The correct option is B. That is, SSE must be equal to zero.
What is linear regression?Linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables. The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression.
Know that the ratio of SSE by SST is the proportion of total variation that cannot be explained by the simple linear regression model.
Now, r²-SSE/SST
Therefore, option B is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
In a regression analysis of r² = 1, then
(a) SSE must also be equal to 1
(b) SSE must be equal to zero
(c) SSE can be any positive value
(d) SSE must be negative
Mazzeo's Appliance Store requires a down payment of 1/3 on all installment purchases. If a refrigerator costs $900, how much is the down payment?
The down payment for the installment purchase for the $900 refrigerator is $300.
What is installment purchaseAn installment purchase is a method of buying high value assets or goods on credit. A percentage of the total purchase price is paid immediately as a down payment, while the remaining amount is settled by paying periodic installments.
the good to be paid for installment after a down payment of 1/3 of the total amount is a refrigerator which cost $900
1/3 of $900 = 1/3 × $900
1/3 of $900 = $900/3
1/3 of $900 = $300
In conclusion, $300 will be the down payment for the installment purchase of the refrigerator.
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The coordinates of the vertices of a triangle are E (-2, 6), F (-2,-2),
and G (5,-3). Triangle EFG is reflected across the y-axis to create
triangle efg
Answer: E' (2,6) F' (2,-2) G' (-5,-3)
Step-by-step explanation: To find the coordinates flipped over the y-axis the rule goes from (x,y) to (-x,y) *Just a reminder the negative sign doesn't necessarily mean negative. It just means the opposite sign, so negative numbers would turn positive.
darius says that 1/4 is a division expression and is not a quotient. Badru says that 1/4 is a division expression and is also the quotetient of 1 / 4. who is correct
On solving the provided question we can say that 1/4 means , 1 divides 4, so it its a division not expression.
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
here,
darius says that 1/4 is a division expression
Badru says that 1/4 is a division
1/4 means , 1 divides 4, so it its a division not expression
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Increase £16470.45 by 13.5%
Give your answer rounded to 2 DP.
Answer: £18704.32.
Step-by-step explanation:
To increase a value by a certain percentage, you can use the formula:
New value = Original value + (Original value x (Percentage increase/100))
In this case, to increase £16470.45 by 13.5%:
New value = 16470.45 + (16470.45 x (13.5/100))
New value = 16470.45 + 2233.8675
New value = 18704.3175
Rounded to 2 decimal places, the new value would be £18704.32.
Answer:
18704.32
Step-by-step explanation:
Central high school had five members on their swim team in 2010. Over the next several years the team increased by an average of 10 members per year, the same school had 35 members in their chorus in 2010. The chorus saw an increase of 5 members per year
The system of equations that models the given situation are;
y = 10x + 35
y = 5x + 35
How to model a system of equations?Let x denote the number of years since 2010
Let y denote the total members
The linear equation in slope intercept form is expressed as;
y = mx + b
where;
m is the slope or unit rate
b is the y-intercept or initial value
For the swim team, since the team increased by an average of 10 members per year, then;
Slope = 10
In 2010, they had 5 members and so; y-intercept = 35
Thus, the equation is; y = 10x + 35
For the chorus team, we can deduce that;
Slope = 5 members per year
In 2010, they had 35 members and so; y-intercept = 35
Thus, the equation is; y = 5x + 35
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Complete question is;
Central High School had five members on their swim team in 2010. Over the next several years, the team increased by an average of 10 members per year. The same school had 35 members in their chorus in 2010. The chorus saw an increase of 5 members per year. Write a system of equations to model this situation, where x represents the number of years since 2010.
What is the rate of change for the equation of y=-12-1/2x
The rate of change of the given function is -1/2.
What is the average and instantaneous rate of change?It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.Average rate of change -[tex]$r(a) = {\frac {f(x+h)-f(x)}{h}}\\\\[/tex]
Instantaneous rate of change -[tex]$r(i) =\lim _{h\to 0}{\frac {f(x+h)-f(x)}{h}}\end{aligned}}}[/tex]
Given is the function as follows -
y = - 12 - (1/2)x
We have the function f(x) as -
y = - 12 - (1/2)x
dy/dx = d/dx(12 - x/2)
dy/dx = 0 - 1/2
dy/dx = -1/2
Therefore, the rate of change of the given function is -1/2.
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There are 6 roads connecting form a to b. You need to go to b, get back to a, and go back to b. You cannot use one road more than once. How many possible ways to do this?
There are 6 roads connecting from a to b. You need to go to b, get back to a, and go back to b. There are 360 ways to complete this task.
What is the number of ways?Generally, If you need to go from a to b and back to a twice, you can think of this as going from a to b and back to a, and then from a to b and back to an again, without returning to b in between.
This means that you need to use two different roads for the first trip and two different roads for the second trip.
Since there are 6 roads to choose from, and you need to choose 2 roads for the first trip and 2 roads for the second trip, the total number of ways you can do this is
6 * 5 * 4 * 3 = 360ways
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At 3:00 AM the temperature was 23 degrees. At 11:00 AM the temperature was 43 degrees. What is the average rate of change in the temperature per hour?
Step-by-step explanation:
In 8 hours temperature different is 20
so average rate is=20/8
2.5
will give branliest!
The normal body temperature for an adult dog is 101° F, but it can vary by as much as 1.5°. Which inequality could be used to determine the range of body temperature?
|t − 101| ≤ 1.5
|t − 1.5| ≤ 101
|t − 101| ≥ 1.5
|t − 1.5| ≥ 1.5
Answer:
|t - 101| ≤ 1.5
Step-by-step explanation:
The correct inequality to determine the range of body temperature for an adult dog is |t - 101| ≤ 1.5. This inequality states that the body temperature t can be as much as 1.5 degrees less than or 1.5 degrees more than 101 degrees Fahrenheit.
What’s the multiplication factor of 28?
Answer:
Step-by-step explanation:
1 times 28
2 times 14
4 times 7
7 times 4
14 times 2
28 times 1
If A ⊂ B, then A ∩ B = A ∪ B.
1. Sometimes
2. Never
3. Always
Answer:
never
Step-by-step explanation:
because The union of a and b cannot be equal to the intersection of a and b
you got out to dinner with Ben , Carla , david when the bill arrives you decide to split the bill evenly the total bill including tip and tax was $96. How much did you pay ?
Answer: $24
Step-by-step explanation: There were 4 people splitting the bill You, Ben, Carla, and David the bill was 96
divide 96 by four so that you each pay the same amount
96 divided by 4 is 24 so everyone payed $24
24+24+24+24 equals 96 so it is the correct answer
Ari has a map with a scale of 1/2 inch represents 18 miles. To get between two cities on the map, she measures 4 inches. How far would that be in real life?
By using the given scale, we will find that the real distance between the two cities is 144 miles.
How to find the real distance?We know that in our map the scale is:
1/2 inch = 18 miles.
If we multiply that by 2 we get:
2*(1/2) inch = 2*18 miles.
1 inch = 36 miles
Now, if the distance in the map is 4 inches, then we need to multiply that by the scale:
4 inches = 4*( 1 inch) = 4*( 36 miles) = 144 miles.
The real distance is 144 miles.
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find a formula for rn for the function f(x) = (3x)2 on [−1, 5] in terms of n.
The formula for for Rn is given as Rn = Σ 18/n (1 - 12i/n + 36i²/n²).
We are given the function f(x) = 3x² on the interval [-1, 5] . This gives
Δx =6/n and xi= -1 + 6i/n.
Therefore,
Rn = Σ f(xi) Δx
= Σ 3 (-1 + 6i/n)² 6/n
= Σ 18/n (1 - 12i/n + 36i²/n²)
The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input.
Informally, a function f gives each input x an output f(x). If f(x) approaches L as x approaches input p, we say that the function has a limit L at that location. More specifically, any input that is sufficiently close to p when f is applied forces the output value arbitrarily close to L.
The concept of limit is specifically used in the various definitions of continuity. Roughly speaking, a function is continuous if all of its limits agree with the values of the function. The term "limit" is also used in the definition of the mathematical term "derivative," which in one-variable calculus refers to the maximum value of the slope of secant lines on a function's graph.
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6. Write the function in graphing form, then state the center and
radius.
x² + y² - 16x + 10y + 8 = 0
The graphing form of the function is,
⇒ (x - 8)² + (y + 5)² = 9²
And, The center of function = (8, - 5)
The radius of the function is,
⇒ r = 9
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The function is,
⇒ x² + y² - 16x + 10y + 8 = 0
Now,
Since, The function is,
⇒ x² + y² - 16x + 10y + 8 = 0
We can write as;
⇒ x² - 2 × 8 × x + y² + 2 × 5 × y + 8 = 0
⇒ x² - 2×8×x + 64 - 64 + y² + 2×5×y + 25 - 25 + 8 = 0
⇒ (x² - 2×8×x + 64) + (y² + 2×5×y + 25) - 64 - 25 + 8 = 0
⇒ (x - 8)² + (y + 5)² = 81
⇒ (x - 8)² + (y + 5)² = 9²
Thus, The graphing form of the function is,
⇒ (x - 8)² + (y + 5)² = 9²
Clearly, This represent the equation of circle with center (8, - 5) and radius 9.
And, The center of function = (8, - 5)
The radius of the function is,
⇒ r = 9
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Maxine compiled a list of these car prices:$7,500,$6,500,$5,750,$4,900,$6,250 and $4,200.Find the mean of these prices
Answer: 5,850
Step-by-step explanation:
Answer:
[tex]\huge\boxed{\sf Mean = \$ \ 5850}[/tex]
Step-by-step explanation:
Mean:[tex]\displaystyle Mean = \frac{Sum \ of \ data}{No. \ of \ data}[/tex]
Here,
Data: $7500, $6500, $5750, $4900, $6250, $4200
So,
[tex]\displaystyle Mean =\frac{Sum \ of \ all \ prices }{No. \ of \ prices} \\\\Mean =\frac{7500+6500+5750+4900+6250+4200}{6} \\\\Mean = \frac{35100}{6} \\\\Mean = \$ \ 5850\\\\\rule[225]{225}{2}[/tex]
What is wrong with the following piece of mRNA? TACCAGGATCACTTTGCCA Multiple Choice It contains A. O It does not include an equal number of As and Ts. It does not include an equal number of Gs and Cs. It contains T and not U.
The wrong with following piece of mRNA, TACCAGGATCACTTTGCCA is that it contains T and not U. So, option(D) is right choice here.
Messenger RNA (mRNA) is present in DNA. DNA uses four bases in its code, adenine (A), guanine (G), cytosine (C) and thymine (T). RNA also uses four bases. However, instead of using "T" as DNA, it uses uracil (U). So, if your DNA sequence is 3' T C G T T C A G T 5', the mRNA sequence would be 5' A G C A A G U C A 3'. A strand of DNA is a template strand that has a nucleotide sequence on it that is read by RNA polymerases. Rna polymerase reads the template strand and encodes the m-RNA using the base-pairing rule. According to the rule, adenine pairs with thymine and guanosine with cytosine. So if the template DNA reads TAC GTT ACG, RNA polymerase will read it as AUG CAA UGC. Since no thymine is present in RNA, it will code for U instead of T.
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I don't know how to solve this. I've been trying for hours and can't find the solution. Does anyone know HOW to get the answer step by step?
The volume of image of triangular pyramid A which is triangular pyramid B would be = 28km³
What is a triangular pyramid?A triangular pyramid is the type of pyramid that is made up of edges which are triangular in shape.
The image of the triangular pyramid A = Triangular pyramid B.
The volume of triangular pyramid A = 56 km³
The dilation factor = 1/2
The volume of the image of triangular pyramid A which is triangular pyramid B;
= volume of triangular pyramid A × scale factor
= 56 × 1/2
= 28km³
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It takes one pipe 15 days to fill a large pool. It takes another pipe 21 days to fill the same pool. It would take both pipes i days working together to fill the pool.
O True
O False
Answer: True
Step-by-step explanation:
devise a recursive algorithm to find a2n , where a is a real number and n is a positive integer.
A recursive algorithm to find a^2n, where a is a real number and n is a positive integer, is as follows:
Start with the input value of n.If n is equal to 1, return the value of a^2.If n is greater than 1, divide the value of n by 2 and store the result in a new variable m.Find the value of a^(2m) using the recursive algorithm with the input value of m.If n is even, return the value of a^(2m) * a^(2m).If n is odd, return the value of a^(2m) * a^(2m) * a.This algorithm uses the property of exponentiation that a^(2n) = (a^n)^2, and divides the problem of finding a^2n into a smaller subproblem of finding a^n. It takes advantage of the recursive nature of the problem by calling the same algorithm with a smaller value of n.
The time complexity of this algorithm is O(log n) as it divides the problem into half at each recursive step.
It should be noticed that this algorithm assumes that the input value of n is positive, otherwise it would be necessary to add a check for a negative value or zero.
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Determine whether each sequence is arithmetic or geometric. Find the next three terms.
Answer:
B
Step-by-step explanation:
Each individual outcome of an experiment is called a. the sample space. b. a sample point. c.a trial. d. an event.
Each individual outcome of an experiment is called a sample point. So, the right answer is option(b).
The set of all possible outcomes of a random experiment is the sample space , S or the outcome space. An event always associated with a random experiment is a subset of the sample space. Each result in sample space is called a sample point. Also, it is called an element or member of the sample space. For example, there are possible two outcomes for tossing a coin, i.e., the sample space, S = {heads, tails}, or S = {H, T}. If we toss two coins, there are four outcomes : { HH, HT, TH , TT }, where the first letter refers to the outcome of the first tossing and the second to that of the second tossing, each outcome is called a sample point.
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Each car is traveling at a constant speed. Find the number of miles each car travels in 1 hour at the given rate. 97 1/2 miles in 3/2 hours
The number of miles each car travels in 1 hour is 16 1/4 miles
How to determine the number of miles each car travels in 1 hour?From the question, we have the following parameters that can be used in our computation:
Given rate. 97 1/2 miles in 3/2 hours
The number of miles each car travels in 1 hour can be calculated as
Number of miles = 97 1/2 miles/3/2 hours * 1 hour
This gives
Number of miles = 97 1/2 miles/3/2
Evaluate the quotient
So, we have the following representation
Number of miles = 16 1/4 miles
Hence, the number of miles is 16 1/4 miles
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please check the image, thank you
Answer:
Step-by-step explanation:
URGENT DUE TODAY I NEED HELP!!!!!!
If ax+b ax+c ?
equation in slope-intercept form of the line that pae through the point (4, 7) and is parallel to the line represented by y = 2x - 5 is ( y - y1 ) = m( x - x1 ) => y - 7 = 2 (x-8) => 2x - y - 1 = 0
What is slope?A number that specifies a line's direction and slope is known as the slope or slope of a line in mathematics. A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x).
equation is -
y = 2x - 5
since these are parallel to each other,
slope, m= 2
now the equation is -
( y - y1 ) = m( x - x1 )
y - 7 = 2 (x-8)
2x - y - 1 = 0
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A bridge is made with segments of concrete 50 m long. If the linear expansion coefficient is 12 x 10^-6 (oc)^-1, how much spacing (in cm) is needed to allow for expansion during an extreme temperature change of 150 ^of?.
The amount of spacing needed to allow for expansion is 0.09 m
What is length?Length is the distance between two point.
To calculate the amount of spacing needed to allow for expansion, we use the formula below.
Formula:
ΔL = L₁-αΔTL₁............................... Equation 1Where:
ΔL = Change in length concreteL₁ = Original length of the concreteΔT = Change in temperatureα = Coefficient of linear expansivityFrom the question,
L₁ = 50 mΔT = 150 °Cα = 12×10⁻⁶ °C⁻¹Substitute these values into equation 1
ΔL = 50×150×12×10⁻⁶ °C⁻¹ΔL = 0.09ΔL = 0.09 mHence, the amount of spacing is 0.09 m.
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amounts of yearly rainfall in miami over the last 5 years are an example of which type of data?
Answer:quantitative
Step-by-step explanation:
Jane bought a car for $30,303. The value of the car depreciated at a constant rate per year. The table shows the value of the car after the first and second years: year 1 2 value (in dollars) 25,757. 55 21,893. 92 which function best represents the value of the car after t years?.
The correct option representing the function is f(t) = 30,303(0.85)t based on the deprivation rate.
Firstly calculating the depreciation rate -
30,303 - x%×30,303 = 25,757
x×303.03 = 30,303 - 25,757
Performing subtraction on Right Hand Side of the equation
x×303.03 = 4546
x = 4546/303.03
Performing division
x = 15%
The formula to be used for function is -
P = Po[tex] {(1+r)}^{t} [/tex], where P is the final value, Po is the original value, r is growth rate and t is time.
P = 30,303 [tex] {(1 - 0.15)}^{t} [/tex]
Performing subtraction on Right Hand Side of the equation
P = 30,303 [tex] {(0.85)}^{t} [/tex]
The value of car after t years is 30,303 [tex] {(0.85)}^{t} [/tex].
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The complete question is-
Jane bought a car for $30,303. The value of the car depreciated at a constant rate per year. The table below shows the value of the car after the first and second years:
Year 1 2
Value (in dollars) 25,757.55 21,893.92
Which function best represents the value of the car after t years?
f(t) = 25,757.55(0.85)t
f(t) = 30,303(0.85)t
f(t) = 30,303 (0.15)t
f(t) = 25,757.55 (0.15)t
Name Algebra 2 Test 4, page 3 FUNCTIONS: Write the correct answer in the blank 17. Write the difference of the given functions (f-g)x): fx)-x+2x-6 and g(x)-x+ 5 18. Write the product of the given functions (fg)lx): fx)-x-9 and g(x) =x + 1. 19. Write the composition (f g)(x) of the given functions: fx) x+2x-6 and g(x)-x+ 5 20. Write the composition (gof(x) of the given functions: flx) x+2x-6 and g(x) x+5 DOMAIN: Find the domain of each function. 21. f(x)-x+8x-1 22. g(x) + 13 23. fx) RANGE: Find the range of each function. 24. g(x)=6 25. f(x)- -3 +1 26. h(x)= Copyrightmaud Pensacola Christian College Not e seprodaced (cont.) 45
17. (f-g)(x) = ( -x + 2x - 6 ) - ( -x + 5 ) = -2x + 11
18. (fg)(x) = ( -x - 9 )( x + 1 ) = -x² - x - 9
19. (f g)(x) = f(g(x)) = (x + 2x - 6)(-x + 5) = -x² + 6x - 30
20. (g o f)(x) = g(f(x)) = x + 5(x + 2x - 6) = x + 5x + 10x - 30
21. Domain: All real numbers
22. Domain: All real numbers
23. Range: Not given
24. Range: {6}
25. Range: All real numbers
26. Range: Not given
The functions and their operationSpecifically, it provides the difference, product, and composition of the given functions, as well as the domain and range of certain functions. The problems involve algebraic equations and simplifying expressions.
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What do the following two equations represent?
.y=6x-2
.2x-12y=24
The given lines are intersecting but not perpendicular.
What is intersecting lines?
In Euclidean geometry, the empty set, a point, or another line can intersect another line. For instance, computer graphics, motion planning, and collision detection can all benefit from differentiating these cases and locating the intersection.
Given:
y = 6x - 2
2x - 12y = 24
⇒ 6x - y = 2 ..(1)
2x - 12y = 24 ..(2)
Multiply second equation by 3,
6x - 36y = 72 ..(3)
Subtract equation (1) from equation (3).
6x - 12y = 24
- 6x - y = 2
_______________
-11y = 22
y = -2
Plug y = -2 in equation (1)
6x - (-2) = 2
6x + 2 = 2
6x = 2 - 2
6x = 0
x = 0
The solution of the given system is (0, -2).
Hence, the given lines are intersecting but not perpendicular.
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