When the length of the crowbar is 120 cm, the force needed is 1.8 N, based on the assumption of a linear relationship between length and force.
From the given information, we have a data point that relates the length of the crowbar to the force needed. When the length is 80 cm, the force needed is 1.5 N. To find the force needed when the length is 120 cm, we can use the concept of proportionality. Since the relationship between length and force is not specified further, we assume a linear relationship. This means that the force needed is directly proportional to the length of the crowbar.
Using the given data point, we can set up a proportion:
80 cm / 1.5 N = 120 cm / x N
Solving for x, we can cross-multiply and get:
80 cm * x N = 1.5 N * 120 cm
x = (1.5 N * 120 cm) / 80 cm
x = 1.8 N
Therefore, when the length of the crowbar is 120 cm, the force needed is 1.8 N, based on the assumption of a linear relationship between length and force.
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I'm not sure what theorem to use for this question
The statement that <A > <C and <B > <D has been proved
How to prove that <A > <C and <B > <D?In geometry, the side length opposite the largest angle is the longest side.
Similarly, the side length opposite the smallest angle is the shortest side.
From the given figure of quadrilateral, we have the following sides in increasing order:
Side length ABSide length BCSide length ADSide length CDThe angles opposite the side lengths are:
Angle DAngle BAngle CAngle AThis means that:
<A > <C and <B > <D
Hence, the statement that <A > <C and <B > <D has been proved
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how many cards from a standard deck must be drawn to guarantee atleast 3 cards of the same suit have been drawn, pidgeon hole
The number of cards which must be drawn from the standard deck is 12.
Given a standard deck of cards.
We have to find the number of cards to be drawn so that we will get atleast 3 cards from each suit. Because they have used atleast in the question so the cards can be more also so we have to reach at minimum level of cards to be drawn to guarantee atleast 3 cards of the same suit.
Number of suits in a standard deck= 4 (Clubs, Hearts, Diamond, Spades)
Cards in 1 suit=13
We need atleast 3 cards of the same suit so we need atleast 3*4=12 cards. (3 from each suit)
Hence the minimum cards which must be drawn to get atleast 3 cards of the same suit is 12.
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Suppose . has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if or if and . Also, determine whether the critical point a local maximum, a local minimim, or a saddle point.
The points are (0,0) Minimum and (1/6, 1/18) is the saddle point.
What is the saddle point?
A saddle point, also known as a minimax point, is a place on the surface of a function's graph where the slopes in orthogonal directions are all zero but the function does not have a local extremum.To solve the question we have:
f(x,y) = xy(1-2x-6y)
Therefore, f(x,y) = xy-2x²y-6xy²
Finding the partial derivative of the above gives:
fₓ = y - 4xy-6y²
= x - 2x²-12xy
Therefore, when the above equations are set to 0 we get:
y - 4xy-6y² = 0.......(1)
x - 2x²-12xy = 0......(2)
Dividing equations (1) and (2) by y and x respectively give:
1 - 4x - 6y = 0
1 - 2x - 12y = 0
Solving gives:
x = 0.167 = 1/6
y = 0.056 = 1/18
When we place x in equation (1) we have:
y - 4(1/6)y-6y² = 0
y = 0 or y = 1/18
Similarly, x = 0 or 1/6
Therefore, the four critical points are:
(0,0) (1/6,1/18)
When x = 0 and y = 0
f(x,y) = 0 Hence this is a minimum
When x = 1/6 and y = 1/18
f (x,y) = 1/324 Which is a saddle point.
Therefore, the points are (0,0) Minimum, and (1/6, 1/18) is the saddle point.
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The question you are looking for is here:
(1 point) The function f(x,y)=xy(1−2x−6y) has 4 critical points. List them and select the type of critical point. Points should be entered as ordered pairs and listed in increasing lexicographic order. By that, we mean that (x,y) comes before (z,w) if x
find area and perimeter show your work
Answer:
A= 16
P=16
Step-by-step explanation:
A=h^bxb/ 2
P= side+base+side
What is the radius for a circle whose equation is x² + y² = 16?
OA. 4
OB. 16
C. 8
OD. 256
Answer:The radius is √16.
Step-by-step explanation:
Write the equation for a parabola with a focus at (7,2) and a directrix at y = -2 y = ?
Equation of the parabola is [tex]y=\frac{1}{8} (x-7)^2[/tex] with a focus at [tex](7,2)[/tex] and a directrix at [tex]y=-2[/tex]
How to find the equation of parabola with focus and directrix ?
We know that focus of the parabola [tex](h,k+p)=(7,2)[/tex]
So [tex]k+p=2[/tex]......(a)
And directrix of the parabola
[tex]y=k-p\\=-2[/tex]
[tex]k-p=-2[/tex]........(b)
So add the equation (a) AND (b)
[tex]k+p=2\\k-p=-2\\------------\\2k=0\\k=0\\p=2[/tex]
Equation of the parabola with directrix and focus
[tex]y-k=\frac{1}{4p} (x-h)^2[/tex]
Substitute all the values
[tex]y-0=\frac{1}{4(2)} (x-7)^2\\y=\frac{1}{8} (x-7)^2[/tex]
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What value(s) of x will make x²=81 true?
Answer: 9,-9
Step-by-step explanation:
Answer: 9
Step-by-step explanation:
9x9=81
There is a total of 32 cubic centimeters of a liquid in two beakers. one of these beakers contains 15 cubic centimeters of the liquid. how much liquid does the other beaker contain? a. 13 cc b. 15 cc c. 16 cc d. 17 cc
The correct option is (d).
The other beaker contains 17 cc (cubic centimetres) of the liquid.
What is cubic centimetres of liquid mean?The volume of a cube with dimensions of 1 cm ×1 cm× 1 cm is equal to one cubic centimetre (or cubic centimetre in US English) (SI unit symbol: cm³; non-SI abbreviations: cc and ccm). A millilitre's volume is equal to one cubic centimetre.
According to the question,
The total liquid is 32 in cubic centimetres which is stored in the two beakers.
In the first beaker the liquid stored is 15 cubic centimetres.
The second beaker will contain the liquid = total liquid stored in both beakers - liquid stored in the first beaker.
Liquid in second beaker = 32 - 15
= 17
Therefore, the liquid stored in the second beaker is 17 cc (cubic centimetres).
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The length of a rectangle is 4 times the width. If the perimeter is to be less than or equal to 100 meters. What are the possible values for the width
The possible values for the width is w≥10.
Given that the length of a rectangle is 4 times the width and perimeter is to be less than or equal to 100 meters.
The perimeter of a rectangle is the total distance of its four outer boundaries. The perimeter of the object is twice the length and width of the object. This calculation is made using the formula:
perimeter = 2(length + width).
Here Perimeter=100 and length=4w
Substituting these values in the formula to find width, and we get
100≤2(4w+w)
100≤2(5w)
Divide both sides by 2, and we get
100/2≤(2(5w))/2
50≤5w
Divide both sides by 5, and we get
50/5≤5w/5
10≤w
Hence, the possible value for width when the length of a rectangle is 4 times the width is w≥10.
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The diameter of a semicircle is 26 meters. What is the semicircle's perimeter? Use 3.14 for .
The perimeter of the semicircle is 66. 846 meters
How to find the perimeterThe formula for finding the perimeter of a semicircle is
Perimeter = πr + 2r
We were given diameter = 26meters
Radius, r = diameter/2
radius = 26/ 2 = 13 meters
π = 3. 142
Substitute value into the formula
Perimeter = 3. 142 × 13 + 2 × 13
Perimeter = 40. 846 + 26
Perimeter = 66. 846 meters
Thus, the perimeter of the semicircle is 66. 846 meters
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please help me 20 points
Out of 2000 pizzas he sells next time he should expect 797 stuffed crust or pan style. This can be obtained by using formula of probability and multiplying the total number of pizzas.
Find the expected value:The formula for Expected value:
EV = P(X) × n
where EV is the expected value and P(X) is the probability of X and n is the total number.
In the question it is given that,
Thin crust ⇒ number of thin crust sold = 307 Thick crust ⇒ number of thick crust sold = 224Stuffed crust ⇒ number of stuffed crust sold = 161Pan style ⇒ number of pan style sold = 191First we have to find the probability of stuffed crust or pan style,
P( stuffed crust or pan style) = P(stuffed crust) + P(pan style)
The number of stuffed crust and pan style = 161 + 191 = 352
The total number of crusts sold are ⇒ 307 + 224 + 161 + 191 = 883
⇒ P( stuffed crust or pan style) = 161/883 + 191/883
= 352/883
The expected value of stuffed crust or pan style,
n = 2000, P(X) = 352/883
EV = P(X) × n = (352/883) × 2000 = 797.28 ≈ 797
Hence out of 2000 pizzas he sells next time he should expect 797 stuffed crust or pan style.
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A train leaves Geneva at 09:10 and arrives at Verona at 14:10 the distance from Geneva to Verona is 390 km calculate the average speed of the train in km/h
What is f[g(7)] for the following functions?
f(x) = 3x2 − 4
g(x) = 2x − 5
f[g(7)] = 9
f[g(7)] = 143
f[g(7)] = 239
f[g(7)] =281
Answer: 239
Step-by-step explanation:
[tex]g(7)=2(7)-5=9\\\\f[g(7)]=f(9)=3(9)^2 - 4=239[/tex]
A rectangular paperboard measuring 20 invhes long and 15 inches wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for pie, and do not round your answer. Be sure to include the correct unit in your answer.)
The perimeter of the rectangle is 70 Inches square
How to determine the perimeterThe formula for perimeter of a rectangle is given as;
Perimeter = 2 ( l + w)
length = 20 inches
width = 15 inches
Perimeter = 2 ( 20 + 15 )
Perimeter = 2 ( 35)
Perimeter = 70 Inches square
Thus, the perimeter of the rectangle is 70 Inches square
Note that it is a general knowledge on the given question.
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Describe the difference between plots that show a strong correlation and plots that show a weak correlation.
We need to find the difference between plots that show a strong correlation and plots that show a weak correlation.
The point of creating a scatter plot is to determine if there is a correlation. Correlation means the relationship between two quantities. For example, there is a correlation between how much a person studies and the grade they get on a test, but there is no correlation between how much money a person earns and what pets they own. In mathematics, correlation between data means that the points follow a pattern and go in the same direction. There are two types of correlation:
Positive: the trend is rising from left to right
Negative: the trend is decreasing from left to right
If the dots on the scatter plot do not follow a pattern, there is no correlation.
All correlations have two properties: strength and direction. The strength of the correlation is determined by its numerical value. The direction of the correlation is determined by whether the correlation is positive or negative.
The strength of the correlation indicates how strong the relationship is between the two variables. The strength is determined by the numerical value of the correlation. A correlation of 1, whether +1 or -1, is a perfect correlation. In perfect correlations, the data points lie directly on the fit line. The further the data is from the fit line, the weaker the correlation. A correlation of 0 means there is no correlation
If the value of correlation coefficient is nearer to to 1 or -1 , then there exist a strong correlation.
If the value of correlation coefficient is nearer to to 0 , then there exist a weak correlation.
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The data points are a little closer for a weak correlation, and you can see that there is some sort of relationship between these factors.
Data points for a strong correlation are in close proximity to one another, making it possible to build a line by imitating their pattern.
A statistic called correlation gauges how much two variables change in connection to one another.
Correlation and diversification, the idea that certain types of risk can be reduced by investing in assets that are not connected, are closely related concepts.
Correlation cannot determine whether x causes y or vice versa, or whether a third component is responsible for the association.
A scatter plot may make it easier to spot correlation, particularly when the variables have a non-linear but nevertheless significant association.
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Mario is 63 years older than his grandson Jonas. How many years ago was Mario's age 10 times Jonas's age if Mario's age is currently four times Jonas's age?
Answer:
14 years ago
Explanation:
Let Mario's age be m, Jonas age be j.
From, Mario is 63 years older than Jonas
Equation 1: m = j + 63
From, Mario's age is four times Jonas age
Equation 2: m = 4j
Solve them by substitution:
m = j + 63
4j = j + 63
4j - j = 63
3j = 63
j = 21
Find Mario's age:
m = j + 63
m = 21 + 63
m = 84
Follow this steps:
m - y = 10(j - y)
84 - y = 10(21 - y)
84 - y = 210 - 10y
-y + 10y = 210 - 84
9y = 126
y = 14
The answer is 14 years ago.
Let Mario's age be M, and Jonas' age be J.
The formed equations :
M = J + 63M = 4JTo find their current ages, substitute the 2nd equation in the 1st equation.
4J = J + 63
3J = 63
J = 21
M = 4(21)
M = 84
For Mario to be 10 times Jonas' age, he has to be an age that is a multiple of 10.
Case (1) : Mario's age = 80
Subtract 4 from both their ages.
Mario : 84 - 4 = 80
Jonas : 21 - 4 = 17
17 × 10 ≠ 80
Case (2) : Mario's age = 70
Subtract 14 from both their ages.
Mario : 84 - 14 = 70
Jonas : 21 - 14 = 7
7 × 10 = 70
What are the coordinates of the terminal point corresponding to 0=-120?
Using the unit circle, the coordinates of the terminal point corresponding to [tex]\theta = 120^\circ[/tex] is: (-0.5, 0.866).
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
In this problem, the angle is of [tex]\theta = 120^\circ[/tex], hence:
[tex]\cos{\theta} = \cos{120^\circ} = -0.5[/tex].[tex]\sin{\theta} = \sin{120^\circ} = 0.866[/tex].Hence the terminal point is:
(-0.5, 0.866).
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Find the surface area of the prism. Round to the nearest tenth if necessary.
The surface area of the prism according to the segment labels is; 480mm².
What is the surface area of the prism?The prism given in the task content is five-faced and hence, its surface area can be evaluated as follows;
Surface area = 2(0.5×15×8)+(15×9)+(8×9) + (17×9).
Hence, the surface area of the prism upon evaluation is; 480mm².
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Question 6 of 20
What is the common difference between consecutive terms in the following
arithmetic sequence?
51, 47, 43, 39, ...
OA. 3
B. -3
O C. -4
D. 4
Common difference formula
[tex]\boxed{\sf d=t_2-t_1}[/tex]
So
Here
[tex]\\ \tt{:}\longrightarrow d=47-51[/tex]
[tex]\\ \tt{:}\longrightarrow d=-4[/tex]
Option C
Answer:
C. -4
Step-by-step explanation:
Given sequence: 51, 47, 43, 39, ...
To find the common difference (d) between consecutive terms in an arithmetic sequence, subtract the previous term from the next term:
[tex]\implies \sf d=47-51=-4[/tex]
[tex]\implies \sf d=43-47=-4[/tex]
[tex]\implies \sf d=39-43=-4[/tex]
Therefore, the common difference for the given arithmetic sequence is -4.
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i need help please! I think I know the answer but for some reason my brain's telling me that it's wrong so if someone could explain how to get the answer so I can check that would be great.
Considering the slopes of the segments, the correct option is:
D. No, because the triangle ABC doesn't have a pair of perpendicular sides.
When are lines parallel, perpendicular or neither?The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:
If they are equal, the lines are parallel.If their multiplication is of -1, they are perpendicular.Otherwise, they are neither.Here, we have to find if there are perpendicular segments, that is, if two slopes multiplied have a value of -1, then:
mAB = (-7 - 9)/(11 - 1) = -8/5.mAC = (3 - 9)/(-9 - 1) = 3/5.mBC = (3 - (-7))/(-9 - 11) = -1/2.No sides are perpendicular, hence option D is correct.
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In our solar system, 6 of the 8 planets have moons.
What percentage of the planets have moons?
Answer:
75%
Step-by-step explanation:
help please i’m not sure if it’s c
the answer is infact c!
MULTIPLE CHOICE
Question 13
Which best describes the range of f(x)?
Based on the function, the range of f(x) = 2(3)^x can best be described as y > 0.
What is the range of f(x) = 2(3)^x?When a number is raised to a power, the result will always be positive even if the number is raised to a negative number.
This means that 3^x will always be positive which means that 2(3)^x will also be positive. y will therefore always be greater than 0.
Full question is:
Which best describes the range of the function f(x) = 2(3)^x?
y > 0
y ≥ 0
y > 2
y ≥ 2
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27. The attendance at a party consisted of 35 men, a number of women and some children. The number of women was one and a half that of the children present. a) If there are a total of 65 participants, how many women attended the party?
Answer:
There are 35 Men, 12 Children, and 18 Women
Step-by-step explanation:
Men(M), Women(W) and Children(C)
We learn that:
M = 35
W = 1.5C , and
M+W+C = 65
----
M+W+C = 65
M+1.5C+C = 65
35+1.5C+C = 65
2.5C = 30
C = 12
If C=12 and W=1.5C, then W=18
----
There are 35 Men, 12 Children, and 18 Women
(35+12+18) = 65 participants
Quick algebra 1 assignment for 50 points!
Only answer if you know the answer, tysm!
1. Create 5 questions referencing “Relations and Functions”Below is an example of one.
——————————————————————
Example :
For the problem below read the scenario and answer the questions.
Tai volunteered to sell tickets to an upcoming school play. There are a total of 75 tickets available for a cost of $3 each.
Let M represent the total amount of money she receives from ticket sales and t represent the number of tickets.
A) Write a function M(t) to represent the total amount of money Tao receives from ticket sales.
B) What is the domain of the function? Explain your reasoning.
——————————————————————
2. Answer each question and write a brief step by step process on how you got the answer to each of your questions.
The examples and solutions to the functions are illustrated below based on the information given.
How to illustrate the functions?1st example: The cost of a bag of rice is $100 and subsequent bags cost $95. Illustrate. the function to calculate the cost for p bags of rice.
The function will be:
C = 100 + (95 × p)
C = 100 + 95p
2nd example: The cost of a pen is $5. Find the cost of s pens.
The function will be:
C = 5 × p
C = 5p
3rd example: Calculate the total amount for m tickets if each ticket is $20.
The function will be;
C = 20 × m
C = 20m
4th example: Bon bought g mangoes at $2 each and d oranges at $3.40 each. Calculate the total cost.
C = (2 × g) + (3.40 × d)
C = 2g + 3.4d
5th example: The average age of k number of boys is 7. Find their total age.
The function will be:
a = (7 × k)
a = 7k
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Question 1: Akira sells lemonade at 50 cents a glass. Let m be the amount of money they make in total for g glasses. Akira only has enough lemonade for 20 glasses.
A) Write a function m(g) to represent the total money (in dollars) they make from lemonade sales.
B) What is the domain of the function? Why?
Answer:
A) m(g) = 0.5g
This is since she makes 0.5 dollars per glass
B) The domain is [tex]0 \leq g \leq 20[/tex] where g is an integer. This is since it's impossible to make less than 0 glasses and they cannot make more than 20.
Question 2: Danyon sells CD's at $20 per CD. He has only 15 CD's left.
A) Write a function m(c) to represent the total money he makes from selling c CD's.
B) What is the domain of the function? Why?
Answer:
A) m(c) = 20c, as he makes 20 dollars per CD.
B) The domain is [tex]0 \leq c \leq 15[/tex] where c is an integer, as he can't make less than 0 CD's, and he has only 15 left.
Question 3: A factory is capable of making 60 units per hour. The factory can only run for 24 hours before cool down, and 150 units have already been made.
A) Write a function u(h) to represent the number of units after h hours.
B) What is the domain of the function? Why?
Answer:
A) u(h) = 60h + 150 as it makes 60 units per hour and 150 are already made.
B) The domain is [tex]0 \leq h \leq 24[/tex] as the factory can't run for negative hours and has to cool down after 24 hours.
Question 4: Alazne sells sunglasses at $7 per pair. She has only 30 left before she needs to re-stock.
A) Write a function m(s) which calculates the amount of money she makes after selling s sunglasses.
B) What is the domain of the function? Why?
Answer:
A) m(s) = 7s, as she gets $7 per pair of sunglasses
B) [tex]0 \leq s \leq 30[/tex] where s is an integer, one cannot have a fraction of a pair and she only has 30. She also cannot sell negative sunglasses.
Question 5: Lincoln works at a burger joint in the summer. He makes $3 from every burger he makes. He already has $22 saved. He cannot make more than 10 burgers a day.
A) Write a function m(b) which calculates how much money he gets after making b burgers.
B) What is an appropriate domain for this function?
Answer:
A) m(b) = 3b + 22, as he already has 22 dollars and makes 3 more for every burger.
B) [tex]0\leq b\leq10[/tex], where b is an integer. This is since he cannot make a fraction of a burger, negative burgers, or more than 10 burgers.
A candy distributor needs to mix a 10% fat-content chocolate with a 60% fat-content chocolate to create 100 kilograms of a 25% fat-content chocolate. How many kilograms of each kind of chocolate must they use
The candy distributor must use 70 kg and 30 kg of 10% fat-content chocolate and 60% fat-content chocolate respectively.
How to find the correct quantity of chocolate that should be used?Let x be the quantity of 10% fat-content chocolate.
Fat in 10% fat-content chocolate + Fat in 60% fat-content chocolate = Total fat in 25% fat-content chocolate
0.10x + 0.60(100 - x) = 0.25*100
10x + 60*100 - 60x = 25*100
-50x = 25*100 - 60*100
-50x = 100(25 - 60)
50x = 3500
x = 3500/50
x = 70 kg
This is the quantity of 10% fat-content chocolate required.
100 - x = 30 kg
This is the quantity of 60% fat-content chocolate required.
Therefore, we have found that the candy distributor must use 70 kg and 30 kg of 10% fat-content chocolate and 60% fat-content chocolate respectively.
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Need help checking my answer for #1 (solving special inequalities)
Inequality are expressions not separated by an equal sign. The inequality shown has no solution
Inequality expressionsInequality are expressions not separated by an equal sign. Given the inequality expression
2(x-3) ≤ 3 + 2x
Expand
2x - 6 ≤ 3 + 2x
2x - 2x ≤ 3 +6
0x ≤ 9
x≤9/0
Hence the inequality shown has no solution
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When she adds 2 to both sides, the equation 4x = 3x results. Which solution will best illustrate what happens to x ?
The solution will illustrate that the equation has one solution at x=0.
Given that adds 2 to both sides, the equation 4x = 3x results.
An algebraic equation may be described as a mathematical declaration wherein expressions are set the same as every other.
The equation is 4x=3x.
As given that add 2 on both sides, we get
4x+2=3x+2
Now, we will subtract 3x from both sides, we get
4x+2-3x=3x+2-3x
x+2=2
Further, we will subtract 2 from both sides, we get
x+2-2=2-2
x=0
Hence, When adds 2 to both sides, the equation 4x = 3x results that the equation has one solution x=0.
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What would be the value of the sum of squares due to regression (SSR) if the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89
The value of the sum of squares due to regression is 18.43.
Given the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89.
A common measure used in regression analysis is the sum of squares total (SST). The square of each difference is added to the sum of squares to obtain the squared disparities between individual data points and their mean. The variance is calculated using the sum of squares, which is also used to assess how well a regression curve fits the data.
We will use the total sum of squares (SST) is given as the summation of the sum of squares due to regression (SSR) and sum of squares error (SSE);
SST = SSR + SSE
Here, SST=25.32 and SSE=6.89
Substitute the values in the formula, we get
25.32=SSR+6.89
Now, we will subtract 6.89 from both sides, we get
25.32-6.89=SSR+6.89-6.89
18.43=SSR
Hence, the value of the sum of squares due to regression (SSR) when the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89 is 18.43.
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Please help! i will give you a lot of points if you do!
i don't understand how to solve number 19 through 31, only the odd numbers.
please show work
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.