Find the first five terms of the sequence in which a = 3 and an = 2an - 1 + 13, if n 2 2.
A. O 3, 19, 51, 115, 243
B. O 3, 19, 32, 45, 58
C.O3, 16, 29, 42, 55
D. O3, 41, 535, 6957, 175,761

Please help

The value of x in the solution set of the inequality is -4.

Inequalities are of two types, > and <. The > sign means that left hand side is greater than the right hand side, while the < sign means that the left hand side is less than than the right hand side.

We can solve the inequality by assuming the inequality sign as the = sign, except that when we divide or multiply one side by (-1), the inequality sign will reverse (for eg it will change from > to <).

9(2x+1) < 9x - 18

2x+1 < x - 2

2x < x - 3

x < -3

This means that x can be any value less than -3 (but not equal to -3 since the sign is < and not ≤) . Hence, the answer is -4.

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Answer:

-4

Step-by-step explanation:
taking  test

The value that is a solution of the rational equation that must be discarded because of the context is (b) x = -10

What is rational equation?

An equation with at least one rational expression, or you may say a fraction, is known as a rational equation. An illustration of a rational equation is 2x+14 = x3. These fractions could make up both sides of the equation or only one. Another possibility is the ratio of two polynomials.

The equation given is

1/x + 1 / (x + 18) = 1 / 40

Take the LCM

( x + 18 + x ) / ( x(x + 18)) = 1 / 40

(2x + 18) / (x(x + 18)) = 1 / 40

Cross Multiplying

40(2x+18) = x(x+18)

80x + 720 = x² + 18 x

x² - 62x -720 = 0

Using graphing calculator

x = 72 or x = -10

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There is no solution in this case. Finally, we write the solution set as:1 < x < 6

Given quadratic inequality is x² - 7x + 6 ≤ 0To find: solution set for this inequality.

The quadratic expression can be factorized as follows:x² - 7x + 6 = (x - 1)(x - 6)Now, the quadratic inequality can be written as:

(x - 1)(x - 6) ≤ 0

The product of two factors is less than or equal to zero only when one factor is positive and the other factor is negative.  

So, we consider two cases:

Case 1: (x - 1) > 0 and (x - 6) < 0

In this case, x > 1 and x < 6. But the inequality (x - 1) > 0 is redundant because it is already implied in (x - 6) < 0.

So, the solution is 1 < x < 6.Case 2: (x - 1) < 0 and (x - 6) > 0In this case, x < 1 and x > 6. But the inequality (x - 6) > 0 is redundant because it is already implied in (x - 1) < 0.

Therefore, there is no solution in this case. Finally, we write the solution set as:1 < x < 6

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Answer:  each-121      leftover: 5

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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Answer:8.66666666

Step-by-step explanation:

Answer:

32. Good luck............

Answer:

u=14, v=2

Step-by-step explanation:

Here's my attempt:

Proving triangle congruency:

We need to prove that the two triangles are congruent.

First, we need to see which sides/angles correspond (basically how the two triangles overlap each other).

Well, we can see that m∠F = 90° and that m∠D = 90°, so we know that ∠F and ∠D are congruent, and so they correspond.

So, if you drag ΔHFG over to ΔCDE, then sides DC and FH would be right on top of each other. (try drawing this to make it clearer)

Solving for v:

So if sides DC and FH are congruent, then their values are also equal.

DC = 17v and FH = v+32

So if DC=FH, then 17v=v+32

Then, we simplify this:

17v=v+32     [original equation]

16v=32     [subtract v from both sides]

v=2     [divide both sides by 16 to isolate v]

So, we have our value for v: v=2

Solving for u:

Now, it's time to find u:  (also, it doesn't matter if you found v first or u first in this problem)

When we overlapped ΔHFG and ΔCDE, we saw that EC = GH

So, using the same method as we used to find v, we can say that

EC=7u and GH = 10u-42

If EC=GH, then 7u=10u-42

Then, we simplify:

7u=10u-42     [original equation]
-3u=-42     [subtract 10u from both sides to get u on just one side]
u=14     [subtract both sides by -3 to isolate u]

Finally, we have our value for u: u=14

But we're not done yet: let's check our work:

Firstly, let's plug our answer for v into our equation for v:

17v=v+32
17(2)=(2)+32
34=34     It works!

Next, we'll plug in our answer for u into our equation for u:

7u=10u-42

7(14)=10(14)-42

98=140-42

98=98     It works!

I hope you read through my explanation and that it helped! :D

0.003 is the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations

To calculate the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations.The mean is the expected number of calls involving a fax transmission, while the standard deviation is the measure of variability in the distribution. We then use this information to calculate the probability of exceeding the expected number by more than 2 standard deviations, which can be done using the z-score formula. The z-score for values more than 2 standard deviations away from the mean is 2.33, which corresponds to a probability of 0.003. Thus, the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations is 0.003.

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The inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

To find the inverse Laplace transform of each function, we need to express them in terms of known Laplace transforms. Here are the solutions for each function:

a)

\(F(s) = \large{\frac{2e^{-0.5s}}{s^2-6s+9}}\)

To find the inverse Laplace transform, we first need to factor the denominator of F(s). The denominator factors as (s - 3)². Therefore, we can rewrite F(s) as:

\(F(s) = \large{\frac{2e^{-0.5s}}{(s-3)^2}}\)

Now, we know that the Laplace transform of eᵃᵗ is 1/(s - a). Therefore, the inverse Laplace transform of

\(e^(-0.5s) \: is \: e^(0.5t).\)

Applying this, we get:

\(f(t) = 2e^(0.5t) * t \\

b) F(s) = \large{\frac{s-1}{s^2-3s+2}}\)

We can factor the denominator of F(s) as (s - 1)(s - 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{s-1}{(s-1)(s-2)}}\)

Simplifying, we have:

\(F(s) = \large{\frac{1}{s-2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(2t) \\

c) F(s) = \large{\frac{s-1}{s^2+s-2}}

\)

We factor the denominator of F(s) as (s - 1)(s + 2). The expression becomes:

\(F(s) = \large{\frac{s-1}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{1}{s+2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-2t) \\

d) F(s) = \large{\frac{e^{-s}(s-1)}{s^2+s-2}}\)

We can factor the denominator of F(s) as (s - 1)(s + 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{e^{-s}(s-1)}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{e^{-s}}{s+2}}\)

The Laplace transform of

\(e^(-s) \: is \: 1/(s + 1).\)

Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

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The interquartile range is a useful tool for measuring variability in a set of data because it overcomes the difficulty of the range being influenced too much by extreme values

The interquartile range is a measure of variability that is commonly used in statistics to describe the spread of a set of data. It is particularly useful because it overcomes the difficulty of the range being influenced too much by extreme values.

In mathematical terms, the interquartile range is defined as the difference between the upper quartile (Q3) and the lower quartile (Q1).

The upper quartile represents the 75th percentile of the data and the lower quartile represents the 25th percentile of the data.

This means that 25% of the data falls below the lower quartile and 75% of the data falls above the upper quartile.

The interquartile range provides a better representation of the spread of the data because it eliminates the influence of extreme values.

These values, also known as outliers, can have a significant impact on the range and can make it appear as though the data is more spread out than it actually is.

By using the interquartile range, the outliers are excluded and a more accurate representation of the spread of the data is obtained.

Therefore, option (a) is correct.

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Answer:

No

Step-by-step explanation:

Angle measures of a triangle must add up to 180 and this only adds up to 87

Answer:

im trying to figure out the same thing

Step-by-step explanation:

Answer:

m = -12/0 = N/A [Undefined]

x = 5

Step-by-step explanation:

m = ∆y/∆x = y₂-y₁/x₂-x₁

m = (-9) - (3) / (5) - (5) = -12 / 0

Domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

To find the approximate direction angle of vector v = ⟨8, -1⟩, we can use trigonometry and the inverse tangent function (arctan). Therefore, the approximate direction angle of vector v is approximately -0.1244 radians or -7.12 degrees.

The direction angle (θ) of a vector can be calculated using the formula:

θ = arctan(y/x)

where (x, y) are the components of the vector.

For the given vector v = ⟨8, -1⟩, we have x = 8 and y = -1.

θ = arctan((-1)/8)

Using a calculator or a mathematical software, we can evaluate this expression to find the approximate direction angle:

θ ≈ -0.1244 radians or approximately -7.12 degrees.

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Therefore, the value of the given equation of  x comes out to be  x =5.

Equations can be classified as either identities or conditioned equations. For each amount of the variables, an identity is true. Only specific values of the variables make a conditional equation legitimate. The equality sign ("="), which separate the two expressions, is a symbol for an equation.

Here,

Given data: A, B, and C are parallel, B is located between A and C, AC equals 24, AB equals 2x+1, and BC equals 3x-2.

In the event where A, B, and C are collinear and B is positioned between A and C, we obtain

Replace the given equation with AC = 24, AB = 2x+1, and BC = 3x-2.

AB plus BC equals AC

=>  AC= AB + BC

On combining like terms we get

=> 2x+1 + 3x-2 = 24

=> 5x -1 =24

=>5x =25

=>x =5

Therefore, the value of x comes out to be  x =5.

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Answer: 6 2/25

Step-by-step explanation:

8/100 + 6

6= 6/1

6/1 + 8/100= 6 6/25 = 6.08

Answer:

6.08

Step-by-step explanation:

1. 1 hundredth is equal to 0.01 because it's 1 unit of out 100.

2. 1 whole is equal to 1 because it's just one, whole unit.

3. Given this information, 8 hundredths would be 0.08 and 6 wholes would be 6.

4. Now, to find the sum, just add these two numbers together:

Therefore, the answer is 6.08.

The number of ways a dinner patron can select appetizers and vegetables will depend on the number of options available for each course.

Let's say there are "m" appetizer options and "n" vegetable options on the menu.

Then, the patron has m options for the appetizer course and n options for the vegetable course. To find the total number of ways the patron can select both courses, you would multiply the number of options for each course:

m x n ways

So, if the patron has 4 options for appetizers and 3 options for vegetables, the total number of ways the patron can select both courses would be 4 x 3 = 12.

Therefore, the number of ways a dinner patron can select appetizers and vegetables will depend on the specific number of options available for each course.

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If the company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by P(x)=−3(x−5) ^2+12, the maximum profit is $87 million.

The given profit function is in the form of a quadratic equation with a negative coefficient of the squared term. This means that the graph of the function is a downward-facing parabola, and the vertex of this parabola represents the maximum value of the function.

To find the vertex, we need to convert the given function into vertex form:

P(x) = -3(x - 5)^2 + 12

= -3(x^2 - 10x + 25) + 12

= -3x^2 + 30x - 63

Completing the square, we get:

P(x) = -3(x - 5)^2 + 12 + 75

= -3(x - 5)^2 + 87

The vertex of this parabola is at the point (5, 87), which represents the maximum profit the company can earn.

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The correct option is E. The population mean is less than 125. As, 125 is does not comes in the interval of 135 to 160, the interval tends to refute the claim that the population mean is less than 125.

The 90% confidence interval for the mean of the population is computed to be 135 to 160. This means that we are 90% confident that the true population mean falls within this range.

Since 125 is not within the interval of 135 to 160, the interval tends to refute the claim that the population mean is less than 125.

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A unity feedback control system is characterized by an open-loop transfer function G(s)H(s)=k/s(s+10). The system gain k so that the system will have a damping ratio of 0.5 is 4. The corresponding rise time is 2.3s, settling time is 4.4s, and peak overshoot is 0.26.

To determine the system gain k so that the system will have a damping ratio of 0.5, we can use the equation  ζ=1/2ωn. Rearranging the equation yields k=2ωn2. Using the damping ratio of 0.5, this yields k=4.
For this value of k, the rise time, settling time, and peak overshoot can be determined using the following equations:
Rise Time: Tr=4.6/ωn
Settling Time: Ts=4.4/ζωn
Peak Overshoot: Mp=e^(-ζπ/√1-ζ^2)
Given that the damping ratio is 0.5 and the system is subjected to a step input of 1V, we can determine the rise time, settling time, and peak overshoot.
Rise Time: Tr=4.6/ωn=4.6/2=2.3s
Settling Time: Ts=4.4/0.5ωn=4.4/1=4.4s
Peak Overshoot: Mp=e^(-0.5π/√1-0.5^2)=0.26

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A college is interested in improving its food offerings on campus. It employs a research firm that selects a representative sample of students who say they currently eat six or more meals on campus weekly. After interviewing these students, the firm then makes generalizations about what all students at the college want in their food choices The method used in this scenario is Statistical Inference.

Statistical inference is the process of using sample data to make generalizations about a population. In this case, the research firm is using sample data from a representative group of students who eat six or more meals on campus weekly  and then making generalizations about what all students at the college want in their food choices.

Statistical inference involves four steps: (1) collecting data from the sample; (2) analyzing the data; (3) forming conclusions about the population; and (4) testing these conclusions. The analysis usually involves using descriptive and inferential statistics to draw meaningful conclusions about the population. For example, the research firm might use descriptive statistics to analyze the number and type of meals that the students prefer, and then use inferential statistics to make generalizations about the entire student population.

The research firm must also consider the limitations of their study, such as the sample size, sampling techniques, and data collection methods. Additionally, the research firm must take measures to ensure that its conclusions are valid and reliable. For example, they might use sensitivity analysis to test the stability of the results.

Overall, statistical inference is a powerful tool that can help the college gain valuable insights into their student population’s food preferences. It allows them to make informed decisions that are backed up by data.

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In the US, housing prices and consumption generally change in the same direction.

Changes in housing prices can have an impact on consumption patterns in the US. Generally, when housing prices increase, consumption also tends to increase, and when housing prices decrease, consumption tends to decrease as well. This relationship can be attributed to several factors. Firstly, when housing prices rise, homeowners experience an increase in their wealth through home equity.

This increase in wealth can lead to higher consumer confidence and a willingness to spend more on goods and services, thereby boosting consumption. Secondly, rising housing prices can also lead to a "wealth effect" for homeowners. This means that homeowners may feel wealthier and more financially secure, leading them to increase their discretionary spending and overall consumption. Conversely, when housing prices decline, homeowners may experience a decrease in their wealth and financial security.

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Answer:

Please check the explanation.

Step-by-step explanation:

We need to write 35% as a fraction, percent, and a decimal.

35% as a fraction:

All we need is to divide 35 by 100 as 35 is basically the 35th part of 100 parts.

Thus, 35% as a fraction would be: 35/100

35% as a decimal:

All we need is to divide 35 by 100 and calculate the result such as:

35/100 = 0.35

Thus, 35% as a decimal would be:  0.35

35% as a percent:

35% is already mentioned as a percent.  

Thus, 35% as a percent would be:  35%

Answer:

3xn=27

Step-by-step explanation:

n=days

3 per day

per=multiply

3xday

3 x n

27 total so

3 x n=27

Answer:

3x n=27

Step-by-step explanation:

This is a multiplication problem involving a total of 27, which only applies to option 2.

Option 1 does not =27, option 3 and 4 are not multiplying

Answer:-355/4

Step-by-step explanation:

Answer:

= -355/4

Step-by-step explanation:

= 5/4 + 4(3/4 - 12)(2)

= 5/4 + (-45)(2)

= 5/4 + -90

= -355/3