Answer:
1.581
Step-by-step explanation:
Given the data:
13 15 14 16 12
The point estimate of the standard deviation will be :
√Σ(x - mean)²/n-1
Mean = Σx / n = 70 / 5 = 14
√[(13 - 14)² + (15 - 14)² + (14 - 14)² + (16 - 14)² + (12 - 14)² / (5 - 1)]
The point estimate of standard deviation is :
1.581
(b) An economy has an agricultural industry and a textile industry. Each unit of agricultural output requires 0.4 unit of agricultural input and 0.1 unit of textiles input. Each unit of textiles output requires 0.1 unit of agricultural input and 0.2 unit of textiles input.
(i) Write the technology matrix for this economy. [2 marks]
(ii) If surpluses of 5 units of agricultural products and 195 units of textiles are desired, find the gross production of each industry
Leontief input output model (technology matrix) is an economic model that shows the quantitative relationship and sectorial interdependency in a national economy
The responses with regards to the question are;
(i) The technology matrix for the economy is presented as follows;
[tex]\mathbf{ A} =\left[\begin{array}{ccc}Agric&&Textile\\0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] \begin{array}{ccc}\mathbf{Per \ Unit}\\Agriculture\\\\Textile\end{array}\right][/tex]
(ii) The required gross production of each industry to meet the desired surplus are;
50 units of agriculture and 250 units of textile
The reason the above values are correct is as follows:
(i) The given parameters are;
The industries in the economy = Agricultural industry and textile industry
Units of agricultural input required per unit of agricultural output = 0.4
Units of textile input required per unit of agricultural output = 0.1
Units of agricultural input required per unit of textile output = 0.1
Units of textile input required per unit of textile output = 0.2
Let X represent agriculture, and let Y represent textile, we have;
[tex]Agric \ for \ agric = \dfrac{0.4 \ units \ of \ agriculture}{1\ unit \ of \ agric \ produced} \times X \ Agric \ produced= 0.4 \cdot X[/tex]
[tex]Agric \ for \ textile = \dfrac{0.1 \ units \ of \ agriculture}{1\ unit \ of \ textile \ produced} \times Y \ textile \ produced= 0.1 \cdot Y[/tex]
We also have;
Textile for agriculture = 0.1·X
Textile for textile = 0.2·Y
Therefore;
X = 0.4·X + 0.1·Y
Y = 0.1·X + 0.2·Y
Therefore;
The technology matrix for the economy is presented as follows;
[tex]\mathbf{Technology \ matrix, A} =\left[\begin{array}{ccc}Agric&&Textile\\0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] \begin{array}{ccc}\mathbf{Per \ Unit}\\Agriculture\\\\Textile\end{array}\right][/tex]
(ii) Let P represent the production vector, and let d represent the demand vector, we have;
[tex]P = \left[\begin{array}{c}X \\Y\end{array}\right][/tex], [tex]d = \left[\begin{array}{c}5 \\195\end{array}\right][/tex]
P = A·P + d
∴ P - A·P = d
Therefore;
[tex]P = \mathbf{ \dfrac{d}{(I - A)}}[/tex]
Where I = The 2 by 2 identity matrix
We get;
[tex]I - A =\left[\begin{array}{ccc}1&&0\\&&\\0&&1\end{array}\right] - \left[\begin{array}{ccc}0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] = \mathbf{\left[\begin{array}{ccc}0.6&&-0.1\\&&\\-0.1&&0.8\end{array}\right]}[/tex]
With the use of a graphing calculator, we have;
[tex]P =\left[\begin{array}{c}X \\Y\end{array}\right] = \dfrac{\left[\begin{array}{c}5 \\195\end{array}\right]}{\left[\begin{array}{ccc}0.6&&-0.1\\&&\\-0.1&&0.8\end{array}\right]} = \left[\begin{array}{ccc}50\\\\\ 250\end{array}\right][/tex]
The required gross product of agriculture, X = 50 units
The required gross product of textile, Y = 250 units
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We have that he technology matrix for this economy and the the gross production of each industry are
a) [tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]
b) [tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex]
From the Question we have told that
Each unit of agricultural output requires 0.4 unit of agricultural input
Each unit of agricultural output requires 0.1 unit of textiles input.
Each unit of textiles output requires 0.1 unit of agricultural input
Each unit of textiles output requires 0.2 unit of textiles input.
Generally the technology matrix for this economy is given below
With
X =Agricultural industry Gross output
Y= Textile industry Gross Output
Therefore
[tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]
b)
From the Question we are told that
Surpluses of 5 units of agricultural products and 195 units of textiles are desired.
Therefore, we have Desired surplus matrix of
[tex]D= \begin{vmatrix}5\\195\end{vmatrix}[/tex]
Generally the Technology equation is mathematically given as
[tex](I-X)\phi=D[/tex]
Where
X =Agricultural industry Gross output
I=A Unit matrix
\phi=Matrix of gross production
Therefore
[tex]\begin{vmatrix}1 & 0\\0 & 1\end{vmatrix}-(\begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}))\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}5\\195\end{vmatrix}[/tex]
[tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex]
In conclusion
The technology matrix for this economy and the the gross production of each industry are
[tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]
[tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex] Respectively
In conclusion
https://brainly.com/question/16863924
if x+y=2 and x=4 then x+2y
Write a word phrase for each algebraic expression.
13. n + 6
14. 5 - c
15. 11.5 + y
17. 3x + 10
16. x/4 - 17
18. 10x + 7z
Step-by-step explanation:
6 more than nc is subtracted from 5y more than 11.510 more than thrice of x17 less than x divided by 4The product of 7 and z is added to the product of 10 and x.What is the equation of the line that passes through the point (6, -6) and has a slope
of – 5/3?
Answer:
y = -5/3x + 4Step-by-step explanation:
Use the point-slope equation:
y - y₁ = m(x - x₁), where (x₁, y₁) is the given pointThe line is:
y - (-6) = -5/3(x - 6) y + 6 = -5/3x + 10y = -5/3x + 4What is the solution to 4x + 2 = 6(-2x - 5) ?
Group of answer choices
16
2
-16
-2
Answer:
x= -2
Step-by-step explanation:
4x + 2 = 6(-2x - 5)
Distribute
4x+2 = -12x-30
Add 12x to each side
4x+2+12x = -12x-30+12x
16x+2 = -30
Subtract 2 from each side
16x+2-2=-30-2
16x = -32
Divide by 16
16x/16x = -32/16
x = -2
Find x.
60°
45°
6
—————
Answer:
Step-by-step explanation:
Ben travels a regular distance of 80 miles to reach office. Today, he used an alternative route that covered a distance of only 75 miles. What is the decrease in the percentage of the distance travelled by ben
Answer:
Ben traveled 93.75% of his usual distance.
Step-by-step explanation:
Given that Ben travels a regular distance of 80 miles to reach office, and today he used an alternative route that covered a distance of only 75 miles, to determine what is the decrease in the percentage of the distance traveled by Ben, the following calculation must be done:
80 = 100
75 = X
75 x 100/80 = X
93.75 = X
Therefore, Ben traveled 93.75% of his usual distance.
If a ants can dig b tunnels in c hours, how many tunnels can b ants dig in a hours?
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Answer:
b²/c tunnels
Step-by-step explanation:
The number of tunnels per ant-hour is ...
b/(ac)
Multiplying that by the new number of ant-hours, we have ...
(b/(ac))(ab) = b²/c . . . . tunnels
I need help with this question!
Which function has a maximum with the same maximum value as
Answer:
Step-by-step explanation:
How many natrual numbers in between 68 and 145
Answer:
76 natural number not including the first
Hope this helps <3 Comment if you want more thanks and be sure to give brainliest (4 left) <3
There are 78 natural numbers between 68 and 145.
What are the Natural numbers?The Natural numbers are defined as it used for counting and are a component of the number system, which includes all positive integers from 1 to infinity. It does not include zero (0).
The set of natural numbers includes only the positive integers, i.e., 1, 2, 3, 4, 5, 6, ……….∞.
Sum of natural numbers are n(n+1)/2
Sn = n(n+1)/2
Hence, this is the formula to calculate sum of 'n' natural numbers.
Given that numbers are 68 and 145
We will start counting from 68 to 144
Number of natural numbers between 68 and 145 = (144 - 67)+1
Number of natural numbers between 68 and 145= 77 +1
Number of natural numbers between 68 and 145 = 78
Hence, there are 78 natural numbers between 68 and 145.
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What is the US TREASURY BONDS pretax expected return?
Answer:
this is the return on an investment that does not include the taxes the investor must pay on this return
What is the shortest distance Jill can travel is she leaves her house, goes to City Hall, to the Post Office, and then returns home?
A. 9 miles
B. 16 miles
C. 38 miles
D. 48 miles
Can you post an image of the map?
Answer:
i believe that the answer is 38 please trust me
The width of a rectangle is 5 units less than the length. If the area is 150 square units, then find the dimensions of the rectangle
⇛L = W + 5
⇛L × W = 150 sq. units
⇛W (W + 5) = 150
⇛W² + 5W = 150
⇛W² + 5W - 150 = 0
⇛[(W - 10) (W + 15)] = 0
⇛W = -10 , 15 (reject negative width)
☞ Width of rectangle is 10 units
☞ Length of rectangle is 15 units
f(x)=4(2)^x
what would a graph of this look like?
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Answer:
see attached
Step-by-step explanation:
A graphing calculator can do a nice job of showing you what the graph looks like.
The initial factor of 4 is the value when x=0, the y-intercept. The base of 2 tells you the function value is multiplied by 2 for each unit of x to the right, and divided by 2 for each unit of x to the left. (The curve quickly goes off the top of the graph.)
The horizontal asymptote is y=0, as it is for all exponential functions (that have not been translated).
Help please. For the hign school basketball game, it costs $8 for every 4 tickets. Complete the table below showing the cost and the number of tickets.
Answer:
$2 for 1 ticket, 7 tickets for $14, $18 for 9 tickets, 10 tickets for $20
Step-by-step explanation:
Since we know that it $8 for 4 tickets, we can simplify the ratio down to 2:1, meaning that each ticket is $2.
You're welcome and good luck with your classes young one
The term "downers" refers to ..
In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____. a. parabolic band of points b. band of points having a slope consistent with that of the regression equation c. horizontal band of points centered near 0 d. widening band of points
Answer:
In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____.
c. horizontal band of points centered near 0
Step-by-step explanation:
This residual graph or plot shows the residual values (or the difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line) on the vertical axis and displays the independent variable on the horizontal axis. A linear regression model becomes appropriate for a dataset when the points are randomly dispersed around the horizontal axis near 0; otherwise, a nonlinear model becomes more appropriate.
11. The unit digit in the expression (31 + 132 + 143 + 414 + 515 +156 + 61) i (A) 4 (B) 3 (C) 2 . (D) 1
Answer:
Step-by-step explanation:
[tex]we \ add \ \ only \ \ units \ we \ do \ not \ need \ the \ rest \\\\ \bf (3\underline 1 + 13\underline2 + 14\underline3 + 41\underline4 + 51\underline5 +15\underline6 + 6\underline1)= \\\\ 1+2+3+4+5+6+1=2\underline 2 \\\\ Answer: C) \ 2[/tex]
I don’t remember learning this, need some help!
Answer:
4
Step-by-step explanation:
(y+2)²=[(-4)+2]²
=(-4+2)²
=-2²
=4
sipho's dad used 4/11 of the packet of oranges to make juice.The next day he used another 4/11 of the packet of oranges.How many eleventh were left of the pocket of oranges?
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Answer:
3/11 were left
Step-by-step explanation:
A packet of oranges is 11/11. Subtracting 4/11 +4/11 = 8/11 from that leaves ...
11/11 -8/11 = (11 -8)/11 = 3/11
3 elevenths were left.
find area of shaded region
Answer:
The answer is 21.98. I just took area of the whole circle and subtracted it with the area of two circles in it
Answer:
21. 99
Step-by-step explanation:
[tex]s = \pi \times {r}^{2} \\ s1 = 3.14 \times 9 = 28.27 \\ s2 = 3.14 \times 1 = 3.14 \\ a = 28.27 - (3.14 \times 2) = 28.27 - 6.28 = 21.99[/tex]
Find the missing side round your answer to the nearest tenth.
Answer: 20.5
Step-by-step explanation:
Cos 43 = X/28
O.73 = x/28
(0.73)(28)=20.5
seven times a number decreased by the number is -48 . Find the number.
Answer:
a = -8
Step-by-step explanation:
Let the required number be "a".
Given that, seven times a number minus the number is -48
7 × a - a = -48
7a - a = -48
6a = -48
a = (- 48) / 6
a = -8
If triangle ABC has one angle measuring 90o and one angle measuring 45o, which of the following is true?
ABC is a right angle
Third angle 45°
Its a isoceles Right Triangle because base angles are equal then two sides are also equal.
Must click thanks and mark brainliest
You need a 75% alcohol solution. On hand, you have a 60 mL of a 55% alcohol mixture. You also have 85% alcohol mixture. How much of the 85% mixture will you need to add to obtain the desired solution?
You will need_____ mL of the 85% solution
60 mL=55% alcohol
?mL=85% alcohol
85×60÷55
=92.727 mL
I think do like this....I'm not sure
Hope this help you
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Answer:
120 mL
Step-by-step explanation:
Let x represent the amount of 85% solution needed. Then the total amount of alcohol in the mix is ...
0.55(60) +0.85(x) = 0.75(60 +x)
33 + 0.85x = 45 +0.75x . . . . . . . eliminate parentheses
0.85x = 12 +0.75x . . . . . . . . . .subtract 33
0.10x = 12 . . . . . . . . . . . . . . subtract 0.75x
x = 120 . . . . . . . . . . . . . . multiply by 10
You will need 120 mL of the 85% solution.
The daily production of electronic motors at a certain factory averaged 120 with a variance of 100. The fraction of days that will have production levels between 100 and 140 assuming doubt about the normality of the data is
find the value of the trigonometric ratio. make sure to simplify the fraction if needed
Answer:
Cos C = a/h
= 21/35
Step-by-step explanation:
since cos is equal to adjacent angle over hypotenuse angle, so from the question we conclude Cos C = 21/35
Find the area of the shaded regions
Sector area
Area of whole = 51.313
Area of unshaded = 9.424
Area of shaded = 41.8886
Answer:
40π/3Step-by-step explanation:
Find the area of the bigger circle:
A = πr² = π(4 + 3)² = 49πFind the area of 120° sector AOC:
A = 120°/360°*A = 1/3*49π = 49π/3Find the area of smaller circle:
A = π(3²) = 9πFind the area of 120° sector of DOB:
A = 120°/360°*9π = 3πNow find the shaded area, the difference of areas of sectors:
49π/3 - 3π = 40π/3Help me solve the question in picture
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Answer:
√5 +√6
Step-by-step explanation:
We know that the square of a binomial is ...
(a +b)^2 = a^2 +2ab +b^2
Then the square root of it is ...
a + b = √(a^2 +b^2 +2ab)
Using a=√x and b=√y, this is ...
√x +√y = √(x + y + 2√(xy))
__
For the given expression, we need to find x and y such that ...
xy = 30 and x+y = 11
Using x=5, y=6, we meet those requirements.
[tex]\displaystyle \sqrt{11+2\sqrt{30}}=\sqrt{5+6+2\sqrt{5\cdot6}}=\boxed{\sqrt{5}+\sqrt{6}}[/tex]
Answer:
√5+√6 ≈ 4.68555772
Step-by-step explanation:
I hope it's correct
