Compute the following integral. Hint: Complete the square and make a substitution to create a quantity of the form a^2 - u^2. Remember that x^2 + bx + c = (x + b/2)^2 + c - (b/2)^2 ∫ √5+4x-x^2 dx
(A) 9/2 [arcsin (x-2/3) + (x-2) √9-(x-2)^2)/9 + C (B) 3/2 [arcsin (x-2/3) + (x-2) √9-(x-2)^2)/3 + C (C) 9/2 [arcsin (x-2) + (x-2) √9-(x-2)^2)/9 + C (D) 9/2 [arcsin (x-2/3) - (x-2) √9-(x-2)^2)/9 + C (E) None of these

False. The complement of an event A, denoted by A', is the event consisting of all outcomes in the sample space S that are not in A.

In probability theory, a sample space S represents the set of all possible outcomes of an experiment or random phenomenon. An event A is a subset of the sample space S, representing a specific outcome or a combination of outcomes of interest.

The complement of event A, denoted by A', includes all the outcomes in the sample space S that are not part of event A. In other words, A' consists of all outcomes that do not satisfy the conditions for event A to occur.

For example, let's consider rolling a fair six-sided die. The sample space S consists of the numbers {1, 2, 3, 4, 5, 6}. Now, let event A be the event of rolling an odd number. In this case, A = {1, 3, 5}, and the complement of A, denoted by A', would be A' = {2, 4, 6}. A' includes all the outcomes that are not odd numbers.

It's important to note that the complement of an event A and the event itself together cover the entire sample space S. In other words, A and A' are mutually exclusive and exhaustive, meaning that any outcome must either be in A or in A'.

So, in summary, the complement of an event A is the set of all outcomes in the sample space S that do not belong to A.

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By the definition of lunar month, it can be inferred that-

If the moon were farther from earth than it is now, then lunar month will be more than 28 days.

What is lunar month?

Time taken by the moon to make one complete revolution around the earth is called lunar month.

If the moon were farther from earth than it is now, then the moon will have to travel a greater distance to make one complete revolution around the moon. So time taken by the moon to make one complete  revolution around the earth will increase. So lunar month will be more than 28 days.

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Answer:

Graph B

Step-by-step explanation:

The equation for direct variation is y=kx, with k being the slope. As you can see from the equation, there is no y-intercept. In graph A, you would add 8; therefore, it does not meet the requirements for direct variation.

Answer:

5 was not multiplied by -1

hi, I'm no bot just in case...

the grapgh of the line shows y intercept of -9 and rate of change by 4

SoThe equation of the lline will be: \(y=4x-9\)

With the help of standard deviation we can conclude our answer.

acc to our question-

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Answer:

TV = 9.71

Step-by-step explanation:

sin 47° = TV/13.28

0.7314 = TV/13.28

TV = 9.71

Answer:

8.7

Step-by-step explanation:

a = side of a regular hexagon inscribed in a circle = radius of the circle

Area of a hexagon = (3√3 / 2)a² =  (3√3 / 2)4² = 41.57

Acircle = πr² = π4² = 50.27

Area of shaded region = Acircle - Ahexagon = 50.27 - 41.57 = 8.7

Answer:

-3

Step-by-step explanation:

-8(1-4x)=-104

1-4x=-104/-8

1-4x=13

4x=1-13

4x=-12

x=-12/4

x=-3

Answer:

10. y degree = 102 degree

11. x degree = 103 degree

Step-by-step explanation:

The formula to calculate the sum of the interior range of polygons is (n-2) * 180.

With n being the number of sides.

From that sum, you can then deduce the angles of y or x, by substracting the other angles.

10. n = 4 => ( 4 - 2 ) * 180 = 2 * 180 = 360 degree

y = 360 - 120 - 85 - 53 = 102 degree

11. n = 5 => (5 - 2) * 180 = 3 * 180 = 540 degree

x = 540 - 117 - 100 - 105 - 115 = 103 degree

Answer:

1

intercepts on the y line

Answer:

m BC = 100

Step-by-step explanation:

Since the angle is at the center, the arc has the same measurement as the angle

m BC = 100

The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

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There fore, the correct answer is C. Quartic binomial.

The polynomial x^2-x^4+2x^2 can be expressed in the standard form by combining like terms.x^2-x^4+2x^2 = -x^4 + 3x^2To classify the polynomial, we first note that the degree of the polynomial is 4. A polynomial with a degree of 4 is called a quartic polynomial. The polynomial has only two terms, which makes it a binomial. Thus, the polynomial -x^4 + 3x^2 is a quartic binomial .

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If the length of one side of the rhombus is 6m and the radius of the rhombus as 4 m then the area of the rhombus is 24 m².

What is the area of the rhombus?

The Area of a Rhombus = A = ½ × d1 × d2,

Where d1 and d2 are the diagonals of the rhombus.

The area of a rhombus can be found using the formula:

Area = (diagonal 1 x diagonal 2) / 2

or

Area = (base x height) / 2

We are given the length of one side of the rhombus as 6 m, which means the length of the other side is also 6 m since all sides of a rhombus are congruent. We are also given the radius of the rhombus as 4 m, which is half the length of the diagonal.

Using the Pythagorean theorem, we can find the length of the other diagonal:

diagonal 2 = 2(radius) = 2(4) = 8 m

Now we can use the formula to find the area of the rhombus:

Area = (diagonal 1 x diagonal 2) / 2

Area = (6 m x 8 m) / 2

Area = 24 m²

Therefore, the area of the rhombus is 24 m².

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The given statement "The genitive singular form of the relative pronoun is quod" is False. What is Genitive? The genitive is a grammatical case in some languages that expresses a possessive relationship or a close relationship that might be equivalent to many English prepositional phrases.

Latin is a language that has this kind of case. It is employed to show possession, the whole of which is often equivalent to the English "of" construction. What is a pronoun? A pronoun is a word that takes the place of a noun in a sentence. It's used to avoid redundancy and to make sentences more straightforward. Pronouns may also aid in the clarity and conciseness of a sentence. A relative pronoun, like a typical pronoun, substitutes for a noun in a sentence.

It is used to link two clauses together and to represent a noun or a noun phrase in the second clause that refers back to a noun in the first clause. In Latin, the genitive singular form of the relative pronoun is cujus, not quod. Therefore, the given statement "The genitive singular form of the relative pronoun is quod" is False.

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Answer:

ithink the first one :p

Step-by-step explanation:

The association is neither positive nor negative because it is not linear. The solution has been obtained by using the concept of linear relationship.

What is linear relationship?

In statistics, a linear relationship is a connection that runs in a straight line between two variables (or linear association).

We know that a linear relationship can be represented mathematically, and graphically, in which the variable and constant are connected by a straight line.

From the figure, we can see that the points are scattered and do not form a straight line.

So, it is not linear.

Hence, the association is neither positive nor negative because it is not linear.

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Step-by-step explanation:

Equation of circle with center h,k and radius r

  (x-h)^2  + (y-k)^2  = r^2

for this one this becomes    (center  9,-2  and radius 4 )

  (x-9)^2 + ( y+2)^2 =  16

The customers of Rhythm Time, an online music service, downloaded 397,970 songs last year.

Rhythm Time, an online music service, had 278,579 songs downloaded this year by its customers. That figure is 30% less than last year. Last year

We can begin by assuming that the total number of songs downloaded last year was x. According to the problem statement, 278,579 songs were downloaded this year, which is 30% less than last year. We can write it as an equation:x - 0.30x = 278,579 Simplifying, we get:0.70x = 278,579 Dividing both sides by 0.70, we get:x = 397,970Therefore, last year, Rhythm Time's customers downloaded 397,970 songs.

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Premise 1: Hard water can damage home appliances. Premise 2: A water softening system can prevent hard water. Conclusion: Therefore, a water softening system can prevent damage to home appliances.

The argument consists of two premises and a conclusion. Premise 1 states that hard water can cause damage to home appliances. Premise 2 states that a water softening system can prevent hard water. The conclusion drawn from these premises is that a water-softening system can prevent damage to home appliances.

In standard form, the argument is presented by listing the premises first, followed by the conclusion. This format helps to clearly identify the statements being made and their logical relationship. By representing the argument in this way, it becomes easier to analyze the structure and validity of the reasoning presented.

Therefore, the standard form representation of the argument is:

Premise 1: Hard water can damage home appliances.

Premise 2: A water softening system can prevent hard water.

Conclusion: Therefore, a water softening system can prevent damage to home appliances.

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on using  disjunctive syllogism to derive Q from the second premise and the derived value of A. if P is true, then Q must also be true..

In logic, a compound statement is made up of two or more simple statements, known as premises or assumptions, that are combined using logical operators such as "and," "or," and "not." To prove a compound statement, we use rules of inference to derive a conclusion based on the given premises.

In the first proof question, we are given three premises: P, P or R, and not S or A. We need to prove the statement Q using these premises. To do so, we use the disjunctive syllogism rule, which states that if one of two disjunctive statements is false, then the other must be true. By assuming ~P, we derive ~S from the third premise using the rule of disjunction. Then, using modus ponens, we derive A from the assumption of ~P and the third premise. Finally, we use disjunctive syllogism to derive Q from the second premise and the derived value of A.

In the second proof question, we are given three premises: not P or S, not S, and R or Q. We need to prove the statement P implies Q using a conditional world proof. We assume P is true and derive S using the first premise. Using the second premise and modus tollens, we derive not R. Finally, using disjunctive syllogism, we derive Q from the third premise and the derived value of not R. Therefore, we show that if P is true, then Q must also be true..

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If Mr. Phil T. Rich had a boat load of money. The original value of his estate is $152,000.

Let's call the original value of Mr. Phil T. Rich's estate "x".

After he gave 1/2 of the estate to his wife, he was left with x/2.

After he gave 30,000 to his daughter, he was left with x/2 - 30,000.

After he gave half of what was left to his butler Niles, he was left with (x/2 - 30,000)/2.

After he gave half of what was left to Bubbles, he was left with (x/2 - 30,000)/4.

Finally, after he donated the 8,000 to charity, he was left with (x/2 - 30,000)/4 - 8,000.

We know that the final amount after all these transactions was $0, so we can set up an equation to solve for x:

0 = (x/2 - 30,000$)/4 - 8,000

Multiplying both sides by 4 to isolate x/2:

0 * 4 = (x/2 - 30,000) - 8,000 * 4

Expanding the right side:

0 = (x/2 - 30,000) - 32,000

Adding 30,000 and 32,000 to both sides:

30,000+ 32,000 = (x/2)

Dividing both sides by 1/2:

62,000 * 2 = x

Multiplying both sides by 2:

62,000* 2 * 2 = x * 2

Expanding the left side:

62,000* 4 = x

Dividing both sides by 4:

62,000 * 4 / 4 = x / 4

Expanding the left side:

$62,000 = x

Therefore the original value of Mr. Phil T. Rich's estate was $62,000.

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Answer:

X^158

Step-by-step explanation:

X^60xX^-18x(    )=X^200

X^42x(   )=X^200

x^158

The variables a and b have a possible value of 7 and 11

The given parameters are

GCF(a, b)• LCM (a, b) = 77

As a general rule, the product of two numbers equals the product of the greatest common factor and the least common multiple of the numbers

This implies that

a * b = GCF(a, b)• LCM (a, b)

So, we have

a * b = 77

Express 77 as 7 * 11

a * b = 7 * 11

By comparison, we have

a = 7 and b = 11

Hence, the possible values are a = 7 and b = 11

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Answer:

Answer = 32

Step-by-step explanation:

p= 8

4p

(4)(8)

=32

Answer:

I got, 8 x 4 = 32

Answer:

length = 13 in, width = 7 in , area = 91 in²

Step-by-step explanation:

let width be w then length = 2w - 1

perimeter(P) of rectangle is calculated as

P = 2 × length + 2× width

  = 2(2w - 1) + 2w

  = 4w - 2 + 2w

  = 6w - 2

given P = 40 , then

6w - 2 = 40 ( add 2 to both sides )

6w = 42 ( divide both sides by 6 )

w = 7

then

width = 7 in and length = 2w - 1 = 2(7) - 1 = 14 - 1 = 13 in

the area (A) of a rectangle is calculated as

A = length × width = 13 × 7 = 91 in²