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
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Starting with a fresh bar of soap, you weigh the bar each day after you take a shower. Then you find the regression line for predicting weight from number of days elapsed. The slope of this line will be:__________.
Answer:
The slope will be negative
Step-by-step explanation:
The slope of the regression line tells us about the relationship or behavior of the dependent and independent variables. In the scenario above, where the weight is being compared with the number of days elapsed. What is expected of the weight and quantity of a bar soap each time it is used for a shower is that it will decrease in weight. Therefore, as the number of days increases, and hence, number of showers rise, the weight of soap will decrease. Hence, we'll obtain a negative slope, one in which the increase in a variable leads to decrease in the other.
Anna earned $9 an hour babysitting. She wants
to buy a 16 GB iPod that is $120. Anna has
saved $45 so far. How many more hours of
babysitting does she need to do to earn the rest
to purchase the iPod
Answer:
8.33 hours
Step-by-step explanation:
120-45 = 75
75 ÷ 9 = 8.33
Please help me to find this answer
Step-by-step explanation:
angle of a triangle is 180, therefore to get the remaining one, subtract the sum of the two knows from 180, also for the second one; angle on a straight line is as well 180, since you have fine the interior one, subtract it from 180 to get the second answer
Answer:
so angles in a triangle add up to 180,
32+50+m<MQP=180
82+m<MQP=180
m<MQP=180-82
=98°
and angles on a straight line add up to 180 therefore
m<MQR=180-m<MQP
=180-98
=82
I hope this helps and if you don't understand feel free to ask
The HCF of two numbers is 175. The LCM of these two numbers is 12600. Both numbers are greater than their HCF. Find the two numbers
Answer:
Hello,
Answer : 1400 and 1575
Step-by-step explanation:
Let's say a and b the ywo numbers
[tex]HCF(a,b)=a\vee b=175=5^2*7\\LCM(a,b)=a\wedge b=12600\\\\a*b=(a\vee b)*(a\wedge b)=(2^3*3^2*5^2*7)*(5^2*7)=2^3*3^2*(5^2*7^2)^2\\\\Both\ numbers\ are\ greater\ than\ their HCF\\a=175*k_1\\b=175*k_2\\\\k_1=2^3\ and\ k_2=3^2\\\\a=175*2^3=1400\\b=175*3^2=1575\\\\[/tex]
Solve each system by graphing.
Answer:
(2,-1)
Step-by-step explanation:
Solved using math.
Answer:
The solution is (2, -1) to show this by graphing do y = -1 by making a straight horizontal line at (0,-1) . And then for the other equation make a line where it starts at (0,4) and passes point (2,-1). Just plot those two points and connect them and you'll have made the line.
Step-by-step explanation:
The total number of branches in a tree diagram will be which of the following values?
the probability of an event occurring
the denominator of a probability
the numerator of a probability
Answer:
The total number of branches = total possibilities = the denominator of a probability.
So the second choice is correct.
Let me know if this helps!
Answer:
Step-by-step explanation: answer B (the denominator of a probability)
The polygons in each pair are similar. Find the missing side length.
Let missing side be x
If both polygons are similar
[tex]\\ \sf\longmapsto \dfrac{3}{4}=\dfrac{18}{x}[/tex]
[tex]\\ \sf\longmapsto 3x=4(18)[/tex]
[tex]\\ \sf\longmapsto 3x=72[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{72}{3}[/tex]
[tex]\\ \sf\longmapsto x=24[/tex]
Factors and rewrite the expression 25x-15
Answer:
5(5x-3)
Step-by-step explanation:
The common factor in this expression is 5 so divide 5 to all the values
25/5=5
-15/5= -3
Put these values into parenthesis and leave the 5 on the left side and out of the parenthesis
5(5x-3)
Answer:
5(5x - 3)
Step-by-step explanation:
The greatest common factor here is 5. Divide each term by 5 and simplify.
25x/5 = 5x
15/5 = 3
Therefore, the answer is 5(5x - 3).
Select the correct answer.
Given the following formula, solve for l.
A.
B.
C.
D.
Answer:
c
Step-by-step explanation:
took the test so i assume its this question
Suppose the distributor charges the artist a $40.00 cost for distribution, and the streaming services pays $4.00 per unit. (Note: One unit = one thousand streams)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Formula: y = 40x + 4 (Graph Attached)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
After how many streams will you pay for the distributor charges? (Hint: this is where the line crosses the x-axis, round to the nearest thousand)
Answer:
356 streams
Step-by-step explanation:
From the graph, you will see that the line cross the x-axis at x = 8.8
Substitute into the expression y = 40x + 4
y = 40(8.8)+4
y = 352 + 4
y = 356
Hence the distributor charges will be paid for after 356 streams
Find the inequality represented by the graph
I'm using khan academy btw
Answer:
Step-by-step explanation:
slope of line through (0,0) and (4,3) =(3-0)/(4-0)=3/4
eq. of line is y-0=3/4(x-0)
y=3/4 x
put x=4
y=2
2=3/4×4
2=3
which is true if 2<3
2<3
so y<3/4 x
12. Convert 30.283° into a degree-minute-second format.
O A. 18° 16' 98"
B. 18° 28' 30"
C. 30° 16' 58"
D. 30° 28' 30"
The angle of 30.283° in a degree-minute-second format will be 30° 16' 58". Then the correct option is C.
What is conversion?Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The angle is given below.
⇒ 30.283°
Convert 30.283° into a degree-minute-second format. Then we have
⇒ 30° (0.83 x 60')
⇒ 30° 16.98'
⇒ 30° 16' (0.98 x 60'')
⇒ 30° 16' 58"
The angle of 30.283° in a degree-minute-second format will be 30° 16' 58". Then the correct option is C.
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please helpppp i need it by tonight its very important
Answer:
m<1=145
m<2=35
m<3=35
Step-by-step explanation:
measure one is supplementary(the angles add to 180) to measure four.
so we do 180-35=145
measure 2 is congruent to measure four because they are corresponding angles
so measure 2=35
and measure 3 is also congruent to measure 4 because the are corresponding angles
so m<3=35
The area of a circle is 144cm².Find the radius
Answer:
It's a decimal, so it's around 6.771cm
Step-by-step explanation:
First, divide 144cm² by pi, or 3.14. Then find the square root of the answer, giving you the radius. The formula for the area of a circle is pi x radius squared, so to find out the radius you just use this formula in reverse.
If I messed up or didn't make my explanation clear, please comment.
Answer:
radius is [tex]\frac{12}{\sqrt{\pi } }[/tex] = 6.77 cm
Step-by-step explanation:
we know,
[tex]\pi[/tex] × r² = Area
⇒ [tex]\pi[/tex] × r² = 144
⇒ r² =[tex]\frac{144}{\pi}[/tex]
⇒ r= [tex]\frac{12}{\sqrt{\pi } }[/tex]
∴ r= [tex]\frac{12}{\sqrt{\pi } }[/tex]
pls mark this as the braniliest
Rotation 90° counterclockwise around the origin of the point (-8,1)
what should be the rate of simpe interest such that the interest is double of the sun at 10 years
Answer:
you never showed the chocies
Step-by-step explanation:
PLSS HELPPPP WILL GIVE BRAINLESSS A 22-foot ladder is resting against the side of a building. The bottom of the ladder is 3 feet from the building. Find the measure of the angle the ladder makes with the ground. Round your answer to the nearest tenth of a degree.
Answer:
The answer is 82.2
Step-by-step explanation
hope this helps
If p is true and ~ q is false, then p ~ q is _____ false.
a. sometimes
b. always
c. never
The segments shown below could form a triangle.
A
C
7
9
12
B
А
a
A. True
B. False
Answer:
TRUE
Step-by-step explanation:
I SEEN SOME ONE ELSE WIT 5 STARS SAY SO(:
The given segment can form triangle. Therefore, the given statement is true.
What is triangle?A polygon has three edges as well as three vertices is called a triangle. It's one of the fundamental geometric shapes. In Euclidean geometry, each and every three points that are not collinear produce a distinct triangle and a distinct plane. In other words, every triangle was contained in a plane, and there is only single plane that encompasses that triangle.
All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Unless when otherwise specified, this article discusses triangles within Euclidean geometry, namely the Euclidean plane. The given segment can form triangle.
Therefore, the given statement is true.
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Are the ratios 6:3 and 2:1 equivalent?
Surface Area of cones
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
9514 1404 393
Answer:
64.1 ft²
Step-by-step explanation:
The area of the cone is given by ...
A = πr(r +h) . . . . for radius r and slant height h
A = π(2 ft)(2 ft +8.2 ft) ≈ 64.1 ft²
Need help with this- Precalculus
use x^2 when x=0 because the restriction for it is "use x if x is less than or equal to 1"
when x = 0, (0)^2 will make f(x) = 0
the graph of f(x) will just be a dot at 0
create a graph of 4.95 + 3.99
Answer:
????
Step-by-step explanation:
as in y = 4.95 + 3.99 or points? if so just draw a horizontal line at 8.94
Devaughn is 6 years older than Sydney. The sum of their ages is 56 . What is Sydney's age?
Answer:
Devaughn = 31, Sydney = 25
Step-by-step explanation:
(56-6)÷2= 25
So they would both be 25 if they were the same age but Devaughn is 6 years older so 25+6=31
ATQ
[tex]\\ \sf\longmapsto x+x+6=56[/tex]
[tex]\\ \sf\longmapsto 2x+6=56[/tex]
[tex]\\ \sf\longmapsto 2x=56-6[/tex]
[tex]\\ \sf\longmapsto 2x=50[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{50}{2}[/tex]
[tex]\\ \sf\longmapsto x=25[/tex]
Simplify 13 x - 4[ x + (3 - x )].
A.9x-1
B.8x-12
C.13x-12
13x - 4[x + (3 - x)] =
= 13x - 4(x + 3 - x) =
= 13x - 4 · 3 = 13x - 12
C.
Answer:
13x -12
Step-by-step explanation:
13 x - 4[ x + (3 - x )].
Combine like terms inside the brackets
13 x - 4[ 3 -0x]
13x - 4[3]
Multiply
13x -12
Which is a perfect square?
6’1
6’2
6’3
6’5
Answer:
6'2
Step-by-step explanation:
Find the quotient of 90 over -10
90/-10
= 9/-1
= -9
So, -9 is the quotient.
100 x 20 + 30 help me
[tex]\boxed{\underline{\bf \: Answer}}[/tex]
[tex] \sf100 \times 20 + 30[/tex]
First multiply 100 & 20 together.
[tex] \sf= 2000 + 30[/tex]
Now add 2000 & 30. You'll get :-
[tex]= \boxed{ \bf 2030}[/tex]
____
Hope it helps.
RainbowSalt2222
[tex]\\ \rm\longmapsto 100\times 20+30[/tex]
[tex]\\ \rm\longmapsto (100\times 20)+30[/tex]
Solve bracket[tex]\\ \rm\longmapsto 2000+30[/tex]
[tex]\\ \rm\longmapsto 2030[/tex]
factorize : ( p- q ) cube
Answer:
[tex]( {p - q}^{3} ) \\ = {p}^{2} - 3 {p}^{2} q + 3p {q}^{2} - {q}^{3} [/tex]
Triangle DEF has sides of length x, x+3, and x−1. What are all the possible types of DEF?
Triangle DEF is scalene
Must click thanks and mark brainliest
The triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
What is a scalene triangle?A scalene triangle is a type of triangle which have all the sides to be unequal and similarly, all the angles will also be unequal to each other.
Given that:-
Triangle DEF has sides of length x, x+3, and x−1it is given that all the sides of the triangle are x, x+3, and x−1 we can clearly see that for any value of x all the three sides will have different values. we can conclude from this that the triangle DEF is a scalene triangle.
Therefore triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
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