Which expression is equivalent to sin(84°)cos(43°) + cos(84°)sin(43°)?

sin(41°)
cos(41°)
sin(127°)
cos(127°)

The given statement: n(n+1)(2n+1) is divisible by 6 for all positive integers n.

Step-by-step explanation: We need to prove that n(n+1)(2n+1) is divisible by 6 for all positive integers n using mathematical induction.

Step 1: First, lets prove the statement for the smallest possible value of n. The smallest value of n is 1. So, let's check whether the given statement is true for n = 1 or not.

\(LHS = 1(1+1)(2*1+1) = 6\)

It is divisible by 6. Hence, the statement is true for n=1.

Step 2: Let's assume that the statement is true for n=k. So, we can say that n(n+1)(2n+1) is divisible by 6 for n=k. i.e., n(n+1)(2n+1) = 6a (for some integer a).

Step 3: We need to prove the statement is true for n=k+1.

So, we need to prove that (k+1){(k+1)+1}[2(k+1)+1] is divisible by 6

Using the assumption we made in step 2.

\(LHS = (k+1){(k+2)}[2k+3] = (k+1)(k+2)(2k+3)LHS = (2k+3)k(k+1)(k+2)LHS = 2[k(k+1)(k+2)] + 3[k(k+1)]\)

Now, k(k+1)(k+2) is divisible by 6 using the assumption made in step 2.

So, LHS = 2[k(k+1)(k+2)] + 3[k(k+1)] is also divisible by 6.

Hence, the statement is true for n=k+1.

Step 4: Using steps 1 to 3, we can say that the given statement is true for n=1 and if it is true for n=k, then it is also true for n=k+1.

Hence, by mathematical induction, we can say that the statement is true for all positive integers n.

Hence, it is proved that n(n+1)(2n+1) is divisible by 6 for all positive integers n.

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Answer:

17, 15, and  30

Step-by-step explanation:

sorry if I'm wrong

The surds are √17, √15 and √30.

The square roots of numbers that cannot be divided into a whole or rational number are known as surds ().

It is not capable of being correctly expressed in a fraction. A surd, then, is the root of a whole integer with an irrational value.

Take the example of 2 1.414213. If we leave it as a surd 2, it will be more correct.

As, surds those roots that cannot have square root of a number.

So, from the given number √17, √15 and √30 which do not have square roots.

Hence, the surds are √17, √15 and √30.

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Answer:

Step-by-step explanation:

(a)Total number of candies = 120

The number of candies in the rows form AP sequence:

The first term is a=3 and common difference is d=2

Sum of n terms:

Substitute values and solve for n:

Correct choice is (ii) 10

(b) Formula for nth term:

Correct choice is (ii) 21

(c) Use same formula:

Correct choice is (i) 8

(d) Sum of candies in 15 rows

Correct choice is (iii) 255

(e) Number of candies in 12th row:

Correct choice is (iii) 25

Answer:

This would equal 13.

2x2=4, 6/2=3, 3x3=9, 9+4=13

The number of  children bought meal tickets =  700

The number of adult  bought meal tickets = 950

A linear equation is one that can be written as display style a 1x 1+ldots +a nx n+b=0, where x 1, ldots, x n are the variables and display style b, a 1, ldots, a n are the coefficients, which are frequently real integers.

Let x and y be the quantity of kid and adult tickets sold, respectively. 1650 tickets were sold in total, as far as we know.

x + y = 1650

x = 1650 - y

At $12 for adults and $4 for children, the total revenue from tickets is $14200. There are

4x + 12y = 14200

substituting the value of x in the equation:

4(1650 - y) + 12y = 14200

6600 - 4y + 12y = 14200

6600 + 8y = 14200

8y = 14200 - 6600 = 7600

y = 7600 / 8

= 950 adult tickets

x = 1650 - 950

= 700 children tickets

The number of  children bought meal tickets =  700

The number of adult  bought meal tickets = 950

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Answer:

-5(36x-1)x

Step-by-step explanation:

Answer:

the answer is b 455

Step-by-step explanation:

15/(4×12)=455

Answer:

A byte is 8 bits.

1. The main difference between the triple constraints and the iron triangle is that the iron triangle incorporates quality as a crucial factor in determining scope, time, and cost.

2. The constraints in project management interact and impact each other as changes in one constraint, such as scope, can affect both time and cost, and changes in time or cost can influence the scope.

3. A project focuses on a specific objective, while a program consists of multiple interconnected projects aimed at achieving strategic goals.

4. The steps in the project management process include initiation, planning, execution, monitoring and control, and closure.

5. The product development cycle aligns with the project management process as project management provides the framework for effectively planning, executing, and controlling the product development activities.

The constraints are time, cost, and other items such as resources. The triple constraints refer to the relationship between a project's scope, time, and cost. Whereas the iron triangle is scope, time, and cost all depend on quality. There's a slight difference between the two because an iron triangle focuses mainly on the effective management of quality.

The constraints are time, cost, and other items such as resources. These constraints interact and impact each other because they are all crucial for one another. For example, if you would like to expand the task it would take you more time and money, but if you were to accelerate the task you might reduce the expenses but won't be able to see as good results. As a result, these constraints are closely linked to each other.

A project is specializing in one thing, whereas a program contains many projects. An example is me, I'm in a business administration program which requires many projects that consist of classes.

The steps in the project management process are:

The product development cycle fits with the project management process because in a product development cycle, you are using knowledge, skills, tools, and techniques that are transferred over to product development to create the end product. Hence, both processes are correlated with each other.

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Step-by-step explanation:

\( \frac{(y - b)}{(x - a)} = m \\ y - b = m(x - a) \\ y - b = mx - am \\ mx = y - b + am \\ x = \frac{y - b + am}{m} \)

Beau can wrap 32 inches of ribbon outside the mirror.

Area of Beau Thai's mirror is 60 sq. inches.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The word "area" refers to a free space. A shape's length and width are used to compute its area.

Given information:

Length of mirror = 6 inches

Width of mirror = 10 inches

To Find:

The amount of ribbon Beau could wrap around the outside of the mirror.

Perimeter of the mirror = 2(6+10)

                                       = 2(16)

                                       = 32 inches

The area of Beau Thai's mirror.

Area of the mirror = 6*10

                              = 60 sq. inches

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Let's go through each answer.

A.

Answer: The amount left over was 4.05 L.

Estimation: 3.15 + 4.75 is about 7.

7 L – 4 L = 3 L

The amount left over was about 3 L.

This is incorrect because 3.15+4.75 is closer to 8 than 7.

B.

Answer: The amount left over was 3.95 L.

Estimation: 3.15 + 4.75 is about 8.

8 L – 4 L = 4 L

The amount left over was a little less than 4 L.

This is correct because 3.15+4.75 is close to 8 and to find the amount left over you do have to subtract.

The correct answer is B.

Answer: The amount left over was 3.95 L.

Estimation: 3.15 + 4.75 is about 8.

8 L – 4 L = 4 L

The amount left over was a little less than 4 L.

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1. The function f(30) represents the D. number of items sold when the price is 30.2. The quantity f^(-1)(45) represents the F. price at which 45 items will be sold.

1. The function f(p) represents the relationship between the price (p) and the number of items sold (q) at that price.

When we evaluate f(30), it gives us the value of q, which is the number of items sold when the price is 30. Therefore, the answer is D. number of items sold when the price is 30.

2. The inverse function f^(-1)(45) represents the price (p) at which a certain quantity of 45 items will be sold. So, f^(-1)(45) gives us the price at which 45 items will be sold, hence the answer is F. price at which 45 items will be sold.

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Based on the given data, the probability of a room being occupied on any particular weekend night is 0.75. To calculate the probability that at least 4 out of the 7 rooms are occupied on a weekend night, we can use the binomial probability formula. By summing up the probabilities for 4, 5, 6, and 7 occupied rooms, we find that the probability is approximately 0.923.

To calculate the probability, we can use the binomial probability formula, which states that the probability of getting exactly k successes in n independent Bernoulli trials, each with a probability p of success, is given by the formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

In this case, we want to find the probability of at least 4 out of 7 rooms being occupied on a weekend night. We can calculate this by summing up the probabilities of getting 4, 5, 6, and 7 occupied rooms.

For 4 occupied rooms:
P(X = 4) = (7 choose 4) * 0.75^4 * (1 - 0.75)^(7 - 4) = 0.339

For 5 occupied rooms:
P(X = 5) = (7 choose 5) * 0.75^5 * (1 - 0.75)^(7 - 5) = 0.395

For 6 occupied rooms:
P(X = 6) = (7 choose 6) * 0.75^6 * (1 - 0.75)^(7 - 6) = 0.266

For 7 occupied rooms:
P(X = 7) = (7 choose 7) * 0.75^7 * (1 - 0.75)^(7 - 7) = 0.122

To find the probability of at least 4 occupied rooms, we sum up the probabilities for 4, 5, 6, and 7 occupied rooms:

P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.339 + 0.395 + 0.266 + 0.122 = 0.923

Therefore, the probability that at least 4 out of the 7 hotel rooms are occupied on any weekend night is approximately 0.923, or 92.3% when rounded to three decimal places.

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Based on the given data, the probability of a room being occupied on any particular weekend night is 0.75.

To calculate the probability that at least 4 out of the 7 rooms are occupied on a weekend night, we can use the binomial probability formula. By summing up the probabilities for 4, 5, 6, and 7 occupied rooms, we find that the probability is approximately 0.923.

To calculate the probability, we can use the binomial probability formula, which states that the probability of getting exactly k successes in n independent Bernoulli trials, each with a probability p of success, is given by the formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

In this case, we want to find the probability of at least 4 out of 7 rooms being occupied on a weekend night. We can calculate this by summing up the probabilities of getting 4, 5, 6, and 7 occupied rooms. For 4 occupied rooms:
P(X = 4) = (7 choose 4) * 0.75^4 * (1 - 0.75)^(7 - 4) = 0.339

For 5 occupied rooms:
P(X = 5) = (7 choose 5) * 0.75^5 * (1 - 0.75)^(7 - 5) = 0.395
For 6 occupied rooms:
P(X = 6) = (7 choose 6) * 0.75^6 * (1 - 0.75)^(7 - 6) = 0.266
For 7 occupied rooms:
P(X = 7) = (7 choose 7) * 0.75^7 * (1 - 0.75)^(7 - 7) = 0.122
To find the probability of at least 4 occupied rooms, we sum up the probabilities for 4, 5, 6, and 7 occupied rooms:

P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.339 + 0.395 + 0.266 + 0.122 = 0.923. Therefore, the probability that at least 4 out of the 7 hotel rooms are occupied on any weekend night is approximately 0.923, or 92.3% when rounded to three decimal places.

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Answer:

Step-by-step explanation:

lol put ur books or notes or whatever behind the device and cheat

BUT I really don’t advice u to cheat just try preparing for the exam or do as much as u can and don’t waste ur time at least u would know something while solving the exam.

Answer:

\(x = 2 \\ f(2) = > 2( {2})^{2} - 3(2) + 7a = 0 \\ 2 + 7a = 0 \\ 7a = - 2 \\ a = - \frac{2}{7} \)

Answer:

If 2=0 than x=2

p(x)=2x² - 3x + 7a

p(2)=0

2*2²-3*2+7a=0.

8-6+7a=0

a=\( \frac{-2}{7} \)

Consequently, the room has a 7 meter width. The room's length is

\(= 7 * 3 meters = 21 meters\)

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Given that the length of the rectangular space is three times its breadth

The chamber has a 56-meter perimeter.

Assume that the room's width is x.

As a result, the room is three times as long.

The room's perimeter is now equal to 2(3x + x).

\(Here, 2(3x + x) = 56\\ 2 * 4x = 56\\ 8x = 56\\ x = 7.\)

Consequently, the room has a 7 meter width.

The room's length is

\(= 7 * 3 meters\\= 21 meters\)

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Answer:

Step-by-step explanation:

\((3x+15)\\\\3x+15\\\\\mathrm{Rewrite\:}15\mathrm{\:as\:}3\times\:5\\\\=3x+3\times\:5\\\\\mathrm{Factor\:out\:common\:term\:}3\\\\=3\left(x+5\right)\)

Answer:

Q5) 6.5833 (rounded to nearest 4 d.p.)

Q6) \(\frac{3}{10}\)

Step-by-step explanation:

Q5) \(\sqrt{2.38 + 6.4^{2} }\) = \(\sqrt{2.38 + 40.96}\)

                           = \(\sqrt{43.34}\)

                           ≈ 6.5833 (rounded to nearest 4 d.p.)

Q6) When working with mixed numbers, I would change them to improper fractions first for easier calculations.

1\(\frac{3}{4}\) × \(\frac{6}{35}\) = \(\frac{7}{4}\) × \(\frac{6}{35}\)

          = \(\frac{42}{140}\) (Simplify by dividing by 2)

          = \(\frac{21}{70}\) (Simplify by dividing by 7)

          = \(\frac{3}{10}\)

The empire state building is taller than a chair seat by three orders of magnitude.

Orders of magnitude refer to the classification based on the sizes of two objects against each other.

Orders of magnitude range in the power of 10 or 10ⁿ.

Orders of Magnitude:

10x = 1 order of magnitude

100x = 2nd order of magnitude

1000x = 3rd order of magnitude

Empire State Building = 1,500 feet

Chair seat = 1.5 feet

Order of magnitude = 1,000x (1,500/1.5)

Thus, the Empire State Building is about a thousand times taller than a chair seat or three orders of magnitude.

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By sοlving the equatiοn, x is apprοximately equal tο 4.

An equatiοn is a mathematical statement that shοws that twο expressiοns are equal. It cοnsists οf twο sides separated by an equals sign (=).

Tο sοlve fοr x in the equatiοn:

91 =3ˣ + 10

We can first isοlate the expοnential term οn οne side οf the equatiοn by subtracting 10 frοm bοth sides:

81 =3ˣ

Nοw we can use lοgarithms tο sοlve fοr x. Taking the natural lοgarithm οf bοth sides, we have:

ln(81) = ln(3ˣ)

Using the lοgarithmic identity that ln(3ˣ) = b ln(a), we can simplify the right-hand side:

ln(81) = x ln(3)

x = ln(81) / ln(3)

x = ln(3⁴) / ln(3)

x = 4*ln(3) / ln(3)

x = 4

Therefοre, x is apprοximately equal tο 4.

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Answer:

We had this question last week let me check my book real quick.

Answer:

Такое тёплое место, но там, на улице,

Где ждут отпечатков наших ног,

Там сапоги сияют звёздной пылью.

Здесь пастыри и мягкое кресло,

Ослепительные сны под ярким солнечным шаром,

Курок не был нажат, когда было нужно.

Step-by-step explanation:

We have a circle that has an area of 36π square units.

We have to find the radius.

The area in function of the radius is πr², so we can find the radius r as:

Answer: the radius is 6 units.

Answer:

Vertical

Step-by-step explanation:

Angles a and b reflect each other, which is what vertical angles are.

Answer:

25%

6.5%

35%

Step-by-step explanation:

Given the invoice :

Bill for a pair of Jean

Jeans ______39.99

Discount ___ - 10.00

Subtotal ____ 29.99

Sales tax ____ 1.95

Total _______ 31.94

A) % of discount to the nearest %

Discount amount = % discount * price

10 = x% * 39.99

10/39.99 = x%

0.2500625 = x%

x = 0.2500625 * 100%

% discount = 25%

% of sales tax:

Sales tax amount = % tax * Subtotal

1.95 = x% * 29.99

1.95/29.99 = x%

0.06502 = x%

x = 0.06502 * 100%

x = 6.5%

Markup before discount = 60%

Markup after discount = (60 - 25)% = 35%

No function f(r,θ) is given, we cannot evaluate the integral further.

To write ∬rfda as an iterated integral in polar coordinates for the given region rr, we need to determine the limits of integration for r and θ.

Let's first look at the region rr. From the given graph, we can see that the region is bounded by the circle with radius 3 centered at the origin. Therefore, we can express the region as:

r ≤ 3

To determine the limits for θ, we need to examine the region rr more closely. We can see that the region is symmetric about the x-axis, which means that the limits for θ are:

0 ≤ θ ≤ π

Now, we can write the iterated integral as:

∬rfda = ∫₀³ ∫₀ᴨ f(r,θ) r dθ dr

where f(r,θ) is the integrand function and r and θ are the limits of integration. Note that r is integrated first, followed by θ.

In this case, since no function f(r,θ) is given, we cannot evaluate the integral further.

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Answer:

y = 1.2x + 770

Step-by-step explanation:

y = m*x + b

Equation One

y = mx + b

1370 = m*500 + b

Equation Two

y = mx + b

1730 =  m*800 + b

Solution

1730 = 800*m + b

1370 = 500*m + b                Subtract. The b's cancel

360 = 300 * m                      Divide both sides by 300

360/300 = m

1.2    = m

Now use the second equation to solve for b

y = 1730

x = 800

1730 = 1.2*800 + b

1730 = 960 + b                      Subtract 960 from both sides

b = 770