HELP!!!!
Use quadratic regression to find the
equation for the parabola going
through these 3 points.
(2, 19) (6, 99) (-1, 1)
Answers
Answer:
The equation for the parabola is [tex]y = 2\cdot x^{2}+4\cdot x +3[/tex].
Step-by-step explanation:
Let be [tex]P(x,y) = (2, 19)[/tex], [tex]Q(x,y) = (6,99)[/tex] and [tex]R(x,y) = (-1, 1)[/tex] and quadratic regression is represented by a second-order polynomial of the form:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex] (1)
Where:
[tex]x[/tex] - Independent variable
[tex]y[/tex] - Dependent variable
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients
Algebraically speaking, we need three distinct points on plane to determine the quadratic regression. By using all information, we form the following system of linear equations:
[tex]4\cdot a +2\cdot b + c = 19[/tex] (2)
[tex]36\cdot a + 6\cdot b + c = 99[/tex] (3)
[tex]a -b + c = 1[/tex] (4)
The solution of this system is: [tex]a = 2[/tex], [tex]b = 4[/tex], [tex]c = 3[/tex]. Hence, the equation for the parabola is [tex]y = 2\cdot x^{2}+4\cdot x +3[/tex].
Related Questions
Evaluate 24 = (8-2).
Answers
Answer:
24 ÷ ( 8 - 2 )
= 24 ÷ 6
= 4
so, 4 is the answer
Answer:
on your question it says “=“ but on the picture it says “÷”
so for 24=(8-12) it would be 30
and for 24÷ (8-12) it would be -6
Step-by-step explanation:
Hope this helps, have a good day
PLEASE ANSWER ASAP I WILL MARK BRAINLIEST WHEN ANSWERING PLZ PUT ANSWER IN ORDER PLS THANK YOU :)
1.) Dana has 5 times as many french fries as Abdullah and Abdullah has twice as many French Fries as Jonathan. If they have 26 French Fries all together, how many does Dana have? ALSO
2.) After finishing their fries, they pooled all their money to buy as much soda as they could. Dana had $5.12. Abdullah had $2.77 and Jonathan had only $4. If soda is $1.99 for a 2-liter bottle, how many bottles could they purchase?
Answers
Answer:
Dana has 20 French fries.
They can purchase 5 bottles.
Step-by-step explanation:
1.
Let x rep. the amount of French fries Johnathan has.
Let 2x rep. the amount of French fries Abdullah has.
Let 10x rep. the amount of french fries Dana has.
If :
x+2x+10x=26
13x=26
x=2
So Johnny boy has 2 french fries which means Dana has 10 times as much as that.
10(x)=10(2)
10x=20
Therefore Dana has 20 French fries.
2.
Well
5.12+2.77+4=$11.89
11.89/1.99= APPROX. 5.9
Note you can't buy a fraction of a bottle. We gotta round down for this question cause you can't just give less amount of cash to get an extra bottle even if it's very close. Unless your teacher said to round something.
Therefore they can only purchase 5 bottles.
The function F(x) varies inversely with x and f(x) = 25 when x = 6 what is f(x) when x= 18
Answers
Answer:
8.333
Step-by-step explanation:
F(x) α 1/ x
F(x) = k/x
F(x) = 25 ; x = 6
Lets use the information above to obtain the value of k
25 = k/6
k = 25 * 6 = 150
k = 150
Therefore, the value of f(x) when x = 18 will be :
Using the relation :
F(x) = k/x
k = 150, x = 18
F(x) = 150 / 18
F(x) = 8.333
At the Italian deli, the sandwich maker cut 4 2/3 lb of turkey and 9 3/5 of roast beef. How many more pounds of roast beef were cut?
Answers
Answer:
4 14/15 more pounds of roast beef
Step-by-step explanation:
subtract 4 2/3 from 9 3/5
9 3/5 - 4 2/3= 4 14/15
So your answer is 4 14/15
A 1/2-mile long train enters a 2-mile long tunnel traveling at a speed of 10 mi/h. How many minutes pass from the time the front of the first train car enters the tunnel until the rear of the last train car exits the tunnel?
Answers
Answer:
15 minStep-by-step explanation:
The distance required is the length of the tunnel added to the length of the train
d = 1/2 + 2 = 5/2 miless = 10 mile/hour = 10/60 mile/min= 1/6 mile/minTime is:
t = d/st = 5/2 : 1/6 = 5/2*6= 15 minBrianna has a container with a volume of 1.5 L she estimates the volume to be 2.1 m what is the percent error
Answers
===================================================
Work Shown:
Subtract the values to get 2.1-1.5 = 0.6
Brianna is off by 0.6 liters
Divide that error by the true value 1.5 to get 0.6/1.5 = 0.40
Then move the decimal point 2 spots to the right to arrive at 40%
Therefore, the percent error is 40%
------------------
The formula you can apply is:
[tex]P = \frac{|G-T|}{T}*100\%[/tex]
where
P = percent error
G = guess value (in this case it is 2.1)
T = true value (which is 1.5 in this case)
If we were to apply the formula, then we get:
[tex]P = \frac{|G-T|}{T}*100\%\\\\P = \frac{|2.1-1.5|}{1.5}*100\%\\\\P = \frac{|0.6|}{1.5}*100\%\\\\P = \frac{0.6}{1.5}*100\%\\\\P = 0.40*100\%\\\\P = 40\%\\\\[/tex]
A three digit number is selected at random from the set of all three digit numbers. The probability that the selected number has all the three digits the same is:__________.A.1/9B. 1/10C. 1/50D. 1/100
Answers
Answer:
1 /100
Step-by-step explanation:
Probability = (number of required outcomes / number of total possible outcomes)
Total possible outcomes = count of all 3 digit numbers ={100, 101,... 999} = 900
Required outcome = count of Three digit numbers with all 3 digits being the same = {111,222,333,444,555,666,777,888,999} = 9
Hence, probability that selected number has all 3 digits being the same :
9 / 900 = 1 /100
Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating.
20% tip on a bill of $36.04
The amount of the tip is approximately $
$7.00
O $7.20
0 $7.25
$7.50
Answers
Answer:
36.04
The amount of the tip is approximately $
$7.00
O $7.20
0 $7.25
$7.50
Step-by-step explanation:
Which equation represents the rectangular form of Theta = StartFraction 5 pi Over 6 EndFraction?
StartRoot 3 EndRoot x minus y = 0
StartRoot 3 EndRoot x + y = 0
StartRoot 3 EndRoot x minus 3 y = 0
StartRoot 3 EndRoot x + 3 y = 0
Answers
Answer:
D. StartRoot 3 EndRoot x + 3 y = 0 (or √3x + 3y = 0)Step-by-step explanation:
This is about converting polar coordinate to rectangular
Relationship between coordinates is:
x = r cosθy = r sinθthen
y/x = sinθ/cosθy/x = tanθWe have θ = 5π/6, finding the value of tan:
tan 5π/6 = tan (π - π/6) = - 1/√3 = - √3/3Substitute tan with its value:
y/x = -√3/3 3y = -√3x3y + √3x = 0√3x + 3y = 0Correct option is D
Answer:
I did option d !!
Step-by-step explanation:
1,Find the eighth term of the geometric sequence whose 1st term is 5 and whose 4th term is
1/25.
Answers
Answer:
Solution will be 1/15625
Step-by-step explanation:
Substitute the value of first term for ar^(4-1) for the third term with 1/25 on RHS, make r the subject (which is the common ratio)
you'll get r as 1/5
Now for the eighth term, replace the "4" in the formula with "8" and a with "5" and observe the magic.
Graph this function using intercepts: 27x–15y=1,350. Provide x and y intercepts
I really don't know how to do it myself and when I try to solve using a website they can't even do it
Answers
Answer:
graph attached
Step-by-step explanation:
27x - 15y = 1350
15y = 27x -1350
y = 27/15 x - 1350/15
y = 9/5 x - 90
y = mx + b y intercept (b) = -90
y=0 x = 90 * 5/9 = 50 x intercept
Step-by-step explanation:
Given function
27x – 15y = 1350Easy way to find x- and y-intercepts and graph the line:
x-intercept found when y = 0
27x - 15*0 = 135027x = 1350x = 1350/27x = 50y-intercept found when x = 0
27*0 - 15y = 1350-15y = 1350y = -1350/15y = - 90So the points are:
(0, -90) and (50, 0)Plot these two points on a coordinate plane and connect with a line
If Z is a standard normal variable find the probability. The probability that Z lies between -0.558 and 0.558
Answers
Answer:
0.4245
Step-by-step explanation:
The probability that Z lies between -0.558 and 0.558 can be written as;
P(-0.558 < z < 0.558) = P(z < 0.558) - P(z < -0.558)
Using z - distribution table, we have;
P(z < 0.558) = 0.7122
P(z < -0.558) = 0.2877
Thus;
P(z < 0.558) - P(z < -0.558) = 0.7122 - 0.2877 = 0.4245
Which list shows the numbers in order from least to greatest?
479, 4.79, 4.709
479, 4.709, 4,79
4.709, 479, 4.79
4.79, 479, 4.709
4.79, 4.709, 479
Answers
Billy was standing on a diving board that was 4 feet above the water. He dove into the pool which was 8 feet deep and touched the bottom. Which statement accurately describes this
situation?
Answers
Maximus is playing a game. When he rolls the dice he wins if he gets an even number and loses if he gets an odd number. Which of the following statements is FALSE?
a. The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution
b. Rolling an even number is considered a success
c. The count of rolling an even number can be approximated with a normal distribution
d. The count of rolling an odd number can be approximated with a normal distribution
Answers
Answer:
a. The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution.
Step-by-step explanation:
Whenever we roll a fair dice, the possible outcomes are { 1, 2, 3, 4, 5, 6}. In this three numbers are even numbers, i.e. {2, 4, 6}.
The probability of getting an even number is [tex]$p (\text{even}) =\frac{3}{6} = \frac{1}{2}$[/tex]
Since each of the rolls is independent and each probability of getting even remains the same.
Using the central limit theorem, the sampling distribution of a large sample, usually more than 30 can be approximated by the normal distribution. A single roll of an even or odd number cannot be approximated by a normal distribution, it follows the Binomial distribution.
If number of rolls are large, then a normal approximation can be used.
Answer:
The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution.
Step-by-step explanation:
Beads are dropped to create a conical pile such that the ratio of its radius to the height of the pile is constant at 2:3 and the volume is increasing at a rate of 5 cm^3/s. Find the rate of change of height at h = 15cm.
Answers
Answer:
[tex]\displaystyle \frac{dh}{dt} = \frac{1}{20 \pi} \ cm/s[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Equality PropertiesGeometry
Volume of a Cone: [tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]Calculus
Derivatives
Derivative Notation
Differentiating with respect to time
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{r}{h} = \frac{2}{3} \\\frac{dV}{dt} = 5 \ cm^3/s\\h = 15 \ cm[/tex]
Step 2: Rewrite Cone Volume Formula
Find the volume of the cone with respect to height.
Define ratio: [tex]\displaystyle \frac{r}{h} = \frac{2}{3}[/tex]Isolate r: [tex]\displaystyle r = \frac{2}{3} h[/tex]Substitute in r [VC]: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{2}{3}h)^2h[/tex]Exponents: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{4}{9}h^2)h[/tex]Multiply: [tex]\displaystyle V = \frac{4}{27} \pi h^3[/tex]Step 3: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dV}{dt} = \frac{4}{27} \pi \cdot 3 \cdot h^{3-1} \cdot \frac{dh}{dt}[/tex]Simplify: [tex]\displaystyle \frac{dV}{dt} = \frac{4}{9} \pi h^{2} \frac{dh}{dt}[/tex]Step 4: Find Height Rate
Find dh/dt.
Substitute in known variables: [tex]\displaystyle 5 \ cm^3/s = \frac{4}{9} \pi (15 \ cm)^{2} \frac{dh}{dt}[/tex]Isolate dh/dt: [tex]\displaystyle \frac{5 \ cm^3/s}{\frac{4}{9} \pi (15 \ cm)^{2} } = \frac{dh}{dt}[/tex]Rewrite: [tex]\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{\frac{4}{9} \pi (15 \ cm)^{2} }[/tex]Evaluate Exponents: [tex]\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{\frac{4}{9} \pi (225 \ cm^2) }[/tex]Evaluate Multiplication: [tex]\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{100 \pi cm^2 }[/tex]Simplify: [tex]\displaystyle \frac{dh}{dt} = \frac{1}{20 \pi} \ cm/s[/tex]Is 17/23 a irrational number
Answers
Answer:
NO.
Step-by-step explanation:
An irrational number cannot be written as a fraction.
What fraction more of the coupon books did Jabar sell than Guto?
Answers
Answer:
1/20
Step-by-step explanation:
Take 1/12 and 2/15 and find a common denomitator of 180 then multiply the tops to get 24/180 for 1/2 and 15/180 for 2/15 and then subtract to get 9/180
Finally simify to get 1/20
Rachel and David were shopping for holiday gifts when they noticed a Thanksgiving sweater on the discount rack. Rachel really wanted the sweater, even though she wouldn’t be wearing it until Thanksgiving of 2021! Part A: If the original price of the sweater was $24.00, and the sweater is on sale for 60% off, what is the sale price?
Answers
Answer:
$9.60Step-by-step explanation:
Original price = $24Discount = 60%Discount amount:
$24*0.6 = $14.40Sale price:
$24 - $14.40 = $9.60Answer:
9.60
Step-by-step explanation:
i did the quiz
What is an equation of the line that passes through the point (-6, -3) and is
parallel to the line 5x – 3y = 9?
Answer:
Submit Answer
Answers
9514 1404 393
Answer:
5x -3y = -21
Step-by-step explanation:
The parallel line will have the same x- and y-coefficients, but a constant suitable for the given point.
5x -3y = constant
5(-6) -3(-3) = constant = -30 +9 = -21
The equation of the line is ...
5x -3y = -21
I need help anyone can anyone help
Answers
Answer:
14
Step-by-step explanation:
The perimeter is the sum of the sides, so we have
2x+x+15+4x-7=57
= 7x+8
Subtracting 8 from both sides, we get
7x= 49
Dividing 7 from both sides, we get
x=7
Our sides are then 2x=14, x+15=22, and 4x-7=21. 14 is our answer
Answer:
The shortest length of the triangle is: 14
Hence, option B is correct.
Step-by-step explanation:
Given the triangle with the lengths
[tex]x+15[/tex][tex]4x-7[/tex][tex]2x[/tex]Given that the perimeter of triangle = P = 57
We know that the perimeter of a triangle is the sum of the lengths of the sides of a triangle.
so
[tex]P = (x+15)+(4x-7)+(2x)[/tex]
substitute P = 57
[tex]57 = (x+15)+(4x-7)+(2x)[/tex]
switch sides
[tex]\left(x+15\right)+\left(4x-7\right)+\left(2x\right)=57[/tex]
[tex]x+15+4x-7+2x=57[/tex]
Group like terms
[tex]x+4x+2x+15-7=57[/tex]
Add similar elements
[tex]7x+15-7=57[/tex]
[tex]7x=49[/tex]
divide both sides by 7
[tex]\frac{7x}{7}=\frac{49}{7}[/tex]
simplify
[tex]x=7[/tex]
Now, measuring the lengths by substituting x = 7
[tex]x+15 = 7+15 = 22[/tex][tex]4x-7 = 4(7)-7 = 28 - 7 = 21[/tex][tex]2x = 2(7) = 14[/tex]Therefore, the shortest length of the triangle is: 14
Hence, option B is correct.
Write a Play
Write a short play about the
adventures of characters x, y, m, b,
as they travel around the coordinate
plane. Have your characters meet
many friends and relatives along the
way. The purpose of your play is
to educate the audience about the
mathematics in this topic through
action, dialogue, staging, and props.
Answers
Answer:
math is a difficult subject
When the area of a square is increasing four times as fast as the diagonals, what is the length of a side of the square
Answers
Answer:
Length of a side of a square = 2√2 units
Step-by-step explanation:
Let the length of a square is 'x' units.
Therefore, Area of the square A = (Side)²
= x² square units
And by Pythagoras theorem,
(Diagonal)²= (Side 1)² + (Side 2)²
= x² + x²
= 2x²
Diagonal 'p' = x√2 units
It is given in the question that area of the square is increasing four times as fast as the diagonals.
[tex]\frac{d(A)}{dt}=4(\frac{dp}{dt} )[/tex] -------(1)
[tex]\frac{d(A)}{dt}=\frac{d(x^2)}{dt}[/tex]
[tex]\frac{d(A)}{dt}=2x\frac{d(x)}{dt}[/tex]
Similarly, [tex]\frac{d(p)}{dt}=\frac{d(x\sqrt{2})}{dt}[/tex]
[tex]=\sqrt{2}\frac{dx}{dt}[/tex]
Now by placing the value of [tex]\frac{d(A)}{dt}[/tex] and [tex]\frac{d(p)}{dt}[/tex] in equation (1),
[tex]2x\frac{dx}{dt}=4\sqrt{2}\frac{dx}{dt}[/tex]
[tex](2x - 4\sqrt{2})\frac{dx}{dt}=0[/tex]
Since, [tex]\frac{dx}{dt}\neq 0[/tex]
[tex](2x - 4\sqrt{2})=0[/tex]
x = 2√2
Therefore, length of a side of the square is 2√2.
Ema’s family has completed 60% of a trip. They have traveled 45 miles. How far is the trip?
Answers
Answer:
72 miles
Step-by-step explanation:
60% times 45 = 27
27 + 45 = 72
Answer is 72 miles
Answer:
Ema's Family would drive 72 miles
Step-by-step explanation:
Hope this helps :)
And I hope this is correct
At 1:00 P.M., oil begins leaking from a tank at a rate of (6 0.77t) gallons per hour. (Round your answers to three decimal places.) (a) How much oil is lost from 1:00 P.M. to 4:00 P.M.
Answers
Answer:
[tex]Amount = 8.31[/tex]
Step-by-step explanation:
Given
[tex]Rate = 6 + 0.77t[/tex]
Required
Determine the gallons of oil lost between 1pm to 4pm
[tex]Rate = 6 + 0.77t[/tex]
Where t represents number of hours
First, we need to calculate the duration between 1pm and 4m.
[tex]t = 4pm - 1pm[/tex]
[tex]t = 3\ hours[/tex]
Substitute 3 for t in [tex]Rate = 6 + 0.77t[/tex]
[tex]Amount = 6 + 0.77 * 3[/tex]
[tex]Amount = 6 + 2.31[/tex]
[tex]Amount = 8.31[/tex]
Hence, 8.31 gallons of oil has been lost
Find the value of x that makes mll n.
150°
(3x-15)
Answers
Answer:
[tex]3x - 15 = 150 \\ 3x = 165 \\ x = 55[/tex]
55° is the right answer.What's 7.3 and 23 as a precent and what's 2/5 as a precent
Answers
Answer:
730% 23% and 40%
Step-by-step explanation:
.......
Someone please tell me the answer
Answers
Answer:
30 times three
Step-by-step explanation:
because all the bottom number are multiplying buy three.
Please help!!!!!!!!
Answers
Answer:
He rode 20 miles in 2 hours
⚠️please help!!!⚠️
find the value of x then find the measure of the labeled angle
x°=.......°
(x-35)°=......°
Answers
Step-by-step explanation:
x° + (x - 34)° = 180°. (C-angles)
Thereforr 2x - 34 = 180 and x = 107.
x° = 107°.
(x - 34)° = 73°.