Hi can somebody please explain the second question and how you got it?

Thank you in advance!

The expression as product is sin(a)(4 + 2cos(a) - 4sin²(a))

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

sin(a)+sin(2a)+sin(3a)

By sine rule, we have

sin(a)+sin(2a)+sin(3a) = sin(a) + 2sin(a)cos(a) + sin(3a)

Factor out sin(a)

sin(a)+sin(2a)+sin(3a) = sin(a)(1 + 2cos(a)) + sin(3a)

Expanding sin(3a), we have

sin(a) + sin(2a) + sin(3a) = sin(a)(1 + 2cos(a)) + 3sin(a) - 4sin³(a)

So, we have

sin(a) + sin(2a) + sin(3a) = sin(a)(1 + 2cos(a) + 3 - 4sin²(a))

Evaluate the like terms

sin(a) + sin(2a) + sin(3a) = sin(a)(4 + 2cos(a) - 4sin²(a))

Hence, the product expression is sin(a)(4 + 2cos(a) - 4sin²(a))

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The cube has a surface area of 1536 inches².

A three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given [tex]$ \mathrm{S = 6V^{\frac{2}{3} }}[/tex]

S is surface Area ‘A’, in square units, of a cube

V is volume of cube in cubic units.

Now in the given question,

V = 4096 cubic inches

The formula below can be used to get the cube's surface area:

Surface area = [tex]$ \mathrm{ 6V^{\frac{2}{3} }}[/tex]

Surface area = 6 × [tex]4096^{\frac{2}{3} }[/tex]

Surface area = 6 × 16²  = 6  × 256

Surface area = 1536 inches²

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Proverbs 21:5 says, “The plans of the diligent lead to profit as surely as haste leads to poverty.” This verse encourages us to be diligent in our work as it is the path to success and profit.

Profit is the money left over when all expenses are paid. It is the reward for running a successful business. Profit is the additional income that results from a business venture beyond what is initially invested. It is a financial gain that is realized when the amount of revenue generated from a business activity exceeds the expenses, costs, and taxes needed to sustain the activity. Profit is an important measure of a business’s long-term viability and overall financial health.

Diligence, or hard work and perseverance, is the key to achieving anything. As we practice diligence, it will lead us to success and material gain. We will be rewarded in the end for our hard work.

Not only will diligence lead to financial gain, but it will also bring many other benefits. Diligence will create good habits, increase self-discipline, and help us to develop our skills. We will become more organized and efficient in our work, leading to better quality results. Hard work and diligence will also give us a sense of satisfaction and accomplishment which will bring more joy and fulfillment. In addition, it will also help us to build strong relationships with those around us, as our commitment to our work will be seen and appreciated.

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The function constructed is y = 90x + 60.

"Information available from the question"

Jahlil is saving money at a constant rate to buy a new TV. After saving for 3 months, After saving for 3 months, Jahlil has $330. After saving for 5 months, Jahlil has $510.

Let x represents the months

and y represents the dollars

To find the dollars/month and by finding the slope.

(3, 330), (5, 510)

[tex]\frac{510-330}{5-3}[/tex] = 90

Since its a constant rate, the function will be in the form, y = mx+b, and since we found the slope we can plug m=90.

y=90x+b

To find b, we simply substitute one of the points.

330 = 90(3) + b

b = 60

Thus, plugging it in,

y = 90x + 60

Hence, The function constructed is y = 90x + 60.

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The expression (2x + 7)(x - 3) is a factor of 2x^2 - 11x - 21.

Expression is a combination of variables, numbers, and operators (such as +, -, *, /) that represents a mathematical value. For example, 2x + 3, x^2 - 5x + 6, and (x + 2)(x - 3) are all expressions. Expressions can be simplified or evaluated to find their numerical value for a given value of the variable(s).

The expression (2x + 7)(x - 3) is a factor of 2x^2 - 11x - 21.

To see this, we can expand the right-hand side:

(2x + 7)(x - 3) = 2x(x) + 2x(3) + 7(x) - 7(3)

= 2x^2 + 6x + 7x - 21

= 2x^2 + 13x - 21

As we can see, (2x + 7)(x - 3) is indeed a factor of 2x^2 - 11x - 21.

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The existence, uniqueness, and minimum radius of convergence of a Taylor series expansion about a point depend on the function being expanded. In general, there is no guarantee that a Taylor series will exist or be unique for every function.

A Taylor series expansion of a function about a point is a representation of the function as an infinite sum of terms involving powers of the difference between the independent variable and the point. If the function is well-behaved near the point, its Taylor series will converge to the function within some interval around the point. The smallest such interval is called the radius of convergence.

If the function is infinitely differentiable (i.e. has derivatives of all orders) near the point, its Taylor series will converge to the function within the entire interval of convergence. In this case, the solution is said to be unique. However, if the function is not infinitely differentiable, it may not be possible to find a Taylor series that converges to the function, or there may be multiple Taylor series that converge to the function within different intervals.

The minimum radius of convergence of a Taylor series is difficult to determine in general, as it depends on the behavior of the function at infinity. In some cases, the radius of convergence can be estimated using techniques such as Cauchy-Hadamard theorem. However, in general, determining the exact radius of convergence requires knowledge of the behavior of the function at all points, not just near the point of expansion.

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The equations are H = 4x + 60 and P = 8x + 20. We need to rent 10 tables to ensure that the cost of the rental will be the same.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

Let us suppose tables as x.

Given that,

The happy party rents tables for $4 per table plus a delivery fee of 60. This is expressed as:

H = 4x + 60

Party Rental rents tables for $8 per table plus a $20 delivery fee.

P = 8x + 20

To get the same cost of the rent:

H = P

4x + 60 = 8x + 20

60 - 20 = 8x - 4x

40 = 4x

x = 10

Hence, we need to rent 10 tables to ensure that the cost of the rental will be the same.

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Considering all the given information, the probability that the subcommittee consists of 3 republicans is 0.0345, or 3.45%.

To find the probability that the subcommittee consists of 3 Republican’s, we first calculate the number of ways to choose 3 Republicans out of 5:

C(5, 3) = 5! / (3! (5 - 3)!)

=5! / (3! 2!)

= (5 ×4 × 3!) / (3 × 2 × 3!)

= (5 × 4) / (2 × 2)

= 10.

The total number of ways to choose 3 members out of a committee of 5 Republicans, 6 Democrats, and 2 Independents is:

C(13, 3) = 13! / (3! (13 - 3)!)

=13! / (3! 10!)

= (13 × 12 × 11 × 10!) / (3 × 2 × 1 × 10!)

= (13 × 12 × 11) / (3 × 2 × 1)

= 286

So the probability of choosing 3 Republicans is:

P(3 Republicans) = 10 / 286 = 1/29

Therefore the probability of the subcommittee consisting of 3 Republicans is approximately 0.0345, or 3.45%.

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Q: A Senate committee consists of 5 Republicans, 6 Democrats, and 2 Independents. A subcommittee of 3 members is randomly chosen. What is the probability that the subcommittee consists of three Republicans?

Answer:81

Step-by-step explanation: AB=base 1 DC=base 2

Base1+Base2 divided by 2

The length of the midsegment of the trapezoid is 81 units.

The midsegment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid.

The length of the midsegment of a trapezium is half the sum of the top and bottom of the trapezoid.

Therefore, let's find LM, the midsegment of the trapezoid.

Hence,

LM = 1 / 2 (AB + DC)

AB = 34

DC = 128

LM = 1 / 2 (34 + 128)

LM = 1 / 2 (162)

LM = 81

Therefore,

LM = 81 units

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so we know the EQUATion of the line, now let's work out the inequality of it.

the shaded area is the "true" region or area, and the non-shaded is the "false" region, hmmm let's work our way from the "false" region.

first off, the line is solid, that means the line includes values in the inequality, meaning the shaded part extends to the borderline, so the inequality will be either ⩾ or ⩽, let's work it out from the "false" region, by picking out a point there, hmmm let's use say x = 6 and y = -4, so the point is (6 , -4) and let's plug it in the EQUATion.

[tex]y ~~ \square ~~ \cfrac{3}{4}x-3\hspace{5em}(6~~,~-4)\qquad \implies \qquad -4 ~~ \square ~~ \cfrac{3}{4}(6)-3 \\\\\\ -4 ~~ \square ~~ \cfrac{18}{4}-3\implies -4 ~~ \square ~~ \cfrac{9}{2}-3\implies -4 ~~ \square ~~ \cfrac{9-6}{2}\implies -4 ~~ \square ~~ \cfrac{3}{2} \\\\\\ -4 ~~ \square ~~ 1.5\qquad \textit{is -4 greater or less than 1.5?}[/tex]

well, clearly -4 is less than 1.5, however to  make that a false statement, we can say that -4 is more than 15, now, is not true, is "false" and since we're working from the "false" region, that is what we need, "more than", or ⩾

[tex]{\Large \begin{array}{llll} y\geqslant \cfrac{3}{4}x-3 \end{array}}[/tex]

now, bear in mind that we could have started from the "true" region, the shaded one, and pick a point in it like (0 , 0), if you test, that gives us something like 0 [ ] -3, to make that true, we make it 0 ⩾ -3, because that is true, 0 is really greater than -3, and working for the "true" region, that's what we need.

Assuming that the order of the cities matters, the number of possible routes is 11! (11 factorial), which is 39916800.

The number of possible routes for an overnight express company that includes eleven cities on its route is 39916800. This is because when the order of the cities matters, the number of possible routes can be calculated by finding 11 factorial, which is:

This calculation results in 39916800, which means that there are 39916800 potential routes for an overnight express company with eleven cities on its route.

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Answer:

give the diagram please

Answer:

The measure of the missing angle is 37°.

Answer:Data and research on investment including guidelines for multinational enterprises, private sector development, FDI, bribery, conflict minerals and ...

Step-by-step explanation:

The value of q = 25.96

This can be solved using the concept of triangle similarity.

Triangulus, which means "three-cornered" or "having three angles," is a Latin word with roots in tri-, "three," and angulus, "angle or corner." Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed at a point where the three sides are joined end to end. The summation of the triangle's three angles equals 180 degrees. Triangles can be classified as equilateral, isosceles, or scalene depending on how long their sides are.

Consider, the triangle ABC and the mid-segment line becomes CD.

Now, from similarity

Δ DBA ≅ Δ ABC

AB² = BC. BD ............... (i)

Δ ADB ≅ Δ ABC

AD² = BD. CD ............. (ii)

thus, Δ ADC ≈ Δ ABC

AC² = BC. CD

Thus, q² = (17.5 + 21) × (17.5)

or, q² = 673.75

or, q = 25.96

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Each flower that Gavin bought will cost $0.875 and the approximate value of each flower will be $0.90

6.5 dozen of carnations = 6 × 12 + 6 (one dozen has 12 units)

(half dozen is half of 12 that is 6)

the total number of flowers Galvin bought = 72 + 6 = 78

total amount Gavin spent on carnations is $68.25

let the amount spent on one flower be x

then the ratio of flower to amount of flowers

ratio = [tex]\frac{net quantity}{amount}[/tex] = [tex]\frac{78}{68.25}[/tex] = [tex]\frac{1}{x}[/tex]

therefore, x = 1 × [tex]\frac{68.25}{78}[/tex]

x = 0. 875 or 0.88

x ≈ 0.90

∴ the approximate amount spent on one flower is $0.90

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Answer:

p = -4

q = 9

Step-by-step explanation:

The vertex form of a parabola is:

y = a (x − h)² + k

Given that the leading coefficient is 1 and the vertex is (2,5):

y = (x − 2)² + 5

Distributing:

y = x² − 4x + 4 + 5

y = x² − 4x + 9

Alternatively, using calculus, if y = x² + px + q, then the derivative is:

dy/dx = 2x + p

The turning point occurs when the derivative is 0:

0 = 2x + p

0 = 2(2) + p

p = -4

Plugging in and solving for q:

y = x² − 4x + q

5 = (2)² − 4(2) + q

5 = 4 − 8 + q

q = 9

Answer: A

Step-by-step explanation:

Flame length = l

Fire speed = s

In graph d, when l = 10, s does not equal 2.

It is eliminated.

In graph b, when l = 35, s=8, but in the graph, when l=30, s=8.

It is eliminated.

In graph c, when l=50, s=9, but in the graph when l=55, s=9.

It is eliminated.

The correct answer is a.

Answer:

Step-by-step explanation:

Here are the steps to write the polynomial -15y + 12y² - 9y as a product of polynomials in standard form:

Factor out the coefficient of the linear term: -15y = -15 * y

Factor out the coefficient of the quadratic term: 12y² = 12 * y^2

Add the two factored polynomials: -15 * y + 12 * y^2 - 9 * y

Simplify the expression: (-15 * y + 9 * y) + 12 * y^2 = -6 * y + 12 * y^2

And there you have it, the polynomial -15y + 12y² - 9y can be written as a product of two polynomials in standard form, -6 * y + 12 * y^2.

18,995 × 0.82^(6) = $5,774 so he should not sell

if the percentage decrease is 18% then do 100% - 18% which is 82. divide by 100 = 0.82. if it does this for 6 years then do 18,995 × 0.82^(6) because it's 6 years. the number is larger than Manuel's offer therefore he shouldnt sell

Answer:

  g(x) = -1/4x²

Step-by-step explanation:

Given f(x) = x² and point (2, -1) on the graph of g(x), which is a scaled version of f(x), you want the equation for g(x).

The scale factor k will satisfy ...

  g(x) = k·f(x)

  g(2) = k·f(2) . . . . . . true at the given point

  -1 = k·2² = 4k . . . . use the coordinates of the given point

  k = -1/4 . . . . . . . . . divide by 4

The equation of g(x) is ...

  g(x) = -1/4x²

In mathematics, the term "discrete" is often used to refer to objects or structures that are distinct and separate, rather than being continuous or flowing. In the context of this course, the term "discrete" is used to describe a particular branch of mathematics known as "discrete mathematics" or "discrete structures."

Discrete mathematics is concerned with mathematical structures that are countable and finite, rather than continuous or infinite. These structures are typically represented by sets, graphs, or other discrete objects, and can be used to model a wide range of phenomena, from computer algorithms to social networks.

One of the key features of discrete structures is that they are composed of individual, separate elements, rather than being continuous or flowing. For example, a set of integers is a discrete structure, because it consists of separate, distinct integers, rather than a continuous range of numbers. Similarly, a graph is a discrete structure, because it consists of separate vertices and edges, rather than a continuous line.

Because of their discrete nature, these structures can be analyzed and manipulated using a range of mathematical tools and techniques, such as combinatorics, graph theory, and probability theory. This makes discrete mathematics a fundamental part of many areas of computer science, engineering, and other fields that rely on mathematical modeling and analysis.

In contrast, continuous structures, such as real numbers or geometric shapes, are often analyzed using calculus or other techniques that deal with the infinite and continuous nature of these objects.

In summary, when we talk about "discrete structures" or "discrete mathematics," we are referring to mathematical objects and structures that are countable, finite, and composed of individual, separate elements. These structures can be analyzed and manipulated using a range of mathematical tools, and are a fundamental part of many areas of computer science, engineering, and other fields that rely on mathematical modeling and analysis.

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The divisors of 60 are the numbers that evenly divide 60 without leaving a remainder. In other words, if we divide 60 by one of its divisors, the result will be a whole number.

For example, if we divide 60 by 2, we get 30. If we divide 60 by 3, we get 20. And so on.

When the teacher wants to form equal groups of students, she needs to ensure that the number of students in each group is one of the divisors of 60. This way, she can divide the class into groups with an equal number of students in each group.

So, in this case, the different groups the teacher can make are:

1 group of 60 students

2 groups of 30 students each

3 groups of 20 students each

4 groups of 15 students each

5 groups of 12 students each

6 groups of 10 students each

10 groups of 6 students each

12 groups of 5 students each

15 groups of 4 students each

20 groups of 3 students each

30 groups of 2 students each

60 groups of 1 student each

These are the 12 different options for forming equal groups of students.

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According to scientists with the USGS Cascades Volcanic Observatory, a lahar could take four hours to reach Puyallup but less than an hour to reach Orting.

The Washington Emergency Management Division has issued a survey to Pierce County residents to learn more about lahars, which are volcanic mudflows that contain a mixture of water and volcanic debris such as boulders. The survey is scheduled to close on Friday.

Hazard maps show that if Mount Rainier erupts, lahar could travel through river valleys as far as Puyallup, Tacoma, and Randle.

Some areas would have more time than others to evacuate. According to the US Geological Survey, previous Mount Rainier lahars travelled at 45-50 miles per hour.

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Answer:

Correct, the inequality y ≥ 0.8x + 1.5 accurately describes the relation between the duration of the hike (x) and the amount of water needed (y). This inequality means that for any duration of the hike (x), the amount of water needed (y) must be greater than or equal to 0.8x + 1.5.

the flow curve expresses the behavior of a metal in plastic region of the stress strain curve.

When a sample is exposed to various shear rates or shear stressors, the change in shear viscosity is graphically shown by a flow curve.

A flow curve is a measurement performed on a rotating viscometer or rheometer in which the shear rate is increased stepwise and the corresponding shear stress is calculated for each shear rate. The characteristics of the instrument are used to compute the associated shear stress and viscosity.

Thus, the flow curve expresses the behavior of a metal in the plastic region of the stress strain curve.

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Answer:

Step-by-step explanation:

That’s the same as 10n + 4n = -56

= 14n = -56

= n = -56/14

n = -4

Answer:

n = -4

Step-by-step explanation:

10n + 56 = -4n

56 = -14n

n = -4

Rounding to the nearest tenth, the angular speed of the propeller is 157.1 rad/s.

A radian is a unit of measurement for angles in mathematics. It is defined as the ratio of the length of an arc of a circle to the radius of the circle. In other words, one radian is equal to the angle created at the center of a circle by an arc that is equal in length to the radius of the circle.

Radians are used as a more natural and convenient way to measure angles than degrees, especially in calculus and other branches of mathematics that deal with the study of curves and functions. For example, the trigonometric functions (sine, cosine, and tangent) are defined in terms of radians, and the derivatives of these functions are easier to work with in radians than in degrees

To convert from revolutions per minute to radians per second, we need to divide by the number of minutes in one hour and multiply by the number of radians in one revolution. We can write this conversion as:

4700 rev/min * (2π rad/rev) / (60 min/hr) = w rad/s

where w denotes the angle's rotational speed in radians per second. Plugging in the conversion factor for one revolution, we get:

w = 4700 rev/min * (2π rad/rev) / (60 min/hr) = (4700 * 2π) / 60 = 157.07 rad/s

Rounding to the nearest tenth, the angular speed of the propeller is 157.1 rad/s.

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The value of b, given the lines that are parallel in the figure, would be D. 27. 67.

Given that the lines are parallel, then we can infer that angles 92 degrees and ( 3b + 5 ) degrees are supplementary angles which means that they add up to 180 degrees.

We can therefore solve for b by equating the sum of both angles to 180 degrees as shown in the formula below :

92 + ( 3b + 5 ) = 180

92 + 5 + 3 b = 180

3b = 180 - 92 - 5

b = 83 / 3

b = 27. 67

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Answer:

4= 16 quarts

Step-by-step explanation:

Answer: 16 quarts

Step-by-step explanation:

1 gallon = 4 quarts

4 gallon = 4 x 4 = 16 quarts

This is a direct proportion