Travel and Transportation A recent report by AAA estimated that 88 million Americans, and in particular 44% of millennials, are planning to take a family trip in 2018. Liberty Travel would like to determine if a different proportion of baby boomers are planning to take a trip. State the null and the alternative hypotheses in terms of the population proportion of baby boomers who are planning to take a family trip.

The sample size (n) needed can be calculated using

\(0.025 =2.33\sqrt{\frac{0.79*0.21}{n} }\).

Given:

We have the following confidence interval of proportions in a sample of n people who were polled, with a success probability of \(\pi\) and a confidence level of \(1- \alpha\).

π ± \(z\sqrt{\frac{\pi (1-\pi )}{n} }\)

Here z is the z score which has a pvalue of

\(1 -\alpha /2\)

The margin of error is given as:

\(M = z\sqrt{\frac{\pi (1-\pi )}{n} }\)

79 percent of adults age 18 years and older in the United States use the Internet as found by a survey.

So, \(\pi =0.79\)

98% confidence level

Now \(\pi =0.02\), z is the value of Z that has a pvalue of  \(1-\frac{0.02}{2} =0.99\).

So, Z =2.33.

The sample size (n) needed can be estimated using:

We have to find n for which M = 0.025

The required equation is:

\(M =z\sqrt{ \frac{\pi (1-\pi )}{n} }\)

\(0.025 = 2.33\sqrt{\frac{0.79*0.21}{n} }\)

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If a customer purchases 3 of the products, the probability of getting at least one that is defective is 38.59%.

In order to determine the probability of getting at least one defective product if a customer purchases three products with a defective rate of 7.5%, we can use the concept of complementary probability.

The probability of getting at least one defective product can be calculated as the complement of the probability of getting none defective products.

So, the probability of getting no defective products is:

P(none defective) = (1 - 0.075)³ = 0.6141

Therefore, the probability of getting at least one defective product is:

P(at least one defective) = 1 - P(none defective) = 1 - 0.6141 = 0.3859 or 38.59%

.So, the probability of getting at least one that is defective is 38.59%.

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Thus, the number of significant figures, the solubility of O2 in water is 2.3 x 10^-4 M.

To calculate the solubility of O2 in water, we can use Henry's law, which states that the concentration of a gas in a solution is directly proportional to its partial pressure above the solution.

First, we need to find the partial pressure of O2 in air:

partial pressure of O2 = mole fraction of O2 x total pressure
partial pressure of O2 = 0.21 x 0.83 atm
partial pressure of O2 = 0.1743 atm

Next, we can use Henry's law:

[O2] = kh x partial pressure of O2
[O2] = (1.3 x 10^-3 m/atm) x (0.1743 atm)
[O2] = 2.2629 x 10^-4 M

Rounding to the appropriate number of significant figures, the solubility of O2 in water is 2.3 x 10^-4 M.

Therefore, the correct answer is 2.3 x 10^-4 M.

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EXPLANATION

We are asked to describe the translation of the functions with respect to f(x) =x

To translate the function up and down, you simply add or subtract numbers from the whole function. If you add a positive number (or subtract a negative number), you translate the function up. If you subtract a positive number (or add a negative number), you translate the function down.

In function notation, to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.

To do so, we will have to plot the graph of each function and compare it with f(x) represented by the red lines below

Part A

Thus, we will have

For part B

when

The translation here is

Part C

For the function

The graph is

Thus, we have the translation as A horizontal shift to the left by 2 units

Part D

The given function is

The transformed graph is

The translation is a shift to the right by 7.5 units

Answer:

D

Step-by-step explanation:

the definition of \(\left[\begin{array}{ccc}n\\k\\\end{array}\right]\)

= \(\frac{n!}{k!(n-k)!}\)

After one time constant has passed, 63.2% of the initial potential remains. After two time constants, 36.8% of the initial potential remains. After three time constants, 13.5% of the initial potential remains.


The time constant (τ) is a measure of how quickly a system reaches equilibrium or returns to its initial state after a disturbance. It is commonly used in electronics and other fields to describe the behavior of circuits, systems, and processes.

The equation for the percentage of initial potential remaining after a time constant is:

Percentage remaining = 100 * e^(-t/τ)

Where t is the time elapsed and τ is the time constant.

After one time constant (t = τ), the equation becomes:

Percentage remaining = 100 * e^(-1) = 63.2%

After two time constants (t = 2τ), the equation becomes:

Percentage remaining = 100 * e^(-2) = 36.8%

After three time constants (t = 3τ), the equation becomes:

Percentage remaining = 100 * e^(-3) = 13.5%

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c.

Step-by-step explanation:

you can check the the correct answer by giving tables value for eg f(x)= 2 g(f(x))= 1/2(2)²=2

as you can see in the graph g(x) (2,2)

Answer:

\(5x^{2}(x+7)(x-3)\)

Step-by-step explanation:

5x4+20x3-105x2

5x2( x^2 +4x -21)

\(5x^{2}(x+7)(x-3)\)

The perimeter of circle having radius 13 meter is 40.82 meter

Given that

Diameter of circle = 13 meters

We know that,

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.

Since we also know that,

Radius of circle is half of diameter,

Therefore,

Radius = r = 13/2

                 =  6.5 meters

Since, we know that,

Circumference of circles is = 2πr

                                             = 2x3.14x6.5

                                             = 40.82 meter

Hence perimeter = 40.82 meter

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The correct steps that best describe the scientific method are:

The scientific method has five basic steps, plus one feedback step:

The scientific method is a systematic approach to scientific inquiry that involves a series of steps used to investigate, test, and understand natural phenomena

The process of the scientific method involves making conjectures (hypotheses), deriving predictions from them as logical consequences, and then carrying out experiments or empirical observations based on those predictions.

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:a. sec(β) = `6/11`b. sin (β) = `5/6`c. Cot(β) = `2.01` (approximately)d. Sin(β - 90˚) = `√11/6` = `0.95` (approximately) are the exact values of each indicated trigonometric function.

Given function value is `cos(β) = √11/6` where `0˚ ≤ β ≤ 90˚` and `0 ≤ β ≤ π/2`.

To find the exact value of each indicated trigonometric function, we need to first find sin(β), tan(β), cos(β), csc(β), sec(β), and cot(β) where `0˚ ≤ β ≤ 90˚` and `0 ≤ β ≤ π/2`.

We know that `sin²(β) + cos²(β) = 1`.So, `sin(β) = ± √(1 - cos²(β))`Since `0˚ ≤ β ≤ 90˚`, `sin(β) = √(1 - cos²(β))`Now, `sin(β) = √(1 - (√11/6)²)`  = √(1 - 11/6)  = √(6/6 - 11/6)  = √(-5/6)

Since the value of β lies in the first quadrant, sin(β) is positive. Therefore, `sin(β) = √(5/6)`We also know that `tan(β) = sin(β)/cos(β)`.So, `tan(β) = (√(5/6))/((√11)/6)`

Now, `tan(β) = (6√5)/11`Similarly, we can find the values of all other trigonometric functions.a. sec(β) = `1/cos(β)` = `1/(√11/6)` = `6/√11` = `6/11`b. sin (β) = `√(5/6)` = `5/6`c. Cot(β) = `1/tan(β)` = `1/((6√5)/11)` = `11/(6√5)` = `(11/6) * (1/√5)` = `11/(6√5)` * `(√5/√5)` = `(11√5)/30` = `(11/5.48)` = `2.01` (approximately)d. Sin(β - 90˚) = `cos(β)` = `√11/6`

Therefore, the exact value of each indicated trigonometric function is:a. sec(β) = `6/11`b. sin (β) = `5/6`c. Cot(β) = `2.01` (approximately)d. Sin(β - 90˚) = `√11/6` = `0.95` (approximately).

Therefore, the options (a), (b), (c), and (d) are (6/11), (25/36), (11/5), and (11/6) respectively.

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Answer:

Step-by-step explanation:

According to the ratio:

Josh has 9 sweets less than John.

Use the difference to find the value of x:

John has:

a set is a collection of distinct objects, considered as an entity on its own

To find the requested operations on the given relations, let's evaluate each one:

(a) R²: To find the composition of R with itself, we need to find all pairs (x, z) such that there exists a y in A for which (x, y) ∈ R and (y, z) ∈ R.

R² = {(a, d), (b, e), (c, d), (d, e)}

(b) R · S: To find the composition of R and S, we need to find all pairs (x, z) such that there exists a y in A for which (x, y) ∈ R and (y, z) ∈ S.

R · S = {(a, a), (b, a), (b, c), (b, d), (c, a), (c, c), (d, a), (d, b), (d, d)}

(c) S · R: To find the composition of S and R, we need to find all pairs (x, z) such that there exists a y in A for which (x, y) ∈ S and (y, z) ∈ R.

S · R = {(b, b), (b, d), (d, a), (d, b), (d, d), (e, b)}

(d) The reflexive closure of R: To obtain the reflexive closure of R, we need to add pairs (x, x) for all x in A that are not already in R.

Reflexive closure of R = {(a, b), (b, d), (c, b), (d, e), (d, d), (e, e)}

(e) The symmetric closure of R: To obtain the symmetric closure of R, we need to add the reverse pairs for all existing pairs in R.

Symmetric closure of R = {(a, b), (b, a), (b, d), (c, b), (d, b), (d, e)}

(f) The transitive closure of R: To obtain the transitive closure of R, we need to add pairs (x, z) such that there exists a y in A for which (x, y) and (y, z) are already in R, or there is a sequence of pairs in R that connect x to z.

Transitive closure of R = {(a, b), (a, d), (b, b), (b, d), (b, e), (c, b), (c, d), (d, d), (d, e), (e, e)}

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Answer:

The graph of the horizontal parabola is not a function.

Step-by-step explanation:

A function is a relation in which no two ordered pairs have the same input (or x-values) and different outputs (y-values).

Remember that a function can only take on one output for each input.

The Vertical Line Test allows us to know whether or not a graph is actually a function.  If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.  

As you can see on the attached screenshot, each vertical line crossed the graph more than once (as evidenced by the two green dots per vertical line).  Therefore, the graph does not represent a function of x because the indicated value of x is paired with two y-values. Graphically, this means that a vertical line intersects the graph more than once.

For example, the input value, x = 9, has two corresponding output values: y = 3, and y = -3. The same thing goes with the other plotted points and vertical lines drawn.

Therefore, the graph does not represent a function.        

The correct response is d) All the above. The arithmetic mean is equal to the median, the median is equal to the mode, and the mode is equal to the arithmetic mean.

If the data are graphed symmetrically, the distribution demonstrates 0% skewness regardless of how long or fat the tails are. When the median of a data set is utilized, 50% of the data points in the collection have values lower than or equal to the median, and 50% of them have values greater than or equal to the median. The middle score in the set is known as the median. The first step in calculating the median is to order the data points from smallest to greatest. The median in an odd-numbered set will be the value that falls exactly in the middle of the list. You must determine the average of the two middle numbers in a set of even numbers. The average is determined by summing up each value individually and dividing that sum by the total number of observations.

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a) Given statement: skipped : I'm not sure what statement you're referring to, as there is no statement labeled "a" in  question.

Hence answer provided.

b) As the degrees of freedom increase, the t distribution curve does become more similar to the standard normal curve.

True. Because the t distribution resembles the normal distribution when the degrees of freedom are high.

c) The two mean non-pooled test is used for 2 independent populations under the assumption that the two populations have different standard deviations.

False - Because the non-pooled t-test can be used to compare the means of the two populations when the assumption of equal variances is true.

d) The standard error is the standard deviation of the sampling distribution and is calculated by dividing the sample standard deviation by the square root of the sample size.

False - Because the standard error, which is determined as the sample standard deviation divided by the square root of the sample size, is a measure of the variability of the sample mean.

a)  Given statement: skipped : I'm not sure what statement you're referring to, as there is no statement labeled "a" in  question.
b) Given statement : As the degrees of freedom increase, the t distribution curve does become more similar to the standard normal curve.

The given statement is true.

Because, When the degrees of freedom are large, the t distribution approaches the standard normal distribution.
c) Given statement: The two mean non-pooled test is used for 2 independent populations under the assumption that the two populations share the same standard deviation.

The given statement is true.

Because, When the assumption of equal variances is met, the non-pooled t-test can be used to compare the means of the two populations.
d)  Given statement: The standard error is not always equal to the sample standard deviation.  

The given statement false.

Because, The standard error is a measure of the variability of the sample mean, and it is calculated as the sample standard deviation divided by the square root of the sample size.

The sample standard deviation is a measure of the variability within the sample itself.

The standard error tends to be smaller than the sample standard deviation because it accounts for the effect of the sample size on the variability of the sample mean.

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Answer:43.289

Step-by-step explana

The probability that X is greater than 145.28 is approximately 0.0465.

Given that X is normally distributed with mean (μ) of 110 and standard deviation (σ) of 21. We are to find the probability that X is greater than 145.28. It can be calculated as follows: We can calculate the Z-score value with the help of the following formula, Z = (X - μ) / σWhere X is the random variable value, μ is the mean, and σ is the standard deviation. Substituting the values in the formula, we get: Z = (145.28 - 110) / 21Z = 1.68476 Using the Z-table, we can find the probability that X is greater than 145.28 as follows: From the Z-table, we get: P(Z > 1.68) = 0.0465

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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The area of the customer's yard is 580π.

The distance formula is given as -

d = √(x₂ - x₁)² + (y₂ - y₁)²

Given is that this grid represents the customer’s yard. The bottom left corner is the origin point  O(0, 0), and the x- and y- axes represent the two fences. The rose bush is at point P(16, 18).

We can write the area of the customer's yard -

A = πr²

Here -

r = d

r² = d²

We can write -

A = πd²

A = π {(x₂ - x₁)² + (y₂ - y₁)²}

A = π{16 x 16 + 18 x 18}

A = 580π

Therefore, the area of the customer's yard is 580π.

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The critical value for the 0.05 level of significance is k = 21.

To find the critical value, we can use the binomial distribution. The binomial distribution models the number of successes in n independent Bernoulli trials, each with probability p of success. In this case, the number of successes is the number of dog owners who say Woof Chow is their regular brand, and the number of trials is n = 100. The null hypothesis is that the true market share of Woof Chow is 25%, and the alternative hypothesis is that it is not 25%.

We can use the binomial cumulative distribution function (CDF) to find the critical value. The CDF gives the probability of getting k or fewer successes in n trials, given a probability of success p. The critical value is the smallest value of k such that the CDF at k is greater than or equal to 1 - alpha, where alpha is the level of significance. In this case, alpha = 0.05.

So, we want to find the smallest k such that:

P(X <= k) >= 1 - 0.05

where X is a random variable representing the number of dog owners who say Woof Chow is their regular brand. We can use a binomial calculator or a software package to calculate the binomial CDF, or we can use a table of critical values for the binomial distribution.

The critical value for the 0.05 level of significance is k = 21. This means that if the true market share of Woof Chow is 25%, then the probability of getting 23 or more dog owners who say Woof Chow is their regular brand is less than 0.05. Since the observed number of dog owners who say Woof Chow is their regular brand is 23, which is greater than 21, we can reject the null hypothesis that the true market share is 25%.

This means that based on the survey results, we cannot conclude that Woof Chow has a market share of 25%. The survey results suggest that Woof Chow may have a market share that is greater than 25%.

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The length of the circular arc is s = 20.106.

To find the length of the circular arc, we use the formula s = rθ, where s is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.

First, we need to convert the central angle from degrees to radians. We can do this by multiplying the angle in degrees by π/180:

θ = 128° × π/180 = 2.234 radians

Next, we can plug in the values of r and θ into the formula:

s = rθ = 9 × 2.234 = 20.106

Therefore, the length of the circular arc is s = 20.106.

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Answer:

Step-by-step explanation:

-17+n/5 = 33

+17          +17

n/5 = 50

x 5    x 5

n = 250

-17+250/5 = 33

-17 + 50 = 33

Solution:

Given:

To calculate the surface area of a rectangular prism, the formula below is used:

Substituting the given values into the formula:

Therefore, the correct answer is OPTION C.

Answer:

570 86/1000

Step-by-step explanation:

decimal goes into thousandths place

570 is a whole number

simplified is 570 43/500

(5×100)+(7×10)+(8×.010)+(6×.001)

Hopefully this the correct answer 15 percent I am not sure

Step-by-step explanation:

Answer:

c.

Step-by-step explanation:

From the last row in the matrix z = 1.

From the second row:

y + 5z = -4

y = -4 -5(1) = -9.

From the first row:

x + -1 = -3

x = - 3 + 1

x = -2.