What is 6/6 as a sum of fractions in three different ways

The number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

We can solve this inequality by introducing an auxiliary variable x4, such that x1 + x2 + x3 + x4 = 11. Here, x1, x2, x3, and x4 are all nonnegative integers.

We can interpret this equation as follows: imagine we have 11 identical objects and we want to distribute them among four boxes (x1, x2, x3, and x4). Each box can contain any number of objects, including zero. The number of solutions to this equation will give us the number of nonnegative integer solutions to the original inequality.

We can use a technique known as stars and bars to count the number of solutions to this equation. Imagine we represent the 11 objects as stars: ***********.

We can then place three bars to divide the stars into four groups, each group representing one of the variables x1, x2, x3, and x4. For example, if we place the first bar after the first star, the second bar after the third star, and the third bar after the fifth star, we get the following arrangement:

| ** | * | ****

This arrangement corresponds to the solution x1=1, x2=2, x3=1, and x4=7. Notice that the number of stars to the left of the first bar gives the value of x1, the number of stars between the first and second bars gives the value of x2, and so on.

We can place the bars in any order, so we need to count the number of ways to arrange three bars among 14 positions (11 stars and 3 bars). This is equivalent to choosing 3 positions out of 14 to place the bars, which can be done in C(14,3) ways.

Therefore, the number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

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Answer:

x = 12

Step-by-step explanation:

8x-4 = 92

Corresponding Angle

8x = 92+4

8x = 96

Divide by 8

x = 12

Answer:

128 x 7 = 896

896 + 3 = 899

Correct

Answer:

15 years

Step-by-step explanation:

1100 + 45y

2000 - 15y

plug 15 into y and the equations answer should be the same

Answer:

Step-by-step explanation:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\U (-1,4)\quad\implies\quad x_1=-1\,,\ \ y_1=4 \\\\B (8,5)\quad\implies\quad x_2=8\,,\ \ y_2=5\\\\\frac12d=\frac23\sqrt{(8+1)^2+(5-4)^2}=\frac23\sqrt{81+1}=\frac23\sqrt{82}\approx6.037\)

a. Simplifying the surd √28 + √1575 + √45 = 17√7 + 3√5

b. Simplifying the indices (√T³) (x²)²x³ = (√T³) x⁷

Surds are square roots of integers.

Indices are numbers raised to a given power.

Since we have the surd expression  √28 + √1575 + √45, we simplify it as follows.

√28 + √1575 + √45 = √(7 × 4)+ √(25 × 9 × 7) + √(9 × 5)

= √7 × √4 + √25 × √9 × √7) + √9 × √5

= √7 × 2 + 5 × 3 × √7 + 3 × √5

= 2√7 + 15√7 + 3√5

= 17√7 + 3√5

So, √28 + √1575 + √45 = 17√7 + 3√5

Since we have the indices (√T³) (x²)²x³

Using

So, simplifying the expression, we have

(√T³) (x²)²x³ = (√T³) x²⁺² × x³

= (√T³) x⁴ × x³

= (√T³) x⁴⁺³

= (√T³) x⁷

So, (√T³) (x²)²x³ = (√T³) x⁷

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The final pressure (P2) is 750 kPa when the volume is reduced from 2.5L to 2.0L.

To determine the final pressure when the volume of a gas is changed, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature remains constant.

Boyle's Law can be expressed as:

P1 * V1 = P2 * V2

Where:

P1 = Initial pressure

V1 = Initial volume

P2 = Final pressure

V2 = Final volume

In this case, we have an initial volume (V1) of 2.5L and an initial pressure (P1) of 300kPa. The final volume (V2) is 2.0L, and we need to determine the final pressure (P2).

Using Boyle's Law, we can set up the equation:

P1 * V1 = P2 * V2

300kPa * 2.5L = P2 * 2.0L

Simplifying the equation:

750 kPa * L = P2 * 2.0L

Dividing both sides by 2.0L:

750 kPa = P2

Therefore, the final pressure (P2) is 750 kPa when the volume is reduced from 2.5L to 2.0L.

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Answer:

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. Here is a shorter definition, A linear equation is an equation that describes a straight line on a graph. You can remember this by the "line" part of the name linear equation. Standard Form. Linear equations have a standard form that looks like this: Ax + By = C. For example...

Step-by-step explanation:

x+2=7

2x+3y=4

y=-2x+10

there are 120 permutations of 6 letters taken 3 at a time without repetition.
To find the number of permutations of 6 letters taken 3 at a time without repetition, we can use the formula for permutations:

P(n, r) = n! / (n - r)!

where n is the total number of objects and r is the number of objects taken at a time.

In this case, we have 6 letters and we are taking them 3 at a time, so n = 6 and r = 3.

P(6, 3) = 6! / (6 - 3)!
        = 6! / 3!

Now, let's calculate the factorial values:

6! = 6 × 5 × 4 × 3 × 2 × 1
3! = 3 × 2 × 1

Substituting the values into the formula:

P(6, 3) = (6 × 5 × 4 × 3 × 2 × 1) / (3 × 2 × 1)
       = 6 × 5 × 4
       = 120

Therefore, there are 120 permutations of 6 letters taken 3 at a time without repetition.

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Answer:

180x

Step-by-step explanation:

Volume is length*width*height, so we multiply all the numbers together.

15*12=180

180*x=180x

So, your answer is 180x ft^2

Answer:

150c + 13,700 < 23,000

Step-by-step explanation:

Greatest weight that can be loaded into the container = 23,000 kilograms

Weight of each crate = 150 kilogram

Weight of other shipment = 13,700 kilograms

c = total number of 150-kilogram crates that can be loaded

This can be represented by the inequality:

150c + 13,700 < 23,000

That is, Weight of each crate multiplied by total number of 150-kilogram crates that can be loaded Plus Weight of other shipment less than greatest weight that can be loaded into the container

Answer:

c<62

Step-by-step explanation:

We know:

\color{blue}{\text{weight preloaded}}=

weight preloaded=

\,\,\color{blue}{13700}

13700

\color{red}{\text{weight per crate}}=

weight per crate=

\,\,\color{red}{150}

150

\color{purple}{\text{weight capacity}}=

weight capacity=

\,\,\color{purple}{23000}

23000

150

150

150

...

13700

23000

weight of all crates

Method 1 (Unwinding):

\color{green}{\text{weight of all crates}}=

weight of all crates=

\,\,\color{purple}{\text{weight capacity}}-\color{blue}{\text{weight preloaded}}

weight capacity−weight preloaded

=

=

\,\,\color{purple}{23000}-\color{blue}{13700}

23000−13700

=

=

\,\,\color{green}{9300}

9300

\text{number of crates}=

number of crates=

\,\,\frac{\color{green}{\text{weight of all crates}}}{\color{red}{\text{weight per crate}}}

weight per crate

weight of all crates

​

=

=

\,\,\frac{\color{green}{9300}}{\color{red}{150}}

150

9300

​

=

=

\,\,62

62

6262 is the number of crates that can be loaded into the shipping container for a total weight of 23000 kilograms. But the "greatest" weight means less than 23000 kilograms can also be loaded into the container, so fewer than 62 (61, 60, ...) crates can also be loaded.

c \leq62

c≤62

\leq≤ or "less than or equal to" means that exact amount or less

Method 2 (Algebra):

\text{\(c=\) number of crates}

c= number of crates

The greatest weight means less than 23000 kilograms can also be loaded into the container, so we will use the \leq≤ ("less than or equal to") symbol:

\color{red}{\text{weight per crate}}\cdot\text{\# of crates}+\color{blue}{\text{weight preloaded}}\leq\color{purple}{\text{weight capacity}}

weight per crate⋅# of crates+weight preloaded≤weight capacity

\color{red}{150}c+\color{blue}{13700}\leq

150c+13700≤

\,\,\color{purple}{23000}

23000

-\color{blue}{13700}\phantom{=}

−13700=

\,\,-\color{blue}{13700}

−13700

Subtract 13700 from both sides

\color{red}{150}c\leq

150c≤

\,\,9300

9300

\frac{\color{red}{150}c}{\color{red}{150}}\leq

150

150c

​

≤

\,\,\frac{9300}{\color{red}{150}}

150

9300

​

Divide both sides by 150

c\leq

c≤

\,\,62

62

Answer:

  $22

Step-by-step explanation:

Given a table of popcorn volumes and prices, you want to know a reasonable price for 60 ounces of popcorn.

Plotting the given sizes and costs on a graph, we see that the relationship is linear. Using the two points (size, cost) = (10, 6) and (20, 8), we find the relation to be ...

  m = (y2 -y1)/(x2 -x1) = (8 -6)/(20 -10) = 2/10 = 0.2 . . . . slope

  b = y1 -m(x1) = 6 -0.2(10) = 4 . . . . . . y-intercept

Then the equation of the line is ...

  y = mx +b

  y = 0.2x +4

Using x=60, we find the corresponding price is ...

  y = 0.2(60) +4 = 12 +4 = 16

A consistent price is $16 for a 60-ounce container of popcorn.

__

Additional comment

The price equation suggests a fixed cost ($4) and a volume-related cost ($0.20 per ounce).

By using the approximation of 62,500 inches to the mile, you can simplify and expedite various calculations involving distances and conversions between inches and miles, providing a convenient tool for numerical analysis and problem-solving

The approximation of 62,500 inches to the mile is commonly used in various calculations, especially in scenarios where conversions between inches and miles are involved. This approximation simplifies the conversion process and allows for easier calculations.

For example, if you need to convert a distance from miles to inches, you can simply multiply the number of miles by 62,500 to obtain the equivalent distance in inches. Conversely, if you have a measurement in inches and want to convert it to miles, you divide the number of inches by 62,500 to get the distance in miles.

Additionally, this approximation can be useful in other applications, such as determining the number of inches in a given number of miles, or calculating the length of a specific distance in miles based on its measurement in inches.

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.

The correct answer is option d. The theoretical Probability of spinning a multiple of 3 with one spin is 0.

The theoretical probability of an event, we need to identify the number of favorable outcomes (the desired event) and the total number of possible outcomes.

In this case, the event is spinning a multiple of 3 on the spinner. Let's examine the possible outcomes and identify the favorable outcomes:

Possible outcomes on the spinner: {1, 2, 3, 4, 5, 6}

Favorable outcomes (multiples of 3): {3, 6}

The total number of possible outcomes is 6, and the number of favorable outcomes is 2.

The theoretical probability of spinning a multiple of 3 can be calculated as:

P(multiple of 3) = (Number of favorable outcomes) / (Total number of possible outcomes)

P(multiple of 3) = 2 / 6

Simplifying the fraction, we get:

P(multiple of 3) = 1 / 3

Therefore, the correct answer is option d. The theoretical probability of spinning a multiple of 3 with one spin is 0.

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Answer:

If 1 + 1 = 2, then we can say that 1 = 2 - 1. Now, if we have 3x + 5x, we can factor out the common term of x to get: 3x + 5x = (3 + 5)x = 8x So, 3x + 5x = 8x.

Answer:

Step-by-step explanation:

let Josh's current age be x.

2+ 25 times his current age= 25x+2

25x+2=77

25x= 77-2

     = 75

x= 75/25

 =3

The angle which would be tangent  a 90 degree in the given diagram would be ∠JYQ, ∠JYW  , ∠FYG and ∠FHG

A circle's tangent is a single-pointed line that intersects the circle. The point of tangency is the location where the circle and the tangent cross. The circle's radius, where the tangent touches it, is perpendicular to it.

Therefore, JY is perpendicular to QW which means

∠JYQ=∠JYW=90 degrees

Since, J is the center of circle and GF is diameter, there is a theorem which says that angle substended by diameter at any point of circle is 90 degree.

Therefore, ∠FYG =∠FHG=90 degrees.

Hence, ∠JYQ, ∠JYW  , ∠FYG and ∠FHG are all the equal to 90 degree.

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Answer:-6s-2r

Step-by-step explanation:

you must add all like terms in this case S -4-3 is -7. -7+1=-6.
-6s-2r

Answer:

-6r - 2s

Step-by-step explanation:

Given expression,

→ -4r + s - 2r - 3s

Let's simplify the expression,

→ -4r + s - 2r - 3s

→ (-4r - 2r) + (s - 3s)

→ -6r + (-2s)

→ -6r - 2s

Hence, the answer is -6r - 2s.

Answer:

6/10, 9/15, 12/20, 15/25, 18/30, etc so Edgar is wrong. 3/5 is not equivalent to 18/32

Step-by-step explanation:

(Gimme Brainliest Please)

Answer:

Option 4: 6^7

Step-by-step explanation:

The rule is that when multiplying same bases with different exponents, the exponents only get added.

In other words, (x^a)(x^b)=x^(a+b)

In this case, (6^3)(6^4)=6^(3+4)=6^7

Therefore, Option 4 is correct

Answer:

Easy

Step-by-step explanation:

Y=5x

I hope this helps

Answer: ITS A! I HAVE THE SAME TEST!

Step-by-step explanation:

The measure of angle 7 (m < 7) would be 61°

From the question, we are to determine what the measure of <7 would be

In the given diagram, we can observe that

< 2 = < 6 (Corresponding angles theorem)

From the given information,

< 2 = 119°

∴ < 6 = 119°

Also,

< 6 + < 7 = 180° (Sum of angles on a line segment)

Thus,

119° + < 7 = 180°

< 7 = 180° - 119°

< 7 = 61°

Hence, the measure of angle 7 (m < 7) is 61°

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From the computation done, it can be denoted that the total price that will be paid will be $12.90.

1 Krispy Kosmos at $2.89 = $2.89

2 Chewy Chocos at $3.19 each = 2 × $3.19 = $6.38

1 Gooey Globs at $2.99 = $2.99

Total = $2.89 + $6.38 + $2.99 = $12.26

We'll then add the sales tax of 5.2%, therefore, the total value will be:

= $12.26 + (5.2% × $12.26)

= $12.26 + $0.638

= $12.90

In conclusion, the correct option is $12.90.

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Answer:

C

Step-by-step explanation:

Edg 2022

Answer:

A) 8inches long and 4 inches wide

Step-by-step explanation:

perimeter is the measurement of the outside of the shape. So for a quilt that'd be 2 lengths and 2 widths. 8+8=16 4+4=8, 16+8=24

The evaluated expression, corrected to the nearest whole number, is -139.

To evaluate the expression with the given values of a = 17.54, b = -36.2, and c = 4.33 and round to the nearest whole number, we can perform the necessary calculations as follows:

Expression: a + b * c

Substituting the values:

17.54 + (-36.2) * 4.33

Calculating the multiplication:

17.54 + (-156.826)

Adding the values:

-139.286

Rounding to the nearest whole number:

-139

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Given that a = 17.54, b= -36.2 and c = 4.33 evaluate and correct to the nearest whole number

The arc length is D) 3.14 meters.

What is arc length?

In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.

It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.

The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.

                                      \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

Here the give circle Radius PR = 3m and θ=60°.

Now using arc length formula then,

=> Arc length \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

=> \(A_L=\frac{60}{360} \times2\times3.14\times3\)

=> \(A_L=\frac{1}{6}\times2\times3.14\times3\)

=> \(A_L\) = 3.14 m.

Hence the arc length is D) 3.14 meters.

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I think the answer is the second one?

The set of numbers whose decimal representations are neither repeating nor terminating is known as the set of irrational numbers.

Irrational numbers are numbers that cannot be expressed as fractions and have non-repeating and non-terminating decimal representations. Examples of irrational numbers include √2, π (pi), and e (Euler's number). These numbers are infinite and non-repeating, meaning their decimal representation goes on forever without following a specific pattern. The proof that √2 is irrational was first demonstrated by the ancient Greeks, and the irrationality of π and e was proven much later in history. Irrational numbers play a significant role in mathematics and are essential for understanding concepts like limits, calculus, and geometry.

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What is the mathematical term for the set of numbers whose decimal representations are neither terminating (finite decimal) nor repeating (infinite periodic decimal)?