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The distance between Ernie and Elmo is 20.38 feet.

Consider the distance between Ernie and Elmo be x

Law of sines is a formula relating the length of the sides of a triangle to the angles of the triangle.

[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]

The Sine rule is used to solve angles and sides of triangle.

If a triangle ABC has angles A, B and C at the vertices of the triangles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is;

Given parameters;

A = 30°

a = x = ?

B = 105°

b = 12 m

Therefore, [tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b}[/tex]

0.5/ x = 0.9659 / 12

Cross multiplication;

0.9659x = (12) (0.5)

0.9659x = 6

Divide both sides by 0.9659;

(0.9659x/0.9659) = (6/0.9659)

x = 6.21 m

Since 1 m = 3.281 ft

Then;

6.21 m = (6.21) (3.281) = 20.38 ft

Hence, the distance between Ernie and Elmo is 20.38 feet.

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1. 110

2. 20

3. 15? IM NOT SURE

Answer:

[tex]74[/tex]

Step-by-step explanation:

[tex]2 {x}^{2} - 5xy + y \\ 2 \times {3}^{2} - 5 \times 3 \times - 4 + ( - 4) \\ 2 \times 9 - 15 \times - 4 - 4 \\ 18 + 60 - 4 \\ 78 - 4 \\ = 74[/tex]

Hope this helps you.

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Answer:

74

Step-by-step explanation:

2x² - 5xy + y

Substitute x and y into the equation.

2(3)² - 5(3)(-4) + (-4)

Square the three.

2(9) - 5(3)(-4) + (-4)

Multiply the 2 and the 9.

18 - 5(3)(-4) + (-4)

Multiply 3 and -4.

18 - 5(-12) + (-4)

Multiply -5 and -12.

18 + 60 + (-4)

Add 18 and 60.

78 + (-4)

or

78 - 4

Subtract

74

Answer:

[tex]x = \{13,14\}[/tex]

Step-by-step explanation:

Given

[tex]x + 2x + 6 < 50[/tex]

Required

True values of x

We have:

[tex]x + 2x + 6 < 50\\[/tex]

[tex]3x + 6 < 50[/tex]

Collect like terms

[tex]3x < 50-6[/tex]

[tex]3x < 44[/tex]

Divide both sides by 3

[tex]x < 44/3[/tex]

[tex]x < 14.67[/tex]

This means that x has a value lesser than 14.67.

Hence, the valid values are:

[tex]x = \{13,14\}[/tex]

Answer: (13,14)

Step-by-step explanation:

Answer:

9-2x=1

-2x=-8

x=4

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Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

-3x-x=1-9

-4x=-8

x=-8/-4

x=2

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The simplified form of expression is, 12x⁶.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ √144 x³⁶

Now, By the property of square root;

⇒ √ ab = √a × √b

We get;

⇒ √144 x³⁶ = √144 × √x³⁶

And, By using the exponent property, we get;

⇒ xᵃᵇ = xᵃ × xᵇ

So, We get;

⇒ √144 x³⁶ = √144 × √x³⁶

                  = √144 × √x⁶ × √x⁶

                  = √12×12 × √x⁶ × √x⁶

                  = 12 × x⁶

                  = 12x⁶

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if you dog like something

Answer:

x = 5in

y = 16in

Step-by-step explanation:

Hypotenuse: 32/8 = 4

So, x = 20/4

x = 5

y = 4*4

y = 16

Answer:

Step-by-step explanation:

L = 2W + 2 (length is 2 ft greater than twice the width)

A.  The perimeter of the garden is P = 2L + 2W, which here is:

     P = 2(2W + 2) + 2W, or P = 4W + 4 + 2W, or P = 6W + 4

B.  If W = 5 ft, then P = 6(5 ft) + 4 ft = 34 ft

The coefficient of y2 in 9xy2z is 9xy.

In mathematics, a coefficient is any integer or symbol that multiplies the variable of a single term or the terms of a polynomial to represent a constant value. It is typically a number, however, in other expressions, a letter might be used instead. In the formula: ax2 + bx + c, for instance, x is the variable and a and b are the coefficients.

A coefficient is what?

A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it. It is assumed that the variables with no associated number have a coefficient of 1.

coefficient of y 2  in 9x(y 2 )z is 9xy.

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Answer:

.2778

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Formula for sum of interior angles of a   n - gon

(n-2) * 180

for this 12 sided 'gon

  (12-2) * 180 = 1800°        

            ( and for a 'regular' dodecagon each would be 1800/12 = 150°

Answer:

Option C) 1,800°

Step-by-step explanation:

To Find : Interior Angles of a Decagon

In order to find interior angles of any polygon we usually use the formula

(n-2)x180

Over Here it is a 12 sided polygon

So,

(12-2)x180

10x180

1800

Hence the interior angles of a decagon is 1800°

Answer:

9

Step-by-step explanation:

9 is the only number that is far away from the rest of the number of cakes sold

How likely something is to occur is known as its probability.Probability when die rolled 1st time is 6C1 i.e. (1,2,3,4,5,6).

How likely something is to occur is known as its probability.We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.

Probability when die rolled 1st time=6C1 i.e. (1,2,3,4,5,6) suppose 1 comes, then 2nd time it should not be .as it is given that no 2 people will roll same number.

so 2nd time probability=5C1 i.e. (2,3,4,5,6). same way 3rd and 4th time probability=4C1 and 3C1 respectively.Probability that no one rolls the same no. = 6*5*4*3and total possibility =6^4 

p(same number)= 6*5*4*3/ 6^4

= 5/18

p(no same number will roll)=1-5/18

=13/18

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A reflection in the line y = -2 and then translation of 2 units right will create the same area so option (C) will be correct.

f we shift the triangle anywhere then there will be no change in the area but if we apply the scale factor then since the dimension changes so its area will also change.

In all options, there is a scale factor so it will change area but in option C

A reflection in the line y = -2 reflection gives a mirror image about y = -2 but no changes in area then translation of 2 units right will shift triangle 2 units right but no effect in the area.

Hence "A reflection in the line y = -2 and then translation of 2 units right will create the same area".

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Answer:

600 centimeters

Step-by-step explanation:

Solving the question asked, we can say: If you win tonight, your odds of winning the next game are [tex]$58.33\%$[/tex]. After that, if you lose, you have a [tex]$38.88 \%$[/tex] chance of winning the game.

Probability theory is a branch of mathematics that measures the probability that an event or statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating that the event is unlikely and 1 indicating that it is certain. Probability is a numerical representation of the disease that a particular event will occur. Another way to express probability is as a percentage from 0% to 100% or 0 to 1. Proportion of occurrences in the complete set of equally likely possibilities leading to a particular occurrence compared to the total number of outcomes.

[tex]$$\begin{aligned}& (2 / 3+1 / 2) / 2=X \\& 1,666 / 2=X \\& 0.58333=X \\& ((2 / 3+1 / 2 / 2) x 2 / 3=X \\& 0.58333 x 0.666=X .3888=X\end{aligned}$$[/tex]

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The total cost will be $480.

What is an Equations?

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) symbol. It demonstrates how the expressions written on the left and right sides are equivalent. Equations can be solved to find the value of a variable that represents an unknown quantity. If there is no "equal to" symbol in a sentence, it is not an equation. It will be viewed as a phrase.

There should be two equations

For Plumber A = 60x

For Plumber B = 40 + 55x

Now in order to consider the cost to be the same we equate these two equations

60x = 40 + 55x

5x = 40

x = 8 hours

And, the total cost for plumber B is

= 40 + 55(8)

= 480

Hence, The total cost will be $480.

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Answer:

c. 7i

Step-by-step explanation:

it has to be an imaginary number

The way that the new volume compares to the original volume of the block is that the new volume is half of the original volume.

The volume of a rectangular block is gotten from the formula;

Volume = length * width * height

Now, we are given;

Width = 4 cm

Length = 4 cm

Height = 8 cm

Thus;

Volume of block = 4 * 4 * 8

= 128 cm³

Now, if you are cutting the block into 2 exactly equal halves, then you can say that;

New length = 4/2 = 2cm

Thus;

Volume of cut block = 2 * 4 * 8

= 64 cm²

This is concluded to be half of the original block.

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Answer:

263 cents

Step-by-step explanation:

Answer:

263¢

Step-by-step explanation:

Answer: a. Plotting a graph of the data on a graph paper, you can represent the time on the x-axis and the temperature on the y-axis. And plot the given points (15,20), (30,30), (45,40), (60,50), (75,60), (90,70) as ordered pairs on the graph. This will give you a line graph, showing the temperature increasing over time.

b. To find the linear model, T(x), for the temperature of the liquid with respect to time, you can use the slope-intercept form, y = mx + b, where y is the temperature, x is the time, m is the slope and b is the y-intercept. Using two of the given points, you can find the slope of the line by calculating the change in y over the change in x,

m = (y2 - y1) / (x2 - x1).

where x1,y1 and x2,y2 are two distinct points on the graph.

Once you have the slope, you can use one of the points to find the y-intercept, by substituting the point's coordinates into the slope-intercept form equation and solving for b.

Once you have the slope and y-intercept, you can write the linear model as T(x) = mx + b

c. To find the temperature of the water after 85 minutes, you can substitute the value of x = 85 into the linear model equation that you found in the previous step to get the corresponding value of y (temperature).

Please keep in mind that the temperature and time value here are random and are not based on any real-life scenario, and they were provided to show you the concept of linear model.

Step-by-step explanation:

Enchanted Rock State Natural Area is located at latitude 30.506130 and longitude -98.820064. The geographic coordinates of Enchanted Rock State Natural Area in Fredericksburg, United States, are 30° 30' 22.068" N and 98° 49' 12.2304" W. Enchanted Rock State Natural Area falls under the Mysterious Sites category.

The standard datum used by default for GPS devices used for commercial and recreational purposes is WGS84. GPS users are advised to always verify the datum of the maps they are utilising.

WGS 84, also known as the datum, is now in use by US forces.

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Answer:

m > = 1204 minutes

Step-by-step explanation:

28 + 0.05m>=88.20

Subtract 28 from both sides. Then divide both sides by 0.05 to get:  

m >=1204 minutes

Answer:

The answer is 1204 minutes.

Step-by-step explanation:

First, take away the monthly fee of 28$ of 88.20$. This gets you 60.20$. Then you divide by 0.05$ because this is how much for each minute. 60.20$/0.05$= 1204. Meaning it is 1240 minutes.

88.20-28= 60.20

60.20/0.05= 1240

Hope these formulas help! (:

The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁).

Now, According to the question:

Finding Slope From Two Points Formula

The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁). Here,

m = slope of the line

x₁ = the x-coordinate of the first point

y₁ = the y-coordinate of the first point

x₂ = the x-coordinate of the second point

y₂ = the x-coordinate of the second point

Then rise from A to B = y₂ - y₁

Run from A to B = x₂ - x₁

Then the slope, m = rise/run = (y₂ - y₁) / (x₂ - x₁)

Hence, we derived the slope formula.

Here are the steps to find the slope of a line given two points on it.

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Answer:

31.4

Step-by-step explanation:

5 x 2 x 3.14 (pi) = 31.4 rounded.

Answer:

390 ft²

Step-by-step explanation:

The longer base of a trapezoid is 8 ft. The longer base of a similar trapezoid is 13 ft. The area of the smaller trapezoid is 240 ft² What is the area of the larger trapezoid?

We solve the above question using proportion

(Longer base/Area of trapezoid) smaller trapezoid = (Longer base/Area of trapezoid) bigger trapezoid

Let the the Area of the bigger trapezoid = x

Hence,

= 8ft/240ft = 13ft/x ft

Cross Multiply

8ft × x = 240ft × 13ft

x = 240ft² × 12 ft/8 ft

x = 390 ft²

Answer:

Step A is incorrect because Lauren identified the wrong formula for sine(θ). Instead, sin(θ) would be equal to opposite / hypotenuse. Then you can substitute getting: 12/15, and once you simplify you get 4/5.

this is a question of arithmetic and the solution is as follows,

The expression 8x + 12y represents the sum of harry and mike’s total monthly wages.

Generally the equation for the  The Distributive property is mathematically given as,

a x (b +c) = a x b+ b x c.

Where

8x+12y

Therefore,

= 4 x 2x + 4 x 3x

= 4 x( 2x + 3x)

= 4( 2x + 3x)

Arithmetic

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division.

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