Find the probability of drawing
the desired marbles.
1 Orange
and
1 Blue
No Replacement
What's the probability of
drawing an orange marble?
[?] 1
10
X
금

Answer:

-3,-2,-1 is less than -4 and not greater than

Step-by-step explanation:

Answer:

972 square feet

Step-by-step explanation:

length, a, of rectangle with  width, b, will have area a X b (simplified to just ab).

so area = 36 (feet) X 27 (feet) = 972 (square feet)  

Answer:

The answer is 2,000,

Step-by-step explanation:

Probability :- Probability is a way to gauge how likely something is to happen. It is represented by a number between [tex]0[/tex] and [tex]1[/tex], with [tex]0[/tex] denoting an impossibility and [tex]1[/tex] denoting a certainty. By dividing the number of favorable outcomes by the total number of possible outcomes, the probability of an event is determined.

A total of  [tex]32 + 40 + 300 = 372[/tex]  children either take bus number seven, bus number ten, or walk to school.

The proportion of students that ride bus [tex]7[/tex] or bus [tex]10[/tex] to the total number of students determines the likelihood that a student will board either bus [tex]7[/tex]or bus [tex]10[/tex].

[tex]P(taking bus number seven or ten) = (32 + 40) / 1000[/tex]

[tex]P(taking bus number seven or ten) = 72/1000[/tex]

[tex]P(using bus number 7 or ten) = 0.072[/tex]

Therefore, the probability that the student either rides on bus 7 or rides on bus 10 is 0.072 or 7.2%.

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The value of the missing side length x in the right triangle is 15 inches.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

( hypotenuse )² = ( leg 1 )² + ( leg 2 )²

The image in the diagram is a right triangle:

Hypotenuse = 17 inches

Leg 1 = 8 inches

Leg 2 = x

To solve for x, we use the pythagorean theorem.

( hypotenuse )² = ( leg 1 )² + ( leg 2 )²

( leg 2 )² = ( hypotenuse )² - ( leg 1 )²

( leg 2 )² = ( 17 )² - ( 8 )²

( leg 2 )² = 289 - 64

( leg 2 )² = 225

Take the square roots

Leg 2 = √225

Leg 2 = 15 inches.

Therefore, the value of x is 15 inches.

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The equation of the polynomial is f ( x ) = -13.5 ( x + 2 )²( x - 3 )

Given data ,

The equation of degree 3 polynomial function with real coefficients

And ,  zeros x = - 2 with multiplicity 2 and x = 3 with multiplicity 1

where function passes through the point (1, 54)

If a polynomial function has a zero x = a with multiplicity k, then the factor (x - a)^k appears in its factored form.

Therefore, a degree 3 polynomial function with zeros x = -2 with multiplicity 2 and x = 3 with multiplicity 1 can be written in factored form as:

f(x) = a(x + 2)²(x - 3)

where a is a constant factor. To find the value of a, we use the fact that the function passes through the point (1, 54):

f(1) = a(1 + 2)²(1 - 3) = 54

a(-1)²(-2) = 54

-4a = 54

Divide by -4 on both sides , we get

a = -13.5

Hence , the equation of the degree 3 polynomial function with the given zeros and passing through the point (1, 54) is f ( x ) = -13.5 ( x + 2 )²( x - 3 )

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The required perimeter of the equilateral triangle is 12.72 cm.

An equilateral triangle has all three sides equal in length. Therefore, if the edge of an equilateral triangle is 4.24 cm, then all three sides are 4.24 cm.

To find the perimeter of the equilateral triangle, we need to add the length of all three sides together:

Perimeter = 4.24 cm + 4.24 cm + 4.24 cm

Perimeter = 12.72 cm

Therefore, the perimeter of the equilateral triangle is 12.72 cm.

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Applying the angle of intersecting secant-tangent theorem, the measure of arc VT is calculated as: m(VT) = 116°.

Given that the lines appear tangent, the measure of the arc VT indicated above can be calculated using the angle of intersecting secant-tangent theorem which states that:

m<U = 1/2(m(WT) - m(VT))

Given the following:

measure of angle U = 37 degrees.

measure of arc WT = 190 degrees.

Plug in the values:

37 = 1/2(190 - m(VT))

74 = 190 - m(VT)

m(VT) = 190 - 74

m(VT) = 116°

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When not considering the order of choice, there are also 3 ways to choose 2 letters from a, b, and c.

When choosing 2 letters without replacement from the 3 letters a, b, and c, the number of ways can be calculated considering the order of choice and without considering the order of choice.

1. Considering the order of choice:

In this case, the order in which the letters are chosen matters. We can think of this as a permutation problem.

To calculate the number of ways when order matters, we use the formula for permutations:

[tex]nPr = n! / (n - r)![/tex]

where n is the total number of items and r is the number of items chosen.

In this case, we have 3 letters and we want to choose 2, so n = 3 and r = 2.

Using the formula, we get:

[tex]3P2 = 3! / (3 - 2)![/tex]

 [tex]= 3! / 1![/tex]

    = 3

Therefore, when considering the order of choice, there are 3 ways to choose 2 letters from a, b, and c.

2. Without considering the order of choice:

In this case, the order in which the letters are chosen does not matter. We can think of this as a combination problem.

To calculate the number of ways when order does not matter, we use the formula for combinations:

[tex]nCr = n! / (r!(n - r)!)[/tex]

Using the same values of n = 3 and r = 2, we get:

[tex]3C2 = 3! / (2!(3 - 2)!)[/tex]

    = [tex]3! / (2! * 1!)[/tex]

    = 3

Therefore, when not considering the order of choice, there are also 3 ways to choose 2 letters from a, b, and c.

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Answer: 5, 9

Step-by-step explanation:

factors of 45:

1, 3, 5, 9, 15, 45

Sums: 46, 24, 14

the factors 5 and 9 multiply to get 45 and add to get 14

voila!

Part A: The total value of the loan with simple interest is $59,660.50.

Part B: The total value of the loan with quarterly compounded interest is $60,357.91.

Part C: The total value of the loan with continuously compounded interest is $60,441.82.

Part D: The best choice for the small business owner is the loan with simple interest, as it has the lowest total value and thus the lowest cost to repay.

Part A:

To calculate the total value of the loan with simple interest, we can use the formula:

[tex]Total value = Principal \times (1 + interest rate \times time)[/tex]

Where,

Principal = $50,000

Interest rate = 5.25% = 0.0525

Time = 3 years and 8 months = 3.67 years.

[tex]Total $ value = $50,000 \times (1 + 0.0525 \times 3.67) = $59,660.50[/tex]

Therefore, the total value of the loan with simple interest is $59,660.50.

Part B:

To calculate the total value of the loan with quarterly compounded interest, we can use the formula:

[tex]Total value = Principal \times (1 + (interest rate / n))^{(n \times time) }[/tex]

Where,

Principal = $50,000

Interest rate = 5.25% = 0.0525

Time = 3 years and 8 months = 3.67 years

n = 4 (since interest compounds quarterly)

[tex]Total value = $50,000 \times (1 + (0.0525 / 4))^{(4 \times3.67) } = $60,357.91[/tex]

Therefore, the total value of the loan with quarterly compounded interest is $60,357.91.

Part C:

To calculate the total value of the loan with continuously compounded interest, we can use the formula:

[tex]Total value = Principal \times e^{(interest rate \times time)}[/tex]

Where,

Principal = $50,000

Interest rate = 5.25% = 0.0525

Time = 3 years and 8 months = 3.67 years

[tex]Total value = $50,000 \times e^{(0.0525 \times 3.67) } = $60,441.82[/tex]

Therefore, the total value of the loan with continuously compounded interest is $60,441.82.

Part D:

From the calculations in Parts A, B, and C, we can see that the loan with continuously compounded interest has the highest total value of $60,441.82.

This is followed by the loan with quarterly compounded interest with a total value of $60,357.91, and finally the loan with simple interest with a total value of $59,660.50.

Therefore, the best choice for the small business owner would be to take the loan with simple interest, as it has the lowest total value and thus the lowest cost to repay.

However, if the small business owner is willing to pay a higher cost for the loan, they could consider the loan with quarterly or continuously compounded interest, which have higher total values.

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The mean and standard deviation are less than 88 peanuts: z = (88 - 94) / 3 = -2

between 88 and 91 peanuts: z = (91 - 94) / 3 = -1

between 91 and 94 peanuts: z = (94 - 94) / 3 = 0

between 94 and 97 peanuts: z = (97 - 94) / 3 = 1

greater than 97 peanuts: z = (97 - 94) / 3 = 1

The probability that a 16-ounce can of Nut Munchies will contain between 88 and 97 nuts is 0.8186, or approximately 82%.

The probability of the former event is 0.4772, which is greater than the probability of the latter event, which is 0.1587.

(a) The intervals below the normal distribution can be labeled using z-scores, which are calculated using the formula:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

The intervals and their corresponding z-scores are:

less than 88 peanuts: z = (88 - 94) / 3 = -2

between 88 and 91 peanuts: z = (91 - 94) / 3 = -1

between 91 and 94 peanuts: z = (94 - 94) / 3 = 0

between 94 and 97 peanuts: z = (97 - 94) / 3 = 1

greater than 97 peanuts: z = (97 - 94) / 3 = 1

(b) To find the probability that a 16-ounce can of Nut Munchies will contain between 88 and 97 nuts, we need to find the area under the normal distribution curve between the corresponding z-scores. Using a standard normal distribution table or a calculator, we can find that:

P(88 ≤ X ≤ 97) = P(-2 ≤ Z ≤ 1) = 0.8186

Therefore, the probability that a 16-ounce can of Nut Munchies will contain between 88 and 97 nuts is 0.8186, or approximately 82%.

(c) To determine which event is more likely, we can compare the probabilities of each event. Using the same method as in part (b), we can find that:

P(88 ≤ X ≤ 94) = P(-2 ≤ Z ≤ 0) = 0.4772

P(X > 97) = P(Z > 1) = 0.1587

Therefore, it is more likely for a 16-ounce can of Nut Munchies to have between 88 and 94 nuts than to have over 97 nuts, since the probability of the former event is 0.4772, which is greater than the probability of the latter event, which is 0.1587.

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The segment lengths for this problem are given as follows:

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates given by [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Hence the length of segment AB is given as follows:

[tex]AB = \sqrt{(2 - (-5))^2 + (4 - 4)^2} = 7[/tex]

The length of segment AE is given as follows:

[tex]AE = \sqrt{(-5 - (-5))^2 + (4 - (-5))^2} = 9[/tex]

The length of segment BC is given as follows:

[tex]BC = \sqrt{(5-4)^2 + (5 - (-5))^2} = 10.05[/tex]

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Answer:

15

if you count the length and breadth with the height and multiply them it'll give you 15

Diagonals that bisect each other: Rhombus, Rectangle, Square.

Diagonals that bisect each other and are congruent: Rectangle, Square.

Diagonals that bisect each other and are perpendicular to each other: Square.

A parallelogram does not necessarily have diagonals that bisect each other.

A rhombus has diagonals that bisect each other.

This means that the diagonals intersect at their midpoints.

A rectangle has diagonals that bisect each other.

Additionally, the diagonals of a rectangle are congruent, meaning they have the same length.

A square has diagonals that bisect each other.

The diagonals of a square are congruent and perpendicular to each other.

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The volume of each figure is given below:

Figure 1: [tex]819 \ feet[/tex]³

Figure 2: [tex]1,728 \ m[/tex]³

Figure 3: [tex]10,696 \pi[/tex] yards³

Figure 4: [tex]1,079.5[/tex] m³

Figure 5: [tex]4,680[/tex] yards³

Figure 1: In the first figure we can see a Cuboid. So below is the method to find the cuboid's volume:

Given dimensions:

Length (l) = [tex]9[/tex] feet, Breadth (b) = [tex]13[/tex] feet, Width (w) = [tex]7[/tex] feet.

Formula:

[tex]\[ V = l \times b \times w \][/tex]

[tex]\[ V = 9 \, \text{feet} \times 13 \, \text{feet} \times 7 \, \text{feet} \][/tex]

Figure 2: In the given figure we see a Prism. Below is the method to find its volume:

Given dimensions:

Hypotenuse = [tex]15[/tex] m, Base = [tex]9[/tex] m, Height = [tex]12[/tex] m, Width = [tex]16[/tex] m.

Formula:

[tex]\[ V = \text{Base} \times \text{Height} \times \text{Width} \][/tex]

[tex]\[ V = 9 \, \text{m} \times 12 \, \text{m} \times 16 \, \text{m} \][/tex]

Figure 3: Here we have the method to find the volume of a Cylinder:

Given dimensions:

Length (l) = [tex]26[/tex] yards, Radius (r) = [tex]11[/tex] yards.

Formula:

[tex]\[ V = \pi \times r^2 \times l \][/tex]

[tex]\[ V = \pi \times (11 \, \text{yards})^2 \times 26 \, \text{yards} \][/tex]

Figure 4: Here, we have the method to find the volume of a Cuboid:

Given dimensions are:

Length (l) = [tex]9[/tex] m, Breadth (b) = [tex]9[/tex] m, Height (h) = [tex]13.5[/tex] m.

Formula:

[tex]\[ V = l \times b \times h \][/tex]

[tex]\[ V = 9 \, \text{m} \times 9 \, \text{m} \times 13.5 \, \text{m} \][/tex]

Figure 5: Next figure is a Prism.

The dimensions that have been given to us are:

Hypotenuse = [tex]15[/tex] yards, Base = [tex]15[/tex] yards, Height = [tex]13[/tex] yards, Width = [tex]24[/tex] yards.

Formula:

[tex]\[ V = \text{Base} \times \text{Height} \times \text{Width} \][/tex]

Now we will calculate it according to the values given in the question:

[tex]\[ V = 15 \, \text{yards} \times 13 \, \text{yards} \times 24 \, \text{yards} \][/tex]

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Answer:

The median is the best measure of center, and it equals 19.

Step-by-step explanation:

The line for the median is exactly on 19

The line in the box of a box plot represents the median of the data. For this particular data set shown in the box plot, the median is 19.

In the described box plot, the line in the box that is at the number 19 represents the median of the data. This is because a box plot illustrates the five number summary of a data set: the minimum, the first quartile, the median (second quartile), the third quartile, and the maximum. The line inside the box always represents the median. Therefore, the correct choice is: The median is the best measure of center, and it equals 19.

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At the end of 2 years, Jackson's account balance is $700.40.

We have,

The formula for calculating simple interest is:

I = Prt

Where:

I is the interest earned

P is the principal amount

r is the interest rate

t is the time period

In this case,

Jackson invested $680.00 at an annual interest rate of 1.5% for 2 years. Therefore:

P = $680.00

r = 1.5% = 0.015

t = 2 years

Plugging these values.

I = Prt = $680.00 x 0.015 x 2 = $20.40

So,

Jackson earned $20.40 in interest over 2 years.

To find his total account balance at the end of 2 years, we need to add the interest earned to the initial principal:

Total balance

= $680.00 + $20.40

= $700.40

Therefore,

At the end of 2 years, Jackson's account balance is $700.40.

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4.5 mm is the measurement of the given line AB.

In the given graph both lines AE and BD are parallel.

So, the ratio between the two lines will be the same,

Thus, from the above property

AC/AB= EC/ED

in the given case,

AC =36 mm

EC = 72 mm

ED = 9 mm

Substitute the value in the above equation,

36/AB = 72/9

AB = 9/2

AB = 4.5 mm

Therefore, the measurement of line AB is 4.5 mm.

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The correct answer is Add all of the numbers, then divide.

Given that we need to determine which choice demonstrates the process for calculating the mean,

We know that the mean is calculated by,

You must add up all the values in a dataset and divide the total by the overall number of values in order to determine the mean, also known as the average.

The following steps should be followed to determine the mean:

Add up all the figures.

Subtract the amount from the overall value set.

In order to determine the mean, the option "Add all of the numbers, then divide" is the proper course of action.

Hence the correct answer is Add all of the numbers, then divide.

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Answer:

40 is the surface area.

Explanation on hiw to get the answer:

The graph of the function is added as an attachment

The asymptote: y = 7 and the points are (-5, 6) and (-7, -18)

From the question, we have the following parameters that can be used in our computation:

f(x) = -(1/5)ˣ ⁺ ⁵+ 7

The above function is an exponential function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment, where we have the following points

Asymptote: y = 7

(-5, 6) and (-7, -18)

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The angles that we can determine their measure are ∠1, ∠5, ∠6, and ∠7.

option A is the correct answer.

The measure of the angles of the polygon is calculated as follows;

The following angles were given;

angle 3 = 60⁰

angle 8 = 135⁰

The following angles can be determined as follows;

angle 5 = 180 - 60⁰  ( sum of angles on a straight line )

angle 5 = 120⁰

angle 7 = angle 3 = 60⁰ (corresponding angles )

angle 5 = angle 1 = 120⁰  (corresponding angles )

The value of angle 6 is calculated as;

∠5 + ∠6 + ∠7 + ∠8 = 360 (sum of angles in quadrilateral)

120 + ∠6 + 60 + 135 = 360

315 + ∠6 = 360

∠6 = 360 - 315

∠6 = 45⁰

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In this example, a positive relationship between the x- and y-values is demonstrated. This basically demonstrates that when one value increases, the other typically does too, and vice versa when one value decreases in the graph.

An x and y coordinate plane with values between -6 and +10 is displayed on the graph.

The points (2, 0), (4, 2), (6, 4), (negative 2, negative 4), and (negative 4, negative 6) are all connected by a line. The y values rise in proportion to the x values because the line has a positive slope.

In this example, a positive relationship between the x- and y-values is demonstrated. This basically demonstrates that when one value increases, the other typically does too, and vice versa when one value decreases.

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The complete question is-

Which statement describes the relationship between the x- and y-values shown in the graph?

A coordinate plane has x-axis and y-axis with values ranging from negative 6 to 10. A positive slope passes through the points (negative 4, negative 6), (negative 2, negative 4), (2, 0), (4, 2), and (6, 4).

The solutions to the original equation are:

x = π - 3π/2 = -π/2

x = 3π/2 - 3π/2 = 0

So the values of x that satisfy the equation are -π/2 and 0.

To solve the given equation, we can use the following             trigonometric identity:

sin(A) + sin(B) = 2*sin((A+B)/2)*cos((A-B)/2)

Applying this identity to sin(3π/2+x) + sin(3π/2+x), we get:

sin(3π/2+x) + sin(3π/2+x) = 2*sin((3π/2+x + 3π/2+x)/2)cos((3π/2+x - 3π/2+x)/2)

= 2sin(3π/2+x)cos(0)

= 2(-cos(x))

Therefore, the equation can be simplified to:

-2*cos(x) = 2

Dividing both sides by -2, we get:

cos(x) = -1

This means that x is either π or 3π/2, since those are the values where cos(x) = -1.

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Answer:

See below for proof.

Step-by-step explanation:

[tex]\boxed{\textsf{Prove that}\;\;\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(240^{\circ}+ A) = \sin^3A}[/tex]

Rewrite 240° as (180° + 60°):

[tex]\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(180^{\circ}+60^{\circ}+ A)[/tex]

As sin(180° + x) = -sin(x), we can rewrite sin³(180° + 60° + A) as:

[tex]\sin^3(180^{\circ}+60^{\circ}+ A)=-\sin^3(60^{\circ}+ A)[/tex]

Substitute this into the expression:

[tex]\sin^3A + \sin^3(60^{\circ} + A) -\sin^3(60^{\circ}+ A)[/tex]

As the last two terms cancel each other, we have:

[tex]\sin^3A[/tex]

Hence proving that:

[tex]\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(240^{\circ}+ A) = \sin^3A[/tex]

As one calculation:

    [tex]\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(240^{\circ}+ A)[/tex]

[tex]=\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(180^{\circ}+60^{\circ}+ A)[/tex]

[tex]=\sin^3A + \sin^3(60^{\circ} + A) -\sin^3(60^{\circ}+ A)[/tex]

[tex]=\sin^3A[/tex]

[tex]\hrulefill[/tex]

[tex]\boxed{\textsf{Prove that}\;\;\sin^3A + \sin^3(120^{\circ} + A) + \sin^3(240^{\circ}+ A) = -\dfrac{3}{4}\sin 3A}[/tex]

Use the sine and cos double angle identities to rewrite sin(3x) in terms of sin(x):

[tex]\begin{aligned}\sin(3x)&=\sin(2x+x)\\&=\sin2 (x)\cos (x)+\sin (x)\cos2 (x)\\&=(2\sin (x)\cos (x))\cos (x)+\sin (x)(1-2\sin^2 (x))\\&=2\sin (x)\cos^2 (x)+\sin (x)-2\sin^3 (x)\\&=2\sin (x)(1-\sin^2 (x))+\sin (x)-2\sin^3 (x)\\&=2\sin (x)-2\sin^3 (x)+\sin (x)-2\sin^3 (x)\\&=3\sin (x)-4\sin^3 (x)\end{aligned}[/tex]

Rearrange to isolate sin³x:

[tex]\begin{aligned}\sin(3x)&=3\sin (x)-4\sin^3 (x)\\\\4\sin^3 (x)&=3\sin (x)-\sin (3x)\\\\\sin^3 (x)&=\dfrac{3\sin (x)-\sin (3x)}{4}\end{aligned}[/tex]

Use this expression to rewrite the terms in sin³A on the left side of the equation:

   [tex]\sin^3A + \sin^3(120^{\circ} + A) + \sin^3(240^{\circ}+ A)[/tex]

[tex]=\dfrac{3\sin A-\sin3A}{4}+ \dfrac{3\sin (120^{\circ} + A)-\sin (3(120^{\circ} + A))}{4}+\dfrac{3\sin (240^{\circ}+ A)-\sin (3(240^{\circ}+ A))}{4}[/tex]

[tex]=\dfrac{3\sin A-\sin3A+3\sin (120^{\circ} + A)-\sin (360^{\circ} + 3A)+3\sin (240^{\circ}+ A)-\sin (720^{\circ}+ 3A)}{4}[/tex]

As sin(x ± 360°n) = sin(x), we can simplify:

[tex]\sin(360^{\circ}+3A) = \sin (3A)[/tex]

[tex]\sin(720^{\circ}+3A) = \sin (3A)[/tex]

Therefore:

[tex]=\dfrac{3\sin A-\sin3A+3\sin (120^{\circ} + A)-\sin (3A)+3\sin (240^{\circ}+ A)-\sin (3A)}{4}[/tex]

[tex]=\dfrac{3\sin A-3\sin3A+3\sin (120^{\circ} + A)+3\sin (240^{\circ}+ A)}{4}[/tex]

Factor out the 3 in the numerator:

[tex]=\dfrac{3\left(\sin A-\sin3A+\sin (120^{\circ} + A)+\sin (240^{\circ}+ A)\right)}{4}[/tex]

Rewrite 240° = 180° + 60°:

[tex]\sin(240^{\circ} + A) = \sin(180^{\circ} + 60^{\circ} + A)[/tex]

As sin(180° + x) = -sin(x), we can rewrite sin(180° + 60° + A) as:

[tex]- \sin(60^{\circ} + A)[/tex]

Therefore:

[tex]=\dfrac{3\left(\sin A-\sin3A+\sin (120^{\circ} + A)-\sin (60^{\circ}+ A)\right)}{4}[/tex]

As sin(120° + x) = sin(60° - x) then:

[tex]=\dfrac{3\left(\sin A-\sin3A+\sin (60^{\circ} -A)-\sin (60^{\circ}+ A)\right)}{4}[/tex]

As sin(60° - x) - sin(60° + x) = -sin(x), then:

[tex]=\dfrac{3\left(\sin A-\sin3A-\sin A\right)}{4}[/tex]

Simplify:

[tex]=\dfrac{-3\sin3A}{4}[/tex]

[tex]=-\dfrac{3}{4}\sin3A[/tex]

Hence proving that:

[tex]\sin^3A + \sin^3(120^{\circ} + A) + \sin^3(240^{\circ}+ A) = -\dfrac{3}{4}\sin 3A[/tex]

Answer:

The flux of material past x = 0 is zero for all times.

The flux of material past x = 0 can be calculated by integrating the product of density and velocity over the spatial domain.

This is calculated as;

Φ = ∫ ρv dx

ρ = exp[cos(t − x)]

v = sin(t − x)

where;

The flux of material past x = 0 is calculated as;

Φ = ∫ exp[cos(t − x)] sin(t − x) dx

∫ exp[cos(t − x)] sin(t − x) dx, is the integration of an odd function over a symmetric interval [-π, π] which is zero.

Φ = ∫ exp[cos(t − x)] sin(t − x) dx = 0

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The probability that a randomly selected resident is in favor of the dog park is option

B. 7/18

To find the probability that a randomly selected resident is in favor of the dog park  we  have  to determine the number of residents who are in favor and divide it by the total number of residents surveyed

the number of residents in favor of the dog park

= in favor both male and female

=  19 + 16

= 35.

total number of residents surveyed is  90

the probability

P(In Favor) = Number of residents in favor / total number of residents surveyed

= 35 / 90

= 7/18

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The solution of the exponential equation is x = -16

From the question, we have the following parameters that can be used in our computation:

5^-x/16=5

Take the logarithm of both sides of the equation

So, we have the following representation

-x/16 log(5) = log(5)

Divide both sides of the equation by log(5)

-x/16 = 1

So, we have

x = -16 * 1

Evaluate

x = -16

Hence, the solution to the equation is x = -16

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