calculate the volume of the solid obtaining by rotating the region bounded by the parabola 364 X² = and the the square root function y = √366 around the 2 x-axis Q) Determine the surface area of the solid obtained by rotating of (18+) (18+) y - 1x1 < 2 about X-axis 00 Q) Determine whether {(und)"} 3" Converges or diverges no

Answer:

D

Step-by-step explanation:

30 from the beginning of the week plus 50 that you bought.

80-x=30

50=x

Answer is D

Answer:50

Step-by-step explanation:

30+50=80

80-30=50

So he sell 50

Answer:

6.4

Step-by-step explanation:

Just plug in the distance formula.

(4+1)^2+(1-5)^2

(5)^2+(-4)^

25+16

41

(square root 41) and get 6.4

Train A speed = x + 20

Train B = x

We know that 46 minutes is 23/30 of an hour.

Use D = rt

Take it from here.

Answer: C

Step-by-step explanation:

Answer:

Step-by-step explanation:

its 9

we have ∫R∫R f(x, y) dxdy = ∫R∫R f(x, y) dydx = 0. The function f: R^2 → R defined as f(x, y) = x^2 + y^2 * sgn(xy), where (x, y) ≠ (0, 0), is not integrable over R^2. This means that it does not have a well-defined double integral over the entire plane.

To see why f is not integrable, we need to consider its behavior near the origin (0, 0). Let's examine the limits as (x, y) approaches (0, 0) along different paths.

Along the x-axis, as y approaches 0, f(x, y) = x^2 + 0 * sgn(xy) = x^2. This indicates that the function approaches 0 along the x-axis.

Along the y-axis, as x approaches 0, f(x, y) = 0^2 + y^2 * sgn(0y) = 0. This indicates that the function approaches 0 along the y-axis.

However, when we approach the origin along the line y = x, the function becomes f(x, x) = x^2 + x^2 * sgn(x^2) = 2x^2. This shows that the function does not approach a single value as (x, y) approaches (0, 0) along this line.

Since the function does not have a limit as (x, y) approaches (0, 0), it fails to satisfy the necessary condition for integrability. Therefore, f is not integrable over R^2.

Additionally, since the function f(x, y) = x^2 + y^2 * sgn(xy) is symmetric with respect to the x-axis and y-axis, the double integral ∫R∫R f(x, y) dxdy is equal to ∫R∫R f(x, y) dydx.

By symmetry, the integral over the entire plane can be split into four quadrants, each having the same contribution. Since the function f(x, y) changes sign in each quadrant, the integral cancels out and becomes zero in each quadrant.

Therefore, we have ∫R∫R f(x, y) dxdy = ∫R∫R f(x, y) dydx = 0.

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Yes, there is a relationship like a straight line between the raises administrators at State University receive and their performance on the job

To obtain this interpretation, we consider the equation of the regression line, which relates the predicted raise amount (y hat) to the job performance rating (x). The y-intercept term in this equation is the value of y hat when x equals zero. Therefore, the estimated y-intercept of $14,000 represents the predicted raise amount for an administrator whose job performance rating is zero, which corresponds to the base raise amount at State University.

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Answer:

1/7

Step-by-step explanation:

Answer:

p²q³ + pq and pq(pq² + 1)

Step-by-step explanation:

Given

3p²q² - 3p²q³ +4p²q³ -3p²q² + pq

Required

Collect like terms

We start by rewriting the expression

3p²q² - 3p²q³ +4p²q³ -3p²q² + pq

Collect like terms

3p²q² -3p²q² - 3p²q³ +4p²q³ + pq

Group like terms

(3p²q² -3p²q²) - (3p²q³ - 4p²q³ ) + pq

Perform arithmetic operations on like terms

(0) - (-p²q³) + pq

- (-p²q³) + pq

Open bracket

p²q³ + pq

The answer can be further simplified

Factorize p²q³ + pq

pq(pq² + 1)

Hence, 3p²q² - 3p²q³ +4p²q³ -3p²q² + pq is equivalent to p²q³ + pq and pq(pq² + 1)

The probability of the win the taste test when he is just guessing and when he get right answer with probability 0.9 is given by 0.0547 and 0.4241 respectively.

Let X be the number of beers that David correctly identifies.

Use binomial probability ,

David is just guessing,

Probability of correctly identifying a beer is 0.5,

since he has two options.

⇒ probability of him correctly identifying 8 or more beers is,

P(X ≥ 8)

= 1 - P(X ≤ 7)

= 1 - (¹⁰C₀)(0.5)^0(0.5)^10 - (¹⁰C₁(0.5)^1(0.5)^9 - ... - (¹⁰C₇)(0.5)^7(0.5)^3

Using a binomial probability table,

P(X ≥ 8) = 0.0547

Probability of him winning the taste test is approximately 0.0547.

David correctly identify a beer with a probability 0.9,

Probability of correctly identifying 8 or more beers is,

P(X ≥ 8)

= (¹⁰C₈)(0.9)^8(0.1)^2 + (¹⁰C₉)(0.9)^9(0.1)^1 + (¹⁰C₁₀)(0.9)^10(0.1)^0

Simplify it we get,

⇒ P(X ≥ 8) = 0.4241

Probability of him winning the taste test is approximately 0.4241.

Therefore, the probability of just guessing and right answer with probability 0.9 is equals to 0.0547 and 0.4241 respectively.

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Answer: 15

Step-by-step explanation:

(5-1)^2 - (6-5)^3

(4)^2 - (1)^3

16-1

=15

Answer:

The numbers are 10 and 21.

Step-by-step explanation:

x + y = 31

xy = 210

x = 31 - y

(31 - y)y = 210

31y - y² = 210

y² - 31y + 210 = 0

(y - 21)(y - 10) = 0

y - 21 = 0  or  y - 10 = 0

y = 21  or  y = 10

The two real numbers are 10 and 21.

Quadratic Equations are algebraic expressions of degree 2 in one variable and are of the form ax² + bx + c = 0.

In simpler terms, a quadratic equation is be defined as a polynomial equation of degree 2.

Given that, there are two real numbers with a sum of 31 and a product of 210.

We need to find their values using the concept of quadratic equation,

So, according to the question,

x + y = 31 (eq 1)

xy = 210 (eq 2)

x = 31 - y

(31 - y) y = 210

31y - y² = 210

y² - 31y + 210 = 0

(y - 21) (y - 10) = 0

y - 21 = 0 or y - 10 = 0

y = 21 or y = 10

Hence, the two real numbers are 10 and 21.

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Answer:

x = 1, y = 2

Step-by-step explanation:

Multiply 2x - 8y = -14 ​by 5 to get 10x - 40y = -70

Subtract (10x - 40y = -70) - (10x - 9y = -8)

Solve -31y = -62 for y

y = 2

Plug in y value to get x value

x = 1

The direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

To find the maximum rate of change of the function f at the given point (5, 6, -1) and the direction in which it occurs, we can calculate the gradient of f at that point.

The gradient vector represents the direction of maximum increase of the function, and its magnitude represents the rate of change in that direction.

The gradient vector (∇f) of f(x, y, z) = (8x + 5y)/z can be found by taking the partial derivatives with respect to each variable:

∂f/∂x = 8/z

∂f/∂y = 5/z

∂f/∂z = -(8x + 5y)/z^2

Evaluated at the point (5, 6, -1), we have:

∂f/∂x = 8/(-1) = -8

∂f/∂y = 5/(-1) = -5

∂f/∂z = -((8(5) + 5(6))/(-1)^2) = -46

So, the gradient vector (∇f) at the point (5, 6, -1) is (-8, -5, -46).

The maximum rate of change of f at this point is given by the magnitude of the gradient vector:

|∇f| = √((-8)^2 + (-5)^2 + (-46)^2) = √(64 + 25 + 2116) = √2205 = 47.

Therefore, the maximum rate of change of f at the point (5, 6, -1) is 47.

To determine the direction in which this maximum rate of change occurs, we normalize the gradient vector by dividing it by its magnitude:

Direction vector = (∇f) / |∇f| = (-8/47, -5/47, -46/47).

Hence, the direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

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Answer:

no 36x is not a solution the answer is 36/9=4

Step-by-step explanation:

you plug in 36 for x and then divide by 9

Answer:

b

Step-by-step explanation:

cut it in half, boom equal

Answer:

b

Step-by-step explanation:

1)  XY' + Z + X'Z' + YZ'

2) equation 2 is correct.

3) equation 3 is incorrect .

1)

Simplifying algebraically,

XY' +Z+ (X' + Y)Z'

So,

XY' + Z + X'Z' + YZ'

2)

D(A + B)(A + B')C

Simplifying,

(AD + DB) (A + B')C

Further,

ADC + AB'CD + ABCD + BB'CD

ACD + ABCD + AB'CD

= ACD

Thus equation 2 is correct .

Hence proved .

3)

(a + b)(b + c)(c + a) = f1

Simplifying further,

abc + ab + bc + ac = f1

Let f2 = (a'+ b')(b' + c')(c' + a')

Simplify further,

f2 = a'b'c' + a'b' + b'c' + a'c'

Here,

f1 ≠ f2

Thus we disprove equation 3 .

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Answer:

Step-by-step explanation:

two lines are guaranteed to be coplanar if they lie in the same plane

Answer:

it would be true

Step-by-step explanation:

its guaranteed

The ratio of the volumes of the similar solids expressed in lowest terms is 64 : 27

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

Two similar solids have a scale factor of 4:3

This means that

Ratio = 4 : 3

To calculate the ratio of their volumes expressed in lowest terms, we cube both sides of the expression

So, we have

Volume ratio = 64 : 27

Hence, the ratio of their volumes expressed in lowest terms is 64 : 27

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Answer:

Interval Notation:

(−∞,∞)

Step-by-step explanation:

Any value of q makes the equation true.

Hope this helps :)

Answer:

10^7

Step-by-step explanation:

There are seven tens that you are multiplying together.  So, it would be ten to the seventh power or ten times ten times ten times ten times ten times ten times ten.

There are several statistics that are robust to outliers: Median, Interquartile range, Winsorized mean and Trimmed mean.

These statistics are more suitable for datasets that contain outliers as they are less influenced by the extreme values and provide more accurate information about the central tendency and variability of the data.

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The theorem is false, as demonstrated by a counterexample, and to ensure its truth, the condition L ≠ 1 must be imposed, resulting in a limit of f(x) equal to -ln((1-L)/L) as x approaches a.

(a) To prove that the theorem is false, we need to provide a counterexample. Consider the function f(x) = -x, defined on the interval

(-∞, a). The limit of eᶠ⁽ˣ⁾/(1+eᶠ⁽ˣ⁾) as x approaches a is:

lim e⁻ˣ)/(1+e⁻ˣ) = 0/(1+0)

= 0

However, the limit of f(x) as x approaches a is:

lim f(x) = lim (-x) = -a

Since the limit of f(x) does not exist (it is -a), the theorem is false.

(b) In order to ensure that the theorem is true, we need to impose additional conditions on L. The most general condition is L ≠ 1, which means the limit of  eᶠ⁽ˣ⁾/(1+eᶠ⁽ˣ⁾) must be any value other than 1.

To prove the modified theorem, assuming L ≠ 1, we can use the fact that  e⁻ᶠ⁽ˣ⁾/(1+e⁻ᶠ⁽ˣ⁾) = 1 -  eᶠ⁽ˣ⁾/(1+eᶠ⁽ˣ⁾). Then, using algebraic manipulations and the continuity of exponential and logarithmic functions, we can show that the limit of f(x) exists and is equal to -ln((1-L)/L) as x approaches a.

Therefore, the original theorem is false, as shown by the counterexample. However, with the additional condition L ≠ 1, the modified theorem holds true, and the limit of f(x) exists and is equal to

-ln((1-L)/L) as x approaches a.

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Step-by-step explanation:

tan K = 32/24 = 4/3

hope this helps you.

Answer:

tan K = 4/3

Step-by-step explanation:

Tangent puts together the OPPOSITE side of a triangle compared to the ADJACENT side in a ratio (looks like a fraction)

tan K = 32/24 reduce this fraction for your final answer.

tan K = 4/3

d) Rolling an even number that is less than 2 is not a valid outcome when rolling a die.therefore, option d) is correct.

The outcome that is not possible is (d) rolling an even number that is less than 2 on a die.

A standard die has six sides numbered from 1 to 6, and all the even numbers on a standard die are 2, 4, and 6.

The statement "rolling an even number that is less than 2" contradicts the fact that the lowest even number on a die is 2.

Thus, it is not possible to roll an even number that is less than 2 on a standard die, making it an invalid outcome.

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Answer:

c: 128

Step-by-step explanation:

A discrete probability distribution is a statistical distribution that relates to a set of outcomes that can take on a countable number of values, whereas a continuous probability distribution is one that can take on any value within a given range.Therefore, the main difference between the two types of distributions is the type of outcomes that they apply to.

An example of a discrete probability distribution is the probability of getting a particular number when a dice is rolled. The possible outcomes are only the numbers one through six, and each outcome has an equal probability of 1/6. Another example is the probability of getting a certain number of heads when a coin is flipped several times.

On the other hand, an example of a continuous probability distribution is the distribution of heights of students in a school. Here, the range of heights is continuous, and it can take on any value within a given range.

The expected value of a probability distribution measures the central tendency or average of the distribution. In other words, it is the long-term average of the outcome that would be observed if the experiment was repeated many times.

For a discrete probability distribution, the expected value is computed by multiplying each outcome by its probability and then adding the results. In mathematical terms, this can be written as E(x) = Σ(xP(x)), where E(x) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome.

For example, consider the probability distribution of the number of heads when a coin is flipped three times. The possible outcomes are 0, 1, 2, and 3 heads, with probabilities of 1/8, 3/8, 3/8, and 1/8, respectively. The expected value can be computed as E(x) = (0*1/8) + (1*3/8) + (2*3/8) + (3*1/8) = 1.5.

Therefore, the expected value of the distribution is 1.5, which means that if the experiment of flipping a coin three times is repeated many times, the long-term average number of heads observed will be 1.5.

Gavin spend 35 minutes in reading.

Unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Gavin spent 1 hour 35 minutes less than Lucas

Lucas spent 47 minutes less than Pete.

Pete spent 3 hours reading.

Since, pete spent 3 hours. So, Lucas spent

= 3 hours or (180 minutes) - 47 minutes

= 2 hours 13 minutes.

Now, Gavin spent = 2 hrs 13 minutes - 1 hour 35 minutes  

                             = 38 minutes

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The correct option that describes the set being linearly dependent is option A: f2(x) = c1 f1(x) + c2 f3(x) + c3 f4(x).

If one of the functions in the set can be expressed as a linear combination of the other functions, it implies that the set is linearly dependent. In option A, f2(x) can be written as a linear combination of f1(x), f3(x), and f4(x), indicating that the set is linearly dependent.

Option B does not necessarily imply linear dependence, as it represents a specific linear combination of the functions rather than one function being a linear combination of the others.

Option C refers to the Wronskian, which is a concept used to test linear independence of functions, but its value not being zero does not necessarily imply linear dependence.

Option D, stating that the functions are not multiples of each other, does not provide enough information to determine linear dependence or independence.

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