#3 find domain and range using interval notation

5th term of the sequence is -4

To find the 5th term in the sequence, we need to substitute n =  5 into the expression given

 \(a_5\) =  26- 6( 5)  

\(a_5\) =  26- 30

\(a_5\) = -4  

The formula given, an =  26- 6n, represents an  computation sequence with a common difference of-6.

This means that each term in the sequence is  attained by obtain 6 from the  former term.  

It's important to note that the formula is written in general form, meaning that it can be used to find any term in the sequence by simply plugging in the  matching value of  n.

 In this case, we were asked to find the 5th term, so we substituted n =  5 into the formula to get a5 = -4.

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Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

A sample is only a small portion of the population.

Let's imagine you were interested in determining the average income for all Americans in your population.

Instead of knocking on every door in America because of time and money constraints, you decide to ask 1,000 random people. Your sample consists of these a thousand persons.

Given, A gardener wants to determine which of two brands of fertilizer is best for the plants.

And the gardener decides to conduct an experiment using 28 individual plants.

Plan A will be a biased sampling and the experiment would not yield

desired results.

Therefore, The gardener should choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

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Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

1 2/3

Step-by-step explanation:

if your dividing fractions you have to multiply

the answer is 15

The purpose of data is to provide information and insights that can be used to make informed decisions, draw conclusions, and gain knowledge about a particular subject or phenomenon.

Data plays a crucial role in various fields, including science, business, research, healthcare, and everyday life.One primary purpose of data is to describe and understand the world around us.

By collecting and analyzing data, we can identify patterns, trends, and relationships that exist within a dataset. This helps us gain a deeper understanding of complex systems and phenomena.

For example, in scientific research, data is used to study the behavior of natural processes, investigate the effects of interventions, and formulate theories and models.

Data also serves as a foundation for making informed decisions. By examining relevant data, individuals and organizations can assess the potential outcomes of different choices and select the most optimal course of action.

Data-driven decision-making enables organizations to improve efficiency, identify opportunities, mitigate risks, and enhance overall performance. In fields like marketing and finance, data is extensively used for market research, customer segmentation, trend analysis, and financial forecasting.

Furthermore, data is crucial for monitoring and evaluating performance. By collecting data over time, organizations can track progress, measure outcomes, and identify areas for improvement. Data-driven monitoring allows for evidence-based assessments and adjustments to strategies or interventions.

Overall, the purpose of data is to provide reliable information that can be used to enhance understanding, support decision-making, and drive progress in various domains. It empowers individuals and organizations with the ability to derive insights, solve problems, and make meaningful contributions to society.

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The woman will withdraw $300 given 6%   interest rate annually.

We can use the formula for simple interest to solve this problem:

I = Prt

where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years. Since the interest rate is given as an annual rate, we need to convert it to a daily rate by dividing by 365:

r = 0.06/365 = 0.00016438356

The time in years is 120/365 = 0.3287671233 years. Now we can plug in the values and solve for I:

I = 300 * 0.00016438356 * 0.3287671233 = 0.01699999999

The interest earned is $0.017, which is negligible. Therefore, the woman will withdraw the entire principal plus any interest earned, which is:

300 + 0.017 = $300.02

Rounding to the nearest dollar, the woman will withdraw $300.

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The probability that someone who tests positive for opium use actually uses opium is  0.854  .

In the question ,

it is given that , the false positivity rate is 2% .

Let the sample size be of  100 .

11% of the people actually use opium = 100*0.11 = 11.

People who do not use opium = 100 - 11 = 89.

the test for opium has a 2% false positive , that is

= 2% of 89 = 89*0.02 = 1.78

So , the True negative = 89-1.78 = 87.22

the test for opium has a 5% false negative , that is

= 5% of 11 = 11*0.05 = 0.55

So , the True positive = 11-0.55 = 10.45

Probability is calculated by favorable/total.

Total (positive) = true + false = 10.45 + 1.78 = 12.23  .

Favorable (true) = 10.45

Probability is = 10.45/12.23 = 0.854

Therefore , the required probability is 0.854    .

The given question is incomplete , the complete question is

Suppose that a test for opium use has a 2% false positive rate and a 5% false negative rate. that is, 2% of people who do not use opium test positive for opium and 5% of opium users test negative for opium. furthermore, suppose that 11% of people actually use opium.

Find the probability that someone who tests positive for opium use actually uses opium.

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Answer:

Step-by-step explanation:

An example of time-ordered typical sample statistics is shown in the Control chart. It is used to process the Mean bar.

A control chart is a statistical tool for monitoring the effectiveness of a process over time. It has the form of a graph with two additional lines representing the upper control limit and lower control limit. The central line in the graph represents the mean or average of the data.

Control charts are a type of graph used in production control to assess the effectiveness of exceptional production procedures under challenging circumstances. Control charts are actually the tools used in control strategies. These curves were produced using historical data.

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In order to calculate the x-intercept of the function, we need to find the value of x for y = 0.

In the same way, to calculate the y-intercept we need to find the value of y for x = 0.

So:

So the x-intercept is (5, 0) and the y-intercept is (0, 5).

Now, graphing these two points and the corresponding line between them, we have:

It is noticed that the factors then the x-intercepts are the same value as that of factors.

Given that, the quadratic equation represented on the graph in factored form is y=(x-3)(x+2).

From the graph, x-intercepts are x=-2 and x=3.

The vertex of the given quadratic graph is (0.5, -6)

Therefore, it is noticed that the factors then the x-intercepts are the same value as that of factors.

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Answer:

Length of the hypotenuse = 3√5 units

Step-by-step explanation:

Given:

Right triangle sides

a = 3

b = 6

Find:

Length of the hypotenuse

Computation:

Length of the hypotenuse = √a² + b²

Length of the hypotenuse = √3² + 6²

Length of the hypotenuse = √9 + 36

Length of the hypotenuse = √45

Length of the hypotenuse = 3√5 units

Answer:

125.4

Step-by-step explanation:

Given

\(Number = 125.3546\)

Required

Round to 1 decimal place

Up till the first decimal place, the number is:

\(Number = 125.3\)

The digit after .3 is 5

The conditions for approximation are:

In this case: 5 > 4, so we approximate to 1

Add this "1" to the last digit of 125.3. This becomes 125.4

Hence: when the number is approximated to 1 decimal place, the digit is 125.4

Answer:

rbghjkieknwhbkhw2l1;p

Step-by-step explanation:

The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

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Answer:reflection image of the other

Source:trust me bro

Valor inicial: 48 pulgadas

incremento : 25 %

Multiplica el valor inicial por el incremento en forma decimal. (dividido por 100)

48 x (25/100) = 48 x 0.25 = 12 pulgadas

Suma el incremento al valor inicial.

48+12 = 60 pulgadas

Los tallos tienen una altura de 60 pulgadas ahora.

Answer:

Step-by-step explanation:

Q3 asks for reasons of statements in a theorem proof.

1 Given is correct

2 Definition of right angle is correct

3 should be sum of interior angles in a triangle

4 is substitution

5 subtracting 90degree from left and right hand side

6 is definition of complementary

x=16/3

10=3x-6

10+6=3x-6+6

10+6=3x-6+6

16=3x-6+6

16=3x-6+6

16=3x

16/3 3x/3

16/3 3x/3

16/3

\(12 \frac{2}{5}=\frac{62}{5}\\\\\frac{62/5}{1/4}=4\left(\frac{62}{5} \right)=\frac{248}{5}=\boxed{49 \frac{3}{5}}\)

Answer:

Step-by-step explanation:

37

Answer:

Listed below.

Step-by-step explanation:

(Let y be the length of the room and x be the width of the room.)

Because the width of the room is 5 feet less than the length of the room, we have:

The area of the room can be solved by multiplying its length and width, so we have x × y or xy = 750.

Substituting x for y - 5 into this equation:

If we expand the left side of the equation, we get:

Subtracting 750 from both sides, we get:

The equation \(y^{2}\) - 5y - 750 = 0 can be factored into:

Therefore, 3 equations you can use are:

Answer:

y = -3x -10

Step-by-step explanation:

The slope will be the reciprocal which is -3x

y=-3x+a

-10=-3(0) +a

-10=0 + a

a=-10

y= -3x -10

The equation for a line that is perpendicular to the line y=-1/3x and passes through the point (0,-10) is y = 3x - 10

A linear equation is of the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept

Two lines are perpendicular if the product of their slopes is -1. That is the slope of one line is the negative inverse of the other line.

The slope of the line perpendicular to  y=-1/3x is 3. Since it passes through the point (0,-10), hence:

\(y-y_1=m(x-x_1)\\\\y-(-10)=3(x-0)\\\\y+10=3x\\\\y=3x-10\\\)

Hence the equation for a line that is perpendicular to the line y=-1/3x and passes through the point (0,-10) is y = 3x - 10

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Given

The least-squares regression line that describes this relation is y= -0.0579x + 2.9408.

(a) Predict the grade-point average of a student who plays video games 8 hours per week.

The predicted grade-point average is

Procedure

We have information from the linear regression model as a function of the number of hours played.

Where x = 8 hours

the predicted grade-point average of a student who plays video games 8 hours per week is 2.4776

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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The expression for the total cost of Sal's purchases is 7x + 5y cents.

We know that Sal paid (x + 2y) cents for a quart of milk and (2x + y) cents each for three cartons of orange juice.To find the total cost of Sal's purchases we need to add the cost of the milk and the cost of the three cartons of orange juice and simplify the expression.The cost of the milk is given as (x + 2y) cents. The cost of three cartons of orange juice is (2x + y) cents each.

Therefore, the cost of three cartons of orange juice is (3 × (2x + y)) cents. To find the total cost of Sal's purchases, we add the cost of the milk and the cost of the three cartons of orange juice.(x + 2y) + (3 × (2x + y)) cents = x + 2y + 6x + 3y cents= 7x + 5y cents.

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Complete Question

A researcher is funded to obtain an estimate for the population proportion of smokers who have tried using e-cigarettes. She plans to interview 100 smokers. Previous studies have estimated that 20% of smokers have tried e-cigarettes. She finds that 23% of smokers have tried e-cigarettes.

Which of the following is correct?

A

0.23 is the population proportion

B

The margin of error for a 95% confidence interval is 8%

C

The standard error of the sample proportion is 0.177

D

This is a biased estimate because it is based on smokers none of the above

Answer:

The correct option is  B

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  100

     The  population proportion is  p =  0.20

      The sample proportion is  \(\r p = 0.23\)

Generally the standard error is mathematically represented as

        \(SEp = \sqrt{\frac{\r p(1 - \r p)}{n} }\)

=>     \(SEp = \sqrt{\frac{0.23 (1 - 0.23)}{100} }\)

=>     \(SEp = 0.04208\)

Generally for a 95% confidence level is level of significance is

      \(\alpha = (100 - 95)\%\)

      \(\alpha = 5\%\)

     \(\alpha = 0.05\)

Now the critical value  of  \(\frac{\alpha }{2}\) obtained from the normal distribution table is  

     \(Z_{\frac{\alpha }{2} } = 1.96\)

Generally the percentage margin of error is mathematically represented as

      \(E = Z_{\frac{\alpha }{2} } * SE_p * 100\)

     \(E = 1.96* 0.04208 * 100\)

     \(E = 8\%\)

Answer:

x = 11/2

Step-by-step explanation:

\( = > \frac{2}{3} x + \frac{1}{3} = 4 \)

\( = > \frac{2}{3} x = 4 - \frac{1}{3} \)

→Take the LCM

\( = > \frac{2}{3} x = \frac{12 - 1}{3} \)

\( = > \frac{2}{3} x = \frac{11}{3} \)

\( = > x = \frac{11 \times 3}{3 \times 2} \)

\( = > x = \frac{11}{2} \)

Answer:  9c²

Step-by-step explanation:

To find the Greatest Common Factor of 207c³ and 108c², first factor them down to their primes and see what they have in common.

                207c³                     108c²

                 ∧   ∧                        ∧  ∧

             9·23  c·c·c              9·12   c·c

            ∧                            ∧  ∧

           3·3                         3·3 3·4

                                                  ∧

                                                 2·2

207c³: 3·3·23  c·c·c

108c²:  2·2·3·3·3·4 c·c

GCF = 3·3 c·c

        = 9c²

The GCF of 207c^3 and 108c² is 9c²

Given the expressions \(207c^3 \ and \ 108c^2\)

We are to find the GCF of both terms

First, we need to get the factors as shown::

207c³ = 9 * 23 * c² * c

108c² =  9 * 12 * c²

From the factors, we can see that 9 and c² are common to both terms:

The GCF of 207c^3 and 108c² is 9c²

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