a. The following is the input/output table for two industries X and Y. The values are in million of rupees.

Producers

X

Y

X

14

7

Users

Y

6

Final Demand

8

Total Output

28

18

11

36

Determine the outputs if the final demand changes to 20 for X and 30 for Y.

[3]

The value of sin 75 without using a calculator is 1/4(√2 +√6)

From the question, we have the following parameters that can be used in our computation:

sin(75)

This can be expanded as

sin(75) = sin(45 + 30)

Using the sine rule, we have

sin(75) = sin(45)sin(30) + cos(45)cos(30)

Evaluate the trigonometry ratios

So, we have

sin(75) = √2/2 * 1/2 + √2/2 * √3/2

So, we have

sin(75) = √2/4 + √6/4

Evaluate the sum

sin(75) = 1/4(√2 +√6)

Hence, the value is sin(75) = 1/4(√2 +√6)

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Answer:

  2035.8 ft³

Step-by-step explanation:

You want to know the volume of a cylinder with radius 6 ft and height 18 ft.

The volume of a cylinder is given by the formula ...

  V = πr²h

For the given dimensions, the volume is ...

  V = π(6 ft)²(18 ft) ≈ 2035.8 ft³

The volume of the cylinder is about 2035.8 cubic feet.

__

Additional comment

If you use 3.14 for π, you get 2034.7 cubic feet.

<95141404393>

Answer:

V = 62.8 m[tex]^{3}[/tex]

Step-by-step explanation:

V = pi × (radius)[tex]^{2}[/tex] × height

V = [tex]\pi[/tex] × [tex]r^{2}[/tex] × h

V = (3.14 × [[tex]2^{2}[/tex]]) × 5

V = (3.14 × 4) × 5

V = 12.56 × 5

V = 62.8 m[tex]^{3}[/tex]

Step-by-step explanation:

1/3 ÷ 3

=  1/3 ÷ 3/1

= 1/3  X  1/3  =  1/9

Similarly

1/4 ÷ 5   =   1/4  X  1/5 = 1/20

Answer:

  (d)  5i -j

Step-by-step explanation:

You want the value of the expression 2u -v where u=3i and v=i+j.

Use the given definitions of u and v, and simplify in the usual way.

  2u -v = 2(3i) -(i+j)

  = 6i -i -j . . . . . . . . . eliminate parentheses

  = 5i -j

__

Additional comment

The unit vectors i and j can be treated as though they were variables. The usual properties of equality and (scalar) arithmetic apply.

Answer:

what?

Step-by-step explanation:

Answer:

x= -13/15

Step-by-step explanation:

x(15x +13)

x =0

15x + 13 = 0

15x = -13

x =-13/15

If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.

Option A is the correct answer.

We have,

A horizontal translation moves every point of a figure the same distance in the same direction.

In this case, since the second polygon is to the right of the first one, we know that every point of the polygon has been translated to the right by the same amount.

A vertical translation would move every point of the figure the same distance in the same direction, but vertically instead of horizontally.

A reflection across the x-axis would flip the figure over the x-axis, so points that were above the x-axis would end up below it and vice versa.

A 90° clockwise rotation would rotate the figure 90 degrees to the right.

Thus,

If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.

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Answer: √35/6

Step-by-step explanation:

see image for explanation

[tex](2x^3)^2\cdot (3x)^4\implies (2^2 x^{3\cdot 2})\cdot (3^4x^4)\implies 4x^6\cdot 81x^4 \\\\\\ (4)(81)x^{6+4}\implies 324x^{10}[/tex]

The only graph that represents a function is: Graph D

A function is defined as a relationship or expression that involves one or more variables. It typically has a set of input and outputs.  Each input has only one output. The function is the description of how the inputs relate to the output.

A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.

From the graphs, we can see that:

Graph A has 2 outputs at x = -2

Graph B has 2 outputs at x = 0

Graph C has two outputs at x = -1

Graph D has a unique output for every input and as such it is a function

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The measure of the angle CAB in a right angled triangle ABC using given measurements is equal to  37°.

In the triangle ABC,

From the figure we have,

Measure of angle ABC = 90 degrees

Measure of angle ACB= 53 degrees

Sum of all the interior angles of a triangle is equal to 180 degrees .

⇒Measure of angle ABC + Measure of angle ACB + Measure of angle CAB = 180 degrees

⇒ 90° + 53° + Measure of angle CAB = 180°

⇒143° + Measure of angle CAB = 180°

⇒ Measure of angle CAB = 180° - 143°

⇒ Measure of angle CAB = 37°

Therefore, the measure of the angle CAB is equal to  37°.

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The value of SV, given that point J is the centroid, would be A. 9.

Seeing as we have point J as the centroid for triangle SZU, we can then tell that JV would be:

JV = 1 / 3 x SV

Knowing this, we can make SV the subject of the formula to become:

(JV = 1 / 3 x SV ) / 1 / 3

3 x JV = SV

SV = 3 JV

SV would then be:

SV = 3 x JV

SV = 3 x 3

SV = 9

In conclusion, SV would be 9.

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Answer:

answer is B. 9 :)

Step-by-step explanation:

The volume of the sphere with a radius of 5 feet to the nearest cubic foot is 166.67π feet³.

Given a sphere.

Radius of the sphere = 5 feet

The formula to find the volume of the sphere is,

Volume of the sphere = 4/3 πr³,

where r is the radius of the sphere.

Substituting the given radius,

Volume of the sphere = 4/3 × π × (5)³

                                     = 4/3 × π × 125

                                     = 166.67π

Hence the volume of the sphere is 166.67π feet³.

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Answer: $9,000 is invested in the 5% bond, and $24,000 is invested in the 6.5% bond.

Step-by-step explanation: x + y = 33,000 (the full sum contributed)

We too know that the yearly intrigued earned is $2,010.00, which is the whole of the intrigued earned from each bond. Utilizing the equation for basic intrigued:

intrigued = principal x rate x time

ready to calculate the intrigued earned from each bond:

0.05x (for the 5% bond)

0.065y (for the 6.5% bond)

So we have another condition:

0.05x + 0.065y = 2,010

Presently we have two conditions with two factors, which we are able illuminate utilizing substitution or end.

Let's utilize substitution:

x + y = 33,000 --> y = 33,000 - x

0.05x + 0.065y = 2,010 --> 0.05x + 0.065(33,000 - x) = 2,010

Streamlining:

0.05x + 2,145 - 0.065x = 2,010

-0.015x = -135

x = 9,000

So the sum contributed within the 5% bond is $9,000, and the sum contributed within the 6.5% bond is:

y = 33,000 - x = 33,000 - 9,000 = $24,000

Answer:

Area = 7 7/18 or 39/2 square units

Step-by-step explanation:

To find the area of a rectangle, you need to multiply its length by its width.

Given:

Length = 1 5/6

Width = 4 1/3

Convert mixed numbers to improper fractions:

Length = (6 + 5) / 6 = 11/6

Width = (3 x 4 + 1) / 3 = 13/3

Area = Length x Width

Area = (11/6) x (13/3)

Area = (143/18)

Simplify the result to mixed number or improper fraction:

Area = 7 7/18 or 39/2 square units (if we want the answer in fraction form)

The equation of tangent plane to the surfacez = 8x² - 9y² at the point (2,1,23) is 32(x - 2) - 18(y - 1) -1(z - 23) = 0

Here, the equation of the surface is

z = 8x² - 9y²

Let us assume that f(x, y, z) =  8x² - 9y² - z

The partial derivative of f(x, y, z) would be:

[tex]\frac{\partial f}{\partial x}[/tex] = 16x

[tex]\frac{\partial f}{\partial y}[/tex] = -18y

[tex]\frac{\partial f}{\partial z}[/tex] = -1

At point (2, 1, 23) the partial derivative of f(x, y, z),

[tex]\frac{\partial f}{\partial x}[/tex] = 32

[tex]\frac{\partial f}{\partial y}[/tex] = -18

[tex]\frac{\partial f}{\partial z}[/tex] = -1

So, the equation of tangent plane would be,

32(x - 2) - 18(y - 1) -1(z - 23) = 0

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Answer:

  15

Step-by-step explanation:

You want the remainder from division of f(x) = 2x³ +5x² -12x by x -(-1).

The table used for synthetic division is built by listing the zero of the divisor at upper left, and the coefficients of the polynomial across the top to the right of that. They are listed in order of decreasing degree, with any necessary zero coefficients put in the appropriate place(s).

The attachment shows the table and the instructions for filling it out. The value at the bottom in the rightmost column is the remainder from the division.

The remainder theorem tells you that is also the value of the function for x = k.

The remainder from f(x) ÷ (x +1) is 15.

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The monthly payment will be $618.71

We know that the formula for the loans are:

[tex]P_0=\frac{d(1-(1+\frac{r}{k} )^{-Nk})}{\frac{r}{k}}[/tex]

where

P₀ is principal

d is monthly payment, annual payment

r is the annual interest rate in decimal form.

k is the number of compounding periods in one year.

and N is the length of the loan, in years.

Here, P₀ =  $32,000

r = 0.06

N = 5

k = 12

Using above formula of loan we need to find value of d.

[tex]P_0=\frac{d(1-(1+\frac{r}{k} )^{-Nk})}{\frac{r}{k}} \\\\32000 =\frac{d(1-(1+\frac{0.06}{12} )^{-60})}{\frac{0.06}{12}}\\\\32,000 =\frac{d(1-(1+0.005)^{-60})}{0.005} \\\\32000\times 0.05=d(1-(1.005)^{-60})\\\\160=d\times (1-0.7414)\\\\d = 160/0.2586\\\\d=618.72[/tex]

Therefore, the monthly payment = $618.71

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The period of the function in the graph is 2π

Period represents the distance across horizontally located between successive duplicates of an equivalent outline within a graphed function.

In other words, we can say that period is the distance to complete an oscillation where this distance is counted in time. Hence period is measured is seconds

In the graph, the period can be calculated using the points

These points shows a complete oscillation.

Using from 2π to 0

= 2π - 0

= 2π

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Two ten thousandths are 0.0002.

The number 2 will be in ten thousand place

TENS   ONES    .       TENTHS       HUNDREDTHS        THOUSANDTHS    

                          .               0                       0                                 0              

TEN THOUSANDTHS

            2

The missing values are 60, 100 and 40 if the Median and Mode of the  wage distribution are known to be $33.5 and $34 respectively

Wages (in Rs)_freq____        CF

0-10________4___________4

10-20_______16________20

20-30_______x________20+x

30-40______y_________20+x+y

40-50______z________20+x+y+z

50-60______6_______26+x+y+z

60-70______4______30+x+y+z

Since total 230

So, 30+x+y+z=230

x+y+z=200

Mode =34

Median = 33.5

By solving the equations we get x=60, y=100 and z=40

Hence, the missing values are 60, 100 and 40

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The length of u to the nearest centimeter is about 30 cm.

We are given that;'

s = 730 cm, t = 270 cm and U=125°.

Now,

The Law of Cosines states that for any triangle with sides a, b and c and angle C opposite to side c, we have:

c2=a2+b2−2abcosC

To find c = u. Plugging in the values, we get:

u2=7302+2702−2×730×270×cos125°

Using a calculator, we get:

u2≈912.9

Taking the square root of both sides, we get:

u≈30.21

Rounding to the nearest centimeter, we get:

u≈30cm

Therefore, by the law of cosine the answer will be 30 cm.

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By expanding and simplifying the algebraic expression (y + 7)(y - 5), we have the result y² + 2y - 35

To expand an algebraic expression in brackets, we need to use the distributive property to make is easy for simplification, thus we expand and simplify the expression as follows:

(y + 7)(y - 5) = y(y - 5) + 7(y - 5) {distributive property}

(y + 7)(y - 5) = y² - 5y + 7y - 35

by simplification, we have;

(y + 7)(y - 5) = y² + 2y - 35

Therefore, the expansion and simplification of the algebraic expression (y + 7)(y - 5), gives the result y² + 2y - 35.

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Result:

sin(tan⁻¹(x) - tan⁻¹(y)) in terms of x and y only = (x - y) / (1 + xy).

For us to write the expression, we shall use this formular formula:

tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))

where:

a = tan⁻¹(x)

b = tan⁻¹(y)

Next, we have:

tan(tan⁻¹(x) - tan⁻¹(y)) = (tan(tan⁻¹(x)) - tan(tan⁻¹(y))) / (1 + tan(tan⁻¹(x))tan(tan⁻¹(y)))

= (x - y) / (1 + xy)

From both sides, we have sine:

sin(tan⁻¹(x) - tan⁻¹(y)) = sin(tan(x - y / 1 + xy))

So, sin(tan⁻¹(x) - tan⁻¹(y))  

= sin(tan⁻¹(x) - tan⁻¹(y))

= (x - y) / (1 + xy) in terms of x and y.

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Answer:

Step-by-step explanation: