the volume of a solid obtained by revolving about y-axis enclosed between the ellipse x^2+9y^2=9 and the straight line x+3y=3 in the first quadrant is
A. 3π
B. 4π
C. 6π
D. 9π

Answer:

the answer is B. $14,434.20

The answer is B. $14,434.20

To calculate the statistical measures for the given data points, we need the actual values of the X and Y variables.

Without the specific data values, we cannot perform the calculations. However, I can explain the formulas and concepts behind each measure.

a. Covariance (cov xy): Covariance measures the relationship between two variables and indicates the extent to which they vary together. It is calculated by taking the sum of the products of the differences between each corresponding X and Y value and the means of X and Y, respectively, and dividing by the number of data points minus one.

b. Standard deviation of X (s x): The standard deviation measures the dispersion or spread of a dataset. It is calculated by taking the square root of the variance of X. Variance is the average of the squared differences between each X value and the mean of X.

c. Standard deviation of Y (s y): Similar to the standard deviation of X, the standard deviation of Y measures the spread of the Y variable. It is calculated by taking the square root of the variance of Y, which is the average of the squared differences between each Y value and the mean of Y.

d. Correlation of X and Y (r xy): Correlation measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1. A positive value indicates a positive linear relationship, while a negative value indicates a negative linear relationship. Correlation is calculated by dividing the covariance of X and Y by the product of their standard deviations.

To accurately calculate the covariance, standard deviations, and correlation, the actual data points for X and Y are required. With the specific data, these calculations can be performed to determine the relationship between the number of pets people own (X) and their stress levels (Y) on a scale of 0-80.

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Answer:

1

You're welcome!

A coefficient is a constant which stands in front of a variable

For example, the coefficient of 3x is 3.  

Or, the coefficient of 9xy is 9

Same with 2x^2*z.  2

In this case, because there is nothing visible, the coefficient is 1.

Answer:

10

Step-by-step explanation:

Answer:

Quadratic

Step-by-step explanation:

The type of graph is quadratic

∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information

Two angles are given.

∠g = (2x-90)°

∠h = (180-2x)°

We have to find the statement which is true about the angles g and h.

If both angles are greater than zero.

Complementary angles add up to 90 degrees

i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.

Substituting the given values:

∠g + ∠h

= (2x-90)° + (180-2x)° = 90°

Thus, ∠g and ∠h are complementary angles.

and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h  are acute.

So the statement ∠g and ∠h are acute angles is also true

Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements

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In the first question, we are asked to evaluate the algebraic expression 8x² + 2y for the given values of x = 6 and y = 9. The options provided are a) 2736, b) 660, c) 306, and d) 2322.

In the second question, we are asked to use the formula C = (F - 32) to convert 104°F to its equivalent temperature on the Celsius scale. The options provided are a) 40°C, b) 76°C, c) 8°C, and d) 130°C.

For the first question, we substitute the given values into the expression 8x² + 2y:

8(6)² + 2(9) = 288 + 18 = 306.

Therefore, the correct answer is c) 306.

For the second question, we use the given formula C = (F - 32) and substitute F = 104:

C = (104 - 32) = 72.

Therefore, the equivalent temperature of 104°F on the Celsius scale is 72°C.

The correct answer is not among the options provided, as none of the options matches the calculated value of 72°C.

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Answer:

\(x = \sqrt{ {28.46}^{2} - {27}^{2} } = \sqrt{80.9716} = 9.00\)

Answer: $41.47

Step-by-step explanation: .15 x 39.50 = 5.925 (round up to 5.93), 39.50-5.93=33.57, .20 x 39.50 = 7.90, 33.57 + 7.90 = $41.47

Answer:

Step-by-step explanation:

6

Two angles that share a common side add up the angle containing both parts.

7

Find <MKL (6x + 12)

3x + 6 + 6x + 12 = 54                     Combine Like terms

9x + 18 =54                                    Subtract 18 from both sides

9x = 54 - 18                                   Combine the right

9x = 36                                          Divide by 9

x = 36/9

x = 4

6x + 12 = 6*4 + 12

<MKL = 36

The required arc length of sector VW is 8\(\pi\).

Given that, in a circle U, radius  UV = 9 and  central angle of sector m∠VUW = 160°.

To find the arc length of sector VW, we can use the formula:

Arc length = (central angle / 360) x circumference of the circle.

First,  find the circumference of the circle by the  formula for the circumference of a circle is given by:

Circumference = 2 x \(\pi\) x radius.

Circumference = 2 x \(\pi\) x 9 = 18π.

Now, let's find the arc length of sector VW using the central angle of 160 degrees:

Arc length = (160/360) x 18π

Arc length = (4/9) * 18\(\pi\) = 8\(\pi\).

Therefore, the arc length of sector VW is 8\(\pi\).

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Answer: You write the latitude first, followed by a comma, and then the longitude.

Step-by-step explanation:

The correct answer is (b) The probability is less than 0.5.

The odds of an event occurring are defined as the ratio of the probability of the event happening to the probability of the event not happening. If the odds of an event occurring are less than 1, it means that the probability of the event happening is less than the probability of the event not happening.

Since the probability of an event happening is always between 0 and 1, and the odds are less than 1, it implies that the probability is less than 0.5.

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Answer:

-8.66666667 feet because:

Step-by-step explanation:

-2 1/3 x 3 = 7

-2 1/3 ÷ 2 = 1.66666666667

7 + 1.6666666667 = 8.66666667

The expression that is equivalent to the given expression, (8x²y² - 9x²y + 9y) - (6x²y - xy² + 4y), is 8x²y² - 15x²y + xy² + 5y

From the question, we are to determine the expression that is equivalent to the given expression.

The given expression is

(8x²y² - 9x²y + 9y) - (6x²y - xy² + 4y)

To determine the expression that is equivalent to the given expression, we will simplify the given expression.

Simplifying the expression

(8x²y² - 9x²y + 9y) - (6x²y - xy² + 4y)

Clear the parentheses by applying the distributive property

8x²y² - 9x²y + 9y - 6x²y + xy² - 4y

Collect like terms

8x²y² - 9x²y - 6x²y + xy² - 4y + 9y

Simplify

8x²y² - 15x²y + xy² + 5y

Hence, the equivalent expression is 8x²y² - 15x²y + xy² + 5y

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(a) Definition of uniform convergence of a sequence of functions on (0, +∞):

A sequence of functions {f_n(x)} is said to converge uniformly on the interval (0, +∞) if for every ε > 0, there exists a positive integer N such that for all n ≥ N and for all x ∈ (0, +∞), |f_n(x) - f(x)| < ε, where f(x) is the limit function.

Negation of the definition of uniform convergence of a sequence of functions on (0, +∞):

A sequence of functions {f_n(x)} does not converge uniformly on the interval (0, +∞) if there exists an ε > 0 such that for every positive integer N, there exists an n ≥ N and an x ∈ (0, +∞) such that |f_n(x) - f(x)| ≥ ε, where f(x) is the limit function.

(b) Consider the sequence of functions {f_n(x)} defined as f_n(x) = n + n^2x^2 on the interval [0, +∞).

Pointwise convergence:

For each fixed x ∈ [0, +∞), as n approaches infinity, the term n^2x^2 dominates the sequence and tends to infinity. Therefore, {f_n(x)} does not converge pointwise to any function on [0, +∞).

Uniform convergence:

To analyze uniform convergence, we need to check if the sequence of functions satisfies the definition of uniform convergence. For any ε > 0, we need to find a positive integer N such that for all n ≥ N and for all x ∈ [0, +∞), |f_n(x) - f(x)| < ε.

Let's consider the difference |f_n(x) - f(x)|:

|f_n(x) - f(x)| = |n + n^2x^2 - f(x)| = |n + n^2x^2 - 0| = n + n^2x^2

For any fixed x ∈ [0, +∞), as n approaches infinity, the term n + n^2x^2 also tends to infinity. Therefore, for any given ε > 0, it is not possible to find a positive integer N such that |f_n(x) - f(x)| < ε for all n ≥ N and for all x ∈ [0, +∞). Thus, the sequence {f_n(x)} does not converge uniformly on [0, +∞).

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Answer:

2 bags of mushrooms

Step-by-step explanation:

The time taken by the object to fall from 15 m on the Mercury which has a gravity of 3.7 m/s² is 10.54 seconds.

It is the study of the motion of a body without considering mass. And the reason behind them is neglected.

The object is on Mercury and starts falling from rest.

As it is on Mercury there is no air resistance to account for.

Gravity on Mercury is 3.7 m/s².

Then the time taken by the object to fall from 15 m will be given as

\(\rm t = \sqrt{2gh}\\\\t = \sqrt{2\times 3.7\times 15}\\\\t = 10.5356 \approx 10.54 \ seconds\)

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Answer:

$305.9022863 or $305.90 (rounded to 2 decimal places)

Step-by-step explanation:

It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula  

A= P(1+R)^n

A= the total amount P=Initial amount       R= rate  n=time period

P=$100 R=15% or 0.15(decimal)  n=8 (years)  

A= 100 (1.15)^8

A= 100(3.059022863)

A=305.9022863

The amount you will have after 8 years is $220

The formula for calculating simple interest is expressed as:

SI =PRT

P is the principal = $100

T is the time = 8 years

R is the rate. = 15%

SI = 100 * 8 * 0.15
SI = $120

Amount after 8years = $100 + $120
Amount after 8years = $220

Hence the amount you will have after 8 years is $220

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Answer:   \(\text{x}\sqrt{3\text{x}}\)   which is Choice A

=========================================

Work Shown:

Let \(y = \sqrt{3\text{x}}\)

So,

\(4\text{x}\sqrt{3\text{x}}-\text{x}\sqrt{3\text{x}}-2\text{x}\sqrt{3\text{x}}\\\\4\text{x}y-\text{x}y-2\text{x}y\\\\(4\text{x}-\text{x}-2\text{x})y\\\\\text{x}y\\\\\text{x}\sqrt{3\text{x}}\\\\\)

This therefore means:

\(4\text{x}\sqrt{3\text{x}}-\text{x}\sqrt{3\text{x}}-2\text{x}\sqrt{3\text{x}}=\text{x}\sqrt{3\text{x}}\\\\\)

as long is x is nonnegative.

Answer:

i think the answer to this question is 2.461

Step-by-step explanation:

For a semicircle, the total perimeter includes half of the circumference + the diameter.

The half circumference is given by 2 pi r / 2

So the perimeter of 19.02 = 2pi r/ 2 + 2r

Answer:

$415.0575

Step-by-step explanation:

Given:

Scale measurement

1 inch = 3 feet.

In the drawing, the length is 5.5 inches and the width is 3.25 inches.

Length = 5.5 × 3

= 16.5 feet

Width = 3.25 × 3

= 9.75 feet

Area of the bedroom = length × width

= 16.5 feet × 9.75 feet

= 160.875 square feet

carpets cost $2.58 per square foot

Cost of carpeting the bedroom = Area of the bedroom × cost of carpet per square foot

= 160.875 × 2.58

= $415.0575

Cost of carpeting the bedroom = $415.0575

Answer:

\( \sqrt[3]{ \frac{ {y}^{5} }{27 {y}^{3} } } = \sqrt[3]{ \frac{ {y}^{3} ({y}^{2}) }{27 {y}^{3} } } \\ \\ \\ = \sqrt[3]{ \frac{ {y}^{2} }{27} } = \frac{ \sqrt[3]{ {y}^{2} } }{ \sqrt[3]{27} } \\ \\ \\ = \frac{ \sqrt[3]{ {y}^{2} } }{3} \)

I hope I helped you^_^

Answer:

you needed to mark this question for the science section

Step-by-step explanation:

Answer:

Surface area of prism = 1301 cm²

Step-by-step explanation:

A triangular pyramid has 3 rectangular sides and 2 triangular sides.

Now, we are told that the triangular side is isosceles.

This means that two of the rectangular sides which share a side with the equal side of the triangle are equal as well as the 2 triangular sides.

Surface area of prism = 2(area of triangular face) + 2(area of rectangle sharing one side with the equal side of the triangle) + (area of rectangle sharing side with the unequal side of the triangle).

Area of triangle = ½ × base × height

Area of triangle = ½ × 9 × 13 = 58.5 cm²

Since height of prism is 32 cm, then;

area of rectangle sharing one side with the equal side of the triangle = 32 × 14 = 448 cm²

area of rectangle sharing side with the unequal side of the triangle = 32 × 9 = 288 cm²

Thus;

Surface area of prism = 2(58.5) + 2(448) + 288

Surface area of prism = 1301 cm²

Answer:

27

Step-by-step explanation:

Answer:

you can go on a maximum of 11 rides

Step-by-step explanation:

you first have to subtract 30 from 100 since that is the admissons fee.

So now you are left with 70 dollars.

You divide 70 by 6 since you need 6 dollars to go on each ride.

and 70 divided by 6 is 11.6666666667 but round it to 11 since that the whole number you're left with.

hope this helped :)

The person is making money more than the half of the population of the teachers.

Given, a person is making the median salary for a construction worker.

we have to find that more than how many teachers the person is making money

as, we know that the median is more than the half of the population.

So, the person is making money more than the half of the population of the teachers.

Hence, the person is making money more than the half of the population of the teachers.

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