Emptying a tank A vertical right-circular cylindrical tank measures 30 ft high and 20 ft in diameter. It is full of kerosene weighing 51.2 lb>ft3 . How much work does it take to pump the kerosene to the level of the top of the tank

To determine the number of ways to select a committee of three faculty members and two students from a group of five faculty and seven students, we need to calculate the combination of faculty members and students separately and then multiply the results.

The number of ways to select three faculty members from a group of five is given by the combination formula:

C(5, 3) = 5! / (3!(5 - 3)!) = 10

Similarly, the number of ways to select two students from a group of seven is given by:

C(7, 2) = 7! / (2!(7 - 2)!) = 21

To find the total number of ways to select a committee consisting of three faculty members and two students, we multiply these two values:

Total ways = 10 * 21 = 210

Therefore, there are 210 ways to select a committee of three faculty members and two students from the given group.

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a) The probability of getting all answers correct is approximately 0.0002562%. b) The probability of getting all answers wrong is approximately 32.7680%.

To determine the number of different ways to answer all the questions on the exam, we can use the Fundamental Counting Principle. Since there are 5 possible answers for each of the 8 questions, the total number of different ways to answer all the questions is 5^8 = 390,625.

a) To calculate the probability that the student got all of the answers correct, we need to consider that for each question, there is only one correct answer out of the 5 options. Thus, the probability of getting one question correct by random guessing is 1/5, and since there are 8 questions, the probability of getting all the answers correct is (1/5)^8 = 1/390,625. Converting this to a percentage, the probability is approximately 0.0002562%.

b) Similarly, the probability of getting all of the answers wrong is the probability of guessing the incorrect answer for each of the 8 questions. The probability of guessing one question wrong is 4/5, and since there are 8 questions, the probability of getting all the answers wrong is (4/5)^8. Converting this to a percentage, the probability is approximately 32.7680%.

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Answer:

This is gebber gabber but yes

Step-by-step explanation:

6000

Step-by-step explanation:

\(16t ^{2} - 80t\)

substitute t to 5(seconds)

\(16(5) ^{2} - 80(5) \\ 6400 - 400 \\ = 6000\)

The value of {x} for which the equation → 26 = -1 + (27x)³/4 holds true is {x} = 0.18.

A function is a relation between a dependent and independent variable. Mathematically, we can write -

y = f(x) = ax + b

Given is the function as -

26 = -1 + (27x) ³/4

We have the equation as -

26 = -1 + (27x)³/4

(27x)³/4 = 26 + 1

(27x)³/4 = 27

(27x)³ = 27 x 4

(27x)³ = 108

(27)³x³ = 108

x³ = 108/(27)³

x³ = 108/19683

x = 0.0055

x = 0.18 {approx.}

Therefore, the value of {x} for which the equation → 26 = -1 + (27x)³/4 holds true is {x} = 0.18.

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If billion dollars in taxes were collected in 2005, then 30 billion was collected in 2017.

In 2005 the population was 2 million and it had increased to 3 million by 2017.

If 20 billion dollars in taxes were collected in 2005 then we have to determine how much tax was collected in 2017.

The amount of taxes of the city is proportion to the population of that city.

Tax(T) = kP(Population)

where k is a constant.

In 2005 Population = 2 millions and T = 20 billion. So

20 = 2k

Divide by 2 on both side, we get

k = 10

In 2017 Population = 3 millions and k = 10. So the tax collection in 2017 is:

t = 10 × 3

t = 30 billion

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The complete question is:

The amount of taxes a city collects is proportional to the population of the city. In 2005 the population was 2 million and it had increased to 3 million by 2017. If 20 billion dollars in taxes were collected in 2005 how much was collected in 2017? billion dollars help?

The value of the angle and side using trigonometric ratio is:

∠B = 45°

sin B = 1/√2

The three primary trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

From the diagram, using trigonometric ratios, we have:

sin B = (x + 5)/√(2x² + 20x + 50)

Now, using Pythagoras theorem, we can find the side BC. Thus:

BC = √[(2x² + 20x + 50) - (x + 5)²]

BC = √(2x² + 20x + 50 - x² - 10x - 25)

BC = √x² + 10x + 25

BC = √(x + 5)²

BC = x + 5

Since AC = BC, it means it is an Isosceles triangle and so ∠B = 45°

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Answer:

Whichever distance you can count the metric units and see that the x value is 7 on

Step-by-step explanation:

Whichever distance you can count the metric units and see that the x value is 7 on

Answer:

Yes, the triangles are congruent. The triangle are congruent by HL since it has each triangle has a right angle.

Step-by-step explanation:

Answer: a

Step-by-step explanation: simple math

Answer: Answer on the bottom below

Step-by-step explanation: And p.s this is worth 18 points because it needed to divide the points in two.- Have a brilliant day mate ^_^

Travelling towards each other, if the cars meet in 2 hours, the rate of the slower car is 86 km/hr.

Let the speed of the slower car is x

The speed of the faster car is 18 kilometer more than slower car, that is x+18.

The time taken by both the cars is 2 hours.

The distance covered by both the cars is 380 kilometers.

speed= distance/time

distance= speed*time

2x+2(x+18)=380

2x+2x+36=380

4x+36=380

4x=344

x=344/4

x=86

The speed of the faster car is

x+18=86+18

=104

The speed of the faster car is 104 km/hr

Therefore, the speed of the slower car is 86 km/hr.

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Let's denote the rate of the slower car as "x" kilometers per hour. Since the rate of the faster car is 18 kilometers per hour greater, we can represent it as "x + 18" kilometers per hour.

We know that the two cars are traveling towards each other and will meet in 2 hr. Therefore, the total distance covered by both cars will be the sum of their distances traveled.The slower car travels at a rate of "x"km/hr for 2 hr,covering a distance of 2x km.The faster car travels at a rate of "x + 18"km/hr for 2 hours, covering a distance of 2(x+18)km.

The total distance covered by both cars is the sum of these distances, which should be equal to the total distance of 380 kilometers:

2x + 2(x + 18) = 380

Now we can solve this equation to find the rate of the slower car:

2x + 2x + 36 = 380

4x + 36 = 380

4x = 380 - 36

4x = 344

x = 344 / 4

x ≈ 86

Therefore, the rate of the slower car is approximately 86 kilometers per hour.

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Step-by-step explanation:

first of all we have to change kg into ton= 48500kg into ton =53.462ton(48500/907.168)

after that we add all the weight of 4 container = 28+45+16.8+53.462

total will be his total mass of tones he had =143.262

The reward-to-variability ratio of the best feasible is 0.4221 that is option a.

The proportion of stocks invested in the optimal risky portfolio can be calculated with the use of following formula:

Portfolio Invested in the Stock = [(Expected Return of the Stock - Risk Free Rate)*(Standard Deviation of Bond)^2 - (Expected Return of the Bond - Risk Free Rate)*Covariance between Bond and Stock]/[(Expected Return of the Stock - Risk Free Rate)*(Standard Deviation of Bond)^2 + (Expected Return of the Bond - Risk Free Rate)*(Standard Deviation of Stock)^2 - (Expected Return of Stock - Risk Free Rate + Expected Return of Bond - Risk Free Rate)]*Covariance between Bond and Stock

Portfolio Invested in Bond = 1 - Portfolio Invested in the Stock

Here, Risk Free Rate = 4 and Covariance = 32*24*.1250 = 96

Using these values and other information provided in the question, we get,

Portfolio Invested in the Stock = [(10 - 4)*(24)^2 - (7 - 4)*96]/(10 - 4)*(24)^2 + (7 - 4)*(32)^2 - [(10 - 4 + 7 - 4)]*96 = .5593

Portfolio Invested in Bond = 1-.5593 = .4407

Step 2: Calculate Expected Return and Standard Deviation of the Optimal Risky Portfolio

Expected Return = Portfolio Invested in Stock*Expected Return of Stock Portfolio Invested in Bond*Expected Return of Bond = .5593*10% + .4407*7% = 8.68%

Standard Deviation = [(Portfolio Invested in Stock)^2*(Standard Deviation of Stock)^2 + (Portfolio Invested in Bond)^2*(Standard Deviation of Bond)^2 + 2*(Portfolio Invested in Stock)*(Portfolio Invested in Bond)]^(1/2) = [(.5593)^2*(32)^2 + (.4407)^2*(24)^2 + 2*(.5593)*(.4407)*(96)]^(1/2) = 21.90%

Step 3: Calculate Reward-to-Volatility Ratio

The reward-to-volatility ratio can be calculated with the use of following formula:

Reward-to-Volatility Ratio = (Expected Return of the Portfolio - Risk Free Rate)/Standard Deviation of Portfolio = (8.68 - 4)/21.90 = .4221

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Answer:

0.79

Step-by-step explanation:

This value is the most opposite of the value above R, meaning that there is an association between the variables.

Answer:

.79

Step-by-step explanation:

Bc y not

Answer:

10

Step-by-step explanation:

Answer:

B.)

Step-by-step explanation:

A rational number is a number with no repeating decimals or decimals that go on “forever” like pi.  An expample of a rational number is 2 where 2.3333333... is not a rational number.  Pi isn’t a rational number either since forth there is no known end to that.  

So, when solved:

A.) = 1.58113883...  (irrational)

B.) = -8 (rational)

C.) = 8.94427191... (irrational)

D.) = 3.794733192... (irrational)

I hope you see the pattern.  Hope this helps!

Variables would make each algebraic equation a true statement is;

d² = 36 is true for d = ±6.4s = 2s - 2 + 3s is true for s = 2.b + 25 = b - 25 is true for no value of b will make the equation true.

The given algebraic equations will be true if the following values of the given variables are used:

d² = 36 is true for, d = ±6

We know that the square of a number gives us a positive value only.

So, d = ±6.4s = 2s - 2 + 3s is true for.

Since both sides of the equation have terms with s in them, let's simplify it:

4s = 2s + 3s - 2⇒ 4s = 5s - 2⇒ 4s - 5s = -2⇒ -s = -2⇒ s = 2.

Thus, 4(2) = 2(2) - 2 + 3(2) is true for b + 25 = b - 25 is true for

Let's simplify the given equation

b + 25 = b - 25⇒ b - b = -25 - 25⇒ 0 = -50

The given equation is always false.

There is no value of b that will make it true.

Complete the following statements by determining which value(s) of the given variables would make each algebraic equation a true statement:

d² = 36 is true for d = ±6.4s = 2s - 2 + 3s is true for s = 2.b + 25 = b - 25 is true for no value of b will make the equation true.

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The matrix in its reduced row echelon form is:[4, -1 | 2] [0, 1 | 2]

Given the system of equations is:4x - y = 2 and -x + y = 4To solve the given system of equations using the augmented matrix and elementary row operations, we represent the system as a matrix equation of the form AX = B, where A is the coefficient matrix of the variables, X is the matrix of the variables, and B is the constant matrix.

Therefore, we get the matrix as:⇒ [4, -1 | 2] [ -1, 1 | 4]To simplify this matrix into its reduced row echelon form, we perform elementary row operations as follows:R2 → R2 + R1Hence the matrix in its reduced row echelon form is:[4, -1 | 2] [0, 1 | 2]

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\(\\ \rm\hookrightarrow \dfrac{BC}{AB}=\dfrac{CE}{ET}\)

\(\\ \rm\hookrightarrow \dfrac{4}{7}=\dfrac{8}{x}\)

\(\\ \rm\hookrightarrow 4x=56\)

\(\\ \rm\hookrightarrow ET=x=14\)

a) The relationship between b and c is that c cannot be zero.

b) b can be any nonzero constant and c is equal to 2.5 in this case.

In two dimensions, the compatibility equations for strain are,0

∂εx/∂y + ∂γxy/∂x = 0

∂εy/∂x + ∂γxy/∂y = 0

where εx and εy are the normal strains in the x and y directions, respectively, and γxy is the shear strain.

Using the given strain field, we can calculate the strains,

εx = -4.5cx² + 10.5cy

εy = 1.5cx² - 7.5cy²

γxy = 1.5bxy

Taking partial derivatives and plugging them into the compatibility equations, we get,

⇒ -9cx + 0 = 0

⇒ 0 + (-15cy) = 0

These equations must be satisfied for the strain field to be compatible. From the first equation,

We get cx = 0, which means c cannot be zero.

From the second equation, we get cy = 0,

Which means b can be any nonzero constant.

For part b:

We are asked to find the displacements u and v corresponding to the given strain field at points (3, 7), assuming they are zero at point (0, 0) and using c = 2.5.

To find the displacement components,

We need to integrate the strains with respect to x and y. We get,

u = ∫∫εx dx dy = ∫(10.5cy) dy = 5.25cy²

v = ∫∫εy dx dy = ∫(1.5cx² ) dx - ∫(7.5cy²) dy = 0.5cx³ - 2.5cy³

Plugging in the values of c and b, we get,

u = 5.25(2.5)(7)²  = 767.62

v = 0.5(2.5)(3)³ - 2.5(7)³ = -8583.75

Therefore,

The displacements at points (3, 7) are u = 767.62 and v = -8583.75.

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Answer:



Step-by-step explanation:

X+

(2x+3)-(x+2)

First you subtract 3 by 2. You wil get 1.

They you subtract 2x by x. You will get 1

So, your answer is x+1

The graph of y = x(x² - 2)(x² + x + 1) intersects the x-axis in three different points.

The answer is (C) Three.To determine the number of points where the graph of the equation y = x(x² - 2)(x² + x + 1) intersects the x-axis, we need to find the x-values that make the equation equal to zero.

Setting y = 0, we have:

0 = x(x² - 2)(x² + x + 1)

Since the product of three factors is zero, at least one of the factors must be zero.

1. Setting x = 0:

0 = 0(x² - 2)(x² + x + 1)

This gives us one solution: x = 0.

2. Setting x² - 2 = 0:

x² = 2

Taking the square root of both sides:

x = ±√2

This gives us two additional solutions: x = √2 and x = -√2.

3. Setting x² + x + 1 = 0:

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 1, and c = 1. Substituting these values into the quadratic formula:

x = (-1 ± √(1² - 4(1)(1))) / (2(1))

Simplifying:

x = (-1 ± √(-3)) / 2

Since the discriminant is negative, there are no real solutions for this quadratic equation.

In summary, we have found three different x-values where the equation intersects the x-axis: x = 0, x = √2, and x = -√2.

Therefore, the graph of y = x(x² - 2)(x² + x + 1) intersects the x-axis in three different points. The answer is (C) Three.

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Answer:

he is fifty years old

Step-by-step explanation:

six years ago he would have been 44 yearsold

Answer: 25.00$

Step-by-step explanation:50.00 take away 50% from it you have 25$

Answer:

$25

Step-by-step explanation:

It would be 25 because half of 50 is 25.

a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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Answer:

x=40

Step-by-step explanation:

3x=120

you divide 3 on both sides to get x=40

Answer:

  296.1 yards

Step-by-step explanation:

The surveyor is interested in solving a triangle with two sides and the enclosed angle known. The Law of Cosines is used for that purpose.

The angle interior to the triangle where the surveyor turned is the supplement of the turning angle:

  180° -110° = 70°

The law of cosines tells us the relation of the given sides (a, b) and angle (C) to the unknown side (c) is ...

  c² = a² +b² -2ab·cos(C)

  c² = 245² +270² -2·245·270·cos(70°) ≈ 87675.7350

  c ≈ √87675.7350 ≈ 296.10

The length of the lake is about 296.1 yards.

The given equation of the plane is 5x - 3y + z = 15. To sketch a graph of the plane, plot the three points of intersection with the coordinate axes: (3, 0, 0), (0, -5, 0), and (0, 0, 15).

The given equation of the plane is 5x - 3y + z = 15. To find the points at which the plane intersects the coordinate axes, we set one of the variables to zero while solving for the other two variables.

Intersection with x-axis (y = 0, z = 0):

Setting y and z to zero, we have 5x = 15, which gives x = 3. Therefore, the plane intersects the x-axis at the point (3, 0, 0).

Intersection with y-axis (x = 0, z = 0):

Setting x and z to zero, we have -3y = 15, which gives y = -5. So, the plane intersects the y-axis at the point (0, -5, 0).

Intersection with z-axis (x = 0, y = 0):

Setting x and y to zero, we have z = 15. Thus, the plane intersects the z-axis at the point (0, 0, 15).

To find the equations of the lines where the plane intersects the coordinate plane, we set one of the variables to zero while solving for the other two variables.

Intersection with xy-plane (z = 0):

Setting z to zero, we have 5x - 3y = 15. This equation represents a line in the xy-plane.

Intersection with xz-plane (y = 0):

Setting y to zero, we have 5x + z = 15. This equation represents a line in the xz-plane.

Intersection with yz-plane (x = 0):

Setting x to zero, we have -3y + z = 15. This equation represents a line in the yz-plane.

To sketch a graph of the plane, plot the three points of intersection with the coordinate axes: (3, 0, 0), (0, -5, 0), and (0, 0, 15). Then, draw a plane passing through these points to visualize the graph of the given equation.

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