Exercise 3 Architecture designing a Moto at 10,000 ft.² available space for rooms . It will have a s small rooms which are 250 ft.² large rooms with her at 400 ft.² each

Answer:

3/8

Step-by-step explanation:

Given that:

Work required to stretch a string:

3 ft = 6ft - lb

The work required to stretch it 9 inches

Given that :

Work(W) = kx

Take the integral of W at 3 fts beyond its natural length;

W = ∫kx dx at 0 to 3

W = k ∫xdx at 0 to 3

W = 6

W = k[x²/2] at x =0 to x = 3

6 = k[3² /2] - 0

6 = k[9/2]

12 = 9k

k = 12/9 = 4/3 = 1.333

Converting inches to feet:

1 inch 0.0833 ft

9 inches = 0.75 ft

W = ∫kx dx at 0.75 to 0

W = 4/3 ∫xdx at 0 to 0.75 = 3/4

W = 4/3[x²/2] at x =0.75 to 0

W = 4/3[(3/4)²/2] at 0.75 to 0

W = 4/3[(9/16) / 2]

W = 4/3 * (9/16 * 1/2)

W = 36/96

W = 6/16 = 3/8 ft - lbs

Answer:

6:12:21

Step-by-step explanation:

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Answer:

In order to find the missing number (X), you must first identify the pattern in the set of numbers. Upon a glance, you can determine that the pattern starts with 4 and then the next number is 2n+1, with n being the preceding number in the set.

By applying Inscribed angle theorem the angles and arc measures can be calculated as follows:

Inscribed angle theorem states that the measure of the central angle is equal to twice the inscribed angle if both angles face the same arc.

central angle = 2 x inscribed angle, where:

The total angles in a triangle are 180°.

Now we look at the picture and apply this theorem:

∠C = 1/2 * ∠DSE

     = 1/2 * 52 = 26°

∠B = 1/2 * ∠DSE

     = 1/2 * 52 = 26°

∠B + ∠D + ∠BSD = 180°

26° + 57° + ∠BSD = 180°

                  ∠BSD = 97°

∠CSE = ∠BSD = 97°

∠C + ∠E + ∠CSE = 180°

   26° + ∠E + 97° = 180°

                      ∠E = 57°

mBC = 2 * ∠E = 2 * ∠D

        = 2 * 57°

        = 114°

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Answer:

Step-by-step explanation:

∠F = 180 - 24 - 34

∠F = 122

∠GFD = 180 - 122

∠GFD = 58°

Answer:

1640

Step-by-step explanation:

Are of the square

a = \(s^{2}\)

a = \(10^{2}\)

a = 100

Area of a trapezoid

a = 1/2(a + b)h

a = 1/2(48 + 40)35

a = 1/2 (48 + 40)35

a = 1/2(88)35

a = 44(35)

a = 1540

100 + 1540 = 1640

Helping in the name of Jesus.

Answer:

The area is 1640 square meters

Step-by-step explanation:

the area of the short block(top right) is

\((10)(10) = 100\\\)

Now, the total length of the top side is(of the bottom portion),

38 + 10 = 48

We can divide the bottom portion into a square and triangular part,

for the square part we get the area,

\((40)(35)=1400\)

For the triangle, we first have to find the length of the base,

which we see from the figure that it will be,

48 - 40 = 8

(and height is 35)

so the area of the triangle is,

\((1/2)(8)(35)=140\)

so the total area of the park is

\(140 + 1400 + 100 = 1640\)

The length of AB which is the missing length side of the similar triangles would be = 28 cm.

To calculate the missing length of the triangle = AB , the scale factor should be determined.

The scale factor that exists between two similar object shows the number of times the original object can be found in the new formed one.

The scale factor = dimensions of new object/ dimensions of original object.

A side of original = EF =22cm

A side of the new triangle = BC = 44

Scale factor = 44/22 = 2

Therefore the missing length of the new triangle = 14×2 = 28cm

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We can use the trigonometric identities to find the exact values of the expressions.

First, we can find cos(alpha) and cos(beta) using the Pythagorean identity:

cos(alpha) = sqrt(1 - sin^2(alpha)) = sqrt(1 - (24/25)^2) = 7/25

cos(beta) = -sqrt(1 - sin^2(beta)) = -sqrt(1 - (15/17)^2) = -8/17 (since beta is in quadrant II, where cosine is negative)

Next, we can use the sum formulas for sine and cosine to find sin(alpha + beta) and cos(alpha + beta):

sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta) = (24/25)(-8/17) + (7/25)(15/17) = -117/425

cos(alpha + beta) = cos(alpha)cos(beta) - sin(alpha)sin(beta) = (7/25)(-8/17) - (24/25)(15/17) = -24/85

Finally, we can use the quotient identity for tangent to find tan(alpha + beta):

tan(alpha + beta) = sin(alpha + beta) / cos(alpha + beta) = (-117/425) / (-24/85) = 39/85

Therefore, cos(alpha + beta) sin(alpha + beta) = (-24/85)(-117/425) = 936/7225, and tan(alpha + beta) = 39/85.

53 years for the Population of the United States to reach 300 million people according to this model.

The recursive formula of the population of the United States is given by ao = an1.015a - 1

Let's solve this to get a formula that is not recursive.a0 = a0 givena1 = 1.015a0 - 1a2 = 1.015a1 - 1 = 1.015 (1.015a0 - 1) - 1 = 1.0152 a0 - 1.015 - 1a3 = 1.015a2 - 1 = 1.015(1.015²a0 - 1.015 - 1) - 1 = 1.015³ a0 - 1.015² - 1.015 - 1a4 = 1.015a3 - 1 = 1.015(1.015³a0 - 1.015² - 1.015 - 1) - 1 = 1.015⁴ a0 - 1.015³ - 1.015² - 1.015 - 1an = 1.015na0 - 1.015n-1 - 1.015n-2 - ... - 1.015 - 1We can rewrite this asan = a0(1.015)

where a0 is the population of the United States in 1910 (92.2 million people) .

Now, we need to write an exponential function to find the population of the United States as a function of time in years since 1910.P(t) = 92.2(1.015)

To find the number of years it takes for the population to reach 300 million people, we need to solve the equation92.2(1.015)t = 300

Dividing both sides by 92.2, we get1.015t = 3.2596

Taking the natural logarithm of both sides, we get ln(1.015) = ln(3.2596)t = ln(3.2596)/ln(1.015) ≈ 53.2

Therefore,  approximately 53 years for the population of the United States to reach 300 million people according to this model.

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Considering the expression of a line, the price of the guitar in 2011 is $354.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points, the value of the ordinate to the origin b can be obtained.

Being:

the slope can be calculated as:

m= (300 - 246)÷ (2008 - 2005)

m= 54÷ 3

m= 18

Considering point 2 and the slope m, you obtain:

300= 18×2008 + b

300= 36,144 + b

300- 36,144 = b

-35,844 = b

Finally, the equation of the line is Price= 18×Year - 35,844

Now, you want to know the price of the guitar in 2011. Replacing in the linear equation, you get:

Price= 18×2011 - 35,844

Solving:

Price= 36,198- 35,844

Price= 354

In summary, the price of the guitar by 2011 is $354.

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Firm shown in the graph will produce q0, but all the firms in the market will produce a total of Q0.

A perfect market, sometimes known as an atomistic market, is described in economics by numerous idealizing requirements, together known as perfect competition, or atomistic competition. A competitive market is one in which no one customer or producer has sway over the market. Its reaction to supply and demand varies with the supply curve, which represents the quantity of a commodity. Perfect competition, monopolistic competition, oligopoly, and monopoly are the four types of economic market systems.

Here,

The business on the graph will create q0, but the market as a whole will yield Q0.

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Answer:

A) 45

the other solutions would be too small to be it.

Answer:

width = 4in

length = 8in

Step-by-step explanation:

A = LxW = 32

L = W + 4

W(W+4) = 32

W² + 4W - 32 = 0

(W + 8)(W - 4) = 0

W ≠ -8 (dimensions cannot be negative)

W = 4in

L = W+4 = 4+4 = 8in

Answer:

D. A solid boundary line, because the values on the line should be included in the solution set.

Step-by-step explanation:

Given.

Part time = 7.25 per hour.

Mowing of Lawn = 9 each time

Required

Determine the type of boundary

From the question, we understand that x represents the number of hours he worked (part time) and y represent number of lawn he mows.

So, his earnings can be expressed as:

7.25x + 9y

The question also says that he needs to earn atleast 300

Atleast 300 means ≤ 300

So, his earnings can be fully represented as:

7.25x + 9y ≤ 300

When plotting an inequality graph that involves ≤, we make use of a solid line.

This is so, because the values on the solid line are also a part of the line equation.

From the list of given options, option D answers the question.

The house with the higher property tax is the home in Big Creek with a difference of $72.14.

The property tax liability on a home is computed by multiplying the mill rate by the assessed value.

The assessed value depends on the area and the assessment rate applied to the appraised value.

Home appraised value = $125,000

Assessed value = 100% or $125,000

Property tax rate = $1.85 per $100

Property tax = $2,312.50 ($125,000 x $1.85/$100)

Home appraised value = $138,000

Assessed value = 80% or $110,400

Property tax rate = 21.6 mills

Property tax = $2,384.64 ($110,400 x 21.6/1,000)

Difference in property tax = $72.14 ($2,384.64 - $2,312.50)

Thus, Big Creek attracts higher property tax than the home in Louisville.

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

$29.40

Step-by-step explanation:

29.40 dollars as 100 - the sum of the cost = 29.4

Answer:

81x^8

Step-by-step explanation:

i hope this helps :)

We have the number:

We have to answer if it is rational or irrational.

In order to be rational, a number has to be able to be represented in a fraction.

In this case, we start by separating the number in the whole part and the decimal part:

We can express the decimal part as a fraction, because:

Then, we have:

As we have a fractional expresion for the number, it is not an irrational number.

4.3... is a rational number.

The equation that states the sum of the tickets sold is -

30x + 45y = 60900.

We have concert promoter.

We have to write an equation that states that the total amount received from the sale, which is 60,900 dollars.

The equation modelling is a process of writing a mathematical equation from a mathematical statement involving variables, constants etc.

According to the question -

Money earned from $30 tickets = $30x

Money earned from $45 tickets = $45y

Total money from 1780 tickets = $60,900

Therefore -

30x + 45y = 60900

Hence, the equation that states the sum of the tickets sold is -

30x + 45y = 60900.

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[ The given question is incomplete, the complete question is

A concert promoter needs to make $60,900 from the sale of 1780 tickets. The promoter charges $30 for some tickets and $45 for the others. Let x represent the number of $30 tickets and y represent the number of $45 tickets. Write an equation that states that the total amount received from the sale is 60900 dollars.]

Answer:

r = 7

Step-by-step explanation:

hope this was helpful let me know  you need the steps! :)

Answer: 1.75 or 1 3/4

Step-by-step explanation:

Because first you need to get R by it’s self by dividing it by 1/2 then if you divided it by one side you have to divide it by the other side so you get r=1.75 or 1 3/4.

The amount of water the farmer can put in the tank increase when the larger tank is built is 106.33%.It takes 4days for the horses to drink all the water in the larger tank.

Percentage is a way of expressing a proportion or a fraction out of 100. It represents the number of parts per hundred of a quantity.

Dimension refers to a measurable aspect of an object or a system, such as length, width, height, depth, volume, area, or mass. In mathematics, dimension also refers to the number of coordinates required to specify a point in a space. For example, a two-dimensional shape like a square has two dimensions, length and width, while a three-dimensional object like a cube has three dimensions, length, width, and height.

To find the percentage increase in the amount of water the farmer can put in the larger tank, we need to calculate the volume of the original tank and the volume of the larger tank, and then compare the two.

The original tank has dimensions of 2 4/5 ft, 2 2/5 ft, and 2 1/2 ft. We can convert these mixed numbers to improper fractions for easier calculations:

2 4/5 ft = (2 x 5 + 4)/5 ft = 14/5 ft

2 2/5 ft = (2 x 5 + 2)/5 ft = 12/5 ft

2 1/2 ft = (2 x 2 + 1)/2 ft = 5/2 ft

The volume of the original tank is then:

Volume = Length x Width x Height = 14/5 ft x 12/5 ft x 5/2 ft

Now, the farmer plans to increase measurement  by 25%. To do this, we multiply each measurement by 1.25.

The dimensions of the larger tank would be:

Length = 14/5 ft x 1.25 = 3.5 ft

Width = 12/5 ft x 1.25 = 3 ft

Height = 5/2 ft x 1.25 = 3.125 ft

The volume of the larger tank is then:

Volume = Length x Width x Height = 3.5 ft x 3 ft x 3.125 ft

To find the percentage increase, we can compare the two volumes:

Percentage increase = ((Volume of larger tank - Volume of original tank) / Volume of original tank) x 100

Plugging in the values we found:

Percentage increase = ((3.5 ft x 3 ft x 3.125 ft - 14/5 ft x 12/5 ft x 5/2 ft) / (14/5 ft x 12/5 ft x 5/2 ft)) x 100

After calculating the above expression, we find that the percentage increase is approximately 106.33%. So, the amount of water the farmer can put in the larger tank will increase by approximately 106.33% when the larger tank is built.

Now, to find how many days it will take the horses to drink all the water in the larger tank, we can assume that the rate at which the horses drink water remains constant. Since the volume of the larger tank is approximately 106.33% more than the original tank, it will take the horses approximately the same amount of time to drink all the water in the larger tank, which is 4 days.

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The Jocelyn estimate's percent error is 2.181 centimeters..

What is percent error ?

Percent error calculates the difference between an estimate and a right number and expresses it as a percentage. Analysts can use this statistic to determine how big the mistake is in relation to the actual number. It is also referred to as % error and percentage error.

There are three steps to determining the % error:

1. Determine the error, which is the estimated value minus the actual value.

2. Multiply by the accurate value.

3. In order to create a percentage, multiply by 100.

Given information:

The size of a piece of wood (Exact value)= 5.5 cm

if it really does measure(Approximate value)=5.62 cm

percentage error={(approximate value-exact value)/exact value}×100

percentage error = ((5.62-5.5)/5.5)×100

percentage error = 2.181cm

Consequently, 2.181cm is the Jocelyn estimate's percent error.

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Answer:

There are 80 men on the train.

Step-by-step explanation:

M : W

4  : 5

W : C

10 : 9

As you can see, the units for women is not equal, so I shall multiply the first ratio by 2 so that the units for women is 10.

M : W

8  : 10

Now that everything has the same units, I can put the ratio of men, women and children together:

M : W : C

8  : 10 : 9

Total number of units = 8 + 10 + 9

                                    = 27

27 units = 270

No. of men (8 units) = \(\frac{8}{27}\) × 270

                                 = 80  

The value of x, y and z in the system equation is (1, 2, 3).

The solution of the equation can be determined by using Cramer's rule as follows;

[-5    -6      0] = [ -17]

[-3     -5     5]    [2   ]

[-6    -5      1]     [-13 ]

The determinant of the matrix is calculate as;

Δ = -5 (-5 + 25) + 6(-3 + 30) + 0(15 + 30)

Δ = 62

The x-determinant of the matrix is calculated as follows;

Δx = -17(-5 + 25) + 6(2 + 65) + 0

Δx = 62

The y-determinant of the matrix is calculated as follows;

Δy = -5(2 + 65) + 17(-3 + 30) + 0

Δy = 124

The z-determinant of the matrix is calculated as follows;

Δz = -5(65 + 10) + 6 (39 + 12) - 17(15 - 30)

Δz =  186

The value of x, y and z is calculated as follows;

x = Δx/Δ = 62/62 = 1

y = Δy/Δ = 124/62 = 2

z = Δz/Δ = 186/62 = 3

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Answer:

156 cm³

Step-by-step explanation:

The solid is a prism with a trapezoid base.

volume = (area of base) × height

V = (8 cm + 5 cm)(1/2)(4 cm) × 6 cm

V = 156 cm³

Answer:

ST=26

Step-by-step explanation:

RS+ST=RT

17+x+16=4x+3

x+33=4x+3

33-3=4x=x

3x=30

x=30/3

x=10

ST=x+16

ST=10+16

ST=26

Answer:

Step-by-step explanation:

1/4 of all of it

Answer:

-15/9

Step-by-step explanation:

The slope is the steepness of the line. To find it, you divide how far up it goes by how far across it goes. This equals the diagonal incline. To find it with points, you find the difference between the y values and divide that by the difference in the x values!

-9-6=-15

10-1=9

-15/9=-15/9

This slope means that for every nine units the line goes across, it goes down 15 units!

Have a wonderful day :D

The per capita emissions for each country is:

Using this formula to find the  Per capita emissions for each country

Per capita emissions = C02 Emission (tons of carbon dioxide ) /  Total emissions by population

China

Per capita emissions =8,782,000,000/1,359,750,000

Per capita emissions = 6.46

United States

Per capita emissions =5,144,000,000/316,597,000

Per capita emissions= 16.25

India

Per capita emissions = 2,185,000,000 /1,233,460,000

Per capita emissions = 1.77

Russia

Per capita emissions=1,646,000,000/143,400,000

Per capita emissions = 11.48

Japan

Per capita emissions = 1,232,000,000/127,310,000

Per capita emissions = 9.68

Germany

Per capita emissions = 733,000,000/80,523,700

Per capita emissions = 9.10

Iran

Per capita emissions = 583,000,000/76,876,000

Per capita emissions = 7.58

South Korea

Per capita emissions = 576,000,000/50,219,669

Per capita emissions = 11.47

Indonesia

Per capita emissions = 535,000,000/237,641,326

Per capita emissions = 2.25

Canada

Per capita emissions = 528,000,000/35,141,542

Per capita emissions =15.02

Therefore China per capita emissions is 6.46.

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