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The dimensions of the rectangular garden are 20 feet and 29 feet respectively.

It is vital to note that the formula for the area of a rectangle is expressed as;

Area = lw

Where;

From the information given, we have that;

Area =  580ft²

Length = 9 + width

L = 9 + w

Substitute the values into the formula, we have;

580 = (9 +w)(w)

expand the bracket

580 = 9w + w²

Make into quadratic equation

w² + 9w - 580 = 0

Factorize the equation

w² + 29w - 20w - 580 = 0

Factor the common terms

w( w + 29) - 20(w + 29) = 0

Then,

w + 29 = 0

w = -29

and w - 20 = 20 feet

We have the expression of length as l = 9 + w

Length, l = 9 + 20

Length, l = 29 feet

Thus, the values are 20 feet and 29 feet

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Answer:

Step-by-step explanation:

The most appropriate choice for perimeter of rectangle will be given by-

Mr Smith must buy 61 m of fencing.

What is perimeter of rectangle?

It is equal to the total distance of the boundary of the rectangle.

If length of rectangle is l m and breadth of rectangle is b m, perimeter of rectangle is 2 x (l + b) [tex]m^2[/tex]

Here,

Length of yard = 61 ft

Breadth of yard = 39 ft

Perimeter of yard = 2 x (61 + 39)

                             = 2 x 100

                             = 200 ft

1 ft = 0.305 m

200 ft = 0.305 x 200 m

          = 61 m

Mr Smith must buy 61 m of fencing.

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To convert the number given in base 7 to a bse 10 number we follow the procedure shown, that is, we need to multiply each number by the appropiate power of seven (given by their position) and then add them, then we have that:

Therefore:

6/18=×/36

solve for x

x=(6/18)36

x=6(36/18)

x=6(2)

x=12

As given by the question

There are given that the expression

Now,

Multiply by 5 on both side of the equation

So,

Hence, the value of a is 110.

If Nolan is dividing 2 by 11 and he continues the process, the the result will be repeating quotient 0.181818...

Here Nolan is dividing 2 by 11.

Division is one of  the basic arithmetic operation. Division is operation of splitting a specific number into equal parts

The quotient is the result from dividing a number from another number.

Divide the given terms and the result will be

2/11 = 0.1818...

The result will be a repeating quotient . Here the pattern is repeating endlessly

Hence, if Nolan is dividing 2 by 11 and he continues the process, the the result will be repeating quotient 0.181818...

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Expected value:

For the given scenario:

Answer:

2:3

Step-by-step explanation:

The width of the rectangle DOGS is 119cm

To solve this, since is a ratio problem, we know that the two ratios must add to the total. This is, for a ratio of 5:7, 5 + 7 = 12 is the total "divisions" for the ratio.

This means that if 12 of 12 parts add to the perimeter (408cm):

12/12 represents the perimeter 408cm.

The, we can divide the perimeter by 12 and get:

Since the width is 7/12 of the perimeter:

But, we are taking the perimeter of a rectangle, which is twice the width plus twice the length, thus we need to divide this number by 2:

And we get the final answer of 119cm

Answer:

4826.166666km

Step-by-step explanation:

d=distance

  [tex]\frac{1259km}{1h} =\frac{d}{23/6h}[/tex]

= [tex]\frac{1259km}{1h}= \frac{6d}{23}[/tex]

= [tex]1259=\frac{6d}{23}[/tex]

= [tex]1259*23=6d[/tex]

= [tex]28,957=6d[/tex]

= [tex]\frac{28,957}{6}=d[/tex] ≈4826.166666

Volume of solid of revolution formed by rotating about the x axis the region between the graph of f(x)= x /2 and the x axis between x=2 and x=5 is 117π /12unit³.

As given,

Volume of solid of revolution formed by rotating about the x-axis region between the graph of f(x)= x /2:

Volume = π∫[f(x)]²dx  

⇒Volume =π∫(x/2)²dx

⇒Volume =(π/4)∫x²dx

⇒Volume =(π/4) (x³/3)

                 =(π/12)(x³)

x axis between x=2 and x=5

Volume =(π/12)(125-8)

             =117π/12 unit³

Therefore, volume of solid of revolution formed by rotating about the x axis the region between the graph of f(x)= x /2 and the x axis between x=2 and x=5 is 117π /12unit³.

The complete question is:

Find the volume of the solid of revolution formed by rotating about the x axis the region between the graph of

f(x)= x /2

and the x axis between x=2 and x=5.

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The probability that at least 75 students arrive at the library is 0.1440.

From the information, the undergraduate library at State U tends to have 33.4 students enter every hour during normal operation.

The expected number of students for the two hours will be:

= 2 × 33.4

= 66.8

The probability that at least 75 students arrive at the library will be:

P(x >= 75) = 1 - P(x <= 74)

This will be looked at in the distribution table

= 1 - 0.8560

= 1.440

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The factorised form of the algebraic expression 16cd − 56c²d as given in the task content is; 8cd (2 - 7c).

It follows from the task content that the factorised form of the expression; 16cd − 56c²d as given is to be determined.

Since the given expression is;

16cd − 56c²d

First, each of the terms can be factored as follows;

16cd = 2 × 2 × 2 × 2 × c × d

56c²d = 2 × 2 × 2 × 2 × 7 × c × c × d

Therefore, since the factors which are common to both terms as follows; 2 × 2 × 2 × c × d = 8cd.

Therefore the factorised form of the expression is;

8cd (2 - 7c).

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(a) 291/2020

Divide the total for the 10-14 year column by the total.

(b) 77/465

There are 465 people from the east, 77 of which were loyal for 10 to 14 years

(c) 437/1010

There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.

(d) 145/376

376 people are from the West, (45+100)=145 of which are at least 10.

(e) 32/157

157 people were loyal for less than a year, 32 of which were from the East.

(f) 53/157

157 people were loyal for less than a year, 53 of which were from the South.

(g) 433/465

465-32=433 people were loyal for at least 1 year out of the 465 people from the East.

(h) 335/376

376-41=355 people were loyal for at least 1 year out of the 376 people from the West.

The simplified form for (3x² + 2y² - 5x + y) + (2x² - 2xy - 2y² -5x + 3y) is (5x² + 0y² - 10x + 4y - 2xy).

At least one squared term must be present because a quadratic is a second-degree polynomial equation. It is also known as quadratic equations. The answers to the issue are the values of the x that satisfy the quadratic equation. These solutions are called the roots or zeros of the quadratic equations. The solutions to the given equation are any polynomial's roots. A polynomial equation with a maximum degree of two is known as a quadratic equation, or simply quadratics.

The equation can be made simpler by adding up all of the coefficients for the specified correspondent term through constructive addition or subtraction of terms, as suggested in the question.

Given, the equation is (3x² + 2y² - 5x + y) + (2x² - 2xy - 2y² -5x + 3y)
Removing brackets and the adding we get,
3x² + 2x² + 2y² - 2y² + (- 5x) + (- 5x) + y + 3y + (- 2xy) = (5x² + 0y² - 10x + 4y - 2xy)

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As we can see in the card, on Monday the worker clocked in at 08:15 and clocked out at 12:15. This means they worked 4 hours.

They then clocked in at 13:00 and clocked out at 17:30. This means they worked for 4 and a half hours.

Since they earn a wage of $14.50/h, they earned:

So that day they earned $123.25

Answer: 1049

Step-by-step explanation:

If An industrial scale is guaranteed by the manufacturer to have a percent error of no more than 1%. Its  possible reading on the scale if you put 500 kilograms of iron ore on it is :495, 505.

Percent error = 1%

Kilogram of iron ore = 500 kilograms

First step is to find the 1% of 500 kilograms

= .01 × 500 kilograms

= 5

Second step is to find the possible reading

Possible reading :

500 - 5

=495

500 + 5

= 505

Therefore we can conclude that  based on the above analysis the possible reading can be between 495 and 505.

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Answer:

6 is the awnswer

Step-by-step explanation:

Answer:

The rate at which the surface area is changing with respect to time when r = 40 cm is 22400π cm²/min

Not sure if you want it in absolute values since the question says use symbolic notation but if so, multiplying by π gives 70371.675 cm²/min

Step-by-step explanation:

[tex]\text {Volume of a sphere of radius r is given by }\\\\ \text {$V = \dfrac{3}{4}\pi r^3$}[/tex]

The surface area of a sphere of radius r is given by:

[tex]\\S = 4\pi r^2\\[/tex]

The rate of change of surface area is given by
[tex]\dfrac{dS}{dt} = \dfrac{d}{dt}\left(4\pi r^2\right)}\\\\\dfrac{dS}{dt} = 4 \pi \dfrac{d}{dt}\left( r^2\right)}\\\\\\\dfrac{d}{dt}(r^2) = 2r\dfrac{dr}{dt}\\\\\\[/tex]

[tex]\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}[/tex]

We are given that [tex]\text{$\dfrac{dr}{dt}$}[/tex] = 70 cm/min and asked to find rate of change of S when r = 40 cm

Substituting these values into the equation for [tex]\dfrac{dS}{dt}[/tex]
[tex]\dfrac{dS}{dt} = 8 \pi \cdot 40 \cdot 70\\\\\\\\\dfrac{dS}{dt} = 22400 \pi \;cm^2/min[/tex]

In absolute values

Answer:

Step-by-step explanation:

x-84/6

Notice that the values for w are multiples of 9, and their respective factor is expressed on the values of z. Therefore, the equation to describe the relationship between w and z is w=9z

Answer:

Step-by-step explanation:

[tex]2\frac{5}{8} =\frac{2 \times 8+5}{8} =\frac{21}{8} \\2\frac{1}{4} =\frac{2 \times 4+1}{4} =\frac{9}{4} \\2\frac{5}{8} / 2\frac{1}{4} \\=\frac{21}{8} /\frac{9}{4} \\=\frac{21}{8} \times \frac{4}{9} \\=\frac{7}{6} \\=1\frac{1}{6}[/tex]

Using transformations, the functions that could represent the one graphed are given as follows:

A transformation is when a function undergoes a change in it's definition. Depending on the type of the transformation, the function can keep the same orientation, same side lengths, and so on.

In the context of this problem, the function kept the same orientation, it just changed it's position, hence the type of transformation that the function underwent was a translation.

The possible translations are given as follows:

The domain of the graphed function is given by:

x ≥ 0.

Which is the same domain as the parent square root function, given as follows:

y = sqrt(x).

From the graph, the function was translated down a units, changing it's range, hence the function has the following format:

y = sqrt(x) - a.

Hence the first two options can be correct, either with a = 1 or with a = 3. The last two options change the range but not the domain, hence they are incorrect.

The image at the end of the answer gives the complete problem.

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Using the formula for the area of a circle calculate the area for both deals.

for the 18-inch pizza

for the two 12-inch pizza

The distance expression of the number of units between points A and B is √[(-2 - 3)^2 + (5 - 5)^2]

From the question, we have the following parameters:

This means that

A = (-2, 5)

B = (3, 5)

The distance between the points is calculated as

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

Where

A = (x1, y1) = (-2, 5)

B = (x2, y2) = (3, 5)

Substitute the known values in the above equation

So, we have

Distance = √[(-2 - 3)^2 + (5 - 5)^2]

The question does not imply that the we simplify the above expression

So, we leave the expression unsimplified

Hence, the expression of the distance between A and B is √[(-2 - 3)^2 + (5 - 5)^2]

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Answer:

C). Or SAS~with 3/2 proportionate sides.

Step-by-step explanation:

You can tell because the similar angle shows which sides should be proportional to the other on the corresponding triangle, and of those sides, 6/4 = 10.5/7

Easily simplifying to 3/2 both times to find the rate at which the side lengths where changed.

Hope this helps.

.