Use quadratic regression to find the equation of a quadratic function that fits the given points. x 0 1 2 3. Y. 49 50.4 39.5. 21
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The regression Quadratic equation y = 49 + 7.55x - 6.15x².
What is Regression Equation?The technique of finding the equation of a parabola that most closely matches a collection of data is known as quadratic regression. The graph points that make up the parabola-shaped shape of this set of data are given. The parabola's equation is written as y = ax² + bx + c, where a never equals zero.
For data presented as ordered pairs, you can calculate the model's degree by identifying differences between dependent values. The model will be linear if the initial difference has the same value. The model will be quadratic if the second difference has the same value as the first.
As, we know the Quadratic model
Quadratic model, y = a + bx + cx²
Now, value of
a = 49
b = 7.55
c = -6.15
Then, the Regression Quadratic model is
y = 49 + 7.55x - 6.15x²
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Related Questions
Use the drawing tools to the graph the solution to this system of inequalities on the coordinate plane.
y> 2x + 4
x+y≤6
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The solution to the system of inequalities y> 2x + 4 , x+y≤6 on the coordinate plane is shown below .
in the question ,
the system of inequality is given
y> 2x + 4
x+y≤6
to plot these inequalities on the coordinate plane ,we need to find the intercepts of both.
y>2x+4
put x = 0 we get y as 4 , (0,4)
put y = 0 we get x as -2 ,(-2,0)
x+y≤6
put x = 0 , we get y as 6 , (0,6)
put y = 0 , we get x as 6 , (6,0)
the solution of both the inequality is shown below .
Therefore , the solution to the system of inequalities y> 2x + 4 , x+y≤6 on the coordinate plane is shown below .
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Which expression simplifies to 5. A. 27/3 - 14. B. 27/3+4. C. -27/3-4. D. -27/3+14
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Find the volume of the solid. Round your answer to the nearest hundredth. I keep getting the wrong answer. Need help!
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Volume is area * height
area of pentagon is 1/4 * root(5(5 + 2root(5))) a^2
a being length of 1 side
if a =2, area is 6.88
6.88 * 4 = 27.52 yards^3
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(x+9)°
42°
104°
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Answer:
Step-by-step explanation:
first do 104 + 42 it should be 146
second since it is x+9 do 146 - 189, it should be 43.
third check your work by doing 43 + 146
if it equals 189 then do 43 - 9, you should get 34
so x = 34
the sum of the reciprocal of two consecutive positive integers is 17/72. Write an equation that can be used to find the two integers. What are the integers?
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Answer:
[tex]\frac{1}{x}+\frac{1}{x+1}=\frac{17}{72}[/tex]The two consecutive positive integers are 8 and 9.
Explanation:
Let the 1st positive integer be x and the 2nd be x + 1, so their reciprocal will be 1/x and 1/x+1.
The equation can then be written as;
[tex]\frac{1}{x}+\frac{1}{x+1}=\frac{17}{72}[/tex]To solve for x, the 1st step is to find the LCM of the left-hand side of the equation;
[tex]\begin{gathered} \frac{(x+1)+x}{x(x+1)}=\frac{17}{72} \\ \frac{2x+1}{x(x+1)}=\frac{17}{72} \end{gathered}[/tex]We can equate the numerators and solve for x as shown below;
[tex]\begin{gathered} 2x+1=17 \\ 2x=17-1 \\ x=\frac{16}{2} \\ x=8 \end{gathered}[/tex]If the 1st positive integer, x, is 8, therefore the 2nd integer, x + 1, will be;
[tex]x+1=8+1=9[/tex]ur answer as a polynomial in standard form.=f(x) = 5x + 1g(x) = x2 – 3x + 12=Find: (fog)(x)
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(fog)(x) = 5x² - 15x + 61
Explanation:The given functions are:
f(x) = 5x + 1
g(x) = x² - 3x + 12
(fog)(x) = f(g(x))
This means that we are substituting g(x) into f(x)
(fog)(x) = 5(x² - 3x + 12) + 1
(fog)(x) = 5x² - 15x + 60 + 1
This can be further simplified as:
(fog)(x) = 5x² - 15x + 61
Translate the sentence into an equation.Eight more than the quotient of a number and 3 is equal to 4.Use the variable w for the unknown number.
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We are to translate into an equation
Eight more than the quotient of a number and 3 is equal to 4.
Let the number be w
Hence, quotient of w and 3 is
[tex]\frac{w}{3}[/tex]Therefore, eight more than the quotient of a number and 3 is equal to 4
Is given as
[tex]\frac{w}{3}+8=4[/tex]Solving for w
we have
[tex]\begin{gathered} \frac{w}{3}=4-8 \\ \frac{w}{3}=-4 \\ w=-12 \end{gathered}[/tex]Therefpore, the equation is
[tex]\frac{w}{3}+8=4[/tex]triangle QRS is shown below using the information given determine the measure of r
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What is the value of the expression below when z6?9z + 8
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Hello!
Let's solve your expression:
[tex]9z+8[/tex]Let's replace where's z by 6, look:
[tex]\begin{gathered} (9\cdot z)+18 \\ (9\cdot6)+18 \\ 54+18 \\ =72 \end{gathered}[/tex]So the value of this expression when z=6 is 72.
Sarah needs to lease out a music studio to record her new album. The studio chargesan initial studio-use fee plus an hourly fee for each hour in the studio. The fixed fee touse the studio is $150 and the total cost charged for 2 hours is $300. Write anequation for P, in terms of t, representing the amount of money Sarah would have topay to use the studio for t hours.
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Fixed fee is 150
Total cost for 2 hours is 300
If the fixed fee is 150, and Sarah paid 300, then she paid 150 for the fixed fee and anohter 150 for the two hours, that means that each hour is 75
Then we can write the equation:
P = 75t + 150
Answer:
P = 75t + 150
If an investment grew to $13,500 in 2 years and the interest amount earned was $1,150, calculate the nominal interest rate compounded quarterly.
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The nominal interest rate compounded quarterly is 1.33%.
Given,
If an investment grew to $13,500 in 2 years.
and, the interest amount earned was $1,150.
To find the nominal interest rate compounded quarterly.
What is nominal interest rate?
The interest rate before inflation is referred to as the nominal interest rate.
Nominal can also refer to the advertised or stated interest rate on a loan, excluding any fees or interest compounding.
Now, According to the question:
Here given ,
P = $13500
i = ?
A = $1150
t = 2 yrs
n = 4 x 2 = 8
Formula of compound interest ,
A = P( 1 + I )ⁿ
$1150 = $13500 ( 1 + i ) ⁸
$1150 / $13500 = (1 + i)⁸
0.0851 = (1+ i) ⁸
1 +i = 8√.0851
1 + i = 2.33
i = 2.33 -1
i = 1.33 %
Hence, The nominal interest rate compounded quarterly is 1.33%.
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Use the parabola tool to graph the quadratic function f(1) = 2x^2+16x+30Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answers
vertex(-4,-2)
focus(-4,-15/8)
Axis of symmetry,x=-4
directrix, y=-17/8
x y
-6 6
-5 0
-4 -2
-3 0
-2 6
Hi. Been out due to medical issues trying to catch-up and learn my work. Thank you in advance
Answers
The break even point is where cost is equal to revenue
cost : y = 25.96x + 22752
Revenue : y = 57.56x
Set the two equations equal to determine x
25.96x + 22752 = 57.56x
Subtract 25.96x from each side
25.96x-25.96x + 22752 = 57.56x-25.96x
22752 = 31.6x
Divide each side by 31.6
22752/31.6 = 31.6x/31.6
720 =x
Now find the value of y
y = 57.56x
y = 57.56 (720)
y = 41443.20
( 720, 41443.20)
Answer: ( 720, 41443.20)
Point-Slope Form: y + 2 = -7(x − 4)Rewrite the equation in slope-intercept form
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Given the equation of a line in Point-Slope Form:
[tex]y+2=-7(x-4)[/tex]You need to rewrite it in Slope-Intercept Form:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Then, you have to solve for "y":
1. Apply the Distributive Property on the right side of the equation. Remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]Then:
[tex]y+2=(-7)(x)+(-7)(-4)[/tex][tex]y+2=-7x+28[/tex]2. Apply the Subtraction Property of Equality by subtracting 2 from both sides of the equation:
[tex]y+2-(2)=-7x+28-(2)[/tex][tex]y=-7x+26[/tex]Hence, the answer is:
[tex]y=-7x+26[/tex]Test scores are normally distributed with a mean of 86 and a standard devotion of 2.2 what percent scored between 83.8 and 92.6? What percent scored below 83.8?
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Z- Score formula is:
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z\text{ is the z-score (Standard score)} \\ X\text{ is the value to be standardized} \\ \mu\text{ is the mean} \\ \sigma\text{ is the standard deviation} \end{gathered}[/tex]Here, the mean is 86, while the standard deviation is 2.2
Percent between 83.8 and 92.6 is;
[tex]P(\frac{83.8-86}{2.2}The percent between 83.8 and 92.6 = 0.83999[tex]P(Z<-1)=\text{ 0.15866}[/tex]Percent score below 83.8 is 0.15866
Identify the measurement that cannot be taken directly if you were constructing a two-
dimensional visual representation of the fish tank.
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The measurement that cannot be taken directly in 2-D is depth
What do you mean by measurement?
Measurement is the quantification of an object's or event's properties for comparison with other objects or occurrences. Measurement, in other terms, is the act of establishing how large or little a physical amount is in comparison to a fundamental reference quantity of the same sort. The scope and use of measurement are context and discipline dependent. Measurements do not apply to nominal qualities of things or events in natural sciences and engineering, which is compatible with the recommendations of the International Bureau of Weights and Measures' International lexicon of metrology. However, measures in other domains, such as statistics and the social and behavioral sciences, can have numerous levels.
The measurement that cannot be taken directly in 2-D is depth
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5 1/7 * 4 2/3 equals
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We have to solve this operation with mixed numbers.
We can solve this applying the distributive property or by converting the mixed numbers into fractions.
We will solve this converting the numbers into fractions:
[tex]\begin{gathered} (5+\frac{1}{7})\cdot(4+\frac{2}{3}) \\ \frac{5\cdot7+1}{7}\cdot\frac{4\cdot3+2}{3} \\ \frac{35+1}{7}\cdot\frac{12+2}{3} \\ \frac{36}{7}\cdot\frac{14}{3} \\ \frac{36}{3}\cdot\frac{14}{7} \\ 12\cdot2 \\ 24 \end{gathered}[/tex]Answer: 24
Which of the following is a valid application of the distributive property?
A. 5.2+3=5 (2+3)
B. 5 2+3=5 (2) +5. (3)
ONeither A nor B
OB only
O A only
O Both A and B
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5 2+3=5 (2) +5. (3) is a valid application of the distributive property.
What is a distributive property?
According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Given that,
A. 5.2+3=5 (2+3)
B. 5 2+3=5 (2) +5. (3)
Distributive property
a*(b+c) = a*b+a*c
In option A the RHS part is not correct.
In option B both part is correct.
5*(2+3)= 5*2+5*3
5*5 = 10+15
25 = 25
LHS = RHS
Hence, Option B is correct.
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hi can someone help me
Answers
This type of function is non linear.
Define function.A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output. You can tell if a relation is a function by looking at the inputs (the x-coordinates) and outputs (the y-coordinates). Keep in mind that each input has only one output in a function. A function is an equation with a single solution for y for each value of x. Each input of a particular type receives exactly one output when using a function.
Given,
f(x) = x²
This type of function is non linear.
The end behavior is:
as x ⇒ ∞ , y ⇒ ∞
x ⇒ -∞ , y ⇒ -∞
The function graphed is f(x) = (x -3)²
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an athlete eats 46 g of protein per day while training. how much protein will she eat during 23 days of training?
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ANSWER
1058 grams
EXPLANATION
Each day she eats 46 grams of protein. In 23 days of training, she will eat 23 times that amount,
[tex]46g\times23=1058g[/tex]Hence, in 23 days she will eat 1058 g of protein.
What is the slope of the line below? If necessary, enter your answer as afraction in lowest terms, using the slash (/) as the fraction bar. Do not enteryour answer as a decimal number or an equation.
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To find the slope of a line use two points (x,y) in the next formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In the given line you have the points: (-4, -9) and (-2, -3)
[tex]m=\frac{-3-(-9)}{-2-(-4)}=\frac{-3+9}{-2+4}=\frac{6}{2}=3[/tex]Then, the slope of the given line is 3Given the function [tex]y=(m^2-1)x^2+2(m-1)x+2[/tex] , find the values of parameter m for which the function is always positive.
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Answer: [tex](-\infty, -1) \cup (1, \infty)[/tex]
Step-by-step explanation:
The function is always positive when it has a positive leading coefficient (since that means the graph will open up), and when the discriminant is negative (meaning the graph will never cross the x-axis).
Condition I. Leading coefficient is positive
[tex]m^2 -1 > 0 \implies m < -1 \text{ or } m > 1[/tex]
Condition II. Discriminant is negative
[tex](2(m-1))^2 -4(m^2 -1)(2) < 0\\\\4(m^2 -2m+1)-8(m^2 -1) < 0\\\\4m^2 -8m+4-8m^2 +8 < 0\\\\-4m^2 -8m+12 < 0\\\\m^2 +2m-3 > 0\\\\(m+3)(m-1) > 0\\\\m < -3 \text{ or } m > 1[/tex]
Taking the intersection of these intervals, we get [tex]m < -1[/tex] or [tex]m > 1[/tex].
How many solutions does this equation have?-4k + 4k = 0
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Let's try so solve this equation:
[tex]\begin{gathered} -4k+4k=0 \\ 0=0 \end{gathered}[/tex]When you have a result of 0 = 0, that means the equation has infinite solutions, that is, any value of k we use would satisfy the equation.
So the equation has infinitely many solutions.
Do you know how to solve? I got 3.99 for the mean (it was correct)For the sample standard deviation I got 1.1285 ( but it was wrong)
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Explanation
Given the sample below, we are asked to find the mean and the standard deviation.
Part A
We can find the mean below using the formula
[tex]\begin{gathered} \text{Mean}=\frac{\sum ^{}_{}x}{n} \\ \text{where x is the sample value and n is the sample size} \end{gathered}[/tex]Therefore,
[tex]\text{Mean }=\frac{79.8}{20}=3.99[/tex]Answer =3.99
Part B
The standard deviation of the sample size can be found using the formula below;
[tex]\begin{gathered} S.D=\sqrt[]{\sum ^{}_{}\frac{(x-\bar{x})^2}{N-1}} \\ =\sqrt[]{\frac{20.938}{19}} \\ =\sqrt[]{1.102} \\ =1.05 \\ \end{gathered}[/tex]Answer: 1.05
Find the following. complete parts a-h. a. The first seven terms of the Fibonacci-like sequence with the seeds 0,3. *(parts b-h will appear as we answer this previous parts.) 7 parts in total for the question*
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Recall that in a Fibonacci-like sequence, the sum of two consecutive terms yields the third term.
Mathematically,
[tex]t_n=t_{n-2}+t_{n-1}[/tex]Since we are given the first two terms, we can find the third term and so on...
F₁ = 0
F₂ = 3
[tex]\begin{gathered} F_3=F_2+F_1=3+0=3 \\ F_4=F_3+F_2=3+3=6 \\ F_5=F_4+F_3=6+3=9 \\ F_6=F_5+F_4=9+6=15 \\ F_7=F_6+F_5=15+9=24 \end{gathered}[/tex]Robin Sparkles invests $3,760 in a savingsaccount at her local bank which gives 1.8%simple annual interest. She also invests$2,400 in an online savings account whichgives 5.3% simple annual interest. After fiveyears, which one will have earned moreinterest, and how much more interest will ithave earned, to the nearest dollar?
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The formula for determining simple interest is expressed as
I = PRT/100
where
I = interest
P = principal or amount invested
T = time in years
R = interest rate
Considering the amount invested in her local bank,
P = 3760
R = 1.8
T = 5
I = (3760 x 1.8 x 5)/100 = 338.4
Considering the amount invested in online savings,
P = 2400
R = 5.3
T = 5
I = (2400 x 5.3 x 5)/100 = 636
After 5 years, the investment in the online savings account earned more interest.
The difference in interest earned is
636 - 338.4 = $298 to the nearest dollar
It has earned $298 more than the local bank's interest
you raise pigs when you purchase the pig it weigh 46 pounds with in 5-6 months you pig will gain 380% in weight how much should it weigh by then round to the nearest whole number
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The weight of the pigs is 220.8 pounds.
How to calculate the value?From the information, when you raise pigs when you purchase the pig it weigh 46 pounds with in 5-6 months you pig will gain 380% in weight.
Therefore, the weight by then will be:
= Normal weight + ( Percentage × Previous weight)
= 46 + (380% × 46)
= 46 + 174.8
= 220.8
The weight is 220.8 pounds.
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What’s the volume and surface area of the object shown ?
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Volume of object = 42 cubic cm
Surface area of object = 96 square cm
Explanations:The given figure is a triangular prism.The formula for calculating its volume is expressed as:
[tex]volume\text{ }of\text{ prism}=BH[/tex]where:
B is the base area
H is the height of prism
[tex]\begin{gathered} volume\text{ of }prism=(\frac{1}{2}\times4\times3)\times7 \\ volume\text{ of }prism=6\times7 \\ volume\text{ of }prism=42cm^3 \end{gathered}[/tex]Determine the surface area of the prism
The surface area if the sum of all the faces of the prism.The faces consists of 3 rectangles and 2 triangles. The surface area is calculated as:
[tex]\begin{gathered} Surface\text{ area}=2(0.5\times3\times4)+(7\times4)+(3\times7)+(5\times7) \\ Surface\text{ area}=12cm^2+28cm^2+21cm^2+35cm^2 \\ Surface\text{ area}=96cm^2 \end{gathered}[/tex]Hence the surface area of the object shown is 96 square cm
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!
Answers
Answer:
A. reflection over the y-axis
B. translation 3 units right
C. translation 4 down
D. reflection over the x-axis
how do I find the correct answer? (answers in the dropbox below)
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A rhombus have 4 sides and angles
it first must be proven to have 4 sides, or 4 angles
thats a definition for Quadrilateral
then correct option is D
