how many non-empty subsets of consist entirely of prime numbers? (we form a subset of the group of numbers by choosing some number of them, without regard to order. so, is the same as .)

Answer:

400

Step-by-step explanation:

[tex] = ( \sqrt{15} - \sqrt{3} )( \sqrt{15} - \sqrt{3} ) \\ = \sqrt{15} ( \sqrt{15} - \sqrt{3} ) - \sqrt{3} ( \sqrt{15} - \sqrt{3} ) \\ = 15 - \sqrt{45} - \sqrt{45} + 3 \\ = 15 + 3 - 2 \sqrt{45} \\ = 18 - 2( \sqrt{9 \times 5} ) \\ = 1 - 2(3 \sqrt{5} ) \\ = 1 - 6 \sqrt{5} [/tex]

ATTACHED IS THE SOLUTION

The density of the piece of form will be 0.14 g/cm³.

Density is defined as the ratio of the mass of the object to the volume of the object. It does not depend upon the whole mass it only depends upon the mass per unit volume.

Volume is defined as the space occupied by the object in the three-dimensional space.

Given that a piece of foam padding has a volume of 1,500 cm³ and a mass of 200 g.

The density of the foam will be calculated as,

D = mass / Volume

D = 200 / 1500

D = 0.1333333333 or 0.14 g/cm³

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He will need 14 boxes which can store can store 8 tins of coffee and 6 boxes that can store 12 tins of coffee.

let us assume:

Number of 8- tin boxes= x

Number of 12- tin boxes= y

we are given the condition that total number of boxes are 20, so-

x+y=20

⇒ x= 20-y

We are also given the condition that he has 184 tins of coffee, so-

8x+12y= 184

⇒ 8(20-y) + 12y = 184

⇒ 160 -8y +12y = 184

⇒ 4y= 24

⇒ y=6

⇒ x=20 -y

⇒ x= 20 - 6

⇒ x= 14

What do you mean by conditional linear equations?

A linear equation is an identity if solving it results in a true assertion, such as 0 = 0. The answer set is "all real numbers." An equation is conditional if there is only one solution to a linear equation, such as x = 3.

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Answer: x = 2 - 1/2 y

Step-by-step explanation:

12x + 6y = 24

12x = 24 - 6y

x = 2 - 1/2 y

Answer:

98 + (-24)

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

Answer: 11r² + 8 ==> C

Step-by-step explanation:

P=Sum of all sides

P=4r² - 1 + r² + 3 + r² + 4 + 5r² + 2

P=4r² + r² + r² + 5r² - 1 + 3 + 4 + 2

P=5r² + 6r² + 2 + 6

P=11r² + 8 ==> C

The least integer of the four consecutive even integers is 42

From the question, we are to determine the least integer.

Let the least integer be x

From the given information,

"the sum of four consecutive even integers is 180"

Then,

We can write that

x + (x + 2) + (x + 4) + (x + 6) = 180

x + x + 2 + x + 4 + x + 6 = 180

4x +  12 = 180

4x = 180 - 12

4x = 168

x = 168/4

x = 42

Hence, the least integer is 42

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Answer: r = √(v/πh)

Step-by-step explanation:

v = πr^2h

v/(πh) = r^2

√(v/πh) = r

Answer:

I need alot of letter in order tot ype an anwser but long story sort its ten percent

[tex]5sin^2(x)-3sin(x)=0\implies sin(x)[5sin(x)-3]=0 \\\\[-0.35em] ~\dotfill\\\\ sin(x)=0\implies x=sin^{-1}(0)\implies x= \begin{cases} 0\\ 180^o\\ 360^o \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 5sin(x)-3=0\implies 5sin(x)=3\implies sin(x)=\cfrac{3}{5} \\\\\\ x=sin^{-1}\left( \cfrac{3}{5} \right)\implies x\approx \begin{cases} \stackrel{I~Quadrant}{36.87^o}\\\\ \stackrel{II~Quadrant}{143.13^o} \end{cases}[/tex]

The conversion of 98 pounds to kilograms is 44.5 pounds.

This is a question of conversion of weights.

Unitary method

The unitary method is used to find the value of a single unit from a given multiple. For example, the price of 40 pens is Rs. 400, then how to find the value of one pen here.

Also, once we have found the value of a single unit, then we can calculate the value of the required units by multiplying the single value unit.

We know that,

1 pound = 0.45359237 kilograms ≈ 0.454 kilograms

Hence, using unitary method, we can write,

98 pounds = 98*0.454 kilograms = 44.492 kilograms ≈ 44.5 pounds.

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       In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

The meaning of inequality

       A social discrepancy is one example of a characteristic that is unequal or uneven. b: unequal opportunity or distribution.

     A disparity in size, quantity, quality, social standing, or another aspect is what is meant by the term "inequality." When you have ten of something and someone else has none, that is an instance of inequality.

A number = n 12

multiplied by a number = n+12

which is 32 less than the number = 3n-32

n+12 =3n-32

44 =2

The result is equal to 2n n=22.

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Finding a grouping, ordering, or assignment of a discrete, finite set of things that complies with predetermined requirements is the goal of combinatorial issues.

She has 210 different combinations.

A new wave of research methodology called the combinatorial approach to materials seeks to greatly speed up the discovery and development of novel substances.

The area of mathematics concerned with finding solutions to conundrums involving the selection and arrangement of parts of particular (often finite) sets in line with predetermined norms.

Finding a grouping, ordering, or assignment of a discrete, finite set of things that complies with predetermined requirements is the goal of combinatorial issues. Candidate solutions are combinations of solution elements that could be found while trying to find a solution, but they don't have to meet all the requirements.

So, she has [tex]$C_1^4=\frac{A H}{A \frac{A}{4}}=\frac{10 \times 2 \times 8 \times 7}{1 \times 2 \times 3 \times 4}=210$[/tex]

So she has 210 different combinations.

[tex]$c_{1=}^4=\frac{4 \%}{A f}$[/tex]

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In linear equation, oil required to cover oil all the pieces in one box of big pasta with same thin layer of oil = 1/2 of the oil.

What are a definition and an example of a linear equation?

Let the dimensions of one piece of your favorite kind of pasta  be l, b, h.

Volume of one piece of pasta = l b h

Surface area of one piece of pasta = 2( lb + bh + lh)

Let the no of pasta piece in the box ( favorite  one ) be 'n' = .

Total volume = n × lbh

Total  Surface area = n . 2( lb + bh + lh)

In the bigger size pasta box dimensions of one piece of  of pasta 2l , 2h , 2b .

∴ Volume of one piece of pasta = 2l × 2b  × 2h   = 8lbh

Surface area of one piece of pasta = 2( 4lb × 4bh × 4lh)

                                                         = 2 × 4 ( lb × bh × lh )

Let the no of pasta pieces in the bigger pasta box in m.

Total volume of pasta = m × 8lbh

total surface area = m . 4 × 2 ( lb × bh × lh )

the total volume of pasta is also same in the box.

  mass =  density ×  volume

D × m .8 lbh  =  D × n . lbh

  m = n/8

total surface  area of  pastas in bigger pasta box = m × 4 × 2 ( lb × bh × lh)

                                                                           = n/8 × 4 × 2  ( lb × bh × lh )

                                                              =      n/8 × 1/2 × n× 2  ( lb × bh × lh )

                                                      = 1/2 × surface area (total) of small pasta

∴ oil required to cover oil all the pieces in one box of big pasta with same thin layer of oil = 1/2 of the oil

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Answer:

99 grams of zinc

Step-by-step explanation:

Ser up a proportion

[tex]\frac{zinc}{copper}[/tex] = [tex]\frac{zinc}{copper}[/tex]  Put in the ration and the actual amount of copper i and solve for the actual number of zinc

[tex]\frac{3}{16}[/tex] = [tex]\frac{z}{528}[/tex]  cross multiply to solve for z

16z = 3(528)

16z = 1584  Divide both sides of the equation by 16

z = 99

Answer:

I will give you the formula and than it will be easy for you to solve this.

Answer: 2x-1=7x+44

2x-7x=44+1

-5x=45

x=-9

Step-by-step explanation:

Answer:.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the zeros of f(x) = x³ -5x² -22x -16, given that a factor is x+2.

Using synthetic division (see attachment), we find the quadratic factor to be (x² -7x -8), so we have ...

  f(x) = (x +2)(x² -7x -8)

The quadratic can be factored using our knowledge of the divisors of -8 to give ...

  f(x) = (x +2)(x +1)(x -8)

The zeros of f(x) are the values of x that make these factors zero:

  x = -2, -1, 8 . . . . . zeros of f(x)

__

Additional comment

We know the product of binomial factors is ...

  (x -a)(x +b) = x² -(a-b)x -ab

This means we can factor the quadratic by looking for factors of 8 that have a difference of 7. We know that 8 = 8·1 and that 8-1=7, so the values of 'a' and 'b' we're looking for are a=8, b=1.

The "zero product rule" tells you a product is zero only if one of the factors is zero. That is how we know to look for the zeros of the binomial factors of f(x). For example, x+2=0 ⇒ x=-2 is a zero of f(x). (The remainder of 0 in the synthetic division also tells us f(-2)=0.)

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Answer:

centre =

diameter = ab

radius = (ab)/2

Step-by-step explanation: hope this helps

The statement that proves the congruency of the two triangles is (c) ASA

The given parameter is the two triangles in the figure

For the angles or the sides of the triangles to be congruent, the sides or the angles must be marked with the same identifier

Using the above as a guide,

Two corresponding angles in the triangles are marked with the same symbol

This is represented as AA i.e. Angle-Angle

Also, the triangles share a common side length

This is represented with S i.e. Side

This common side length is between the angles

So, we have

ASA i.e. Angle Side Angle

Hence, the congruency of the two triangles is by the ASA congruent theorem

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The coefficient of the variable term in the equation 6s - 3/4 is 6. The variable term is s while the constant term is -3/4

given data

6s-3/4

The coefficient of the variable term is the number multiplying the variable term. The variable term in the equation is "s"

The number in the given equation is 6

The equation could be written as

6 * s - 3/4

from the rewritten equation we can see that 6 is multiplying the variable and hence the coefficient.

The other term in the equation is constant term and this is - 3/4

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Answer:

396 cm³

Step-by-step explanation:

Volume= πr²*height

r=3

3² π *14

9*14*π= 396cm³

volume of a cylinder with radius as 3cm and height as 14cm is 396cm^3

The number of gigabytes that Sydney can use while staying within her budget is less than 2.9 gigabytes.

gigabytes (GB) – pronounced with two hard Gs – is a unit of storage capacity equal to approximately 1 billion bytes. In decimal form (base 10), a gigabyte is exactly one billion bytes. In binary form, a gigabyte is 230 bytes or 1,073,71,82 bytes. Giga comes from the Greek word for giant. Werner Buchholz is credited with coining the term byte in 1956 and helped design IBM's 7030 Stretch, the first transistorized supercomputer.

gigabytes has been a common unit of measurement for data storage products since the mid-1980s. In recent years, terabytes (TB) have become a more common measure of storage capacity, especially for hard drives and solid-state drives.

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The volume of one fish food cubes is: 1/64 ft³

Using the volume formula, the volume of the shipping box is: 15/4 × 3 × 13/4 = 585/16 ft³

The number of fish food cubes that can be packed in the shipping box is: 2,340 fish food cubes.

The volume of a box = length × width × height

A cube has equal side lengths, therefore, the volume of a cube = (side length)³ = side length × side length × side length.

We are given that the fish food cubes have side lengths of 1/4 ft. Therefore:

Volume of fish food cubes = 1/4 × 1/4 × 1/4

Volume of fish food cubes = (1 × 1 × 1)/(4 × 4 × 4)

Volume of fish food cubes = 1/64 ft³

Using the volume formula, we are given the parameters of the box as:

Length (l) = 3¾ = 15/4 ft

Width (w) = 3 ft

Height (h) = 3¼ = 13/4 ft

Therefore,

Volume of shipping box = 15/4 × 3 × 13/4

Volume of shipping box = (15 × 3 × 13)/(4 × 4) = 585/16 ft³

The number of fish food cubes that can be packed in the shipping box = volume of shipping box/volume of one fish food cube

= 585/16 ÷ 1/64

= 585/16 × 64/1

= (585 × 64)/(16 × 1)

= 37,440/16

= 2,340 fish food cubes.

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Answer:

14 pounds per hour

Step-by-step explanation:

[tex] \frac{490}{7\times 5} = \frac{490}{35} = 14[/tex]

Equation of the line is x +y = -5.

Equation is a declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

Given Data

coordinates (4,1) and (1,4)

A line is singular if you are aware that it goes through two specific coordinates (x₁ , y₁) and (x₂ , y₂) .The equation for the line is if the points are

[tex]\frac{x - x}{x_{1} - x}[/tex]¹₂ = [tex]\frac{y - y_{1} }{y_{1}- y_{2} }[/tex]

Equating coordinates:

[tex]\frac{x-4}{4-1}[/tex] = [tex]\frac{y-1}{1-4}[/tex]

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

Cross multiplying,

-3(x-4) = 3(y-1)

-3x + 12 = 3y -3

3x + 3y = -15

x +y = -5

Equation of the line is x +y = -5.

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