choice C; 33.(3)%.
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An object is dropped from 40 feet below the tip of the pinnacle atop a 716-ft tall building. The height h of the object after t seconds is given by the equation h=−16t2+676. Find how many seconds pass before the object reaches the ground.
Answer:
Below
Step-by-step explanation:
When it reaches the ground h = 0
h = 0 = -16t^2+676
16t^2 = 676
t^2 = 42.25 t = 6.5 s
The Leap of Faith water slide in Atlantis stands 60 feet high. If the base of the slide is 37 feet from the pool, then what is the length of the slide? Round your answer to the nearest tenth.
The Atlantis water slide measures 70.69 feet in length when the slide's base is 37 feet from the pool and it is 60 feet tall.
what is Pythagoras theorem ?The Pythagorean Theorem, often known as the Mathematicians, is the fundamental Euclidean geometry relation between the three sides of a right triangle. The area of a cube with the velocity vector side equals the sum of the areas of polygons with the other two sides, according to this rule. The Pythagorean Theorem says that the square that spans a right triangle's hypotenuse opposite the perfect distance equals a sum of the squares that span its sides. It is sometimes written as the basic algebra notation a2 + b2 = c2.
given
According to Pythagoras's Theorem, which states that
c2 = a2 + b2
c2 = 3600 + 1369
c2 = 4969
c = 70.49, the water slide in Atlantis is 60 feet high and has a base that is 37 feet from the pool.
The Atlantis water slide measures 70.69 feet in length when the slide's base is 37 feet from the pool and it is 60 feet tall.
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How do you solve y =- 3x?
the solution of equation y=x+2 and y=3x-2 are x= 2 and y=4
y = x+2 ------------ equation 1
y = 3x -2 ------------ equation 2
in the first equation y = x +2
in the second equation y = 3x -2
this mean equation 1 = equation 2
then we can equate the two together to get one of the variable
remember, we have to unknown variables which are x and y, so we need to isolate y to get x
x + 2 = 3x -2
let collect the like terms
x - 3x = -2 -2
let us factorize out x on the right hand side of the equation
x(1 - 3) = -4
x(-2) = -4
-2x = -4
divide both sides by -2
-2x/-2 = -4/-2
x = 2
to find y put x in any of the above equations
let us use equation one
y = 2 + 2
y = 4
complete question
How do you solve, y=x+2 y=3x-2
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For a part-time job, Jeannie conducted a survey with two questionnaires, Type A
and Type B. She chose 500 homes and mailed questionnaires at a cost of $.19 for
Type A and $.23 for Type B. If the total cost of the mailing was $106.20, how
many of each type did she mail?
Out of the 500 homes, 226 Type A forms were sent while 274 Type B forms were sent.
How many of the forms were sent?To determine the number of forms sent, we can begin by identifying how much Jeannie spent on mailing each of the questionnaires. The sum of $0.19 and $0.23 is $0.42. Now, we will find out how much of these were the total cost as follows:
Type A:
$0.19 / $0.42 × $106.20
= $48.
Type B:
$0.23 / $0.42 × $106.20
= $58.2
Next, we will determine how much of these went into the 500 homes as follows:
Type A:
$48 / 106.2 × 500
= 225. 9 ≈ 226 homes
Type B:
$58.2 / $106.2 × 500
= 274 homes
So, while Type A was sent to 226 homes, Type B was sent to 274 homes.
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Where do we find value table?
The proper method of finding a value table has been mentioned and explained below.
Value tables are a part of domain definition. The value table is maintained at the domain level and thus, is also called domain-level validation. Whenever you create a domain, you can enter the required values. Whenever you use this Domain, the system will make it so that you are forced to enter only these values. This is a sort of master check.
This means that if you want to enter values into this table you have to create a development request & transport the same. The system, then, proposes the value table as a check table. The check against the value table only takes place when a foreign key is defined
.
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Do you multiply in dilation?
Yes, dilation is a type of transformation that involves multiplying the coordinates of a figure by a scale factor.
This scale factor can be greater than 1, which is an enlargement, or less than 1, which is a reduction. To calculate the coordinates of a dilation, the following formula is used: (x, y) → (kx, ky), where (x, y) are the coordinates of the original point and (kx, ky) are the coordinates of the transformed point. The scale factor, k, is the same for both the x and y coordinates. For example, if the scale factor is 2 and the original coordinates are (2, 4), the new coordinates would be (4, 8). This means that the point (2, 4) has been enlarged to (4, 8).
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A florit hop keep a contant ratio of roe to tulip at 5 : 3. If the hop ha 70 roe, how many tulip do they have?
As per the given ratio, the number of roses is 45 and the number of tulips is 27
The term ratio also known as proportion is defined as an ordered pair of numbers a and b, written a / b where b does not equal 0
Here we have given that the ratio of roses to tulips is 5: 3.
Here we also know that the shop has 72 tulips on Friday morning.
And then let us consider that if the florist uses up half of each type of flower to fill an order, then the ratio of roses to tulips in the shop change is calculated as,
=> 5x + 3x = 72
=> 8x = 72
Then the value of x is calculated as,
=> x = 9
Therefore, the number of roses is
=> 5(9) = 45
And the number of tulips is written as,
=> 3(9) = 27
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Just the photo, please help, the 9 weeks end today and I need these turned in soon as possible
Answer:
3/4 : 1 1/2 1 2/4 : 3. 5 : 10
Step-by-step explanation:
Here is a question on angle measures in real-life.
Angle FED is equal to what amount?
Answer:235
Step-by-step explanation: its because.......
Solve the equation -8x < 32
Answer: x < -4
Step-by-step explanation: This is a question of an inequality. Here, everything proceeds like a normal equation that we solve. To obtain the value of x, we will divide 32 by 8.
-8x<32
x<-32/8
x<-4 (On dividing -32 by 8)
This means x can take any value less than -4 i.e. -5,-6,-7,......
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which is an equation with a degree of 3, a zero located at x=4 and a y-intercept located at (0,60)
The degree 3 polynomial equation is 1/2(4 - x)(x - 1)(x - 2).
What is a polynomial equation?A polynomial equation is one in which a polynomial is set to zero. It is an equation composed of variables, non-negative integer exponents, and coefficients, as well as operations and an equal sign. It has various exponents. The highest one represents the equation's degree.A third-degree polynomial is defined as p(x) = ax³ + bx² + cx + d, where 'a' is not equal to zero. Because it has a degree of three, it is also known as a cubic polynomial.Here given,
With zeros and a coefficient, the function is:
f(x) = a(x - 4)(x - 1)(x - 2)
Regarding the y-intercept:
f(0) = a(0 - 4)(0 - 1)(0 - 2)
4 = a(-4)(-1)(-2)
4 = -8a
a = -1/2
As a result, the function is:
f(x) = -1/2(x - 4) (x - 1)(x - 2)
= 1/2(4 - x)(x - 1)(x - 2)
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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
Answer:
C) One solution-------------------------
Given system:
- x + 6y = 76x - 30y = - 34We can solve it by elimination.
Multiply the first equation by 6 and add up to get:
-6x + 36y + 6x - 30y = 42 - 346y = 8y = 8/6y = 4/3Without solving for x we can see there is one solution.
The last answer choice is the correct one.
Answer:
The given system of equations has exactly one solution (1, ⁴/₃).
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}-x+6y=7\\6x-30y=-34\end{cases}[/tex]
To solve the given system of equations, multiply all terms of the first equation by 5:
[tex]\implies -x \cdot 5+6y \cdot 5=7 \cdot 5[/tex]
[tex]\implies -5x+30y=35[/tex]
Add this to the second equation to eliminate the term in y:
[tex]\begin{array}{crcccl}&6x & - & 30y & = &-34\\\vphantom{\dfrac12}+ & (-5x & + & 30y & = & \;\;\:35)\\\cline{2-6}\vphantom{\dfrac12}&x&&&=&\;\;\;\;\:1\\\cline{2-6}\end{array}[/tex]
Therefore, x = 1.
Substitute the found value of x into the first equation and solve for y:
[tex]\implies -(1)+6y=7[/tex]
[tex]\implies 6y=8[/tex]
[tex]\implies y=\dfrac{8}{6}[/tex]
[tex]\implies y=\dfrac{4}{3}[/tex]
Therefore, the given system of equations has exactly one solution (1, ⁴/₃).
What is a infinitely many solution?
An infinite solution has both sides equal.
What number has an unlimited number of answers?
There are infinitely many possible solutions to some equations. In these equations, the equation is true regardless of the value given to the variable.
If you attempt to solve an equation and it yields a variable or value that is equal to itself, then the equation has an endless number of solutions. 2x and 2x should be combined.
Are all possible solutions parallel?
There are no answers when the lines are parallel, and occasionally the two equations will graph as the same line, in which case there are an endless number of solutions. These kinds of systems are occasionally described using specific words.
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