Please help.
Solve for a

Answer: B. 6

Step-by-step explanation:

Integration by ordinary substitution is a general technique for simplifying integrals by changing variables, while integration by trigonometric substitution is a specific technique for evaluating integrals involving square roots and trigonometric functions.

Integration by ordinary substitution and integration by trigonometric substitution are two different techniques used to evaluate integrals in calculus.

Integration by ordinary substitution, also known as u-substitution, involves making a change of variables to simplify the integral. It is based on the chain rule for differentiation. The general steps for integration by ordinary substitution are as follows:

1. Identify a part of the integrand that can be replaced by a single variable, denoted by u.

2. Compute the derivative du/dx of the new variable u.

3. Substitute the expression for u and du into the integral, replacing the original integrand.

4. Integrate the resulting expression with respect to u.

5. Replace the variable u with the original variable or expression to obtain the final result.

Integration by trigonometric substitution, on the other hand, is a technique specifically used for integrals involving square roots of quadratic expressions or expressions with a combination of squares. It is based on trigonometric identities and is particularly useful when dealing with integrals that can be simplified using trigonometric functions. The general steps for integration by trigonometric substitution are as follows:

1. Identify a part of the integrand that can be expressed in terms of a trigonometric function.

2. Make a substitution using a trigonometric identity to replace the relevant part of the integrand.

3. Express all other terms in the integrand in terms of the same trigonometric function.

4. Simplify the integral using trigonometric identities and algebraic manipulations.

5. Integrate the resulting expression with respect to the new variable (usually denoted by θ).

6. Replace the trigonometric function with the original variable or expression to obtain the final result.

In summary, integration by ordinary substitution is a general technique for simplifying integrals by changing variables, while integration by trigonometric substitution is a specific technique for evaluating integrals involving square roots and trigonometric functions.

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Step-by-step explanation:

Option A is correct...

hope this answer helps you dear!

The function for the perimeter of the square is P = 4x.

The term function is defined as a relationship between inputs where each input is related to exactly one output.

Here we have given that Function p represents the perimeter, in inches, of a square with side length x inches.

As we all know that the term square is referred as a regular polygon having four equal sides and equal angles that measure 90° each.

And the term perimeter is defined as  the distance around the edge of a shape.

as we all know the the square has 4 sides which is represented by the term x.

Then the perimeter is calculated as

p = x + x + x + x

Therefore, the resulting function is written as

p = 4x.

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(a) The probability that every passenger who shows up can take the flight is approximately 0.163 or 16.3%. (b) The probability that the flight departs with empty seats is approximately 0.003 or 0.3%.

(a) In order for every passenger who shows up to take the flight, none of the 120 passengers who show up should be denied boarding due to the flight being overbooked. Since the airline sells 125 tickets for a flight that holds only 120 passengers, there is a possibility that more passengers show up than there are available seats. The probability that a passenger shows up is 1 minus the probability that they do not show up, which is 0.90 (1 - 0.10). Assuming the passengers behave independently, we can calculate the probability that all 120 passengers who show up can take the flight by multiplying the probability of each passenger showing up: 0.90^120 ≈ 0.163 or 16.3%.

(b) The probability that the flight departs with empty seats means that there are more available seats than the number of passengers who show up. In this case, the flight can accommodate all the passengers who show up, and there are empty seats remaining. Since the airline sells 125 tickets for a flight that holds 120 passengers, the flight will depart with empty seats only if less than 120 passengers show up. The probability that a passenger does not show up is 0.10, so the probability that a specific passenger shows up is 1 - 0.10 = 0.90. Using the binomial distribution, we can calculate the probability of fewer than 120 passengers showing up out of the 125 tickets sold. This probability is approximately 0.003 or 0.3%.

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Answer:

-5x + 4

Step-by-step explanation:

Answer:

2x-6y=-24

2x=-24+6y

x=-24+6y÷2

x=-12+3y equation 1

x+(-5y)=-22

-12+3y-5y=-22

-13-2y=-22

-2y=-22+13

-2y=-9

y=-9÷2

y=4.5equation 2

putting value of equation 2 in equation 1

x=-12+3y

x=-12+3×4.5

x=-12+13.5

x=1.5 answer!!!

Answer:

6x: 312

x: 52

Step-by-step explanation:

Let the deck be denoted by x then

6x:  312

There are 312 cards in 6x decks

In 1 deck x there are 312/6= 52 cards

6x: 312

6x/6: 312/6        Cancelling both sides by 6

x: 52

In ratio both the sides are divided by the same number to get equivalent fractions.

In 1 deck there are 52 cards

Answer:

A. Draw perpendicular lines

Step-by-step explanation:

Perpendicular lines are lines that intersect at a 90 degree angle. Unless you are constructing a right angle - or 45 degree angle - you would not need to draw perpendicular lines.

Therefore, answer A is correct.

Answer:

Step-by-step explanation:

x+2y+z=-5

2x-y-3z=5

x+y+2z=0

The given system of equations is a 3×4 matrix:

\(\left[\begin{array}{ccccc}1&2&1&|&-5\\2&-1&-3&|&5\\1&1&2&|&0\end{array}\right]\)

We need to find the echelon form of the rows of this matrix

Multiply line 1 by (-2) and add it to line 2:

\(\left[\begin{array}{ccccc}1&2&1&|&-5\\0&-5&-5&|&15\\1&1&2&|&0\end{array}\right]\)

Multiply line 1 by (-1) and add it to line 3:

\(\left[\begin{array}{ccccc}1&2&1&|&-5\\0&-5&-5&|&15\\0&-1&1&|&5\end{array}\right]\)

Divide the line 2 by (-5) and add it to row 3:

\(\left[\begin{array}{ccccc}1&2&1&|&-5\\0&-5&-5&|&15\\0&0&2&|&2\end{array}\right]\)

Consequently, the matrix in the form of an echelon of rows has the form:

\(\left[\begin{array}{ccccc}1&2&1&-5\\0&-5&-5&15\\0&0&2&2\end{array}\right]\)

For the given standard deviation the minimum value we would assign is 22.the maximum value we would assign is 88.

To calculate the minimum and maximum values based on the given information, we need to consider the standard deviation and the respective interest rates for the 3-year and 10-year periods.

Given:

S = 26.32 (Initial value)

E = 55 (Expected value)

t = 3 (Years)

Standard deviation = 60% (of the expected value)

3-year interest rate = 2.4%

10-year interest rate = 3.1%

To find the minimum value, we will calculate the value at the end of the 3-year period using the lowest possible growth rate.

Minimum value calculation:

Minimum value = E - (Standard deviation * E) = 55 - (0.6 * 55) = 55 - 33 = 22

Therefore, the minimum value we would assign is 22.

To find the maximum value, we will calculate the value at the end of the 10-year period using the highest possible growth rate.

Maximum value calculation:

Maximum value = E + (Standard deviation * E) = 55 + (0.6 * 55) = 55 + 33 = 88

Therefore, the maximum value we would assign is 88.

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5(x + 27) >= 6(x + 26)

5x + 135 >= 6x + 156

-x >= 21

x <= -21

Answer: Choice B.

Answer:

5

Step-by-step explanation:

keep change flip

   3         -       -2

3 + 2

Answer:

\( \frac{ {x}^{3} - 1}{x - 1} \\ = \frac{ {x}^{3} - {1}^{3} }{x - 1} \\ = > but : {(x - 1)}^{3} = (x - 1)( {x}^{2} - 2x + 1) \\ \therefore \: = \frac{(x - 1)( {x}^{2} - 2x + 1) }{(x - 1)} \\ = {x}^{2} - 2x + 1 \\ = {(x - 1)}^{2} \)

\( \frac{ {x}^{3} - 1 }{ x- 1} \\ = \frac{ {x}^{3} - 1 }{x - 1} \\ = \frac{( {x} - 1)( {x}^{2} + x + 1) }{x - 1} \\

= {x}^{2} +x+1\)

The cost for Farris Pharmacy to store one bottle of Zithromax antibiotics is 8,005.

The given function is c(x)=5x+8000/x

We can calculate the cost for Farris Pharmacy to store one bottle of Zithromax antibiotics by using the provided equation C(x).

To find the cost of storing one bottle, we will simply set x equal to 1. Therefore, C(1) = 5(1) + 8,000/1 = 8,005.

This means that the cost for Farris Pharmacy to store one bottle of Zithromax antibiotics is 8,005.

Therefore, the cost for Farris Pharmacy to store one bottle of Zithromax antibiotics is 8,005.

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To maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

To maximize the seating area, we need to determine the dimensions of the rectangular auditorium that will give us the largest possible area while using the given length of light strips.

Let the length of the rectangular auditorium be L, and its width be W.

The seating area consists of the rectangular portion minus the semicircular stage. So, the seating area's length is L - 2r (subtracting the semicircle's diameter) and the seating area's width is W - 2r.

The perimeter of the seating area is the sum of the lengths of its four sides, excluding the semicircular stage. The perimeter is given as 45π + 60 meters.

Perimeter = 2(L - 2r) + 2(W - 2r) + πr = 45π + 60

Simplifying: 2L + 2W - 8r + πr = 45π + 60

Rearranging: 2L + 2W = 8r + 44π + 60

The area of the seating area is given by A = (L - 2r)(W - 2r).

We want to maximize A, so we need to express it in terms of a single variable. Since we have an equation with two variables (L and W), we can rewrite one of the variables in terms of the other.

Rearranging the perimeter equation: 2L + 2W = 8r + 44π + 60

Solving for L: L = (8r + 44π + 60 - 2W) / 2

Substituting L in terms of W into the area equation: A = [(8r + 44π + 60 - 2W) / 2 - 2r] (W - 2r)

Simplifying: A = (4r + 22π + 30 - W) (W - 2r)

Now we have the area equation in terms of a single variable, W. To maximize A, we can take the derivative of A with respect to W, set it equal to zero, and solve for W.

dA/dW = 2(4r + 22π + 30 - W) - (W - 2r) = 0

Solving for W: 8r + 44π + 60 - W = W - 2r

Simplifying: 10r + 44π + 60 = 2W

W = 5r + 22π + 30

Now that we have W in terms of r, we can substitute this expression back into the area equation to get the area in terms of r only.

A = (4r + 22π + 30 - (5r + 22π + 30)) ((5r + 22π + 30) - 2r)

Simplifying: A = (r - 22π) (3r + 22π + 30)

Expanding: A = 3r² + 8rπ + 30r - 66πr - 660π

Now, to find the maximum area, we can take the derivative of A with respect to r, set it equal to zero, and solve for r.

dA/dr = 6r + 8π + 30 - 66π = 0

Simplifying: 6r - 58π + 30 = 0

6r = 58π - 30

r = (58π - 30) / 6

r ≈ 29π/3 - 5

Therefore, to maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

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Answer:

12.25cm2

Step-by-step explanation:

Area of a square= S ×S

3 1/2 × 3 1/2 = 3.5×3.5 = 12.25

Answer:

Step-by-step explanation:

0.267

Answer:

there is no question. but these are two of the same lines with different Y-intercepts.

Adam needs to show that the diagonals are perpendicular, congruent, and bisect each other.Therefore Option D is correct.

To prove that PQRS is a square, Adam needs to show that all four sides are congruent and that all four angles are right angles.

One way to do this is by showing that the diagonals of PQRS are perpendicular, congruent, and bisect each other.

If the diagonals are perpendicular, then opposite angles are congruent and the quadrilateral is a kite.

If the diagonals bisect each other, then opposite sides are congruent and the kite is a rhombus.

If the diagonals are also congruent, then all sides are congruent and the rhombus is a square.

Therefore, He needs to show that the diagonals of PQRS are perpendicular, congruent, and bisect each other to prove that PQRS is a square.

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Answer:

She needs to get at least 96 on the 4th test to earn an average of at least 90 in the class.

Step-by-step explanation:

(97+78+89+?) divided by 4 at\geq 90

It is divided by 4 because it is the average of 4 test scores.

To Solve: (97+78+89+?) divided by 4 at\geq 90

Multiply by 4 on both sides 97+78+89+? at\geq 360

Isolate variable: ? at\geq 96

As a professional tutor, I will explain how to calculate the perimeter of a badge in the shape of a quarter circle with a 9 cm base and 9 cm height.

Let's break the badge down into its three segments: the two straight sides (the base and height) and the curved outer edge.

1. Straight sides: The base and height are both 9 cm, so this part is straightforward. The combined length of the base and height is 9 cm + 9 cm = 18 cm.

2. Curved outer edge: To calculate the curved outer edge, we need to understand that it is one-fourth of the circumference of the entire circle from which it is cut. The formula for the circumference C of a circle with radius r is C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14. Since the base and height are both 9 cm, it's clear that the radius of the circle is 9 cm. Thus, the circumference of the full circle is C = 2π(9 cm) ≈ 56.55 cm. Since we only have a quarter of the circle, the curved outer edge is 1/4 of this, which is about 56.55 cm / 4 ≈ 14.14 cm.

3. Perimeter: Finally, add up the lengths of the three segments: 18 cm (straight sides) + 14.14 cm (curved outer edge) ≈ 32.14 cm.

So, the perimeter of the badge in the shape of a quarter circle with a 9 cm base and 9 cm height is approximately 32.14 cm (rounded to two decimal places).

The sequence cos(0),cos(π),cos(2π),cos(3π),cos(4π),… can be represented as a function k: N -> R, where N is the set of natural numbers and R is the set of real numbers. The domain of the function is the set of natural numbers, and the codomain is the set of real numbers. The function l: N -> {-1,1}, where l(n) = (-1)^(n).

The sequence 1,14,19,116,… can be represented as a function f: N -> N, where N is the set of natural numbers. The rule for determining the outputs of the function is as follows: f(1) = 1, f(2) = 14, f(3) = 19, f(4) = 116, and so on.
The sequence 13,19,127,181,… can be represented as a function g: N -> N, where N is the set of natural numbers. The rule for determining the outputs of the function is as follows: g(1) = 13, g(2) = 19, g(3) = 127, g(4) = 181, and so on. The domain of the function is the set of natural numbers, and the codomain is also the set of natural numbers. We can see that this sequence is not equal to any of the other sequences given.

The sequence 1,−1,1,−1,1,−1,… can be represented as a function h: N -> {-1,1}, where N is the set of natural numbers. The rule for determining the outputs of the function is as follows: h(1) = 1, h(2) = -1, h(3) = 1, h(4) = -1, and so on. The domain of the function is the set of natural numbers, and the codomain is the set {-1,1}. We can see that this sequence is equal to the function f: N -> {-1,1}, where f(n) = (-1)^(n+1).

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Answer:

D

Step-by-step explanation:

just count how many spaces one of the points have moved

x moved 6 spaces to the left so it'll be x-6 and it moved up 2 so itll be y+2

The area of the square is changing at 12√2 + 2√2t square inches/minute when the circle is increasing at 1 in/min.

Let us find the relationship between r and s using the Pythagorean theorem. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.

2r = s√2
Squaring both sides, we get:
4r² = 2s²or s² = 2r²
Dividing by 2 on both sides, we get:
s²/2 = r²
Differentiating both sides with respect to t, we get:
ds²/dt = 2r (dr/dt)
Dividing both sides by 2s, we get:
ds/dt = r (dr/dt) / s

Substituting r² = s²/2,

\(ds/dt = r (dr/dt) / √2s2s ds/dt = r (dr/dt)s ds/dt = (r/2) (dr/dt)2s ds/dt = r (dr/dt) or dA/dt = 2s ds/dt = 2r (dr/dt)\)

Now, substituting r² = s²/2,

dA/dt = 2s ds/dt = 2(√2 s) (dr/dt) = 2(√2) r (dr/dt)

Now, substituting dr/dt = 1 in/min and r = 6 in (since the circle is increasing at 1 in/min, the radius after t minutes is 6 + t),

dA/dt = 2(√2) (6 + t) (1) = 12√2 + 2√2t square inches/minute

Therefore, the area of the square is changing at a rate of 12√2 + 2√2t square inches/minute.

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Answer:

\(49x^{6}\)\(y^{8}\)

Step-by-step explanation:

1. Factor 2401 into its prime factors

          2401 = 74

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

          2401 = 74

No factors remain inside the root!!

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

          49 = 72

At the end of this step the partly simplified SQRT looks like this:

        49√(x^12y^16)

2. Rules for simplifying variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

     (3.1) √(x8)=x4

    (3.2) √(x-6)=x-3

   (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     (4.1) √(x5)=x2•√(x)

    (4.2) √(x-7)=x-3•√(x-1)

Applying these rules to our case we find out that

     SQRT(x12y16) = x6y8

Combine both simplifications:

 sqrt (2401x12y16) =

       49x6y8

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The length of AB is 25 units

The given parameters are

AC = 15 cm

BC = 20 cm

The triangle is right -angled at C.

So, we have:

AB^2 = AC^2 + BC^2

This gives

AB^2 = 15^2 + 20^2

Evaluate

AB^2 = 625

Take the square roots

AB = 25

Hence, the length of AB is 25 units

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