The position of a particle moving in a straight line is given by the equation, s = f(t) = t3 - 91? + 12t for t > 0 (a) Find the velocity at timet (b) What is the particle at rest? (c) When is the particle moving forward? (d) Find the acceleration at timet (d) Find the acceleration at time t (e) When is the particle speeding up and slowing down?

Answer:

2.41666666667

Step-by-step explanation:

I hope this is right

a. The fiber-matrix load ratio is 3.02

b. The actual load carried by the fiber phase is 149200 N

c. The actual load carried by the matrix phase is  -99800 N

d. The stress on the fiber phase is 481 MPa

e. The stress on the matrix phase is -322 MPa

f.  The expected strain in the composite is approximately 0.22%.

Fiber-matrix load ratio is the ratio of the load carried by the fiber phase to the load carried by the matrix phase.

To calculate this ratio use the rule of mixtures

\(f_fiber\) = Vi * Ef

\(f_matrix\) = Vm * Em

where;

\(f_fiber\) and \(f_matrix\) are the stresses carried by the fiber and matrix phases, respectively, and

Ef and Em are the Young moduli of the fiber and matrix materials, respectively.

The fiber-matrix load ratio is

\(f_fiber / f_matrix = (Vi * Ef) / (Vm * Em) \approx 3.02\)

The actual load carried by the fiber phase is

\(f_fiber\) = (\(f_fiber\) / \(f_matrix\)) * f_total = (3.02) * 49400 N

≈ 149200 N

where f_total is the total load applied to the composite.

The actual load carried by the matrix phase is

\(f_matrix\) = f_total - \(f_fiber\) = 49400 N - 149200 N = -99800 N

The negative value indicates that the matrix is under compression.

The stress on the fiber phase is

= 149200 N / 310 \(mm^2\)

≈ 481 MPa

The stress on the matrix phase is

\(\sigma_matrix\)=  \(f_matrix\) / Am = -99800 N / 310\(mm^2\)

≈ -322 MPa

where Am is the cross sectional area of the matrix phase.

The strain expected by the composite can be calculated using the rule of mixtures

\(\epsilon_composite = Vi * \epsilon_fiber + Vm * \epsilon_matrix\)

where ε_fiber and ε_matrix are the strains in the fiber and matrix phases, respectively.

Assuming that the composite is in a state of uniaxial stress, Hooke's law can be used to relate the stress and strain in each phase

\(\sigma_fiber = Ef * \epsilon_fiber\)

\(\sigma_matrix = Em * \epsilon_matrix\)

\(\epsilon_composite = (\sigma_fiber / Ef) * Vi + (\sigma_matrix / Em) * Vm\)

Substitute the values we have obtained

\(\epsilon_composite\) ≈ 0.0022

Therefore, the expected strain in the composite is approximately 0.22%.

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The equation that represents the length of the square dining room in feet is (1/4)x - 5/6.

The area of a square is a product of it's any two sides or a product of diagonals divided by two. If a side has a length 'a' then the diagonal is a√2.

The perimeter of a square is the sum of the lengths of all the sides.

We know the perimeter of a square is 4×side.

We also know that 1 foot is equal 12 inches.

Given, A square dining room table has a perimeter of (12x - 40)".

Now if we factor out a 4 we'll have the side inside the bracket which is,

4(3x - 10)'', This is in inches to convert it to feet we have to divide what is inside the bracket by 12 which is,

= (3/12)x - 10/12 feet.

= (1/4)x - 5/6 feet.

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Answer:2.86

Step-by-step explanation:

3.5(x +2) = 17

3.5x + 7 = 17

3.5x =17 - 7

3.5x =10

x = 10/3.5

x = 2.86

Answer:

C

Step-by-step explanation:

Just replaced the x with 5 and check if it is a true statement

A ternary string is a string composed of characters 0, 1, and 2. The number of ternary strings that contain exactly n characters, each of which is one of three types, is 3^n.Exactly 5 0s, 5 1s, and 5 2s are required for the ternary string, which means that the total number of characters is 15.

Each of these characters can be one of three types (0, 1, or 2). As a result, the total number of possible strings is 3^15. This is equivalent to 14,348,907. We arrived at this conclusion by computing 3 to the fifteenth power.Explanation:When constructing a sequence of three symbols, the first symbol has three alternatives, the second symbol has three alternatives, and so on. There are n choices for each of the n characters, resulting in a total of 3^n possible sequences.Example 1:Let's assume we have to create 5-character sequences with three symbols: a, b, and c. There are 3*3*3*3*3 = 243 possible sequences since there are three choices for each symbol.Example 2:Let's assume we have to construct a 10-character sequence using three symbols: 0, 1, and 2. There are 3*3*3*3*3*3*3*3*3*3 = 59,049, a total of 59,049 possible 10-character sequences. We can perform the same calculation for 15-character strings using the same logic.

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Answer:

Twice a number decressed by five

Answer:

C

Step-by-step explanation:

the product of two and five less than a number

Answer:

Step-by-step explanation:

To maximize the volume of the box, we need to find the height that will maximize the volume of the box.

Let's start by finding an expression for the volume of the box. The box has dimensions of 14-2x by 10-2x by x, where x is the height of the box. The volume of the box is:

V(x) = (14-2x)(10-2x)(x)

Expanding this expression, we get:

V(x) = 4x^3 - 48x^2 + 140x

To find the value of x that maximizes this expression, we can take the derivative of V(x) with respect to x and set it equal to zero:

V'(x) = 12x^2 - 96x + 140 = 0

We can solve this quadratic equation using the quadratic formula:

x = [96 ± sqrt(96^2 - 4(12)(140))]/(2(12)) = [96 ± 16sqrt(6)]/24

We can simplify this to:

x = 4 ± sqrt(6)/3

Since the dimensions of the box must be positive, we can discard the negative solution:

x = 4 + sqrt(6)/3

So the height of the box that will give a maximum volume is approximately 5.61 inches (rounded to two decimal places).

Answer:

41

Step-by-step explanation:

Ok, so the time for homework is already simplified to minutes.

2/3 of an hour is x/60

60/3 = 20

20*2 = 40

so 2/3 = 40/60

40/60 = 40 minutes

[]

540 seconds is..

540/60

54/6=9

9 minutes

[]

40+9 = 49

90-49 = 41

So, he spent 41 more minutes on homework than on making lunch and reading.

Considering the given table and the periodicity concept, it is found that the data set is not periodic.

The period of a function is given by the distance between it's repetitions.

An example of a periodic data-set with a period of 3 would be 1,2,3,1,2,3,1,2,3,...

In this problem, looking at the table, it is found that there are no patterns of repetitions, that is, the number of cars washed do not follow a repeated pattern, hence the data set is not periodic.

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Answer:

This should explain it

Step-by-step explanation:

If its the graph question I think it is this is the answer screenshot.

The width of a parabola is determined by the value of a, the coefficient of the quadratic term. If a is greater than 1, the parabola will be narrower than y = x².

How to solve the parabola?

The statement "the parabola opens" can have different endings depending on the specific equation of the parabola. However, in general, a parabola can open upwards or downwards. If the coefficient of the quadratic term (x²) is positive, the parabola opens upwards, and if it is negative, the parabola opens downwards.

The vertex of a parabola is the point at which the curve changes direction. For a parabola opening upwards, the vertex is the lowest point on the curve, and for a parabola opening downwards, the vertex is the highest point on the curve. Therefore, if the parabola opens upwards, the vertex will be a minimum point, and if it opens downwards, the vertex will be a maximum point.

The vertex of a parabola is located at the coordinates (h, k), where h is the x-coordinate and k is the y-coordinate. To find the vertex, one can use the formula h = -b/2a and k = f(h), where a, b, and c are the coefficients of the quadratic equation f(x) = ax² + bx + c.

If the vertex of a parabola is at (h, k), then the parabola has been shifted h units horizontally and k units vertically from the standard position of y = x². If h is positive, the parabola has shifted to the right, and if it is negative, the parabola has shifted to the left. If k is positive, the parabola has shifted upwards, and if it is negative, the parabola has shifted downwards.

The width of a parabola is determined by the value of a, the coefficient of the quadratic term. If a is greater than 1, the parabola will be narrower than y = x², and if a is less than 1, the parabola will be wider than y = x². If a is negative, the parabola will be inverted compared to y = x², but the same principles apply.

In summary, the opening direction of a parabola, the type of vertex, the location of the vertex, the amount of horizontal and vertical shift from the standard position, and the width of the parabola are all determined by the coefficients of the quadratic equation.

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The loan option with the lowest total value is the one with simple interest, which amounts to $57,247.50. Therefore, the small business owner would be better off choosing the loan with Simple interest, as it results in a lower overall cost compared to the other options.

Part A: To calculate the total value of the loan with simple interest, we use the formula: Total Value = Principal + (Principal * Rate * Time).

Here, the Principal (P) is $50,000, the Rate (R) is 4.35% or 0.0435, and the Time (T) is 3 years and 4 months, which is equivalent to 3.33 years.

Plugging the values into the formula, we have:

Total Value = $50,000 + ($50,000 * 0.0435 * 3.33)

Total Value ≈ $50,000 + $7247.5

Total Value ≈ $57,247.50

Part B: To calculate the total value of the loan with quarterly compounded interest, we use the formula: Total Value = Principal * (1 + (Rate / n))^(n * Time).

Here, n represents the number of compounding periods per year, which is 4 (quarterly compounding).

Plugging the values into the formula, we have:

Total Value = $50,000 * (1 + (0.0435 / 4))^(4 * 3.33)

Total Value ≈ $50,000 * (1.010875)^13.32

Total Value ≈ $50,000 * 1.156977

Total Value ≈ $57,848.85

Part C: To calculate the total value of the loan with continuously compounded interest, we use the formula: Total Value = Principal * e^(Rate * Time).

Here, e represents the mathematical constant approximately equal to 2.71828.

Plugging the values into the formula, we have:

Total Value = $50,000 * e^(0.0435 * 3.33)

Total Value ≈ $50,000 * e^(0.145005)

Total Value ≈ $50,000 * 1.15514

Total Value ≈ $57,757.00

Part D: Comparing the total values of the loans, we find that:

- The total value with simple interest is $57,247.50.

- The total value with quarterly compounded interest is $57,848.85.

- The total value with continuously compounded interest is $57,757.00.

Based on these calculations, the loan option with the lowest total value is the one with simple interest, which amounts to $57,247.50. Therefore, the small business owner would be better off choosing the loan with simple interest, as it results in a lower overall cost compared to the other options.

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Function: This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

A function is a mathematical relation between two sets of values, usually between an input and an output. It can be thought of as a machine that takes a certain input and produces a certain output.

2.7 x 10^3 is about 0.049 times smaller than 5.481 x 10^5.
To determine this, we can divide the two numbers. 5.481 x 10^5 divided by 2.7 x 10^3 equals about 201.593.
This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

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Answer: 2 4/15 months

Step-by-step explanation:

From the question, we are informed that a wagon train traveled from Missouri to Wyoming in 1 2/3 months and from Wyoming to Utah in 3/5 month.

The number of months that it will take the wagon train to travel from Missouri to Utah will be:

= 1 2/3 + 3/5

The common lowest multiple is 15

= 1 10/15 + 9/15

= 1 19/15

= 1 + 1 4/15

= 2 4/15 months

It will take they train 2 4/15 months to travel from Missouri to Utah.

Answer:

Step-by-step explanation:

To determine the number of ways to select 3 men and 2 women for a committee from a union chapter consisting of 6 men and 4 women, we can use the concept of combinations.

The number of ways to select 3 men from 6 men is given by the combination formula: C(6, 3) = 6! / (3! * (6 - 3)!) = 20.

Similarly, the number of ways to select 2 women from 4 women is given by the combination formula: C(4, 2) = 4! / (2! * (4 - 2)!) = 6.

To obtain the total number of ways to select 3 men and 2 women for the committee, we multiply these two combinations together: 20 * 6 = 120.

Therefore, there are 120 ways to select 3 men and 2 women for a committee from the given union chapter.

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The bottleneck time is 18.18%. Therefore, option A is the correct answer.

In economics terms, the bottleneck is a chain of supply of resources that wants the most extended time in the supply chain operation for specific demand. It also evaluated to estimate the supply chain throughput.

Through put time = Sum of all times=1+2+3+4+5+6+7+8+9+10=55

Given,

Assembly line has 10 stations

Throughput time is 55

The formula for bottleneck time is:

Bottle neck time = Total stations/Throughput time ×100

= 10/55 ×100

= 18.18%

The bottleneck time is 18.18%. Therefore, option A is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

An assembly line has 10 stations with times of 1, 2, 3, 4,...,10, respectively. What is the bottleneck time?

a. 18.18% of the throughput time

b. 100% of the throughput time

c. 550% of the throughput time

d. 50% of the throughput time

e. 1.82% of the throughput time

The tangent point and a second tangent point of a line with the same slope as the given line are (2.67, 6) and (2.57, 6.1).

The slope of the given line is -0.75.

The radius of the circle is |6 - 1.25| / -0.75 = 7.

The equation of the tangent line is y = -0.75x + c.

Substituting the coordinates of the center of the circle into this equation, we get 6 = -0.75 * 2 + c

Solving for c, we get c = 8.

The equation of the tangent line is y = -0.75x + 8.

The point of tangency is the point where the tangent line intersects the circle. To find the point of tangency, we need to solve the equation of the tangent line for x.

y = -0.75x + 8

6 = -0.75x + 8

-2 = -0.75x

x = 2.67

The point of tangency is (2.67, 6).

The second tangent point is the point where the tangent line intersects the circle at a different location. The direction of the tangent line is the same as the direction of the vector (-0.75, 1).

We can move the point of tangency a small distance in the direction of the tangent line by adding a small multiple of the vector (-0.75, 1) to the point of tangency.

Let's add a multiple of 0.1 to the point of tangency.

(2.67, 6) + 0.1 * (-0.75, 1)

= (2.57, 6.1)

The second tangent point is (2.57, 6.1).

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The line y = - 0.75x + 1.25 is tangent to a circle whose center is located at (2, 6) Find the tangent point and a second tangent point of a line with the same slope as the given line

Answer:

10

Step-by-step explanation:

The square root is √62 = 7.874.

round to the nearest tenth 10

Developers determine the specifics of how to build a system in the design phase. b

The design phase and its importance:
Define Objectives:

The design phase begins after the completion of the analysis phase, where developers have gathered and evaluated requirements.

The main objective of the design phase is to create a blueprint for the system that addresses all identified requirements.
Create Architectural Design:

During this step, developers establish the overall structure of the system, including its components, their relationships, and the interactions between them.

This architectural design provides a high-level view of the system's organization.
Design System Components:

With the architectural design in place, developers focus on designing individual components or modules of the system. They create detailed specifications, which include the functionality, inputs, outputs, and processes for each component.
Design User Interface:

The user interface design involves creating a user-friendly and efficient way for end-users to interact with the system. This can include designing screen layouts, menus, buttons, and other interface elements.
Validate Design:

The final step in the design phase is to ensure that the proposed design meets all the requirements identified during the analysis phase.

Developers may use various methods, such as reviews and simulations, to validate their design before proceeding to the implementation phase.
The design phase is a crucial part of the system development process, as it defines how the system will be built, ensuring it meets the needs of its users and the project's objectives.

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x-12=9

x-12+12=9+12

x=21

Answer:

x=21

Step-by-step explanation:

Step 1: Add 12 to both sides.

x−12+12=9+12

Answer:

x = 82.5

Step-by-step explanation:

2x + 5 = 170

     -5       -5

2x = 165

divide by 2

x = 82.5

Step-by-step explanation:

The values for a, b, and c for the quadratic formula, are a = 1, b = 4, c = -9

The quadratic formula is a formula that provides the solution to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring, completing the square, graphing and others.

Given that, Brandon is solving an equation, x²+4x=9, he used quadratic formula, to solve the equation,

x²+4x=9

x²+4x-9 = 0

Using the quadratic formula, we get,

x = -b±√b²-4ac /2a

Here, the terms are,

a = 1, b = 4 and c = -9

Hence, the values for a, b, and c for the quadratic formula, are a = 1, b = 4, c = -9

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Answer:

30/5=6

Step-by-step explanation:

There’s 30 fish put into five bowls, and there’s six fish in each

Step-by-step explanation:

AB and DC are parallel

AD and BC are parallel

It can't be a rectangle bcz sides AB and BC are not perpendicular to each other

Answer:

Step-by-step explanation:

Number of successful free throws:

The reasonable estimate for the solution is (2.29, -4.87)

The reasonable estimate for the solution is the point where the two lines intersect each other.

To get the point where they intersect, we will simply equate the system of equations given as shown:

\(-3x+2=\frac{1}{2}x-6\\Collect \ the \ like \ terms\\-3x-\frac{1}{2}x=-6-2\\\frac{-7x}{2}=-8\\-7x=-16\\x=\frac{16}{7} \\x=2.29\)

Substitute x = 2.29 into any of the equation

Using the equation y = -3x+2

y = -3(2.29)+2

y = -6.87+2

y =-4.87

This shows that the reasonable estimate for the solution is (2.29, -4.87)

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The point of intersection of the linear equations is approximately \((x,y) = (2.286, -4.857)\).

The most quickest approach that offers a reasonable solution consist in representing both linear functions graphically by means of a graphing tool (i.e. Desmos). As there is a system of two equation and two variables, the system can be represented by 2D-graphing tool.

The solution of this system is represented by the point, in which both lines intercepts each other. Let be the following two linear functions:

\(y = 3\cdot x + 2\) (1)

\(y = \frac{1}{2}\cdot x - 6\) (2)

The result from graphic tool is presented below and the point of intersection is approximately \((x,y) = (2.286, -4.857)\).

Answer:

The experimental probability of the coin landing heads up is 110/200 = 11/20.

The probability is 1/2.

The correct statement in Mai's experiment is, The experimental probability of the coin landing heads up is (11/20) and the theoretical probability of the coin landing heads up is (1/2)

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Experimental probability is repeating an experiment and observing the outcomes and theoretical probability is the expected value.

In the given context the expected value is 200×(1/2) = 100, As P(H) = 1/2 and P(T) = 1/2.

Upon experiment, the coin landed 110 times heads up.

Therefore, The theoretical likelihood of the coin landing heads up is (1/2), while the experimental probability is (11/20).

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Answer:

The bars above the decimals are called bar notations. Bar notations are used when more than one digits that repeat.

Random sampling is a method of choosing a sample of observations from a population to make assumptions about the population. It is also called probability sampling.

To determine the p-value for each value of the calculated test statistic, we need to consult the t-distribution table or use statistical software. The p-value represents the probability of observing a test statistic as extreme as or more extreme than the calculated test statistic under the assumption that the null hypothesis is true.

Given that the alternative hypothesis is u ≠ 50 (two-tailed test), we need to find the area in both tails of the t-distribution that corresponds to the absolute value of the test statistic.

a) t = -2.7707

The p-value for t = -2.7707 can be found by looking up the area to the left of -2.7707 in the t-distribution table or using statistical software. Assuming a significance level (alpha) of 0.05, if the p-value is less than alpha, we reject the null hypothesis; otherwise, we fail to reject it.

b) Given Part a, if the p-value is less than 0.05, we reject the null hypothesis at the 0.05 significance level. Otherwise, we fail to reject it.

c) t = -1.7033

Similar to part a, calculate the p-value for t = -1.7033 and compare it to the significance level of 0.05.

d) Given Part c, follow the same decision rule as in part b.

e) t = -2.2911

Calculate the p-value for t = -2.2911 and compare it to 0.05.

f) Given Part e, apply the decision rule as in part b.

g) t = -1.1458

Compute the p-value for t = -1.1458 and compare it to 0.05.

h) Given Part g, apply the decision rule as in part b.

By comparing the calculated p-values to the significance level of 0.05, you can make a decision about the null hypothesis in each part. If the p-value is less than 0.05, reject the null hypothesis. Otherwise, fail to reject it.

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