Demonstrate and explain how to evaluate the derivative for each of the following definite integrals using the fundamental theorem of calculus. ?A)d/xd∫ 4x(2(6cos(t)+7) 4)dtB)d/xd∫ x3(4sin(t 3−3))dt

Yes her plan to construct a square inscribed in a circle is her plan correct.

Let's check if her plan is correct:

In order to construct a square inscribed in a circle,

the following steps should be followed

STEP 1:Draw a circle and its centre, O.

STEP 2:Draw a diameter PQ through the centre of the circle.

STEP 3:Mark the midpoint R of PQ.

STEP 4:Draw a perpendicular bisector of PQ, it should pass through R

STEP 5:It cuts PQ at right angles at R. Label the point where the perpendicular bisector cuts PQ as T.

STEP 6:Connect OT and RT to intersect the circle at points S and U respectively.

Now we have a square INSIDE the circle, where O is the center, and the square's diagonal is the circle's diameter, while the square's sides are the circle's radii.

So, Molly's plan is correct.

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(a) The value of angle VUW is 31⁰.

(b) The value of angle WUX is 59⁰.

The measure of angle WUX is calculated by applying the following principle.

So angle ∠VUW is calculated as follows;

m ∠VUW = ¹/₂ arc UVW (angle formed by chords at circumference is twice the angle of opposite tangent)

m ∠VUW = ¹/₂ x ( 242 - 180)

m ∠VUW = 31⁰

The value of angle WUX is calculated as follows;

m ∠WUX = 90 - 31⁰ ( sum of angles subtended by the diameter of a circle)

m ∠WUX = 59⁰

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Using the given data, the equation of the regression line is y=7.033+0.683x.

An equation is a mathematical statement that two expressions are equal. It is composed of two expressions, one on either side of an "equals" sign. Equations can be used to solve problems and express relationships between different quantities. Equations can also provide insights into the behavior of a system. Equations are an essential part of mathematics and are used in almost all areas of science.

To determine if the regression equation is appropriate for making predictions at the 0.05 level of significance, a t-test must be performed. The t-statistic associated with the slope is 3.521 and is significant at the 0.01 level of significance (p-value < 0.01). Therefore, the regression equation is appropriate for making predictions at the 0.05 level of significance.

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The regression line's equation for the provided data is y=7.033+0.683x.

What is equation?

A mathematical equation is a declaration that two expressions are equal. Two expressions make up this phrase, one on either side of the equals sign. Equations are a useful tool for problem-solving and expressing relationships between various quantities.

A t-test must be carried out to see if the regression equation is suitable for making predictions at the 0.05 level of significance. At the 0.01 level of significance, the slope's t-statistic of 3.521 is significant (p-value < 0.01). Hence, at the 0.05 level of significance, predictions can be made using the regression equation.

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Area of sector = 56.977 square inches and Arc length = 15.380 inches (rounded to three decimal places).in order to get these answer we need to use simple sector area formula

what is Area of sector ?

The area of a sector is a region bounded by two radii of a circle and the arc intercepted by the central angle. The formula for the area of a sector is:

Area of sector = (angle / 360) x πr²

In the given question,

To find the area of a circle sector, we need to use the formula:

Area of sector = (angle / 360) x πr²

where r is the radius of the circle, and angle is the central angle of the sector in degrees.

In this case, the radius is 22 inches, and the central angle is 44 degrees. So, we can plug these values into the formula:

Area of sector = (44/360) x π(22)²

Area of sector = (11/90) x π(484)

Area of sector = 56.977 square inches (rounded to three decimal places)

To find the arc length of the sector, we need to use the formula:

Arc length = (angle / 360) x 2πr

where r is the radius of the circle, and angle is the central angle of the sector in degrees.

In this case, the radius is 22 inches, and the central angle is 44 degrees. So, we can plug these values into the formula:

Arc length = (44/360) x 2π(22)

Arc length = (11/90) x 44π

Arc length = 15.380 inches (rounded to three decimal places).

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Answer:

The amount of the discount is calculated by multiplying the subtotal by 15%:

discount = 0.15 x 85.28 = 12.79

The new subtotal after the discount is applied is:

new subtotal = 85.28 - 12.79 = 72.49

The tax on the new subtotal is calculated by multiplying the new subtotal by 6.5%:

tax = 0.065 x 72.49 = 4.71

The final bill, including the tax, is the sum of the new subtotal and the tax:

final bill = 72.49 + 4.71 = 77.20

Therefore, the final bill after the coupon is applied and the tax is paid is $77.20.

The maximum kinetic energy Dina can reach is 250 joules, calculated by multiplying her mass of 50 kg, gravitational acceleration of 9.8 m/s2, and the height of the slope of 5 m.

50 kg x 9.8 m/s2 x 5 m = 250 joules

The maximum kinetic energy that Dina can reach when she skis to the bottom of the slope is calculated by the equation pe = m × g × h. This equation states that the potential energy of an object is equal to its mass multiplied by the gravitational acceleration, which is 9.8 m/s2, and the height of the slope. In Dina’s case, her mass is 50 kg and the height of the slope is 5 m, so the potential energy is equal to 50 kg x 9.8 m/s2 x 5 m, which is equal to 250 joules. This means that the maximum kinetic energy Dina can reach when she skis to the bottom of the slope is 250 joules. This equation is valid as long as air resistance and friction are both ignored, as these can have a significant effect on the kinetic energy of an object.

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Algorithm's worst-case recursion on high side has constant c with |H| = cn + O(1), and worst-case running time is T(n) = T(2n/3) + T(n/3) + O(n). Using the Master Theorem, we can prove that T(n) = O(n lg n) and T(n) = Ω(n lg n), which means T(n) = Θ(n lg n) for the given algorithm.

Answer: (a) In the worst case, the algorithm will have to recurse on the high side H with a constant c such that |H| = cn + O(1). This means that the size of H will be proportional to the size of the input n, with a constant factor c and a constant term O(1).

The largest size of H will be when c = 2/3, because in this case the algorithm will have to recurse on 2/3 of the input. This constant is the same for the low side, because the algorithm will have to recurse on the same proportion of the input.

The recursion for the worst-case running time T(n) will be T(n) = T(2n/3) + T(n/3) + O(n), because the algorithm will have to recurse on the high side and the low side, and will also have to do some work proportional to the size of the input.

(b) To prove that T(n) = O(n lg n), we can use the Master Theorem.

The Master Theorem states that if T(n) = aT(n/b) + f(n), where a ≥ 1, b > 1, and f(n) is a function, then T(n) = O(n^logba) if f(n) = O(n^logba-ε) for some constant ε > 0. In this case, a = 2, b = 3, and f(n) = O(n), so we can apply the Master Theorem and get T(n) = O(n^log32) = O(n^0.63) = O(n lg n).

Similarly, to prove that T(n) = Ω(n lg n), we can use the Master Theorem again and get T(n) = Ω(n^log32) = Ω(n^0.63) = Ω(n lg n). Therefore, T(n) = O(n lg n) and T(n) = Ω(n lg n), which means that T(n) = Θ(n lg n).

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The correct statement regarding the association between the variables is given as follows:

C. A student who feels some pressure from homework is most likely to prefer to be rich.

The two variables for this problem are defined as follows:

For the people who feel some pressure from homework, the preferred status are given as follows:

As rich has the highest proportion, the student is most likely to prefer to be rich, hence option C is the correct option.

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The probability that the two marbles are the same colour is 3/7. This is because out of the 7 marbles, 3 of them are red, so the probability of taking two red marbles is 3/7.

The probability of taking two marbles of the same colour from a bag containing 3 red marbles and 4 blue marbles is 3/7. This is because out of the 7 marbles in the bag, 3 of them are red, so the probability of taking two red marbles is 3/7. The probability of taking two blue marbles is also 3/7, as there are 4 blue marbles in the bag. If a marble is taken out and then replaced, the probability of the two marbles being the same colour does not change. The number of red marbles and the number of blue marbles will remain the same, so the probability of taking two marbles of the same colour will remain 3/7. This is because the replacement marble has the same chance of being either red or blue as the other marbles in the bag.

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The effect on the graph of the parent function after transformation is:

C.The graph will shift 2 units up and will be vertically compressed so that the graph will appear wider.

The vertical shift depends on the value of k. The vertical shift is described as:

f(x) = f(x) + k - The graph is shifted up k units.

f(x) = f(x) − k - The graph is shifted down k units.

Now, we are told that  f(x) = x³, is transformed to f(x) = ¹/₂x³ + 2

Thus, the graph is shifted up by 2 units.

Compressing and stretching depends on the value of a.

When a is greater than 1: Vertically stretched

When a is between 0 and 1: Vertically compressed

In this case, a is 1/2 which is between 0 and 1 and so is Vertically compressed

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Answer:

0.785

Step-by-step explanation:

formula = (a/360)2r π

Answer:

2/3^-3 = 27/8 = 3 3/8 = 3.375

Step-by-step explanation:

A is the correct answer

a. The radius of the jump ball circle is 6 feet. b. The area of the rectangle (lane) is 228 square feet.

Area is a measure of the size of a two-dimensional shape or surface, typically expressed in square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²). The area of a shape or surface is the amount of space it occupies, and it is calculated by multiplying the length by the width, or base by height, depending on the shape.

The area of other shapes, such as trapezoids, parallelograms, and irregular polygons, can be calculated using specific formulas or by dividing the shape into smaller, more familiar shapes.

Areas are used in many real-world applications, such as measuring the floor space of a room, calculating the amount of paint needed to cover a wall, or determining the amount of land needed for farming or construction. Areas are also used in calculus to find the area under a curve and to calculate volumes and other quantities in three-dimensional space.

a. The area of the circle is given as 113.04 square feet. Using the formula for the area of a circle, A=πr², we can solve for the radius, r:

113.04 = 3.14r²

r² = 113.04/3.14

r² = 36

r = √36

r = 6 feet

Therefore, the radius of the jump ball circle is 6 feet.

b. The width of the free throw line is 12 feet, so the dimensions of the rectangle (the lane) are 19 feet by 12 feet. The area of a rectangle is given by the formula A = lw, where l is the length and w is the width. Thus, the area of the lane is

A = 19 x 12

A = 228 square feet

Therefore, the area of the rectangle (lane) is 228 square feet.

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To calculate the interest due, we first need to determine the average daily balance for the month.

From the beginning of the month until the 9th day, the balance is $660. From the 10th to the 27th, the balance is $660 - $90 = $570. On the 28th, the balance increases to $570 + $320 = $890.

So the average daily balance is:

[(31 - 9) x $570 + 9 x $660 + 22 x $890] / 31 = $691.29

Next, we need to calculate the monthly interest rate:

26% APR = 0.26 / 12 = 0.02167

Finally, we can calculate the interest due:

$691.29 x 0.02167 = $14.98

Therefore, the answer is closest to option (a) $7.48.

36-8z = 4(9-2z) this is the factored form of 36-8z.

To factor out the greatest common factor (GCF) from an algebraic expression, we look for the largest factor that divides into all of the terms. In this case, the terms 36 and 8z have a common factor of 4, which is the GCF.

To factor out the GCF, we divide each term by 4, which gives us:

36/4 = 9

8z/4 = 2z

Therefore, we can rewrite 36-8z as:

36-8z = 4(9-2z)

This is the factored form of 36-8z after factoring out the greatest common factor. We can see that 4 is a factor of both 36 and 8z, and we are left with the expression (9-2z), which cannot be factored any further.

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The probability that a single randomly selected nurse's salary is greater than $50,516 is 0.5533 and the probability that a random sample of 95 nurses have a salary greater than $50,516 is 0.9098.

a. To find the probability that a single randomly selected nurse's salary is greater than $50,516, we need to standardize the value using the mean and standard deviation of the distribution, and then use a standard normal table or calculator to find the probability.

The standardized value (z-score) is:

z = (x - μ) / σ = (50,516 - 50,650) / 1,000 = -0.134

Using a standard normal table or calculator, we can find the probability that a randomly selected nurse's salary is greater than $50,516:

P(x > 50,516) = P(z > -0.134) = 0.5517

Therefore, the probability that a single randomly selected nurse's salary is greater than $50,516 is 0.5533.

b. To find the probability that a random sample of 95 nurses have a salary greater than $50,516, we need to use the central limit theorem, which states that the distribution of the sample means approaches a normal distribution with mean μ and standard deviation σ/√n, where n is the sample size.

The mean of the sample means is still μ = 50,650, but the standard deviation of the sample means is now:

σ/√n = 1,000 / √95 = 102.06

We want to find the probability that the sample mean is greater than $50,516:

P(x > 50,516) = P(z > (50,516 - 50,650) / (1,000 / √95)) = P(z > -1.335)

Using a standard normal table or calculator, we can find the probability:

P(x > 50,516) = P(z > -1.335) = 0.9098

Therefore, the probability that a random sample of 95 nurses have a salary greater than $50,516 is 0.9098.

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the only cube number between 20 and 50 is 27.

Step 1: Find the smallest cube greater than 20.

To find the smallest cube greater than 20, we can start by checking the cube of the smallest integer, which is 1. Since [tex]1^3[/tex]= 1, which is less than 20, we move on to the cube of the next integer, which is 2. We find that [tex]2^3[/tex]= 8, which is still less than 20. Finally, we check the cube of the next integer, which is 3. We find that [tex]3^3[/tex]= 27, which is the smallest cube greater than 20.

Step 2: Find the largest cube less than 50.

To find the largest cube less than 50, we can start by checking the cube of the largest integer that is less than the cube root of 50. The cube root of 50 is approximately 3.68, so the largest integer less than the cube root of 50 is 3. We find that [tex]3^3[/tex] = 27, which is less than 50. Since the next cube, [tex]4^3[/tex] = 64, is greater than 50, we know that [tex]3^3[/tex] is the largest cube less than 50.

Step 3: List all the cubes between the smallest cube greater than 20 and the largest cube less than 50.

Now that we have found the smallest cube greater than 20 and the largest cube less than 50, we can list all the cubes between them. The cubes between 27 and 27 are just 27, so we have:27

Therefore, the only cube number between 20 and 50 is 27.

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y = 2x + 4 is the equation of the line that connects the coordinates (0, 4) and (1, 6).

The points that the line passes through are (0, 4) and (1, 6). The equation of a line can be found by using the point-slope form:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is one of the line's points.

Then, we may determine the line's slope:

[tex]m = \frac{(y2 - y1)}{(x2 - x1)}[/tex]

where (x1, y1) = (0, 4) and (x2, y2) = (1, 6)

[tex]m = (6 - 4) / (1 - 0) = 2[/tex]

Now we can use the point-slope form with one of the points, say (0, 4):

y - 4 = 2(x - 0)

Simplifying, we get:

y - 4 = 2x

Adding x to both sides, we get:

y = 2x + 4

So the equation of the line that passes through the points (0, 4) and (1, 6) is y = 2x + 4.

The complete question is"=

Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus

A coordinate plane. The x- and y-axes each scale by one. A graph of a line goes through the points zero, four and one, six.

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Answer:

Step-by-step explanation:

[tex]-\frac{4}{5} (30x-40)+(42x+4)=-\frac{4}{5} (10)(3x-4)+2(21x+2)[/tex]

                                         [tex]=-8(3x-4)+2(21x+2)[/tex]

                                         [tex]=-24x+32+42x+4[/tex]

                                         [tex]=-18x+36[/tex]

                                         [tex]=-18(x-2)[/tex]

Answer: the absolute change in tuition is $8,000 and the relative change in tuition is 15.2%.

Step-by-step explanation: The absolute change in tuition is the difference between the new tuition and the old tuition. Therefore:

Absolute change = New tuition - Old tuition

Absolute change = $60,500 - $52,500

Absolute change = $8,000

The relative change in tuition is the ratio of the absolute change to the old tuition, expressed as a percentage. Therefore:

Relative change = (Absolute change / Old tuition) x 100%

Relative change = ($8,000 / $52,500) x 100%

Relative change = 15.2%

Answer:

The area of the figure is 90 yd²

Step-by-step explanation:

Dividing the shape into three leading to 3 rectangles

The area of a rectangle is length * breadth;

First section + Second section + Third section

(9 * 3) + ( 9 * 4) + (9 * 3) = 27 + 36 + 27 = 90 yd²

Answer:

74yd²

Step-by-step explanation:

You can divide into 3 rectangles from bottom down

Area = length x width

1st rectangle = 9 x 3 = 27yd²

2nd rectangle = 5x 4 = 20yd²

3rd rectangle = 9 x 3 = 27yd²

Add all the area

27 +20+27 = 74yd²

Another method

Find the area of the whole rectangle with the white area closed and included

Lenght 10yd, width 9yd

Area = 10 x9 = 90yd²

Find the area of the white area only

A = 4 x4 =16yd ²

Subract the area of the white square from the whole area of the rectangle

90 - 16 =74yd²

A linear model is not appropriate because the residual plot shows a clear pattern.

The residuals (i.e., the discrepancies between the actual observed values and the anticipated values) are shown against the independent variable in a residual plot (i.e. the variable that the model is trying to predict). The x-variable is often the independent variable in a linear model.

The residual plot displays a curved pattern, which indicates that comparing driving speed and fuel economy should not be done using a linear model. This suggests that there may be other factors besides speed that have an impact on fuel economy and that the connection between speed and fuel efficiency is not strictly linear.

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Answer:140125

Step-by-step explanation:

Answer: 5605 x 25 is 140,125

Step-by-step explanation:

Multiply the ones digit in the bottom number by each digit in the top number

6 × 4 = 24

Put the 4 in Ones place

Carry the 2 to Tens place

6 × 3 = 18

Add the 2 that you carried = 20

Put the 0 in the Tens place

Carry the 2 to the Hundreds place

Add the 2 that you carried = 14

This is the last number to multiply so write the whole number answer. No need to carry the 1.

Move one place to the left. Multiply the tens digit in the bottom number by each digit in the top number.

5 × 4 = 20

Add a row to your multiplication answer

When you write your answer, shift one column to the left

Put the 0 in Ones place

Carry the 2 to Tens place

5 × 3 = 15

Add the 2 that you carried = 17

Put the 7 in the Tens place

Carry the 1 to the Hundreds place

5 × 2 = 10

Add the 1 that you carried = 11

This is the last number to multiply so write the whole number answer. No need to carry the 1.

Add the numbers in the columns using long addition

4 + 0 = 4

0 + 0 = 0

4 + 7 = 11

write the 1 and carry 1

1 + 1 + 1 = 3

Once you add the columns you can see the long multiplication result: 234 × 56 = 13104.

Answer:

$2.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

02.25 is your answer because 10% off of 22.50 is 20.25:)

As per the given options, the uniform probability distribution can be defined as the probabilities of drawing any individual card in a deck with one draw.

A uniform distribution is a statistical probability function that assigns equal probability across the distribution's entire range. For example, when rolling a fair die, each of the six outcomes has an equal probability of 1/6, which is a uniform probability distribution.

The formula for a Uniform Distribution.The probability density function of the uniform distribution is:f (x) = {1 / (b - a)}   for a ≤ x ≤ bWhere, a = lower limitb = upper limitx = random variablef (x) = probability density function.

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The salesman earned a total sum of $2,165.

Given that, a shoe salesman sold $4,125 in shoes and earns a 4% commission, his base salary is $2000.

The amount of commission earned by the shoe salesman is equal to the product of the total sales and the commission rate, which is 4% or 0.04 as a decimal:

Commission = Total sales x Commission rate

Commission = $4,125 × 0.04

Commission = $165

To find the total earnings of the salesman, we add his commission to his base salary:

Total earnings = Base salary + Commission

Total earnings = $2,000 + $165

Total earnings = $2,165

Therefore, the salesman earned $2,165.

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Answer:

Step-by-step explanation:

divide 150 by sides of rectangle = 4 .
= 37.5 then multiply x3 = 112.5

Answer:

99992

Step-by-step explanation:

The price elasticity of demand when P=15 is -0.9

To find the price elasticity of demand when P=15, we need to calculate the percentage change in quantity demanded and the percentage change in price. Let's start with the percentage change in quantity demanded.

ΔQ/Q = (Q2 - Q1)/Q1

where Q1 is the initial quantity demanded and Q2 is the new quantity demanded.

Substituting the values from the demand function, we get:

ΔQ/Q = [(75 - 3P2) - (75 - 3P1)]/(75 - 3P1)

where P1 = 15 and P2 = P1 + ΔP = 15 + 15% = 17.25 (since ΔP/P = 15%).

ΔQ/Q = [(75 - 3(17.25)) - (75 - 3(15))]/(75 - 3(15))

ΔQ/Q = (-8.25)/60

ΔQ/Q = -0.1375

Therefore, the percentage change in quantity demanded is -13.75%.

Now, let's calculate the percentage change in price:

ΔP/P = (P2 - P1)/P1

ΔP/P = (17.25 - 15)/15

ΔP/P = 0.15

Therefore, the percentage change in price is 15%.

Substituting these values in the formula for price elasticity of demand, we get:

E = (-0.1375) / 0.15

E = -0.9167

The price elasticity of demand when P=15 is approximately -0.9.

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