The relationship between a dependent variable, y, and one or more independent variables, X, is described by a linear regression model.
What is linear regression model?The relationship between a dependent variable, y, and one or more independent variables, X, is described by a linear regression model. The response variable is another name for the dependent variable. Explanatory or predictive variables are other names for independent variables. Models with a single predictor are known as simple linear regression. Multiple predictor models are known as multiple linear regression. Models for numerous response variables using multivariate linear regression. Finding the weights (namely, W0 and W1) that result in the best-fitting line for the input data (i.e., the X characteristics) that we have is how linear regression functions. The line with the lowest price is chosen to be the greatest fit.Using an online multiple regression calculator, the estimated multiple linear regression equation that can be used to forecast the annual income using the number of school years completed (Education), length of tenure in the current employment, and age is as follows:
y = - 143481.1924 + 10011.9212x1 - 2193.8838x2 + 2689.2405x3
According to the general form of a multiple linear regression model:
-143481.1924 = intercept(c) ; where regression line crosses the origin
10011.9212x1 - 2193.8838x2 + 2689.2405x3 are weight coefficients of the three predictor variables ; x1, x2, and x3
y = predicted variable
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Raul estimated that a fish tank contained 20
gallons of water. He later found that the fish
tank had a 40-gallon capacity. Calculate his
error as a percent.
Answer: 50%
Step-by-step explanation:
The error percent of the fish tank is 50%
Error percent:
Error percent means the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. It is also known as the percent error is the relative error multiplied by 100.
The formula to calculate the error percent is
δ = |vA - vE|/vA x 100
δ = percent error
vA = actual value observed
vE = expected value
Given,
Raul estimated that a fish tank contained 20 gallons of water. He later found that the fish tank had a 40-gallon capacity.
Here we need to calculate the error percent.
According to the error percent formula,
In this question
The estimated value = 20 gallons
Actual value = 40 gallons.
Now, we have to apply the values on the formula, then we get,
P% = (40 - 20)/40 x 100
P% = 20/40 x 100
P% = 1/2 x 100
P% = 0.5 x 100
P% = 50.
Therefore, the error percent is 50%.
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What is (9 x 10^4) (6 x 10^-7)?
Answer:0.0008994
Step-by-step explanation:
Given: ZADB = ZCBD ZABDZCDB m ZA= 3x + 15 mZC=8x-20 Find: x and m ZA A4 D B
Answer:
x = 7 , ∠ A = 36°
Step-by-step explanation:
since ∠ ADB ≅ ∠ CBD ( alternate angles )
and ∠ ABD ≅ ∠ CDB ( alternate angles )
then ABCD is a parallelogram
the opposite angles of a parallelogram are congruent , so
∠ C = ∠ A , that is
8x - 20 = 3x + 15 ( subtract 3x from both sides )
5x - 20 = 15 ( add 20 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7
Then
∠ A = 3x + 15 = 3(7) + 15 = 21 + 15 = 36°
Answer: x = 7 and m∠A = 36
Step-by-step explanation:
Here ∠ADB ≅ ∠CBD and ∠ABD ≅ ∠CDB
This configuration is found when a quadrilateral has two parallel sides which have a diagonal as their transversal. Thus the figure is of parallelogram. In a parallelogram, opposite angles are equal. Thus m∠A = m∠C
⇒3x +15 = 8x - 20
⇒3x + 15 - 3x = 8x - 3x -20
⇒5x = 20 + 15
⇒x = 7
Now m∠A = (3X7) +15 = 36
What’s the answer plss
The length of XY=19.894 cm when the angle XYZ=90° and angle YZX=61° and the length of hypotenuse=17.4 cm. Using the property of trigonometry, a=b.sinα/sinβ.
What is trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc).
What is Hypotenuse?The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.
Here,
a=b.sinα/sinβ
=17.4·sin(90°)/sin(61°)
=19.89436 cm
≈19.9 cm
When the hypotenuse is 17.4 cm long and the angles XYZ and YZX are 90° and 61°, respectively, the length of XY is 19.894 cm. Using the trigonometric formula a=b.sinα/sinβ.
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When and where does the story The circuit take place?
Answer:
Mexico to the United States in 1947
Step-by-step explanation:
pulse rates of adult females are normally distributed with a mean of 74.0 beats per minute (bpm) and a standard deviation of 12.5 bpm. what is the percentage of adult females with pulse rates between 49.0 bpm and 86.5 bpm? what percentage of adult females have pulse rates below 90 bpm?
The percentage of adult females with pulse rates between 49.0 bpm and 86.5 bpm - 81.86%
The percentage of adult females have pulse rates below 90 bpm - 89.97%
a)
X ~ N ( µ = 74 , σ = 12.5 )
P ( 49 < X < 86.5 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 49 - 74 ) / 12.5
Z = -2
Z = ( 86.5 - 74 ) / 12.5
Z = 1
P ( -2 < Z < 1 )
P ( 49 < X < 86.5 ) = P ( Z < 1 ) - P ( Z < -2 )
P ( 49 < X < 86.5 ) = 0.8413 - 0.0228
P ( 49 < X < 86.5 ) = 0.8186 ≈ 81.86%
b)
X ~ N ( µ = 74 , σ = 12.5 )
P ( X < 90 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 90 - 74 ) / 12.5
Z = 1.28
P ( ( X - µ ) / σ ) < ( 90 - 74 ) / 12.5 )
P ( X < 90 ) = P ( Z < 1.28 )
P ( X < 90 ) = 0.8997 ≈ 89.97%
What is pulse rate ?
The pulse rate, or the number of times the heart beats each minute, is gauged by the pulse rate. The arteries enlarge and constrict with the flow of blood as the heart pumps blood through them. An elevated heart rate, or tachycardia, can occur for any reason. Exercise-induced or stress-related heart rate increases are two possible causes (sinus tachycardia). Sinus tachycardia is not seen as an illness but rather a symptom. Another factor contributing to tachycardia is an unsteady heartbeat (arrhythmia).
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The length of a rectangle is 3 inches greater than the width. (Hint: draw a pictureand label itA. Write a polynomial that represents the area of the rectangle.B. Find the area of the rectangle when the width is 4 inches..
We are given that the length of a rectangle is 3 inches greater than the width.
Let us draw a rectangle and label the width and length.
Part A:
Let the width of the rectangle is x inches.
Then the length of the rectangle is (x + 3) inches.
Now recall that the area of a rectangle is given by
[tex]A=L\cdot W[/tex]Where L is the length and W is the width of the rectangle.
[tex]\begin{gathered} A=(x+3)\cdot x \\ A=x^2+3x \end{gathered}[/tex]Therefore, the above polynomial represents the area of the rectangle.
Part B:
We are given that the width is 4 inches.
Substitute the width (x = 4) into the equation of the area that we found in part A.
[tex]\begin{gathered} A=x^2+3x \\ A=(4)^2+3(4) \\ A=16+12 \\ A=28in^2 \end{gathered}[/tex]Therefore, the area of the rectangle is 28 square inches.
8b^2 + 56b + 48 = 0
Solve for X
Answer:
b= -1, -6
Step-by-step explanation:
divide by common factor
then use x=- b+- sqrt b^2-4ac/2a
separate the equations and solve them
Choose the number and type of roots of each quadratic function.
Function
f(x)=x²-9x + 21
f(x) = x² + 16x - 64
f(x) = -4x²-4x²10x +84
f(x) = 3x² + 24
The number and type of roots of each quadratic function are:
f(x) = x² - 9·x + 21, Has complex rootsf(x) = x² + 16·x - 64 has two real and distinct rootsf(x) = -4·x² + 10·x + 84 has two real and distinct rootsf(x) = 3·x² + 24 has complex rootsWhat determines the type of root that a quadratic function has?The type of roots of a quadratic function is given by the value of the discriminant, which is the value under the square root of the quadratic formula.
The types of roots of a quadratic equation are;
Two real and distinct rootsTwo real and equal rootsComplex rootsThe roots or solution to the quadratic equation, a·x² + b·x + c = 0, are given by the quadratic formula, [tex]x = \dfrac{-b\pm \sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}[/tex]
Where:
b² - 4·a·c is known as the discriminant of the quadratic equation.
The type of root of a quadratic equation is given by the discriminant, b² - 4·a·c, as follows:
If the discriminant, b² - 4·a·c is less than 0, then the quadratic equation has no roots or no real rootsIf b² - 4·a·c = 0, then the quadratic equation has two real and equal roots (or one real root)If the discriminant, b² - 4·a·c > 0, then the quadratic equation has two real and distinct roots.The given functions are:
f(x) = x² - 9·x + 21Comparing the above equation to the, general form of a quadratic equation, f(x) = a·x² + b·x + c, we have;
a = 1, b = -9, and c = 21
The discriminant is therefore, (-9)² - 4 × 1 × 21 = -3 < 0
The quadratic equation therefore, has complex roots.
f(x) = x² + 16·x - 64The quadratic equation, f(x) = x² + 16·x - 64 has a discriminant given as follows;
The discriminant is: 16² - 4 × 1 × (-64) = 512 > 0, therefore, the quadratic equation two real roots, given by the equation;
[tex]x = \dfrac{-16\pm \sqrt{16^2 - 4\times 1 \times 64} }{2\times 1}= \dfrac{-16\pm \sqrt{512} }{2}= \dfrac{-16\pm 16\cdot \sqrt{2} }{2}[/tex]
x = -8 + 8·√2 or x = -8 - 8·√2
f(x) = -4x² + 10·x + 84The value of the discriminant is 10² - 4 × (-4) × 84 = 1444 > 0, therefore, the equation has two real and distinct roots, given by the equation;[tex]x = \dfrac{-10\pm \sqrt{1444} }{2\times (-4)}= \dfrac{-10\pm 38 }{-8}[/tex]
[tex]x = \dfrac{28 }{-8}= -3.5[/tex] and [tex]x = \dfrac{-48 }{-8}= 6[/tex]
f(x) = 3·x² + 24The discriminant of the above quadratic equation is; 0² - 4 × 3 ×24 = -288 < 0
Therefore, the quadratic equation, f(x) = 3·x² + 24, has no real roots or complex roots
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triangle RST had coordinates: R(-2, 1) S(-8, 2) T(-4, 5) Draw the translation of RST 8 units right and 4 units down on your recording sheet. what are 3 coordinates of R'A. R'(-3, 6)B. R'(0, -2) C. R'(6, -3) D. R'(4, 1)
Since the translation is 8 units right and 4 units down, we have to add 8 to the x coordinate and subtract 4 to the y coordinate.
R=(-2,1)
R' = (-2+8,1-4)= (6,-3)
R' = (6,-3)
PLEASE HELP NOW DUE AT 11 PM. Are the linear expressions equivalent? Drag the choices to the boxes to correctly complete the table. .
In these linear expressions one is equivalent which is 3- 2( - 2.6x + 2.1) = 5.2x - 1.2 and one is not .
What are linear expressions?An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power.
Alternatively pluging; we will see that none of the exponents can be greater than 1.
2x - 3(1.3x - 2.5) = 5.9x + 7.5
2x -3.9x + 7.5 = 5.9 + 7.5
-1.9x + 7.5 ≠ 5.9 + 7.5
thus linear expression is not equivalent.
3- 2( - 2.6x + 2.1) = 5.2x - 1.2
3 + 5.2x - 4.2 = 5.2x - 1.2
5.2x - 1.2 = 5.2x - 1.2
thus, linear expression is equivalent.
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A bag contains 4 blue and 6 white tokens. Two tokens are drawn from the bag one after another, without replacement. Find the probability that: the first is blue and the second is white.
Concept; Probability
Step1: The total number of tokens is
[tex]6\text{white +4 Blue}=\text{ 10 tokens}[/tex]let the probability of blue be P(B) and the probability of red be P(R)
The probability that the first is Blue is
[tex]\begin{gathered} P(B)=\frac{number\text{ of blue }}{total\text{ number of tokens}}=\frac{4}{10}=\frac{2}{5} \\ \end{gathered}[/tex]The probability the second is white without replacement is
[tex]P(R)=\frac{number\text{ of white}}{total\text{ token}}=\frac{6}{9}=\frac{2}{3}[/tex]Hence the combined probability of Blue and Red is
[tex]P(BR)=\frac{2}{5}\times\frac{2}{3}=\frac{4}{15}[/tex]Therefore the probability that the first is blue and the second is white is 4/15
In a race, Kara ran eight- eighteenths of a kilometer and cycled sixteen-eighteenths of a kilometer. Estimate how many kilometers the race was in all.
a) 1/2 kilometer
b) 1 kilometer
c) 1 1/2 kilometers
d) 2 kilometers
Number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.
Given that, Kara ran 8/18 of a kilometer and cycled 16/18 of a kilometer.
What is addition of two fractions?To add two fractions, with different denominators, we need to rationalise the denominators by taking out the LCM and make the denominator same. Then add the numerators of the fractions, keeping the denominator common.
Now, total distance in race
8/18 + 16/18
= (8+16)/18
= 24/18
= 4/3
= [tex]1\frac{1}{3}[/tex] kilometers
Therefore, number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.
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150 14 Solve for x. Round to the nearest tenth. 63.5 54.1 3.6 74.9
The given triangle is a right angled triangle having the follwoing sides;
Hypotenuse = x (longest side)
Opposite = 14 (side facing the given acute angle)
Theta = 15 degrees
Using the SOH trigonometry identity;
sin 15 = opposite/hypotenuse
sin15 = 14/x
x = 14/sin15
x = 14/0.2588
x = 54.09
x is approximately equal to 54.1. Option B is coorect
Here are some ingredients for bolognaise sauce 400g of minced beef 800g of tomato sauce 300 ml stock 300ml red wine. julia has 300g of minced beef. how much of the other ingredients does she need
Answer:
Step-by-step explanation:
she would have to use 3/4 of the ingrediants to the 400g of minced beef.
tomato sauce would be 600g
stock would be 225g
and red wine would be 225g
The quantity of chopped tomatoes is 600 g, of stock is 225 ml, and of red wine is 225 ml if Julie only has 300 g of minced beef.
The ratio is the comparison of two quantities to determine how frequently one quantity obtains the other. It can be shown as a fraction between two numbers.
Quantity of minced beef = 400 g
Quantity of chopped tomatoes = 800 g
Quantity of stock = 300 ml
Quantity of red wine = 300 ml
Taking ratios of all the quantities, we get:
minced beef: chopped tomatoes:stock: red wine
= 400:800:300:300
= 100:200:75:75 ( Dividing by 4, as a common factor)
Multiplying the above ratio by three to make the quantity of minced beef 300 g
= 300:600:225:225
Thus, the quantity of chopped tomatoes is 600 g, the quantity of stock is 225 ml, and the quantity of red wine is 225 ml if Julie only has 300 g of minced beef.
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Product of two rational no. is 1 , if one of them is ⁵/², then the other no. isa) ⅖b) -1 c) 0
Given:
Product of two numbers is 1.
The one number is 5/2.
Let the another number be x.
[tex]\begin{gathered} x\times\frac{5}{2}=1 \\ x=1\times\frac{2}{5} \\ x=\frac{2}{5} \end{gathered}[/tex]Answer: Option a) is correct. the other number is 2/5.
The first equation should be multiplied by 7 and the second equation by -6.
Answer:
Step-by-step explanation:
Find the value of x.
Find the radius of a cylinder whose height is 10 cm and the total surface area is 352 cm².
Answer: the radius of a cylinder is 4 cm
Step-by-step explanation:
[tex]S_{ts}=352\ cm\ \ \ \ H=10\ cm\ \ \ \ \ r=?[/tex]
The total surface area:
[tex]\displaystyle\\ S_{ts}= 2\pi r^2+2\pi rH\\\\S_{ts}=2\pi (r^2+rH)\\\\352=2\pi (r^2+10r)\\\\[/tex]
Divide both parts of the equation by 2π:
[tex]\displaystyle\\56=r^2+10r\\\\56-56=r^2+10r-56\\\\0=r^2+10r-56\\\\Thus,\\\\ r^2+10r-56=0\\\\D=(-10)^2-4(1)(-56)\\\\D=100+224\\\\D=324\\\\\sqrt{D}=\sqrt{324} \\\\\sqrt{D}=18\\\\ r=\frac{-10б18}{2(1)} \\\\r=-14\notin\ (r > 0)\\\\r=4\ cm[/tex]
Answer:
r ≈ 4 cm
Step-by-step explanation:
Total Surface Area of a cylinder
A = Base Area x 2 + Lateral Surface Area
A = 2(πr²) + 2πrh
where r = radius of base and h = height of cylinder
Solving for r we get
[tex]\displaystyle r = \dfrac{1}{2} \sqrt{h^2 + 2 \dfrac{A}{\pi} }-\dfrac{h}{2}\\\\[/tex]
Given h = 10 cm and A = 325 we get
[tex]\displaystyle r = \dfrac{1}{2} \sqrt{10^2 + 2 \dfrac{352}{\pi} }-\dfrac{10}{2}\\\\\\[/tex]
[tex]\sqrt{10^2 + 2 \dfrac{352}{\pi} } =\sqrt{100+\dfrac{704}{\pi }}\\\\= \sqrt{100 + 224.09}\\\\\\[/tex]
= [tex]\sqrt{324.09}[/tex]
= 18.0025
1/2 x 18.0025 ≈ 9
So r ≈ 9 - 10/2 = 9 -5 = 4
r ≈ 4 cm
Tom’s car has 1119 gallons of gas. If he uses 38 of the gas, how much gas does the car have left?
Answer:
1,081 gallons
Step-by-step explanation:
1,119 - 38 = 1,081
an industrial manufacturing company uses an inverted conical (cone-shaped) tank to dispense liquid into containers. the tank measure 24 inches with a base radius of 48 inches. if the liquid flows out of the tank at a rate of 40 cubic inches per minute, at what rate is the height of the liquid falling when the height of the liquid is 10 inches deep?
If the liquid flows out of the tank at a rate of 40 cubic inches per minute, the height of the liquid will decrease at rate 0.0318 in./minute
Referring to the attached picture, the two triangles in a cone are similar. Hence,
r/h = 48/24
or
r = 2h.
The volume of the liquid is given by:
V = 1/3 . πr²h
Substitute r = 2h,
V = 1/3 . π(2h)²h = 4/3 . πh³
Take the derivative with respect to t
dV/dt = 4/3 . 3πh² . dh/dt
dV/dt = 4 . πh² . dh/dt
Substitute dV/dt = -40 and h = 10
-40 = 4 . π(10)² . dh/dt
dh/dt = - 0.0318 in./minute
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Wich is closest to the volume of the cone in cubic feet?
Therefore let us input the values to find the volume of the cone
[tex]\begin{gathered} \text{volume}=\frac{1}{3}\pi r^2h \\ r=\frac{8}{2}=4\text{ ft} \\ h=9ft \\ \text{volume}=\frac{1}{3}\pi r^2h \\ \text{volume}=\frac{1}{3}\times3.14\times4^2\times^{}9 \\ \text{volume}=\frac{1}{3}\times3.14\times16\times9 \\ \text{volume}=\frac{452.16}{3} \\ \text{volume}=\text{ }150.72ft^2 \end{gathered}[/tex]The answer should be A.
solve for y, 3x−5y = 6
Answer:
y = [tex]\frac{3x -6}{5}[/tex]
Step-by-step explanation:
3x - 5y = 6 ( subtract 3x from both sides )
- 5y = - 3x + 6 ( multiply through by - 1 )
5y = 3x - 6 ( divide both sides by 5 )
y = [tex]\frac{3x-6}{5}[/tex]
What is the equation of a line that passes though the Point (3, -7) and has a slope of -2?
Answer:
y = - 2x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (3, - 7 ) into the partial equation
- 7 = - 6 + c ⇒ c = - 7 + 6 = - 1
y = - 2x - 1 ← equation of line
Do You Like Guns N' Roses, If So, What Is Your Favorite Song?
Answer:golden hour by JVKE
Step-by-step explanation:
Rain fell at a rate of .25 inches per hour. Before the rain began, 6 inches had already fallen that month. At this rate, how much total rain will have fallen after 4 hours?
Answer:
y=.25x+6
Step-by-step explanation:
X=
//////////////////////////
Answer:
x = 15
Step-by-step explanation:
150+3x-15=180 because of same-side interior angles therorem.
Then, we solve the problem to get 15.
Hope this helped! :)
3/4+(1/2+1/4) 2⋅2
NEED HELP.
Answer:
15/8 for exact form
1.875 for decimal form
And
1 and 7/8 for mixed number form
hope this helps you!
(also already in the simplest form :)
it is decided that this barrel must be painted pink and the barrel's surface area is requested in order to determine the amount of paint needed. what is the surface area of the barrel g
The surface area of the barrel needs to be calculated in order to determine the amount of paint. The surface area of the barrel, including the lid, is 13 m²
Missing data from the problem:
radius of the barrel = 0.4 meters
height of the barrel = 1.2 meters
The shape of a barrel is cylinder. The surface area of the barrel, including the lid) is:
A = 2. πr² + 2. πr.h
Where:
r = radius
h = height
Plug the parameters into the formula:
A = 2. π(0.4)² + 2. π(0.4).(1.2)
A = 13 m²
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Either Table A or Table B shows a proportional relationship.
Plot the points from the table that shows a proportional relationship.
Table A shows a proportional relationship
What is proportional relationship?
When the value of independent variable changes the value of dependent variable changes. that means if the value independent variables is increase the value of dependent variable will also be increased.
In the figure we are given 2 tables
We plot both the curve on the graph we get
Table A shows a linear relationship where are Table b Does not shows a proportional relationship
Hence Table A shows a proportional relationship
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Answer:
Step-by-step explanation: