xyx2xy1645256720 2258 484 1,2762873 7842,044 3294 1,0243,008 45141 2,025 6,345 ∑x=143 ∑y=411 ∑x2=4,573 ∑xy=13,393 Which regression equation correctly models the data?y = 2.87x + 0.12y = 2.87x + 11.85y = 3.39x – 14.75y = 3.39x – 9.24
Answers
We are asked to identify the correct regression equation.
The regression equation is given by
[tex]y=bx+a[/tex]Where the coefficients a and b are
[tex]a=\frac{\sum y\cdot\sum x^2-\sum x\cdot\sum xy}{n\cdot\sum x^2-(\sum x)^2}[/tex][tex]b=\frac{n\cdot\sum xy-\sum x\cdot\sum y}{n\cdot\sum x^2-(\sum x)^2}[/tex]Where n is the number of observations that is 5.
Let us substitute the following into the above formula.
∑x=143
∑y=411
∑x^2=4,573
∑xy=13,393
[tex]a=\frac{411\cdot4573-143\cdot13393}{5\cdot4573-(143)^2}=-14.75[/tex][tex]b=\frac{5\cdot13393-143\cdot411}{5\cdot4573-(143)^2}=3.39[/tex]So, the coefficients are
a = -14.75
b = 3.39
Therefore, the correct regression equation is
[tex]y=3.39x-14.75[/tex]Related Questions
The sum of three numbers is140 . The first number is 8 more than the third. The second number is 4 times the third. What are the numbers? First number: Second number: Third number:
Answers
Answer:
x= 30
y= 88
z= 22
Step-by-step explanation:
x= z+8
y= 4z
x + y + z = 140
we substitute to the third equation (z+8) + (4z) + z= 140 so we obtain 6z+8= 140. Z is then equal to 140-8/6= 22.
Then x= 22+8= 30, y=22(4)= 88
30+88+22= 140
Write a cosine function that has a midline of 4, an amplitude of 3 and a period of 8/5
Answers
A cosine function has the form
[tex]y=A\cdot\cos (Bx+C)+D[/tex]Where A is the amplitude, B is 2pi/T, and C is null in this case because the phase is not being specified, and D is the vertical shift (midline).
Using all the given information, we have
[tex]y=3\cdot\cos (\frac{2\pi}{T}x)+4[/tex]Then,
[tex]y=3\cdot\cos (\frac{2\pi}{\frac{8}{5}}x)+4=3\cdot\cos (\frac{10\pi}{8}x)+4=3\cdot\cos (\frac{5\pi}{4}x)+4[/tex]Hence, the function is
[tex]y=3\cos (\frac{5\pi}{4}x)+4[/tex]Please help me I need this done fast I will give brainliest to whoever answers first
Answers
Consider that a standard quadratic equation is given by,
[tex]y=ax^2+bx+c[/tex]The curve passes through the point (-5,0),
[tex]\begin{gathered} 0=a(-5)^2+(-5)b+c \\ 0=25a-5b+c \\ c=-25a+5b\ldots\ldots\ldots(1) \end{gathered}[/tex]The curve passes through the point (3,0),
[tex]\begin{gathered} 0=a(3)^2+(3)b+c \\ 0=9a+3b+c \end{gathered}[/tex]Substitute value from equation (1),
[tex]\begin{gathered} 0=9a+3b+(-25a+5b) \\ 0=-16a+8b \\ b=2a\ldots\ldots\ldots(2) \end{gathered}[/tex]The curve passes through the point (4,9),
[tex]\begin{gathered} 9=a(4)^2+(4)b+c \\ 9=16a+4b+c \end{gathered}[/tex]Substitute tha values from (1) and (2),
[tex]\begin{gathered} 9=16a+4(2a)+(-25a+5(2a)) \\ 9=16a+8a-25a+10a \\ 9=9a \\ a=1 \end{gathered}[/tex]Substitute in equation (2),
[tex]\begin{gathered} b=2(1) \\ b=2 \end{gathered}[/tex]Substitute the values in equation (1),
[tex]\begin{gathered} c=-25(1)+5(2) \\ c=-25+10 \\ c=-15 \end{gathered}[/tex]Substitute the values of a, b, and c, in the standard equation,
[tex]\begin{gathered} y=(1)x^2+(2)x+(-15) \\ y=x^2+2x-15 \end{gathered}[/tex]This is the equation of the given parabola.
Therefore, option B is the correct choice.
14. Given: JM bisects JL JM perpendicular to KLProve: TRIANGLE JMK congruent to TRIANGLE JML
Answers
1) is already written, so we start with the second line.
2)
JM is parallel to KL ----> Given
3) ∠KML = ∠JML ----> They are angles on two perpendicular lines, and Since JM bisects LK, they are equal.
4) ∠KJL=∠MKL ---> Since JM bisects ∠J, the angles KJL and MKL are equal
5) ∠JKM=∠JLM ----> Since 3) and 4), the angles JKM and JLM must also be equal so that the sum of internal angles of each triangle will be 180°
Thus: Triangle JMK is congruent to triangle JML
Caitlyn is 160 centimeters tall. How tall is she in feet and inches, rounded to the nearest inch?
Answers
Answer:
5 ft 3 in.
Explanation:
First, recall the standard conversion rates below.
• 1 foot = 30.48 cm
,• 1 foot = 12 inches
First, convert 160 cm to feet.
[tex]\begin{gathered} \frac{1ft}{30.48\operatorname{cm}}=\frac{x\text{ ft}}{160\text{ cm}} \\ 30.48x=160 \\ x=\frac{160}{30.48} \\ x=5.2493\text{ ft} \\ x=(5+0.2493)\text{ ft} \end{gathered}[/tex]Next, we convert the decimal part (0.2493 ft) of the result above to inches.
[tex]\begin{gathered} 1ft=12\text{ inches} \\ \frac{1\text{ ft}}{12\text{ inches}}=\frac{0.2493\text{ ft}}{y\text{ inches}} \\ y=0.2493\times12 \\ y=2.9916 \\ y\approx3\text{ inches (to the nearest inch)} \end{gathered}[/tex]Therefore, 160 centimeters in feet and inches is:
[tex]5\text{ feet 3 inches}[/tex]-Given that f(x) = 6(x - 1). Choose the correct statement. A. f-1(12) = 3.5 B. f-1(3) = 1 c. f-16) = 3 D. f-1(9) = 2.5
Answers
Given that function is f(x) = 6(x - 1).
Let y = 6(x - 1). Replace x with y and then solve for y.
[tex]\begin{gathered} x=6(y-1) \\ \Rightarrow x=6y-6 \\ \Rightarrow6y=x+6 \\ \Rightarrow y=\frac{x+6}{6} \end{gathered}[/tex]Thus, f^-1(x) = (x + 6)/6.
[tex]f^{-1}(12)=\frac{12+6}{6}=3[/tex][tex]f^{-1}(3)=\frac{3+6}{6}=1.5[/tex][tex]f^{-1}(6)=\frac{6+6}{6}=2[/tex][tex]f^{-1}(9)=\frac{9+6}{6}=2.5[/tex]Thus, option D is correct.
Translate to an equation and solve W divided by 6 is equal to 36 w=
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Answer:
[tex]w\text{ = 216}[/tex]Explanation:
Here, we want to translate it into an equation and solve
W divided by 6 equal to 36:
[tex]\begin{gathered} \frac{w}{6}\text{ = 36} \\ \\ w\text{ = 6}\times36 \\ w\text{ = 216} \end{gathered}[/tex]The next algebra test is worth 100 points and contains 35 problems. Multiple-Choice questions are worth 2 points each and word problems are 7 points each. How many of each type equation are there?
Answers
Let
x ----->number of multiple-choice questions
y ----> number of word problems
so
we have
x+y=35 --------> equation 1
2x+7y=100 -----> equation 2
solve the system of equations
Solve by graphing
using a graphing tool
see the attached figure
therefore
x=29
y=6
number of multiple-choice questions is 29
number of word problems is 6
What are the coordinates of the point on the directed line segment from (−8,−4)(−8,−4) to (−5,8)(−5,8) that partitions the segment into a ratio of 5 to 1?
Answers
The length of the hypotenuse in a 30°-60°-90° triangle is 6√10yd. What is thelength of the long leg?
Answers
In order to calculate the length of the long leg, we can use the sine relation of the 60° angle.
The sine relation is the length of the opposite side to the angle over the length of the hypotenuse.
So we have:
[tex]\begin{gathered} \sin (60\degree)=\frac{x}{6\sqrt[]{10}} \\ \frac{\sqrt[]{3}}{2}=\frac{x}{6\sqrt[]{10}} \\ 2x=6\sqrt[]{30} \\ x=3\sqrt[]{30} \end{gathered}[/tex]So the length of the long leg is 3√30 yd.
If R is between G and Z, GZ = 12in., and RG =3in., then RZ =
Answers
Given R is between G and Z.
GZ=12 inches
RG=3 inches.
Since, R is between G and Z,
[tex]GZ=GR+RZ[/tex]It follows
[tex]\begin{gathered} RZ=GZ-GR \\ =12-3 \\ =9 \end{gathered}[/tex]So, RZ is 9 inches.
explain why 4 x 3/5=12x 1/5
Answers
Answer:
They equal because when you simplify each side, you will arrive at the same answer.
[tex]\begin{gathered} 4\times\frac{3}{5}=\frac{4\times3}{5} \\ =\frac{12}{5} \end{gathered}[/tex]also;
[tex]\begin{gathered} 12\times\frac{1}{5}=\frac{12\times1}{5} \\ =\frac{12}{5} \end{gathered}[/tex]Explanation:
We want to explain why;
[tex]4\times\frac{3}{5}=12\times\frac{1}{5}[/tex]They equal because when you simplify each side, you will arrive at the same answer.
[tex]\begin{gathered} 4\times\frac{3}{5}=\frac{4\times3}{5} \\ =\frac{12}{5} \end{gathered}[/tex]also;
[tex]\begin{gathered} 12\times\frac{1}{5}=\frac{12\times1}{5} \\ =\frac{12}{5} \end{gathered}[/tex]So, they give the same answer when simplified.
Also you can derive one from the other;
[tex]\begin{gathered} 4\times\frac{3}{5}=12\times\frac{1}{5} \\ 4\times3\times\frac{1}{5}=12\times\frac{1}{5} \\ 12\times\frac{1}{5}=12\times\frac{1}{5} \\ \frac{12}{5}=\frac{12}{5} \end{gathered}[/tex]Therefore, both sides are equal.
Write using set-builder notation: -2x + 1 < 27
Answers
Instead of describing the constituents of a set, a set-builder notation describes them. The set-builder notation exists A = {x: x is a natural number less than 27}.
What is meant by set-builder notation?A set can be represented by its elements or the properties that each of its members must meet can be described using set-builder notation.
Set-builder notation is a mathematical notation for defining a set by enumerating its elements or by specifying the properties that each of its members must satisfy. It is used in set theory and its applications to logic, mathematics, and computer science.
Let the given inequality be 2x+1 < 27
Subtract 1 from both sides, we get
-2x+1-1 < 27-1
Simplifying the above equation, we get
-2 x < 26
Multiply both sides by - 1 (reverse the inequality)
(-2 x)(-1) > 26(-1)
Simplifying the above equation, we get
2x > -26
Divide both sides by 2
[tex]$\frac{2 x}{2} > \frac{-26}{2}[/tex]
x > -13
Therefore, the set-builder notation exists
A = {x: x is a natural number less than 27}.
To learn more about set-builder notation refer to:
https://brainly.com/question/14657951
#SPJ13
find the minimum value of the function f(x)=2x2-22x+68 to the nearest hundredth
Answers
Minimum value of the function
[tex]f(x)=2x^2-22x+68[/tex]To calculate the minimum value we will use the derivative.
[tex]\begin{gathered} f^{\prime}(x)=4x-22 \\ 4x-22=0 \\ 4x=22 \\ x=\frac{22}{4} \\ x=5.5 \end{gathered}[/tex]The answer would be 5.5
Solve each system of the equation by elimination method. x+3y=-204x+5y=-38
Answers
Given the equation system:
[tex]\begin{gathered} x+3y=-20 \\ 4x+5y=-38 \end{gathered}[/tex]To solve this system using the elimination method, the first step is to multiply the first equation by 4 so that the leading coefficient is the same, i.e., both equations start with "4x"
[tex]\begin{gathered} 4(x+3y=-20) \\ 4\cdot x+4\cdot3y=4\cdot(-20) \\ 4x+12y=-80 \end{gathered}[/tex]Then subtract the second equation from the first one
From the resulting expression, you can calculate the value of y
[tex]\begin{gathered} 7y=-42 \\ \frac{7y}{7}=-\frac{42}{7} \\ y=-6 \end{gathered}[/tex]Next, you have to substitute the value of y in either the first or second equation to find the value of x:
[tex]\begin{gathered} x+3y=-20 \\ x+3\cdot(-6)=-20 \\ x-18=-20 \\ x=-20+18 \\ x=-2 \end{gathered}[/tex]The solution of the system is (-2,-6)
Kara categorized her spending for this month into four categories: Rent, Food, Fun, and Other. Theamounts she spent in each category are pictured here.Food$333Rent$417Other$500Fun$250What percent of her total spending did she spend on Fun? Answer to the nearest whole percent.
Answers
In this problem we have to calculate the total spences so we add all the costs so:
[tex]\begin{gathered} T=333+417+500+250 \\ T=1500 \end{gathered}[/tex]So 1500 is the 100% so now we can calculate which percentage correspount to 250 so:
[tex]\begin{gathered} 1500\to100 \\ 250\to x \end{gathered}[/tex]so the equation is:
[tex]\begin{gathered} x=\frac{250\cdot100}{1500} \\ x=16.66 \end{gathered}[/tex]So she spend 16.66% in fun
At a carry-out pizza restaurant, an order of 3 slices of pizza, 4 breadsticks, and 2 juice drinks costs $12. A second order of 5 slices of pizza, 2 breadsticks, and 3 juice drinks costs $15. If four breadsticks and a juice drink cost $.30 more than a slice of pizza, write a system that represents these statements. p: slices of pizza b: bread sticks d: juice drinks Choose the correct verbal expressions for problems into a system of equations or inequalities.
Answers
p = slices of pizza
b = bread sticks
d = juice drinks
Equation 1
3p + 4b + 2d = 12
Equation 2
5p + 2b + 3d = 15
Equation 3
4b + 1d = 1p + 0.3
That's all
Julian is decorating the outside of a box in the shape of a right rectangular prism. Thefigure below shows a net for the box.
Answers
The surface area of the box equals the sum of the surface area of each of its parts.
And the area of each rectangle that form the box is found by multiplying the width by the height of that rectangle.
We have two ractangles with sides 7 ft and 10 ft. So the area of each one is:
7 ft * 10 ft = 7 * 10 * ft * ft = 70 ft²
Since there's two of this rectangle, their areas sum up to
2 * 70 ft² = 140 ft²
Now, we also have two rectangles with sides 7 ft and 14 ft (the second and the fourth rectangles from left to right in the image). So, their areas sum up to:
2 * (7 ft * 14 ft) = 2 * (98 ft²) = 196 ft²
Finally, we also have two rectangles with sides 10 ft and 14 ft. Then, their area together is:
2 * (10 ft * 14 ft) = 2 * (140 ft²) = 280 ft²
Therefore the total surface area of the box is the sum:
140 ft² + 196 ft² + 280 ft² = 616 ft²
What is the slope of the line with points (3,7) and (3,-2)
Answers
Answer:
slope = 0
Given:
(3, 7)
(3, -2)
The formula for the slope is solved by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the given, we know that:
x₁ = 3
x₂ = 3
y₁ = 7
y₂ = -2
Substituting these values to the formula, we will get:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{-2-7}{3-3} \\ m=\frac{-9}{0} \\ m=0 \end{gathered}[/tex]Therefore, the slope would be 0.
DataNot ReceivingReceivingFinancial AidFinancial AidUndergraduates422238988120Graduates18797312610Total6101462910730If a student is selected at random, what is theprobability that the student receives aid and is agraduate (rounded to the nearest percent)? [? ]%UniversityTotal
Answers
There are 10730 students total as shown in the bottom right hand corner. So, the probability that the student receives aid and is a graduate is given by:
[tex]P=\frac{1879}{10730}\times100=17.51[/tex]Round to the nearest percent is 17.5%
Answer: 17.5%
Answer:
There are a total of 10730 students and 1879 students who are graduates as well as receiving financial aid. So the probability would be
(1879/10730)*100 = 17.51%
According to the theory of the color yellow + red = orange. If Luisa has x liters of yellow paint and/ 4 liters of red paint. How many liters of orange paint will he get Louise? And if I had 4 liters of yellow paint, could I get exact 5 liters of paint orange?
Answers
Yellow + red = Orange
Yellow paint , x liters
Red paint , 4 liters
a) Because addition applies , adding x liters of Yellow + 4 liters of red and the result is x + 4 liters of orange
b) for second question apply equation
4 • yellow + Red •N = 5
then find N
its possible to obtain 5 liters of paint orange with
2 liters of yellow, 2 liters of red, and adding
0.5 liters of yellow, 0.5 liters of red.
Which of the following could be the points that Jamur plots?
Answers
To solve this problem, we need to calculate the midpoint for the two points in each option and check if it corresponds to the given midpoint (-3,4).
Calculating the midpoint for the two points of option A.
We have the points:
[tex](-1,7)and(2,3)[/tex]We label the coordinates as follows:
[tex]\begin{gathered} x_1=-1 \\ y_1=7 \\ x_2=2 \\ y_2=3 \end{gathered}[/tex]And use the midpoint formula:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Substituting our values:
[tex](\frac{-1_{}+2_{}}{2},\frac{7_{}+3_{}}{2})[/tex]Solving the operations:
[tex](\frac{1_{}}{2},\frac{10_{}}{2})=(\frac{1_{}}{2},5)[/tex]Since the midpoint is not the one given by the problem, this option is not correct.
Calculating the midpoint for the two points of option B.
We have the points:
[tex](-2,6)and(-4,2)[/tex]We follow the same procedure, label the coordinates:
[tex]\begin{gathered} x_1=-2 \\ y_1=6 \\ x_2=-4 \\ y_2=2 \end{gathered}[/tex]And use the midpoint formula:
[tex]\begin{gathered} (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \text{Substituting our values} \\ (\frac{-2-4_{}}{2},\frac{6+2_{}}{2}) \\ \text{Solving the operations:} \\ (\frac{-6}{2},\frac{8}{2}) \\ (-3,4) \end{gathered}[/tex]The midpoint for the two points in option B is (-3,4) which is the midpoint given by the problem.
Answer: B (-2,6) and (-4,2)
can you help me figure out the equation in the drop down menus
Answers
To find:
The piecewise function for the graph.
Solution:
From the graph, it is clear that when x is less than -1, the graph passes through (-1, -3) and (-2, -5).
It is known that the equation of a line passes through two points is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]So, the equation of line passing through (-1, -3) and (-2, -5) is:
[tex]\begin{gathered} y-(-3)=\frac{-5-(-3)}{-2-(-1)}(x-(-1)) \\ y+3=\frac{-2}{-1}(x+1) \\ y+3=2x+2 \\ y=2x-1 \end{gathered}[/tex]So, the first drop down is "2x - 1", and second drop down is "x is less than or equal to -1".
Now, the graph passes through (1, 5) and (2, 6). So, the equation of the line is:
[tex]\begin{gathered} y-5=\frac{6-5}{2-1}(x-1) \\ y-5=x-1 \\ y=x+4 \end{gathered}[/tex]So, the third drop down menu is "x + 4" and the fourth drop down menu is "x is greater than or equal to 1".
A rectangular parking lot has length that is 3 yards less than twice its width. If the area of the land is 299 square yards, what are the dimensions of the land?The parking lot has a width of square yards.
Answers
Answer:
• Width = 13 yards
,• Length = 23 yards
Explanation:
Let the width of the parking lot = w yards.
The length is 3 yards less than twice its width.
[tex]\implies\text{Length}=(2w-3)\text{ yards}[/tex]The area of the land = 299 square yards.
[tex]w(2w-3)=299[/tex]We then solve the equation above for w.
[tex]\begin{gathered} 2w^2-3w=299 \\ \implies2w^2-3w-299=0 \end{gathered}[/tex]Factor the resulting quadratic expression.
[tex]\begin{gathered} 2w^2-26w+23w-299=0 \\ 2w(w-13)+23(w-13)=0 \\ (2w+23)(w-13)=0 \end{gathered}[/tex]Solve for w.
[tex]\begin{gathered} 2w+23=0\text{ or }w-13=0 \\ 2w=-23\text{ or }w=13 \\ w\neq-\frac{23}{2},w=13 \end{gathered}[/tex]Since w cannot be negative, the parking lot has a width of 13 yards.
Finally, find the length of the parking lot.
[tex]\begin{gathered} 13l=299 \\ l=\frac{299}{13}=23\text{ yards} \end{gathered}[/tex]The length of the parking lot is 23 yards.
find the distance between the given points. if the answer is not exact, use a calculator and give an approximation to the nearest tenth (-7,-2), (5,3)
Answers
The distance is:
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]By replacing x and y
[tex]d=\sqrt[]{(5-(-7))^2+(3-(-2))^2}[/tex]Then solve
[tex]\begin{gathered} d=\sqrt[]{(5+7)^2+(3+2)^2} \\ d=\sqrt[]{12^2+5^2} \\ d=\sqrt[]{144+25}^{} \\ d=\sqrt[]{169} \\ d=13 \end{gathered}[/tex]Answer: 13
using the converse of the same-side interior angles postulate what equation shows that g∥h
Answers
Answer: [tex]\angle 2+\angle 4=180^{\circ}[/tex] or [tex]\angle 1+\angle 3=180^{\circ}[/tex]
Given that line S and line T are parallel, and line R is a transversal that cuts through lines S and T, which angles are alternate interior anglesZА A
Answers
The alternate interior angles theorem states that, when two parallel lines are cut by a transversal, the resulting alternate inferior angles are congruent.
In this case:
Blossom's Computer Repair Shop started the year with total assets of $318000 and total liabilities of $211000. During the year, the
business recorded $505000 in computer repair revenues, $311000 in expenses, and Blossom paid dividends of $50200. Stockholders'
equity at the end of the year was
Answers
Ur welcome
HELP ASAP!!!
Find the square of 1-4i.
Answers
ANSAWER:
−15+8i
Explanation:
First, you can expand the square of the bynomial:
Round 7488 to the nearest thousand
Answers
The thousand place value is the 4th digit to the left of the decimal point. This means that the digit is 7.
If the first digit after 7 is greater than or equal to 5, 7 would increase by 1. If it is less than 5, 7 remains the same. Since 4 is less than 5, 7 remains. The rest digits turns to 0. Thus, the answer is
7000