Answer: (a) y = 2.7394x - 118.1368
(b) R² = 0.8215 or 82.15%
Step-by-step explanation: Regression line is the best line that relates the variables in the data.
To calculate the fitted regression equation:
1) Calculate average of x-values ([tex]x_{i}[/tex]) and average of y-values ([tex]y_{i}[/tex]);
2) Calculate the slope, b, by doing:
[tex]b=\frac{\Sigma (x-x_{i})(y-y_{i})}{\Sigma (x-x_{i})^{2}}[/tex]
3) Calculate y-intercept, a, by doing:
[tex]a=y_{i}-bx_{i}[/tex]
4) Then, it gives regression equation: y = bx + a
For the data on chemical reactions:
(a) [tex]b=\frac{ [(136.24-105.3955)+...+(86.18-105.3955)].[(234.5-170.58)+...+(106-170.58)]}{(136.24-105.3955)^{2}+...+(86.18-105.3955)^{2}}[/tex]
b = 2.7394
[tex]a=170.58-2.7394(105.3955)[/tex]
a = -118.1368
y = 2.7394x - 118.1368
The fittest regression equation is y = 2.7394x - 118.1368.
(b) R is correlation coefficient and measures the strength of the relationship between the variables. It is calculated as:
[tex]R=\frac{n\Sigma(xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^{2}-(\Sigma x^{2})][n\Sigma y^{2}-(\Sigmay^{2})]} }[/tex]
For this fit, R = 0.9064
The variable R² is the coefficient of determination, is the square of correlation coefficient and is usually stated as a percent.
What the variable represents is the percent of variation in the dependent variable (y) explained by the variation in the independent variable (x).
For this fit:
[tex]R^{2} = 0.9064^{2}[/tex]
[tex]R^{2} =[/tex] 0.8215
What it entails is that 82.15% of the variation of retention time is due to the molecular weight of each chemical compound.
I need help with this question plz thx
Answer:
[tex]7x^2 - 3y + 9[/tex]
Step-by-step explanation:
Hey there!
Well to solve the given,
2y - y + 7 - 1 + 3 + 7x^2 - 4y
We need to combine like terms
[tex]2y - y + 7 - 1 + 3 + 7x^2 - 4y\\7x^2 - 3y + 9\\[/tex]
Hope this helps :)
Answer:
7x^2 - 3y + 9
Step-by-step explanation:
2y - y + 7 - 1 + 3 + 7x^2 - 4y [Combine like terms]
= (2y - y - 4y) + (7- 1 + 3) + 7x^2
= -3y + 9 + 7x^2 [Order the terms from most exponents to least]
= 7x^2 - 3y + 9
Which of the following is an integer?
O 9.1
0-6
0 -2.3
-O
Answer:
The answer is -6
Step-by-step explanation:
. A system consists of three subsystems in parallel. Subsystem A has a reliability of 0.98, subsystem B has a reliability of 0.85, and subsystem C has a reliability of 0.88. Calculate the overall system reliability.
Answer:
[tex]P(System) = 0.73304[/tex]
Step-by-step explanation:
Given
Reliability of:
A = 0.98
B = 0.85
C = 0.88
Required
Determine the overall reliability
The overall system reliability is calculated by multiplying the individual reliability of each subsystems;
i.e.
[tex]P(System) = P(A) * P(B) * P(C)[/tex]
[tex]P(System) = 0.98 * 0.85 * 0.88[/tex]
[tex]P(System) = 0.73304[/tex]
Hence, the overall reliability is 0.73304
Can someone please help?
Answer:
I answered the 1st one on your other post
2nd: 1/8
3rd: I don't know anything about inchwe study in cm so I don't know the answer
Step-by-step explanation:
we throw a coin. it has 2 probabilities: heads or tails
each probability is 1/2
1st throw 1/2
2nd throw 1/2
3rd throw 1/2
as all these throws are independent from one another, we put × between them. so: 1/2 ×1/2 ×1/2= 1/8
Tyler wants to calculate his grade in his accounting class. His test grades are a 77%, 62% 85%, 80%. What is his average in the class?
Answer:
76%Step-by-step explanation:
Given Tyler test grades to be 77%, 62% 85% and 80%, to find its average in the class, we will find the mean of his grades.
Mean is the ratio of the sum of the grades to the total number of grades given.
[tex]mean (\overline x) = \frac{\sum Xi}{N}[/tex]
Xi are the individual grades
N is the total number of grades = 4
[tex]\overline x = \dfrac{77+62+85+80}{4} \\\overline x = \frac{304}{4}\\ \overline x = 76 % \\[/tex]
Hence his average in the class is 76%
the chef has eight blocks of butter. she cuts the butter into fourths. how many slices of butter does the chef have now
Answer:
32 Blocks of Butter
Explanation:
Since the chef is starting with 8, and I'm guessing they are cutting all the blocks of butter into fourths; this is a multiplication equation. 8×4=32
Answer:
[tex]\huge\boxed{32\ blocks\ of\ butter}[/tex]
Step-by-step explanation:
The chef had = 8 blocks
She cuts/ divides the blocks into fourths.
The chef has now:
=> [tex]8 / \frac{1}{4}[/tex]
=> [tex]8 * 4[/tex]
=> 32 blocks of butter
Need help plzzz anyone
Answer:
A) √61
Step-by-step explanation:
a²+b²=c²
(4-(-2))²+(5-0)²=c²
6²+5²=c²
36+25=c²
61=c²
c=√61
For each of the following examples, solve the given problem and write your answer in scientific notation using the proper number of significant figures. Make sure to include all units in your final answers.
The distance from the Earth to the Sun is a measure of distance called the Astronomical Unit (AU). Given: 1.000 AU = 1.496108 km:
a. convert Uranus’ distance of 19.1903 AU to kilometers (km) =
b. convert the distance to the center of the Milky Way galaxy of 2.6x1017 km to AU =
Answer:
the answer is pythagoras thorium
(1) Determine whether the relation R on the set of all integers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ∈ R if and only if (a) x − y = 0 (b) x = |y| (c) x + y is odd (2) Which, if any, of the relations from the previous two problems is an equivalence relation?
Answer:
Step-by-step explanation:
1)
a) x-y = 0
Reflexive :
x-x=0, where x and 0 are whole numbers is valid for all x
In this way, x-x is a number
Which infers that (x,x) ∈ R
In this way, R is reflexive
Symmetric :-
(x-y) is a whole number
Which infers - (x-y) is likewise a whole number
Which infers (y-x) is a number
In this way, (x-y) is a number infers that (y-x) is likewise a whole number
i.e If (x,y)∈R at that point (y,x)∈R
In this way, R is Symmetric.
Against Symmetric:-
(x,y)∈R
x-y=0, where x and y are whole numbers
Which infers x=y
Assume, (y,x)∈R
y-x=0, where x and y are whole numbers
Which infers y=x
Consequently, (x-y) is a whole number suggests (y-x) is additionally a whole number
for example In the event that (x,y)∈R at that point (y,x)∈R, where x=y
R is Anti-Symmetric.
Transitive:-
Given,
(x-y)∈R and (y-z)∈R - (I)
To demonstrate that,
(x,z)∈R
from (I)
x-y= 0 and y-z=0
Including both, we get
(x-y)+(y-z)=0
x-z=0
Consequently demonstrated that (x,y)∈R and (y,z)∈R infers that (x,z)∈R
Since the above connection is symmetric, reflexive advertisement transitive. Consequently, it is an identicalness connection.
b) x=|y|
Reflexive:-
x isn't reflexive.
Since for - 2
- 2 ≠|-2|, where - 2 is a whole number.
- 2≠|2|
Consequently, (x,x) isn't Reflexive.
Symmetric:-
(x,y)∈R, infers
x=|y|, where x and y are whole numbers ...(i)
Let x =-2 and y= - 2
- 2≠|-2|
- 2≠|2|
Which infers (x,y) itself doesn't have a place with R.
Consequently R isn't symmetric.
Against Symmetric:-
(x,y)∈R, suggests
x=|y|, where x and y are numbers
let x= - 2 and y =-2
- 2 ≠ |-2|
- 2≠|2|
R isn't hostile to symmetric.
Transitive:-
x=|y| and y=|z| ∈ R
let x=2, y=-2 and z= 2
infers that
2=|-2| and - 2≠|2|
for example 2=|2| and - 2∉|2|
In this way, R isn't transitive.
c) x+y is odd
Reflexive:-
x+x is even, where x is a whole number.
In this way, (x,x)∉R.
R isn't Reflexive.
Symmetric:-
(x,y)∈R
x+y is odd, where x and y are whole numbers
Additionally, (y,x) is odd
infers that y+x is additionally odd
In this way, (y,x)∈R
R is Symmetric.
Against Symmetric:-
(x,y)∈R
infers x+y is odd, where x and y are whole numbers
infers that y+x is additionally odd
In this way, (y,x)∈R
R is Anti-Symmetric.
Transitive:-
Given,
(x,y)∈R and (y,z)∈R, where x,y and z are whole numbers ...(i)
To demonstrate that
(x,z)∈ R
from (I)
x+y is odd and y+z is odd''
Including both we get
x+2y+z is odd
which infers (x,z)∉R
In this way, R isn't transitive.
2) x-y=0 is reflexive, symmetric and transitive in this way it is an equality connection.
while x=|y| and x+y is odd are not equality relations.
Ready Maid Service charges $25.00 per house, plus an additional $22.00 per hour, h. What
is the constant in this situation?
Answer:
$25 per house.
Step-by-step explanation:
h, is the variable in this sitution. Quite literally this means that # of hours is the only value that will CHANGE/be variable. Since $25 has no variable assigned with it, it will be constant.
Combine like terms:
-3x^3+1+4x^3-3y^3-1+5x^3-7−3x3+1+4x3−3y3−1+5x3−7
Answer:
12[tex]x^{3}[/tex] - 6[tex]y^{3}[/tex] - 14
Manuel buys 7.9 pounds of strawberries. Each pound costs $3.89. Which expression gives the best estimate of the cost of the strawberries?
Answer:
x= 3.89 x 7.9
Step-by-step explanation:
x= 3.89 x 7.9
x=30.731
Answer: (8)($4)
Answer with an explanation:
What we need to know: Any number 5 or higher is automatically rounded up, any number 4 or lower is automatically round down. Also if the number is after the decimal you can say 5 or higher with a zero because it doesnt do anything to the number, so you could say .50 or higher or .40 or lower and if it has three decimal places just add another zero so it would be .500 higher or .400 lower.
So, 7.9 is rounded up to 8.0 because 9 is 5 or higher.
$3.89 is rounded up to $4.00 because .89 is higher than .50.
Now just take off the zeros from 8.0 and $4.00 to get (8)($4)
Hope this helps.
btw my hands are numb from answering all the questions I have answered today so brainliest would be appreciated. :))
1.Square roots are the ____ of perfect squares.
5. Tia invests $2,500 at an interest rate of 4%, compounded quarterly. How much is the investment worth at the end of 5 years? Look at the concept summary if you forgot the formula for compound interest.
Answer:
$3050.48
Step-by-step explanation:
If 4% is compounded quarterly, that means it's 1% every quarter. since we have 5 years, that's 1.01^20, which is approx. 1.2202. We multiply this by the orignal $2500, so our investment at the end of 5 years is $3050.48 (rounded to nearest cent)
The amount of money that Tia's investment would be worth at the end of 5 years is equal to $3050.5.
Given the following data:
Principal = $2,500Interest rate = 4% = 0.04Time = 5 yearsNumber of times = 4To determine how much is the investment worth at the end of 5 years:
Mathematically, compound interest is given by the formula:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where;
A is the future value.P is the principal (starting amount).r is annual interest rate.n is the number of times the interest is compounded in a year.t is the number of years for the compound interest.Substituting the given parameters into the formula, we have;
[tex]A = 2500(1 + \frac{0.04}{4})^{4\times 5}\\\\A = 2500(1 +0.01)^{20}\\\\A = 2500(1.01)^{20}\\\\A = 2500(1.2202)[/tex]
Future value, A = $3050.5
Read more: https://brainly.com/question/22339845
solve 6(x-2) ^2 + 7 = 223
Answer:
x = 8 or -4
Step-by-step explanation:
6(x - 2)² + 7 = 223
PEMDAS
expand (x - 2)² first using FOIL
(x - 2)(x - 2)
x² - 2x - 2x + 4
x² - 4x + 4
rewrite equation
6(x² - 4x + 4) + 7 = 223
distribute the 6 through the parentheses
6x² - 24x + 24
rewrite equation
6x² - 24x + 24 + 7 = 223
combine like terms
6x² - 24x + 31 = 223
subtract both sides by 223
6x² - 24x - 192 = 0
divide both sides by 6
x² - 4x - 32 = 0
factor with factoring X
x² - 8x + 4x - 32 = 0
factor by grouping
(x² - 8x) + (4x - 32) = 0
x(x - 8) +4 (x - 8) = 0
(x - 8)(x + 4) = 0
x = 8 or -4
20. How does the graph of
g(x) = 2x + 3 differ from the
graph of f(x) = 2x?
A It is moved up 3 units.
B It is moved down 3 units.
C It is moved right 3 units.
D It is moved left 3 units.
Answer:
A. It is moved up 3 units
Step-by-step explanation:
The 3 in 2x+3 tells you that the line is moved up 3 units
Nadia says the hypotenuse of this right triangle has a length of 73 because the Pythagorean theorem states that
(28+45) -73
GOS
28
45
Which best describes Nadia's solution?
Answer:28
Step-by-step explanation:
Answer:
C. She is incorrect because she should have squared each leg length and then found the sum.
Step-by-step explanation:
A piece of rope is 33 1/3 yards long and was cut into equal pieces. How many yards was each piece?
Answer:
11 ¹/₉ yardsStep-by-step explanation:
You didn't say how many pieces. My answer is for 3 equal pieces.[tex]33\frac13\div3=(33+\frac13)\div3=33\div3+\frac13\div3=11+\frac13\times\frac13=11+\frac19=11\frac19[/tex]
For two it would be:
[tex]33\frac13\div2=(33+\frac13)\div2=33\div2+\frac13\div2=16\frac12+\frac13\times\frac12=\\\\=16\frac36+\frac16=16\frac46=16\frac23[/tex]
What is 5 8/12 as a mixed number in its simplest form
Answer:
5 2/3
Step-by-step explanation:
Just keep simplifying 8/12 until you end up with 2/3
Find the GCF of both the numerator and denominator and you end up with 2/3
Just to make it clear 8/12 = 2/3
If two points that are coplanar are also _________________.
Answer:
If two points that are coplanar are also __ collinear
Solve the inequality. Negative 3 x + 6 greater-than negative 2
Answer:
[tex]x < 2 \frac{2}{3} [/tex]
Step-by-step explanation:
The symbol for greater than is '>'.
-3x +6 > -2
Bring constants to one side:
-3x > -6 -2
Simplify:
-3x > -8
Divide both sides by -1, change sign:
3x < 8
Divide by 3 on both sides:
[tex]x < \frac{8}{3} \\ x < 2 \frac{2}{3} [/tex]
Answer:
it is a
Step-by-step explanation:
just got it right
John has a box of nails. The box contains 65 small nails, 40 medium nails, and 45 large nails. Susan has a box of nails that has the same
proportion of small, medium, and large nails as John's box. There are 176 medium nails in Susan's box.
What is the total number of nails in Susan's box? Enter the answer in the box
Answer:
Susan has a total of 660 nails
Step-by-step explanation:
John box contains 65 small nails, 40 medium nails, and 45 large nails.
The proportion of John nails is
65/5:40/5:45/5
13:8:9
Total = 30
If Susan has 176 medium nails and same proportion to John's nails
8/30(x) = 176
Where x is the total number of nails for Susan box
X= (176*30)/8
X= 22*30
X= 660 nails
Susan has a total of 660 nails
Solve for x with work
Answer:
47 degrees
Step-by-step explanation:
The two angles shown are "vertical angles" and thus are equal.
Thus, 2x + 3 = x + 50
Combining like terms, we get:
x = 47 degrees
solve for x with work
Can you please help me with this I’ll give you a playlist for sure
Answer:
Option A
Step-by-step explanation:
Margot preformed a refection. A reflection is a rigid transformation.
A rigid transformation does not change the size nor the shape of the figure. Rigid transformations only change the position of the shape.
The parallel lines stay 4 centimetres apart after the transformation.
Hope this helps.
3/5(4.3 – 7.8) + 2 1/9 ?
Answer:
0.01
Step-by-step explanation:
Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the
length of the run 20 feet. She writes and solves the equation 21+ 2W - 62 to find the width of the run.
Which statements are true of the solution? Check all that apply.
The value of w is 10 feet.
The value of w can be zero.
The value of w cannot be a negative number.
O Substitution is used to replace the variable l with a value of 20.
The subtraction property of equality is used to isolate the term with the variable w.
Answer:The value of w cannot be a negative number, substitution is used to replace the variable L with a value of 20, the subtraction property of equality is used to isolate the term with the variable w.
Step-by-step explanation:
Answer:
C, D, and E
Step-by-step explanation:
Just checked it and got 100on edge
A concession stand at a baseball game sells 3 apples for $2.00. How can you find the cost for 10 apples? A. x=320 B. x=302 C. x=203 D. x=230
Step-by-step explanation:
In order to solve this question we use ratio and proportion
From the question
3 apples were sold for $2.00
Then
10 apples will be sold for what
That's
[tex] \frac{10 \times 2}{3} \\ = \frac{20}{3} [/tex]Hope this helps you
M(8,3) is the midpoint between the points A(4,5) and B. Find the coordinates of B.
Answer:
(12,-1)
Step-by-step explanation:
Let the coordinates of v to be x and y
(4+x)/2=8
4+x=16
X=12
(5+y)/2=3
5+y=2×3
5+y=6
Y=-1
B(12,-1)
I'll give you brainliest if you answer! All I need is help with number 15!
Answer:
120 minutes
Step-by-step explanation:
The lowest number that all three trains times can evenly go into is 120. 60 is not divisible by 8, but 120 is. So is 12 and 10, so 120.