The school newspaper wants to do an article about DLDs at DHS by interviewing the Dacula Leadership Team. They wish to get quotes from 8 of the 30 seniors on DLT. 18 of the senior DLT members are athletes, while 12 are non-athletes. Determine the probability that the newspaper staff receives quotes from exactly 3 athletes. Round to two decimal places.

Answer:

<acb=90°

inscribed angle from the diameter is 90°

The optimal feasible solution is x1 = 1, x2 = 0.4, and the problem is a regular linear programming problem.

To solve the given linear programming problem, let's define the decision variables and formulate the objective function and constraints:

Decision Variables:

x1, x2

Objective Function:

Maximize: 2x1 + 6x2

Constraints:

2x1 + 5x2 ≤ 4

4x1 + x2 ≤ 6

x1, x2 > 0

To find the optimal feasible solution, we can use a linear programming solver. Here is the optimal solution for the given problem:

Optimal Solution:

x1 = 1

x2 = 0.4

The maximum value of the objective function is obtained when x1 = 1 and x2 = 0.4. The maximum value is 2(1) + 6(0.4) = 4.8.

Now let's analyze if the solution is a special case of linear programming.

This problem falls under the category of Linear Programming (LP) problems. However, it does not represent any specific special case of LP such as degeneracy, unboundedness, or infeasibility. The given problem has a feasible solution, and the objective function is maximized within the given constraints. Hence, it is a regular LP problem without any special case conditions.

Note: Since the solution is text-based, there is no need to scan or provide a separate file.

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Answer:

Fahad gets 15 litres

Linda gets 9 litres

Step-by-step explanation:

For Fahad:

24 litres X 5 ÷ 8

=15

For Linda:

24 litres X 3 ÷ 8

=9

The correct statement regarding the unit rate in this problem is given as follows:

Point (1,2) shows that the unit rate is of $2 per ounce.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The point of the graph is given as follows:

(1,2) -> x = 1, y = 2.

Hence the unit rate is given as follows:

k = y/x = 2/1 = 2.

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a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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By finding common factors, we conclude that we can divide the trees in 6 or in 9 parts, but not in 8.

We know that each of these parts needs to have the same number of each type of trees.

So we need to see if 6, 8, or 9, are common factors between 36 and 54.

First:

6*6 = 36

9*4 = 36

So 9 and 6 are factors of 36.

And 9*6 = 54

So 9 and 6 are factors of 54.

(8 is not a factor of neither)

So 9 and 6 are common factors between 36 and 54.

Then we can divide the trees in 6 or in 9 parts, but not in 8.

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Answer:

2r(d-2)

Step-by-step explanation:

Answer:

The answer is I don't know

The probability of Thuy rolling a 4 exactly 2 times is 1/6 × 1/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 = 5⁵/6⁷

We know that:

Thuy rolls a number cube 7 times,

so the total outcomes are: 6.

Also, it is asked to find the probability of rolling a 4 exactly 2 times.

So it could be done by the method that:

1/6 × 1/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6,

where 1/6 denotes the probability of rolling a 4 and 5/6 denotes the probability of rolling a number other than 4

therefore we know that, the probability of rolling a 4 exactly 2 times is 1/6 × 1/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 = 5⁵/6⁷

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Answer:

B, C, D

Step-by-step explanation:

the distance from (0,0) to (3,2) would be (3,2). Flip that and you get (2,3).

the distance from (1,5) to (4,7) is (3,2). Also flip that and you get (2,3)

the distance from (-2,-2) from (4,2) is (6,4). flip that and you get (4,6). break it down and you'll get (2,3)

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\( \frac{x}{9} + 7 \geqslant 10 \\ \)

Subtract sides 7

\( \frac{x}{9} + 7 - 7 \geqslant 10 - 7 \\ \)

\( \frac{x}{9} \geqslant 3 \\ \)

Multiply sides by 9

\(9 \times \frac{x}{9} \geqslant 9 \times 3 \\ \)

\(x \geqslant 27\)

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Thus the correct answer is (( A )) .

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

x = 12, y = 4

Step-by-step explanation:

For the triangles to be congruent by HL , then

x = y + 8 → (1)

4y = x + 4 → (2)

Substitute x = y + 8 into (2)

4y = y + 8 + 4

4y = y + 12 ( subtract y from both sides )

3y = 12 ( divide both sides by 3 )

y = 4

Substitute y = 4 into (1)

x = 4 + 8 = 12

From the sequence 2 \(\frac{1}{2}\), 2 \(\frac{1}{3}\), 2 \(\frac{1}{4}\), ..., f(n) can be expressed as 2 + \(\frac{1}{(n+1)}\) where n is the term number in the sequence. Hence, the correct answer is A.

Each term in the sequence is 2 plus a fraction where the denominator is one more than the term number. For example:

In general, the n-th term in the sequence will have the fraction \(\frac{1}{(n+1)}\).

Therefore, the function f(n) that generates this sequence is 2 + \(\frac{1}{(n+1)}\). This function takes an input of n and outputs the corresponding term in the sequence.

This question should be written as:

Given the sequence 2 \(\frac{1}{2}\), 2 \(\frac{1}{3}\), 2 \(\frac{1}{4}\), ....,  what is f (n)?

The correct answer is A.

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The equation of the graph shown can be written in factored form as follows:

y = a(x - h)(x - k)(x - m)

To find the equation, we need to identify the x-intercepts and the minimum point of the graph.

From the description, we know that the graph starts at the top left and continues down through the x-axis at x = -4. This means that one of the factors is (x + 4).

Next, the graph reaches a minimum around y = -2.8. This indicates that the graph touches the x-axis at this point, so another factor is (x + 2).

Moving forward, the graph goes back down to another minimum around y = -0.4. Again, this means the graph touches the x-axis at this point. So we have another factor, (x + 1).

Now we have all the necessary factors: (x + 4), (x + 2), and (x + 1). To determine the coefficient "a," we can use the fact that the graph goes up after crossing the x-axis at x = -2. This suggests that "a" must be positive.

Therefore, the equation of the graph in factored form is:

y = a(x + 4)(x + 2)(x + 1)

Please note that without specific points, it is not possible to determine the exact value of "a" or the precise shape of the graph. The equation provided represents a general equation that satisfies the given conditions.

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Answer:

400

Step-by-step explanation:

10% is 50, so 20% would be 100, which is how many people won. That means 400 didn't win.

Answer: 13 Hours

Step-by-step explanation:

1. 270/9 = 30 dollars per hour

2. 390/30 = 13 hours

Answer: 1 & 2 are congruent

Step-by-step explanation:

They both have the same amount of space to get to the other point .

1.  AC is congruent to BD.

2. BD and CE are not congruent.

3. AD and BE are not congruent.

4.  BC and CE are not congruent.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

1. The segment AC is (1 - (-8)) = 9 units, and the line segment

BD is (3 -(-6)) = 9 units.

So, AC ≅ BD.

2. Line segment BD is 9 units and line segment CE is (7 - 1) = 6 units.

So, BD and CE are not congruent.

3. Line segment AD is (3 - (-8)) = 12 units and line segment BE is (7 - (-6)) = 13 units. (not congruent)

So, line segment AD and BE are not congruent.

4. Line segment BC is (1 - (-6)) = 7 units and line segment CE is (7 - 1) = 6 units.

So, Line segments BC and CE are not congruent.

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Answer:

B.) 132.56 degrees

Step-by-step explanation:

Answer:

y= -2x+6

Step-by-step explanation:

If ur able to use a calculator there is a slope calculator online and it's easy to use

To solve for the distance covered in the first two hours, we need to calculate the velocity at time t = 0 and t = 2.The car will have covered 44 miles during the first 2 hours of driving.

The velocity of the car t hours after leaving Austin is given by the equation V = 12 + 5t - 32. To solve for the distance covered in the first two hours, we need to calculate the velocity at t = 0 and t = 2.

At t = 0, V = 12 - 32 = -20. This means that the car was travelling at -20 miles per hour when it left Austin. Since velocity and distance are inversely proportional, the car had covered 0 miles when it left Austin.

At t = 2, V = 12 + 10 - 32 = -10. This means that the car was travelling at -10 miles per hour after 2 hours. Since velocity and distance are inversely proportional, the car had covered 44 miles after 2 hours by time.

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Answer:

Step-by-step explanation:

The theme of each epic poem is sublime, elegant, and has universal significance. It may not be an insignificant theme, which is only limited to the personality or the locality of the poet. It deals with the entire humanity.

Epic poem

An epic poem, or simply an epic, is a lengthy narrative poem typically about the extraordinary deeds of extraordinary characters who, in dealings with gods or other superhuman forces, gave shape to the verse mortal universe their descendants.

'epic' could refer to all poetry in dactylic hexameter , which included not only Homer but also the wisdom poetry of Hesiod, the utterances of the Delphic oracle.

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Answer:

(1, 4)

Step-by-step explanation:

im assuming that the point is h(1) = 4

this point is basically just h(x) = y

1 is your x

4 is your y

you plot it at the point (1, 4)

The equation that describes the greatest horizontal length, H, in terms of the greatest vertical length, V is given as follows:

H = 8V/7.

The ratio between two amounts a and b is given as follows:

a to b.

Which is also the division of the two amounts.

The ratio of the horizontal length and the vertical length is 8:7, hence:

H/V = 8/7

Applying cross multiplication, the equation is given as follows:

H = 8V/7.

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Answer:b

Step-by-step explanation:

B

The zeroes of the quadratic function f(x) = 6x² - 11x + 3 will be (1/3,3/2).

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given function is f(x) = 6x² - 11x + 3. The zeroes of the function will be calculated by factoring the equation.

The zeroes are calculated as,

6x² - 11x + 3 = 0

6x² - 9x -2x + 3 = 0

3x(2x-3)-1(2x-3) = 0

(3x - 1)(2x - 3 ) = 0

x = 1 / 3 and x = 3 / 2

Therefore, the zeroes of the quadratic function f(x) = 6x² - 11x + 3 will be (1/3,3/2).

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The provided paragraph appears to be describing the process of encrypting a plaintext block using Simplified Data Encryption Standard (SDES) with specific inputs. Here's the aligned and corrected version:

Simplified Data Encryption Standard (SDES) is a symmetric encryption algorithm that operates on 8-bit data blocks. In SDES, the plaintext consists of a single 8-bit block, and the key is a 10-bit block.

The algorithm involves two rounds of operations. Let's represent the plaintext block as P = P7P6P5P4P3P2P1P0,

where Pi is the ith bit in the plaintext, and the key as

K = k9k8k7k6k5k4k3k2k1k0,

where ki is the ith bit in the key.

To obtain the ciphertext, we need to apply SDES. Let's perform the SDES operations:

R1(01001000, k1 = " ") = 01001000 ⊕ 00000000 = 01001000

P4P3P2P1P0 = 1000

EP(1000E, k2 = "!") = (1000E) ⊕ 1 = 11000101

P4P3P2P1P0 = 0101

D4(0101D4, k1 = " ") = 0101D4 ⊕ 00100000 = 0111D4

P4P3P2P1P0 = 1101

Thus, the resulting ciphertext is 1101. Therefore, the ciphertext is "1101".

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Using polar coordinates, the volume of the given solid is:

π√(2a)(511/3)

For the volume of the given solid using polar coordinates, we need to express the equations of the cone and the ring in terms of polar coordinates.

In polar coordinates, the cone equation can be written as:

z = √(2a)(x^2 + y^2)  ⇒  z = √(2a)(r^2)

The ring equation can be expressed as:

1 ≤ x^2 + y^2 ≤ 64  ⇒  1 ≤ r^2 ≤ 64

To evaluate the integral, we'll set up the triple integral in cylindrical coordinates and integrate over the appropriate bounds.

The volume of the solid can be calculated using the following integral:

V = ∫∫∫ dV

where the limits of integration are:

1) For r: 1 ≤ r ≤ 8 (taking the square root of 64)

2) For θ: 0 ≤ θ ≤ 2π (covering a full circle)

3) For z: 0 ≤ z ≤ √(2a)(r^2)

The triple integral in cylindrical coordinates is:

V = ∫∫∫ r dz dr dθ

Now, let's evaluate the integral step by step:

V = ∫∫∫ r dz dr dθ

  = ∫₀²π ∫₁⁸ ∫₀^(√(2a)r²) r dz dr dθ

Now, integrating with respect to z:

V = ∫₀²π ∫₁⁸ [0.5√(2a)r²]₀^(√(2a)r²) dr dθ

  = ∫₀²π ∫₁⁸ 0.5√(2a)r² dr dθ

Next, integrating with respect to r:

V = ∫₀²π [0.5√(2a)(1/3)r³]₁⁸ dθ

  = ∫₀²π 0.5√(2a)(1/3)(8³ - 1³) dθ

Simplifying:

V = ∫₀²π 0.5√(2a)(1/3)(512 - 1) dθ

  = ∫₀²π (0.5√(2a)/3)(511) dθ

  = (0.5√(2a)/3)(511) ∫₀²π dθ

  = (0.5√(2a)/3)(511)(2π)

  = π√(2a)(511/3)

Therefore, the volume of the given solid is π√(2a)(511/3).

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Answer:

There is no solution.

Step-by-step explanation:

Math

Way

The situation in which the quantities combine to make 0 is "On Monday, Huang withdraws $30 from a bank account. On Friday, she deposits $30 into the account".

For two quantities two make 0, it is necessary to add two numbers with the same value but different sign (positive or negative). Here is an example:

For example if you buy 10 apples but use 10 apples to make a pie.

Based on this, the correct situation is "On Monday, Huang withdraws $30 from a bank account..." as -30 + 30 = 0.

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Answer:

b

Step-by-step explanation:

Answer:

C. 0.5 times 1 = 0.5