If the arc length of a circle with a radius of 5 cm is 18.5 cm, what is the area of the sector, to the nearest hundredth



i need it quick please

The quadratic function in standard form that passes through the given points would be f (x ) = 5x ² - 70x + 225

A quadratic function in standard form is given by the equation:

f ( x ) = ax ²  + bx + c

The system of equations would be:

25 a + 5b + c = 0

81 a + 9b + c = 0

49 a + 7b + c = -20

With a series of calculations, we can find the value of b and c :

b = - 14 a = - 14 ( 5 ) = -70

25 ( 5 ) - 70 (5) + c = 0

125 - 350 + c = 0

c = 225

This gives us the quadratic function of :

f ( x ) = 5x ² - 70x + 225

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The probability that an M&M picked at random is brown is 30% if m&m picked brown at random. Probability refers to the measure of the likelihood of an event occurring.

To find the probability that an M&M picked at random is brown, we need to consider the given percentages of the other colors. Given that 20% are yellow, 20% are red, 10% are orange, 10% are blue, and 10% are green. First, let's add these percentages together:
20% + 20% + 10% + 10% + 10% = 70%

Since the total percentage should add up to 100%, we can find the percentage of brown M&Ms by subtracting the sum of the other colors' percentages from 100%:
100% - 70% = 30%
So, the probability that an M&M picked at random is brown is 30%.

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The standard parametric equations for the tangent line to the curve r(t) at t = T₀ = 4 are: x = 24(t-4) + 48, y = 15(t-4) - 3, z = 64(t-4) + 64

To find the parametric equations for the tangent line to the curve r(t) at t = T₀ = 4, we can follow these steps:

Step 1: Find the point on the curve at t = T₀.

To find the point on the curve at t = T₀ = 4, we simply evaluate r(4):

r(4) = 3(4²)i + (4(4)-1)j + 4³k

= 48i + 15j + 64k

So the point on the curve at t = 4 is (48, 15, 64).

Step 2: Find the direction of the tangent line at t = T₀.

To find the direction of the tangent line, we need to take the derivative of r(t) and evaluate it at t = 4. So we first find r'(t):

r'(t) = 6ti + 4j + 3t²k

Then we evaluate r'(t) at t = 4:

r'(4) = 6(4)i + 4j + 3(4²)k

= 24i + 4j + 48k

So the direction of the tangent line at t = 4 is the vector <24, 4, 48>.

Step 3: Write the parametric equations for the tangent line.

To write the parametric equations for the tangent line, we use the point and direction found in steps 1 and 2. We can write the parametric equations as:

x = 48 + 24(t-4)

y = 15 + 4(t-4)

z = 64 + 48(t-4)

Simplifying these equations gives us:

x = 24t + 48

y = 4t - 3

z = 48t + 64

These are the standard parametric equations for the tangent line to the curve r(t) at t = 4.

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Answer:

To solve this equation for x, we can begin by simplifying the left side of the equation using the common denominator of 20:

20(3x - 1/4) - 20(2x + 3/5) = 20(1 - x/10)

Next, we can distribute the 20 to each term:

60x - 5 - 40x - 12 = 20 - 2x

Simplifying the left side of the equation:

20x - 17 = 20 - 2x

Adding 2x to both sides:

22x - 17 = 20

Adding 17 to both sides:

22x = 37

Dividing by 22 on both sides:

x = 37/22

Therefore, the solution to the equation 3x-1/4 - 2x+3/5 = 1-x/10 is x = 37/22.

The function used to model the monthly profit for x trinkets produced are f(x) = -4(x - 50)(x - 250). The maximum profit occurs when 150 trinkets are produced.

The quadratic function that can be used to model the monthly profit for x trinkets produced is:

f(x) = -4(x - 50)(x - 250)

This is because the function is in the form of a quadratic equation, which is y = ax² + bx + c. In this case, a = -4, b = 1200, and c = 0. When we expand and simplify the equation, we get:

f(x) = -4x² + 1200x

This equation represents a parabola with a maximum value at x = 150. Therefore, the maximum profit occurs when 150 trinkets are produced.

The other answer choices are not correct because they are not quadratic functions. For example, f(x) = (x - 50)(x - 250) is a product of linear factors, and f(x) = 28(x - 50)(x + 250) and f(x) = (x + 50)(x + 250) have a coefficient of x² that is not equal to -4.

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a) The profit at a sales level of 14 trees is $180.40.

b) The average change in profit sales is $13.96 per tree [(ΔP/Δx) = 97.75/7].

c) The instantaneous rate of change of profit at a sales level of 14 trees is $19.72 per tree.

d) The equation of the tangent line at (5, f(5)) is y = 6x - 25.

a. To find the profit at a sales level of 14 trees, we need to evaluate the profit function at x = 14:

P(x) = 20x - 0.01x^2 - 100

P(14) = 20(14) - 0.01(14)^2 - 100 = $180.40

Therefore, the profit at a sales level of 14 trees is $180.40.

b. To find the average change in profit sales from 12 to 19 trees, we need to calculate the average rate of change of the profit function over this interval:

Δx = 19 - 12 = 7

ΔP = P(19) - P(12) = (2019 - 0.0119^2 - 100) - (2012 - 0.0112^2 - 100) = $97.75

Therefore, the average change in profit sales is $13.96 per tree [(ΔP/Δx) = 97.75/7].

c. To find the instantaneous rate of change of profit at a sales level of 14 trees, we need to find the derivative of the profit function at x = 14:

P(x) = 20x - 0.01x^2 - 100

P'(x) = 20 - 0.02x

P'(14) = 20 - 0.02(14) = $19.72

Therefore, the instantaneous rate of change of profit at a sales level of 14 trees is $19.72 per tree.

d. To find the equation of the tangent line at (5, f(5)), we need to find the slope of the tangent line and its y-intercept:

f(x) = x^2 - 4x

f'(x) = 2x - 4

f'(5) = 2(5) - 4 = 6

The slope of the tangent line at (5, f(5)) is 6.

To find the y-intercept of the tangent line, we can use the point-slope form of a line:

y - f(5) = m(x - 5)

y - (5^2 - 4*5) = 6(x - 5)

y - 5 = 6x - 30

y = 6x - 25

Therefore, the equation of the tangent line at (5, f(5)) is y = 6x - 25.

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The cost of fencing for the semicircular statuary garden is $651.99.

Finding the circumference of the full circle:
C = πd, where d is the diameter.
C = 3.14 × 26
C ≈ 81.64 feet

Since it's a semicircular garden, dividing the circumference by 2:
Semi-circular perimeter = 81.64 ÷ 2
Semi-circular perimeter ≈ 40.82 feet

Now, Adding the diameter to the semi-circular perimeter to get the total fence length:
Total fence length = 40.82 + 26
Total fence length ≈ 66.82 feet

Then, Calculating the total cost of fencing:
Cost = Total fence length × Cost per linear foot
Cost = 66.82 × $9.75
Cost ≈ $651.99

So, the cost of fencing the semicircular statuary garden will be approximately $651.99.

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The measure of angle OAC if major arc AB measures 220 degrees is 110 degrees. Therefore, the correct option is C.

To find the measure of angle OAC, we need to use the central angle theorem which states that the measure of an inscribed angle is equal to half the measure of the intercepted arc.

Here, we are given that the major arc AB measures 220 degrees. So, the measure of angle AOB (the central angle) is 220 degrees.

Since angle OAC is an inscribed angle that intercepts arc AB, its measure is half the measure of arc AB.

Therefore, measure of angle OAC = (1/2) * 220 = 110 degrees.

So, the correct answer is option (c) 110.

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Options B & C

There is an asymptote at y = 40.

There is an asymptote at x = 0.

Concept 1. Zeros of rational functions

Concept 2. Vertical asymptotes of rational functions

Concept 3. Horizontal asymptotes of rational functions

Concept 4. Transformations - vertical shift

Rational functions have zeros at values of x where the numerator is zero, while the denominator is not also zero.

[tex]f(x)=\dfrac{40x+99}{x}[/tex]

Values that make the denominator zero
Note that for the function f(x), x=0 is the only value that will make the denominator zero.

Values that make the numerator zero
To find the value that makes the numerator zero, set the numerator equal to zero, and solve for the value of x that makes it true:

[tex]40x+99=0[/tex]

[tex]40x=-99[/tex]

[tex]x=\frac{-99}{40}[/tex]

So, [tex]x=\frac{-99}{40}[/tex] is the only value that will make the numerator zero

Note that this doesn't simultaneously make the denominator zero, so [tex]x=\frac{-99}{40}[/tex] is a zero (and the only zero) of the function f(x).

Therefore, Option A is NOT a correct answer.

Rational functions have Horizontal Asymptotes if the degree of the polynomial in the numerator is less than or equal to the degree of the polynomial in the denominator.

If the Degree of the denominator is greater, the Horizontal Asymptote is at a y=0.

If the Degrees are equal, the Horizontal Asymptote is at a y-value equal to the ratio of the leading coefficients.

[tex]f(x)=\dfrac{40x+99}{x}[/tex]

Note that for f(x), the degrees of the polynomials in the numerator and denominator are both 1.  So, a horizontal asymptote does exist, and it is at a height of the ratio of the leading coefficients.

The leading coefficient of the numerator is 40, while the leading coefficient of the denominator is 1.

The ratio of the leading coefficients, 40/1, so the horizontal asymptote is y=40.

Therefore, Option B is a correct answer choice.

Rational functions have Vertical Asymptotes at values of x where the denominator is zero, while the numerator is not also zero (the opposite of finding "zeros" of the function).

Recalling the values that make the numerator and denominator zero from Concept 1:

Since x=0 doesn't also make the numerator zero, x=0 is a vertical asymptote for the function f(x).

Therefore, Option C is a correct answer choice.

Rational functions have been vertically shifted if after all the main rational function fraction, there is a number added or subtracted.

I provide an example of a different function (which I'll call g(x)) here:

[tex]g(x)=\dfrac{3}{x}+2[/tex]

Observe that the "+2" is after all of the main fraction, so the graph of 3/x would have been shifted vertically up 2 units.

This is NOT the case for the function f(x) from the question.  The "99" is part of the fraction, so it does not represent a vertical shift.

Therefore, Option D is NOT a correct answer choice.

The amount of penny that you should receive from your friend after the seventh shoveling job would be = 2,187 pennies.

To calculate the number of penny that you will receive after the seventh job the following is carried out.

The agreement stated that the money would be tripled for each completed shoveling job.

That is for 2 jobs = 3×3 = 9

3 jobs = 3×3×3 = 27

7 jobs = 3×3×3×3×3×3×3

= 2,187 pennies.

Therefore, the 2,187 pennies would be received from your friend after the seventh shoveling job.

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The unit rate in teaspoons per cup is 2 teaspoons per cup

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Unit rate = teaspoons/Recipe

Substitute the known values in the above equation, so, we have the following representation

Unit rate = (4/3)/(2/3)

Evaluate

Unit rate = 2

Hence, the unit rate is 2

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Walmart's decision to use its own fleet of trucks to pick up products directly from manufacturers and deliver them to its stores is a strategic move that has the potential to benefit both Walmart and manufacturers.

By using its own fleet, Walmart will be able to cut down on transportation costs and gain more control over the supply chain, which can lead to better efficiency and cost savings. This is especially important given Walmart's massive scale, with over 4,000 stores in the US alone.

For manufacturers, this move by Walmart could be a relief as they can focus on their core competency of making products rather than managing logistics. With Walmart taking over the transportation aspect, manufacturers can rest assured that their products will be delivered on time and in the right condition.

The fact that Walmart already has a large fleet of trucks and trailers means that it has the capacity to implement this new program without too much additional investment. However, it remains to be seen how manufacturers will respond to this proposal, as they may have existing contracts with other carriers or may be hesitant to rely too heavily on Walmart for their transportation needs.

Overall, Walmart's move towards using its own fleet of trucks is a smart one that has the potential to benefit both the retailer and its suppliers.

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Answer:

D.5

Step-by-step explanation:

8x – 6 > 12 + 2x

= 8x−2x>12+6= 6x>18

= x>38x−2x>12+6

= 6x>18

= x>3

From the given options the only value which is greater than 3 is Option (D) 5

The interest he had received in total after eight years is 1396.59 kroner

From the question, we have the following parameters that can be used in our computation:

Principal, P = 7000

Rate, r = 2.3%

Time, t = 8

The interest he had received in total after eight years is calculated as

I = P(1 + r)^t - P

Substitute the known values in the above equation, so, we have the following representation

I = 7000(1 + 2.3%)^8 - 7000

Evaluate

I = 1396.59

Hence, the total interest is 1396.59 kroner

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When the value of x is 7 the value of p will be equal to 8.

It is given that P varies inversely with x, so we can write that

p=k/x

where k is the proportionality constant.

here we can find the value of k by substituting the value of p and x with 7 and 8 in the relation that is given above, we get:

7=k/8

k=7*8

k=56

we the value of k to be 56 after putting the values in the relation.

Now if x is changed to 7, and k is equal to 56 we can get the value of p by putting the known values in the same relation.

p=k/x

p=56/7

p=8.

Therefore, when the value of x is 7 the value for p will be equal to 8.

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In a rectangle, a diagonal forms a 36° angle with a side. To find the measure of the angle between the diagonals, which lies opposite to a shorter side, follow these steps:

1. Let's denote the angle between the diagonal and the shorter side as θ (which is given as 36°). Since the rectangle has four right angles (90°), the angle between the diagonal and the longer side can be found by subtracting θ from 90°: 90° - 36° = 54°.

2. Now, consider the right-angled triangle formed by the diagonal, shorter side, and longer side of the rectangle. The angle between the diagonal and the longer side is 54°, as calculated in step 1.

3. In a right-angled triangle, the sum of the other two angles (besides the right angle) must equal 90°. Thus, the angle opposite the shorter side in this triangle (let's call it α) can be calculated as: 90° - 54° = 36°.

4. Finally, the angle between the diagonals can be found by doubling α, as the diagonals bisect each other at a right angle: 2 * 36° = 72°.

Hence, the measure of the angle between the diagonals, which lies opposite to a shorter side, is 72°.

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In general, the cost of the visit will depend on the number of cavities found by the dentist as: Cost = $50 + $100 * n.

An equation is a mathematical statement that says that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). An equation expresses a relationship between the quantities involved and represents a balance or equality between the two sides. Equations are used in various fields of mathematics, science, and engineering to model real-world situations and solve problems. They can be linear or nonlinear, simple or complex, and involve different types of variables, functions, and operators. Solving equations is an essential skill in mathematics and involves applying various techniques and strategies to find the solution or solutions to the equation.

Here,

If the dentist finds n cavities, the cost of the visit will be:

Cost = $50 + $100 * n

So, if the dentist finds, for example, 3 cavities, the cost of the visit will be:

Cost = $50 + $100 * 3 = $350

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Complete question:

The price of a visit to the dentist is $50 if the dentist feels any cavities in additional charge of $100 per cavity get added to the bill. If the dentist finds n cavities What will the cost of the visit be?

The function f(x) = x Sqrt (x^2 + 4) is concave down on the entire interval. The inflection point is at x is equal to 0. There is no minimum or maximum in the interval.

To find the concavity, we need to find the second derivative

f(x) = x√(x^2+4)

f'(x) = √(x^2+4) + x^2/√(x^2+4)

f''(x) = -4x^3/(x^2+4)^(3/2)

The second derivative is negative for all x, which means the function is concave down on the entire interval.

To find the inflection point, we need to solve

f''(x) = 0

-4x^3/(x^2+4)^(3/2) = 0

This is true only when x = 0. Therefore, the inflection point is at x = 0.

To find the minimum and maximum, we need to find the critical points. The critical points are found by setting the first derivative equal to zero

f'(x) = √(x^2+4) + x^2/√(x^2+4) = 0

Multiplying both sides by √(x^2+4), we get

x^2+4 + x^2 = 0

2x^2 = -4

x^2 = -2

This equation has no real solutions, which means there are no critical points in the interval. Therefore, there is no minimum or maximum in the interval.

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The statement "La tangente de 60° es igual al triple de la tangente de 20°" is not true.

To solve the problem "La tangente de 60° es igual al triple de la tangente de 20°," follow these steps:

Step 1: Write down the equation based on the problem statement:
tan(60°) = 3 * tan(20°)

Step 2: Find the tangent values for the given angles:
tan(60°) = √3
tan(20°) = 0.36397 (approximate value)

Step 3: Plug the tangent values into the equation and check if the statement is true:
√3 = 3 * 0.36397

Step 4: Calculate the right side of the equation:
3 * 0.36397 = 1.09191 (approximate value)

Step 5: Compare the two values:
√3 ≈ 1.73205 (approximate value)

Since 1.73205 ≠ 1.09191, the statement "La tangente de 60° es igual al triple de la tangente de 20°" is not true.

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To completely recharge a 1.5-volt cell, each electron in the cell must be

supplied with a minimum energy of 2.403 × 10^-19 joules.

To completely recharge a 1.5-volt cell, each electron in the cell must be

supplied with an energy greater than or equal to the potential difference of

the cell, which is 1.5 volts.

The minimum energy required to supply to each electron can be

calculated

using the formula:

E = qV

where E is the energy in joules (J), q is the charge of an electron (1.602 ×

10^-19 coulombs), and V is the potential difference in volts.

Substituting the given values, we get:

[tex]E = (1.602 × 10^-19 C) × (1.5 V)E = 2.403 × 10^-19 J[/tex]

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To solve the inequality -1/4a > 3a, we need to first multiply both sides by -4 to get rid of the fraction:
-1a > 12a
Next, we can subtract 12a from both sides to get:
-13a > 0
Dividing both sides by -13 gives us:
a < 0

To solve the inequality b – 12 > -3, we can add 12 to both sides:
b > 9

Now we need to find values of a and b that satisfy both inequalities. Since a < 0, we can try any negative value of a. Let's try a = -1:

-1/4(-1) > 3(-1)
1/4 > -3

This inequality is true, so we can move on to the next inequality. Let's plug in a = -1 and see if it satisfies b > 9:

b – 12 > -3
b > 9

Since -1 satisfies both inequalities, the values that make both inequalities true are: a = -1 and any value of b greater than 9.

Keep in mind that if Lourdes is able to pay off her credit card balance at the end of the month, she won't be charged any interest, making the credit card the better option in that case.

To determine whether Lourdes should use a debit card or credit card, we need to consider the ATM fee and the potential interest charges from the credit card.

Step 1: Determine the ATM fee
Find out how much Lourdes would be charged for using the ATM to withdraw cash.

Step 2: Determine the interest rate on the credit card
Check the credit card's terms and conditions to find the annual percentage rate (APR). This will help us calculate the potential interest charges.

Step 3: Calculate the potential interest charges
Assuming Lourdes doesn't pay off the credit card balance by the end of the month, divide the APR by 12 to get the monthly interest rate. Multiply this rate by the $48 grocery cost to find the potential interest charges.

Step 4: Compare costs
Compare the ATM fee and potential interest charges to determine the cheaper option. If the ATM fee is less than the potential interest charges, Lourdes should use her debit card. If the potential interest charges are less than the ATM fee, she should use her credit card.

Keep in mind that if Lourdes is able to pay off her credit card balance at the end of the month, she won't be charged any interest, making the credit card the better option in that case.

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If the terminal side of angle λ intersects the unit circle at point (-0. 358, 0. 934), the approximate decimal value of cot(λ) is -0.383.

To find the approximate decimal value of cot(λ), we first need to determine the values of x and y on the unit circle. Since the given point (-0.358, 0.934) lies on the unit circle, we can use the Pythagorean theorem to find the missing side:

x² + y² = 1
(-0.358)² + (0.934)² = 1
0.128 + 0.872 = 1
1 = 1

Therefore, we have x = -0.358 and y = 0.934. Since cot(λ) = cos(λ)/sin(λ), we can use the values of x and y to calculate the cosine and sine of λ:

cos(λ) = x = -0.358
sin(λ) = y = 0.934

Substituting these values into the formula for cot(λ), we get:

cot(λ) = cos(λ)/sin(λ) = -0.358/0.934 ≈ -0.383

Therefore, the approximate decimal value of cot(λ) is -0.383.

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The value of x in the data set is 101.

The mean of a data set is the sum of all the data divided by the count n.

Therefore, let's find the mean of the data set as follows:

The mean is  the sum of the data divided by the total number of data.

Hence, let's find the value of x using the mean

108  = 102 + 120 + 103 + 112 + 110 + x  / 6

108 = 547 + x / 6

Cross multiply

108 × 6 = 547 + x

648 = 547 + x

x = 648 - 547

x = 101

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The critical number A is 2

To find the critical number A for the function f(x) = 7(x-2)^(2/3):

We need to first find the derivative of the function and then set it equal to zero or identify where it is undefined.

Step 1: Find the derivative of f(x).
f'(x) = d/dx[7(x-2)^(2/3)]
Using the chain rule, we get:
f'(x) = (2/3) * 7(x-2)^(-1/3) * (1)

= (14/3)(x-2)^(-1/3)

Step 2: Set the derivative equal to zero or identify where it is undefined.
The derivative will never be zero since (14/3) is a constant and (x-2)^(-1/3) will never equal zero.

However, the derivative is undefined when the exponent -1/3 leads to a division by zero in the denominator.

This occurs when (x-2) = 0.

Solving for x, we get:
x-2 = 0
x = 2

Therefore, the critical number A is 2. The two important intervals for the function f(x) = 7(x-2)^(2/3) are (-∞, 2) and (2, ∞).

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---------------------------

|           | Popcorn | No Popcorn |

---------------------------

| Drink     |    74   |     15     |

---------------------------

| No Drink  |    10   |     6      |

---------------------------

The completed two-way table is as shown above.

We construct a two-way table summarizing the results. Let's use the information provided:

1. 105 people entered the theatre
2. 84 people had popcorn
3. 10 out of 84 people with popcorn did not have a drink
4. 6 people walked in without popcorn or a drink

Now let's construct the two-way table:

---------------------------
|           | Popcorn | No Popcorn |
---------------------------
| Drink     |    A    |     B      |
---------------------------
| No Drink  |    C    |     D      |
---------------------------

We need to fill in the values for A, B, C, and D:

1. A = People with popcorn and a drink = Total with popcorn - those without a drink = 84 - 10 = 74
2. C = People with popcorn but no drink = 10 (given in the question)
3. D = People with neither popcorn nor a drink = 6 (given in the question)
4. To find B, we need to find the total number of people with a drink. We know 105 people entered, and 6 had neither popcorn nor a drink, so there were 105 - 6 = 99 people with either popcorn or a drink. Since 84 people had popcorn, this means there were 99 - 84 = 15 people with only a drink.
5. B = People with a drink but no popcorn = 15

Now let's fill in the table:

---------------------------
|           | Popcorn | No Popcorn |
---------------------------
| Drink     |    74   |     15     |
---------------------------
| No Drink  |    10   |     6      |
---------------------------

So, the completed two-way table is as shown above.

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Answer:  Note that we used the table of general integration formulas to recognize that the integral of csc(x) dx is -       ln|csc(x) + cot(x)| + C.

Explanation:

To evaluate the indefinite integral of csc(x) cot(x) dx, we can use substitution.

Let u = cot(x), then du/dx = -csc^2(x) and dx = -du/csc^2(x).

Substituting these values in the integral, we get:  

∫ csc(x) cot(x) dx = ∫ -du/u = -ln|u| + C

Now substituting back u = cot(x),

we get: ∫ csc(x) cot(x) dx = -ln|cot(x)| + C

This is the final answer.

Note that we used the table of general integration formulas to recognize that the integral of csc(x) dx is -ln|csc(x) + cot(x)| + C. We then used the substitution technique and the general integration formula for ln|u| to arrive at the final answer.

The calculated area of the rectangle is 70 + 7x

From the question, we have the following parameters that can be used in our computation:

Mario cuts out and arranged the trapezoids to form a rectangle.

Using the above as a guide, we have the following:

Area of rectangle  = base * height

In this case, we have

base = 10 + x

Where x is the length of the missing side

Next, we have

height = 7

Substitute the known values in the above equation, so, we have the following representation

Area = 7 * (10 + x)

Evaluate

Area = 70 + 7x

Hence, the area of the rectangle is 70 + 7x

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