What the area of the small triangle

Solution:

The amount, A, over a period of time, t, is;

Given;

CORRECT OPTION: (D) $283.70

About two-thirds of aluminum cans are recycled today. Aluminum cans are the most sustainable beverage package on virtually every measure.

According to the Can Manufacturers Institute, aluminum cans are recycled at a rate of 63.6% in the United States in 2019. This means that more than two-thirds of aluminum cans are recycled, which makes aluminum cans one of the most recycled beverage containers in the world.

In the recycling process, the aluminum is shredded, melted, and formed into blocks called ingots. These ingots can be used to make new aluminum cans, which saves energy and conserves natural resources.

Aluminum cans are infinitely recyclable, which means they can be recycled repeatedly without losing quality. Recycling one aluminum can saves enough energy to power a TV for three hours, and it saves enough energy to light a 100-watt bulb for 20 hours.

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The length of side b is 56m, angle A is 45°, and angle C is 67°.

In the given triangle with side lengths a = 74m, b ≈ 56m, and c = 36m, the length of side b is approximately 56m.

To solve the triangle, we can use the Law of Cosines and the fact that the sum of angles in a triangle is 180 degrees. Given angle B = 67°51', we have:

Using the Law of Cosines, we have:

b² = a² + c² - 2ac * cos(B)

Substituting the known values:

b² = 74² + 36² - 2 * 74 * 36 * cos(67°51')

Calculating the value of b:

b ≈ √(74² + 36² - 2 * 74 * 36 * cos(67°51'))

b ≈ 55.92m (rounded to the nearest whole number, b ≈ 56m)

Using the Law of Cosines again, we have:

cos(A) = (b² + c² - a²) / (2 * b * c)

Substituting the known values:

cos(A) = (56² + 36² - 74²) / (2 * 56 * 36)

Calculating the value of A:

A = cos⁻¹((56² + 36² - 74²) / (2 * 56 * 36))

A ≈ 45° (rounded to the nearest whole number)

Using the fact that the sum of angles in a triangle is 180 degrees:

C = 180° - A - B

Substituting the known values:

C ≈ 180° - 45° - 67°51'

Calculating the value of C:

C ≈ 67°9' (rounded to the nearest whole number, C ≈ 67°)

Therefore, in the given triangle, the length of side b is approximately 56m, angle A is approximately 45°, and angle C is approximately 67°.

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Answer: 4

Step-by-step explanation:

Plug 3 in for x.

f(3) = (3)^2-6(3)+13

f(3) = 9-18+13

f(3) = -9+13

f(3) = 4

The point (11,11) will lie on the graph of the function f(x) = IxI

What is coordinate?

The x-coordinate informs us of a point's separation from the y-axis, which is the vertical axis. The abscissa is another term for the x-coordinate. The y-coordinate shows how far a point is from the horizontal axis, or x-axis. The term "ordinate" also applies to the y-coordinate.

the function: f(x) = IxI

The function will have every positive and negative integer contained within itself.

So coordinates of another point with the same y value (11,11) will lies on the graph so as (-11,11).

Hence point (11,11) will lie on the graph of the function f(x) = IxI

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Answer:

37.1

Step-by-step explanation:

12²=144

39²= 1521

1521-144 =1377

Then find the square root of 1377

=37.1

The correct unit of measure for the mean of the sampling distribution of I is A. Dollars.

The original distribution of prices for the car model is given in dollars, and the mean of the sampling distribution represents the average price of a random sample of 4 cars from that distribution. Hence, the correct unit of measure should be in dollars also.

In statistics, the mean is a measure of central tendency that represents the average value of a dataset. It is calculated by adding up all the values in a dataset and dividing by the number of observations. The formula for the mean of a dataset is:

mean = (sum of observations) / (number of observations)

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Answer:

honest or no?

Step-by-step explanation:

Answer:

0.54

Step-by-step explanation:

sin 105 / 2 = sin 15 / b

b = sin 15 / 0.48296

b = 0.54

Answer:

Step-by-step explanation:

Given the function

f(x) = 4(4x + 3)(x + 1)² (x^2– 3)

The x-intercept occurs at a point where f(x) = 0

f(x) = 4(4x + 3)(x + 1)² (x^2– 3)

4(4x + 3)(x + 1)² (x^2– 3) = 0

4x+3 = 0

4x = -3

x = -3/4

(x + 1)² = 0

x + 1 = 0

x = 0-1

x = -1

x^2-3 = 0

x^2 = 0+3

x^2 = 3

x  = ±√3

hence the x intercepts are -3/4, -1, √3 and -√3. This shows that there are 4 x intercepts

The true statement is: "Octave is the name of a particular interval size."

In music theory, an octave refers to the interval between two pitches where the higher pitch has a frequency that is exactly twice that of the lower pitch. It represents a doubling or halving of the frequency. For example, if we start on the note A and move up to the next A, we have traversed an octave.

An interval, on the other hand, refers to the distance between two pitches. It is the numerical representation of the difference in pitch between two notes.

The statement mentioning "interval as the name of a particular octave size" is incorrect because the octave is a specific interval size, not the other way around.

The statement suggesting that "the fifth is a kind of octave" is also incorrect. The fifth is a specific interval that represents the distance of five diatonic scale steps between two pitches.

Lastly, the statement that "a synonym for distance is octave" is not true. While an octave represents a specific interval size, the term "distance" is a more general term that can refer to the measurement between any two pitches, regardless of the specific interval size.

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The volume generated by rotating the region bounded by the curves y = 10x - x^2 and y = 21 about the line x = 3 is 79π/3 cubic units.

To use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves y = 10x - x^2 and y = 21 about the line x = 3, we need to:

Express the curves in terms of x.

y = 10x - x^2 -> x^2 - 10x + y = 0 -> x = 5 ± sqrt(25 - y)

y = 21 -> this is a horizontal line

The region is bounded by the curves and the vertical lines x = 0 and x = 10. When we rotate the region about the line x = 3, we will create cylindrical shells with radius 3 and height Δy.

Therefore, the limits of integration will be from y = 0 to y = 21.

Express the volume V as an integral using the formula for the volume of cylindrical shell:

V = 2π∫(radius)(height)(thickness)dy

Since we are rotating about the line x = 3, the radius of each cylindrical shell is 3 - x. The height of each shell is given by the difference in the y-values of the curves at a given x-value, or y = 21 - (10x - x^2). The thickness of each shell is dy.

So we have:

V = 2π∫(3 - x)(21 - (10x - x^2))dy from y = 0 to y = 21

Evaluate the integral.

V = 2π∫(3 - x)(21 - (10x - x^2))dy from y = 0 to y = 21

= 2π∫(3 - x)(21 - 10x + x^2)dy from y = 0 to y = 21

= 2π∫(21(3 - x) - 10x(3 - x) + x^2(3 - x))dy from y = 0 to y = 21

= 2π∫(-x^3 + 13x^2 - 39x + 63)dy from y = 0 to y = 21

= 2π[-(1/4)x^4 + (13/3)x^3 - (39/2)x^2 + 63x] from x = 5 - sqrt(4) to x = 5 + sqrt(4)

= 2π[(79/12) + (79/12)] (after simplification)

= 79π/3

Therefore, the volume bounded by the curves y = 10x - x^2 and y = 21 about the line x = 3 is 79π/3 cubic units.

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Answer:

See below

Step-by-step explanation:

The number of loaves of bread remaining can only go as low as ZERO (you can't have negative loaves) ...and can only go as high as when h = 0

     so    0 = 42-3.5 h    

             3.5 h = 42

                h = 12       and   min is  h = 0   ( when there are 42 loaves to start)

So:

0≤ h ≤ 12

Answer:

15

Step-by-step explanation:

-20 is to the left on the number line which signifies that it is of low numerical value.

15 on the other hand is to the right on the number line which signifies that it holds still low but greater numerical value.

Hope this helps you and have a great day!

The most appropriate variable type is usually level variables or positive variables for a linear program (LP).

In GAMS (General Algebraic Modeling System), there are several variable types available. The five permissible variable types in GAMS are:

1.These variables can take any real value within a defined range. They are typically used in models where quantities can vary continuously, such as production levels or resource allocations.

2.These variables are similar to level variables, but they are constrained to be non-negative. They are commonly used to represent quantities that cannot be negative, such as production quantities or inventory levels.

3.Binary variables can take only two possible values, typically 0 or 1. They are commonly used to represent decisions or choices, where 0 indicates the absence or non-selection of an option, and 1 indicates the presence or selection of an option.

4.Integer variables can take only integer values. They are used when the decision variables need to be restricted to whole numbers, such as representing the number of units to produce or the number of employees to hire.

5.These variables can take a value of either zero or any nonnegative real number within a specified range. They are used to model situations where there is a fixed cost associated with using a resource or when there are minimum usage requirements.

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Answer:

2−12x+36

Step-by-step explanation:

Answer:

(x-6)² = (x-6)(x-6) = x² - 12x + 36

Step-by-step explanation:

The percentage of all possible values of the variable is 5.05 and 14.95

Given, mean= 10, and variance= 3.

P(6 <X<7)= P( (6-10)/3< Z< (7-10)/3 )

=P(-1.33<Z<-1)

=P(Z<-1)- P(Z<-1.33)

=0.669

P(X<=17.5)= P(Z<=(17.5-10)/3)

=P(Z<=2.5)

=0.9938

We need to find x’, such that P(X>=x’)=0.15

=>P(Z>= (x’-10)/3)= 0.15

=>P(z<= (x’-10)/3)= 0.85

Using the Normal table, (x’-10)/3 = 1.04

x’=13.11

We need to find x” such that P(X<=x”)= 0.05

>=P(Z<=(x”-10)/3)= 0.05

Using the Normal Table, (x”-10/3)= -1.65

x”= 5.05

Also, another value x’’’=> 10+ 1.65*3= 14.95

Therefore, the two values are 5.05 and 14.95

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Answer:

AC = 6√3 in

Step-by-step explanation:

Join OC. Now ΔAOC is an isosceles triangle as OA = OC =radius.

 ∠A = ∠C = 30.

 ∠A + ∠C +  ∠AOC = 180 {angle sum property of traingle}

 30 + 30 + ∠AOC  = 180°

                 ∠AOC = 180 -60

                 ∠AOC = Ф = 120°

Find the length of radius using the bellow formula.

         \(\sf \boxed{\bf Arc \ length = \dfrac{\theta}{180}\pi r}\)

            Ф = 120°

                Arc length = 4π

            \(\sf 4\pi =\dfrac{120}{180}*\pi *r\\\\ r =\dfrac{4\pi * 180}{120*\pi }\\\\ r = 6 \ in\)

\(\sf \boxed{\bf chord \ length = 2rSin \ \dfrac{\theta}{2}}\)

                         \(\sf b = 2*6*Sin \ \dfrac{120}{2}\\\\ b = 2 *6 * Sin \ 60^\circ\\\\ b = 2 * 6 * \dfrac{\sqrt{3}}{2}\\\\ \b = 6\sqrt{3}\)

\(\sf \boxed{\bf AC = 6\sqrt{3} \ in}\)

Question 5

The remaining interior angle is \(135^{\circ}\).

\(\frac{x}{\sin 19^{\circ}}=\frac{32}{\sin 135^{\circ}}\\ \\ x=\frac{32 \sin 19^{\circ}}{\sin 135^{\circ}} \\ \\ x \approx 14.7\)

Question 6

The remaining interior angle is \(27^{\circ}\).

\(\frac{x}{\sin 27^{\circ}}=\frac{28}{\sin 75^{\circ}}\\\\x=\frac{28\sin 27^{\circ}}{\sin 75^{\circ}}\\\\x \approx 13.2\)

Question 7

The remaining interior angle is \(59^{\circ}\).

\(\frac{x}{\sin 59^{\circ}}=\frac{9}{\sin 70^{\circ}}\\\\x=\frac{9\sin 59^{\circ}}{\sin 70^{\circ}}\\\\x \approx 8.2\)

Question 8

The remaining interior angle is \(95^{\circ}\).

\(\frac{x}{\sin 33^{\circ}}=\frac{16}{\sin 95^{\circ}}\\\\x=\frac{16 \sin 33^{\circ}}{\sin 95^{\circ}}\\\\x \approx 8.7\)

Answer:

D

Step-by-step explanation:

The slope of the line is - 1/4. The equation of the line is y=(-1/4x)+5

The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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Answer:

Theta of the whole set of this equation is the answer to the question

The statement that's true about the triangle is that WXY + YXZ = 180°.

It should be noted that in the question, the options are related to a linear pair.

According to the linear pair, when a line cuts another line at a point, then the sum of the adjacent angles formed at the point will be 180°.

Therefore, WXY + YXZ = 180°.

The correct option is C.

The complete question is:

Which statement regarding the diagram is true?

m∠WXY = m∠YXZ

m∠WXY < m∠YZX

m∠WXY + m∠YXZ = 180°

m∠WXY + m∠XYZ = 180°

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Answer:

the second and last sentences.

Step-by-step explanation:

Its the most reasonable!

Answer:

It is accutally 1st 2nd and 3rd plz trust me

Step-by-step explanation:

it is the corect

Answer:

Lowest to highest

7/10 ,  11/15,   4/5

Step-by-step explanation:

Probably the easiest way to do this is to convert each of the fractions to decimals which will clearly indicate which is the highest and which the lowest etc.

4/5 = 0.80

11/15 = 0.73

7/10 = 0.7

0.7 is less than 0.73 is less than 0.80
So 7/10, 11/15, 4/5

However, I am assuming they want you to work with fractions

To compare fractions you have to get all the denominators equal and then compare the numerator

To get a common denominator find the Least Common Multiple of the denominators. This is the lowest number that can be divided by all three denominators

Looking at 5, 15 and 10 we can see that 30 is divisible by each denominator. So that becomes our common denominator

Now multiply each fraction denominator by a factor to make the denominator equal to the common denominator. At the same time multiply the numerator by the same factor

4/5 = (4 x 6) / (5 x 6) = 24/30    Highest

11/15 = (11 x 2) / (15 x 2) = 22/30

7/10 = (7 x 3) / (10 x 3) = 21/30      Lowest

Looking at the numerator alone we can see that 7/10 is the lowest, 11/15 is next lowest and 4/5 the highest

Since 50 is an even number, we know that x will be even if y is even (50 times an even number is still even) and odd if y is odd (50 times an odd number is odd). Therefore, the only answer choice that must be odd is x+y.

Given that x and y are integers and x = 50y + 69, let's determine which of the following expressions must be odd.

1. xy: Since x is odd (50y + 69), when it is multiplied by any integer y, the result will always be odd. Therefore, xy must be odd.

2. x + y: If x is odd, adding it to an even integer (y) would result in an odd number. However, adding it to an odd integer (y) would result in an even number. Therefore, x + y does not necessarily have to be odd. xy: We can't determine if this is odd or even without knowing the values of x and y.
- x+y: This expression is always odd. To see why, consider two cases:

If x and y are both odd, then x+y is even+odd=odd.
If x and y are both even, then x+y is even+even=even.
If one of x and y is odd and the other is even, then x + y is odd + even =odd.

3. x+2y: We can't determine if this is odd or even without knowing the values of x and y.
3x-1: This expression will be odd if x is odd (3 times an odd number is odd) and even if x is even (3 times an even number is even).
3x+1: This expression will be odd if x is even (3 times an even number plus 1 is odd) and even if x is odd (3 times an odd number plus 1 is even).
x + 2y: Since x is odd and 2y is always even, their sum must be odd. Therefore, x + 2 y must be odd.

4. 3x - 1: This expression is odd, since 3x will always be odd (as x is odd) and subtracting 1 from an odd number results in an even number. Therefore, 3x - 1 does not necessarily have to be odd.

5. 3x + 1: This expression is odd, since 3x will always be odd (as x is odd) and adding 1 to an odd number results in an even number. Therefore, 3x + 1 must be odd.

In conclusion, the expressions that must be odd are xy, x + 2y, and 3x + 1.

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