Constant variance is the assumption in regression analysis that the standard deviation and variance of the residuals are constant for all values of the independent variables.
Constant variance is the assumption in regression analysis that the standard deviation and variance of the residuals are constant for all values of the independent variables.
Homogeneity of variances means the assumption that the variances of the random variables are constant. This homoscedasticity (that is, constant variances) assumption can be tested using the same diagnostics used for linear regression models.
All data usually consist of the dependent variable and the independent variable itself. Constant variance is about many linear regression assumptions. For example, if you have 325 rows, there should be at least one variance, possibly a constant. The next question is how to compare variables with appropriate variances. The basic fact is that when plotting between a single value and a predicted value, the resulting variance should be constant for the prediction error value.
Var(μ) = E(μ)² = constant
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The table below shows some inputs and outputs of the invertible function f with domain all real numbers.
X 5, 3, 1, 18, 0, 9
f(x) 9, -2, -5, -1, 1, 11
Find the following values:
f-1 (f(58))=
f(f (5)) =
The value of f⁻¹(f(58)) is 58 and the value of the function f(f(5)) is 11
How to solve the function values?As a general rule, we have:
f⁻¹(f(x)) = x
Substitute 58 for x
So, we have:
f⁻¹(f(58)) = 58
Hence, the value of f⁻¹(f(58)) is 58
Also, we have:
f(f(5))
From the table, we have:
f(5) = 9
So, we have:
f(f(5)) = f(9)
From the table, we have:
f(9) = 11
So, we have:
f(f(5)) = 11
Hence, the value of the function f(f(5)) is 11
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If the clock tower in "Back to the Future" had a big hand length of 3 feet, what would be the length of the arc, in feet, the tip travels from 6:00pm to 6:20pm. Round to the nearest foot.
The length of the arc made by the big hand if the tip travels from 6:00pm to 6:20pm is 0.52 feet
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The clock reads 12 hours (720). The angle if the tip travels from 6:00pm to 6:20pm (20 minutes) is:
Ф = (20/720) * 360 = 10°
The length of the arc is given as:
Length of arc = (Ф/360) * 2π * length of hand = (10/360) * 2π(3) = 0.52 feet
The length of the arc made by the big hand if the tip travels from 6:00pm to 6:20pm is 0.52 feet
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by how much does -12 exceed -15
Answer:
By 3.
Step-by-step explanation:
-12-3=-15
Hope this helps!
Answer:
-12 exceeds -15 by 3
Step-by-step explanation:
To find out by how much a exceeds b, subtract a - b.
For example, by how much does 8 exceed 6?
Here, a = 8 and b = 6.
a - b = 8 - 6 = 2
2 is correct since we know that 8 is 2 greater than 6.
Now we do this problem.
By how much does -12 exceed -15?
a = -12; b = -15
a - b = -12 - (-15) = -12 + 15 = 3
Answer: -12 exceeds -15 by 3
Explain how to find the 41st term of the arithmetic sequence where a1 = 5 and a7 = 34.
The 41th term of the arithmetic sequence is 66.
What is arithmetic sequence in math's ?Arithmetic sequences are those that contain these patterns. The difference between successive terms in an arithmetic series is constant. Because the difference between consecutive words is always two, the sequence 3, 5, 7, and 9 is an example of arithmetic.
[tex]a_{n}=a_{1}+(n-1)d[/tex]
[tex]a_n[/tex] = the nᵗʰ term in the sequence.
[tex]a_1[/tex] = the first term in the sequence.
d = the common difference between terms.
According to the given information:Finding arithmetic sequence for the nth term:
aₙ = a₁ + (n-1)d
d = the common difference
a₇ = a₁ + (7-1)d
34 = 5 + 6d
29 = 6d
d = 29/6
Now ,
Finding the 41st term of the arithmetic sequence.
a₄₁ = a₁ + (n-1)d
= 5 + (41-1)d
= 5 + 40d
= 5 + 40(29/6)
= (198)* 1/3
= 66
The 41th term of the arithmetic sequence is 66.
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the base of an isosceles triangle is 4/3 cm . the perimeter of the triangle is 4 2/15 cm.
Answer:
[tex]\sf 1\dfrac{2}{5} \ cm[/tex]
Step-by-step explanation:
Isosceles triangle:If two sides of the triangle are equal, then the triangle is called isosceles triangle.
Let the two equal sides = x cm
Perimeter of the triangle = [tex]\sf 4\dfrac{2}{15}[/tex] cm
[tex]\sf x + x + \dfrac{4}{3}=4\dfrac{2}{15}\\\\[/tex]
[tex]\sf 2x +\dfrac{4}{3}=\dfrac{62}{15}[/tex]
[tex]\sf 2x = \dfrac{62}{15}-\dfrac{4}{3} \ [\text{\bf LCM of 15 , 3 = 15}]\\\\2x = \dfrac{62}{15}-\dfrac{4*5}{3*5}\\\\2x = \dfrac{62}{15}-\dfrac{20}{15}\\\\2x = \dfrac{42}{15} \ [\text{\bf Divide both sides by 2}]\\\\ x = \dfrac{42}{15*2}\\\\ x = \dfrac{7}{5}\\\\ x = 1\dfrac{2}{5}[/tex]
[tex]\sf \boxed{\text{Equal sides of isosceles triangle = $1\dfrac{2}{5}$ cm}}[/tex]
please help
Which reason completes the proof for step 6?
The reason that completes the proof for step 6 is (a) Definition of median
How to complete step 6?From the graph, point R' to be the midpoint of points M' and O'
Also, points P' and Q' are the midpoints of lines M'N' and N'O', respectively
This means that the three points are the median of the sides of the triangle
The line drawn through the three medians meet at point S
Hence, the reason that completes the proof for step 6 is (a) Definition of median
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Answer: median
Step-by-step explanation:
Suppose that tan 0=-5/12 and 90° <0<180°.
Find the exact values of sin
0/2 and
tan
O/2
The exact values of sin θ/2 and tan θ/2 given below as:
sin θ/2 = 0.9806tan θ/2 = 4.99What is the exact values of sin θ/2 and tan θ/2 given that tan θ = -5/12?Given that tan θ = -5/12 and θ lies between 90° and 180°, the values of sin θ/2 and tan θ/2 can be found as follows:
tan θ = -5/12
θ = 180 -tan⁻¹-(5/12)
θ = 157.38
sin θ/2 = sin 157.38/2
sin θ/2 = 0.9806
tan θ/2 = tan 157.38/2
tan θ/2 = 4.99
In conclusion, the values of the sine and tangent are found from the given values.
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what type of correlation relationship is "the number of fire stations in a city is positively correlated with the number of parks"
The type of correlation relationship that exists between the number of fire stations in a city and the number of parks is: accidental correlation relationship.
What is Accidental Correlation Relationship?Accidental relationship is a type of correlation relationship whereby there is a strong correlation between two variables without a logical explanation for such relationship. It is often regarded as coincidental.
Therefore, the type of correlation relationship that exists between the number of fire stations in a city and the number of parks is: accidental correlation relationship.
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Choose the equation that satisfies the data in the table.
Answer:
Step-by-step explanation:
the answer is D
Planes Q and R are parallel. Explain how you know lines a and b are skew. Planes Q and R are parallel. Line a is on plane Q and is diagonal down and to the left. Line b is on plane R and is diagonal up and to the left.
Since the given lines a and b are neither parallel, nor do they intersect each other. Also, they lie on two different planes, P and Q respectively, and thus, are co-planar. hence, a and b can be called skew lines.
Definition of Skew Lines
Skew lines in 3D geometry, are, by definition, a pair of lines that are neither parallel nor intersect each other. Such lines are therefore not coplanar, according to the conclusion.
Skew lines tend to occur frequently in real-world circumstances. Let's say there is a line on the ceiling and a line on the wall. These lines can be skew lines because they lie in distinct planes if they are not parallel to one another and do not meet. Skew lines go on forever in both directions.
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Answer:
Step-by-step explanation:
Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew.
Cuantos litros de agua se necesitan para llenar una piscina de 20m de largada, 12m de ancho y 2m de profundidad
Answer: 480
Step-by-step explanation:
20(12)(2) = 480
Expand (1 + root 2) (3 - root 2)
Give your answer in the form a+b root 2 where a and b are integers.
Answer:
1+2√2
a = 1 b= 2
See the attached page, I've shown the calculation over there.
Can you guys help me with this problem, please I need it right now.
In the graph, the constant of proportionality is 40
Calculating the constant of proportionalityFrom the question, we are to determine the constant of proportionality
The constant of proportionality = [tex]\frac{y}{x}[/tex]
From the graph, a point on the line is (1, 40)
That is,
When x = 1 and y = 40
Thus,
The constant of proportionality = [tex]\frac{40}{1}[/tex]
Constant of proportionality = 40
Hence, the constant of proportionality is 40
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Answer:
40
Step-by-step explanation:
The constant of proportionality is 40/1 which equals 40.
Consider the exponential function f(x)=3(1/3)^x and it’s graph
The given exponential function exists [tex]f(x)=3(1/3)^x[/tex] . The growth value of the function is 1/3.
What is exponential function?An exponential function exists a mathematical function of the following form: [tex]f ( x ) = a^ x[/tex].
where x exists a variable, and a exists a constant named the base of the function.
An exponential function exists of the form [tex]f(x)=ab^x[/tex]
where a ≠ 0, b > 0, b ≠1, and x exists any real number.
when b > 1, the graph increases.
when 0 < b < 1, the graph decreases.
a = initial value
r = growth or decay rate
x = number of time.
The given exponential function exists [tex]f(x)=3(1/3)^x[/tex]
The function exists a stretch of the function [tex]f(x)= (1/3)^x.[/tex]
Therefore, the correct answer is the growth value of the function is 1/3.
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Penny attended a four year state college. she took out a student loan to pay for her tuition and room & board for the four years she was attending the college. her tuition fees were $6,970 per year, and the cost of her room and board was $11,320 per year. now that she has graduated, she will have to start paying back her loan. fortunately, penny has a grace period of one year before she has to start paying back the loan. her loan details are as follows: there is a fixed-rate interest of 4.5% and the interest compounds each month. during her one year grace period, interest will accrue on the loan, so that when she has to start paying the loan back she will owe more than what she owes now. her goal is to be able to payoff the loan in 10 years. what is the new loan amount after the one-year grace period (remember that interest will accrue on the loan during this initial 12-month period that she is not paying anything back on the loan)? this is the amount that she will be responsible for paying back. (round your answer to the nearest whole dollar)
The new loan amount is $113,797
What is compound interest?
Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.
We can find new loan amount as shown below:
Total amount of loan=4*6,970+4*11,320
=27,880+45,280
=$73,160
Now, we will find new loan amount using compound interest formula.
Amount=[tex]P(1+\frac{r}{n})^{nt}[/tex]
P=$73,160
n=12
t=1 year
r=4.5%=0.045
Putting in formula
Amount[tex]=73,160(1+\frac{0.045}{12})^{12}[/tex]
=$113,797.039
Rounding to nearest dollar
=$ 113,797
Hence, new loan amount after one-year grace period is $113.797.
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Find the missing side. Round your answer to the nearest tenth.
Answer:
x = 19.1
Step-by-step explanation:
Because this is a right triangle, we can use trigonometry.
Thus, we must use either sine (opposite / hypotenuse), cosine (adjacent / hypotenuse), or tangent (opposite / adjacent).
If we use 33 as the reference angle, the side measuring 16 is the adjacent side and x is the hypotenuse.
Thus, we can use cosine:
[tex]cos 33=\frac{16}{x} \\x*cos33=16\\x=19.0778=19.1[/tex]
Which best describes the function on the graph?
A) Direct Variation; k=3
B) Direct Variation; k=1/3
C) Inverse Variation; k=3
D) Inverse Variation; k=1/3
Please answer quickly! <3
Direct Variation; k=3 best describes the function on the graph
Option A)
Direct variation is a linear function defined by an equation of the form y = kx when x is not equal to zero. Inverse variation is a nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant. In direct variation, as one number increases, so does the other. This is also called direct proportion: they're the same thing. An example of this is relationship between age and height. As the age in years of a child increases, the height will also increase. In inverse variation, it's exactly the opposite: as one number increases, the other decreases. This is also called inverse proportion. An example would be the relationship between time spent goofing off in class and your grade on the midterm. The more you goof off, the lower your score on the test
The given equation is a Straight line with equation y = 3x.
Thus the given graph is direct Variation graph with k=3.
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If a family has 6 children, in how many ways could the parents have 3 boys and 3 girls?
The parents could have 3 boys and 3 girls in 400 ways
How to determine the number of ways?The given parameters are
Children, n = 6
Boys, r = 3
Girls, r =3
The number of combination is:
[tex]Ways = ^nC_{r1} *^nC_{r2}[/tex]
So, we have:
[tex]Ways = ^6C_3 *^6C_3[/tex]
Apply the combination formula
[tex]Ways = \frac{6!}{3!3!} *\frac{6!}{3!3!}[/tex]
This gives
Ways = 400
Hence, the parents could have 3 boys and 3 girls in 400 ways
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Rhombus A B C D is shown. The length of A B is 9 s + 29 and the length of opposite side D C is 10 s minus 16.
What is the value of s and the length of side BC if ABCD is a rhombus?
s =
BC =
units
The value of s is 45 and the value of BC is 434
How to solve for s and BC?The given parameters are:
AB = 9s + 29
DC = 10s - 16
Opposite sides of rhombus are equal.
So, we have:
9s + 29 = 10s - 16
Evaluate the like terms
s = 45
Substitute s = 45 in AB = 9s + 29
AB = 9 * 45 + 29
Evaluate
AB = 434
This means that
BC = AB = 434
Hence, the value of s is 45 and the value of BC is 434
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the graph of y =-3x+4 is
Answer:
Step-by-step explanation:
hello :
The graph of y =-3x+4 is the line
P(A) = 1/2
P(B) = 1/3
If A and B are independent, what is P(A ∩ B)?
Answer:
Step-by-step explanation:
hello :
P(A ∩ B)=P(A)×P(B)=1/2×1/3 = 1/6
The perimeter of a deck is 33 at the length of the deck is 10 feet what is the width of the deck
The width of the deck is 6.5 feet.
The perimeter of a two-dimensional shape is the total length of the outline. To find the perimeter of a rectangle, we add the lengths of all four sides. Since opposite sides of a rectangle are always equal, we need to find the dimensions of length and width to find the perimeter of a rectangle. We can write the perimeter of the rectangle as twice the sum of its length and width. The perimeter is a linear measure and has units as meters, centimeters, inches, feet, etc.
Assuming the deck is rectangle
Perimeter = 2(length + width)
33ft = 2 (10 + width)
16.5 = 10 + width
width = 6.5 ft
Thus the width of the deck is 6.5 feet.
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Help pls, it’s urgent!! ASAP! (Geometry)
“Compete the proof”
1) [tex]\overline{AB} \cong \overline{CD}[/tex], [tex]\overline{AD} \cong \overline{CB}[/tex], [tex]\overline{AX} \perp \overline{BD}[/tex], [tex]\overline{CY} \perp\overline{BD}[/tex] (given)
2) [tex]\overline{BD} \cong \overline{BD}[/tex] (reflexive property)
3) [tex]\triangle ABD \cong \triangle ACDB[/tex] (SSS)
4) [tex]\angle ADB \cong \angle CBY[/tex] (CPCTC)
5) [tex]\angle CYB[/tex] and [tex]\angle AXD[/tex] are right angles (perpendicular lines form right angles)
6) [tex]\triangle CYB[/tex] and [tex]\triangle AXD[/tex] are right triangles (a triangle with a right angle is a right triangle)
7) [tex]\triangle AXD \cong \triangle CYB[/tex] (HA)
8) [tex]\overline{AX} \cong \overline{CY}[/tex] (CPCTC)
A cube with side length is stacked on another cube with side length . What is the total volume of the cubes in factored form
The total volume of the cubes in factored form is (4p + 2q^2)(16p^2 - 8pq^2 + 4q^4)
What is the volume of a figure?The volume of a figure or a three dimensional shape is the amount of space inside the figure or the three dimensional shape
How to determine the total volume?The two cubes are stacked upon one another, so they form a composite figure.
The side lengths of the cubes are given as
Cube 1 = 4p
Cube 2 = 2q^2
The volume of each cube is calculated as:
Volume = Side length^3
So, the total volume is
Total = (4p)^3 + (2q^2)^3
Evaluate the exponents
Total = 64p^3 + 8q^6
Using the sum of cubes, we have the factored form to be
Total = (4p + 2q^2)(16p^2 - 8pq^2 + 4q^4)
Hence, the total volume of the cubes in factored form is (4p + 2q^2)(16p^2 - 8pq^2 + 4q^4)
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Complete question
A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored form?
Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities
Multiplicative rule's probability is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities
According to the statement
we have to explain about the those law which is used when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities
So, For this purpose we know that the
According to multiplicative rule of probability ,
If A and B are two independent events in a probability experiment, then the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B) In case of dependent events , the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B | A)
and we see that these conditions are fulfilled by the definition of the multiplicative rule.
So, Multiplicative rule is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities
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compare these heights:
5,2 and 46,5
46.5 is higher than 5.2
Comparison of heightNote that:
The larger the magnitude(value) of the heights given the larger the heights
Units are not added to the values representing each height
By carefully considering the heights given:
5.2 is a lesser value than 46.5
Since 46.6 > 5.2, we can conclude that 46.5 is higher than 5.2
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he section of paper shown in the pattern below is 1/4 of a circle. It will be wrapped around a cone. The wrapper will then be painted.
The volume of the cone based on the figure illustrated wil be 196cm³.
Host illustrate the information?The information is incomplete and the complete question wast found online. An overview will be given.
Let's assume that the height is 4cm and the radius of the cone is 7cm. The volume of the cone will be:
= 1/3πr²h
= 1/3 × 3.14 × 7² × 4
= 196cm³
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what operation is evaluated first in the expression 4 + 9 2 /3 x 2 - 2 =
Answer:
You add the numerator
multiply the denominator and substract
then you can divide the expression.
Step-by-step explanation:
According to BODMAS
division comes before multiplication, addition and subtraction.
but in some cases like this, it's difficult to follow that procedure
[tex]\huge\sf\underline{Question}[/tex]
[tex]\sf If \: {x}^{2} + \frac{1}{x ^{2} } = 34[/tex]
[tex]\sf find \: the \: value \: of \: \: \: x + \frac{1}{x} [/tex]
a proper explanation needed :)
Thxx !!
[tex] {\qquad\quad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 34[/tex]
[ add 2 on both sides ]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } + 2 = 34 + 2[/tex]
[ form identity : a² + b² + 2ab ]
[tex]\qquad \sf \dashrightarrow \: {(x)}^{2} + { \bigg(\cfrac{1}{ {x}^{} } \bigg) }^{2} + 2 \sdot(x) \sdot \bigg(\cfrac{1}{x} \bigg) = 36[/tex]
[ a² + b² + 2ab = (a + b)² ]
[tex]\qquad \sf \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^{2} = 36[/tex]
[tex]\qquad \sf \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^{} = \sqrt{ 36}[/tex]
[tex]\qquad \sf \dashrightarrow \: x + \cfrac{1}{x} = \pm 6[/tex]
so, the value of required expression is 6
[usually positive value is considered, but if asked the value can be either positive or negative]
Complete the statement to describe the expression ab+cd+ef+gh
The expression consists of __ terms, and each term contains __ factors.
HELP!
The terms of the expression are ab, cd, ef and gh. This shpws that the expression contains 4 terms and 0 factor.
Terms and factors of an expressionExpression consists of terms and factors. The terms are separated by the mathematical signs.
Given the expression below
ab+cd+ef+gh
The terms of the expression are ab, cd, ef and gh. This shpws that the expression contains 4 terms and 0 factor.
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