Answer:
(i) The estimated regression equation is;
[tex]\hat y[/tex] ≈ 1.6896 + 0.0604·X
The coefficient of 'X' indicates that [tex]\hat y[/tex] increase by a multiple of 0.0604 for each million dollar increase in sales, X
(ii) The estimated earnings for the company is approximately $4.7096 million
(iii) The standard error of estimate is approximately 29.34
The high standard error of estimate indicates that individual mean do not accurately represent the population mean
(iv) The coefficient of determination is approximately 0.57925
The coefficient of determination indicates that the probability of the coordinate of a new point of data to be located on the line is 0.57925
Step-by-step explanation:
The given data is presented as follows;
[tex]\begin{array}{ccc}Sales \ (\$million)&&Earning \ (\$million) \\89.2&&4.9\\18.6&&4.4\\18.2&&1.3\\71.7&&8\\58.6&&6.6\\46.8&&4.1\\17.5&&2.6\\11.9&&1.7\end{array}[/tex]
(i) From the data, we have;
The regression equation can be presented as follows;
[tex]\hat y[/tex] = b₀ + b₁·x
Where;
b₁ = The slope given as follows;
[tex]b_1 = \dfrac{\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}{\Sigma(x_i - \overline x)^2}[/tex]
b₀ = [tex]\overline y[/tex] - b₁·[tex]\overline x[/tex]
From the data, we have;
[tex]{\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}[/tex] = 364.05
[tex]\Sigma(x_i - \overline x)^2}[/tex] = 6,027.259
[tex]\overline y[/tex] = 4.2
[tex]\overline x[/tex] = 41.5625
∴ b₁ = 364.05/6,027.259 ≈ 0.06040059005
b₀ = 4.2 - 0.06040059005 × 41.5625 ≈ 1.68960047605 ≈ 1.69
Therefore, we have the regression equation as follows;
[tex]\hat y[/tex] ≈ 1.6896 + 0.0604·X
The coefficient of 'X' indicates that the earnings increase by a multiple of 0.0604 for each million dollar increase in sales
(ii) For the small company, we have;
X = $50.0 million, therefore, we get;
[tex]\hat y[/tex] = 1.6896 + 0.0604 × 50 = 4.7096
The estimated earnings for the company, [tex]\hat y[/tex] = 4.7096 million
(iii) The standard error of estimate, σ, is given by the following formula;
[tex]\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu \right )^{2} }{n - 1}}[/tex]
Where;
n = The sample size
Therefore, we have;
[tex]\sigma =\sqrt{\dfrac{6,027.259 }{8 - 1}} \approx 29.34[/tex]
The standard error of estimate, σ ≈ 29.34
The high standard error of estimate indicates that it is very unlikely that a given mean value within the data is a representation of the true population mean
(iv) The coefficient of determination (R Square) is given as follows;
[tex]R^2 = \dfrac{SSR}{SST}[/tex]
Where;
SSR = The Sum of Squared Regression ≈ 21.9884
SST = The total variation in the sample ≈ 37.96
Therefore, R² ≈ 21.9884/37.96 ≈ 0.57925
The coefficient of determination, R² ≈ 0.57925.
Therefore, by the coefficient of determination, the likelihood of a new introduced data point to located on the line is 0.57925
The college athletic director recorded the highest noise levels reached during 7 sporting events. The highs were:
88 decibels 88 decibels 88 decibels 87 decibels 84 decibels 97 decibels 95 decibels
What was the mean noise level recorded? Round your answer to the nearest whole number.
Answer:
90
Step-by-step explanation:
Mean:
(88 + 88 + 88 + 87 + 84 + 97 + 95)/7
627/7
89.57
90
what is this i HATE math Oh MY GOD
A ship is 130 m away from the centre of a barrier that measures /
180 m from end to end. What is the minimum angle that the
boat must be turned to avoid hitting the barrier?
Answer:
Step-by-step explanation:
50 meters away
The diagram shows a right-angled triangle.
All the measurements are in centimetres.
The area of the triangle is 18cm^2
Work out the length of the shortest side of the triangle.You must show all your working
Answer:
short side = 4
Step-by-step explanation:
area = 1/2BH
18 = 1/2(x - 1)(x + 4)
18 = 1/2(x² + 4x - x - 4)
multiply both sides of the equation by 2:
36 = x² + 3x - 4
x² + 3x - 40 = 0
(x + 8)(x - 5) = 0
x = 5
short side = 5 - 1 = 4
The shortest length of the right angled triangle is 4 cm.
Area of a triangle:area = 1 / 2 bhwhere
b = base
h = height
Therefore,
area = 18 cm²
18 = [tex]\frac{1}{2}[/tex] × (x - 1)(x + 4)
36 = (x - 1)(x + 4)
x² + 4x - x - 4 = 36
x² + 3x - 4 = 36
x² + 3x - 4 - 36 = 0
x² + 3x - 40 = 0
x² - 5x + 8x - 40 = 0
x(x - 5) + 8(x - 5) = 0
(x + 8)(x - 5) = 0
x = -8 or 5
we can only use positive numbers.
Therefore,
x = 5
The shortest sides is definitely one of the 2 legs . The hypotenuse of a triangle is the longest side.
Therefore,
h = x - 1 = 5 - 1 = 4 cm
b = x + 4 = 5 + 4 = 9 cm
learn more on right angled triangle here: https://brainly.com/question/2292567?referrer=searchResults
After spending 2/3 of his money. Charles has 12 pesos left. How much did he have at first??
The total amount of money charles must have had at the beginning is 36 pesos.
What are fractional linear equations and how one can solve it?
Linear equations which are in the form of fractions are referred as fractional linear equations.
an equation containing the unknown in the denominator of one or more terms (as a/x + b/(x + 1) = c)
It is frequently simplest to eliminate the fraction in the first step when dealing with fractions incorporated into linear equations. Typically, this entails locating the fraction's LCD and multiplying each term in the entire equation.
Solution:
Given:
Money left with charles = 12 pesos
Money spent = 2/3 of the total amount.
Find:
Total Money he had at first = ?
Step-1:
Let x denote the total amount of money he had at the beginning.
After spending 2/3 of his money he is left with 1/3 of part of his money.
Step-2:
So the equation can be written as:
1x/3 = 12
x = 36
Hence the total money he had at the beginning was 36 pesos.
Learn more about "Fractional linear equations" here-
brainly.com/question/14323743
#SPJ2
CAN SOMEONE PLEASEEE HELP SIMPLIFY THESE TWO EXPONENT PROBLEMS I HAVE NO CLUE HOW
Answer:
20. [tex]-\frac{y^{12} }{9x^{4} }[/tex]
Step-by-step explanation:
21. [tex]3 x^{2} y^{2}[/tex]
Mary and Carlos are each saving for new skateboards. So far, Mary has $9 saved
and earns $6 per hour babysitting. Carlos has $3 saved and can earn $9 per hour
working at his family's restaurant. After how many hours of work will Mary and
Carlos have saved the same amount and how much money will they both have?
Answer:
After 3 hours, both will have saved $21.
Step-by-step explanation:
HELP OMG
I LOST MY AIRPODS AT SCHOOL
Answer:
how should we help?
Step-by-step explanation:
Answer:
dang that sucks..... try and play music at max vol and see if you hear any music coming from anywhere that's probably were the airpods are, if they are in the case then i dont know if u would hear anything. It all depends...
~ i hope this has helped ya out some how, hope ya find your airpods my friend!~
Step-by-step explanation:
Which table represents a linear function?
Answer:
the first one on the top left corner
it it bc on the right side of the table is counting by twos and so therefore on the left should be added 2 with that number
Answer:
Top left.
Step-by-step explanation:
Because it's constant. X increases by 2 and y increases by 3.
Which of these is an example of due process?
a search without good reason
a prejudiced jury
a cruel punishment
a fair trial
Answer:
A fair trial.
Answer:
Step-by-step explanation: a search without good reason
What is the correct answer for each box
Answer:
1) A ; 2) D ; 3)B ; 4)C
Step-by-step explanation:
we can solve every option and see what trinomal result
A (2x-3)(x-3) = 2x^2 -6x-3x +9 = 2x^2-9x+9
B (2x+3)(x-3) = 2x^2 -6x+3x-9 = 2x^2-3x+9
C (2x-3)(x+3) = 2x^2+6x-3x-9 = 2x^2+3x-9
D (2x+3)(x+3) = 2x^2+6x+3x+9 = 2x^2+9x+9
What is the slope of the following line?
Answer:
1/2
Step-by-step explanation:
How many solutions does the equation 4x-7(x-2)=3x+2 have?
Answer:
one solution, x=2
Step-by-step explanation:
brainliest?
This is due in 2 minutes
53+2444= ??????? HELP I D K THE ANSWER
Answer:
2497
Step-by-step explanation:
Answer:
2497
Step-by-step explanation:
53 + 2444
= 0053 + 2444
= 2497
Can someone help me with this. Will Mark brainliest.
Answer: True!
Step-by-step explanation: Rhombuses are like squares with an 4 equivalent sides!
hope this helped have a nice day ! :)
With spring break approaching, Travis plans to play more 2k every day. Right nowhe plays about 40 minutes per day. He expects that number will increase by 10 minutes per day
Write an equation that shows the number of minutes of 2k played as a function of the day
Yes or no? Plzzz explain why
Answer: no
Step-by-step explanation:
Steven must have gotten this answer from 11 x 11, which is wrong. The reason is because of the square root.
[tex]\sqrt{11} = 3.3166247903554[/tex]
(roughly 3.32)
So using the formula for a square l x w, the square's area is 11.0224 or 11.02
The function y=-0.2x^2+1.9x models the path of a kicked soccer ball.The height is y,the distance is x, and the units are meters.How high does the soccer ball go?
Answer:
The highest height the ball achieves is 4.5125 meters.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
Quadratic function [tex]y = -0.2x^2 + 1.9x[/tex], which has [tex]a = -0.2, b = 1.9[/tex].
The maximum height of the ball is [tex]y_{v}[/tex].
Then
[tex]\Delta = b^2-4ac = (1.9)^2 - 4*(-0.2)(0) = 3.61[/tex]
[tex]y_{v} = -\frac{3.61}{4(-0.2)} = 4.5125[/tex]
The highest height the ball achieves is 4.5125 meters.
Which of these expressions or phrases can be used to represent the model choose all the correct answers
Pls no BOT part ;(
Step-by-step explanation:
anyway.. for your answer i only know that number of fifths in 1 is correct I dont know about the rest.
9.
Jamal is asked to draw a circle. He is given the center and two points on the
circle, but he isn't told which point is which. The points are (-4,7), (3,6), and
(-1,3). Jamal draws the accurate circle from this information.
What is the equation of the circle he draws?
Answer:
C
Step-by-step explanation:
Hey, so i know you might not need help now, but i got the answer right on mine and it was C.
Hope this helps!
pls help meh plssss asap
Answer:
1.) 150
2.) 10
Step-by-step explanation:
If you look at the chart, above the 25 in the seconds row in the gallons row is 150.
This means that the chart tells you there are 150 gallons for every 25 seconds.
The second question asks about 60 gallons. So, if you look at 60 on the gallons row, and look below it on the seconds row, you see 10.
This means the chart tells you there are 60 gallons for every 10 seconds.
I need help please i don’t understand
9514 1404 393
Answer:
no
Step-by-step explanation:
The dimensions will be those of a rectangular mirror if the diagonal measure is the hypotenuse of the right triangle with the given side lengths.
The Pythagorean theorem would require for some width w ...
w^2 +24^2 = 30^2
w^2 = 900 -576 = 324
w = √324 = 18
A rectangular mirror with a length of 24 inches and a diagonal of 30 inches will have a width of 18 inches, not 16.
__
The attachment shows that a width of 16 inches is not consistent with a right-angle corner.
_____
Additional comment
If you reduce the given numbers to lowest terms by dividing them by 2, they become 8, 12, 15. That is, the two shortest sides are even and the longest is odd. Any set of integer dimensions for a right triangle must have an even number of odd numbers (0 or 2). These numbers cannot be a Pythagorean triple, so cannot make a right triangle.
CHOOSING BRAINLIEST ( SCREENSHOT PROVIDED )
Find the missing number to complete the linear equation that gives the rule for this table.
x | y
0 | 0
1 | 25
2 | 50
3 | 75
Answer:
y= 25
i think
Step-by-step explanation:
Plzzzz guys help me with this i don’t know
Answer: B
Step-by-step explanation:
if I'm wrong sry lol
Answer:
D
Step-by-step explanation:
- 117° is positioned in the 3rd quadrant where sine < 0
The related acute angle is 180° - 117° = 63°
Then
sin(- 117)°
= - sin63° → D
Write an equation for the line, in point slope form given the following information
Slope = 1/4 contains the point (8,-3)
Answer:
y+3=1/4(x-8)
simplified -> y+3=1/4x-2
Step-by-step explanation:
y-y1=m(x-x1)
y-(-3)=1/4(x-8)
y+3=1/4(x-8)
If you want it to be further simplified
y+3=1/4x-2
Find the equation of a line that is perpendicular to 4x+6y=1 and that has a greater intercept to the line 2x+3y=18
Answer:
2y - 3x = -15
Step-by-step explanation:
Slope of the line 4x + 6y = 1 is as shown below;
Rewrite in slope intercept form;
6y = -4x+1
y = -4x/6 + 1/6
y = -2x/3 + 1/6
mx = -2/3x
m = -2/3
The slope of the line perpendicular M = -1/(-2/3)
M = 3/2
Get the x and y intercept of 2x+3y = 18
x intercept occurs when y = 0
2x + 0 = 18
x= 18/2
x = 9
y intercept occurs when x = 0
0 + 3y = 18
3y= 18
y = 18/3
y = 6
The line passes through the point (9,6)
Write the equation in point slope form
y - y0 = m(x-x0)
y - 6 = 3/2(x-9)
2(y-6) = 3(x-9)
2y - 12 = 3x - 27
2y - 3x = -27 + 12
2y - 3x = -15
This gives the required equation
Plz help question is in pic!
will mark brainliest
6. Mrs. Sam buys pencils for $15 per one hundred packs.
a. If she sells them to her students for 10 cents each, what is her profit/loss?
b. If she sells them to her students for 25 cents each, what is her profit/loss?
c. What price should she sell them at to not make or lose any money?
Answer:
a.) her loss is 5 dollars
b.) her profit is 10 dollars
c.) she should sell them for $0.15
Two similar cylinders have heights of 3 cm and 6 cm respectively. If the volume of the smaller cylinder is 30 cm3, find the volume of the larger cylinder.Required to answer. Single line text.
Answer:
the ans is
Step-by-step explanation:
V=πr2h=π·32·6≈169.646