Which equation can be used to find the surface area of the cylinder? A cylinder with a diameter of 6 centimeters and height of 14 centimeters. S = 2 pi (14) squared + 2 pi (14) (6) S = 2 (3) squared + 2 (3) (14) S = 2 pi (6) squared + 2 pi (6) (14) S = 2 pi (3) squared + 2 pi (3) (14) (help asap!)

The answer is A. The function g(x) = x is a unit vector in the vector space C[0, 1] and B. The cosine of the angle between \(f(x) = 5x^2\) and g(x) = 9x is 15 /\((2\sqrt{15})\).

To determine whether the function f(x) = 3x is a unit vector in the vector space C[0, 1] with the given inner product, we need to calculate its norm or magnitude.

The norm of a function f(x) in this vector space is defined as ||f|| = sqrt((f, f)), where (f, f) is the inner product of f with itself.

Using the inner product given, we can calculate the norm of f(x) as follows:

\(||f|| = sqrt(integral^1_0 (3x)^2 dx)\\= sqrt(integral^1_0 9x^2 dx)\\= sqrt[9 * (x^3/3) | from 0 to 1]\)

= sqrt[9/3 - 0]

= sqrt(3).

Since the norm of f(x) is sqrt(3) ≠ 1, we can conclude that f(x) = 3x is not a unit vector in this vector space.

To find a function that is a unit vector, we need to normalize f(x) by dividing it by its norm. Let's denote this normalized function as g(x):

g(x) = f(x) / ||f||

= (3x) / sqrt(3)

= sqrt(3)x / sqrt(3)

= x.

Therefore, the function g(x) = x is a unit vector in the vector space C[0, 1].

(b) To find the cosine of the angle between \(f(x) = 5x^2\) and g(x) = 9x, we can use the inner product and the definition of cosine:

cos(θ) = (f, g) / (||f|| ||g||).

Using the given inner product, we have:

\((f, g) = integral^1_0 (5x^2)(9x) \\\\dx= 45 * integral^1_0 x^3 \\\\dx= 45 * (x^4/4 | from 0 to 1)\)

= 45/4.

The norms of f(x) and g(x) are:

\(||f|| = sqrt(integral^1_0 (5x^2)^2 dx)\\= sqrt(integral^1_0 25x^4 dx)\\= sqrt[25 * (x^5/5) | from 0 to 1]\)

= sqrt(5).

\(= sqrt(integral^1_0 81x^2 dx)\)

\(= sqrt(integral^1_0 81x^2 dx)\)

\(= sqrt[81 * (x^3/3) | from 0 to 1]\)

\(= 3\sqrt{3}\)

Substituting these values into the cosine formula:

cos(θ) = (45/4) / (sqrt(5) * 3√3)

\(= (15/2) * (1 / (sqrt(5) * √3))= (15/2) * (1 / √15)= (15/2) * (1 / (√3 * √5))= 15 / (2√15).\)

Therefore, the cosine of the angle between \(f(x) = 5x^2 and g(x) = 9x is 15 / (2\sqrt{15}).\)

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According to the question Rounded to four decimal places, the probability is approximately 0.00001385, or approximately 0.0014%.

To calculate the probability of obtaining a straight flush in a five-card poker hand, we need to determine the number of possible straight flush hands and divide it by the total number of possible five-card hands.

A straight flush consists of five consecutive cards of the same suit. There are four suits in a standard deck of cards (hearts, diamonds, clubs, and spades), and for each suit, there are nine possible consecutive sequences (Ace, 2, 3, 4, 5, 6, 7, 8, 9; 2, 3, 4, 5, 6, 7, 8, 9, 10; etc.). Therefore, there are \(\(4 \times 9 = 36\)\) possible straight flush hands.

The total number of possible five-card hands can be calculated using the concept of combinations. In a standard deck of 52 cards, there are \(\({52 \choose 5}\)\) different ways to choose five cards. The formula for combinations is \(\({n \choose k} = \frac{n!}{k!(n-k)!}\), where \(n\)\) is the total number of items and \(\(k\)\) is the number of items being chosen.

Using the formula, we have \(\({52 \choose 5} = \frac{52!}{5!(52-5)!} = 2,598,960\).\)

Therefore, the probability of obtaining a straight flush in a five-card poker hand is:

\(\[\frac{\text{{number of straight flush hands}}}{\text{{total number of five-card hands}}} = \frac{36}{2,598,960} \approx 0.00001385\]\)

Rounded to four decimal places, the probability is approximately 0.00001385, or approximately 0.0014%.

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Answer:

C = 12π or 37.7

Step-by-step explanation:

A = πr²

36π = πr²

π's get divided out and you are left with:

r² = 36

if you take the square root of 'r' it will equal the square root of 36, which is 6

C = 2πr

C = 2π(6)

C = 12π or 37.7

Answer

the answer is 12*sqrt pi

Answer:

Step-by-step explanation:2+1+5=8

78.40/8=9.80

B=5x9.80=49

C=1x9.80=9.80

So B-C=39.20 more

Answer:

x= kaylas age

older sister: 2x+1

younger sister: x-3

x+2x+1+x-3=26

4x-2=26

4x=28

x=7 years old

Step-by-step explanation:

The values of E(X) = 3.25 and Var(X) ≈ 2.238 for the number of spades in a hand of 13 cards chosen at random from a 52-card deck.

To find E(X) and Var(X) for the number of spades in a hand of 13 cards chosen at random from a 52-card deck, we will use the concepts of probability and statistics.

E(X), or the expected value, is the average number of spades you would expect to get in a hand of 13 cards. To find E(X), we can use the formula:

E(X) = (Number of spades in the deck / Total number of cards in the deck) * Number of cards drawn

E(X) = (13 spades / 52 cards) * 13 cards drawn
E(X) = (1/4) * 13
E(X) = 3.25

So, the expected number of spades in a 13-card hand is 3.25.

Next, let's find Var(X), or the variance, which is a measure of how much the number of spades can vary from the expected value. We can use the formula for variance of a hypergeometric distribution:

Var(X) = (Number of cards drawn * Number of spades * Number of non-spades) / ((Total number of cards in the deck)^2 * (Total number of cards in the deck - 1))

Var(X) = (13 cards drawn * 13 spades * 39 non-spades) / ((52 cards)^2 * (52 cards - 1))
Var(X) = (13 * 13 * 39) / (52 * 52 * 51)
Var(X) ≈ 2.238

So, the variance for the number of spades in a 13-card hand is approximately 2.238.

In summary, E(X) = 3.25 and Var(X) ≈ 2.238 for the number of spades in a hand of 13 cards chosen at random from a 52-card deck.

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The total surface area of the composite shapes are 69 square cm, 63 square cm and 108 square yd

The surface area of composite shapes can be found by breaking the composite shape down into simpler shapes and then finding the surface area of each individual shape.

Once the surface areas of all the individual shapes are found, they can be added together to find the total surface area of the composite shape.

Figure 1

Here, we have

Area = Area of rectangle + square

So, we have

Area = 5 * 5 + 4 * 11

Area = 69 square cm

Figure 2

Here, we have

Area = Area of  square + triangle

So, we have

Area = 7 * 7 + 1/2 * 7 * 4

Area = 63 square cm

Figure 3

Here, we have

Area = Area of rectangle + square

So, we have

Area = 12 * 6 + 6 * 6

Area = 108 square yd

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The dimensions of the closed right circular cylinder with the smallest surface area and a volume of 1024 cm can be determined by finding the radius and height that minimize the surface area.

To find the dimensions of the cylinder with the smallest surface area, we need to minimize the surface area function while keeping the volume fixed at 1024 cm. The surface area of a closed right circular cylinder is given by the formula A = 2πr² + 2πrh, where r is the radius and h is the height.

To minimize the surface area, we can use calculus. By taking the derivative of the surface area function with respect to either the radius or the height, setting it equal to zero, and solving for the variables, we can find the critical points.

Differentiating the surface area function with respect to the radius, we get dA/dr = 4πr + 2πh. Setting this derivative equal to zero, we find that h = -2r. However, since the height cannot be negative, we discard this solution.

Next, differentiating the surface area function with respect to the height, we get dA/dh = 2πr. Setting this derivative equal to zero, we find that r = 0. Therefore, the only critical point is when r = 0, which means the cylinder has no radius and no surface area.

Since a cylinder without a radius is not possible, we conclude that there is no cylinder with the smallest surface area and a volume of 1024 cm. It is important to note that the surface area can be arbitrarily small as the height approaches infinity, but it cannot be minimized for a fixed volume.

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A mathematical expression is a statement made up of variables, constants, and arithmetic operators. For the equation -3 x^2-9/x+3 , the rational expression is x+3 , Option A

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression’s structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

The complete question is

“Which of the following is equal to the rational expression when x does not equal 1 or 3   ( )

The options are

a. X+3

b. X-3

c. (x -3)/(x+3)”

The expression given in the question is

( )

And have been asked among the option which represents the rational expression when x does not equal 3 or 1

Therefore for the following equation -3 x^2-9/x+3 , the rational expression is x+3 .

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Answer: ]1, 2[

Step-by-step explanation:

\(A \cap B=[0; 2[\\\\(A \cap B)-C=]1, 2[\)

Answer:

26 = <F

Step-by-step explanation:

Since the triangle is isosceles, the base angles are the same

<D = <F

26 = <F

The triangle is a isosceles triangle

\(\\ \rm\Rrightarrow <D=<F\)

\(\\ \rm\Rrightarrow <F=26°\)

Answer:

-2

Step-by-step explanation:

see the attached photo please :)

Answer:

x = -5

Step-by-step explanation:

-34 - 5x = 3x + 6

x = -5

Answer:

x=-5

Step-by-step explanation:

divide each side by a factor thay dont contain  variable

Note that the lateral area for the pyramid with the equilateral base is: 144 sq Units. (Option A)

A pyramid with an equilateral base is a three-dimensional geometric shape that has a base that is an equilateral triangle and triangular faces that meet at a common vertex. The height of the pyramid is the perpendicular distance from the base to the vertex. The vertex is also known as the apex of the pyramid.

The given pyramid has 3 lateral triangular sides as shown below whose sides are 10 units each.; and Base of the triangle = 12 unit

Note that the lateral area of a pyramid is the sum of the areas of all the lateral faces (excluding the base) of the pyramid. In other words, it is the total surface area of the sides of the pyramid.

Thus, to proceed we need to find a perpendicular.

 By Pythagoras' theorem we have

Perpendicular² = 10²-6²

Perpendicular = 8 unit

So the area of 1 lateral triangle = 1/2 x Base x Perpendicular.

= 1/2 x 12 x 8

= 48 unit²

Area of lateral sides = 3 x 48

= 144 unit²    

Therefore, the lateral area for the pyramid with the equilateral base is: 144 sq Units.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Find the lateral area for the pyramid with the equilateral base.

a) 144 sq. units

b) 180 sq. units

c) 288 sq. units

Note that the image remains the same.

Answer:

1 out of 13

Step-by-step explanation:

An effective sampling method is not cast doubt on the usefulness of the sample

The effective sample is a calculation of the approximate sample size needed to obtain the same degree of accuracy as a simple random sample. It is denoted mathematically by the formula n/D, where n represents the sample size and D denotes the design effect. It is employed as a means of condensing the volume of data.

Effective sample size calculations are mostly used for qualitative analyses of the sample size. The sample size calculates the total number of measurements or observations made during an experiment or survey. The effective sample size—rather than the actual sample size—is utilized in this assessment since it is thought that a sample size of 30 is necessary for an analysis to be valid.

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Answer:

20 blocks

Step-by-step explanation:

Paired data refers to observations that are matched or connected in some way. In this case, if we were comparing the rates of return for the two stocks on the same set of 50 days, then it would be considered paired data.

The data comparing the rates of return for the technology company Intel and the U.S. airline Southwest Airlines would not be considered paired data because the samples are not taken on the same days. Paired data refers to observations that are matched or connected in some way. In this case, if we were comparing the rates of return for the two stocks on the same set of 50 days, then it would be considered paired data.

However, in this scenario, two separate random samples of 50 days of stock returns are taken for each company. The days on which the stock returns are recorded are not necessarily the same for both Intel and Southwest Airlines. Therefore, there is no direct pairing or connection between the observations of the two stocks.

To illustrate this further, let's say we take a random sample of 50 days for Intel's stock returns, and another random sample of 50 days for Southwest's stock returns. The first day in the Intel sample may not correspond to the first day in the Southwest sample, and so on. Each sample represents independent observations for each stock, making the data unpaired.

It is important to recognize whether data is paired or unpaired as it can affect the statistical methods used for analysis. In this case, since the data is not paired, we would use different approaches to compare the rates of return for Intel and Southwest Airlines.

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we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Answer:

1. 4/2

2. -3/5

3. 2/2

4. undefined

5. -5/1

6. zero

7. -4/5

8. 1

9. 0

10. 3/4

11. undefined

12. -9/4

The required slope for the lines is given below.

Given that,
Pot of line and points on the lines are given, we have to determine the slopes of the lines.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Slopes of the line can be given as,
m = [y₂ - y₁ ] / [x₂ - x₁]
for points, (-1, -11), (-6, -7)
m = -7 + 11 / -6 + 1
m = -4/5

Similarly,
Slopes of the line can be calculated as
1.) 4/2  2.) -3/5  3.) 2/2
4.) not defined because the denominator becomes zero or perpendicular to x-axis.
5.) -5/1
6.) zero  because the line is parallel to the x-axis
7.) -4/5      8.) 1   9.) 0  10.) 3/4
11.) not defined because the denominator becomes zero or perpendicular to the x-axis.
12.) -9/4

Thus, the required slope for the lines is given above.

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\Step-by-step explanation:

convert to math form:

\(\frac{x}{2} \le5\)

simplify:

\(x \le 10\)

convert to word form(optional):

x is less than or equal to 5.

The relation "r" on the set of all integers, where x = y^2, is not reflexive.

A relation is reflexive if every element in the set is related to itself. In this case, for the relation x = y^2 to be reflexive, every integer "x" should be related to itself, meaning that x = x^2. However, this is not true for all integers.

For example, if we consider x = 2, it is not equal to 2^2 = 4. Similarly, if we consider x = -3, it is not equal to (-3)^2 = 9.

Since there are integers that do not satisfy the condition x = x^2, the relation x = y^2 is not reflexive on the set of all integers.

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Answer:the 3rd option

Step-by-step explanation:

Answer:

You will need to study and get the answer using

Step-by-step explanation:

a link: https://brainly.com/question/16261743. Taking a rescoruce. i surely think that you can do it

Answer:

  72 square units

Step-by-step explanation:

The figure shown has a uniform horizontal cross section, so is equivalent to a rectangle with length 12 and height 6. Its area is given by the rectangle formula:

  A = LW

  A = (12)(6) = 72 . . . . square units

__

Additional comment

Essentially, the semicircle removed from the left side is tacked onto the right side. The rectangle area is unchanged by that.

Answer:

7m + 6

3y+7

15m+9r

4+4k

20+2g

2j+r+h

-2C+8c+12r

9s+4m

Step-by-step explanation:

Hope this helps ;)

good luck .

The option that does not specify certain conditions or assumptions about the parameters of the population is e. Assumption-free tests.

Assumption-free tests, also known as distribution-free tests or non-parametric tests, do not make any specific assumptions about the parameters or distribution of the population from which the sample was drawn. These tests do not rely on assumptions such as normality or underlying continuity of the variable being studied. Instead, they are based on the ranks or orderings of the data.

In contrast, parametric tests (option a) make assumptions about the population parameters, such as assuming a specific distribution (e.g., normal distribution) or estimating parameters (e.g., mean, variance) based on the sample data.

Semi-parametric tests (option c) combine both parametric and non-parametric components. They make some assumptions about certain parameters while remaining non-parametric for other aspects of the analysis.

Non-statistical tests (option d) do not exist as a distinct category in hypothesis testing. The term "non-statistical tests" is not commonly used in the context of hypothesis testing.

Therefore, the correct option is e. Assumption-free tests.

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Answer:

x = 7

Step-by-step explanation:

2(3x-9)=2x+10

6x - 18 = 2x + 10

4x = 28

x = 7

Answer:

x = 7

Step-by-step explanation:

In order to find the value of x, isolate it in the equation.

1) First, distribute the 2 to the terms inside the set of parentheses.

\(2 (3x - 9) = 2x + 10 \\6x - 18 = 2x + 10 \\\)

2) Next, move all the x terms to one side and all the other terms to the other side. Subtract both sides by 2x and add both sides by 18.

\(6x - 18 = 2x + 10 \\4x = 28\)

2) Divide both sides by 4 to finally isolate x.

\(4x = 28 \\x = 7\)

Thus, x = 7.