a) What type of triangle is triangle ABC? b) Give reasons for your answer. I just need B
Answers
Answer:
isosceles triangle
Step-by-step explanation:
line CB is the transversal for the two parallel lines, so angle CBA and angle BCE are the same.
since a straight line is 180 degrees, we can solve for angle BCA by subtracting the other angles on the line from 180
180-80-50 = 50
since triangles have 180 degrees, we can solve for the last angle by subtracting the angles we already know from 180
180-80-50
two of the angles are the same, making this an isosceles triangle
Related Questions
Determine the coefficients of the complex exponential Fourier series of the following signals: (i) x(t) = 1 + cos(2t) + cos(8t + π/2) (ii) x(t) = 2 sin(t) + 3 cos(3t+ π/3)
Answers
The complex exponential Fourier series of a signal can be determined by computing the coefficients A₀ and Aₙ.
For (i), the complex exponential Fourier series is given by:
X(ω) = A₀ + ∑[Ancos(nωt + φn) ], where
A₀ = 1/2
Aₙ = (1/2)[cos(2nπ/8) + cos(2nπ/8 + π/2)]
For (ii), the complex exponential Fourier series is given by:
X(ω) = A₀ + ∑[Ancos(nωt + φn) ], where
A₀ = 1
Aₙ = (2/2)[sin(nπ/3) + 3cos(nπ/3 + π/3)]
In conclusion, the complex exponential Fourier series of a signal can be determined by computing the coefficients A₀ and Aₙ. This technique can be used to analyze any periodic signal or system and is invaluable in signal processing, communications, and control engineering.
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\(f(x)=\frac{2}{3} x+1; r(x) =3f(x)\)
Describe the transformation.
Answers
The description of the transformation f(x) = 2/3x + 1 and r(x) = 3f(x) is that the function f(x) is stretched vertically by a factor of 3 to form r(x)
How to describe the transformation?The equations of the functions are given as
f(x) = 2/3x + 1
r(x) = 3f(x)
The equation r(x) = 3f(x) implies that the function f(x) is stretched vertically by a factor of 3
Hence, the description of the transformation f(x) = 2/3x + 1 and r(x) = 3f(x) is that the function f(x) is stretched vertically by a factor of 3 to form r(x)
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PLS HELP ASAP THANKS
Answers
Answer:
x+(6-4)x-24
x+6x-4x-24
x(1+6)-4(x-6)
(x-4)(x-6)
Answer:
\((x - 4)(x + 6)\)
Step-by-step explanation:
to factor the trinomial, we need to find factors of -24 that have a sum of 2.
24 has factors 1, 2, 3, 4, 6, 8, 12, and 24.
\(6*-4\) is the only set of factors that fit the requirements (factors of -24 and add up to 2).
therefore, the factored trinomial is written as \((x - 4)(x + 6)\).
construct a box plot from the given data. diameters of cans in an assembly line: 5.7,5.6,5.1,5.4,5.2,5.6,5.7,5.3,5.8,5.2
Answers
The resulting box plot for the given data would show a box ranging from 5.2 to 5.7, with the median at 5.4.
A box plot, also known as a box-and-whisker plot, is a graphical representation of numerical data that displays the distribution of a dataset. It provides a visual summary of the minimum, first quartile, median, third quartile, and maximum values, as well as any outliers that may be present.
To construct a box plot from the given data (diameters of cans in an assembly line: 5.7, 5.6, 5.1, 5.4, 5.2, 5.6, 5.7, 5.3, 5.8, 5.2), follow these steps:
1. Sort the data in ascending order: 5.1, 5.2, 5.2, 5.3, 5.4, 5.6, 5.6, 5.7, 5.7, 5.8.
2. Find the median (middle value) of the dataset, which is 5.4.
3. Determine the first quartile (Q1), which is the median of the lower half of the data. In this case, it is the median of the numbers below 5.4: 5.2.
4. Find the third quartile (Q3), which is the median of the upper half of the data. In this case, it is the median of the numbers above 5.4: 5.7.
5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3: 5.7 - 5.2 = 0.5.
6. Identify any outliers in the dataset. Outliers are values that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. In this case, there are no outliers.
7. Construct the box plot using a number line. Draw a box from Q1 to Q3, with a line inside representing the median. Add whiskers (lines) extending from the box to the minimum value (5.1) and the maximum value (5.8).
The resulting box plot for the given data would show a box ranging from 5.2 to 5.7, with the median at 5.4. The whiskers would extend from 5.1 to 5.8. This visual representation provides an overview of the distribution and key statistical measures of the diameters of cans in the assembly line.
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for the matrix samplematrix=[1, 2, 3; 4, 5, 6; 7, 8, 9], to produce samplematrix = [1, 4, 7, 5, 8, 3, 6, 9] with the command samplematrix([n]) = [ ], what should the value of n be?
Answers
To produce `samplematrix = [1, 4, 7, 5, 8, 3, 6, 9]` with the command `samplematrix([n]) = [ ]`, the value of `n` should be 2.
To produce `samplematrix = [1, 4, 7, 5, 8, 3, 6, 9]` with the command `samplematrix([n]) = [ ]`, the value of `n` should be 2. Here's the explanation: Given `samplematrix=[1, 2, 3; 4, 5, 6; 7, 8, 9]`, the command `samplematrix([n]) = [ ]` would remove the nth row from the matrix and leave an empty row in its place.
For example, if `n = 2`, then the command `samplematrix([n]) = [ ]` would remove the second row and leave an empty row in its place.
The resulting matrix would be:`samplematrix = [1, 2, 3; ; 7, 8, 9]`
Notice that there is an empty row in the middle because the second row was removed.
Next, to produce the desired matrix `samplematrix = [1, 4, 7, 5, 8, 3, 6, 9]`, we need to concatenate the rows of the modified `samplematrix` matrix in a specific order. The order is the first row, then the third row, and finally the second row. So, we can use the following code to achieve this:
result = [samplematrix(1,:); samplematrix(3,:); samplematrix(2,:)]
The resulting `result` matrix would be:`result = [1, 2, 3; 7, 8, 9; 4, 5, 6]`
We can then use the colon operator to reshape the matrix into a row vector, like this:`samplematrix = result(:)'`The resulting `samplematrix` vector would be:`samplematrix = [1, 4, 7, 5, 8, 3, 6, 9]`
Therefore, to produce `samplematrix = [1, 4, 7, 5, 8, 3, 6, 9]` with the command `samplematrix([n]) = [ ]`, the value of `n` should be 2.
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Find the area of a rectangle whose width is 6 and whose length is x – 5.
Answers
Answer:
If X is -5 then the answer is -30 but if it is X minus 5, the answer is X-30
Answer:
x-30
Step-by-step explanation:
Area of a rectangle is
length x width
l x w
\(x-5 * 6 = x-30\)
A gardener has a rectangle garden with an area of 374 yd.²The length of the garden is 17 yards the gardener wants to enlarge the garden by doubling only the width of the current garden how much fencing will the gardener need to enclose a new garden?
Answers
Answer:
105 yards
Step-by-step explanation:
The other side is Width = 374/17 = 22.
So, the new width is 44 ( and the length is 17/2).
Perimeter = 2(17/2) + 2(44) = 17+88=105 yds.
So, 105 yards.
Mark me as Brainliest if this is correct! I really appreciate it! :D
The perimeter of the new garden is 105 yards
The area of a rectangle is expressed as:
A = lww = A/l
w = 374/17
w = 22 yards
The perimeter of the new garden if the width is doubled is expressed as:
P = 2(l + w)
P = 2(17/2 + 2(22))
P = 17 + 88
P = 105 yards
Hence the perimeter of the new garden is 105 yards
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distance from (7,4) and (2,8)
Answers
Answer:
5,4 or 9
Step-by-step explanation:
Answer:
Exact form: √ 41
Decimal form: 6.40312423...
Step-by-step explanation:
a spherical tank has a radius of 15 m. a cylindrical tank has a radius of 15 m and a height of 20 m. what is the ratio of the volume of the spherical tank to the volume of the cylindrical tank?
Answers
The volume of a spherical tank with a radius of 15 m is calculated as 4/3πr3, or 4/3π × 153 = 14,137 m3.
The volume of a sphere is calculated using the formula V = 4/3πr³, where r is the radius.The volume of a cylindrical tank with a radius of 15 m and a height of 20 m is calculated as πr2h, or π × 152 × 20 = 11,309 m3.
Therefore, the ratio of the volume of the spherical tank to the volume of the cylindrical tank is 14,137/11,309 = 1.24.
This means that the spherical tank has 24% more volume than the cylindrical tank.
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Answer:
\(r = \sqrt{ \frac{v}{20\pi?} ?} \)
what is the largest integer less than $2010$ that has a remainder of $5$ when divided by $7,$ a remainder of $10$ when divided by $11,$ and a remainder of $10$ when divided by $13$?
Answers
The largest integer less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13. is 1440
Given, a number less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13.
On using the Chinese remainder theorem. As, the numbers 7, 11, 13 are pairwise coprime.
Firstly, an integer m such that m−5 is divisible by 7 and m−10 is divisible by 11 .
The Chinese remainder theorem says that all integers that work will be of the form 54+7⋅11⋅k=54+77k for any integer k .
Next an integer n such that n−10 is divisible by 13 and n−54 is divisible by 77.
Then, by the Chinese remainder theorem, all the integers that also work are of the form 439+13⋅77⋅k=439+1001k .
Hence, the positive integers satisfying the condition are: 439, 439 + 1001 = 1440, 1440 + 1001 = 2441, and so on.
The largest integer less than 2010 is 1440.
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Carey earns $9.75 working part time on weekends. The table below shows the amount, a, Carey earns for working h hours.
Carey’s Earnings
h
0
1
3
a
$0
$9.75
?
Which value completes the table to show the amount Carey earns for working 3 hours?
$9.75
$12.75
$19.50
$29.25
Answers
Answer:
im doing the test rn and i believe the other person is correct :)
Step-by-step explanation:
teacher: how can we change the base of a logarithm? student:
Answers
We can change the base formula by:
logₐ b = logₓ a /logₓ b
OR
logₓ a, logₓ b = logₓ a
The change of base formula is used to change the base of a logarithm. We know that "log" stands for a logarithm of base 10 and "ln" stands for a logarithm of base e. But there is no option to calculate the logarithm of a number with any other bases other than 10 and e.
The change of base formula solves this issue of changing base from e to 10, and from base 10 to e. Also, it is used in solving several logarithms problems.
Base Formula: -
The change of base formula is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm. This is a property of logarithms. You can see the change of base formula here.
Change of base formula
logₐ b = logₓ a /logₓ b
OR
logₓ a, logₓ b = logₓ a
Change of Base Formula
Change of base formula can be represented as follows. Here the base of the given logarithm is also changed to a logarithm with a new base. The basic logarithm with a base is transformed to two logarithms with a new and same base. The change of base formula is:
logₐ b = [logₐ x] / [logₐ y]
In this formula,
The argument of the logarithm in the numerator is the same as the argument of the original logarithm.The argument of the logarithm in the denominator is the same as the base of the original logarithm.The bases of both logarithms of numerator and denominator should be the same and this base can be any positive number other than 1.Change of Base Formula Derivation
Change of base formula derivation can be understood from the following steps. Let us assume that
log ₐ b = p, logₙ a = q, and logₙ b = r.
By converting each of these into exponential form, we get,
a = \(b^{p}\), a = \(x^{q}\), and b = \(n^{r}\)
From the first two equations,
\(x^{q}\) = \(n^{r}\)
Substituting b = \(n^{r}\) (which is from third equation) here,
(\(n^{r}\))\(^{p}\) = \(x^{q}\)
\(n^{r}\))\(^{p}\) = \(x^{q}\)(Using a property of exponents)
p r = q
p = q / r
Substituting the values, we get,
logₐ b = [logₐ x] / [logₐ y]
For Example:
Evaluate the value of log₆₄ 8 using the change of base formula.
Solution:
We will apply the change of base formula (by changing the base to 10). Note that log₁₀ is same as log.
log₆₄ 8 = [log 8] / [log 64]
= [log 8] / [log 82]
= [log 8] / [2 log 8] [∵ log am = m log a]
= 1 / 2
Answer: log₆₄ 8 = 1 / 2
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what is the inverse of f(x)=4x^2-16
Answers
√ x/4 + 4 is the inverse of the function f(x)=4x^2-16
How to find the inverse of a functionWhat is inverse function?
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f
Given f(x)=4x²-16
Let f(x) = y
So we can say y =4x²-16
We will then make x the subject:
Since y = 4x²-16
4x² = y + 16
x² = y + 16/4
x = √ y/4 + 4
since x = f⁻¹(y) = √ y/4 + 4
Thus f⁻¹(x) = √ x/4 + 4
Therefore, the inverse of f(x)=4x^2-16 is √ x/4 + 4
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I need help with this practice problem solving Read the instructions, then answer by filling in the three boxes
Answers
Mike is making a pen for his dog. He wants the pen to be 10X24 feet. Fencing costs
$5.00 a foot. How much will Mike's fence cost?
Answers
$1,200
Step-by-step explanation:
10 × 24 = 240
240 × 5 = 1,200
I think this is right I have no clue though
Answer:
$340
Step-by-step explanation:
10 + 10 + 24 + 24 = 68 feet. Since fencing is $5/foot, multiply the perimeter by the cost.
Since 68 x 5 = 340, the fencing will cost $340.
How are volatility and risk related in an investment
Answers
Answer:
Volatility - the measure of how far the price of an investment moves - is sometimes low, sometimes high, but always a natural part of investing. Risk is the likelihood of an investment losing value, adjusted for inflation, over a longer period of time.
enter the value of x that makes the equation true 12x=3
Answers
Answer:
12 x1/4 or 12x.25=3
Step-by-step explanation:
you can pick between 1/4 or 0.25 they both equal 3
In ΔXYZ and ΔEFG, angles Y and F are right angles. Which set of congruence criteria would be enough to establish that the two triangles are congruent by HL?
A.
XZ ≅ EG and ∠X ≅ ∠E
B.
XZ ≅ EG and YZ ≅ FG
C.
XZ ≅ FG and ∠X ≅ ∠E
D.
XY ≅ EF and YZ ≅ FG
Answers
Answer:
its b
Step-by-step explanation:
XZ ≅ EG and YZ ≅ FG is enough to make triangles to be congruent by HL. Option b is correct.
Two triangles ΔXYZ and ΔEFG, are given with Y and F are right angles.
Condition to be determine that proves triangles to be congruent by HL.
HL implies hypotenuse and leg pair of the right angle triangle.
Here, two right angle triangle ΔXYZ and ΔEFG to be congruent by HL only if their hypotenuse and one leg is equal i.e. XZ ≅ EG and YZ ≅ FG respectively.
Thus, XZ ≅ EG and YZ ≅ FG is enough to make triangles to be congruent by HL.
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Rob made a scale drawing of a summer camp. He used the scale 17 centimeters : 6 meters.
The actual length of the sand volleyball court is 18 meters. How long is the volleyball court in
the drawing?
Answers
Answer:
the volleyball court would be 51 centimeters
Answer:
51 centimeters.
Step-by-step explanation:
My bad if I got it wrong but I'm pretty sure thats the answer
Choose all the expressions that equal 36.
Responses
A (14⋅32)2−28open paren 1 fourth times 32 close paren squared minus 28
B 23 + (58−54)2 + 122 3 + ( 58 - 54 ) 2 + 12
C 92 − (43 + 32) + 3005092 − ( 4 3 + 3 2 ) + 300 50
D 124 + (82 − 42) − 99124 + ( 8 2 − 4 2 ) − 99
E 53 − (2. 5 × 30) − 20
Answers
The expressions that equal 36 is:
E) 53 − (2. 5 × 30) − 20
Calculation of Algebra ExpressionEvaluated the mathematical expressions in each response to see if they equal 36.
A. (14⋅32)2−28 = (448)² - 28 = 14⁴ - 28 = 2016 - 28 = 1988, not equal to 36.
B. 23 + (58−54)2 + 122 = 23 + (4)² + 12 = 23 + 16 + 12 = 51, not equal to 36.
C. 92 − (43 + 32) + 30050 = 9² - (7 + 3) + 30050 = 81 - 10 + 30050 = 30021, not equal to 36.
D. 124 + (82 − 42) − 99 = 124 + (64 - 16) - 99 = 124 + 48 - 99 = 73, not equal to 36.
Thus, only the expressions listed in my previous answer equal 36.
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A company makes concrete paving stones in different sizes. Each stone has a volume of 360 cubic inches and a height of 4 inches.
How many different paving stones could be made if any whole number length and width are possible? different stones could be made. Suppose that the cost of a paving stone is $2.50, plus $0.16 for every 4 cubic inches of concrete. How much would each paving stone cost? Each paving stone would cost $
Answers
Answer:
6 different paving stones could be made.
Each paving stone would cost $16.90.
Step-by-step explanation:
Divide the volume by the height to find the area of the base.
360 cu in. / 4 in. = 90 sq in.
The area of the base is 90 sq in.
Now we need to find all the pairs of positive integers whose product is 90 to find the number of different possible combinations of length and width of the base.
90 =
= 90 * 1
= 45 * 2
= 30 * 3
= 18 * 5
= 15 * 6
= 10 * 9
Answer: 6 different paving stones could be made.
Cost:
$2.50 + $0.16 * 360 cu in. / 4 cu in. = $16.90
Answer: Each paving stone would cost $16.90
3 1/3 minus 1 1/4 an explanation would be great please and thank you
Answers
Exact form: 25/12
Mixed number form: 2 1/12
Decimal: 2.083
please help meee brainliest
Answers
Answer: 19.
Step-by-step explanation:
9 -3 / 1/3 + 1
6 / 1/3 + 1
(6 * 3/1) + 1 also written as (6 * 3) + 1
18 + 1
= 19.
students at a high school are asked to evaluate their experience in the class at the end of each school year. the courses are evaluated on a 1-4 scale – with 4 being the best experience possible. in the history department, the courses typically are evaluated at 10% 1's, 15% 2's, 34% 3's, and 41% 4's. mr. goodman sets a goal to outscore these numbers. at the end of the year he takes a random sample of his evaluations and finds 10 1's, 13 2's, 48 3's, and 52 4's. at the 0.05 level of significance, can mr. goodman claim that his evaluations are significantly different than the history department's?
Answers
No , as we fail to reject the null hypothesis Mr. Goodman claim that his evaluations are significantly different than the history department's.
What is null hypothesis?
Statistics is the study of research and surveys on numerical data in mathematics. In order to conduct surveys, the hypothesis must be established. There are typically two different kinds of hypotheses. A null hypothesis is one that holds true, whereas an alternate hypothesis is another.The null hypothesis is a broad assertion or default stance that there is zero happening or nothing happening in probability and statistics. For instance, there is no relationship between two measured occurrences or a connection between groups. Unless additional evidence has been presented to refute the theory, it is generally accepted that it is true in this context.Test statistic X2 =1.9196
p value =0.5893
No , as we fail to reject the null hypothesis Mr.Goodman claim that his evaluations are significantly different than the history department.
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Need help with all please
Answers
Answer:
Step-by-step explanation:
1 )
a) quotient of powers as dividing two powers with the same base, we subtract the exponents.
b) product of powers when you are multiplying two terms with the same base, you add their exponents
c) property of negative exponents. According to the rules of exponents, a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent.
2)
Yes, when raising a fraction to a power with parentheses, the same principles apply as when raising a fraction to a power without parentheses. When evaluating expressions with fractions and exponents, the order of operations, including parentheses, is followed. To re-write the expressions (1/3)^2 is = (1/9) and (1/3)^-2 is equal to 9 9*(1/9) is 1 which is the rule of the product of powers. then the same applies to the second expression
3)
\((-2.3^{2})^{6}\) power to a power rule
\((\frac{1}{4}) ^{3}\) power of a quotient
\(6^{4}\) power to a power rule
\(7^{-1}\) product of powers
ps: please grade me appropriately if you need more help with problems I am glad to help and these stars mean a lot to me. make sure you study your exponent laws and all the best!
(A = students on lawn and B = students in a lab). Then, all participants indicate their likelihood of scheduling a campus visit on a 10-point scale. Which statistical analysis should she run? a) Paired samples t-test; b) correlation; c) cross-tab; b) ANOVA; d) independent samples t-test
Answers
All participants indicate their likelihood of scheduling a campus visit on a 10-point scale Paired samples t-test.
What is campus?
A college or university's campus is traditionally the area of land on which those institutions' buildings are located. Libraries, lecture halls, dorms, student centres, dining halls, and park-like settings are typically found on college campuses.
An academic or non-academic institution's buildings and grounds are collectively referred to as a campus in modern times. The Apple Campus and the are two examples. The word, which is derived from a Latin word for "field," was first used in 1774 to refer to the sizable field next to Nassau Hall of the College of New Jersey (currently Princeton University). Princeton and the small neighbouring town were separated by a field.
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The owners of a house that is assessed at $\$120,\!000$ pay $\$3,\!000$ in taxes. at the same rate, what is the tax, in dollars, for a house assessed at $\$160,\!000$?
Answers
According to the question The tax for a house assessed at $160,000 would be $4,000.
To find the tax for a house assessed at $160,000 using the same tax rate, we can set up a proportion based on the assessed values and taxes paid:
\(\(\frac{\text{{Assessed value of house 1}}}{\text{{Tax paid for house 1}}}\) = \(\frac{\text{{Assessed value of house 2}}}{\text{{Tax for house 2}}}\)\)
Substituting the given values, we have:
\(\(\frac{120,000}{3,000} = \frac{160,000}{x}\)\)
Cross-multiplying and solving for \(\(x\)\), we get:
\(\(x = \frac{160,000 \times 3,000}{120,000}\)\)
Calculating the expression on the right side, we find:
\(\(x = \$4,000\)\)
Therefore, the tax for a house assessed at $160,000 would be $4,000.
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Which of the following assumptions in a simple linear regression problem was stated incorrectly?
a. The distribution of the error term is normal.
b. The mean of the error term is 0.
c. The variance of the error term increases as x increases.
d. The errors are independent.
Answers
In a simple linear regression problem, some key assumptions are made to ensure the model's validity and reliability. Out of the given options, assumption (c) is stated incorrectly.
Assumption (a) states that the distribution of the error term is normal. This assumption is correct, as the error term's normal distribution allows for accurate statistical inferences and hypothesis testing in the regression analysis.
Assumption (b) states that the mean of the error term is 0. This assumption is also correct, as it implies that there is no systematic bias in the model. The errors, on average, should not overestimate or underestimate the dependent variable.
Assumption (c) states that the variance of the error term increases as x increases. This assumption is incorrect, as it contradicts the homoscedasticity assumption in linear regression. The correct assumption is that the variance of the error term should be constant across all levels of the independent variable (x). This constant variance ensures that the model's predictions are equally reliable for all values of x.
Assumption (d) states that the errors are independent. This assumption is correct and crucial for a linear regression analysis. The independence of errors means that the error term for one observation is not related to the error term of any other observation. This prevents any underlying patterns or relationships in the data from being mistakenly attributed to the linear relationship between the independent and dependent variables.
In summary, assumption (c) is stated incorrectly, as the variance of the error term should remain constant across all values of the independent variable in a simple linear regression analysis.
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One interior angle of a parallelogram is 65 degrees . If the remaining angles have measures of a,b and c, what is the value of a+b+c?
Answers
Answer:
65 + 65 = 130
360 - 130 = 230 degrees
If Paula divides her pencils among three friends and herself, everyone gets the same number of pencils. If Paula divides her pencils among
five friends and herself, everyone will get the same number of pencils.
How many pencils could Paula have?
A 28
B. 30
C. 42
D. 48