Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 3, 13, 23,

b. The value of x is 9

c. The probability that a student picked had just played two games = 11/20

A set is the mathematical model for a collection of different things.

If G represent Gaelic football

R represent Rugby

S represent soccer

therefore,

n(G and R) only = 16-4 = 12

n( G and S) only = 42-4 = 38

n( Sand R) only = x-4

n( G) only = 65-(38+12+4)

= 65-54

= 11

n( S) only = 57-(38+x-4+4)

= 57-38-x

= 19-x

n(R) only = 34-(16+x-4+4)

= 34-16-x

= 18-x

b. 100 = 12+38+x-4+11+19-x+18-x+4+6

100 = 12+38+11+19+18+4+7+x-x-x

100 = 109-x

x = 109-100 = 9

c. probability that a student picked played just two games;

sample space = 12+38+x-4

= 50+9-4

= 55

total outcome = 100

= 55/100 = 11/20

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The pieces of candies that William gave away is 15.

The linear expression that can be used to determine the number of candies left is:

Pieces of candies left = initial pieces of candies - number of candies given out

Pieces of candies left when William gave out candies : 40 - x

Pieces of candies left when Hannah gave out candies : 70 - 3x

If they have the same pieces of candies left, the two above expressions would be equal.

40 - x = 70 - 3x

3x - x = 70 - 40

2x = 30

x = 15

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Answer:

$83.75

Step-by-step explanation:

6.25 plus 7.00 plus 3.50 is 16.75.

16.75 per class.

times the 5 different classes is 83.75

:) Good Luck! You got this, and hope this helps!

The volume of the composite solid is 4095 cubic yd.

A trapezoidal prism is a three-dimensional object that contains rectangular cross-sections in one direction and trapezium cross-sections in the other. This implies that the prism has two congruent trapezoids that are joined to one another by four rectangles. On the top and bottom of the prism, or bases, are these congruent trapezoids. The trapezium prism's lateral sides are the four rectangles. There are six faces, eight vertices, and 12 edges on a trapezoidal prism.

The volume of the composite solid is the addition of all the solids in the figure.

The volume of the trapezoid prism is:

V1 = (a+b)h(l) / 2

Substituting the values we have:

V1 = (19 + 30)(10)(9) / 2

V1 = 2205 cubic yd.

The volume of the rectangular prism is given as:

V2 = lwh

V2 = 7(30)(9)

V2 = 1890 cubic yd.

The total volume of the composite solid is:

V = V1 + V2

V = 2205 + 1890

V = 4095cubic yd.

Hence, the volume of the composite solid is 4095 cubic yd.

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Answer:

A. x + 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle \frac{x^2 - 25}{x - 5}\)

Step 2: Simplify

The integral of (x + 11) / (x^2 + 4x + 8) dx can be evaluated using partial fraction decomposition. The answer is  ln(|x^2 + 4x + 8|) + 2arctan[(x + 2) / √6] + C.

The integral of (x + 11) / (x^2 + 4x + 8) dx is equal to ln(|x^2 + 4x + 8|) + 2arctan[(x + 2) / √6] + C, where C is the constant of integration.

To explain the answer in more detail, we start by completing the square in the denominator. The quadratic expression x^2 + 4x + 8 can be rewritten as (x + 2)^2 + 4. We can then decompose the fraction using partial fractions. We express the given rational function as (A(x + 2) + B) / ((x + 2)^2 + 4), where A and B are constants to be determined.

By equating the numerators and simplifying, we find A = 1 and B = 10. Now we can rewrite the integral as the sum of two simpler integrals: ∫(1 / ((x + 2)^2 + 4)) dx + ∫(10 / ((x + 2)^2 + 4)) dx.

The first integral is a standard integral that gives us the arctan term: arctan((x + 2) / 2). The second integral requires a substitution, u = x + 2, which leads to ∫(10 / (u^2 + 4)) du = 10 * ∫(1 / (u^2 + 4)) du = 10 * (1 / 2) * arctan(u / 2).

Substituting back u = x + 2, we get 10 * (1 / 2) * arctan((x + 2) / 2) = 5arctan((x + 2) / 2). Combining the two integrals and adding the constant of integration, we obtain the final result: ln(|x^2 + 4x + 8|) + 2arctan[(x + 2) / √6] + C.

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The length of the side x is derived to be √2/2 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

The right triangle is also an Isosceles having same base angles so;

x² + x² = 1²

2x² = 1

x² = 1/2

x = √(1/2) {take square root of both sides}

x = 1/√2

x = √2/2 {rationalize}

Therefore, the length of the side x is derived to be √2/2 using the Pythagoras rule.

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Answer:

34

Step-by-step explanation:

There is a 95.52% chance that there are no customers in the system, a 9.93% chance that a customer has to wait in line, and a 31.20% chance that the server is busy.

λ = 2.6  guests per hour( Poisson  appearance rate)  μ =  1/ 12 hours per  client( exponential service rate)  c =  1 garçon( design adviser )  Using Little's Law, we can find the average number of  guests in the  staying line   L =  λ * W  

where W is the average time a  client spends in the system(  staying and being served). To find W, we can use the formula  

W =  1/( μ- λ)   Using these formulas, we get  

W =  1/(1/12-2.6) = 0.1154

hours = 6.92  twinkles

L = 2.6 *0.1154 = 0.3000  guests

 So on average, there will be0.3  guests  staying in line and each  client will  stay for6.92  twinkles before being served.

 We can also  cipher the probability that there are no  guests in the system(P_0), the probability that a  client has to  stay(P_w), and the probability that the garçon is busy

(P_b)   =  1- λ/ μ

= 0.9552  

 λ/ μ2 *( 1/( 1- λ/ μ)) = 0.0993  =  λ/ μ = 0.3120

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(a)The population is the entire grade 10 class at Gonzaga High School in St. John's, Newfoundland.

(b)The population is the entire collection of bottles stored in the manufacturing warehouse.

(a) Population:

The population refers to the complete set of individuals or elements that we want to study or gather information about. In this case, the population is the grade 10 class at Gonzaga High School in St. John's, Newfoundland. It includes all the students in that particular class.

Sample:

A sample is a subset of the population that is selected for study or data collection. In this scenario, the sample consists of 105 students who were randomly chosen from the grade 10 class at Gonzaga High School. The purpose of selecting a sample is to make inferences about the larger population based on the characteristics observed within the sample.

(b) Population:

The population represents the entire group or collection of items or elements that we are interested in studying or analyzing. In this case, the population is the complete set of bottles stored in the manufacturing warehouse. It includes all the bottles present in the warehouse.

Sample:

A sample is a subset of the population that is selected for analysis or examination. In this situation, the sample comprises 66 randomly chosen bottles of Pepsi from the manufacturing warehouse. By studying this sample, we can make observations or draw conclusions about the characteristics, quality, or properties of the entire population of bottles stored in the warehouse.

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To determine the assignment of employees to jobs that minimizes the total time required to perform the four jobs, we need to consider the time taken by each person to complete each job. Using the given Table 50, we can analyze the data and identify the optimal assignment.

By examining Table 50, we can identify the minimum time taken by each person for each job. Starting with Job 1, we see that Person 4 takes the least time of 16 hours. Moving to Job 2, Person 2 takes the least time of 18 hours. For Job 3, Person 1 takes the least time of 25 hours. Lastly, for Job 4, Person 4 takes the least time of 14 hours.

Therefore, the optimal assignment would be:

- Person 4 for Job 1 (16 hours)

- Person 2 for Job 2 (18 hours)

- Person 1 for Job 3 (25 hours)

- Person 4 for Job 4 (14 hours)

This assignment ensures that the minimum total time is required to perform the four jobs, resulting in a total time of 16 + 18 + 25 + 14 = 73 hours.

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On a postsynaptic membrane, the opening of K+ ion channel induces an IPSP (Inhibitory Postsynaptic Potential).

The potential changes in a neuron after the receptor and ion channel activation is called synaptic potential. This potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP).EPSP is a depolarizing potential that results from the opening of the Na+ ion channel. It causes a change in the potential of the neuron towards threshold level that may trigger an action potential.Ion channels and pumps in a postsynaptic neuron regulate the internal potential of the cell. In a typical postsynaptic cell, the resting potential (Vrest) is -70 mV, the threshold value is -55 mV, the reversal potential for Cl- ion (Ec) is -63 mV, the reversal potential for K+ ion (Ex) is -90 mV, and the reversal potential for Na+ ion (ENa) is 60 mV.The opening of Cl- ion channel leads to an inward flow of negative ions and thus results in hyperpolarization. The opening of K+ ion channel leads to an outward flow of K+ ions, and the membrane potential becomes more negative. Thus, it also results in hyperpolarization. The opening of a Na+ ion channel leads to inward flow of Na+ ions, which makes the cell more positive, and it is depolarization. Therefore, the opening of K+ ion channel leads to an IPSP, and it hyperpolarizes the neuron.

The postsynaptic potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP). The opening of the K+ ion channel leads to an outward flow of K+ ions, which makes the cell more negative and hyperpolarizes it, leading to IPSP.

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Answer:

what is the question I don't see it

Answer:

14.40 dollars

Step-by-step explanation:

72 divided in 5

Answer:

y = 3x - 7

Step-by-step explanation:

Since the lines are parallel, the slopes will be the same.  In this case 3.  Now we have to find the y-intercept.  We will use the slope (3), the x (2) and  y (-1) to help us do this.  We get the x and the y from the ordered pair given(2,-1).

y = mx + b

-1 = 3(2) + b   Plug in what you know

-1 = 6 + b       Subtract 6 from both sides

-7 = b

Now we can write the equation

y = 3x -7

Answer:3048.7804878

Step-by-step explanation:

I took the same test p.s. you may need to round.

Answer:

A:(-4,7) have a nice day

Therefore, the height of the oak tree is 25 feet so the correct option is 25 feet.

A triangle is a closed two-dimensional geometric shape with three straight sides and three angles. It is one of the basic shapes in geometry and is formed by connecting three non-collinear points with straight line segments. The sum of the three angles in a triangle is always 180 degrees. Triangles can be classified based on their side lengths and angles, such as equilateral, isosceles, scalene, acute, obtuse, and right triangles.

Here,

We can use proportions to solve this problem:

Let x be the height of the oak tree.

Then, using similar triangles, we can write:

(x / 20) = (5 / 4)

Cross-multiplying, we get:

4x = 100

x = 25

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Answer:

sp of bicycle =5600

cp of bicycle =10

now,

profit(p)=sp-cp

=5600-10

=5,590

The profit of bicycle is Rs 5,599

The given statement "statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results" is true.

Since, descriptive statistics consists of organinsing and summarizing informtaion collected, while inferential statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results.

Inferential statitistics is concerned with making inferences about a population of measurements based on information conatined in a sample of those measurements.

Hence, the given statement "statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results" is true.

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Answer:

\(3x^2 - 10x -5\)

Step-by-step explanation:

\(g(f(x))=g(x-1) \\ \\ =3(x-1)^2-4(x-1)-12 \\ \\ =3(x^2-2x+1)-4(x-1)-12 \\ \\ =3x^2-6x+3-4x+4-12 \\ \\ =3x^2 - 10x -5\)

Answer:

\(g(f(x))=3x^2-10x-5\)

Step-by-step explanation:

Given functions:

\(\begin{cases}f(x)=x-1\\g(x)=3x^2-4x-12\end{cases}\)

Function composition is an operation that takes two functions and produces a third function.

Therefore, the given composite function g(f(x)) means to substitute function f(x) in place of the x in function g(x):

\(\begin{aligned}\implies g(f(x))&=g(x-1)\\& = 3(x-1)^2-4(x-1)-12\\&=3(x-1)(x-1)-4x+4-12\\&=3(x^2-2x+1)-4x-8\\&=3x^2-6x+3-4x-8\\&=3x^2-6x-4x+3-8\\&=3x^2-10x-5\end{aligned}\)

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The additional information that would have to be true for the parallelogram to also be a rhombus is D. Opposite angles congruent

All rhombuses are parallelograms, but not all parallelograms are rhombuses. In a rhombus, all four sides are equal and the diagonals intersect at 90 degrees. In a parallelogram, the opposite sides are equal and the diagonals bisect each other.

Because its sides are parallel to one another, a rhombus can also be referred to as a particular kind of parallelogram. 360° is the total number of angles in a rhombus. Angles on either side of one another are equal, and adjacent angles are supplementary angles.

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Barbara draws a parallelogram. Jason thought it might be a rhombus. What additional information would have to be true for the parallelogram to also be a rhombus?a. Opposite sides congruent.b. Diagonals are perpendicular.c. Consecutive angles supplementary.d. Opposite angles congruent.

Answer:

Hey there!

-16h=16

Divide both sides by -16

h=-1

Hope this helps :)

Answer:

h = -1

Step-by-step explanation:

inverse operation:

16 = -16h

divide by -16 on both side

-1 = h

Answer:

Fx=Px

Plants=3

(Fish)x=(Plants)3

Step-by-step explanation:
I hope this helps

The proportional relationship for the number of fish when there are P plants is given by:

F = .4P;

Hence, when there are 3 plants, there are 1.2 fish, and option 3 is correct.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

\(y = kx\)

In which k is the constant of proportionality.

In this problem, when there are 15 plants there are 6 fish and when there are 20 plants there are 8 fish, hence the constant is:

\(k = \frac{6}{15} = \frac{8}{20} = 0.4\)

Then, the equation is:

\(F = 0.4P\)

When there are 3 plants:

\(F = 0.4(3) = 1.2\)

There are 1.2 fish.

Hence option 3 is correct.

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The interval where the derivative function f'(x) has a relative maximum is -2.478 and 1.732 (B) only.

To find the relative maximum of a function, we need to find the critical points of the derivative function. Critical points are where the derivative function is equal to zero or undefined. In this case, the derivative function is f'(x) = sin(x^2 − 3).

To find the critical points, we need to set the derivative function equal to zero and solve for x:
sin(x² − 3) = 0

x² − 3 = nπ, where n is an integer

x² = nπ + 3

x = ±√(nπ + 3)

We need to find the values of x that are in the interval −3 < x < 3. By plugging in different values of n, we can find the critical points in this interval:

n = 0: x = ±√3 ≈ ±1.732

n = 1: x = ±√(π + 3) ≈ ±2.478

n = 2: x = ±√(2π + 3) ≈ ±2.915 (not in the interval)

So the critical points in the interval are -2.478, -1.732, 1.732, and 2.478.

To determine which of these are relative maximums, we need to look at the sign of the derivative function on either side of the critical points. If the derivative function changes from positive to negative at a critical point, then that point is a relative maximum.

At x = -2.478, the derivative function changes from positive to negative, so this is a relative maximum.

At x = -1.732, the derivative function changes from negative to positive, so this is not a relative maximum.

At x = 1.732, the derivative function changes from positive to negative, so this is a relative maximum.

At x = 2.478, the derivative function changes from negative to positive, so this is not a relative maximum.

Therefore, the values of x in the interval −3 < x < 3 where f has a relative maximum are -2.478 and 1.732.

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