How many gallons are in a 2 liter bottle of soda?

√17 unit is  the components of vector V .

what is components of vector?

A vector quantity has a magnitude and a direction as its two attributes. You must compare both the magnitude and the direction of two vector quantities of the same type.

The initial and terminal points of a vector v  are given by

(6, 3) and (2, 2).

Hence:

The component form of v is

V = ( 2 - 6) ( 2 - 3)

   = (  -4 , -1)

The length of the vector is

l v l = [tex]\sqrt{(-4)^{2} + ( -1)^{2} }[/tex]  = √17 unit

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Answer:

x = 9/11

Step-by-step explanation:

distribute the 2:

6x - 4 + 5x - 3 + 2

combine like terms:

11x - 7 = 2

add 7 to both sides:

11x = 9

divide by 11 to isolate x:

x = 9/11

Step-by-step explanation:

Distribute 2 to 3x-2

[tex]6x - 4 + 5x - 3 = 2[/tex]

Them combined like terms

[tex]11x - 7 = 2[/tex]

Then add 7 to both sides

[tex]11x = 9[/tex]

Then divide by 11 and get

[tex] \frac{9}{11} [/tex]

Answer:

21

Step-by-step explanation:

1+6=7

7+4=11

11+11=21

Answer:

m=7

Step-by-step explanation:

it's in the picture

the left got cut out but there's a bracket at the end of the first line

By critically observing the graph shown above, the set of ordered pairs include the following:

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.

By critically observing the graph shown above, we can logically deduce that the set of ordered pairs include the following:

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If two hundred liters of a punch that contains 35% fruit juice is mixed with 300 liters of another punch and the resulting fruit punch is 20% fruit juice, then the percent of fruit juice in 300 liters of punch is calculated to be 10%.

The percentage of fruit juice in 300 liters of punch can be calculated by forming a linear equation.

A linear equation also termed a first-degree equation is an equation with one or more variables that have the highest power of one.

A linear equation for this problem can be given as:

the volume of the first punch × percentage of fruit juice in the first punch + the volume of the second punch × percentage of fruit juice in the second punch = total volume × total percentage of fruit juice

Consider x = percentage of unknown fruit juice

Now add the given values in the equation:

200 × 35 + 300(x) = 500 × 20

7000 + 300(x) = 10000

300(x) = 10000 - 7000

300(x) = 3000

x = 3000 / 300

x = 10%

Hence, the percentage of fruit juice in 300 liters of punch is calculated to be 10%.

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Step-by-step explanation:

multiply 6x - y = 2 by 3 and subtract the first equation from the second

18x-3y=6 - (-4x+3y=2

3y is cancelled and after the others are subtracted the equation becomes

22x = 4

x = 2/11

Answer:

The value of x = 1/2

The value of y = 1

Step-by-step explanation:

Let's change the equation,

→ 6x - y = 2

→ y = 6x - 2

Then the value of x will be,

→ -4x + 3y = 1

→ -4x + 3(6x - 2) = 1

→ -4x + 18x - 6 = 1

→ 14x = 1 + 6

→ x = 7/14

→ [ x = 1/2 ]

Hence, the value of x is 1/2 (or) 0.5.

Now the value of y will be,

→ y = 6x - 2

→ y = 6(1/2) - 2

→ y = 3 - 2

→ [ y = 1 ]

Hence, the value of y is 1.

Each side of cube is 100 cm.

In Maths or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.

Given that,

Volume of cube = 1 cubic meter

We know that,

1 m = 100 cm

Also  volume of cube = [tex]a^{3}[/tex]

Then,

Volume of cube = 1000000 cm

                   [tex]a^{3}[/tex]  = [tex]100^{3}[/tex]

                   a = 100 cm

Hence, Each side of cube is 100 cm.

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Answer:

5

Step-by-step explanation:

To find a value for y given a value for x, substitute the x-value into the expression

Answer:

Step-by-step explanation:

x + y = 8

Let x = 2

then:

2 + y = 8

y = 8 - 2

y = 6.

This is one integer value for y.

Answer: The cat has left over the milk is 3.625 cups

Step-by-step explanation:

Amount of cups of milk=3(7/8) cups

That means, 3(7/8) cups= 31/8 cups

Amount of milk cat gave=1/4 cups

The amount of left over the milk :

Subtract with this values

=(31/8) -(1/4)

=3.875-0.25

=3.625

The cat has left over the milk is 3.625 cups

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Answer:

50

Step-by-step explanation:

[tex]\frac{x}{5}-9=1 \\ \\ \frac{x}{5}=10 \\ \\ x=50[/tex]

Answer:

p = (7r+16) / (4-q)

Step-by-step explanation:

4p - 7r = pq + 16

Add 7r to both sides.

4p = pq + 16 + 7r

Subtract pq from both sides.

4p - pq = 7r + 16

Factor out p from the left side.

p(4 - q) = 7r + 16

Divide both sides by (4 - q).

p = (7r + 16)/(4 - q)

The 7r and the 16 could be in either order, like 7r+16 or 16+7r. You could show that the answer is a fraction with 7r+16 on top and 4-q on the bottom. If you are writing or on the computer selecting a fraction that is stacked you don't need need the parenthesis.

Answer:

2/3

Step-by-step explanation:

Answer:

f(p) = 18p + 40

Step-by-step explanation:

Since they can make 18 pizzas per hour, number of pizzas made in p hours = 18p

They already have 40 pizzas

So  total number of pizzas at any time p is f(p) = 18p + 40

The probability that atleast one students is taking a language class is 0.7

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Let :

Spanish = S ; French = F ; German = G

SnFnG = 3

(SnF) only = 9 - 3 = 6

(SnG) only = 5 - 3 = 2

(FnG) only = 5 - 3 = 2

S only = 28 - (6+3+2) = 17

F only = 21 - (2+3+2) = 14

G only = 12 - (6+3+2) = 1

Student not taking any of the classes are;

(100 - (17+14+1+2+2+6+3))

100 - 45 = 55

Atleast 1 is taking a language class out of 2 selected

The probability that atleast one students is taking a language class :

(45/100 * 55/99) + (55/100 * 45/99) + (45/100 * 44/99)

= 0.7

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Answer:

[tex]x = \frac r{s + t}[/tex]

Step-by-step explanation:

Hello!

Solve by isolating the variable.

The solution for x is [tex]x = \frac r{s + t}[/tex].

Answer:

the equation is y=1/2+0.5

-14 is the 81th term.

The first step is to determine the relationship between the numbers in the sequence. When examined, it can be seen that the number decline by 1/5.

To confirm : 2 1/5 - 2 = 1/5

The linear equation that can be used to determine the position of a number is:

2 1/5 - 1/5(x)

Where x is the position of the number

For example, the third number is

2 1/5 - 1/5(3)  = 1 4/5

Given the number, the position of the number can be determined using the above linear equation:

-14 = 2 1/5 - 1/5(x)

In order to determine the value of x, take the following steps:

Multiply through by 5

(-14 x 5) = (11/5 x 5) - (x / 5 x 5)

-70 = 11 -x

Combine similar terms: 70 + 11 = x

Add similar terms: x = 81

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The 80th percentile is 125.37.

It is required to find the solution.

A part of a whole expressed in hundredths a high percentage of students attended. Also the result obtained by multiplying a number by a percent the percentage equals the rate times the base.

Given:

The weights (in pounds) of seven people:

100, 115, 135, 140, 180, 197, 230.

We have to find the 80th percentile first we have to find the mean of seven people.

Mean=100+ 115+135+140+ 180+197+ 230/7

Mean=156.71

100 percent=156.71

80  percent=156.71*80/100

80  percent=125.37.

Therefore, the 80th percentile is 125.37.

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Answer:

Step-by-step explanation:12

Answer:

= −10/81g^2+2/27g

Step-by-step explanation:

---------------

Answer:

9

Step-by-step explanation:

So there's 3 1's, 2 2's, 2 3's, 1 4, 2 5's, a 6, a 7, an 8, 2 0's, and no 9's.  

x = 20+ 3y

First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

Jame = x

Brittany  = y

x = 20+ 3y

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Answer:

your answer is xx = (53.80 - 45) / 4

The first step to solve the equation is;

⇒ ''Change 14 1/10 to 14.1''

What is Mixed fraction?

A fraction which is represented with its quotient and remainder is called a mixed fraction.

The problem is given as,

40.8 - 14 1/10

Now, To solve the equation we have firstly change 14 1/10 as

40.8 - 14 1/10

40.8 - 14.1

Then, Subtract the numbers as,

26.7

Solution of the problem is 26.7.

So, The first step to solve the equation is;

⇒ ''Change 14 1/10 to 14.1''

Option 4 is true.

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The Length of perimeter of the shaded shape is; 24 - 8π

Let us first find the rectangle measurements that contains the shaded portions.

Width of rectangle = 2 * 4 = 8

Length of rectangle = 2 + 2 = 4

Perimeter of rectangle = 2(8 + 4) = 24 units

Now, let us find the perimeter of all semi circles and quarter circles that fall into into this rectangle region;

Perimeter of semi circles = πr + πr + πr + πr/2 + πr/2 = 4πr

Perimeter of semi circles inside the rectangle = 4π * 2 = 8π

Thus;

Length of perimeter of shaded shape = 24 - 8π

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The area enclosed by the ellipse [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex] is 60 square units.

The general form of the equation of ellipse is  [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

Given the equation of ellipse is,  [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex]

⇒ [tex]\frac{x^2}{2^2}+\frac{y^2}{9^2}=1[/tex]

That is, a = 2 and b = 9

Now,  [tex]\frac{y^2}{9^2} = 1 -\frac{x^2}{2^2}[/tex]

⇒ [tex]y=\frac{9}{2} \sqrt{4-x^2}[/tex]

Area enclosed by the ellipse = 4 x Area of ellipse in the first quadrant

Therefore, Area of ellipse in the first quadrant, A = [tex]\int\limits^a_0{\frac{9}{2} \sqrt{4-x^2}} \, dx[/tex]

Using Substitution ,x = 2cosθ, then dx = -2sinθdθ and x = 0⇒ θ = π/2 and x = 2⇒ θ = 0

A = [tex]\int\limits^a_0{\frac{9}{2} \sqrt{4-4cos^2\theta}} \, dx[/tex]

  = [tex]\int\limits^2_0{\frac{9}{2}\times2 \sqrt{1-cos^2\theta}} \, dx[/tex]

  = [tex]\int\limits^2_0{9 sin^2\theta} \, dx[/tex]

 = [tex]\int\limits^0_\frac{\pi}{2} {9 sin^2\theta} (-2sinx)\, d\theta[/tex]

  = [tex]\int\limits^\frac{\pi}{2} _0{18 sin^3\theta} \, d\theta[/tex]

  = [tex]\int\limits^\frac{\pi}{2} _0{18 (\frac{3sin\theta-sin3\theta}{4} )} \, d\theta[/tex]

  = [tex]\frac{9}{2} \int\limits^\frac{\pi}{2} _b {3sin\theta} \, d\theta -\frac{9}{2} \int\limits^\frac{\pi}{2} _0 {sin3\theta} \, d\theta[/tex]

  = 27/2 x (-cosθ) - 9/6 x (-cos3θ) |  θ = 0 to  θ =  π/2

  = 15 square units.

Therefore, the area enclosed by ellipse  [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex] = 4 x A = 4 x 15 = 60 square units.

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