An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 290 feet of If
antique picket fencing are to be used to enclose the garden, find the dimensions of the garden.
What is the length of the garden?
The length of the garden is
What is the width of the garden?
The width of the garden is

The first equation is :

5(x-3)=20

5x-15=20

The property is from multiplication, it is called distributive property says that "multiply the outside number with each term inside the parenthesis.

Second equation is

5(x-3)=20

x-3=4

It is an equation property when a number multiply it change to divide the other side of the equality.

Let's first find the number of hours worked per day:

(11:30 - 8:00) + (16:45 - 12:15) = 3:30 + 4:30 = 8 hours

(11:00 - 7:00) + (17:45 - 12:15) = 4 + 5:30 = 9:30 = 9½ = 9.5 hours

(11:15 - 7:45) + (15:40 - 12:10) = 3:30 + 4:30 = 8 hours

(11:50 - 8:20) + (16:30 - 12:15) = 3:30 + 4:15 = 7:45 = 7¾ = 7.75 hours

(11:35 - 6:05) + (16:00 - 12:30) = 5:30 + 4:30 = 10 hours

The total hours worked are:

8 + 9.5 + 8 + 7.75 + 10 = 43.25 hours

Given the rate per hour = $11.25

Shannon's total pay for the week is:

Therefore Shannon's total pay for the week is $486.56

ANSWER:

$486.56

Answer:

24 in long by 12 in wide.

Step-by-step explanation:

l=2w

288=(2w)×w

288=2w^2

144=w^2

12=w

use w=12 to solve for l

l=2(12)

l=24

Remember that

the sum of the exterior angles in any polygon is equal to 360 degrees

so

6.923x=360 degrees

where

x is the number of sides

solve for x

x=360/6.923

The amount paralegal earned from the job is 1860 dollars.

The amount allocated for savings is 1116 dollars.

Paralegal bills the law firm for 15.5 hours of work at a rate of $120 per hour.

Therefore, the law firm have to pay paralegal 120 dollars for every hour worked.

Therefore,

the amount earned by paralegal = 15.5 × 120

the amount earned by paralegal = 1860 dollars

Paralegal splits her earnings between utilities and savings in a ratio of 2 ∶ 3.

Therefore, let's find the amount of money allocated for her savings.

amount allocated for savings = 3 / 5 × 1860

amount allocated for savings = 5580 / 5

Therefore,

amount allocated for savings = 1116 dollars

learn more on rate, saving and earnings here: https://brainly.com/question/9060950

#SPJ1

3900000×18% = 702000

702000÷2500 = 280.8 per share dividend

450×280.8 = 126360

Answer:

the probability that the price will increase is 0.3592 or 35.92%

Step-by-step explanation:

Given the data in the question;

risk free interest rate = 1.98 percent

expectations are ; either increase by 18 percent or decrease by 7 percent over the next 6 months

hence

increment by 18 percent; d = 1 + 18% = 1 + 0.18 = 1.18

reduction by 7 percent; u = 1 - 7% = 1 - 0.07 = 0.93

so the probability that the price of the oil will increase will is;

P = (( 1 + rate ) - u ) / ( d - u )

we substitute

P = (( 1 + 1.98% ) -  0.93 ) / ( 1.18 - 0.93 )

P = (( 1 + 0.0198 ) - 0.93 ) / 0.25

P = ( 1.0198 - 0.93 ) / 0.25

P = 0.0898 / 0.25

P = 0.3592

P = ( 0.3592 × 100 )%

P = 35.92%

Therefore, the probability that the price will increase is 0.3592 or 35.92%

By solving a quadratic equation, we will see that the width is 1.4 inches.

For a rectangle of width W and length L, the surface area is:

A = W*L

In this case, the length will be the length of the picture plus twice the width of the frame, and same for the width, then if we define x as the width of the frame we have:

L = 8in + 2x

W = 6in + 2x

Then the area equation is:

A = (8in + 2x)*(6in + 2x)

Here we know that the area is 95.04 square inches, then we can write:

95.04 in² = (8in + 2x)*(6in + 2x)

Now we need to solve this for x.

95.04 in² = 48 in² + 4x² + (28in)*x

This is a quadratic equation:

48 in² + 4x² + (28in)*x - 95.04 in² = 0

4x² + (28in)*x - 47.04 in² = 0

The solutions are given by Bhaskara's formula:

\(x = \frac{-28 \pm \sqrt{(28)^2 - 4*4*(-47.04)} }{2*4} \\\\x = \frac{-28 \pm 39.2 }{8}\)

So there are two solutions, we only care for the positive one, which is:

x = (-28+ 39.2)/8 = 1.4

This means that the width of the frame is 1.4 inches.

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

#SPJ1

The expression that is equivalent to the given value would be = 18-i . That is option C.

An equivalent expression is defined as the type of expression that is similar to a given value when simplified.

The given expression = ( 3 + 4i) ( 2 - 3i)

Expand the given expression by removing the brackets as follows:

= =2(3+4i)−3i(3+4i)

=(6+8i)−(9i−12)

= (6+12)+i(8−9)

=18−i.

Learn more about multiplication equation here:

https://brainly.com/question/28552292

#SPJ1

Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.

Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).

Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.

Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.

The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.

To determine the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\), we need to consider the situation and the constraints given.

The function A(t) represents the area of the rectangular garden as a function of the length of one of its sides, which is denoted by t.

We are also told that Marama plans to fence the garden with 28 feet of wired fencing.

Now, let's break down the problem and find the appropriate values for the domain.

We know that the perimeter of a rectangle is the sum of all its sides. In this case, since we have a rectangular garden, the perimeter can be represented as:

\(Perimeter = 2t + 2w\),

where t is the length of one side (the width) and w is the length of the other side (the width).

The problem states that Marama plans to use 28 feet of wired fencing. Therefore, the perimeter of the garden must equal 28 feet:

\(2t + 2w = 28\).

Simplifying this equation, we have:

\(t + w = 14\).

We can express w in terms of t as \(w = 14 - t\).

The area of a rectangle is given by the product of its length and width:

\(Area = t \times w\).

Substituting the expression for w from step 2, we have:

\(A(t) = t \times (14 - t)\).

Simplifying further:

\(A(t) = 14t - t^2\).

To determine the appropriate values of the domain, we need to consider the context of the problem. Since we are dealing with a physical garden, both the length and width must be positive numbers. Additionally, the values of t must be feasible given the constraints of the perimeter.

We know that \(t + w = 14\), so \(t + (14 - t) = 14\), which simplifies to \(14 = 14\).

This shows that the value of t can range from 0 to 14, inclusive.

Therefore, the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\) are \(t \epsilon [0, 14]\).

To illustrate this graphically, we can plot the function \(A(t) = -t^2 + 14t\) and mark the appropriate values of the domain on the x-axis (representing t):

   ^

   |

A(t)|

   |

   |_______________________________

   0              t             14

The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.

For such more questions on domain

https://brainly.com/question/28934802

#SPJ8

The original side length of the square is 6 inches.

Let's say that the original side length is S, then the original area is:

A = S²

If we cut 3 inches of the side length, then the new area is:

a = (S - 3)²

And this is 1/4 of the original area, so we can write the equation:

(S - 3)² = (1/4)*S²

Expanding it we will get:

S² - 6S + 9 = (1/4)*S²

4S² - 24S + 36 = S²

3S² - 24S + 36 = 0

So we have a quadratic equation to solve

Using the quadratic formula we will get:

\(S = \frac{24 \pm \sqrt{(-24)^2 - 4*3*36} }{2*3} \\\\S = \frac{24 \pm 12}{6}\)

The positive answer is the one that makes sense (we could not take 3 inches if we take the other one)

S = (24 + 12)/6 = 6

The original side length is 6 inches.

Learn more about quadratic equations at:

https://brainly.com/question/1214333

#SPJ1

Answer:

Area = 324ft²

Perimeter = 72ft

Step-by-step explanation:

Area of a square = length²

Area of a square = (18ft)² = 324ft²

Perimeter of a square = 4*length

Perimeter of a square = 4ft*18 = 72ft

Answer:

D

Step-by-step explanation:

For each triangle, you are given two sides and the included angle (the one between those 2 sides). That's side-angle-side, so it is S-A-S.

The SAS Rule for Similar Triangles says that for 2 triangles X and Y, if you have the SAS of one and the SAS of the other, then X and Y are similar (same shape and proportions) if

(a) the angle in X is congruent (same) as the angle in Y

(b) the ratio between the two given sides in X is the same as the ratio between the two given sides in Y

For this particular problem, the ratio PR/PQ = 18/21 = 6/7 if you simplify by dividing both top and bottom by 3.

So we are looking for another triangle where we have the same ratio. (Put the smaller number on top, in the fraction.)

Answer A:  12/15 simplifies to 4/5, wrong answer

Answer B:  9/12 simplifies to 3/4, wrong answer

Answer C:  6/10 simplifies to 3/5, wrong answer

Answer D: 15/17.5 looks harder, because there is a decimal in it. But we know 17.5 is just 17 and a half, so I would first multiply top and bottom by 2

We get 30/35. That looks a lot better. Now it is easier to see we can divide both top and bottom by 5.

We get 6/7! That is the correct answer, so D is the triangle similar to PQR.

The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.

A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:

Standard Error (SE) = σ / sqrt(n),

where σ is the standard deviation and n is the sample size.

In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.

Plugging in these values into the formula, we have:

SE = 3.25 / sqrt(25).

Calculating the square root of 25, we get:

SE = 3.25 / 5.

Performing the division, we find:

SE ≈ 0.65.

For more such questions on standard error

https://brainly.com/question/14467769

#SPJ8

In general, there were more people per table on Tuesday with 8 number of people per table.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

By critically observing the given dot plots which is used to illustrate the numbers of people per table at a bingo hall on two nights, we can reasonably infer and logically deduce that there were more people per table on Tuesday than on Wednesday.

In conclusion, there were 8 number of people per table on Tuesday while there were 5 number of people per table on Wednesday.

Read more on dot plots here: brainly.com/question/18466974

#SPJ1

Answer:

organelle

Explanation: Mitochondria and the cell wall are both examples of organelles since they have their own specific functions (Mitochondria produces the energy and the cell wall protects the cell from things that might be a danger to the cell.

Each "organelle " in a cell has its own specific function.

Mitochondria and the cell wall are both examples of organelles since they have their own specific functions. Mitochondria produces the energy and the cell wall protects the cell from things that might be a danger to the cell.

A Cellular respiration is a component of a metabolic process which splits the glucose sugar molecule to produce energy in the form of ATP.

Since we know that Krebs' cycle, oxidative phosphorylation, and glycolysis are all components of cellular respiration.

The cellular respiration activities take place in the mitochondria of the cell, where the oxygen-rich environment which causes the sugar-like glucose to break down into an energy molecule.

A cell organelle having a membrane is a 'mitochondria'. It is a location for cellular respiration and metabolic activities which produce energy.

Learn more about mitochondria by using this link:

brainly.com/question/10688306

#SPJ6

Answer:A:28.8

Step-by-step explanation:

Answer: 28.8

Step-by-step explanation:

The surface areas of the figures are:

10.To find the surface area of this rectangular prism, find the area of each face and then add them together.

Face 1: The front and back faces both have dimensions of 12 ft by 14 ft, so the area of each is:

12 ft × 14 ft = 168 ft²

Two of these faces, so the total area is:

2 × 168 ft² = 336 ft²

Face 2: The top and bottom faces both have dimensions of 20 ft by 14 ft, so the area of each is:

20 ft × 14 ft = 280 ft²

Two of these faces, so the total area is:

2 × 280 ft² = 560 ft²

Face 3: The left and right faces both have dimensions of 12 ft by 20 ft, so the area of each is:

12 ft × 20 ft = 240 ft²

Two of these faces, so the total area is:

2 × 240 ft² = 480 ft²

Now add up the areas of all the faces:

336 ft² + 560 ft² + 480 ft² = 1,376 ft²

11. To find the surface area of the figure, add the areas of all six faces.

Find the area of the rectangular faces:

The front and back faces both have dimensions of 14 in by 14 in, so each has an area of 14 in x 14 in = 196 in².

The top and bottom faces both have dimensions of 13 in by 8.9 in, so each has an area of 13 in x 8.9 in = 115.7 in².

Find the area of the triangular faces. Use the Pythagorean theorem to find the length of the third side of each triangle:

The two side faces are congruent triangles with legs of 14 in and 13 in.

Using the Pythagorean theorem, find the length of the hypotenuse to be √(14² + 13²) ≈ 19.14 in. The area of each triangle is then 1/2 base x height = 1/2 x 19.14 in x 8.9 in ≈ 85.3 in².

Using the Pythagorean theorem, find the length of the hypotenuse to be √(8.9² + 13²) ≈ 15.8 in. The area of each triangle is then 1/2 base x height = 1/2 x 15.8 in x 14 in ≈ 110.6 in².

Finally, add up the areas of all six faces:

Front and back faces: 2 x 196 in² = 392 in²

Top and bottom faces: 2 x 115.7 in² = 231.4 in²

Side faces: 2 x 85.3 in² = 170.6 in²

End faces: 2 x 110.6 in² = 221.2 in²

The total surface area is the sum of these areas:

392 in² + 231.4 in² + 170.6 in² + 221.2 in² ≈ 1,015.2 in²

Therefore, the answer is B. 1,058.4 in².

Find out more on surface area here: https://brainly.com/question/76387

#SPJ1

The quotient is found to be 4/5. The correct option is (B).

A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0. The number a is called as the numerator and b is the denominator. In order to divide two fractions take the reciprocal of the other fraction and change the sign as multiplication. It can be shown as a/b ÷ c/d = a/b × d/c.

The given expression is -3/5 ÷ (-3/4).

It can be simplified as follows,

Take the reciprocal of the fraction (-3/4) as -4/3.

And, change the sign of division to multiplication to obtain,

-3/5 ÷ (-3/4)

⇒ -3/5 × -4/3 = 4/5

Which the value of the quotient.

Hence, the quotient for the given arithmetic operation is 4/5.

To know more about fraction click on,

https://brainly.com/question/10354322

#SPJ1

The mean from a Histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

Out of the given options, the display of data for which it is not possible to find the mean is the stem-and-leaf plot.

A histogram displays data in the form of bars, where the height of each bar represents the frequency of data within a specific range. From a histogram, it is possible to calculate the mean by summing up the products of each value with its corresponding frequency and dividing it by the total number of data points.

A table presents data in a structured format, typically with rows and columns, allowing for easy calculation of the mean. By adding up all the values and dividing by the total number of values, the mean can be obtained from a table.

A stem-and-leaf plot organizes data by splitting each value into a stem (the first digit or digits) and a leaf (the last digit). While a stem-and-leaf plot provides a visual representation of the data, it does not directly provide the frequency or count of each value. Hence, it is not possible to determine the mean directly from a stem-and-leaf plot without additional information.

A dot plot represents data using dots along a number line, with each dot representing an occurrence of a value. Similar to a histogram and table, a dot plot allows for the calculation of the mean by summing up the values and dividing by the total number of data points.

In summary, while it is possible to find the mean from a histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

For more questions on Histogram.

https://brainly.com/question/25983327

#SPJ8

Answer:

\(y = \frac{1}{2} x + 7\)

Step-by-step explanation:

Slope-intercept form is written as y = mx + b. So, the y must be isolated. Therefore, to answer this question, isolate the y in 2y - x = 14.

1) Move the x to the other side.

\(2y - x = 14\\2y =x+14\)

2) Divide all terms by 2 to finally isolate x.

\(2y = x + 14\\\frac{2}{2}y= \frac{x}{2} + \frac{14}{2} \\y = \frac{1}{2} x + 7\)

3) Therefore, \(y = \frac{1}{2} x + 7\) must be the answer.

Answer:

4)120

5)13

6)70

7)115

Step-by-step explanation:

Answer: 4. 120 degrees 5. 13 degrees 6. 70 degrees 7. 115 degrees

The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:

\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)

where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).

Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:

\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)

Simplifying each term, we get:

\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)

Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).

Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.

For more question on function visit:

https://brainly.com/question/11624077

#SPJ8

Note the complete question is

The square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given:

Let us consider one length i.e. 16 to be Perpendicular and other length i.e. 19 to be Width.

According to the Pythagoras theorem:

\(\text{Hypotenuse}^2=\text{Perpendicular}^2+\text{Base}^2\)

Let us consider the value of Hypotenuse to be x.

\(x^2=19^2+16^2\)

\(x^2=361+256\)

\(x^2=617\)

\(x=\sqrt{617}\)

\(x=24.84\)

Thus, from the value of x we can infer that the given lengths are not forming Pythagorean triple.

Learn more:

brainly.com/question/343682

Answer:

There is a answer to the question

A) For car 1, a linear function, for car 2, an exponential function can be used to describe its value.  B) Functions are Car 1: f(x) = 18500 - 1104x and Car 2: f(x) = 17500 * (1 - 0.05)^x.  C) The value of Car 1 after 9 years is $8564 and that of car 2 is $11029.36.

Part A:

The value of Car 1 decreases by a fixed amount each year, so a linear function can be used to describe its value. The value of Car 2 decreases by a percentage each year, so an exponential function can be used to describe its value.

Part B:

The following functions can be used to describe the value of each car:

Car 1: f(x) = 18500 - 1104x

Car 2: f(x) = 17500 * (1 - 0.05)^x

Part C:

The value of Car 1 after 9 years is f(9) = 18500 - 1104 * 9 = $8564.

The value of Car 2 after 9 years is f(9) = 17500 * (1 - 0.05)^9 = $11029.36.

There is a significant difference in the value of the two cars after 9 years. Car 2 will have a value of $11029.36, while Car 1 will have a value of $8564. This difference is due to the fact that Car 2 depreciates at a slower rate than Car 1.

Here is a table showing the value of each car after 9 years:

Car Value after 9 years

Car 1 $8564

Car 2 $11029.36

To learn more about function here:

https://brainly.com/question/30721594

#SPJ2

Answer:do homework

Step-by-step explanation: