An engineer created a scale drawing of a building using a scale in witch 0.25 inch represents 2 feet. The length of the actual building is 250 feet. What is the length in inches of the building in the scale drawing?​

55.2% is capital gain of Maria.

To calculate Maria's capital gain, we need to find the difference between the sale price and the purchase price, and then divide that by the purchase price. We can express this as a formula:

capital gain = (sale price - purchase price) / purchase price

Plugging in the numbers we have:

capital gain = ($55.10 - $35.50) / $35.50

Simplifying the expression:

capital gain = $19.60 / $35.50

capital gain = 0.5521

To express this as a percentage, we need to multiply by 100:

capital gain = 55.21%

Rounded to the nearest tenth of a percent:

capital gain = 55.2%

Therefore, Maria's capital gain is 55.2%.

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The exponential decay model that represents the forest cover in the world t years after 1990 is:

We can use the exponential decay model to represent the decrease in the world forest cover over time:

y = a e^(kt)

where

y is the forest cover in 10^6 hectares,

t is the time ,

a is the initial forest cover,

k is the decay rate.

Solving for a and k:

where a = 4168 million hectares  (given)

When t = 20  the forest cover was 4033 million hectares.

y = a e^(kt)

y = 4033 = 4168 e^(k*20)

4033/4168 = e^(k*20)

Taking the natural logarithm of both sides:

ln(4033/4168) = k*20

Solving for k, results to

k = ln (4033 / 4168) / 20

k = -0.00165 (to 5 dp)

therefore we can say that, the decay model is:

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Answer:

1: the balance after 8 years is approximately $151.78.

2:  is approximately 7%.

Step-by-step explanation:

1: The balance after t years with continuous compounding can be calculated using the formula:

B = Pe^(rt)

Where:

P = 120 dollars (initial deposit)

r = 2.5% = 0.025 (interest rate in decimal form)

t = 8 years

Substituting these values into the formula, we get:

B = 120e^(0.025*8) ≈ 151.78

Therefore, the balance after 8 years is approximately $151.78.

2: The interest rate can be found using the formula:

A = Pe^(rt)

Taking the natural logarithm of both sides and solving for r, we get:

r = ln(A/P) / t

Where:

A = 4055 dollars (final amount)

P = 1000 dollars (initial investment)

t = 20 years

Substituting these values into the formula, we get:

r = ln(4055/1000) / 20 ≈ 0.0774

Converting to a percentage and rounding to the nearest whole number, we get:

r ≈ 7%

Therefore, the interest rate, if compounded continuously, is approximately 7%.

Answer:

1. $146.57

2. 7%.

Step-by-step explanation:

1.

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

To use this formula, we first need to convert the annual interest rate to a decimal:

r = 2 1/2 = 2.5%

r = 2.5/100 = 0.025

Now we can plug in the values:

A = 120e^(0.025*8)

A ≈ $146.57

Therefore, the balance after 8 years is approximately $146.57

2.

The formula for continuous compounding is: A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

We can rearrange this formula to solve for the interest rate:

r = ln(A/P)/t

Where ln represents the natural logarithm.

Now we can plug in the given values:

r = ln(4055/1000)/20

r ≈ 0.069or 7.1%

Therefore, the interest rate, rounded to the nearest whole number, is 7%.

Step-by-step explanation:

so to get y all you need to do the equation so let's start with the first 1 which is 2 so 3×2=9-5=4 so y equals to 4

so to find X we need to do the opposite so let's do the second one which y is 4 so instead of subtracting we will add 5 which is 9 then we devide by 3 which is 3 that's how to do it

7+5=12÷3=4

5×3=15-5=10

The simplified expression of the given expression is given by 3√(27x¹²) is 3x⁴.

From the rule exponent we know that the exponents follow the below rules,

aˣ⁺ʸ = (aˣ)*(aʸ)

(aˣ)ʸ = aˣʸ

aˣ⁻ʸ = (aˣ)/(aʸ)

The given expression is,

3√(27x¹²) that is in words "Cube root of 27x¹²"

Now we know that, 3³ = 27 and we can write from exponent formula that,

x¹² = (x⁴)³ [As 4*3 = 12]

So, now simplifying the given expression we get,

3√(3³(x⁴)³) = 3√((3x⁴)³) = 3x⁴ [Omitting the exponent 3 and cube root]

Hence the simplified expression of the given expression is given by 3√(27x¹²) is 3x⁴.

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The answer of the given question based on distance is , the two trains will meet 60 km from Station X.

Speed is the  measure of how fast object is moving. It is the distance an object travels per unit of time. The SI unit for speed is meters per second (m/s), but it can also be expressed in other units, like kilometers per hour (km/h), miles per hour (mph), feet per second (ft/s), etc.

Let's first consider the relative speed between the two trains. Since they are moving towards the each other, we can add their speeds:

Relative speed =Speed of train A+Speed of train B

= 60 km/hr + 30 km/hr

= 90 km/hr

Now, we can use the formula:

distance = speed × time

Let's assume that the two trains meet at a distance of x km from Station X. Then, the distance that train A travels before meeting train B is (180 - x) km.

Using the formula for train A:

distance = speed × time

(180 - x) = 60t

where t is the time taken for the two trains to meet.

Using the formula for train B:

distance = speed × time

x = 30t

Now, we can substitute the value of x from the second equation into the first equation:

(180 - 30t) = 60t

Simplifying this equation, we get:

180 = 90t

t = 2 hours

Therefore, the two trains will meet after 2 hours of travel.

To find the distance from Station X where they meet, we can substitute t = 2 into either of the two equations for x:

x = 30t = 30 × 2 = 60 km

Therefore, the two trains will meet 60 km from Station X.

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Answer:

44.642%

Step-by-step explanation:

To find the percent of dogs that are retrievers, take the number of retrievers over the total dogs.

25/56

0.44642

Change to percent form

44.642%

Answer:

The perimeter of triangle ABC is

[tex]6 + 7 + \sqrt{ {6}^{2} + {7}^{2} } [/tex]

[tex]13 + \sqrt{85} = 22.2[/tex]

We know that the perimeter of the given triangle ABC is 19 units respectively.

A triangle is a polygon with three edges and three vertices.

It belongs to the basic geometric shapes.

The provided object is a triangle with equal sides that has vertices A, B, and C. The triangle shape.

Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.

So, we know that the perimeter of the triangle is = Sum of all 3 sides.

In this case, we will count the units of each side as follows:

AB = 6 units

BC = 7 units

AC = 6 units

Now, get the perimeter as follows:

6+7+6 = 19 units

Therefore, we know that the perimeter of the given triangle ABC is 19 units respectively.

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The graph of the function f(x) is an even function

Given that we have the graph of the function f(x)

As a general rule

The given function is symmetrical with the y-axis

This is so because

f(x) = f(-x)

This means that the function is an even function

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The number of people who attended the movie are as follows;

Number of children = 162 children.

Number of adults = 81 adults.

Number of students = 50 students.

In order to determine the number of children, students, and adults that attended, we would assign a variable c to the the total number of children who attended the movie.

Since there are half as many adults as there are children, we have the following:

Number of adults = c/2.

Similarly, the number of students who attended the movie can be calculated as follows;

Number of students = 293 - (c + c/2)

Number of students = 293 - 3c/2

Since the total ticket sales were $2132, a linear equation to model it is given by:

2132 = 5c + 7(293 - 3c/2) + 12(c/2)

2132 = 5c + 2,051 - 21c/2 + 12c/2

2132 - 2051 = 5c - 9c/2

81 = c/2

c = 162 children.

Students = 293 - 3c/2

Students = 293 - 3(162)/2

Students = 293 - 243

Students = 50 students.

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Answer:

The formula for continuous compounding is given as:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the annual interest rate (as a decimal), t is the time in years, and e is the mathematical constant approximately equal to 2.71828.

To find the time for an investment to double, we can set A/P = 2 and solve for t:

2 = e^(rt)

Taking the natural logarithm of both sides, we get:

ln(2) = rt

Solving for t, we get:

t = ln(2)/r

Substituting r = 0.0575 (since 5.75% = 0.0575 as a decimal), we get:

t = ln(2)/0.0575 ≈ 12.06 years

Therefore, at an annual interest rate of 5.75% compounded continuously, it takes approximately 12.06 years for an investment to double.

The y-intercept of the function g(x) is y-intercept = 5 and the vertex is (3, -4)

Set g(x) = 0 for the x-intercept

So, we have

(x - 1)(x - 5) = 0

Evaluate

x-intercept = 1 and 5

For the y-intercept,

Substitute 0 for x in g(0)

So, we have

g(0) = (0 - 1)(0 - 5)

Evaluate

g(0) = 5

We have

g(x) = (x - 1)(x - 5)

Express in vertex form

g(x) = (x - 3)² - 4

From g(x) = (x - 3)² - 4, the vertex is

Vertex = (3, -4)

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Possible question

The function f(x)=-1/2x+3 and g has a lesser y-intercept than f;

The function g(x) is g(x) = (x - 1)(x - 5)

The increasing and decreasing intervals

Find the vertex and y-intercept of g.

Answer:

area of sector = 282.74 yd²

length of arc = 47.12 yd

Step-by-step explanation:

12 yd is the radius

area of a circle = πr²

area of sector = π12² × 225/360 = 90π yd² or 282.74 yd² (2dp)

circumference of circle = π × diameter

diameter = 12 × 2 = 24

length of arc = 225/360 × 24π = 15π yd or 47.12yds (2dp)

Question 3, part (a)

The tangent line is perpendicular to the radius at the point of tangency.

If AB was tangent to circle C, then radius AC would be perpendicular to segment AB. Meaning that angle BAC should be 90 degrees, and it should lead to triangle ABC being a right triangle.

Use the pythagorean theorem converse to see if we have a right triangle or not.

a^2 + b^2 = c^2

5^2 + 11^2 = 13^2

25 + 121 = 169

146 = 169

The last equation is false so the first equation is false when a = 5, b = 11, c = 13. Triangle ABC is not a right triangle. We've proven angle BAC isn't 90 degrees.

====================================================

Question 3, part (b)

We'll use the same template of steps as done back in part (a).

This time we have:

The order of 'a' and b doesn't matter. The c is always the longest side.

a^2 + b^2 = c^2

6^2 + 8^2 = 10^2

36 + 64 = 100

100 = 100

The last result is true so the first equation is true for the a,b,c values mentioned. Notice the equation would also be true if a = 8, b = 6, c = 10.

Therefore, triangle ABC is a right triangle where the 90 degree angle is at point A.

====================================================

Answer:

(a) No

(b) Yes

Step-by-step explanation:

The tangent of a circle is always perpendicular to the radius.

Since AC is the radius of circle C, if AB is a tangent to circle C, then m∠BAC = 90°.

As we have been given the measures of all three sides of both triangles, we can use Pythagoras Theorem to determine if the measure of angle BAC in both triangles is a right angle.

Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle:

[tex]\boxed{a^2+b^2=c^2}[/tex]

where:

The legs of this triangle are AC and AB. The hypotenuse is BC.

Substitute the measures of the sides into the Pythagoras Theorem formula:

[tex]\implies AC^2+AB^2=BC^2[/tex]

[tex]\implies 5^2+11^2=13^2[/tex]

[tex]\implies25+121=169[/tex]

[tex]\implies146=169[/tex]

As 146 does not equal 169, this proves that the triangle is not a right triangle. Therefore AB is not tangent to circle C.

The legs of this triangle are AC and AB. The hypotenuse is BC.

Substitute the measures of the sides into the Pythagoras Theorem formula:

[tex]\implies AC^2+AB^2=BC^2[/tex]

[tex]\implies 6^2+8^2=10^2[/tex]

[tex]\implies 36+64=100[/tex]

[tex]\implies100=100[/tex]

As both sides of the equation are the same, this proves that the triangle is a right triangle and m∠BAC = 90°. Therefore AB is tangent to circle C.

Answer:

Step-by-step explanation:

Assuming these are lengths of a line segment,

you would add AB to BC to get AC.

18 + 8 = 26

The area of the triangle formed by the x-axis, the y-axis and the line y=−x+12 is found to be 72 square units.

We have to find the vertices of triangle bounded by the x and y-axis and the line y = -x + 12 to solve the problem. The x-intercept of the line y = -x + 12 occurs when y = 0, so we have,

0 = -x + 12

x = 12

So, we get, (0,0), (12,0), (0,12). Using the formula, A = 1/2 x base x height. In this case, the base and height of the triangle are both 12, so we have,

A = 1/2 * 12 * 12

A = 72

Hence, the area of triangle is 72 sq. units.

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Answer:

[tex]\textsf{d)} \quad \sf Secant=\overleftrightarrow{\sf ED}[/tex]

[tex]\sf e) \quad Tangent = line\; \textit{b}[/tex]

[tex]\sf f) \quad Point \;of \;tangency = Point \;B[/tex]

[tex]\sf g)\quad N\:\!ame\;of\;circle=Circle\;A[/tex]

Step-by-step explanation:

A secant is a straight line that intersects a circle at two points and is drawn from outside the circle.

Therefore, the secant in the given diagram is [tex]\overleftrightarrow{\sf ED}[/tex].

A tangent is a straight line that touches a circle at only one point and is drawn from outside the circle.

Therefore, the tangent in the given diagram is line b.

The point of tangency is the point where the tangent meets the circle.

Therefore, the point of tangency in the given diagram is point B.

A circle is named by the point of its center.

As the center of the given circle is point A, then the name of the circle is Circle A.

Based on the information, we can infer that Cliff's experiment will have similar numbers regarding the frequency of each letter while Devon will have a higher frequency of the letters A, E, U than the letters O and I.

To interpret the information from the experiments we must take into account the experiments that each one carried out. In the first case, Cliff always had the same probability of drawing a vowel from the bag, that is, 1/5.

However, in Devon's case, the arrow was less likely to point to the letters O and I because they occupy a smaller area on the spinner.

Based on the above, Cliff's frequency plot is more likely to have the values in a "similar" range for all letters, while Devon is going to have a majority on letters A, E, U.

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Answer:

[tex](y + 6)(y - 6) = {y}^{2} - 36[/tex]

The y and x intercepts of the function are m(0) = 32/3 and x = 5 and x = -8

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

m(x) = [4(x - 5)(x + 8)]/[x^2 - 2x - 15]

Set x = 0 to calculate the y intercepts

So, we have

m(0) = [4(0 - 5)(0 + 8)]/[0^2 - 2(0) - 15]

Evaluate

m(0) = 160/15

So, we have

m(0) = 32/3

Set m(x) = 0 to calculate the x intercepts

So, we have

[4(x - 5)(x + 8)]/[x^2 - 2x - 15] = 0

Evaluate

4(x - 5)(x + 8) = 0

So, we have

x = 5 and x = -8

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Answer:

b= 23.4,. γ = 70°, c= 28.9

Step-by-step explanation:

To solve the triangle with given α = 65°, β = 45°, and a = 30, we can use the law of sines:

b/sin(β) = a/sin(α)

b/sin(45°) = 30/sin(65°)

b ≈ 23.4

Then, to find angle γ, we can use the fact that the sum of angles in a triangle is 180°:

γ = 180° - α - β

γ ≈ 70°

To find side c, we can again use the law of sines:

c/sin(γ) = a/sin(α)

c/sin(70°) = 30/sin(65°)

c ≈ 28.9

Therefore, the solution is b = 23.4, γ = 70°, and c = 28.9.

Note that there is no other possible solution, as the given angles and side lengths do not allow for multiple triangles to be formed.

Answer: There is no box and whisker plot attached

Step-by-step explanation:

Answer:

31.2 m^2

Step-by-step explanation:

6m x 5.2m

The sequence of transformations that can be performed to show that the circles are similar is given as follows:

c) A translation of r units right, and then a dilation, centered at the origin, with a scale factor of 4.

Examples of transformations are given as follows:

The radius of each circle is given as follows:

Hence the dilation had a scale factor of 4.

Circle B has center at the origin, while Circle A has center a r, hence there was a translation of r units right.

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The function that has no horizontal asymptote is B. f(x)=x - 1/3x

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

The list of options

In option (b), we have

f(x)=x - 1/3x

This function is a linear function that evaluates to

f(x) = 2/3x

As a general rule

Linear functions do not have horizontal asymptote

HEnce, the function is (b)

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The statement is false, as the PEMDAS order must be respected, that is, parenthesis operations are done first, then exponents, then multiplication/division and finally addition/subtraction.

The precedence of operations is defined by the PEMDAS acronym, with a highest to lowest order of precedence, as follows:

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Answer:

The answer is (x⁴+y⁴)

Step-by-step explanation:

(x⁵+y⁵)/(x+y)

(x⁵‐¹+y⁵‐¹)

(x⁴+y⁴)

The table of values can be completed using the following f(x) values 6, 1, 1/6, 1/36 and 1/216

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

f(x) = (1/6)ˣ

On the table of values, we have

x = -1, 0 , 1, 2 and 3

Substitute the known values in the above equation, so, we have the following representation

f(-1) = (1/6)⁻¹ = 6

f(0) = (1/6)⁰ = 1

f(1) = (1/6)¹ = 1/6

f(2) = (1/6)² = 1/36

f(3) = (1/6)³ = 1/216

The f(x) values can be used to complete the table of values

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Answer:

60

Step-by-step explanation:

it because you add them all up

Answer: 4th option

Step-by-step explanation:

divide this shape in two parts in which one will be a rectangle and the other will be a square and seperately find out their areas and add them