the given curve is rotated about the y-axis. find the area of the resulting surface. y = 1/4 x^2 − 1/2 ln(x), 3 ≤ x ≤ 5

Answer:

50 and 90

Step-by-step explanation:

(180-40)/(5 + 9) = 10

=> 50 and 90

Ka and Kb are both acid-base equilibrium constants, but they apply to different types of reactions. Ka (acid dissociation constant) is used to describe the dissociation of an acid in water, while Kb (base dissociation constant) is used to describe the dissociation of a base in water.

Specifically, Ka is a measure of the strength of an acid in terms of how easily it donates a proton (H+) to a solvent like water. A higher Ka value indicates a stronger acid, while a lower Ka value indicates a weaker acid. Kb, on the other hand, is a measure of the strength of a base in terms of how easily it accepts a proton (H+) from a solvent like water. A higher Kb value indicates a stronger base, while a lower Kb value indicates a weaker base. There is a mathematical relationship between Ka and Kb for conjugate acid-base pairs, which are molecules or ions that differ by the presence or absence of a single proton. The relationship is expressed by the equation: Ka x Kb = Kw, where Kw is the ion product constant for water, which is 1.0 x 10⁻¹⁴ at 25°C. This relationship shows that the stronger the acid, the weaker its conjugate base, and vice versa.

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Answer:

The answer is 0.0228. Have a good day!

Answer:it’s 0.025

Step-by-step explanation:

Answer: D

Step-by-step explanation:

You can visually see that they are equal to each other, since the dimater goes directly through the center

Answer:

A.

Step-by-step explanation:

Answer:

a regular pentagon has 72 degrees

Step-by-step explanation:

The number of orange tiles that should be bought for a pool with a side length of n tiles will be 2n - 1. This was illustrated in the square tiles.

It should be noted that a square simply means a quadrilateral that has all the sides equal. It should be noted that in a square, the sides contain four right angles. This illustrates that the total angle that will be in a square is 360°.

From the information given, the dimensions of the pool are n ×n. In the given information, we are hit given what n is in the question.

Therefore since the tiles that are given is a square, then the number of orange tiles that should be bought for a pool with a side length of n tiles will be:

= (2 × n) - 1

= 2n - 1

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Answer: See below

Step-by-step explanation:

Using a graphing approach:

If the graph is increasing, then the left-sum is an underestimate of the actual value and the right-sum is an overestimate

If the curve is decreasing then the right-sums are underestimates and the left-sums are overestimates

Answer:

11 + 13i

Step-by-step explanation:

A must know is that

\( \sqrt{i} = - 1\)

Complex numbers

1st: foil the equations

\( - 3(1 - 2i) + 7i(1 - 2i)\)

\( - 3 + 6i + 7i- 14 {i}^{2} \)

2nd Combine like terms and substitute

\(i ^{2} for \: - 1\)

\( - 3 + 14 + 13i\)

\(11 + 13i\)

The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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This is the desired expression for the total solution.

To solve the differential equation, we assume that the solution is of the form y(t) = c(t)eat. Then, we have:

y'(t) = c'(t)eat + aceat

y(0) = c(0)e0a = y

Substituting these into the differential equation, we get:

c'(t)eat + aceat = a(c(t)eat) + bu(t)

Simplifying this equation, we get:

c'(t) = bu(t)e-at

Integrating both sides from 0 to t, we get:

c(t) - c(0) = ∫0t bu(r)e-ar dr

Multiplying both sides by eat, we get:

y(t) - y = e-at(c(0) + ∫0t bu(r)e-ar dr)

Rewriting the right-hand side in terms of a constant c and a function h(t), we get:

y(t) = e-at y + c ∫0t bu(r)e-ar dr

where c = eay and h(t) = bu(t)e-at. This is the desired expression for the total solution.

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there is your answer follow and mark me as brainliest

By using the concept of probability, it can be calculated that

a) State space S(x) = {-1, 0, 1, 2}

b) The required probability mass function is

    P(X = -1) = \(\frac{125}{216}\)

    P(X = 0)  \(= \frac{25}{72}\)

    P(X = 1)  \(= \frac{5}{72}\)

    P(X = 2)  \(= \frac{1}{216}\)

c) Expected value of X  = -0.5

d) the stake of the gambler in  order to make this a fair game is $0.5

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

a) Let a number n be chosen between 1 and 6

Three fair six sided dice are thrown

The following cases can occur

1) Number n occur on none of the three dice

2) Number n occur on one dice

3) Number n occur on two dice

4) Number n occur on three dice

Let X denote your net win after one round of gambling (i.e., the payment received from the casino minus your stake)

1) X = 0  -1 = -1

2) X = 1 - 1 = 0

3) X = 2 - 1 = 1

4) X = 3 - 1 = 2

State space S(x) = {-1, 0, 1, 2}

b) P(X = -1) = \({3 \choose 0}(\frac{1}{6})^0(\frac{5}{6})^3 = (\frac{5}{6})^3 = \frac{125}{216}\)

    P(X = 0) = \({3 \choose 1})(\frac{1}{6})(\frac{5}{6})^2 = \frac{25}{72}\)

    P(X = 1) = \({3 \choose 2}(\frac{1}{6})^2\frac{5}{6} = \frac{5}{72}\)

    P(X = 2) = \({3 \choose 3}(\frac{1}{6})^3(\frac{5}{6})^0 = \frac{1}{216}\)

    The required probability mass function is

    P(X = -1) = \(\frac{125}{216}\)

    P(X = 0)  \(= \frac{25}{72}\)

    P(X = 1)  \(= \frac{5}{72}\)

    P(X = 2)  \(= \frac{1}{216}\)

c) Expected value of X = \(-1 \times \frac{125}{216} + 0 \times \frac{25}{72} + 1 \times \frac{5}{72} + 2\times \frac{1}{216}\)

                                      = \(\frac{-125 + 0 + 15 +2}{216}\\\)

                                      = \(-\frac{108}{125}\)

                                      = -0.5

d) The gambler looses $0.5 on a average

   So this is not a fair game

   Let the stake of the gambler in  order to make this a fair game be t

   By the problem,

   -0.5 + t = 0

     t = 0 + 0.5

     t = $0.5

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72, 2-ounce servings can be made to serve with buffalo wings.

Given that 6 bunches of celery each weighs 2 pounds. We have to find out how many 2-ounce servings can be made to serve with buffalo wings. Also, celery has a 75% yield.

\(Total weight of celery = 6 bunches * 2 pounds\)

each = 12 pounds

Total weight of celery in ounces

  \(= 12 pounds * 16 ounces\)

\(= 192 ounces\)

75% yield of celery means that 75% of the celery is edible.

The edible portion of celery

    = 75% of 192 ounces  

   \(= (75/100)*192 = 144 ounces\)

Now, as we have to find the number of 2-ounce servings that can be made, we need to divide the edible portion of celery by 2 ounces each. Thus, the number of 2-ounce servings can be made to serve with buffalo wings

  \(= 144/2 = 72.\)

Hence, 72 2-ounce servings can be made to serve with buffalo wings.

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There are 10.0g of w – 187 at time zero. If the half-life is 23.9 hours, then the amount of quantity for: 1 day = 4.98 g, 2 day = 2.48 g, on 7th day = 0.0765 g.

A drug's half-life is the duration it takes for the amount of its active ingredient to halve in your body. A radioactive isotope's half-life is the length of time it takes for one half of the isotope to decay. A particular radioactive isotope's half-life is constant; it is unaffected by environmental factors and is unrelated to the starting concentration of that isotope.

time 24.0 hr / 23.9 hr/half-life = 1.0042 half-lives

One day half-life is:

= (1/2)^1.0042

= 0.4985465  

= 4.98 g

For Two days:

= (1/2)^2.0084

= 0.2485486  

= 2.48 g

For Seven days:

= (1/2)^7.0294

= 0.0076549  

= 0.0765 g

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The measure of each angle is equal to the measure of its supplementary angle.

Angle is a figure formed by two rays sharing a common endpoint. It is typically measured in degrees, with a full circle measuring 360°. Angles are used to describe the direction of lines and the relationships between them. Angles can also be used to describe the shape of objects and figures.

(1) Angles subtended by arc PT at the circumference are ∠POT and ∠PTQ.
(2) Angles subtended by arc TS at the circumference are ∠TSQ and ∠TSR.
(3) Angles subtended by arc SR at the circumference are ∠SRP and ∠SRQ.
(4) Angles subtended by arc RQ at the circumference are ∠RQP and ∠RQS.

The angles stated in question 2(a) above are all pairs of supplementary angles, which means that they add up to 180°. This means that the measure of each angle is equal to the measure of its supplementary angle.

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(a) (i) Angles subtended by arc PT at the circumference are ∠POT and ∠PTQ.
(ii) Angles subtended by arc TS at the circumference are ∠TSQ and ∠TSR.
(iii) Angles subtended by arc SR at the circumference are ∠SRP and ∠SRQ.
(iv) Angles subtended by arc RQ at the circumference are ∠RQP and ∠RQS.

(b) The angles stated in question 2(a) above are all pairs of supplementary angles, which means that they add up to 180°.

Angle is a figure formed by two rays sharing a common endpoint. It is typically measured in degrees, with a full circle measuring 360°. Angles are used to describe the direction of lines and the relationships between them. Angles can also be used to describe the shape of objects and figures.

The angles stated in question 2(a) above are all pairs of supplementary angles, which means that they add up to 180°. This means that the measure of each angle is equal to the measure of its supplementary angle.

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The possible zeros of the function f(x)=x³- 4x² + 5x + 6 are

To find the possible zeros of the function f(x)=x³- 4x² + 5x + 6  using the Rational Zeros Theorem, we need to consider the factors of the constant term (6) divided by the factors of the leading coefficient (1).

The factors of 6 are: ±1, ±2, ±3, ±6

The factors of 1 (leading coefficient) are: ±1

Using the Rational Zeros Theorem, the possible zeros can be obtained by taking all possible combinations of the factors and their negations. Therefore, the possible zeros are:

±1, ±2, ±3, ±6

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Answer:

65.21739130434783

Step-by-step explanation:

1. The slope of the line is -3/4. 2. The opportunity cost of producing 3 trucks is - 2/3. 3. The opportunity cost of 3 trucks is equal to the cost of -2/3 cars.

Opportunity cost is the advantage that was lost because a particular option was not selected.

It is necessary to weigh the advantages and disadvantages of each choice offered in order to correctly assess opportunity costs.

Opportunity costs have a value that can help people and businesses make more lucrative decisions.

Opportunity cost is a wholly internal expense that is only utilised for strategic consideration; it is not included in accounting profit and is not reported externally.

The given coordinates of the line are:

(x1, y1) = (0, 3)

(x2, y2) = (4, 0)

The slope is given by the formula:

m = y2 - y1 / x2 - x1

Substituting the values of the coordinates we have:

m = (0 - 3) / (4 - 0)

m = - 3/4

The slope of the line is -3/4.

b. The opportunity cost is calculated as:

Opportunity cost = (y1 - y2) / (x1 - x2)

For producing 3 trucks, the cars that need to be produced are 1.

Thus, (x2, y2) = (3, 1)

while, (x1, y1) = (0, 3)

The opportunity cost is:

Opportunity cost = (3 - 1) / (0 - 3) = - 2/3

c. The opportunity cost of 3 trucks is equal to the cost of -2/3 cars.

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Answer: -6.7

Step-by-step explanation:

64.3−(3)(23)−2

=−6.7

Answer:

-6.7

Step-by-step explanation:

Answer:

2 = 2 (Identity)

Step-by-step explanation:

1/3 (x+2)=-2/5 (x-9) and x=4

Follow distributive property

1/3x + 2/3 = -2/5x + 18/5

Replace x for 4

1/3(4) + 2/3 = -2/5(4) + 18/5

4/3 + 2/3 = -8/5 + 18/5

Add like terms

6/3 = 10/5

Simplify

2 = 2

Also known as Identity

The upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

To determine the upper bound of the 95% confidence interval for the average age in the U.S., we can use the sample data from the survey. The sample size is 1072 people, randomly selected from the U.S. population, with a minimum age of 12. By calculating the average age of the respondents, we can estimate the average age of the entire U.S. population.

Using the given information that the average age of the respondents is 43.56 years, and assuming that the sample is representative of the population, we can calculate the standard error. The standard error measures the variability of the sample mean and indicates how much the sample mean might deviate from the population mean.

Using statistical methods, we can calculate the standard error and construct a confidence interval around the sample mean. The upper bound of the 95% confidence interval represents the highest plausible value for the population average age based on the sample data.

Therefore, based on the provided information and calculations, the upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

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Work Shown:

F = ma

250 = m*5

250/5 = m

50 = m

m = 50

The mass of the object is 50 kg

Answer:

x= -7-11

x=-18

Step-by-step explanation:

Answer:

m∠DEA = 62°

m∠ADB (arc) = 194°

Angle ∠ADB   = 21°.

Step-by-step explanation:

The given information are;

\(AB\left | \right |DC\), m CB (arc) = 62°, m∠DAB (arc) = 104°

arc∠BCD = 360° - 104° = 256°

m DC (arc) = arc∠BCD - arc CB = 256° - 62° (Sum of angles)

Therefore DC (arc) = 194°

m DA ≅ m CB =  62° (Parallel lines congruent arc theorem. Arc between two parallel lines)

m∠DEA = 1/2×(arc DA + arc CB) = 1/2×(62° + 62°) =62°

m∠DEA = 62°

Arc AB = m∠DAB (arc) - m DA = 104° - 62° = 42°

m∠ADB (arc) = 360 - m∠DAB (arc) - m CB (arc) (Sum of angles around a circle or point)

∴  m∠ADB (arc) = 360 - 104 - 62 = 194°

m∠ADB (arc) = 194°

Angle ADB = subtended by arc AB = ∴1/2×arc AB

Angle ∠ADB  = 42/2 = 21°.

Angle = 21°

To find a basis for the corresponding homogeneous equation and an expression of all solutions. Therefore, a basis for the corresponding homogeneous equation is the set.

we need to solve the system of equations and find the parametric form of the solutions.

Given the system of equations:

x + y + z + w + u + v = 0   -- (1)

x - y + z = 1               -- (2)

To find the basis for the homogeneous equation, we need to solve the system by setting the right-hand side of equation (2) to 0:

x - y + z = 0

Now we have the following system of equations:

x + y + z + w + u + v = 0   -- (1)

x - y + z = 0               -- (3)

We can rewrite equation (3) as:

x = y - z

Substituting this into equation (1):

(y - z) + y + z + w + u + v = 0

2y + w + u + v = 0

Now, we can express the variables in terms of parameters. Let's choose two parameters, say t and s, to represent y and w, respectively:

y = t

w = s

Then, substituting these values back into the equation:

2t + s + u + v = 0

Now we have the parametric form of the system of equations:

x = t - z

y = t

z = z

w = s

u = -2t - s

v = -2t - s

To express all the solutions, we can combine the parametric equations:

(x, y, z, w, u, v) = (t - z, t, z, s, -2t - s, -2t - s)

Therefore, a basis for the corresponding homogeneous equation is the set:

{ (1, 0, 0, 0, -2, -2), (-1, 1, 0, 0, -2, -2), (0, 0, 1, 0, -2, -2) }

And the expression of all solutions is given by:

(x, y, z, w, u, v) = t(1, 0, 0, 0, -2, -2) + s(-1, 1, 0, 0, -2, -2) + z(0, 0, 1, 0, -2, -2)

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An angle of rotation is the measure of the amount that a figure is rotated about a fixed point called a point of rotation.

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Answer:

See attached

All points are plotted and we see the figure we got

8. Rectangle

We can visually confirm that

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

9. Square

We can visually confirm that

Answer:

4/49

Step-by-step explanation:

7, 6, 4, 9, 4, 7, 9

total number of cards: 7

number of 7's: 2

First drawing:

p(7) = 2/7

Replace the 7.

total number of cards: 7

number of prime numbers: 2 (only the 7's are prime numbers)

p(7) = 2/7

The events are independent, so the overall probability is the product of the individual probabilities.

p(7 then prime) = 2/7 × 2/7 = 4/49