A toy train set includes a train station building which is a scale model of a real building. The area of
the front side of the toy building is 1 square foot. The real building's front side has an area of 400
square feet. If we view the real building as a dilation of the toy, what is the scale factor?
Your answer

The equation of inverse of the parabola is,

x = y² - 4.

The graph of its inverse is given below.

To find the equation of the parabola, we can start by using the standard form of a quadratic equation, which is y = ax² + bx + c. Since we know the x-intercepts and the y-intercept, we can substitute these values into the equation to solve for the coefficients a, b, and c.

Using the x-intercepts:

For the x-intercept (-2, 0), we have the equation: 0 = a(-2)^2 + b(-2) + c

Simplifying: 0 = 4a - 2b + c --(1)

For the x-intercept (2, 0), we have the equation: 0 = a(2)^2 + b(2) + c

Simplifying: 0 = 4a + 2b + c --(2)

Using the y-intercept:

For the y-intercept (0, 4), we have the equation: 4 = a(0)^2 + b(0) + c

Simplifying: 4 = c --(3)

Now we have a system of three equations (1), (2), and (3) with three variables (a, b, c). We can solve this system of equations to find the values of a, b, and c.

Substituting equation (3) into equations (1) and (2):

0 = 4a - 2b + 4 --(4)

0 = 4a + 2b + 4 --(5)

Adding equations (4) and (5) together, we get:

0 = 8a + 8

Dividing both sides by 8, we find:

a = -1

Substituting this value of a into equation (4), we get:

0 = -4 - 2b + 4

Simplifying, we find:

2b = 0

Dividing both sides by 2, we get:

b = 0

Finally, substituting the values of a = -1 and b = 0 into equation (3), we find:

c = 4

Therefore, the equation of the parabola is y = x² - 4.

To find the equation of the inverse of the parabola, we can swap the x and y variables in the equation and solve for y.

x = y² - 4.

The graph of its inverse is given below.

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The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²

Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

N(x) = 625 + 2.5x

The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:

R(x) = (625 + 2.5x)(400 - x)

Simplifying the expression, we get:

R(x) = 250000 + 375x - 2.5x²

Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:

R(x) = 250000 + 375x - 2.5x²

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Answer:

The tightened spot is 10 feet away from the foot of the pole.

Step-by-step explanation:

1. Draw the diagram. Notice that the shape of the electric pole and its supporting wire creates a right triangle.

2. We know 2 side lengths already (26ft, 24ft), and we need to find 1 more side length. Therefore, to find the 3rd side length of a right-triangle, utilize Pythagoras' Theorem.

⭐What is the Pythagoras' Theorem?

3. Substitute the values of the side lengths into the equation, and solve for the unknown side length.

Let B= the distance from the tightened spot to the foot of the pole.

\((C)^2 = (A)^2 + (B)^2\)

\(26^2 = 24^2 + B^2\)

\(676 = 576 + B^2\)

\(100 = B^2\)

\(\sqrt{100} = \sqrt{(B)^2}\)

\(10 = B\)

∴ The tightened spot is 10 feet away from the foot of the pole.

Diagram:

The following formula: 11(h - 40)/2 Recommended weight is 165 lbs

The  formula is

=11(h - 40)/2

w = weight and h = height in inches.

5 feet 10 inches tall,

so putting the value of h

11(43-40)/2=165lbs

The first big step you can take to improve your health is to achieve your desired body weight. Obesity and being overweight are the root causes of the majority of lifestyle illnesses .

Heart disease, stroke, diabetes, obesity, metabolic syndrome, chronic obstructive pulmonary disease, and some forms of cancer are among them . What was formerly thought to be a "western sickness" or "affluent disease" now affects poor countries as well.

The first big step you can take to improve your health is to achieve your desired body weight. Obesity and being overweight are the root causes of the majority of lifestyle illnesses . Heart disease, stroke, diabetes, obesity, metabolic syndrome, chronic obstructive pulmonary disease, and others are examples.

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Answer:

\(Net\ Worth = \$2800\)

Step-by-step explanation:

Net worth is calculated using;

\(Net\ Worth = Assets - Debts\)

In this question, we have:

\(Laptop = \$1200\) --- 2 years ago

\(Laptop = \$700\) --- presently

\(Car = \$2900\)

\(Debt = \$800\)

Only the current worth of the laptop will be considered;

So, we have:

\(Assets = Laptop + Car\)

\(Assets = \$700 + \$2900\)

\(Assets = \$3600\)

\(Net\ Worth = Assets - Debts\)

\(Net\ Worth = \$3600 - \$800\)

\(Net\ Worth = \$2800\)

Tammy's net worth from the laptop computer and car  is $2600

Cost of the laptop computer two years ago = $1200

Worth of the laptop computer today = $700

Laptop Asset = $1200 - $700

Laptop Asset = $500

Car worth = $2900

Tammy still owes $800 on the car

Debt = $800

Car Asset = $2900 - $800

Car Asset = $2100

Tammy's net worth = Laptop Asset + Car Asset

Tammy's net worth = $500  +   $2100

Tammy's net worth = $2600

Tammy's net worth is $2600

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Answer:

3 to 8

Step-by-step explanation:

There are 24 total shapes, 9 of which are circles. So we have the ratio 9 to 24, or 3 to 8.

Answer:

the line goes through the points (-4, 0) and (0, 3)and slope is rise over run so the line goes up 3 and to the right 4 so you put 3 over 4, the slope is 3/4

Answer:

11

Step-by-step explanation:

3^2 + 1 • 2 = 11

NOTE:

'^' is the exponent symbol

Answer:

a) no

b) yes

c) 0.75(37 + c) ≥ 45

Step-by-step explanation:

lemonade = $0.75 per cup

Saturday sales = 37 cups

Let c = number of cups sold on Sunday

⇒ Total weekend sales = 0.75(37 + c)

a)  No, they will not reach their goal of making at least $45

If c = 12:

Total weekend sales = 0.75(37 + 12)= 0.75 x 49 = $36.75

$36.75 < $45

b) Yes, they will reach their goal of making at least $45

If c = 25:

Total weekend sales = 0.75(37 + 25)= 0.75 x 62 = $46.50

$46.50 > $45

c)

0.75(37 + c) ≥ 45

Answer:

68 i think

Step-by-step explanation:

Step-by-step explanation:

The equation here is,

w° + 124° = 180°

=> w = 180° - 124°

=> w = 56° (Ans)

SOLUTION TO THIS EQUATION

Answer:

6inch

Step-by-step explanation:

Read the excerpt from The Crisis, Number I by Thomas Paine.

“I once felt all that kind of anger, which a man ought to feel, against the mean principles that are held by the Tories: a noted one, who kept a tavern at Amboy, was standing at his door, with as pretty a child in his hand, about eight or nine years old, as I ever saw, and after speaking his mind as freely as he thought was prudent, finished with this unfatherly expression, ‘Well! give me peace in my day.’ Not a man lives on the continent but fully believes that a separation must some time or other finally take place, and a generous parent should have said, ‘If there must be trouble, let it be in my day, that my child may have peace;’ and this single reflection, well applied, is sufficient to awaken every man to duty.”

Which is a central idea of this excerpt?

Paine feels that everyone should be able to speak freely, which is why he supports independence.

Paine believes that colonists should fight for independence so their children can live in peace.

Paine believes that some people are selfish and place their needs above others.

Paine felt anger for the first time when he saw an interaction between a Tory and a child.

The final answer for the surface area of the prism is 32 m^2 + 16h m^2.

To find the surface area of the prism, we need to calculate the area of each face and sum them up.

The prism has two identical square faces and four rectangular faces. The square face has a side length of 4 m. The area of one square face is given by:

Area of square face = side length^2 = 4^2 = 16 m^2

Since there are two square faces, the total area of the square faces is:

Total area of square faces = \(2 * 16 = 32 m^2\)

The rectangular faces have a length equal to the side length of the square face (4 m) and a width equal to the height of the prism. Let's assume the height of the prism is h. The area of one rectangular face is given by:

Area of rectangular face = length * width = \(4 * h = 4h m^2\)

Since there are four rectangular faces, the total area of the rectangular faces is:

Total area of rectangular faces = \(4 * 4h = 16h m^2\)

Therefore, the surface area of the prism is the sum of the areas of the square and rectangular faces:

Surface area of prism = Total area of square faces + Total area of rectangular faces

                          = \(32 m^2 + 16h m^2\)

                          = \(32 m^2 + 16h m^2\)

The answer for the surface area of the prism is 32 m^2 + 16h m^2.

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The value of the car after 3 years is $79, 000

To determine the value, we have to use the formula;

Value = Initial value × (1 - Depreciation rate)ⁿ

Substitute the values given, we get;

Remaining value after 3 years = $100,000 × (1 - 0.10)³

Expand the bracket, we get;

Value after 3 years = $100,000 × (0.90)³

Find the cube value and substitute, we have;

Value after 3 years = $100,000 × 0.729

Multiply the values, we have;

Value after 3 years = $72,900

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what is this

Step-by-step explanation:

Option #1 – charges 5% simple interest per year; this is a short-term loan for only 5-years.

Option #2 – charges 7% simple interest per year; this is a short-term loan for only 3-years.

Option #3 – charges 3.2% simple interest per year; there is no time limit on this loan (as a group determine how long you think it will take you to make enough money to be able to pay back the loan with interest)

Option #4 - charges 10% simple interest per year; only lasts 10 months

Option what is this

Answer:

Its option one

Step-by-step explanation:

Because 135,000/5=27000 then x5=135,000

Answer:

5w+11n

:D

Hope this helped!

My regards

Hello!

surface area

= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)

= 160cm²

\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

_____________________________

If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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I suppose you mean

\(f(x) f(y) = f(x + y) + f(x - y)\)

Let \(x=1\) and \(y=0\). Then

\(f(1) f(0) = f(1 + 0) + f(1 - 0) \implies f(1) f(0) = 2 f(1) \implies f(0) = 2\)

Now if we fix \(y=1\), the functional equation reduces to the recurrence relation

\(f(x) f(1) = f(x + 1) + f(x - 1) \implies f(x+1) - 3f(x) + f(x-1) = 0\)

and we can find \(f(7)\) with a few rounds of substitution.

\(x=1 \implies f(2) - 3f(1) + f(0) = 0 \implies f(2) = 3f(1) - f(0) = 7\)

\(x=2 \implies f(3) - 3f(2) + f(1) = 0 \implies f(3) = 3f(2) - f(1) = 18\)

\(x=3 \implies f(4) - 3f(3) + f(2) = 0 \implies f(4) = 3f(3) - f(2) = 47\)

\(x=4 \implies f(5) - 3f(4) + f(3) = 0 \implies f(5) = 3f(4) - f(3) = 123\)

\(x=5 \implies f(6) - 3f(5) + f(4) = 0 \implies f(6) = 3f(5) - f(4) = 322\)

\(x=6 \implies f(7) - 3f(6) + f(5) = 0 \implies f(7) = 3f(6) - f(5) = \boxed{843}\)

Discuss measures that can be taken to develop the spirit of hard work

\(\displaystyle\bf 4\sqrt{28} :3\sqrt{7} =4\sqrt{4} \cdot \sqrt{7} :3\sqrt{7} =4\cdot2:3=\boxed{\frac{8}{3} }\)

Aircraft A has 312 seats.

Let's assume that Aircraft B has x seats.

According to the given information, Aircraft A has 105 more seats than Aircraft B. So, the number of seats in Aircraft A can be expressed as x + 105.

The total number of seats in both aircraft is 519, which can be represented by the equation:

x + (x + 105) = 519

Simplifying this equation, we have:

2x + 105 = 519

Subtracting 105 from both sides, we get:

2x = 414

Dividing both sides by 2, we find:

x = 207

Therefore, Aircraft B has 207 seats.

To find the number of seats in Aircraft A, we substitute the value of x back into the expression x + 105:

Aircraft A = 207 + 105 = 312

Hence, Aircraft A has 312 seats.

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Answer:

it is too blury to read

Step-by-step explanation:

....................................................................................................................................................................................................................

The probability tree will have three branches at start and then, each branch will have two more branches for ranch and two story houses.

Given information:

There are three cities A, B, and C.

The homes are of two types; two story and ranch.

The sales in A, B, and C is 60%, 25%, and 15%, respectively.

The ranch houses in A, B, and C are 10%, 40%, and 50% respectively.

So, the probability tree will have three branches at first. These three branches will have probability of 0.6, 0.25, and 0.15, for A, B, and C, respectively.

See the attached image.

Therefore, the probability tree will have three branches at start and then, each branch will have two more branches for ranch and two story houses.

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Answer:

The answer is below

Step-by-step explanation:

The height of tank = 12 m = 1200 cm, the diameter of the tank = 8 meters, hence the radius of the tank = 8/2 = 4 m = 400 cm

Let h represent the water level = 8 m = 800 cm. The radius (r) of the water level at a height of 8 m is:

r/h = radius of tank/ height of tank

r/h = 400/1200

r = h/3

\(\frac{change\ in\ volume}{change\ in \ time}=water\ in-water\ out\\ \\\frac{dV}{dt=} water\ in-water\ out\\\\V=\frac{1}{3}\pi r^2h\\ \\r=\frac{1}{3}h \\\\V=\frac{1}{3}\pi (\frac{1}{3}h )^2h\\\\V=\frac{1}{9} \pi h^3\\\\\frac{dV}{dt} =\frac{1}{3} \pi h^2\frac{dh}{dt}\\\\\frac{dh}{dt}=2\ cm/min,h=8\ m=800\ cm\\\\\)

\(\frac{dV}{dt} =\frac{1}{3} \pi (800)^2(2)=426666.7\ cm^3/min\\\\\frac{dV}{dt=} water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-20000\ cm/min\\ \\water\ in=426666.7\ cm^3/min+20000\ cm/min\\\\water\ in=446666.7 \ cm^3/min\)

Financial Maths

A sequence of equal payments (or deposits) at equal periods of time is called an annuity.

The future value of an annuity can be calculated with the formula:

Where:

FV is the future value of the annuity

A is the periodic deposits

n is the number of compounding periods per year

i is the interest rate adjusted to the compounding periods. i = r/n where r is the APR.

t is the duration of the investment in years

The financial variables for this investment are:

A = $1100

r = 3.7% = 0.037

n = 360. Daily compounding

i = 0.037/360 = 0.000102777

It's crucial to keep as many decimals as possible in the calculations.

Applying the formula:

Calculating:

FV = $14,361,798.98

Calculation steps (in strict order)

* Add 1 + 0.00010277 = 1.00010277

* Multiply 360*23 = 8280

* Raise 1.00010277^8280 = 2.341885

* Subtract 1 = 1.341885

* Divide by 0.00010277 = 1.341885/0.00010277=13056.18

* Multiply by 1100: $14,361,798.98

Rounded to the nearest cent

Answer:

the answer is 3

Step-by-step explanation:

21 x 3 =7

hope it helps

Answer:

21/7

Step-by-step explanation:

Move 7 to next side with opposite process it is multiple after move it will be divided so 21x (21/7) it will be 7 although (21/7)equivalent to 1/3

Answer:

$194.05 per hour

Step-by-step explanation:

Divide her total earnings by 28:

5433.35/28

= approximately 194.05

So, Sandra earns about $194.05 per hour