A rectangular yard measuring
30
by
35ft
is bordered (and surrounded) by a fence. Inside, a walk that is
3ft
wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.

Answer:

1.  sin∠EDA is equal to sin∠EBC

2.  sin∠CEB is not equal to sin∠EBC

3.  cos∠BEC is equal to sin∠EBC

4.  cos∠ADE is not equal to sin∠EBC

5.  sin(90 - m∠EBC) is not equal to sin∠EBC

6.  cos(90 - m∠EDA) is equal to sin∠EBC

Step-by-step explanation:

From inspection of the given diagram, ∠EAD = ∠ECB = 90°.

According to the vertical angles theorem, ∠BEC = ∠DEA.

According to AA similarity theorem, ΔADE ~ ΔCBE

Therefore, ∠EDA = ∠EBC.

This means that:

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Since  cos∠BEC = CE/BE  and  sin∠EBC = CE/BE  then:

As  ∠BEC ≠ ∠ADE  then:

As  sin(90° - x) = cos(x)  then  sin(90 - m∠EBC) = cos∠EBC.

As  cos∠EBC ≠ sin∠EBC  then:

As  cos(90° - x) = sin(x)  then  cos(90 - m∠EDA) = sin∠EDA.

As  sin∠EDA = sin∠EBC  then  cos(90 - m∠EDA) = sin∠EBC.

Hence:

Therefore , the solution of the given problem of expression comes out to be 10⁸ One hundred million.

In arithmetic, addition, algebra, and division are necessary. They result in the following when combined: An equation, some statistics, and a mathematical function Values, parameters, and arithmetic processes like additions, subtractions, matrix multiplication, and divisions can all be found in a declaration of fact. Different phrases and terms can be compared and evaluated.

Here,

Given :

Expression : 100000000

To convert into short expression

So,

=> 10⁸

Thus ,One hundred million.

Therefore , the solution of the given problem of expression comes out to be 10⁸ One hundred million.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

Hopefully you pass but without seeing the boxes i cant see! but the answer should be D or E

Answer: The constants in the expression are -3 and 2.

In the expression:

2 y

x−3+²7 - 12/2

X-3+

The term -3 is a constant and does not change its value regardless of the values of any variables. The term 2/2 can also be simplified to 1, which is another constant. Hence, the constants in the expression are -3 and 2.

Step-by-step explanation:

The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines. The hotline is staffed for 16 hours a day.

To calculate the average number of calls in different time intervals and the probability of different events related to these calls.

Part 1:

a. 60-minute interval average number of calls: 400/16 = 25 calls

30-minute interval average number of calls: 25/2 = 12.5 calls

15-minute interval average number of calls: 12.5/2 = 6.25 calls

Part 2:

b. To find the probability of exactly 6 calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of exactly 6 calls in a 15-minute interval is:

P(6 calls) = (e^-6.25)*(6.25^6)/6! = 0.0686

c. To find the probability of no calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of no calls in a 15-minute interval is:

P(0 calls) = e^-6.25 = 0.0047

d. To find the probability of at least two calls in a 15-minute interval, we can use the cumulative distribution function of the Poisson distribution. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of at least two calls in a 15-minute interval is:

P(X >= 2) = 1 - P(0 calls) - P(1 call) = 1 - 0.0047 - (e^-6.25)*(6.25^1)/1! = 0.9906

Thus, the average number of calls in a 60-minute interval is 25, in a 30-minute interval is 12.5, and in a 15-minute interval is 6.25. The probability of exactly 6 calls in a 15-minute interval is 0.0686, the probability of no calls in a 15-minute interval is 0.0047, and the probability of at least two calls in a 15-minute interval is 0.9906.

Learn more about Probability here brainly.com/question/11234923

#SPJ4

Answer:

frequency

Step-by-step explanation:

The correct statement representing the function f(x) = 8x³ is given as follows:

The function is odd because f(-x) = -f(x).

To classify a function as even or odd, we must observe the relation between f(x) and f(-x), as follows:

For any ax³ function, we have that f(-x) = -f(x), hence the function is odd and the fourth statement is correct.

More can be learned about functions at https://brainly.com/question/24808124

#SPJ1

Answer:

Step-by-step explanation:

Answer:

h - 3

See explanation below

Step-by-step explanation:

This is not too difficult

We have (- 2h + 1) + (3h - 4) and we are asked to simplify

Expand the brackets:
(- 2h + 1) = - 2h + 1

(3h - 4) = 3h - 4

Add the two:
(- 2h + 1) + (3h - 4)  = - 2h + 1 + 3h - 4

Group like terms

- 2h + 3h + 1 - 4

-2h + 3h = h

+1 - 4 = -3

- 2h + 1 + 3h - 4 = h - 3

and therefore

(- 2h + 1) + (3h - 4)  = h - 3

The total length of cable needed is given as follows:

358.875 inches.

The total length of cable needed is obtained applying the proportions in the context of this problem.

The separate lengths are given as follows:

Then the total length is obtained adding these lengths as follows:

7 x 6.5 + 4 x 34.75 + 9 x 19.375 = 358.875 inches.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

  see attached

Step-by-step explanation:

You want the boxes of the pyramid shown filled with mixed numbers such that each box is the sum of the two numbers below it.

As the example shows, each box is filled with the difference between the box above and the one adjacent. Work must necessarily proceed from the top down.

As you know, the difference of fractions can be computed as ...

  [tex]\dfrac{a}{b}-\dfrac{c}{d}=\dfrac{ad-bc}{bd}[/tex]

Of course the number 1 can be written in terms of denominator d as ...

  1 = d/d

This can be used to adjust the integer and fractional parts so both are positive.

We will use subscripts rc to indicate the row and column of a box, counting rows from the top down.

  [tex]X_{22}=12\dfrac{3}{4}-8\dfrac{2}{3}=(12-8)+\left(\dfrac{3}{4}-\dfrac{2}{3}\right)=4\dfrac{9-8}{12}=\boxed{4\dfrac{1}{12}}\\\\\\X_{31}=8\dfrac{2}{3}-2\dfrac{4}{5}=(8-2)+\left(\dfrac{2}{3}-\dfrac{4}{5}\right)=6\dfrac{10-12}{15}=\boxed{5\dfrac{13}{15}}\\\\\\X_{33}=4\dfrac{1}{12}-2\dfrac{4}{5}=(4-2)+\left(\dfrac{1}{12}-\dfrac{4}{5}\right)=2\dfrac{5-48}{60}=\boxed{1\dfrac{17}{60}}[/tex]

  [tex]X_{41}=5\dfrac{13}{15}-1\dfrac{5}{9}=(5-1)+\left(\dfrac{13}{15}-\dfrac{5}{9}\right)=4\dfrac{39-25}{45}=\boxed{4\dfrac{14}{45}}\\\\\\X_{43}=2\dfrac{4}{5}-1\dfrac{5}{9}=(2-1)+\left(\dfrac{4}{5}-\dfrac{5}{9}\right)=1\dfrac{36-25}{45}=\boxed{1\dfrac{11}{45}}\\\\\\X_{44}=1\dfrac{17}{60}-1\dfrac{11}{45}=(1-1)+\left(\dfrac{17}{60}-\dfrac{11}{45}\right)=\dfrac{51-44}{180}=\boxed{\dfrac{7}{180}}[/tex]

__

Additional comment

In a couple of places the denominators have a common factor.

For example, 13/15 and 5/9 have denominators that have a common factor of 3: 15=3·5 and 9=3·3. When we did the cross multiplication to find the difference, we divided the cross products by that common factor so the resulting fraction would be in lowest terms.

That is, we used 13·9/3 = 39 and 15·5/3 = 25 for the numerator values, and 15·9/3 = 45 for the denominator value.

You will also recognize that 6+(-2/15) became 5+13/15 by using 6 = 5+15/15.

Many calculators and spreadsheets can perform arithmetic on mixed numbers and give a mixed number result. (That is how we checked our work.)

All possible values of r for which this infinite geometric series is defined is the interval (-1,1).

The infinite geometric series is given by:

[tex]\[2 6r 18r^2 54r^3 \dotsb\][/tex]

This is a geometric series, so it is defined when the absolute value of the common ratio (r) is less than 1. The common ratio of this series is r, so the series converges when |r| < 1. Mathematically, this can be expressed as follows:

|r| < 1

-1 < r < 1

Therefore, all possible values of r for which this infinite geometric series is defined is the interval (-1,1).

Learn more about geometric series here:

https://brainly.com/question/4617980

#SPJ4

The inverse of the function is [tex]g^{-1} (x)= 3x + 12[/tex]

when plotted on the same set of axes, exhibit symmetry. Keep in mind that (3, 2) is a point on its inverse and that (2, 3) is a point on f. In other words, all you have to do to graph the opposite is change the coordinates of each ordered pair.

If the picture with regard to the line y = x is the same or f (x) = y is solved, we get the same function x = f 1 (y) = f (y), then the inverse function can be the same as the original function.

Given the function is g(x) = [tex]\frac{1}{3}x - 4[/tex]

⇒ let [tex]y = \frac{1}{3}x - 4[/tex]'

Re-arranging the equation -

⇒ [tex]y + 4 = \frac{1x}{3}[/tex]

⇒ [tex]x = 3y + 12[/tex]

⇒ [tex]g^{-1} (x)= 3x + 12[/tex]

To know more about function visit:-

brainly.com/question/12431044

#SPJ1

If each calculation stays the same, at 0.0000000009 seconds every calculation, you can use this equation:

Therefore, for the computer to perform 41,000,000,000,000 calculations with each calculation taking 0.0000000009 seconds, it will take the computer 36900 seconds, or 10 hours, 8 minutes and 20 seconds to complete.

The coordinates of the other endpoint, Q is (5, -8).

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.

The formula to find the midpoint of line segment is (x, y) = [(x₁+x₂)/2, (y₁+y₂)/2].

Given that, the midpoint of PQ is M =(1,-5). One endpoint is P= (-3, -2).

Let the coordinates of the other endpoint, Q be (a, b).

Here, (1, -5) = [(-3+a)/2, (-2+b)/2]

1= (-3+a)/2

2=-3+a

a=5

-5=(-2+b)/2

-10=-2+b

b=-8

Therefore, the coordinates of the other endpoint, Q is (5, -8).

To learn more about the formula of midpoint visit:

https://brainly.com/question/4728902.

#SPJ1

The number of different ways that the letters of "recommend" can be arranged is 90720.

What is arrangement?

Generally speaking, an arrangement of objects is just a collection of them. A combination (order is ignored) or permutation is used to determine the number of "arrangements" of the components (order is significant). An arrangement is a group of hyperplanes that divides a space into cells.

If there are n different objects in the system then the number of different ways of arrangement of n objects is n!

If the repetition of the objects are allowed in the system the number of different ways of arrangement is -

n! / (no. of repetition of object 1)! .... (no. of repetition of object r)!

Total number of letters in the word "recommend is 9.

The number of different ways of arangement of the 9 letters is 91

The repetition of letter "e" is 2 and repetition of letter "m" is 2.

The number of different ways that the letters of "recommend" can be arranged is -

9! / 2! × 2!

(9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (2 × 1) × (2 × 1)

(9 × 8 × 7 × 6 × 5 × 3 × 2 × 1)

90720

Therefore, the number of different ways is 90720.

To learn more about arrangement from the given link

https://brainly.com/question/15217393

#SPJ4

Answer: Sure! To simplify the expression -3y + 4 - 2 + 6y, we'll follow these steps:

Start by combining like terms:

-3y + 6y = 3y

Next, add the constant terms:

3y + 4 - 2 = 3y + 2

Finally, simplify the expression by substituting the values:

3y + 2 = 3y + 2

So the simplified expression is 3y + 2.

Step-by-step explanation:

Answer: One way to check Abby's solution using a number line and counting on is as follows:

Start at 5 2/5 on the number line.

Subtract 2 1/2 by counting left 2 and a half units.

Check if the result is 2 9/10.

If the result of the subtraction is 2 9/10, then Abby's solution is correct. If not, then the solution is incorrect and needs to be re-evaluated.

Using this method, we can visually see the subtraction and verify the result.

Step-by-step explanation:

Solving a system of equations we will see that the two integers are 3 and 7.

Let's define the two positive integers as x and y.

With the given information, we can write a system of equations to get:

x = 4y - 5

x*y = 21

Now we can replace the first equation intothe second one to get:

(4y - 5)*y = 21

4y^2 - 5y = 21

4y^2 - 5y - 21 = 0

Now we have a little quadratic equation, we can use the quadratic formula to solve this.

[tex]y = \frac{5 \pm \sqrt{(5)^2 - 4*4*-21} }{2*4} \\\\y = \frac{5 \pm 19 }{8}[/tex]

We know that the integers are positive, so we need to take the positive solution:

y = (5 + 19)/8 = 24/8 = 3

And the other number is:

x = 4*3 - 5

x = 12 - 5 = 7

These are the two integers.

Learn more about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

Answer:

Step-by-step explanation:

haha I won’t delete it nerdyyy

The amount of carbon present after 2000 years is 7.85 grams.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 5 is an equation.

We have,

The equation for half-life.

y = m [tex](1/2)^{t/f}[/tex] _____(1)

Where y = quantity remaining

m = initial quantity

t = time

f = half-life of the substance

Now,

f = 5730 years

m = 10 grams

t = 2000 years

Substituting in (1)

y = m [tex](1/2)^{t/f}[/tex] _____(1)

y = 10 [tex](1/2)^{2000/5730}[/tex]

y = 10 x [tex](1/2)^{0.35}[/tex]

y = 10 x 0.785

y = 7.85

Thus,

7.85 grams of carbon will be present after 2000 years.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

The synthetic division process involves dividing the polynomial by a linear factor in a compact manner. In this case, we are dividing the polynomial 4x^4 - 9x^3 + 14x^2 - 12x - 1 by x - 1.

To perform synthetic division, we first write the coefficients of the polynomial in a row and add a zero at the end. Then, we divide the first coefficient (4) by the leading coefficient of the divisor (x - 1), and write the result (4) above the next coefficient (-9). Next, we multiply the divisor (x - 1) by the first quotient (4) and subtract the result from the row. The new row of coefficients is the result of this subtraction. Repeat this process until all coefficients have been processed or a remainder is left.

Here is the process:

4 -9  14 -12 -1 | 0

+------------------

-4  4  14 -12 -1

-4  4  14 -12 -1

-4 -4  10  12  1

So the result of the division is 4x³ + 10x² + 12x + 1, with a remainder of -4.

Thus, the final answer is 4x³ + 10x² + 12x + 1 + (-4) = 4x³ + 10x² + 12x - 3.

Learn more about synthetic division here:

https://brainly.com/question/29809954

Answer: Let's call the increase from 15 to 20 as "z".

So, 20 is (z / 15) * 100% greater than 15, or x = (z / 15) * 100.

And, 15 is (z / 20) * 100% less than 20, or y = (z / 20) * 100.

Since z is the same in both equations, we can set the two equations equal to each other:

x = (z / 15) * 100

y = (z / 20) * 100

Step-by-step explanation:

Step-by-step explanation:

total ratio= 2+3

5

Grace= 3/5 × 120

Grace= 72 stamps

Answer: grace has 72 stamps

Step-by-step explanation:

120/5 is 24, 24 x 3 is 72

Solving for x gives the axis of symmetry of quadratic equation, where the quadratic equation is given as: y = ax² + bx + c.

How is this determined?

The vertical line that passes through a parabola's vertex is the axis of symmetry, making the parabola's left and right sides symmetric. This line divides the graph of a quadratic equation into two mirror representations in order to make things simpler.

The line on the graph that separates the graph into two symmetrical sides and runs through the vertex of the parabola is known as the axis of symmetry of the parabola.

It is written as:

x = -b /2a.

Hence, for x = -b /2a. Solving for x gives the axis of symmetry of quadratic equation, where the quadratic equation is given as: y = ax² + bx + c.

Learn more about axis of symmetry here:

https://brainly.com/question/22495480

#SPJ4

For the right prism having volume of 360 cm², the total surface area is 408 cm².

What is surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

The right prism has measurements (6 , 8, 10).

The perpendicular is 6 cm, the base is 8 cm.

The area of base is -

Area = 1/2 × base × height

Substitute the values into the equation -

Area = 1/2 × 8 × 6

Area = 24 cm²

The volume of the prism is 360 cm³.

Volume = Area of base × height

Substitute the values into the equation -

360 = 24 × height

height = 260 / 24

height = 15 cm

The lateral surface area of the prism is -

Lateral Surface area = Perimeter of base × height

Substitute the values into the equation -

LSA = (8+6+10) × 15

LSA = 24 × 15

LSA = 360 cm²

The total surface area of the prism is -

Total Surface Area  = Lateral Surface Area + 2(Area of base)

Substitute the values into the equation -

TSA = 360 + 2(24)

TSA = 360 + 48

TSA = 408 cm²

Therefore, the total surface area is 408 cm².

To learn more about surface area from the given link

https://brainly.com/question/20771646

#SPJ1

Find the total surface area of the right prism if it's sides are 6cm , 8cm and 10 cm. The volume of the prism is 360 cm².

If we are to write the following polynomial in descending powers of the variable and with no missing powers 3x^3 -70, it would be 3x^3 - 70 + 0x^2 + 0x + 0

A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.

Hence, it can be seen that descending order is basically when the power of a term decreases for each succeeding term. For example, x3 + x2 + x or 2 x4 + 3 x2 + 7 x are arranged in descending order. Descending order is more commonly used.

The polynomial in descending powers of the variable with no missing powers is:

3x^3 - 70 = 3x^3 - 70 + 0x^2 + 0x^1 + 0x^0

= 3x^3 - 70 + 0x^2 + 0x + 0

Note: The polynomial can also be written as 3x^3 - 70x^0.

Read more about polynomials here:

https://brainly.com/question/24662212

#SPJ1

Answer:

17%

Step-by-step explanation:

area represents the populations

United States has a radius of 4.2 cm and

India has a radius of 8.7 cm.

If 4% of the world's population is in United States,

what percentage of the world's population is in India

US π r² = π*4.2²

India π r² = π*8.7²

so india/US = 4.29

so india = 4.29 *4% = 17%

This formula divides the number of cars in Cell C92 by the average number of people in Cell B92, and calculates the cars per person on day one.

This formula divides the number of cars in Cell C92 by the number of people in Cell B92, and calculates the cars per person on day one. By typing =C92/B92, you can easily calculate the number of cars per person in a single cell. This formula can be used for any data set, and will always give an accurate result. It is an effective way to compare the ratio of cars to people in a given situation, and to compare the results to other data sets. The formula is also simple to use and understand, which makes it a powerful tool for quickly analyzing data. It is a useful tool for making decisions, as it allows you to assess the ratio of cars to people quickly and accurately.

Learn more about average here

https://brainly.com/question/24057012

#SPJ4

The most accurate statement is "Speed is decreasing." This means that the object is moving at a decreasing velocity over the 10 seconds.

What is the Speed is constant?

When we say that the speed of an object is constant, it means that the magnitude of the velocity of the object remains unchanged over time. In other words, the object is moving at a steady pace and its speed does not vary.

The statement "Speed is not constant; Object is at rest" is not accurate.

From the position-time graph, it is clear that the object is moving in one direction and its position is changing with time. Hence, the object is not at rest.

Furthermore, the slope of the position-time graph gives us the velocity of the object, and from the graph, it appears that the slope is changing with time, which means that the speed is not constant. Hence, the statement that "Speed is constant" is also not accurate.

Hence, the most accurate statement is "Speed is decreasing." This means that the object is moving at a decreasing velocity over the 10 seconds.

To learn more about Speed is constant, Visit

https://brainly.com/question/28793272

#SPJ4

Complete question: