Question 2 (essay worth 10 points)
(07.02 mc)

minni is arranging 3 different music cds in a row on a shelf. create a sample space for the arrangement of a jazz cd (j), a pop cd (p), and a rock cd (r).

tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

The tangent of 36° can be expressed in terms of its cofunction, which is the cotangent. The cotangent of an angle is equal to the reciprocal of the tangent of that angle. Therefore, we can rewrite tan 36° as cot (90° - 36°).

Now, cot (90° - 36°) can be simplified further. The angle 90° - 36° is equal to 54°. So, we have cot 54°.

The cotangent of 54° can be determined using the unit circle or trigonometric identities. In this case, the exact answer for cot 54° is (√3 + 1) / (√3 - 1).

Hence, tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

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The value of y is \(\frac{5}{4}\).

The lines PQ and RS are parallel, their slopes are equal. The slope of a line passing through points P(2,-2) and Q(5,8) is:

m1 = (8 - (-2)) / (5 - 2) = \(\frac{10}{3}\)

The slope of a line passing through points R(3,-1) and S(6,7) is:

m2 = (7 - (-1)) / (6 - 3) = \(\frac{8}{3}\)

Since the slopes are equal, we have:

PQ and RS are parallel, the line segments PQ and RS intersect at a point that is equidistant from both lines.

m1 = m2

\(\frac{10}{3}\) = \(\frac{8}{3}\)

Since T is the x-coordinate of the point where PQ and RS intersect, we can solve for it by setting the x-coordinates of P and R equal to each other:

2 + 3T = 3 + 2T

T = 1

Multiplying both sides by 3, we get:

10 = 8y

Subtracting 64/9*\(T^2\) from both sides and simplifying, we get:

4\(T^2\) + 20/3T*(b-y-d+y) + (b-d)*(b+d-2y) = 0

4\(T^2\) + 20/3T*(b-d) + (b-d)*(b+d-2y) = 0

4\(T^2\) + 20/3T + (b-d)*(b+d-2y) = 0

Dividing both sides by 8, we get:

y = \(\frac{10}{8}\) = \(\frac{5}{4}\)

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The value of  y = 20/3.

Since lines PQ and RS are parallel, their slopes are equal.

The slope of line PQ is:

m(PQ) = (8 - (-2)) / (5 - 2) = 10/3

The slope of line RS is:

m(RS) = (7 - (-1)) / (6 - 3) = 8/3

Since m(PQ) = m(RS), the lines are parallel.

We can use the point-slope form of a linear equation to find the equation of line PQ:

y - (-2) = (10/3)(x - 2)

Simplifying this equation, we get:

y = (10/3)x - (4/3) + (-2)

y = (10/3)x - (10/3)

Now, we can use this equation to find the y-coordinate of point Q when x = 5:

y = (10/3)(5) - (10/3) = 10 - 10/3 = 20/3.

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Answer:

3/2

Step-by-step explanation:

sin(3π/4 - β) = sin(3π/4)cosβ - cos(3π/4)sinπ =

\(\sin(\frac{3\pi}{4}-\beta)=\sin(\frac{3\pi}{4})\cos\beta-\cos\frac{3\pi}{4}\sin\beta\\=\frac{1}{\sqrt{2}}\cos\beta-(-\frac{1}{\sqrt{2}})\sin\beta\\\\=\frac{1}{\sqrt{2}}(\cos\beta +\sin\beta)\\\\\sin^2(\frac{3\pi}{4}-\beta)=\frac{1}{2}\cos\beta +\sin\beta)^2=\frac{1}{2}(\cos^2\beta +\sin^2\beta+2\sin\beta\cos\beta\\=\frac{1}{2}(1+\sin2\beta)=\frac{1}{2}(1-\frac{1}{5}) = \frac{2}{5}\\\)

Use \(\cot^2x=\csc^2x-1=\frac{1}{\sin^2x}-1\)

so

\(\cot^2(\frac{3\pi}{4}-\beta)=\frac{1}{\sin^2(\frac{3\pi}{4}-\beta)}-1 = \frac{1}{\frac{2}{5}}-1=\frac{5}{2}-1=\frac{3}{2}\)

The given statement "The standard deviation can be negative" is false.

The standard deviation is a measure of dispersion or variability in a dataset. It represents the average amount of deviation or spread of the data points from the mean. By definition, the standard deviation is always a non-negative value or zero. It cannot be negative because it measures the distance of each data point from the mean, which is always a positive value.

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Answer:

sin(5607) = 0.67641680533

sin(506)  = -0.202179403335

sin(702)  = -0.989367016834

sin(803) = -0.948263002181

sin(562) =  0.33827666045

Step-by-step explanation:

put sin into a calculator and then put in the number

hope this helps! :)

Answer:

X will be your answer be 126 and 110

Step-by-step explanation:

6x3x7=126

y=11x2x5=110

so X>Y

hope it helps!

The number of ways to  match 5 of 6 numbers is 6 ways

The number of ways to  match 4 of 6 numbers is 15 ways

The number of ways to  match 3 of 6 numbers is 20 ways

To calculate number of ways to match 5 of 6 numbers we have to use to formula:

\(nCr =\frac{n!}{(n - r)! . r !}\)

\(6C5=\frac{6!}{(6-5)! . 5!}\)

\(6C5=\frac{6!}{(1)! . 5!}\)

\(6C5=\frac{6.5.4.3.2.1}{1.5.4.3.2.1}\)

\(6C5=\frac{6}{1}\)

\(6C5= 6 \ ways\)

∴ 6 ways are to match 5 of 6 numbers

To calculate number of ways to match 4 of 6 numbers we have to use to formula:

\(nCr =\frac{n!}{(n - r)! . r !}\)

\(6C4=\frac{6!}{(6-4)! . 4!}\)

\(6C4=\frac{6!}{(2)! . 4!}\)

\(6C4=\frac{6.5.4.3.2.1}{2.1.4.3.2.1}\)

\(6C4=\frac{30}{2}\)

\(6C4= 15 \ ways\)

∴ 15 ways are to match 4 of 6 numbers

To calculate number of ways to match 4 of 6 numbers we have to use to formula:

\(nCr =\frac{n!}{(n - r)! . r !}\)

\(6C3=\frac{6!}{(6-3)! . 3!}\)

\(6C3=\frac{6!}{(3)! . 3!}\)

\(6C3=\frac{6.5.4.3.2.1}{3.2.1.3.2.1}\)

\(6C3=\frac{120}{6}\)

\(6C3= 20 \ ways\)

∴ 20 ways are to match 3 of 6 numbers

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Answer:

The answer is -512

Step-by-step explanation

8*8*8= 512 and the cube root of 512 is 8 and the cube root answer is negative so 512 is negative

Answer:

x=24

y=25

Step-by-step explanation:

3y =75 by alternate interior angles theorem

y =25

4x+9+75=180

4x+84=180

4x=96

x=24

The correct description of the graph of the inequality x - 3 ≥ 5, is: D. Closed circle on 8, shading to the right.

An inequality statement compares two unequal quantities. When plotting the graph of an inequality, if the inequality sign involve is "< or >", an open circle is used to mark the value of the variable on the number line, while a closed circle is used when the inequality sign involved is, "≤ or ≥".

Given the inequality, x - 3 ≥ 5, solve for x:

x - 3 ≥ 5

Add 3 to both sides

x - 3 + 3 ≥ 5 + 3 [addition property]

x ≥ 8

This means the possible values of x are greater than or equal to 8. The graph of the inequality would have a closed circle at 8, with the line shaded to the right on the number line.

The correct description is: D. Closed circle on 8, shading to the right.

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No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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Answer:

52 degrees

Step-by-step explanation:

The 3 angles of a triangle add up to 180 degrees

To find angle C, use 180 - B - A = C

180 - 85 - 43 = 52

According to the proof, equal difference property is not satisfied by the function f(x).

There are four binary variables, x1, x2, x3, and x4.

The binary format is now converted to hexadecimal format, and the values are stored as A, B, C, and D, accordingly.

Convert every four bits of a binary value to a hexadecimal value.

ex: Split into 4 bits: x1 = 00000000 = 0000 0000 = 0 0 (convert the 4 bits to hex)

A = 00 ( hexadecimal of x1 )

B= 01 ( hexadecimal of x2 ) ( hexadecimal of x2 )

C=02 ( hexadecimal of x3 ) ( hexadecimal of x3 )

D=03 ( hexadecimal of x4 ) ( hexadecimal of x4 )

The function in question is f(x) = BS(x), which means that it performs byte alternation on the input x.

This means that f(x1) = 63, f(x2) = 7C, f(x3) = 77, and f(x4) = 7B.

We must now demonstrate that x1 xor x2 equals x3 xor x4 and that f(x1) xor f(x2) does not equal f(x3) xor f(x4) (x4).

If x1 xor x2 = 00, then xor 02 = 02 xor 01 = 01 x3 xor x4 03 = 01 So, x1 Equals x2 OR x3 OR x4 In the present, f(x1) xor f(x2) = 63 xor 7C = 1f f(x3) xor f(x4) = 77 xor 7B = 0C Due to f(x1) xor f(x2) not being equivalent to f(x3) xor f(x4).

Hence, the equal difference property is not satisfied by the function f(x), which is the Byte Substitution (BS) function of AES, according to the proof.

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Answer:

FREEEEEEE POINTSSSSSSS

Step-by-step explanation:

The annual maintenance collected in 2014 will be $1,750,000.

To calculate the annual maintenance collected in 2014, we need to find the number of customers who will renew their maintenance contract and the number of customers who will pay for maintenance as a percentage of product sales in 2013.

Number of customers renewing maintenance in 2014 = 80% of $2,000,000 = $1,600,000

Number of customers paying for maintenance in 2014 = 75% of $2,000,000 = $1,500,000

So, the total annual maintenance collected in 2014 will be:

$1,600,000 + $1,500,000*10% = $1,750,000

Therefore, the annual maintenance collected in 2014 will be $1,750,000.

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This option represents a correct sequence of steps in the conventional research model, starting with forming a hypothesis, then designing the research, followed by collecting data, and finally analyzing the data.

The correct sequence of steps in the "conventional" research model is D) Hypothesis formation, research design, data collection, data analysis. The first step is to form a hypothesis or a tentative explanation for the phenomenon being studied. The next step is to design the research study to test the hypothesis. This includes selecting the sample, determining the variables to measure, and deciding on the research methods.

Once the research design is finalized, data collection can begin. This involves gathering data using various techniques such as surveys, interviews, or experiments. Finally, data analysis is performed to examine the data and determine if the results support or refute the hypothesis.
Your answer: D) Hypothesis formation, research design, data collection, data analysis

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Answer:

The area is 12.56 units^2 (same as circumference?)

Step-by-step explanation:

Assuming pi is 3.14, the equation for the circumference is C = 2 pi r

Fill it out for the radius (r)

12.56 = 2 3.14 r

12.56 = 6.28 r

r = 2

With the radius, the equation for the area is A = pi r^2

Fill it out for the area

A = 3.14 2^2

A = 3.14 4

A = 12.56

The set of integers is a Pythagorean triple are option (A) 10, 24, 25 and (D) 6, 8, 10

A Pythagorean triple is a set of three positive integers a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right triangle.

Let's check each set of integers

A. 10^2 + 24^2 = 100 + 576 = 676 = 25^2. Therefore, (10, 24, 25) is a Pythagorean triple.

B. 9^2 + 12^2 = 81 + 144 = 225 = 15^2. Therefore, (9, 12, 15) is a Pythagorean triple. However, the set given is (9, 12, 21), which is not a Pythagorean triple.

C. 8^2 + 15^2 = 64 + 225 = 289 = 17^2. Therefore, (8, 15, 17) is a Pythagorean triple. However, the set given is (8, 15, 23), which is not a Pythagorean triple.

D. 6^2 + 8^2 = 36 + 64 = 100 = 10^2. Therefore, the set of integers (6, 8, 10) is a Pythagorean triple.

Therefore, the correct options are (A) 10, 24, 25 and (D) 6, 8, 10

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The given question is incomplete, the complete question is:

Which set of integers is a Pythagorean triple?

A.

10, 24, 25

B.

9, 12, 21

C.

8, 15, 23

D.

6, 8, 10

Answer:

$46.15

Step-by-step explanation:

$46.15 because 125% of $36.92 is $46.15

Hope this helps!

The domain for all variables is the set of integers.The correct answer is: ∀y ∃x (x+2y=1).

This statement is true because for any integer value of y, there exists an integer value of x that satisfies the equation x+2y=1. For example, if y=0, then x=1; if y=1, then x=-1; if y=2, then x=-3, and so on.

The other statements are not true for all integer values of x and y. For example, ∀x ∃y (x+2y=1) is not true because there are integer values of x for which there is no integer value of y that satisfies the equation (e.g. if x=2, then y= -0.5, which is not an integer). Similarly, ∃y ∀x (x+2y=1) and ∃x ∀y (x+2y=1) are not true because there is no single integer value of y or x that satisfies the equation for all integer values of x or y, respectively.

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Answer:

B is the correct answer

This riddle does not have any mathematical formula or calculation associated with it.

This is an impossible situation, as it is not possible for a doctor to be the patient's parent. It is also not possible for a person to be taller than a building that is 43 stories tall.

The phrase "How is a raven like a writing desk?" is a riddle posed by Lewis Carroll in his novel Alice's Adventures in Wonderland. The answer to the riddle is "they both have the potential to produce a few notes, though they are very different". This phrase does not have any mathematical formula or calculation associated with it.

This riddle does not have any mathematical formula or calculation associated with it.

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Answer:

12cm³

Step-by-step explanation:

1/2x2x6x2=12cm³

Answer:

6x2 well the answer is 24 so like

Step-by-step explanation:

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

y=mx+c.................

Step-by-step explanation:

Enter a problem...

Algebra Examples

Popular Problems

Algebra

Expand using the Binomial Theorem (3x+2)^4

(3x+2)4(3x+2)4

Use the binomial expansion theorem to find each term. The binomial theorem states (a+b)n=n∑k=0nCk⋅(an−kbk)(a+b)n=∑k=0n⁡nCk⋅(an-kbk).

4∑k=04!(4−k)!k!⋅(3x)4−k⋅(2)k∑k=04⁡4!(4-k)!k!⋅(3x)4-k⋅(2)k

Expand the summation.

4!(4−0)!0!⋅(3x)4−0⋅(2)0+4!(4−1)!1!⋅(3x)4−1⋅(2)+4!(4−2)!2!⋅(3x)4−2⋅(2)2+4!(4−3)!3!⋅(3x)4−3⋅(2)3+4!(4−4)!4!⋅(3x)4−4⋅(2)44!(4-0)!0!⋅(3x)4-0⋅(2)0+4!(4-1)!1!⋅(3x)4-1⋅(2)+4!(4-2)!2!⋅(3x)4-2⋅(2)2+4!(4-3)!3!⋅(3x)4-3⋅(2)3+4!(4-4)!4!⋅(3x)4-4⋅(2)4

Simplify the exponents for each term of the expansion.

1⋅(3x)4⋅(2)0+4

Hope this helps!

Answer:81x^4+216x^3+216x^2+96x+16

Step-by-step explanation:cause yussss

Answer:

2000

Step-by-step explanation:

Salim will need to get 2000 clicks in order to get $50 per month or more.

First: 5 cents goes into one dollar 20 times.

Second: You multiply 20 times 50. This is how you get 2000. There is your answer.

Salim needs at least 700 clicks per month  in order to earn $50 per month or more

A linear equation is in the form:

y = mx + b;

where y, x is variable, m is the rate of change and b is the y intercept.

Let y represent the total pay Salim earns and x represent the number of clicks.

Salim's Website earns $15 per month plus $0.05 every time a visitor clicks, hence:

y = 0.05x + 15

To earn for than $50 per month:

0.05x + 15 > 50

0.05x > 35

x > 700

Salim needs at least 700 clicks per month  in order to earn $50 per month or more

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Answer:

Solution,

Onions less than 60 grams = 2 --> Pickling

Onions greater than 120 grams = 5 + 3 = 8 --> Market

Onions between 60 and 120 = 13---> Processing

Total frequency = 2 + 8 + 13 = 23

Now,

\(x = \frac{13}{23} \times 360\)

\(x = 203.48\)

\(x = 203.5\)

Hope this helps ..

Good luck on your assignment...

Answer:

x=190°

Step-by-step explanation:

find the frequency of the given numbers dividing by their numbers

onions less than 60g=(2+2/2)=²/9

onions greater than 120g=(5+3/2)= 4 (4+3/2). =3.5/9

To convert into degrees so that they can fit in the bar graph multiply the frequencies by 360 that is:

picking=²/9×360=80°

market=3.5/9×360=90°

x=360°-90°-80°

x=190°

confirmation

pie chart° add up to 360°

picking=80°

market=90°

x=190°

190°+80°+90°=360°

Answer:

11 remainder 26

Step-by-step explanation:

The triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.

The Angle-Side-Angle (ASA) Congruence Theorem is a postulate in geometry that states that if two triangles have two angles and the included side of one triangle congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.

Triangle YXZ is formed from a reflection and then a dilation of the triangle WVZ, then the relations between the angles are given as follows:

The side lengths WV and YZ, which are the side lengths between these two angles, form a proportional relationship, hence the triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.

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