Write your answer using decimals.Use 3.14 for pi.

CIRCUMFERENCE OF A CIRCLE : 2πr

2×3.142×7.5

47.13 cm

The sample space for this compound event consists of 6 possible outcomes, which can be represented by a table with 3 toppings and 2 crusts. Mathematically, this sample space can be represented by the formula nCr(3,2) × nCr(2,1) which simplifies to 3 × 2 = 6.

The sample space for this compound event can be represented by a table where each row represents one possible outcome. The number of outcomes is the product of the number of toppings and the number of crusts. In this case, the sample space consists of 3 toppings and 2 crusts, so there are 6 possible outcomes. The sample space is:

Table A

Topping 1 | Crust 1

Topping 1 | Crust 2

Topping 2 | Crust 1

Topping 2 | Crust 2

Topping 3 | Crust 1

Topping 3 | Crust 2

Mathematically, this sample space can be represented by the formula nCr(3,2) × nCr(2,1), where nCr(3,2) is the number of combinations of 3 toppings and 2 crusts, and nCr(2,1) is the number of combinations of 2 crusts and 1 topping. The formula can be simplified to 3 × 2 = 6, which is the same number of outcomes in the sample space.

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a. The solution to the system of equations that is graphed in the diagram is: (6, -1).

b. This is the point where the lines intersect each other.

To find the solution of the system of equations graphically, we plot the equations as lines on a coordinate plane and look for the point of intersection, which represents the solution to the system. If the lines are parallel, there is no solution, and if they overlap, there are infinitely many solutions.

a. The solution as shown in the graph given is: (6, -1).

b. We know this because the point where the two lines intersect is the solution of a system of equations.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]x-y=3\implies -y=-x+3\implies y=\stackrel{\stackrel{m}{\downarrow }}{1}x-3\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ 1 \implies \cfrac{1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{1} \implies \text{\LARGE -1}}}[/tex]

weight, color, and clarity ratings

In a regression model, the price of diamonds can be predicted by using a number of predictor variables. The predictor variables that are commonly used to predict the price of diamonds include the weight of the stone, the color rating, and the clarity rating. The weight of the stone is typically measured in carats, where one carat is equivalent to 0.2 grams.The color rating of the diamond is typically measured on a scale of D to I, where D is the most colorless and I is the most yellow. The clarity rating of the diamond is typically measured on a scale of IF to VS2, where IF is the most flawless and VS2 is the most included. By using a regression model to predict the price of diamonds, it is possible to identify which of these predictor variables are most important in determining the price of a particular diamond. The regression model can also be used to estimate the price of a diamond based on its weight, color, and clarity ratings.

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Answer: 1= 6/6 and 2=12/6

Step-by-step explanation: Just Think and use your brain

Step-by-step explanation:

[tex] - \frac{1}{2} [/tex]

Answer: 6√√/2

Step-by-step explanation: just did it

Answer:

Step-by-step explanation:

[tex]-\sqrt{72}=-\sqrt{2*6*6}=-6\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

You want the solutions to the absolute value equations ...

The absolute value function is defined piecewise:

This means each of the equations can be rewritten as two equations on different domains.

For a ≥ 0, this is ...

  a = -a

  2a = 0 . . . . . add a

  a = 0

For a < 0, the equation is ...

  -a = -a . . . . for all a < 0

The solution to the equation is the union of these solutions:

  a ≤ 0

For (a-5) ≥ 0, this is ...

  a -5 = 5 -a

  2a = 10

  a = 5

For (a-5) < 0, this is ...

  -(a -5) = 5 -a

  a = a . . . . for all a < 5

The solution to the equation is the union of these solutions:

  a ≤ 5

__

Additional comment

When a-5 ≥ 0, the value of a is a≥5.

When a-5 < 0, the value of a is a<5.

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From the given data, the answer is approximately 26.5 cubic inches. The closest option is b. 70.65 inches³.

The volume of each coin can be calculated as follows:

Volume of a coin = π × radius² × height

Volume of a coin = 3.14 × (1.2 inches)² × 0.0625 inches

Volume of a coin = 0.106 cubic inches

The total volume of all the coins can be found by multiplying the volume of one coin by the number of coins:

Total volume of coins = 0.106 cubic inches/coin × 250 coins

Total volume of coins = 26.5 cubic inches (rounded to the nearest tenth)

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The area for the parallelogram is equal to 255 square centimeters and the correct option is A = 255 cm²

In calculating for the area of parallelogram, the base is multiplied by the height, as the same way for calculating the area of a rectangle.

we shall calculate for the height h using Pythagoras rule for the triangle as follows:

h² + 9² = 15²

h² + 81 = 225

h² = 225 - 81 {subtract 81 from both sides}

h² = 144

h = √144 {take square root of both sides}

h = 12

area of parallelogram = 21 cm × 12 cm

area of parallelogram = 254 cm²

Therefore, the area for the parallelogram is equal to 255 square centimetres.

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The value of x, considering that 3x and 99º are supplementary angles, is given as follows:

x = 27.

Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if two angles are supplementary, then the sum of their measures is 180 degrees.

Supplementary angles can be adjacent (share a common vertex and a common side) or non-adjacent (do not share a common vertex or side). When two angles are supplementary, they form a straight line, and are sometimes referred to as a linear pair of angles.

For this problem, the angles 3x and 99º are a linear pair, hence the value of x is obtained as follows:

3x + 99 = 180

3x = 81

x = 81/3

x = 27.

The image is presented at the end of the answer.

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There are 60,466,176 different sequences that are possible.

Permutation represents a method of arranging things in order. In a fair 6-sided die rolled 10 times and the resulting sequence of 10 numbers is recorded, the different possible sequences are calculated as shown below:

When rolling a die, the possible outcomes are 1, 2, 3, 4, 5, and 6. As there are ten rolls, each roll has six possible outcomes. Thus, the total number of different sequences will be calculated as follows:6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 = 60,466,176. Therefore, there are 60,466,176 different sequences that are possible.

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The surface area οf the sphere is apprοximately 82,203.84 square yards.

Let's start by using the fοrmula fοr the circumference οf a circle C = 2πr

where C is the circumference, π is the cοnstant pi (which is apprοximately equal tο 3.14), and r is the radius οf the circle. We knοw that the circumference οf the widest circle οf the sphere is 508.68 yards, sο we can set up an equatiοn as fοllοws:

508.68 = 2πr

Sοlving fοr r, we get:

r = 508.68 / (2π)

r = 80.99 yards (rοunded tο twο decimal places)

Nοw that we knοw the radius οf the sphere, we can use the fοrmula fοr the surface area οf a sphere:

A = 4πr²

Plugging in the value οf r, we get:

A = 4π(80.99)²

An ≈ 82,203.84 square yards

Therefοre, the surface area οf the sphere is apprοximately 82,203.84 square yards.

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To solve the system using the elimination method (AKA combining the equations), you want to first set up the system so that one variable will be eliminated when you add the equations together.

The first equation has -2x, while the second one has -8x.  If we multiply the entire first equation by -4, we'd turn that -2x into 8x, which would cancel out when you add that with the -8x in the second equation:

   -4 ( -2x +   y = 10 )    –>       8x - 4y = -40

         -8x + 3y = 32     –>      -8x + 3y = 32

And if you add the new equations on the right, you'll end up with
    0x - y = -8    
which means y = 8.

We could do the something similar to eliminate the y's.  The first equation has y, while the second one has 3y.  If we multiply the entire first equation by -3, we'd turn that y into -3y, which would cancel out when you add that with the 3y in the second equation:

   -3 ( -2x +   y = 10 )    –>      6x - 3y = -30

         -8x + 3y = 32     –>      -8x + 3y = 32

And if you add the new equations on the right, you'll end up with
    -2x + 0y = 2
which means x = -1.

Putting those together, we have a solution of (-1, 8), which checks in both equations.

Answer:

The perimeter of a square is given by the formula P = 4s, where s is the length of one side.

Here, one side of the square is given as 14x + 14 feet. Substituting this into the formula, we get:

P = 4(14x + 14) feet

P = 56x + 56 feet

Therefore, the answer is option B: 56x + 1 feet.