What is the following mystery/2 about?
mystery([],[]).
mystery([X|Y],Z) :- mystery(Y,W), takeout(X,Z,W).
takeout(X,[X|R],R).
takeout(X,[F|R],[F|S]) :- takeout(X,R,S).
A. append
B. prefix
C. permutation
D. reverse
E. suffix
F. member
G. sort

Answer:

circumference = 219.91 cm

65,973 cm

Step-by-step explanation:

circumference = 35 x 2 x π = 219.91 cm

219.91 x 5 x 60 = 65,973 cm

Answer:

Domain (0, ∞)

Range (-∞, ∞)

Step-by-step explanation:

The domain is the input values

The input is from 0 to infinity

Domain (0, ∞)

The range is the output values

The input is from negative infinity to infinity

Range (-∞, ∞)

Answer:

A

Step-by-step explanation:

Answer: Choice D) \(x = a\left(1-\frac{y}{b}\right)\)

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

Work Shown:

\(\frac{x}{a}+\frac{y}{b} = 1\\\\\frac{x}{a} = 1-\frac{y}{b}\\\\x = a\left(1-\frac{y}{b}\right)\\\\\)

Explanation:

First I subtracted y/b from both sides. Then I multiplied both sides by 'a' to fully isolate x. You can optionally distribute the 'a' through to each term inside the parenthesis, but your teacher has chosen not to do this.

Exponential Function doesn't have a graph that intercepts x-axis only if it is f(x) = a^x (when a>0 and a ≠ 1)

If you want to plot five points to graph the function then. I'd rather do from negative number to positive number.

Substitute from -3≤x≤1 (We get 5 points)

f(-3) = 4^-3

f(-3) = 1/4^3

f(-3) = 1/64 (First point) (-3,1/64)

f(-2) = 4^-2

f(-2) = 1/4^2 = 1/16 (Second point) (-2,1/16)

f(-1)=4^-1 = 1/4 (Third point) (-1, 1/4)

f(0) = 4^0 = 1 (Fourth point) (0, 1)

f(1) = 4^1 = 4 (Fifth point) (1,4)

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:

  B)  108°

Step-by-step explanation:

You want the interior angle measure for a regular pentagon.

The interior angles of a regular n-gon will have measure ...

  180° -360°/n

When n = 5, the interior angles have measure ...

  180° -360*/5 = 180° -72° = 108°

The interior angles of a regular pentagon are 108°.

__

Additional comment

The 360°/n comes from the fact that the sum of exterior angles for any convex polygon is 360°. For a regular n-gon, those exterior angles are congruent, so each is 360°/n. The interior angle is its supplement.

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Answer:

\(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\)

Step-by-step explanation:

Integrate v(t) with respect to time

\(\displaystyle \int(3t^3+30t^2+5)\,dt\\\\=\frac{3}{4}t^4+10t^3+5t+C\)

Plug-in initial condition to get C

\(\displaystyle s(0)=\frac{3}{4}(0)^3+10(0)^3+5(0)+C\\\\3=C\)

Thus, the position function is \(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\) given the velocity function and initial condition.

We use the decimal system, which means every place you "move" in a decimal number, we multiply or divide by ten. We have the unit on the left side of the dot, and the tenth 1 place to right of the dot, the hundredth 2 places to the right of the dot. In math terms, let's use the famous number pi as an example.

A mixed number is a combination of the unit and the fractional parts of a number. For our number 4.29, we have 4 units and 29 hundredths, which means we can rewrite as:

Step-by-step explanation:

the correct answer is option a 6a-7

Answer:

I hope this helps!

Answer:

B is your answer

Step-by-step explanation:

The equation of the ellipse with given foci (2,4) and (2,-8) and co-vertices (10, -2) and ( -6 , -2) is equal to (x - 2)²/40 + ( y + 2)²/36 = 1.

As given in the question,

Given foci of the ellipse :

( 2,4) and ( 2, -8)

Co-vertices of the ellipse :

( 10,-2) and (-6 , -2)

From the given foci and vertices ,

Centre 'c' = 2

b = 6

( h, k) = (2, -2)

a² = c² + b²

⇒a² = 4 + 36

⇒a = √40

⇒a = 2√10

Equation of the ellipse is given by:

( x - h)²/ a² + (y - k)²/b² =1

⇒( x - 2)²/ (2√10)² + (y + 2)²/6² = 1

⇒( x - 2)²/ 40 + (y + 2)²/36 = 1

Therefore, equation of the ellipse is equal to (x - 2)²/ 40 + (y +2)²/36 = 1.

The complete question is:

Determine the equation of the ellipse with foci (2,4) and (2,−8), and co-vertices (10,−2) and(−6,−2).

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On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.

To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.

Given:

9 staff members taking calls.

On average, one call arrives every 5 minutes (standard deviation of 5 minutes).

Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).

To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:

"M" stands for Markovian or memoryless arrival and service times.

"c" represents the number of servers.

In our case, we have an M/M/9 queuing model since we have 9 staff members.

The average waiting time for a customer on hold is given by the following formula:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

Where:

c = number of servers (staff members) = 9

μ = average service rate (1 / average service time)

λ = average arrival rate (1 / average interarrival time)

ρ = λ / (c * μ)

First, let's calculate the average arrival rate (λ):

λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute

Next, calculate the average service rate (μ):

μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute

Now, calculate ρ:

ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407

Finally, calculate the waiting time:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))

≈ 1.16 minutes

Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.

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The correct numbers to complete the statements given are 40, 400, and 4000.

This question requires you to complete a statement with a given number (40, 400 or 4000) to make the statement true by dividing the number by 40.1. To find the correct order the numbers must be place using division, let's find out the results of each of these divisions:

Based on the above, it can be concluded:

Based on this, the complete statements are:

Note: This question is incomplete; here is the complete question:

Use each of the numbers 4, 40, and 4000 once to make true statements.The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is close to 1

The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much less than 1.

The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much greater than 1.

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(| 5 - 3x | - 1) - (1 - 3x) = 0

|5 - 3x| - 1 - 1 + 3x = 0

|5 - 3x| - 2 + 3x = 0

1) (5 - 3x) - 2 + 3x = 0, if 5 - 3x >= 0

3 = 0. has no solutions

2) -(5 - 3x) - 2 + 3x = 0, if 5 - 3x < 0

-5 + 3x - 2 + 3x = 0

6x = 7

x = 7/6

5 - 3x < 0

-3x < -5

x > 5/3.

has no solutions

The correct option is (1) less than 10 times the original distance.The original distance was  30 cm and the new distance is 94.86 cm which is less than 10 times the original.

The force of attraction and repulsion among two charged bodies are directly proportional to a product of their charges but inversely proportional to a square of a distance between them, according to Coulomb's law.

It works along the line that connects the two charges that are called point charges.

The formula for Coulomb's law is-

\(f_{}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{}^{2}}\)

where, q₁ and q₂ are the charges;

d is the distance between them.

Now, according to the question;

Two charges that were initially separated by a particular distance are pushed closer together until force between the two is reduced by a factor of ten.

Coulomb's law of force

\(f_{1}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{1}{ }^{2}}\)

d₁ is the initial distance.

So when charges are separated further, a new force is f₂, which is represented as

\(f_{2}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}^{2}}\)

d₂ is the moved distance

As a result, the given force is decreased by ten times its original value.

Thus, \(f_{2}=\frac{f_{1}}{10}\)

use the expression in both forces

\(\begin{gathered} \frac{f_{1}}{10}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}{ }^{2}} \\\frac{q_{1} q_{2}}{4 \times 10 \pi \epsilon d_{1}{ }^{2}}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}{ }^{2}} \\ \frac{1}{10 \times d_{1}{ }^{2}}=\frac{1}{d_{2}{ }^{2}} \\ d_{2}=\sqrt{10} d_{1}\end{gathered}\)

Now, calculate the moved distance d₂,

\(\begin{aligned}& d_{2}=\sqrt{10} d_{1} \\ & d_{2}=\sqrt{10} \times 30 \\& d_{2}=3.162 \times 30 \\ & d_{2}=94.868 \mathrm{~cm}\end{aligned}\)

The new distance is 94.868 cm.

Therefore, the new obtained distance is less than the 10 times the original distance.

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The complete question is-

Two charges originally separated by a certain distance are moved farther apart until the force between them has decreased by a factor of 10.  Is the new distance

(1) less than 10,

(2) equal to 10, or

(3) greater than 10;

times the original distance? If the original distance was 30 cm.

Answer: The answer is 1638 ft

Step-by-step explanation:

The formula to find area is L x W x H

Length x Width x Height

So 9 ft x 7 ft x 26 ft = 1638 ft

Answer:

I think its this:

thirty - seven and six hundred ninety - one hundred thousanths.

Step-by-step explanation:

Hope this is right!

The extended fan sub-equation method is a mathematical technique used to solve nonlinear evolution equations.

We have,

The extended fan sub-equation method is a mathematical technique used to solve a class of nonlinear evolution equations.

It extends the traditional fan sub-equation method by introducing additional terms and parameters to enhance its applicability and effectiveness.

The method involves transforming the original nonlinear evolution equation into a set of sub-equations, which are then solved iteratively using various mathematical tools such as symmetry reductions, similarity transformations, and exact solutions.

The extended fan sub-equation method has been successfully applied to various nonlinear evolution equations in mathematical physics, such as the KdV equation, the Burgers equation, and the Fisher equation, providing valuable insights and solutions to these complex systems.

Thus,

The extended fan sub-equation method is a mathematical technique used to solve nonlinear evolution equations.

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Answer:

8r6s3 – 13r5s4 + r4s5 – 5r3s6 it is D

Step-by-step explanation:

The value of the difference of the polynomials is,

⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The expression is,

⇒ (8r⁶s³ – 9r⁵s⁴ + 3r⁴s⁵) – (2r⁴s⁵ – 5r³s⁶ – 4r⁵s⁴)

Now, We can find the difference as;

⇒ (8r⁶s³ – 9r⁵s⁴ + 3r⁴s⁵) – (2r⁴s⁵ – 5r³s⁶ – 4r⁵s⁴)

⇒ (8r⁶s³ – 9r⁵s⁴ – 4r⁵s⁴ + 3r⁴s⁵ – 2r⁴s⁵ – 5r³s⁶

⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶

Thus, The value of the difference of the polynomials is,

⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶

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Answer: $1, 615

Step-by-step explanation:

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Step-by-step explanation:

-3.5z - 2 + 1z - 3

Solving like terms

-2.5z - 5

For the year in which they earned $176,500, the partners will receive $52,950, $35,300, and $88,250 respectively.

Here let the partners be A, B, and C.

According to the question, A: B: C = 3: 2: 5

This implies that if the profits are divided into

3 + 2 + 5 = 10 equal parts, 3 of those parts will go to A, 2 of those parts will go to B and 5 of those parts will go to C.

Here the profits for the year are $176,500.

Now dividing them into 10 equal parts will give us the value of each part to be

$176, 500/10 = $17,650

Hence A will receive $17,650 X 3 = $52,950

B will receive $17,650 X 2 = $35,300

C will receive $17,650 X 5 = $88,250

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Answer:

I think it's the top left one

Step-by-step explanation:

The length is 6, the width is 3, and the height is 4, which matches the expression.

Step-by-step explanation:

\((6 \times 3 + 3 \times 4 + 4 \times 6) \\ = (18 + 12 + 24) \\ = 54\)

a. The tree diagram that summarizes the given probabilities is attached.

b.  The probability that the individual does not participate in sports, given that he graduate sis  0.2 =  20%.

We apply Bayes' theorem to calculate:

Probability (Does not participate in sports if graduates)  = (P(Does not participate in sports) * P(Graduates | Does not participate in sports)) / P(Graduates)

The given data include: probability of not participating in sports = 0.02 probability of graduating given no participation in sports = 0.82 probability of graduating  = 0.18

Probability (Does not participate in sports if graduates)  = (0.02 * 0.82) / 0.18 = 0.036 / 0.18=  0.2

| Sports | No Sports |

                          |-------|--------|

Student participates | 0.18  | 0.62  |

                          |-------|--------|

Student does not participate | 0.02  | 0.78  |

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