There are 60 seats on a train. 35% of the seats are empty. How many empty seats are there on the train?

The domain of the function shown in the graph is the one in option A:

6 ≤ k ≤ 11

The domain of a function y = f(x) is the set of the inputs of the function. To identify the domain in a graph, we need to look at the horizontal axis (also called the x-axis).

On the graph we can see that it starts at x = 6 with a closed dot, and it ends at x = 11 also with a closed dot.

That means that these values belong to the domain, so we can write the domain as follows:

Domain = 6 ≤ k ≤ 11

(notice that the variable in the horizontal axis is k).

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Answer: D.

Step-by-step explanation:

Using a 0.05 significance level to test a claim that UFO sightings occur in different seasons with the proportions listed in the table the test statistic x² needed to test the claim is 11.562. The correct option is B.

To test the claim that UFO sightings occur in different seasons with the proportions listed in the table, we can use a chi-square goodness-of-fit test.

The null hypothesis is that the observed frequencies in each season are equal to the expected frequencies based on the proportions listed in the table.

The expected frequency for each season can be calculated by multiplying the total number of sightings by the proportion listed in the table. For example, the expected frequency for spring is:

Expected frequency for spring = Total number of sightings × Proportion for spring

= 420 × 0.25

= 105

Similarly, the expected frequencies for summer, fall, and winter are 126, 210, and 105, respectively.

The chi-square test statistic can be calculated as:

χ² = ∑ [(O - E)² / E]

where O is the observed frequency and E is the expected frequency.

Using the observed frequencies from the table and the expected frequencies calculated above, we get:

χ² = [(150-105)²/105] + [(120-126)²/126] + [(100-210)²/210] + [(50-105)²/105]

   = 11.562

The degrees of freedom for the chi-square test is (number of categories - 1), which in this case is 4 - 1 = 3.

Using a chi-square distribution table with 3 degrees of freedom and a significance level of 0.05, the critical value is 7.815.

Since the calculated chi-square value (11.562) is greater than the critical value (7.815), we reject the null hypothesis and conclude that there is evidence of a difference in UFO sightings across seasons. Therefore, the test statistic x² needed to test the claim is 11.562.

The correct answer is (B) 11.562.

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The symbol ∪ represents the "union of events" in the context of probability and set theory.

The symbol ∪ indicates the union of events. This option corresponds to choice (d) in your given list. The union of events refers to the occurrence of at least one of the events in question. In other words, it combines the outcomes of two or more events into a single set, without any repetitions. This concept is essential in understanding probability theory, as it helps to analyze the likelihood of different events happening together or separately.

This means that it represents the set of all outcomes that belong to either one or both of the events being considered. For example, if event A represents rolling an even number on a die and event B represents rolling a number greater than 4, then the union of events A and B would be the set of outcomes {2, 4, 5, 6}. It is important to note that the union of events is different from the intersection of events, which represents the set of outcomes that belong to both events being considered. The sample space, on the other hand, represents the set of all possible outcomes of an experiment. Finally, the symbol ∑ represents the sum of probabilities of events, not the symbol ∪.

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Let A ∈ R^(nxn) and let C ∈ R^(nxm). We will prove the following:

(1) Assume A is positive semidefinite. We need to show that tr(A) = 0 if and only if A = 0.

Proof:

(i) If A = 0, then tr(A) = 0 since the trace of the zero matrix is 0.

(ii) Assume tr(A) = 0. Recall that A is positive semidefinite, which means that its eigenvalues are non-negative. Since the trace of a matrix is the sum of its eigenvalues, having tr(A) = 0 implies that all eigenvalues of A must be zero. Consequently, A is a diagonal matrix with all diagonal elements equal to 0. Therefore, A = 0.

Thus, we have shown that tr(A) = 0 if and only if A = 0.

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The angle is 86.8 degrees and its complement is 3.2 degrees.

let x be the angle and y be the Complementary angle.

If the angles are complementary, then their sum is 90 degrees.

x + y = 90................(1)

and, the angle measures 83.6 degrees more than its complement.

x = y + 83.6

y + 83.6 + y = 90

Solving the equation for y we get

2y + 83.6 = 90

2y = 90 - 83.6

2y = 6.4

y= 3.2

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The 40% clearance discount is already factored into the clearance price of $30, so applying the 20% coupon only reduces the price further by 20% of $30, or $6. Therefore, you would pay $24 for the item with both discounts applied.

Let's break down the discounts and calculate the final price of the item using the terms "normal", "price", and "quantitatively".
The normal price of the item: $50

First, apply the 40% clearance discount:
40% off the normal price = 0.4 * $50 = $20

Subtract the clearance discount from the normal price:
New discounted price = $50 - $20 = $30

Now, apply the 20% off coupon to the discounted price:
20% off the new discounted price = 0.2 * $30 = $6

Quantitatively, the calculation would be:
Normal price = $50
Clearance price (40% off) = $30
Coupon discount (20% off clearance price) = 0.20 x $30 = $6
Final price = $30 - $6 = $24

Subtract the coupon discount from the discounted price:
Final price = $30 - $6 = $24

So, you should pay $24 for the item. It is not the same as taking 60% off the normal price because the discounts are applied sequentially, not combined. Quantitatively, you can see that taking 60% off the normal price would result in a $30 discount ($50 * 0.6), while the actual total discount here is $26 ($20 + $6).

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The constant of proportionality is equal to the unit rate in a proportional relationship. The unit rate for Bolin's tai chi classes is 16.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios or unit rates, and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

In Mathematics, the unit rate is sometimes referred to as unit price or unit ratio and it can be defined as the price that is being charged by a seller for the sale of a single unit of product or quantity, especially in a proportional relationship:

Constant of proportionality, k = y/x

Constant of proportionality, k = 16.

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Answer:

77 cm^2

Step-by-step explanation:

rectangular prism or cuboid

Right rectangular prism Solve for surface area▾

A = 77

L = 2

w = 3

h = 6.5

A=2(wl+hl+hw) = 2.(3.2+6.5.2+6.5.3)=77

chegg

(a) The function f(x) = 0.2, 1 < x < 6 is a probability distribution function (pdf) because it is non-negative for all x in its domain and the total area under the curve is equal to 1.

(b) The cumulative distribution function (cdf) F(x) for 1 < x < 6 is given by F(x) = 0.2(x-1), where F(x) = 0 for x ≤ 1 and F(x) = 1 for x ≥ 6.

(c) The probability P(2 < X < 4) is 0.4, which can be calculated by integrating the pdf f(x) = 0.2 over the interval [2, 4].

(d) The probability P(X > 4) is 0.6, which is obtained by subtracting the cumulative probability F(4) = 0.2(4-1) from 1.

(a) To show that f(x) = 0.2, 1 < x < 6 is a probability distribution function (pdf), we need to show that:

f(x) is non-negative for all x in its domain: f(x) = 0.2 is non-negative for all x between 1 and 6.

The total area under the curve of f(x) is equal to 1:

∫1^6 0.2 dx = 0.2(x)|1^6 = 0.2(6-1) = 1

Since both conditions are satisfied, f(x) is a pdf.

(b) The cumulative distribution function (cdf) F(x) is given by:

F(x) = ∫1^x f(t) dt

For 1 < x < 6, we have:

F(x) = ∫1^x 0.2 dt = 0.2(t)|1^x = 0.2(x-1)

For x ≤ 1, F(x) = 0, and for x ≥ 6, F(x) = 1.

(c) P(2 < X < 4) is given by:

P(2 < X < 4) = ∫2^4 f(x) dx = ∫2^4 0.2 dx = 0.2(x)|2^4 = 0.4

(d) P(X > 4) is given by:

P(X > 4) = 1 - P(X ≤ 4) = 1 - F(4) = 1 - 0.2(4-1) = 0.6

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The modification to a research study that will result in a narrower confidence interval is option D is correct choice

The modification to a research study that will result in a narrower confidence interval is option D: decreasing the confidence level and increasing the sample size. By decreasing the confidence level, we are willing to accept a lower level of certainty in our results, which can lead to a narrower interval. Increasing the sample size also leads to a narrower interval as it reduces the variability in our data and increases the precision of our estimates.

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Answer:  B

Step-by-step explanation:

If you fold that bottom side up.  the door is not on the closer side to the window. so B is wrong because the door is near the window.

Answer: a. true

b. true

c. false

d. true

Step-by-step explanation:

The energy for vacancy formation per atom in the metal M is 0.91 eV/atom.

To calculate the energy (in eV/atom) for vacancy formation in the metal M, we can use the following formula:

E_v = RT * ln(N_v/N)

Where:
- E_v is the energy for vacancy formation per atom
- R is the gas constant (8.314 J/mol*K or 0.008314 eV/mol*K)
- T is the temperature in Kelvin (317°C = 590K)
- N_v is the equilibrium number of vacancies (6.67 × 10^23 m^-3)
- N is the number of atoms per unit volume, which can be calculated using the density and atomic weight of the metal as follows:

N = (6.40 g/cm^3) * (1 mol/27.00 g) * (6.022 × 10^23 atoms/mol) = 1.51 × 10^22 atoms/m^3

Plugging in these values, we get:

E_v = (0.008314 eV/mol*K) * (590 K) * ln(6.67 × 10^23 m^-3 / 1.51 × 10^22 atoms/m^3)
E_v = 0.91 eV/atom

Therefore, the energy for vacancy formation per atom in the metal M is 0.91 eV/atom.

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The rule for the nth term of the geometric sequence is given as follows:

[tex]a_n = 2^n[/tex]

Hence the 10th term of the sequence is given as follows:

1024.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

[tex]a_n = a_0q^{n}[/tex]

In which [tex]a_0[/tex] is the first term.

The parameters in this problem are given as follows:

Hence the rule is given as follows:

[tex]a_n = 2^n[/tex]

Hence the 10th term of the sequence is given as follows:

2^10 = 1024.

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We can conclude that the system represented by the given Gauss-Jordan elimination has infinitely many solutions, and the values of the variables can be expressed in terms of a free variable x4.

The Gauss-Jordan elimination is a method used to solve a system of linear equations. The final step of the method is to transform the augmented matrix of the system into reduced row echelon form, which allows for easy identification of the solution(s) of the system.

In the given final step of the Gauss-Jordan elimination, the augmented matrix of the system is represented as:

11 0 0 51

0  1 0 21

0  0 1 -3

0  0 0  0

The augmented matrix is in reduced row echelon form, where the leading coefficients of each row are all equal to 1, and there are no other non-zero elements in the same columns as the leading coefficients. The last row of the matrix corresponds to the equation 0 = 0, which represents an identity that does not provide any new information about the system.

The system represented by this matrix is:

11x1 + 51x4 = 0

x2 + 21x4 = 0

x3 - 3x4 = 0

We can see that the third row of the matrix corresponds to an equation of the form 0x1 + 0x2 + 0x3 + 0x4 = 0, which indicates that the variable x4 is a free variable. This means that the system has infinitely many solutions, and the value of x4 can be chosen arbitrarily.

The values of x1, x2, and x3 can be expressed in terms of x4 using the equations given by the first three rows of the matrix. For example, we can solve for x1 as follows:

11x1 + 51x4 = 0

x1 = -51/11 x4

Similarly, we can solve for x2 and x3:

x2 = -21 x4

x3 = 3 x4

Therefore, the general solution of the system is:

x1 = -51/11 x4

x2 = -21 x4

x3 = 3 x4

x4 is a free variable

In summary, we can conclude that the system represented by the given Gauss-Jordan elimination has infinitely many solutions, and the values of the variables can be expressed in terms of a free variable x4.

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The answer is not one of the choices provided.

The distribution of sample means follows a normal distribution with a mean equal to the population mean (11) and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

So, for a sample size of 35, the distribution of sample means is normal with a mean of 11 and a standard deviation of 4.7/sqrt(35) = 0.795.

We need to find the probability that the mean blood pressure of the 35 people will be less than 122. We can standardize the distribution of sample means to a standard normal distribution with mean 0 and standard deviation 1 using the z-score formula:

z = (x - mu) / (sigma / sqrt(n))

where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

z = (122 - 11) / (4.7 / sqrt(35)) = 37.98

We can then use a standard normal distribution table or calculator to find the probability of z being less than 37.98. Since the standard normal distribution is symmetric, we can also find this probability as 1 minus the probability of z being greater than 37.98.

Using a standard normal distribution table or calculator, we get:

P(z < 37.98) = 1 (to a very high degree of precision)

Therefore, the probability that the mean blood pressure of 35 people will be less than 122 is essentially 1, or 100%. The answer is not one of the choices provided.

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The experimental probability of rolling a number greater than 4 is 18/60

It will be given by the number of times that the outcome was greater than 4 (so a 5 or a 6) over the total number of trials.

We can see that the total number of trials is 60, and we have:

Adding that: 10 + 8 = 18

Then the experimental probability of a number greater than 4 is:

E = 18/60

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The rule for the composed transformation formed by the translation 8 units right and 5 units down followed by a 180 degree rotation is (x, y) --> (8-x, -5-y)

The rule for the transformation formed by the translation 8 units right and 5 units down followed by a 180-degree rotation can be determined by considering the effect of each transformation separately and then composing them.

First, let's consider the effect of the translation. A translation moves every point in the plane a certain distance in a certain direction. In this case, we are translating 8 units to the right and 5 units down. So, if we have a point (x, y), the translated point will be (x+8, y-5).

Next, let's consider the effect of the 180-degree rotation. A rotation of 180 degrees flips a figure around a line of symmetry, which in this case would be the point where the horizontal line passing through the midpoint of the translation intersects the vertical line passing through the midpoint of the translation. This point is (4, -2.5).

Thus, if we start with a point (x, y), the effect of the translation is to move it to (x+8, y-5), and the effect of the rotation is to flip it around the point (4, -2.5). Therefore, the rule for the composed transformation is:

(x, y) --> (x+8, y-5) --> (8-x, -5-y)

In other words, to apply this transformation to a point, we first translate it 8 units right and 5 units down, and then we reflect it across the point (4, -2.5).

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Complete question is:

What is the rule for the transformation formed by the translation 8 unitys right and 5 units down followed by a 180 degree rotation , assuming the initial point as (x,y)?

The approach to showing uniform continuity will depend on the specific function and domain given.

Without a given function and domain, I cannot provide a specific answer. However, I can provide a general approach to determining whether a function is uniformly continuous on a given domain.

To show that a function is uniformly continuous on a domain, we need to show that for any ε > 0, there exists a δ > 0 such that for any x, y in the domain with |x - y| < δ, we have |f(x) - f(y)| < ε.

One approach to showing uniform continuity is to use the theorem that a continuous function on a closed and bounded interval is uniformly continuous (the Extreme Value Theorem and Corollary). This means that if the domain of the function is a closed and bounded interval, and the function is continuous on that interval, then it is uniformly continuous on that interval.

Another approach is to use the Intermediate Value Theorem. If we can show that the function satisfies the conditions of the Intermediate Value Theorem on the given domain, then we can conclude that the function is uniformly continuous on that domain. The Intermediate Value Theorem states that if f is continuous on a closed interval [a, b], and if M is a number between f(a) and f(b), then there exists a number c in [a, b] such that f(c) = M.

To use the Intermediate Value Theorem to show uniform continuity, we need to show that for any ε > 0, there exists a δ > 0 such that for any x, y in the domain with |x - y| < δ, we have |f(x) - f(y)| < ε/2. Then, using the Intermediate Value Theorem, we can show that for any M such that |M - f(x)| < ε/2, there exists a number c in the domain such that f(c) = M. Combining these two results, we can show that for any ε > 0, there exists a δ > 0 such that for any x, y in the domain with |x - y| < δ, we have |f(x) - f(y)| < ε.

Overall, the approach to showing uniform continuity will depend on the specific function and domain given.

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The average sales for that period is 1375.

The average, also known as the mean, is a statistical measure that represents the central tendency of a set of values. It is calculated by summing up all the values in a dataset and dividing the sum by the total number of values.

Mathematically, the average (mean) is calculated as:

Average = (Sum of all values) / (Total number of values)

To calculate the average sales for the given period, you'll need to follow these steps:

1. Add up the daily sales figures: 1000 + 1200 + 1300 + 2000 = 5500

2. Count the number of days in the period: 4 days

3. Divide the total sales by the number of days to find the average: 5500 / 4 = 1375

So, the average sales for that period is 1375.

Therefore, the correct answer is: B) 1,375

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The translating point will be (x, y) --> (8-x, -5-y).

We have to translate a point 8 units right and 5 units down followed by a 180 degree rotation.

Now, the rule for 180 rotation is

(x, y)  --> (x, -y)

and, to shift 8 unit right apply (8-x)

and, to shift 5 unit down apply (5-y)

Then, the translating point will be (x, y) --> (8-x, -5-y).

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The value of x is determined as 1.

The value of x is calculated by applying the principle of similar triangles.

length SR ≅ length ST

length TU ≅ length RU

We will have the following equation, to solve for the value of x;

TU/SU = RU/SU

TU = RU

x + 9 = 10x

9 = 10x - x

9 = 9x

9/9 = xy

1 = x

Thus, the value of x is calculated by applying the principle of similar triangle.

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The evidence at the 0.05 level of significance contradict claim that the bags should fail inspection.

We can use a one-tailed test with the null hypothesis that the standard deviation of the bags' weights is no more than 4 grams and the alternative hypothesis that the standard deviation is greater than 4 grams.

The test statistic for this hypothesis test is given by:
t = [tex]\frac{\frac{s}{\sqrt{n}}}{\frac{sigma}{\sqrt{n}}}[/tex]
where s is the sample standard deviation, n is the sample size, and sigma is the population standard deviation (which is assumed to be 4 grams).

Plugging in the given values, we get:
t = [tex]\frac{\frac{5.3}{\sqrt{27}}}{\frac{4}{\sqrt{ 27}}}[/tex] ≈ 1.325
Using a t-distribution table with 26 degrees of freedom (since we have a sample size of 27 and are estimating the population standard deviation), we can find the critical value for a one-tailed test at the 0.05 level of significance. The critical value is 1.705.

Since our calculated test statistic (1.325) is less than the critical value (1.705), we can support the null hypothesis and conclude that the bags of potato chips will not fail inspection.

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The solution to the integral equation y(x) = 2 + x [t − ty(t)] dt is: y(x) = 1 + e⁻ˣ

Note that this solution satisfies the initial condition y(0) = 2.

To solve the given integral equation y(x) = 2 + x [t − ty(t)] dt, we need to first find the value of y(x) that satisfies this equation. We can obtain an initial condition for y(x) by setting x=0 in the equation and solving for y(0). Then, we can use a method such as separation of variables or substitution to find the general solution for y(x).

Let's start by finding the initial condition for y(x). Setting x=0 in the integral equation, we get:

y(0) = 2 + 0 [t − t y(t)] dt

y(0) = 2

So, we know that y(0) = 2. This will be useful when we find the general solution for y(x).

Now, let's use substitution to solve the integral equation. Let u = y(x), du/dx = y'(x), and v = t - y(t). Then, we have:

y(x) = 2 + x [t − ty(t)] dt

u = 2 + x [v] dt

du/dx = v + x dv/dx

Substituting du/dx and v in terms of u and x, we get:

v = t - u

du/dx = t - u + x (dv/dx)

du/dx + u = t + x (dv/dx)

We can use the integrating factor method to solve this first-order linear differential equation. The integrating factor is eˣ, so we have:

eˣ du/dx + eˣ u = teˣ + x eˣ (dv/dx)

(d/dx)(eˣ u) = (teˣ)' = eˣ

eˣ u = eˣ + C

u = 1 + Ce⁻ˣ

Substituting u = y(x) and using the initial condition y(0) = 2, we get:

y(x) = 1 + Ce⁻ˣ (general solution)

y(0) = 2 = 1 + C (using initial condition)

C = 1

Therefore, the solution to the integral equation y(x) = 2 + x [t − ty(t)] dt is:

y(x) = 1 + e⁻ˣ

Note that this solution satisfies the initial condition y(0) = 2.

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The probability that a data value is between 60 and 36 is 95.44%.

We have,

Mean = 34

Standard deviation = 2

So, P( 30 < x < 36)

= P (30 - 34/2) - P(36-34/2)

= P(-2) - P(2)

=  0.9772498 -0.0227501

= 0.9544

= 95.44%

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The surface area of the solid formed by the net = 150.72 in²

From the figure we can observe that the solid formed by the net is the net of a cylinder.

The cylinder bases are the 2 circles and the curved surface of the cylinder is the rectangle.

The surface area of the cylinder = Area of the 2 circles + area of the rectangle

Here, the diameter of circle is 4 in

So, the radius of circle = ½ × 4

                                     = 2 in

So, the area of the 2 circles would be,

2(πr²)

= 2 × 3.14 × 2²

= 25.12 in²

Here the width of the rectangle is 10 in. and the length is nothing but the circumference of the circle.

so, length L =  πd

                   = π × 4

                   = 12.56 in

Now the area of rectangle would be,

L × W

= 12.56 × 10

= 125.6 in²

The total surface area of net would be,

Area of the 2 circles + area of the rectangle

= 25.12 + 125.6

= 150.72 in²

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