The time it takes for a planet to complete its orbit around a particular star is called the? planet's sidereal year. The sidereal year of a planet is related to the distance the planet is from the star. The accompanying data show the distances of the planets from a particular star and their sidereal years. Complete parts? (a) through? (e).
I figured out what
(a) is already.
(b) Determine the correlation between distance and sidereal year.
(c) Compute the? least-squares regression line.
(d) Plot the residuals against the distance from the star.
(e) Do you think the? least-squares regression line is a good? model?
Planet
Distance from the? Star, x?(millions of? miles)
Sidereal? Year, y
Planet 1
36
0.22
Planet 2
67
0.62
Planet 3
93
1.00
Planet 4
142
1.86
Planet 5
483
11.8
Planet 6
887
29.5
Planet 7
? 1,785
84.0
Planet 8
? 2,797
165.0
Planet 9
?3,675
248.0
Answers
Answer:
(a) See below
(b) r = 0.9879
(c) y = -12.629 + 0.0654x
(d) See below
(e) No.
Step-by-step explanation:
(a) Plot the data
I used Excel to plot your data and got the graph in Fig 1 below.
(b) Correlation coefficient
One formula for the correlation coefficient is
[tex]r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}[/tex]
The calculation is not difficult, but it is tedious.
(i) Calculate the intermediate numbers
We can display them in a table.
x y xy x² y²
36 0.22 7.92 1296 0.05
67 0.62 42.21 4489 0.40
93 1.00 93.00 20164 3.46
433 11.8 5699.4 233289 139.24
887 29.3 25989.1 786769 858.49
1785 82.0 146370 3186225 6724
2797 163.0 455911 7823209 26569
3675 248.0 911400 13505625 61504
9965 537.81 1545776.75 25569715 95799.63
(ii) Calculate the correlation coefficient
[tex]r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{9\times 1545776.75 - 9965\times 537.81}{\sqrt{[9\times 25569715 -9965^{2}][9\times 95799.63 - 537.81^{2}]}} \approx \mathbf{0.9879}[/tex]
(c) Regression line
The equation for the regression line is
y = a + bx where
[tex]a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\= \dfrac{537.81\times 25569715 - 9965 \times 1545776.75}{9\times 25569715 - 9965^{2}} \approx \mathbf{-12.629}\\\\b = \dfrac{n \sum xy - \sum x \sum y}{n\sum x^{2}- \left (\sum x\right )^{2}} - \dfrac{9\times 1545776.75 - 9965 \times 537.81}{9\times 25569715 - 9965^{2}} \approx\mathbf{0.0654}\\\\\\\text{The equation for the regression line is $\large \boxed{\mathbf{y = -12.629 + 0.0654x}}$}[/tex]
(d) Residuals
Insert the values of x into the regression equation to get the estimated values of y.
Then take the difference between the actual and estimated values to get the residuals.
x y Estimated Residual
36 0.22 -10 10
67 0.62 -8 9
93 1.00 -7 8
142 1.86 -3 5
433 11.8 19 - 7
887 29.3 45 -16
1785 82.0 104 -22
2797 163.0 170 - 7
3675 248.0 228 20
(e) Suitability of regression line
A linear model would have the residuals scattered randomly above and below a horizontal line.
Instead, they appear to lie along a parabola (Fig. 2).
This suggests that linear regression is not a good model for the data.
Related Questions
Please help! Correct answer only, please! The cafeteria manager at a middle school wanted to keep track of how many student breakfast and lunches were sold on a Monday. A. B. C. D.
Answers
Answer:
Hello There Again. The Correct answer is C.
Explanation: Because it shows that the numbers need to be least median then greater of the breakfast lunch.
Hope It Helps! :)
evaluate the following expressions when x=-4 and y=4
Answers
Answer:
1025/4
Step-by-step explanation:
x^6 - x
---------------
4y
Let x =-4 and y = 4
(-4)^6 - (-4)
---------------
4*4
4096 +4
------------------
16
4100/16
1025/4
The answer is C. 1025/4
Which is the solution to the linear equation? 2/3 x-1/2=1/3+5/6x
Answers
Answer: X = -5
Step-by-step explanation:
1) Multiply both sides by 6, which is 4x - 3 = 2 + 5x
2) Move the terms, 4x - 5x = 2 + 3
3) Combine like terms, -x = 5
4) Multiply both sides by -1, x = -5
What is it ansewerr 1/5 of 45
Answers
Answer:
9
Step-by-step explanation:
Please mark me brainliest
The right answer is 9.
please see the attached picture for full solution
Good luck on your assignment
Select four statements from the invertible matrix theorem and show that all four statements are true or false
This learning module introduced the invertible matrix theorem. This theorem is a collection of 12 equivalent statements. This means that when one statement in the theorem is true, all statements in the theorem are true. Similarly, when one statement in the theorem is false, all statements are false. For your initial post, propose a specific n x n matrix A, where n >= 3. Select four statements from the invertible matrix theorem and show that all four statements are true or false, depending on the matrix you selected. Make sure to clearly explain and justify your work. Also, make sure to label your statements using the notation used in the notes (e.g., part (a), part (f), etc.).
Theorem (The Invertible Matrix Theorem): Let A be an n x n matrix. Then the following statements are equivalent:
A is an invertible matrix.
A is row equivalent to the n x n identity matrix.
A has n pivot positions.
The equation Ax = 0 has only the trivial solution.
The columns of A form a linearly independent set.
The linear transformation x à Ax is one-to-one.
There is an n x n matrix C such that CA = I.
There is an n x n matrix D such that AD = I.AT is an invertible matrix.
Answers
Answer:
A) A is an invertible matrix ( TRUE )
B) A is a row equivalent to the n x n identity matrix ( n = 3 ) ( TRUE )
C ) The equation Ax = 0 has only the trivial solution ( TRUE )
D ) The columns of A form a linearly independent set ( TRUE )
Step-by-step explanation:
Assuming a matrix A
[tex]\left[\begin{array}{ccc}1&2&1\\-1&0&3\\4&1&5\end{array}\right][/tex]
det A = 1 [ 0 -3 ] + 2 [12 + 5 ] + 1[-1]
= -3 + 34 -1 = 30 ≠ 0
THEREFORE det A = 30 ≠ 0
Attached is the detailed solution of the given statements above
PLS HELP 20 POINTS
Find the volume of a pyramid with a square base, where the perimeter of the base is
19.8 m and the height of the pyramid is 24.2 m. Round your answer to the nearest
tenth of a cubic meter.
Answers
Answer:197.7m^3
Step-by-step explanation:
Area of base:
B=24.5025
h=24.2
V=1/3(24.5025)(24.2)
197.6535
V≈197.7m^3
Answer:
197.7m
Step-by-step explanation:
wirk out the values of 5x-2y when x=-2 and y = -2
Answers
Step-by-step explanation:
5x - 2y
5(-2) - 2(-2)
-10 + 4
= - 6
Please answer this correctly
Answers
Answer:
3769.57
Step-by-step explanation:
the perimeter of semicircle is
P = d + πd/2
251.86 = d + (3.14d/2)
multiply both side with 2
503.72 = 2d + 3.14d
503.72 = 5.14 d
d = 98 miles
d is diameter, then the radius is 98 : 2 = 49
Area of semicircle
A = ½ π r²
A = 0.5 x 3.14 x 49²
A = 3769.57 miles²
Answer: 3769.57 miles²
Step-by-step explanation:
The perimeter of the semi circle is the sum of the curve and the diameter.
Perimeter of curve
[tex]\dfrac{1}{2}C=\dfrac{1}{2}2\pi r\\\\\\.\quad =\pi r\\[/tex]
Diameter of the semi circle = 2r
[tex]P = \pi r+2r\\\\\\251.86=r(\pi +2)\\\\\\\dfrac{251.86}{\pi +2}=r\\\\\\\dfrac{251.86}{5.14}=r\\\\\\49=r[/tex]
Area of the curve
[tex]\dfrac{1}{2}A=\dfrac{1}{2}\pi r^2\\\\\\.\quad =\dfrac{1}{2}(3.14)(49)^2\\\\\\.\quad =\large\boxed{3769.57}[/tex]
In ΔKLM, the measure of ∠M=90°, MK = 2.7 feet, and KL = 6.6 feet. Find the measure of ∠L to the nearest degree.
Answers
Answer:
24.15° = 24° to the nearest degree
Step-by-step explanation:
If we draw the triangle we would see that the KL is the longest side and the hypothenus;
Also MK would-be the height and ML is the base of the triangle.
Since L and M are the angles at the base;
From Trigonometry Sin L = MK/ KL
= 2.7/6.6
L = Sin^{-1} (2.7/6.6)
L = Sin^{-1} (0.4091)
=24.15°
Note : sin a = height/ longest side
= Opposite/hypothenus
if sin B=8/17 WHAT IS TAN B?
Answers
Answer:
In first quadrant, [tex]\tan B=\frac{8}{15}[/tex]
In second quadrant, [tex]\tan B=\frac{-8}{15}[/tex]
Step-by-step explanation:
Given: [tex]\sin B=\frac{8}{17}[/tex]
To find: [tex]\tan B[/tex]
Solution:
Trigonometry explains the relationship between the sides and the angles of the triangle.
Here,
[tex]\sin B=\frac{8}{17}[/tex]
So, B can be in first or second quadrant as sine is positive both first and second quadrants.
Cosine and tangent are positive in first quadrant but negative in second quadrant.
In first quadrant:
[tex]\cos B=\sqrt{1-\sin ^2B}=\sqrt{1-\left ( \frac{8}{17} \right )^2}=\sqrt{1-\frac{64}{289}}=\sqrt{\frac{225}{289}}=\frac{15}{17}[/tex]
So, [tex]\tan B=\frac{\sin B}{\cos B}=\frac{\frac{8}{17}}{\frac{15}{17}}=\frac{8}{15}[/tex]
In second quadrant:
[tex]\cos B=-\sqrt{1-\sin ^2B}=-\sqrt{1-\left ( \frac{8}{17} \right )^2}=-\sqrt{1-\frac{64}{289}}=-\sqrt{\frac{225}{289}}=\frac{-15}{17}[/tex]
[tex]\tan B=\frac{\sin B}{\cos B}=\frac{\frac{8}{17}}{\frac{-15}{17}}=\frac{-8}{15}[/tex]
Takeisha is placing placemats around a table. Each placemat is 14 inches long and 10 inches wide. The rectangular table is 42 inches long and 48 inches wide. What is the greatest number of placemats that Takeisha can place around the table without overlapping?
Answers
welll i kinda don get ur question but ummmm if u say like the graetest number then 48
Help please! What is the excluded value? no excluded values x = 17 x = 0
Answers
Answer:
wrong question hai right question do
Step-by-step explanation:
0
Answer:
0
Step-by-step explanation:
Zero, because you cannot have (0/17)
After Clara ran 8 times around a square field , she covered a distance of 288km. Calculate the area of the field.
Answers
Answer:
81 km²
Step-by-step explanation:
so the perimeter of the field is 288 : 8 = 36 km
the perimeter of square is 4 time side
4s = 36
s = 36 : 4 = 9 km
Area = side x side = s²
A = 9² = 81 km²
The domain of a function is
Answers
Answer:
The domain of a function is the complete set of possible values of the independent variable. In plain English, this definition means: The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
Step-by-step explanation:
I hope this helped ;)
Michael is making a big batch of granola bars to bring to his soccer game. The oats in the granola bars contain 568.7 grams of carbohydrates.
A 2-column table with 3 rows titled Nutritional Facts Oats (1 cup). Column 1 has entries Calories, Carbohydrates, Protein. Column 2 has entries 607, 103.4 grams, 26.3 grams.
How many cups of oats did Michael use in his recipe?
0.415 cups
0.55 cups
4.15 cups
5.5 cups
Answers
Answer:
5.5
Step-by-step explanation:
From the table; one cup of oat contains 103.4 carbohydrates.
568.7/103.4 = 5.5 cups
-8+4(c-9)-5+6c+2c
plz help me out
Answers
Answer:
12c-49
Step-by-step explanation:
−8+(4)(c)+(4)(−9)+−5+6c+2c
=−8+4c+−36+−5+6c+2c
Combine Like Terms:
=−8+4c+−36+−5+6c+2c
=(4c+6c+2c)+(−8+−36+−5)
=12c−49
pls mark me brainliest
Let’s start by distributing.
-8+4c-36-5+6c+2c
Combine like terms.
-8-36-5+4c+6c+2c
-49+12c
12c-49
there 2,500 first year students at nicks school. Nick found a brochure from the housing office thats stats 70% of students live on campus. based on the statistics how many students live on campus
Answers
Answer:
1750 Students
Step-by-step explanation:
2500*0.7
A vertical right circular cylindrical tank measures 20 ft high and 12 ft in diameter. It is full of liquid weighing 62.4 lb divided by ft cubed. How much work does it take to pump the liquid to the level of the top of the tank?
Answers
Answer:
Step-by-step explanation:
Work done is given as the product of force and distance.
The liquid in the cylindrical tank weighs 62.4 lb/ft^3.
This means that each ft^3 of the tank has 62.4 lb of the liquid.
To find the wight of the liquid in the entire tank, we multiply 62.4 by the volume of the cylindrical tank.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r is its radius and h is its height
The radius of the tank is 6 ft (since its diameter is 12 ft) and its height is 20 ft.
Therefore, the weight of the liquid in the tank is given as:
[tex]V = \pi * 6^2 * 20 = 2261.95 lb[/tex]
This weight is a force.
The height of the tank is 20 ft.
Therefore, the work done in pumping the liquid to the top of the tank is:
W = 2261.95 * 20 = 45239 ft.lb
7. If In 3 = 1.10 and In 6 = 1.79, then In 2
O -2.89
-0.69
O 1.63
0.61
O 0.60
Answers
Answer:
Option (2)
Step-by-step explanation:
Given in the question,
ln(3) = 1.10
ln(6) = 1.79
We have to calculate the value of ln(2).
Since ln(6) = ln(3 × 2)
= ln(3) + ln(2) [From the property of logarithm, ln(a×b) = ln(a) + ln(b)]
1.79 = 1.10 + ln(2)
ln(2) = 1.79 - 1.10
ln(2) = 0.69
Therefore, value of ln(2) will be 0.69.
Option (2) will be the answer.
Answer:
The answer is 0.69.
Step-by-step explanation:
Which of the following describes the translation of the graph of y = x 2 to
obtain the graph of y = -x 2 - 3?
reflect over the x-axis and shift left 3
reflect over the x-axis and shift down 3
reflect over the y-axis and shift down 3
Answers
Answer:
reflect over the x-axis and shift down 3
Step-by-step explanation:
The leading coefficient of -1 means the graph is reflected over the x-axis. The addition of -3 to the function means each graphed point is shifted down 3 units from the original.
The graph of y = -x^2 -3 is the result of the transformation ...
reflect over the x-axis and shift down 3
ABC
ABCD ]````````````````````` .```````````````````[
Answers
Answer:
B then C
Step-by-step explanation:
First screenshot:
Shape B because the net has a square base.
Second screenshot:
It is C
C does not make a cube
A large game cube with a three inch side length is wrapped with shrink wrap. How many square centimeters of shrink wrap will be used to wrap ten game cubes?
Answers
Answer:
see below
Step-by-step explanation:
cube has 6 square faces so 6*s*s
s =3 in =3*2.54 cm = 7.62 cm
1 in = 2.54 cm
1 cube needs 6*7.62² = 348.3864 cm²
10 cubes = 10*348.3864 =3483.864 cm²
If your customers are satisfied 11 out of 15 times how many are satisfied If 350 people come in on Black Friday
Answers
Answer:
257 people are satisfied
Step-by-step explanation:
11/15 is the fraction that are satisfied
11/15 * 350 =256.6(repeating)
Rounding to the nearest whole person
257 people are satisfied
The diameter of the container is 13 centimeters and
its height is 24 centimeters. Determine, in terms of
I, the volume of the ovlinder, in cubie centimeters,
Answers
1. Considere as funções f e g, ambas com domínio Z, dadas por f(x) = x²- 2x e g(x) = x³-1. Associe as colunas e assinale a alternativa que apresenta a sequência correta: * 1 ponto Imagem sem legenda a) C, D, A, B b) A, B, D, C c) D, C, A, B d) A, C, D, B
Answers
Answer:
(A)C,D,A,B
Step-by-step explanation:
[tex]f(x) = x^2- 2x\\g(x) = x^3-1[/tex]
a) f(-2)
[tex]f(-2) = (-2)^2- 2(-2)\\=4-(-4)\\=4+4\\=8$ (C)[/tex]
b) g(-2)
[tex]g(-2) = (-2)^3-1\\\=-8-1\\=-9 $(D)[/tex]
c) f(-1)+g(3)
[tex]f(-1) = (-1)^2- 2(-1)=1+2=3\\g(3) = (3)^3-1=27-1=26\\f(-1) + g(3)=3+26\\=29$ (A)[/tex]
d) f(5) : g(2)
[tex]f(5) = (5)^2- 2(5)=25-10=15\\g(2) = (2)^3-1=8-1=7\\f(5) :g(2)=15/7$ (B)[/tex]
Answer:
letra A confia
Step-by-step explanation:
You are thinking about the things that can go wrong on your trip home over the Thanksgiving break. You have booked a flight with US-Scareways. You know that in 33 percent of the cases the company has canceled the flight you were on. Should such a thing occur, there would be no other air travel option home for you. As a backup, your friend Walter has offered you a ride back. However, you know that Walter only has a seat in his car for you with 88 percent probability. What is the probability of you making it home for the holidays?
Answers
Answer:
0.9604 = 96.04% probability of you making it home for the holidays
Step-by-step explanation:
We have these following probabilities:
100 - 33 = 67% probability of the flight happening.
In the 33%, that is, when the flight does not happen, there is an 88% probability that you get the ride with Walter.
What is the probability of you making it home for the holidays?
0.67 + 0.88*0.33 = 0.9604
0.9604 = 96.04% probability of you making it home for the holidays
A company that produces fine crystal knows from experience that 17% of its goblets have cosmetic flaws and must be classified as "seconds." (Round your answers to four decimal places.)(a)Among seven randomly selected goblets, how likely is it that only one is a second
Answers
Answer:
0.3891 = 38.91% probability that only one is a second
Step-by-step explanation:
For each globet, there are only two possible outcoes. Either they have cosmetic flaws, or they do not. The probability of a goblet having a cosmetic flaw is independent of other globets. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
17% of its goblets have cosmetic flaws and must be classified as "seconds."
This means that [tex]p = 0.17[/tex]
Among seven randomly selected goblets, how likely is it that only one is a second
This is P(X = 1) when n = 7. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{7,1}.(0.17)^{1}.(0.83)^{6} = 0.3891[/tex]
0.3891 = 38.91% probability that only one is a second
Given the functions f(x) = 7x + 13 and g(x) = x + 2, which of the following functions represents f[g(x)] correctly?
Answers
Answer:
f[g(x)]= 7x + 27
Step-by-step explanation:
g(x) = x + 2,
f(x) = 7x + 13,
f[g(x)] means you substitute the value of g(x) into the variable of f(x);
Which is 7( x+2) + 13 = 7x +14 +13
= 7x + 27
Expression equivelent to 2/5 divided by 6
Answers
Answer:
1/15
Step-by-step explanation:
(2/5)/6 = 2/(5*6) = 2/30 = 1/15
Factor 24g - 36h. Remember that your answer needs to be factored completely.
Answers
Answer:
The completed factor is [tex]=12(2g- 3h)[/tex]Step-by-step explanation:
To factor the expression we need to look for a value that is unique to both terms in the expression.
Given the expression
[tex]24g - 36h[/tex]
The available factors common to both terms are 2,3,4,6,8,12. but since we are expected to factor the expression completely we will use the greatest common factor (gcf) to find the solution
The greatest but common factor is 12, hence we have
[tex]=12(2g- 3h)[/tex]
