Calculus II question:
I don't know how to solve this integral for surface area of a solid of revolution!! Show work + exact answer please!

The possible numbers of pounds Keisha will buy are p < 7, where p represents the number of pounds. In interval notation, it can be written as (0, 7).

Let p be the number of pounds Keisha will buy. Since the candy costs $8 per pound, the total cost will be 8p dollars.

According to the given information, Keisha will spend less than $56 on candy. We can express this as an inequality:

8p < 56

To solve for p, we divide both sides of the inequality by 8:

p < 7

Therefore, the possible numbers of pounds Keisha will buy are any value of p that is less than 7. In interval notation, this can be written as (0, 7).

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Each step of Cho's solution should be matched to its appropriate justification as follows;

[tex]B=(x_1+\frac{a}{b} (x_2-x_1),(y_1+\frac{a}{b} (y_2-y_1))[/tex]    ⇒  Fractional distance formula

[tex]=(x_1+\frac{3}{4} (x_2-x_1),(y_1+\frac{3}{4} (y_2-y_1))[/tex]        ⇒  Substitute a = 3 and b = 4.

[tex]=(2+\frac{3}{4} (6-2),(4+\frac{3}{4} (8-4))[/tex]               ⇒  (x₁, y₁) → (2, 4) and (x₂, y₂) → (6, 8)

= (2 + 3), (4 + 3)                                     ⇒  Simplify (1st use)

= (5, 7)                                                   ⇒  Simplify (2nd use).

In this scenario, line ratio or fractional distance formula would be used to determine the coordinates of the point C on the directed line segment AB that partitions the segment into a ratio of 3 to 4.

In Mathematics and Geometry, line ratio or fractional distance formula can be used to determine the coordinates of point C and this is modeled by the following mathematical expression:

C(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

[tex]C=(x_1+\frac{a}{b} (x_2-x_1),(y_1+\frac{a}{b} (y_2-y_1))\\\\C=(2+\frac{3}{4} (6-2),(4+\frac{3}{4} (8-4))[/tex]  

C = (2 + 3), (4 + 3)

C = (5, 7)

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The class had cleaned x × A square miles before lunch.

Let's assume that the area of the park is A square miles, and the portion of the park cleaned by Mai's class before the lunch break is represented by x (a fraction or decimal between 0 and 1).

If the class had cleaned x portion of the park, then the area they had cleaned is x times the total area of the park:

Area cleaned before lunch = x × A

Since x represents a fraction or decimal, multiplying it by the total area A gives us the corresponding portion of the park that was cleaned.

Let's say the park has an area of A square miles, and the area that Mai's class cleaned up before lunch is denoted by the number x (a fraction or decimal between 0 and 1).

If the class had cleaned a certain percentage of the park, their cleaned area would be x times the park's overall area:

Before lunch, the area was cleaned = x A

We may calculate the proportion of the park that was cleaned by multiplying x by the entire area A because it indicates a fraction or decimal.

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For the given sample data, the variance is 48.4 and the standard deviation is approximately 6.96. These measures provide information about the spread or variability of the data points around the mean.

To find the variance and standard deviation for the given sample data: 2, 9, 12, 15, 19, 21, we first need to calculate the mean (X) of the data set.

Calculating the Mean:

Mean (X) = (2 + 9 + 12 + 15 + 19 + 21) / 6

= 78 / 6

= 13

The mean (X) of the data set is 13.

Calculating the Variance:

Variance (S^2) is a measure of the dispersion or spread of the data. It can be calculated using the formula:

S^2 = Σ(Xi - X)^2 / (n - 1)

where Xi represents each individual data point, X is the mean, and n is the sample size.

Using the given data set and the calculated mean, we can calculate the variance:

[tex]S^2 = [(2 - 13)^2 + (9 - 13)^2 + (12 - 13)^2 + (15 - 13)^2 + (19 - 13)^2 + (21 - 13)^2] / (6 - 1)[/tex]

=[tex][(-11)^2 + (-4)^2 + (-1)^2 + (2)^2 + (6)^2 + (8)^2] / 5[/tex]

= [121 + 16 + 1 + 4 + 36 + 64] / 5

= 242 / 5

= 48.4

The variance (S^2) of the data set is 48.4.

Calculating the Standard Deviation:

The standard deviation (S) is the square root of the variance. It measures the average amount of variation or dispersion from the mean.

S = √(S^2)

= √48.4

≈ 6.96

The standard deviation (S) of the data set is approximately 6.96.

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I. The m∠ABC to one half of the mAC.

II. The measure of mAC is 80°.

III. The measure of mABC is 280°.

In Mathematics and Geometry, the inscribed angle of a circle is equal to half of the central angle of a circle. In this context, we can logically deduce that the angle subtended by major arc ABC is equal to one half of the minor arc AC;

m∠ABC = 1/2(mAC)

Part II.

Based on the relationship that we established in Part I above, the measure of minor arc AC can be calculated as follows;

m∠ABC = 1/2(mAC)

mAC = 2m∠ABC

mAC = 2(40)

mAC = 80°.

Part III.

Based on the relationship that we established in Part II above, the measure of major arc ABC can be calculated as follows;

mABC + mAC = 360°

mABC = 360° - mAC

mABC = 360° - 80

mABC = 280°.

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Complete Question:

An arc is a smooth piece of a circle. A major arc of a circle is an arc that is longer than half the circumference of the circle. Find the measure of the major arc ABC.

Part I: The m∠ABC is equal to/one half of the mAC. (Circle one) (1 point)

Part II: Using the relationship you established in Part I, find the mAC. Show your work and explain

your answer. (2 points)

Part III: Using your answer from Part II, find the mABC. Show your work. (2 points)

Let x be the number of pounds of Kenyan coffee and y be the number of pounds of Sumatran coffee. We know that x + y = 26 and 9x + 11y = 260.

Solving the system of equations, we get

x = 14 and y = 12

Therefore, the Coffee Counter should use 14 pounds of Kenyan coffee and 12 pounds of Sumatran coffee to make a 26 pound blend that sells for $10.00 per pound.

To confirm, the average price of the blend is: (9*14 + 11*12) / 26 = 10.00

So the answer is 14,12

The value of the resistor needed in this scenario is approximately 1.2 ohms.

To find the value of the resistor in the given scenario, we can apply Ohm's Law, which states that the current (I) flowing through a resistor is directly proportional to the voltage (V) across it, and inversely proportional to the resistance (R) of the resistor.

Using Ohm's Law, we have the formula:

V = I * R

Where:

V is the voltage across the resistor (12 volts in this case),

I is the current flowing through the resistor (5 amps for each light, so a total of 10 amps),

R is the resistance of the resistor (which we need to find).

Rearranging the formula, we have:

R = V / I

Plugging in the values:

R = 12 volts / 10 amps

R = 1.2 ohms

Therefore, the value of the resistor needed in this scenario is approximately 1.2 ohms.

It's worth noting that this calculation assumes the lights are connected in parallel, as the current remains the same for each light. If the lights were connected in series, the total resistance would be the sum of the individual resistances, and the calculation would be different.

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A woman invests $6,998.66 at 8% and about $24,001.34 at 9.5% .Let's assume that the amount invested at 8% is x dollars. Then the amount invested at 9.5% is (31,000 − x) dollars.The annual income from the investment at 8% would be 0.08x dollars.

Similarly, the annual income from the investment at 9.5% would be 0.095(31,000 − x) dollars.

As per the question, the investment at 9.5% provides $407.50 more income than the investment at 8%, so we can write this in equation form:0.095(31,000 − x) − 0.08x = 407.50.

Solve for x:

0.095(31,000 − x) − 0.08x = 407.50.2945(31,000 − x) − .08x = 407.503,027.50 − .2945x − .08x = 407.50.

Combine like terms :3,027.50 − .3745x = 407.50

Subtract 3,027.50 from both sides:− .3745x = − 2,620

Divide both sides by − .3745:x ≈ 6,998.66

We invested about $6,998.66 at 8% and (31,000 − 6,998.66) ≈ $24,001.34 at 9.5%.

Therefore, a woman invests $6,998.66 at 8% and about $24,001.34 at 9.5%.

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The 6 numbers for the given probabilities can be:

(2, 4, 5, 6, 7, 8)

There are 6 numbers, we know that:

probability of any event = (outcomes that meet the event)/6

Then, if:

probability of an even number = 2/3 = 4/6

This means that there are 4 even numbers.

if:

P Number chosen is less than 5  = 1/3 = 2/6

There are 2 numbers less than 6.

And there is a 50% of gettting a prime, so there are two primes.

Then the 6 numbers could be:

(2, 4, 5, 6, 7, 8)

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Answer:

Step-by-step explanation:

The value of x for this problem, considering the two secant theorem, is given as follows:

x = 15.

The value of c is obtained applying the two secant segment theorem, which means that the following equation will hold true:

8(8 + 19) = 9(9 + x).

(we add the two parts), with the outer part being the multiplier.

Solving the equation, we have that the value of x is given as follows:

27 x 8 = 9/(9 + x)

9 + x = 3 x 8

9 + x = 24

x = 15.

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Answer:

Step-by-step explanation:

[tex]y=(\frac{1}{g} )x[/tex]

Constant up a proportionally is  [tex]\frac{1}{g}[/tex].

There are approximately 1.0875 milligrams of iron in 87 grams of food that contains 0.00125% iron.

To find the amount of iron in 87 grams of food, we first need to convert the percentage into a decimal. The food contains 0.00125% iron, which is equivalent to 0.0000125 as a decimal.

Next, we multiply the decimal by the weight of the food to determine the amount of iron in grams. So, 0.0000125 x 87 = 0.0010875 grams of iron.

Since we want the answer in milligrams, we need to convert grams to milligrams. There are 1,000 milligrams in one gram. Therefore, 0.0010875 grams is equal to 1.0875 milligrams.

It's worth noting that this calculation assumes a homogeneous distribution of iron throughout the food sample. In reality, the iron content may vary within different parts of the food or across different food items.

Additionally, the accuracy of the iron content measurement and the precision of the percentage value provided can also impact the final result.

Therefore, it's always advisable to consult reliable sources or conduct laboratory tests for precise and accurate nutrient information.

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Answer:

4 × 5 × 0 = 0, so 450 = 0.

Step-by-step explanation:

6 × 5 × 2 = 60

5 × 3 × 5 = 75

4 × 8 × 2 = 64

Step-by-step explanation:

To DIVIDE by a fraction, flip the fraction and MULTIPLY

7 / (3/8)  = 7 * 8/3  = 56 / 3 = 18  2/3

Answer:

To graph the position function f(t), velocity function v(t), and acceleration function a(t) for the given scenario, we'll start by calculating these functions using the given equation:

s(t) = 152t - 16t^2

To find the velocity function, we'll take the derivative of the position function with respect to time:

v(t) = ds(t)/dt = f'(t) = d/dt (152t - 16t^2)

Using the power rule of differentiation, we get:

v(t) = 152 - 32t

Next, to find the acceleration function, we'll take the derivative of the velocity function with respect to time:

a(t) = dv(t)/dt = f''(t) = d/dt (152 - 32t)

Since the derivative of a constant is zero, the acceleration function simplifies to:

a(t) = -32

Now that we have the position function f(t), velocity function v(t), and acceleration function a(t), we can plot their graphs.

(a) Graph of f(t) = 152t - 16t^2:

The graph of f(t) will be a downward-opening parabola with a maximum point. Since the range is restricted to 0 ≤ t ≤ 9.5, the graph will be limited within that range.

(b) Graph of v(t) = 152 - 32t:

The graph of v(t) will be a linear function with a negative slope of -32. It will start with a positive velocity and decrease linearly until it reaches zero at t = 4.75 (half of the time interval), and then it will continue to decrease with negative velocity.

(c) Graph of a(t) = -32:

The graph of a(t) will be a horizontal line at -32, indicating a constant acceleration of -32 ft/s^2.

(d) To complete the statement (e), please provide the specific parts that need to be completed.

(e) Statement incomplete. Please provide the specific parts that need to be completed.

(f) Statement incomplete. Please provide the specific parts that need to be completed.

The zeros and the multiplicities are

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

f(x) = (x + 6)³(x - 11)²(x - 6)(x + 5)³

The power of each factor are the multiplicities

So, we have

Zero(s) of multiplicity one:

x - 6 = 0

Zero(s) of multiplicity two:

x - 11 = 0

Zero(s) of multiplicity three:

x + 6 = 0 and x + 5 = 0

When evaluated, we have

Zero(s) of multiplicity one:

x = 6

Zero(s) of multiplicity two:

x = 11

Zero(s) of multiplicity three:

x = -6 and x = -5

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Answer:

Step-by-step explanation:

A. 10

just look at the highest exponent.

Answer:

view the photo

Step-by-step explanation:

Answer:

The probability that one marble drawn at random is not blue is 70%

The graph that represents a function among the options given is the last option. See image below.

To determine if a graph represents a function, check if any vertical line intersects the graph in more than one point. If every vertical line intersects the graph at most once, then the graph represents a function.

Considering the options given, the last option shown in the image given will have only one point intersected on the graph if we run a vertical line on it. The rest will have at more than one point.

Therefore, the graph that is a function is the last option.

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Answer:

0.0138

Step-by-step explanation:

The probability of getting exactly 4 questions right by guessing can be calculated using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where n is the number of trials (17 questions), k is the number of successes (4 correct answers), p is the probability of success on a single trial (1/5 for guessing), and (n choose k) is the binomial coefficient.

Plugging in the values, we get:

P(X = 4) = (17 choose 4) * (1/5)^4 * (4/5)^13

P(X = 4) ≈ 0.0138 (rounded to four decimal places)

Therefore, the probability that the student will get exactly 4 questions right by guessing is approximately 0.0138.

Answer:

B.  10

Step-by-step explanation:

A:

cost = 20 + 3x

B:

cost: 30 + 2x

20 + 3x = 30 + 2x

x = 10

The volume of the cylinder is 132ft³

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a cylinder is expressed as;

V = πr²h

where r is the radius and h is the height.

π = 3

radius = 2ft

height = 11ft

Volume = 3 × 2² × 11

V = 132 ft³

Therefore the volume of the cylinder is 132ft³

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Answer:

Domain: All real numbers except -2

Step-by-step explanation:

The domain of a function is "the set of all possible inputs for the function". In other words, it's all the possible x's you can put into the function without any problems. What do I mean?

Well, take f(x) = x from |R to |R for example. (|R is the set of all real numbers.) The domain of this function is all real numbers. Why? Well, you can put any real number as x, and there wouldn't be any problems!

Another example is f(x) = 1/x from |R to |R. Now, we have a problem. If x = 0, then we would have f(x) = 1/0, and that's undefined. So 0 is not in the domain. But everything else is! So the domain is all real numbers except 0.

Same thing with f(x) = (5x-2)/(x+2) from |R to |R. If x = -2, then we would have f(x) = -12/0, which is also undefined. So the domain of f(x) = (5x-2)/(x+2) from |R to |R is all real numbers except -2.

The correct statement regarding the exponential function in this problem is given as follows:

D. Decay, (0,3).

An exponential function has the definition presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The function for this problem is given as follows:

[tex]f(x) = 3\left(\frac{1}{2}\right)^x[/tex]

Then the parameter values are given as follows:

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Answer:

C.   10

Step-by-step explanation:

The length of any side of a triangle must be between the difference and the sum of the lengths of the other two sides.

Difference of the lengths of the 2 given sides: 13 - 5 = 8

Sum of the lengths of the 2 given sides: 5 + 13 = 18

The third side of the triangle has a length between 8 and 18.

Answer: 10

Answer:

42 feet

Step-by-step explanation:

We are looking for the perimeter of a rectangle.

8 ft 4 in. + 8 ft 4 in = 16 feet 8 inches

12 ft + 8 in. + 12 ft 8 in = 24 ft 16 inches

16 ft  8 in + 24 ft 16 in = 40 feet 24 inches

24 inches is 2 feet

40 feet + 2 feet = 42 feet

To find the amount of fencing needed, calculate the perimeter of the garden. Given that the garden is 8 feet 4 inches wide and 12 feet 8 inches long, the total fencing required is 41 feet 4 inches.

To find out the amount of fencing needed to enclose the garden, we need to calculate the perimeter of the garden. The perimeter of a rectangle (which is our garden in this case) is calculated by adding together the lengths of all its sides. In this case, it is 8 feet 4 inches wide and 12 feet 8 inches long. Hence, the perimeter would be 2*(Length + Width). So, the total fencing required would be 2*((8 feet 4 inches) + (12 feet 8 inches)) = 2*(20 feet 12 inches) = 41 feet 4 inches. Therefore, you will need a fencing of 41 feet 4 inches to completely enclose the garden.

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The relations should be classified according to whether or not they are functions as follows;

In Mathematics and Geometry, a function defines and represents the relationship that exists between two or more variables in a relation, table, ordered pair, or graph.

Part 1.

Based on the given relation -3x = 15, we can logically deduce that it does not represent a function because the input value is not related to an output value.

Part b.

Based on the given equation 2y = 10, we can logically deduce that it represents a function because it takes an input value.

Part c.

Based on the given equation 3x − 0.25y = 3, we can logically deduce that it represents a function because it takes all input values (domain).

Part d.

Based on the mapping diagram, we can logically deduce that it does not represent a function because the input value (d) has more than one output values (123 and 126).

Part e.

Based on the graph, we can logically deduce that it represents a function because it maps all input values or real numbers (domain) to y.

Part f.

Based on the given relation {(2, 3), (1, 3), (5, 3), (2, 6)}, we can logically deduce that it does not represent a function because the input value (x = 2) has more than one output values (y = 3 and y = 6).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.