The table shows the size of outdoor decks (x) in square feet, and the estimated dollar cost to construct them (y).
y
xy
100
600
10,000
60,000
144
850
20,736
122,400
225
1,300
50,625
292,500
324
1,900
104,976
615,600
400
2,300
160,000
920,000
Σχ=1,193 | Σy=6,950 | Ex?=346,337 | Σxy=2,010,500
Which regression equation correctly models the data?
X
xy=5.83x-1.04
y = 5.83x + 17
y = 5.71x + 29
y
= 5.71x + 27.6
Submitted
Answers
The regression equation of the table is y = 5.71x + 27.6
How to estimate the regression equation?From the table of values, we have the following parameters:
[tex]\sum x = 1193[/tex]
[tex]\sum y = 6950[/tex]
[tex]\sum x^2 = 346337[/tex]
[tex]\sum xy = 2010500[/tex]
Calculate A using
[tex]A = \frac{\sum y * \sum x^2 - \sum x * \sum xy}{n\sum x^2 - (\sum x)^2}[/tex]
This gives
[tex]A = \frac{6950 * 346337 - 1193 * 2010500}{5 * 346337 - (1193)^2}[/tex]
Evaluate
[tex]A = \frac{8515650}{308436}[/tex]
Divide
A = 27.6
Calculate B using
[tex]B = \frac{n\sum xy - \sum x * \sum y}{n\sum x^2 - (\sum x)^2}[/tex]
This gives
[tex]B = \frac{5 * 2010500 - 1193 * 6950}{5 * 346337 - (1193)^2}[/tex]
Evaluate
[tex]B = \frac{1761150}{308436}[/tex]
Divide
B = 5.71
The regression equation is represented as:
y = Bx + A
So, we have
y = 5.71x + 27.6
Hence, the regression equation of the table is y = 5.71x + 27.6
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Related Questions
(a) (2x³+4x²y + 5xy²-3y²)-(x²-3x²y +5xy²-2y²)
Answers
Answer:
Your answer is 2x³ + 7x²y + y²- x²
Step-by-step explanation:
(a) ( 2x³ + 4x²y + 5xy² - 3y² ) - ( x² - 3x²y +5xy² - 2y² )
= 2x³ + 4x²y + 5xy² - 3y² - x² + 3x²y - 5xy² + 2y²
= 2x³ + 4x²y + 3x²y + 5xy² - 5xy² + 3y² + 2y² - x²
= 2x³ + 7x²y + y²- x² ans.
Hope its helpful!
Please mark me as brainlist.
Step-by-step explanation:
(a) ( 2x³ + 4x²y + 5xy² - 3y² ) - ( x² - 3x²y +5xy² - 2y² )
= 2x³ + 4x²y + 5xy² - 3y² - x² + 3x²y - 5xy² + 2y²
= 2x³ + 4x²y + 3x²y + 5xy² - 5xy² + 3y² + 2y² - x²
= 2x³ + 7x²y + y²- x² ans.
You start your working career when you are 24 years old. Each month, you deposit $144 into a pension plan. You continue making deposits into the plan you are 68 years old. What is the balance, in dollars, when the plan earns 6%, compounded monthlyRound your answer to the nearest cent
Answers
The balance, in dollars, (future value) when the pension plan earns 6% compounded monthly is $372,134.19.
What is future value?The future value refers to the compounded future value of an asset, for example, a pension plan, based on a growth rate of interest for a future period.
The future value can be determined with the FV formula, table, or using an online finance calculator as follows:
Data and Calculations:N (# of periods) = 528 months (68 - 24 x 12 months)
I/Y (Interest per year) = 6%
PV (Present Value) = $0
PMT (Periodic Payment) = $144
Results:
FV = $372,134.19
Sum of all periodic payments = $76,032 ($144 x 528)
Total Interest = $296,102.19
Thus, the balance, in dollars, (future value) when the pension plan earns 6% compounded monthly is $372,134.19.
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The graph of the function f(x)=log6(x) is stretched vertically by a factor of 7, reflected over the x-axis, reflected over the y-axis, and shifted up by 2 units.
Answers
The resulting function after all transformations have been carried out is; -7log6(-x) - 2.
Which function results from all the Transformations?The transformations which ensued on the function given are as follows;
Stretched vertically by a factor of 7; Hence, we have; 7f(x) = 7log6(x).Reflected over the x-axis; -7f(x) = -7log6(x).Reflected over the y-axis; -7f(x) = -7log6(-x).Shifted up by 2 units; -7f(x) -2 = -7log6(-x) - 2.On this note, it follows that the resulting function upon all the Transformations is; = -7log6(-x) - 2.
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Use the number line below to help you compare the numbers 26.3 and 26.5.
26.0
26.5 < 26.3
26.5 = 26.3
O 26.3 > 26.5
26.3 < 26.5
Answers
Answer: 26.3 < 26.5
Step-by-step explanation:
On the number line, 26.3 lies to the left of 26.5, meaning that 26.3 is less than 26.5.
Twice the sum of two consecutive integers is 22. What are the two integers?
Answers
3(5+7)-6(4-2x) what is equivalent to this equation
Answers
Answer:
[tex]12(1 + x)[/tex]
Step-by-step explanation:
We will use order of operations to simplify this expression.
We will evaluate the brackets first.
3(5+7)-6(4-2x) =
[tex]3(12) - 6(4 - 2x) \\ = 36 - 6(4 - 2x) \\ = 36 - 24 + 12x \\ = 12 + 12x[/tex]
You can further simplify it by factorising it:
[tex]12 + 12x \\ = 12(1 + x)[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3(5 + 7) - 6(4 - 2x)}[/tex]
[tex]\mathsf{= 3(5) + 3(7) - 6(4) - 6(-2x)}[/tex]
[tex]\mathsf{= 15 + 21 - 24 + 12x}[/tex]
[tex]\mathsf{= 36 - 24 + 12x}[/tex]
[tex]\mathsf{= 12 + 12x}[/tex]
[tex]\mathsf{= 12x + 12}[/tex]
[tex]\huge\text{Therefore, your answer should be:\boxed{\mathsf{12x + 12}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
consider the functions f(x) = -2(x-3)² + 2 which is represented by the graph
drag each interval to the correct location in the table to describe key features of f(x) and g(x)
Answers
The intervals of the function on the graph are:
Domain = (-∝, ∝)Range = (-∝, 2]Increases (-∝, 3]Decreases [3, ∝)The key features of the function?The function is given as:
f(x) = -2(x-3)² + 2
See attachment for the graph.
From the graph, we have;
Domain = (-∝, ∝)
Because it takes all real values as its input
Range = (-∝, 2]
Because it has a vertex of (3, 2) and the vertex is a maximum
Also, it increases on the interval (-∝, 3] and decreases on the interval [3, ∝)
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HELP! ASAP!
Thank you in advance :)
Answers
By the corresponding angles theorem,
∠AFG, ∠BGD, and ∠CHD are congruent∠BAF, ∠CBG, and ∠DCH are congruentThus, triangles AFD, BGD, and CHD are similar by AA.
Answer:
If all of these are parralel and all touching a single line(FD), then they must be the same. Also, they are perpendicular. :/
Step-by-step explanation:
factor: (14.25r^4-24.375r^3+10.125)=0
Answers
Answer:
1, 1.5
Step-by-step explanation:
Use the rational roots theorem. Factor out until you get the maximum simplification.
0.375(x−1)(2x−3)(19x2+15x+9)
However, if you wanted to solve this equation for r, you will get 1, 1.5 using the quartic formula.
Given the situation, which inequality models the number of additional weeks marie needs to continue saving to afford the home repairs? select the correct answer.
Answers
In the inequality models, the number of additional weeks is 1558+60x≥2158.
Given that the initial savings is $1558, the amount needed is $2158 and additional savings is $60 weekly.
Let the number of weeks be x.
So, she will save 60x in x weeks.
Total savings after x weeks is
Initial saving +60x .......(1)
According to the question, she needs $1258 for repair.
So, that means the minimum requirement is 2158.
≥2158 ........(2)
Combine equations (1) and (2) and get
Initial savings +60x≥2158
As given that the initial savings is 1558.
Substitute this in above inequality and get
1558+60x≥2158
To find the number of weeks find value of x.
Subtract 1558 from either sides of the inequality.
1558+60x-1558≥2158-1558
60x≥600
Divide both sides with 60 as
60x÷60≥600÷60
x≥10
Hence, the inequality that models the number of additional weeks marie needs to continue saving to afford the home repairs is 1558+60x≥2158 and she needs to save $60 for at least 10 weeks.
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what is the reminder when X³ +4X² - 2X + I is divided by X + 1 what is the reminder when X³ + 4X² - 2X + I is divided by X + 1
Answers
Answer:
6
Step-by-step explanation:
Choose the most convenient method to graph the line y=−13x+5
Select the correct answer below:
Recognize the equation as that of a vertical line passing through the x-axis at 5
Recognize the equation as that of a horizontal line passing through the y-axis at 5
Identify the slope and y-intercept and then graph
Find the x- and y-intercepts and then graph
Answers
Answer:
X and Y intercept
Step-by-step explanation:
X and Y intercept is much easier as the equation is linear it is easy to find the intercepts
Una empresa dedicada a la fabricación de ropa para niños ofrece 300 overoles a S/ 75 por unidad y a un precio de S/. 84 por overol. La misma empresa producirá 600 unidades al mes. Escriba, entonces, la ecuación y determine si es de oferta o demanda.
Answers
The supply equation of the company's total cost is 0.75x
How to determine the equation?The question implies that we determine the equation of the company production and categorize the equation as demand or supply
The given parameters are:
Overalls = 300Cost price = $0.75 per unitSelling price = $0.84 per unitProduction per month = 600The total cost of production is calculated as:
Total Cost = Overalls * Cost price
To determine the equation, we set the number of overalls to x.
So, we have:
Total Cost = x * 0.75
Evaluate
Total Cost = 0.75x
Hence, the equation of the company's total cost is 0.75x
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The manufacturer is considering production quantities of 40,000 units or 80,000 units. For the 40,000 unit plan, assume 95% of product will be sold and 5% will be salvaged; for the 80,000 unit plan, assume 80% of product will be sold and 20% will be salvaged.
Answers
The production quantity of 40,000 units, it is estimated that 38,000 units will be sold and 2,000 units will be salvaged. For the production quantity of 80,000 units, it is estimated that 64,000 units will be sold and 16,000 units will be salvaged.
Based on the information provided, let's analyze the production quantities of 40,000 units and 80,000 units, considering the assumptions for product sales and salvage.
40,000 unit plan:
Sold: 95% of 40,000 units = 0.95 * 40,000 = 38,000 units
Salvaged: 5% of 40,000 units = 0.05 * 40,000 = 2,000 units
80,000 unit plan:
Sold: 80% of 80,000 units = 0.80 * 80,000 = 64,000 units
Salvaged: 20% of 80,000 units = 0.20 * 80,000 = 16,000 units
Therefore, for the production quantity of 40,000 units, it is estimated that 38,000 units will be sold and 2,000 units will be salvaged.
For the production quantity of 80,000 units, it is estimated that 64,000 units will be sold and 16,000 units will be salvaged.
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can someone help me pls :)
Answers
Answer:
Second one i believe
Step-by-step explanation:
Well u know the sides arent given
What is the area of a sector when r = 2 and 0 = 1.75 radians?
Answers
Step-by-step explanation:
Area of sector = (θ/2) × r2
= (1.75/2) × 2×2
= (0.875) ×4
= 3.5 In2
write an equations in slope-intercept form of the line that passes through the point(5,9) with slope 7
Answers
Answer:
[tex]y=7x-26[/tex]
Step-by-step explanation:
1) Write it in the slope-intercept form of [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.
[tex]y=7x +c[/tex]
2) Substitute the given coordinates into [tex]y=7x +b[/tex], and then solve for c.
[tex]9=7(5) +b\\9=35+b\\9-35=b\\b= -26[/tex]
3) Substitute c into [tex]y=7x +b[/tex]
[tex]y=7x-26[/tex]
Therefore, the answer is [tex]y=7x-26[/tex].
In investing $6,150 of a couple's money, a financial planner put some of it into a savings account paying 6% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 9% annual simple interest. The combined interest earned for the first year was $477. How much money was invested at each rate?
Answers
Answer:
3200
Step-by-step explanation:
0.13x + 0.04*(6100-x) = 532 dollars.
0.13x + 0.04*6100 - 0.04x = 532
(0.13 - 0.04)x = 532 - 0.04*6100
x = 532 - 0.04 - 6100/0.13-0.04 = 3200
The couple invested:
$2550 in savings account at 6% simple interest annually, and$3600 in development plan at 9% simple interest annually,to earn $477 as the total interest for the first year.
What is interest over an investment?The interest over an investment is the additional amount that a person receives on investing his/her money in the cause.
How to solve the question?In the question, we are informed that in investing $6,150 of a couple's money, a financial planner put some of it into a savings account paying 6% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 9% annual simple interest. The combined interest earned for the first year was $477.
We are asked to find the amount invested in each rate.
We assume the amount invested in savings account to be $x.
Therefore, the amount invested in development plan is $(6150 - x).
Simple interest on a sum of money (P), at a rate (r) over a time period (t), is given as S.I. = (Prt)/100.
We calculate the interest earned in both investments:-
Investment in savings account:
Amount invested (P) = $x.
Rate of interest (r) = 6%.
Time for investment (t) = 1 year.
Therefore, interest received = (Prt)/100 = $(x*6*1)/100 = $ (6x)/100
Investment in development plan:
Amount invested (P) = $(6150 - x).
Rate of interest (r) = 9%.
Time for investment (t) = 1 year.
Therefore, interest received = (Prt)/100 = $((6150 - x)*9*1)/100 = $ {9(6150 - x)}/100.
We know that the total interest received is $477.
Thus on adding Interests from both the investments, we can write an equation:
(6x)/100 + {9(6150 - x)}/100 = 477
or, 6x + 55350 - 9x = 47700,
or, 55350 - 47700 = 3x,
or, 3x = 7650,
or x = 7650/3 = 2550.
Thus, the investments in:
Savings account = $x = $2550.Development plan = $(6150 - x) = $(6150 - 2550) = $3600.Learn more about simple interests at
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if f(x)=(x^m+9)^2, which statement about f(x) is true? a. f(x) is an even function for all vaues of m. b.f(x) is an even function for all even values of m. c.f(x) is an odd function for all values of m. d.f(x) is an odd function for all odd values of m.
Answers
Answer: b. f(x) is an even function for all even values of m.
Step-by-step explanation:
[tex]f(x)=(x^m +9)^2[/tex]
If m is even, then [tex](-x)^m=x^m[/tex].
This means that [tex]f(-x)=(x^m+9)^2 \implies f(-x)=f(x)[/tex]
Thus, b is the correct answer.
Sheridan Rental Company provided the following information to its auditors. For the year ended March 31, 2017, the company had revenues of $880,300, general and administrative expenses of $353,300, depreciation expenses of $131,455, leasing expenses of $108,195, and interest expenses equal to $78,122. If the company's average tax rate is 34 percent, what is its net income after taxes?
Answers
If the company's average tax rate is 34 percent, Its net income after taxes is: $138,090.48.
Net income after taxes
Revenues of $880,300
General and administrative expenses ($353,300)
Leasing expenses ($108,195)
Earning before interest, taxes, depreciation and amortization $418,805
Depreciation expenses ($131,455)
Earning before interest and taxes $287,350
Interest expenses ($78,122)
Earning before taxes $209,228
Taxes 34% $71,137.52
Net income/Loss $138,090.48
Therefore Its net income after taxes is: $138,090.48.
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Blood contains three types of cells including red blood cells, white blood cells, and platelets. For approximately every 420 red blood cells in humans with certain medical conditions,
there are 30 platelets and 2 white blood cells. Write the ratio of red blood cells to platelet cells.
O Points:
a simplified fraction)
Answers
Step-by-step explanation:
Evalate the expression when m=4 and m=6
5
0000
The value of x is:
3
m_ii હું
15
CN
y
X
Answers
Hello :
3/8 = x/(15 + x)
⇔ 3(15 + x)/8 = x
⇔ (45 + 3x)/8 = x
⇔ 45 + 3x = 8x
⇔ 8x - 3x = 45
⇔ 5x = 45
⇔ x = 45/5
⇔ x = 9
Select all figures that can be proven to be parallelograms by the markings in the diagram. explain answer
Answers
All the figures can be proven to be parallelograms by the markings
How to determine the parallelogram?The properties of parallelogram are:
Parallel opposite sidesCongruent opposite sidesDiagonals may or may not be congruentCongruent opposite anglesBased on the above properties, all the figures can be proven to be parallelograms
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Given the graph of the function f(x) shown below, find the average rate of change of the function f(x) on the interval [5,15].
Answers
Step-by-step Expression;
- Given; The function f(x) on the interval [ 5,15]
- To find the average rate of change of the function f(x)=?
x = 5 , y = 15,
I can't solve it anymore,please can you solving?
If the number of types of massages is represented by 4x + 3 and the number of
types of manicures is represented by -6x + 5 and the number of types of pedicures
is represented by 8x - 7, what is the expression for the total number of services they
have to choose from?
Answers
The expression for the total number of services the have to choose from is 6x - 1
Simplifying an expressionFrom the question, we are to determine the expression for the total number of services
From the given information,
Number of types of massages = 4x + 3
Number of types of manicures = -6x + 5
Number of types of pedicures = 8x - 7
Then,
Total number of services = 4x + 3 + (-6x + 5) + 8x - 7
Total number of services = 4x + 3 - 6x + 5 + 8x - 7
Total number of services = 4x - 6x + 8x - 7 + 3 + 5
Total number of services = 6x - 1
Hence, the expression for the total number of services the have to choose from is 6x - 1
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Answer: the answer is actually 6x+1, not 6x-1
how to find the determinant of a 4×4 matrix
Answers
Answer:
Step-by-step explanation:
Find the y-intercept of the line.
=y−2.1x5.9
Answers
The y-intercept given line equation is 5.9.
Given that, the line of the equation is y-2.1x+5.9.
We need to find the y-intercept of the line.
What is slope-intercept form?The standard form of slope-intercept form is y=mx+c.
Where, m=slope and c=y-intercept.
Using the slope-intercept form to find the y-intercept, we get c=5.9.
Hence, the y-intercept given line equation is 5.9.
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Solve for X show all work. Round to the nearest hundredth if necessary
Answers
The value of x, using the cosine ratio, is approximately: 11.47.
How to Apply the Cosine Ratio?The cosine ratio is:
Cos ∅ = adjacent length/hypotenuse length.
Given the parameters:
∅ = 55°
Adjacent length = x
Hypotenuse length = 20
Apply the cosine ratio:
cos 55 = x/20
x = (cos 55)(20)
x ≈ 11.47
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On the coordinate plane below, what is the length of AB? A coordinate plane is shown with a rectangle with the following points A at negative 6, 5; B at 8, 5; C at 8, negative 4; D at negative 6, negative 4. All points are connected to create a rectangle. 8 units 9 units 13 units 14 units
Answers
The length of AB wit the coordinate (-6, 5) and (8,5). is 14 units
Distance between two pointsA rectangle is a quadrilateral with 4 sides and angles
Taking the length of AB.
Since AB is slant line, the length of AB will be determined using the distance formula as shown;
D = √(-6-8)² +(5-5)
D = √(-14)²
D = AB = 14 units
Hence the length of AB wit the coordinate (-6, 5) and (8,5). is 14 units
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99 points answer fast!!!!
The owner of a coffee shop chain creates a graph representing sales in thousands of dollars. She describes the characteristics as follows:
• There have been two turning points in sales this year.
• Sales are expected to increase in the long run.
• The least amount of sales during the year is about $250,000.
Which graph correctly shows the coffee shop’s sales?
Answers
Answer:
Step-by-step explanation:
So given the three bits of information you can conclude a couple of things. The end behavior towards the right should be increasing and since there is only two turning points this means it was previously going down but had a turning point and starting going up, and before that it was going up and then started going down, those will be the two turning points. So on the left side it should be decreasing and the right side it should be increasing. The last peace of information tells you that at the second turning point, should be equal to 250k when it turned back up OR the y-intercept is 250k. Given all this information the answer should be the first graph in the first picture
Answer: D
Step-by-step explanation: