for the given​ set, first calculate the number of subsets for the​ set, then calculate the number of proper subsets. ​{ 5​, 7​, 17​, 15 ​}

The length of the rectangular garden is 9.01 feet and width of the garden is 2.43 feet, if its area is 22 square feet.

Let the width of the garden be x units.

According to the given question.

The area of the rectangular garden is 22 square feet.

Also, the length of the garden be eight feet less than seven times the width.

⇒ length of the garden = 7x - 8

Thereofore, the area of the rectangular garden is given by

22 = x(7x - 8)

⇒ 22 = 7x^2 - 8x

⇒ 7x^2 - 8x - 22 = 0

⇒ x = [tex]\frac{8 \pm \sqrt{64 + 616} }{14}[/tex]

⇒ x = [tex]\frac{8 \pm \sqrt{680} }{14}[/tex]

⇒ x = [tex]\frac{8\pm 26}{14}[/tex]

⇒ x = 8 + 26/14

⇒ x = 34/14

⇒ x = 2.43 feet  

So,

the length of the rectangular garden = 7(2.43) - 8 = 9.01 feet

Hence, the length of the rectangular garden is 9.01 feet and width of the garden is 2.43 feet, if its area is 22 square feet.

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Answer:

$450

Step-by-step explanation:

let the price of the bench = x

Then, the price of the table is x + 87.

x + x + 87 = 987

2x + 87 = 987

2x = 900

x = 450

Answer: $450

Answer:

Y = 44

Step-by-step explanation:

44/4 - 2 = 9

11 - 2 = 9

Y = 44

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The expression (8x+64) can be rewritten as a common factor as 8(x+8).

According to the question,

We have the following expression:

(8x+64)

It is to be noted that a common factor is such a number including a variable that it can completely divide a term. For example, in this expression, 8 is such a number that it can divide both 8x as well as 64.

(This can be better understood using more examples. For example, 4 is a common factor in 4x+24 and 5 is a common factor in 5x+30.)

Now, taking 8 as a common factor:

8 (x+8)

Hence, the correct expression is D (the fourth one).

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Answer:

Range: [tex]\:f\left(x\right)\ge \:-\frac{68}{11}[/tex]

Interval notation [tex][-\frac{68}{11},\:\infty \:)[/tex]

Step-by-step explanation:

I got a little confused with the x - 1/2x^2 term and I am taking to to be:

[tex]x\:-\frac{1}{2}x^2[/tex]  . If this is incorrect please mention the correct term in your comment and I will edit this post. Or you can re-post the question

We have
[tex]f\left(x\right)=6x^2+x\:-\frac{1}{2}x^2+\:x\:-\:6[/tex]

Simplify by grouping like terms:
[tex]=-\frac{1}{2}x^2+6x^2+x+x-6[/tex]

[tex]= \frac{1}{2}x^2+6x^2+2x-6[/tex]

Add similar elements
[tex]-\frac{1}{2}x^2+6x^2[/tex][tex]= -\frac{1x^2}{2}+\frac{12x^2}{2} = \frac{11x^2}{2}[/tex]

So the original function expression becomes
[tex]y=\frac{11}{2}x^2+2x-6[/tex]

This is the equation of a parabola which in standard form is [tex]ax^2 + bx + c[/tex]

Here
[tex]a=\dfrac{11}{2},\:b=2,\:c=-6[/tex]

We can compute the vertex of this parabola using the fact that the x, y coordinates of the vertex are given by
[tex]x_v =-\dfrac{b}{2a}[/tex]

Plugging in values for b and a give us
[tex]x_v =-\dfrac{b}{2a} = -\dfrac{2}{2\left(\dfrac{11}{2}\right)} =-\dfrac{2}{11}[/tex]

Plugging in this value of [tex]x_v[/tex] into the parabola equation will give the value for [tex]y_v[/tex] which is the function value at the vertex

Plug in [tex]x_v = -\frac{2}{11}[/tex] t find the [tex]y_v[/tex] value:
[tex]y_v=\dfrac{11\left(-\dfrac{2}{11}\right)^2}{2}+2\left(-\dfrac{2}{11}\right)-6[/tex]

Simplify
[tex]\dfrac{11\left(-\dfrac{2}{11}\right)^2}{2} =\dfrac{2}{11}[/tex]

[tex]2\left(-\dfrac{2}{11}\right) = -\dfrac{4}{11}[/tex]

Combining the terms we get
[tex]y_v =[/tex] [tex]\dfrac{2}{11}-\dfrac{4}{11}-6[/tex] [tex]= -\dfrac{68}{11}[/tex]

[tex]\textsf{Therefore the parabola vertex is at }[/tex] [tex]\left(-\dfrac{2}{11},\:-\dfrac{68}{11}\right)[/tex]
For a parabola of the form [tex]ax^2 + bx + c[/tex] with vertex [tex]\left(x_v,\:y_v\right)[/tex]

[tex]\circ \;\mathrm{If}\:a < 0\:\mathrm{the\:range\:is}\:f\left(x\right)\le \:y_v[/tex]
[tex]\circ \;\mathrm{If}\:a > 0\:\mathrm{the\:range\:is}\:f\left(x\right)\ge \:y_v[/tex]

Here [tex]a=\frac{11}{2}[/tex] so the range is [tex]f\left(x\right)\ge \:-\dfrac{68}{11}[/tex]

Answer range of f(x) is
[tex]f\left(x\right)\ge \:-\dfrac{68}{11}[/tex]

In interval notation it is [tex][-\frac{68}{11},\:\infty \:)[/tex]

It is much easier if you visualize it in a graph

Hope that helps

If the city park has a circular pond with a diameter of 4 yards. The pond's circumference is: 12.56 yrd.

Using this formula to determine or to calculate  the pond's circumference

C = π × d

where:

C = Circumference

d = diameter = 4 yards

π = 3.14

Let plug in the formula

C = 3.14×4

C= 12.56 yards

Based on the above calculation the circumference of the pond will be 12.56 yards.

Therefore If the city park has a circular pond with a diameter of 4 yards. The pond's circumference is: 12.56 yrd.

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Answer:

No

Step-by-step explanation:

Does not pass the vertical line test.

Answer:

Because:

30.5^2+73.2^2=79.3^2

=> Right triangle

=> Cos0 = 73.2/79.3 => A

Step-by-step explanation:

Answer:

In points (1,2), 1 is the value of X which represents Time in Hours and 2 is the value of Y which means Cost or $ per hour for the duration of the parking in the lot. I hope this helps.

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

|90| = 90

The number of the dollars given to the charity will be $99,000,000.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that someone has a net worth of 7.92×10¹⁰.Suppose that this individual now decides to give one-eighth of a percent of his new net worth to charity.

The number of dollars given to the charity will be calculated as below:-

Networth: 7.92 × 10¹⁰.

The percentage given to the charity is:-

1/8 %= 0.125 % = 0.00125 × networth

The number of dollars given to the charity is:-

Number of dollars = 0.00125 × 7.92 × 10¹⁰.

Number of dollars = $99,000,000.

Therefore, the number of dollars given to the charity will be $99,000,000.

The complete question is given below:-

If someone has a net worth of 7.92 × 10¹⁰.Suppose that this individual now decides to give one-eighth of a percent of his new net worth to charity. How many dollars are given to charity?

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(a) The expression for Raul's monthly data costs is 29.99 + 10 (n - 5).

(b) The minimum number is 9 GB to make the unlimited plan cheaper.

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The value of box/ square is 5, value of circle is 3 and the value of star is 6.

Let box/ square be denoted by x

let the circles be denoted by y

let the stars be denoted by z

now, let us make three linear equation based on the diagram provided

1. x + x = 10

2. y + z= 9

3. y+ x = 8

solving equation 1

x + x = 10

2x = 10

x = 5

Putting the value of x in equation 3

y + x=8

y + 5 = 8

y = 3

Putting the value of y in equation 2

y + z = 9

3 + z= 9

z = 6

Hence , The value of box/ square is 5, value of circle is 3 and the value of star is 6.

A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant. A linear equation in two variables has the conventional form Ax + By = C.

A linear equation is an equation with the maximum degree of one. This means that in a linear equation, no variable has an exponent greater than 1. A linear equation's graph is always a straight line.

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Answer: $-10

Step-by-step explanation:

The starting value is $50 and you use $35 of it meaning you only have $15 left.

You then deposite $15 meaning you now have $30 in your bank account.

After that, you spend $40 meaning you have $-10 in your bank account.

Answer:

[tex]7.2\leq pH\leq 7.8[/tex]

(any variable can be used in place of "pH")

Step-by-step explanation:

Since the pH has to be between 7.2 and 7.8, it is more than 7.2 and less than 7.8.

The less than equal to sign was used because the pH can also equal 7.2 and 7.8.

Like mentioned, any variable like x can be used instead of the "pH" I put in the equation, but make sure to define your variable.

Hope I helped!!! :)

Answer:

24 roles and 12 biscuits

Step-by-step explanation:

She had 2 trays which each had 12 ROLES and 6 BISCUTS.

Roles:  12x2 = 24

Biscuits: 6x2 = 12

So the total is 24 roles and 12 biscuits.

Answer:

x + 10

Step-by-step explanation:

It says 10 MORE than a number.

SO that's + 10

The numbr is x so:

x + 10

Answer

x + 10

Step-by-step explanation:

The question asking "more than" implies that you need to add, and x represents your unknown number.

The reason are as follows:

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

Given:

3x+6=2x+3

3x+6-2x=2x+3-2x (subtraction of equality i.e., 2x)

x+6=3 (Subtraction)

x+6-6=3-6 (subtraction of equality i.e., 6)

x=(-3) (Subtraction)

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Answer:

{(Red , Green) ; (Green , Red) ; ((Green , Green)}

Step-by-step explanation:

Here ,we notice that we draw two marbles without replacement.

Then

The possible outcomes are :

• Red then Green

• Green then Red

• Green then Green

NOTE : we can’t have the outcome Red then Red ,because if you pick a red marble and keep it to play with. Then your friend has only the choice of picking a Green marble from the bag.

Therefore,

The sample space is {(Red , Green) ; (Green , Red) ; ((Green , Green)}.

The value of the account at the end of three years of the growth factor z will be $1350.684.

According to the growth factor z, the value of the account after three years is,

Given r, is the yearly interest rate that is compounded by a growth factor z= 1 +r.  $500 at the end of each year.

The initial year's deposit is in the amount of $500.

Both the next year and the third-year deposits are made correspondingly, $200 and $600.

As a result, the account will be worth at the end of the three years is:

$(500 x3 + 200 x2 + 600 x) ---(1)

If r= 2%, then x=(1 + 2/100), , substituting the value of x in (1)

The sum will then be:

$(500(1 + 2/100)3 + 200 (1 + 2/100)2 + 600(1+2/100))

Solving the above equation, the amount will be equal to $1350.684.

Hence, The value of the account at the end of three years of the growth factor z will be $1350.684.

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If a quadrilateral is a rhombus, then opposite sides are congruent.    True

If a quadrilateral is a rhombus, then it is a rectangle.                              False

If a quadrilateral has four right angles, then it is a square.                     True

If a quadrilateral is a square, then it is a rectangle.                                  True

With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. Four non-collinear points are connected to produce it. A quadrilateral's internal angles add up to 360 degrees in all cases.

The Latin words "Quadra" for four and "Latus" for "sides" are combined to get the English word quadrilateral. A quadrilateral need not have equally long sides on all four sides. So, depending on the sides and angles, we can have many quadrilateral forms.

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The big-o time analysis for the combined time of attaching all n numbers i O(n).

The big-O running time gives the relationship between the steps taken for the algorithm and its running time. it is denoted by O(.), where . refers to the some f(n). f(n) is determined by the way of the algorithm in each step.

Here, we attach 1, then 2,then 3 and so on up to n to make a sequence of numbers. So at a time, only 1 number is attached and therefore one step of the algorithm is working. So we can say that the big-O time analysis for the combined time of attaching all n numbers is O(n).

This means that at n = 1, only 1 step is taken by the algorithm .At n=2, two steps and continued like this up to n steps.

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The percent makeup on each bag of popcorn is 25%.

When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. The percentages 100%, 50%, 0% indicate all of some quantity, half of the quantity, and none of the quantity respectively.

Popcorn is being sold by a neighborhood nonprofit to support hurricane relief.

The organization paid $4 for each bag of popcorn.

The organization sold each bag of popcorn for $5.

The markup or gain from selling the popcorn is:

$5 - $4 = $1

Therefore, the percent makeup on each bag of popcorn will be:

= ( the gain / the amount organization paid for each bag ) × 100

= ( 1 / 4) × 100

= 0.25 × 100

= 25 %

Hence, the percent makeup on every bag of popcorn is 25%.

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Answer:

Answer on attached figure

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

add

Based on the flat cost paid by Carson for his cell phone plan, and the amount of he wants to keep his bill under, the inequality that can be used to determine g is 37.50 + 40g ≤ 40

The inequality that can be used to find the maximum number of gigabytes that Carson can use while staying in his budget can be found as:

Flat cost for the cell phone plan + Cost per gigabyte x Number of gigabytes  ≤ Maximum preferred bill by Carson

When we put in the figures from Carson's cell phone plan, we get:

37.50 + 3 x g  ≤ 40

37.50 + 3g  ≤  40

In conclusion, the inequality that represents g is 37.50 + 3g  ≤  40.

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