1. Given A = {1,2,3,4}, B ={1,2,4,5), C={3,4,6}, D= {7,8}. U={1,2,3,4,5,6,7,8,9}
What is A UB? Bn C? CD? A'? (A U B)

Using the law of cosines, it is found that the approximate length of side a is 3.99 units.

The law of cosines states that we can find the side c of a triangle as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

in which:

In the context of this problem, we have that side a is opposite to the angle of 53º, hence:

[tex]a^2 = b^2 + c^2 - 2bc\cos{53^\circ}[/tex]

We are given that:

Then:

[tex]a^2 = 34 - 30\cos{53^\circ}[/tex]

a² = 15.95

[tex]a = \sqrt{15.95}[/tex]

a = 3.99.

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The decomposition of the partial fraction is [tex]\frac{4ax-a^2}{(x+ 2a)(x-a)} = \frac{A}{x + 2a} + \frac{B}{x - a}[/tex]

The expression is given as:

[tex]\frac{4ax-a^2}{x^2+ax-2a^2}[/tex]

Expand the denominator

[tex]\frac{4ax-a^2}{x^2- ax+2ax-2a^2}[/tex]

Factorize

[tex]\frac{4ax-a^2}{x(x- a)+2a(x-a)}[/tex]

Factor out x - a

[tex]\frac{4ax-a^2}{(x+ 2a)(x-a)}[/tex]

The denominator of the partial fraction is a product of two linear factors.

So, the decomposition can be represented as:

[tex]\frac{4ax-a^2}{(x+ 2a)(x-a)} = \frac{A}{x + 2a} + \frac{B}{x - a}[/tex]

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Answer:

Cinthia studied 2/3 of her time on Tuesday

Using right triangle relations, we will get:

We assume that bot triangles are equivalent, then the angle B will be the same as the angle Z.

Now remember the relations:

If we step on angle B, we have:

Replacing that, we get:

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The answers to the questions are

a. From the table the probability of having 6 girls in 8 birth is given as

0.109.

b. The probability of 6 or more girls in 8 births

p(6) + p(7) + p(8)

= 0.109 + 0.016 + 0.002

= 0.127

c. The result from b is the relevant factor given that it includes the probability of getting 6, 7 and 8 girls.

D. No six is not a significantly high number of girls in 8 births. This conclusion is from the fact that 0.109 is greater than 0.05.

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Answer:

  A.  -∞ < y < 2

Step-by-step explanation:

The range is the vertical extent of the graph.

The arrow pointing down tells you the graph extends toward -∞.

The arrow pointing right suggests that y=2 is a horizontal asymptote. A graph will approach, but never cross, an asymptote. Thus, we can conclude y < 2.

The range is the set of values that lie between the limits:

  -∞ < y < 2

Answer:

C. 0.12

Step-by-step explanation:

Let's use a sample number of 100

Out of 100 members, 50 are in the brass section

Out of those 50, 24% play the trombone. This means that 12 people total play the trombone.

12/100 is .12.. That is the final answer

Answer:  [tex]\frac{\sqrt{7}}{7}[/tex]

========================================================

Explanation:

The reciprocal of x is 1/x where x is nonzero. Multiplying x with 1/x leads to 1. For example, the numbers 9 and 1/9 are multiplicative inverses of each other.

We'll stick 1 over the given square root expression. Then follow these steps to rationalize the denominator.

[tex]\frac{1}{\sqrt{7}}\\\\\\\frac{1*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\\\frac{\sqrt{7}}{(\sqrt{7})^2}\\\\\\\frac{\sqrt{7}}{7}\\\\[/tex]

In short, [tex]\frac{1}{\sqrt{7}}=\frac{\sqrt{7}}{7}[/tex]

Answer: A. x = 4

Step-by-step explanation:

Substituting 4 for x..

(4+7)^2 = 121

(11)^2 = 121

11 * 11 = 121

Answer:

The correct awnser is A : )

Step-by-step explanation:

This problem is about pension fund management. It is to be noted that the best Feasible Capital Allocation Line (CAL) is: 0.3162.

A graph's capital allocation line depicts all conceivable combinations of risky and risk-free assets, allowing investors to estimate future returns depending on risk.

It is to be noted that the optimal risky portfolio's stock percentage is determined by:

Weight of Stock = ((Return on Stock - Risk Free Rate) * Variance of bond) - ((Return on Bond - Risk Free Rate) * Co-Variance of bond & Stock)/ ((Return on Stock - Risk Free Rate) * Variance of bond + (Return on Bond - Risk Free Rate) * Variance of Stock - ((Return on Bond - Risk Free Rate + Return on Stock - Risk Free Rate + ) * Co-Variance of bond & Stock)

→ The weight of stock

= ((15% - 5.5%) * 529) - ((9% - 5.5%) * 110.40)/ ((15% - 5.5%) * 529) + (9% - 5.5%) * 1,024 - ((15% - 5.5% + 9% - 5.5%) * 110.40)

= [(50.255) * (3.864) /(50.255) + (46.08) - (14.352)]

Weight of Stock = 0.646628

Weight of  Bonds = 1 - 0.646628

Weight of  Bonds= 0.353372

Expected return of portfolio = 0.646628 * 15% + 0.353372 * 9%

= 12.88%

Standard Deviation of Portfolio (SDP)= (0.6466282² * 1,024 + 0.3533722² * 529 + 2 * 0.646628* 0.353372* 110.40)⁰·⁵

SDP = (544.67)⁰·⁵

SDP = 23.34%

Hence,

Best feasible CAL = (12.88% - 5.5%)/ 23.34%

Best feasible CAL = 0.3162

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Full Question

See the attached spread sheet for additional information related to the questions.

Using Green's Theorem to evaluate the given line integral with the given conditions and vertices gives us; -30

The line integral of a vector-valued function along the edges of a rectangle or any other closed curve can be found by converting the line integral into a double integral. We apply Green's theorem to do this. The resulting double integral is integrated over the two-dimensional region bounded by the same closed curve.

Green's Theorem can be applied as follows:

∮_c (P.dx + Q.dy) = ∫∫_R ((dQ/dx) - (dP/dy))dA

The vertices of the rectangle (1,1), (3,1), (1,4), and (3,4).

Applying Green's Theorem to the given function gives;

∮_c (ln x + y) dx - x² dy

= ∫14∫13 Dx(-x2) -Dy(ln(x) +y) dx dy

= ∫₁⁴∫₁³ (-2x - 1) dx dy

= -3·[x² +x]₁³

= -30

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The correct equation of 146 ÷ 7 = 20857 is 146.0 ÷ 7.0 = 20.857

The equation is given as:

146 ÷ 7 = 20857

The above equation is wrong.

The equation can be rewritten as:

146.0 ÷ 7.0 = 20857

The significant digits in 146.0 and 7.0 are 3 and 1, respectively.

3 - 1 = 2

This means that

So, the decimal place in the result must be after the second digit.

So, we have:

146.0 ÷ 7.0 = 20.857

Using the above highlights, we have:

146 ÷ 0.7 = 208.57

1.46 ÷ 7 = 0.20857

14.6 ÷ 0.7 = 20.857

1460 ÷ 70 = 20.857

The reasoning behind the above equations is that the decimal position in the results is dependent on the decimal positions in the dividend and divisor

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Answer:

C

Step-by-step explanation:

y = (x - 2)² = x² - 4x + 4 → (1)

x + y - 2 = 0 → (2)

substitute y = x² - 4x + 4 into (2)

x + x² - 4x + 4 - 2 = 0

x² - 3x + 2 = 0

(x - 1)(x - 2) = 0

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

substitute these values into (2) and solve for y

x = 1 : 1 + y - 2 = 0 ⇒ y - 1 = 0 ⇒ y = 1 ⇒ (1, 1 )

x = 2 : 2 + y - 2 = 0 ⇒ y + 0 = 0 ⇒ y = 0 ⇒ (2, 0 )

the line intersects curve C at 2 points (1, 1 ) and (2, 0 )

No, the average change in population is not the same as it was 50 years ago.

Reason in Support of the Answer:

In many important ways, the demographic future of the United States and the rest of the world is substantially different from the recent past. The world's average population approximately tripled between 1950 and 2010, and the U.S. population nearly doubled.

However, it is anticipated that between 2010 and 2050, both globally and in the United States, average population growth will be substantially slower and will disproportionately favor the oldest age groups. Hence it is seen that the average change in population is never constant. It depends on the demographic trends and conditions, whether the average change in population will be larger or comparatively trivial in the future. And, similarly, it can be said that the average change in population is not the same as it was 50 years ago.

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The total number of snakes in the zoo is 10.

The number of snake can be found using ratio as follows:

The animals in the zoo are lions, tigers and snakes and he has them in the ratio of 5 : 3 : 2. The total animal is 50 animals.

Therefore,

total snakes = 2 / 10 × 50

total snakes = 100 / 10

total snakes = 10

Therefore, the total number of snakes in the zoo is 10.

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Answer:

18/19= X/37 because 18 and x are both between 72 and 45 degrees

Multiply 18 and 37 then divide by 19 to get answer

Step-by-step explanation:

The  bottom cutoff for receiving an A grade is 88.

The bottom cutoff for receiving an A grade is found as follows:

The mean of the distribution = 75

The standard deviation = 9

The z-score for the 93% = 1.476

The score for an A grade, x = mean + z-score * standard deviation

Score for an A grade, x = 75 + 1.476 * 9

Score for an A grade, x = 88

In conclusion, the minimum score for an A grade is obtained from the mean, the z-score and the standard deviation.

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The sum of the ten terms to the nearest whole number is 50857.

Using geometric sequence formula,

nth term = arⁿ⁻¹

where

r = 20 / 8 = 5 / 2

a = 8

Hence,

s₁₀ = a(rⁿ - 1) / r - 1

s₁₀ = 8((5 / 2)¹⁰ - 1) / 5 / 2 - 1

s₁₀ = 8(9535.74316406) / 1.5

s₁₀ = 50857.296875

s₁₀ = 50857

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Answer:

1.The center of the circle lies on the x-axis

2.The radius of the circle is 3 units.

3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The zeros of the given function are x = 2 and x = -1

From the question, we are to determine the zeros of the given function

The given function is

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

To determine the zeros of a function, we will set the function equal to zero

That is,

(x - 2)(3x + 3) = 0

Then,

x - 2 = 0 OR 3x + 3 = 0

x = 2 OR 3x = -3

x = 2 OR x = -3/3

x = 2 OR x = -1

Hence, the zeros of the given function are x = 2 and x = -1

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The correct matching of the exponential form is given.

1: 13^-11 × 13^16 × 13^-3 × 13^-4 × 13^-5

= 13

2. 13^-21 × 13^-4 × 13^-5 × 13^14 × 13^-6

= 13^-22

3. 13^0 × 13^10 × 13^-12 × 13^5 × 13^4

= 13^7

This illustrates the exponential form.

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The answer choice which explains that the three segments cannot be used to construct a triangle is; AC + CB < AB.

Since, It follows from the triangle inequalities theorem that sum of the side lengths of any two sides of a triangle is greater than the length of the third side.

Hence, since the sum of sides AC + CB is less than AB, it follows that the required inequality is; AC + CB < AB.

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Answer: Option 2 or B.  AC + CB < AB

Step-by-step explanation: Trust Me!  It is correct on Edge!

Q: Which inequality can be used to explain why these three segments cannot be used to construct a triangle?

A: AC + CB < AB

Answer:

2=1289/17

Step-by-step explanation:

use the given functions to set up and simplify 2

The graph that represents the given line with slope and y-intercept is as attached below.

We are given the equation;

x - y - 3 = 0

Now, the standard way we should put the equation would be in slope intercept form which is; y = mx + c

where;

m is slope

c is y-intercept

Thus, our equation can be rearranged to get;

y = x - 3

Thus, y-intercept is c = -3

The graph that represents the given line is as attached below.

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Step-by-step explanation:

2y - x = 6

2y = x + 6

y = (x + 6) / 2

the slope is 1 and the y int is 3

In accordance with the function velocity, the car will have a complete stop after 6 seconds.

Herein we have a function of the velocity of a car (v), in feet per second, in terms of time (t), in seconds. The car stops for t > 0 and v = 0, then we have the following expression:

0.5 · t² - 10.5 · t + 45 = 0

t² - 21 · t + 90 = 0

By the quadratic formula we get the following two roots: t₁ = 15, t₂ = 6. The stopping time is the least root of the quadratic equation, that is, the car will have a complete stop after 6 seconds.

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Answer: [tex]\frac{9g}{4y}[/tex]

Step-by-step explanation:

[tex]\frac{6g}{2} \times \frac{3}{4y}=\frac{18g}{8y}=\frac{9g}{4y}[/tex]