You are shopping for a King & Queen size mattress, each of which are shaped like a rectangle. The Queen is 16 inches longer than it is wide. The King is 20 inches wider than the Queen, but has the same length. The area of the King-sized mattress is 1,600 in² larger than the Queen. Find the Area of both mattresses

The purpose of statistical inference population based upon information obtained from the sample.

statistical inference uses sample data to make estimates of or draw conclusions about one or more characteristics of a population.

The purpose of statistical inference is to estimate this sample to sample variation or uncertainty. Understanding how much our results may differ if we did the study again, or how uncertain our findings are, allows us to take this uncertainty into account when drawing conclusions. It allows us to provide a plausible range of values for the true value of something in the population, such as the mean, or size of an effect, and it allows us to make statements about whether our study provides evidence to reject a hypothesis.

We have four ideas for using the statistical inference.

1. Estimating uncertainty.

2. Confidence intervals.

3. Hypothesis tests.

4. Connections with other material.

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The given question is not complete.

The purpose of statistical inference is to make estimates or draw conclusions about a population based upon information obtained from the sample.

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The probability of A given B is 0, and P(A | B) is not equal to P(A). Events A and B are mutually exclusive, meaning that they cannot both occur at the same time, and thus they are not independent. Mutually exclusive events are not necessarily independent and independent events may or may not be mutually exclusive.

P(A) = 0.30 and P(B) = 0.40, so P(A and B) = 0 because the events A and B are mutually exclusive. This means that the probability of A given B is 0, and P(A | B) = 0. P(A | B) is not equal to P(A).Events A and B are mutually exclusive, meaning that they cannot both occur at the same time, and thus they are not independent.The statement that mutually exclusive events and independent events are the same is not accurate. Mutually exclusive events are not necessarily independent and vice versa.Given the results of this problem, we can conclude that mutually exclusive events are not independent, and independent events may or may not be mutually exclusive. The two concepts are not necessarily related as mutually exclusive events do not necessarily need to be independent and independent events do not necessarily need to be mutually exclusive.

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Answer:

B

Step-by-step explanation:

sohcahtoa

sin = opp/hyp

sin A = 16/20= 4/5

Answer:

a=5 ;b=10 ;c= 5 ; d= 5√3

Step-by-step explanation:

sin 45=9/5√2

a=5√2 sin 45

a= 5

tan45= 5/c

c=5/tan45

c= 5

tan 30=a/d

=5/d

d=5/tan 30

d=5√3

sin 30=5/b

b= 5/sin 30

b= 10

One-way independent ANOVA can be used in an experimental situation where there are three or more independent groups.

This is a statistical technique used to determine whether the differences in the means of two or more groups are statistically significant or just by chance. An example experiment that uses a one-way independent ANOVA is where researchers want to compare the effectiveness of three different brands of cough syrup in treating the coughs of patients. Another experiment situation is where a researcher wants to find out the difference in the effectiveness of three different types of fertilizers on plant growth. They would divide their sample of plants into three groups, where each group is treated with a different type of fertilizer. The dependent variable is the growth of the plants, and the independent variable is the type of fertilizer used.

The experiment above can be analyzed using a one-way independent ANOVA. The null hypothesis is that there is no significant difference in the means of the three groups, while the alternative hypothesis is that there is a significant difference in the means of the three groups. After collecting data on the cough syrup or fertilizer effectiveness, the researcher will conduct the ANOVA test to determine the difference in the means of the groups.If the F-ratio calculated from the ANOVA is significant, then the researcher can reject the null hypothesis and conclude that there is a significant difference in the means of the groups. The researcher will then conduct post-hoc tests to determine which groups have a significant difference in means and which ones are not significantly different.

One-way independent ANOVA is a statistical technique used to determine whether the differences in the means of two or more groups are statistically significant or just by chance. This technique can be used in an experimental situation where there are three or more independent groups. A t-test is used when there are only two independent groups. In conclusion, researchers can use ANOVA to compare the effectiveness of different brands of cough syrup or different types of fertilizers in plant growth.

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As the number of the term in the Fibonacci sequence increases, the Fibonacci numbers themselves also increase. The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding numbers.

The sequence starts with 0 and 1, and each subsequent number is found by adding the previous two numbers together.

For example, the first few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. As you can see, each new number in the sequence is obtained by adding the two previous numbers.

As the term number increases, the Fibonacci numbers grow exponentially. This is because each number is the sum of the two preceding numbers, and as the sequence progresses, the numbers being added together become larger.

As the number of the term in the Fibonacci sequence increases, the Fibonacci numbers also increase, growing exponentially with each term. This pattern continues indefinitely as the Fibonacci sequence goes on.

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The matrix of the relation r={(1,2),(2,3),(3,4),(4,5)} on the set x={1, 2, 3, 4, 5}; ordering of x:1,2,3,4,5 is as follows.

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

A relation is a set of ordered pairs.

The matrix of a relation is constructed by using its ordered pairs with their respective values as its entries, and its rows and columns by its domain and range, respectively.

So, the relation r is given as{(1,2),(2,3),(3,4),(4,5)}

The elements in the rows of the matrix correspond to the elements of x, while the elements in the columns of the matrix correspond to the elements of x as well, in that order.

So, the matrix of r on x can be written as:

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

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Answer:

a couple different obes

Step-by-step explanation:

there are five

Answer:

if 5x+2=12 then x=5

Step-by-step explanation:

5x+2=12

5x=10

10/2

x=5

Answer:

I saw an answer for this one and saw it was incorrect

Step-by-step explanation:

5x + 2 = 12

5x = 12 - 2 ( moved the constant to the right )

5x = 10 ( both sided needed to be divided by 5 )

x = 2

Step-by-step explanation:

To solve one step equations you have to do the opposite of whatever operation is being performed on the variable so you have to get the variable by itself

The most important thing to remember is that whatever you do to one side of the equation, you have to do the same thing to the other side.

Complement of set A is the set of all elements in the universal set that are not in the set .

If there is a subset of the universal set (U) called A, then the complement of set A, denoted by the symbol A', is different from the elements of set A and contains the elements of the universal set but not the elements of set A.

In this case, A' = x U: x A.

In other words, the complement of a set A is the difference between the universal set and set A.

For example: U = {1, 2, 3, 5, 7, 9, 15 ,14, 13}, A = {1, 2, 3, 5,7,9}, find the complement of A.

A' = U - A = {1, 2, 3, 5, 7, 9, 15,14,13} - {1, 2, 3, 5,7,9} = {15,14, 13}

A set that contains items from all related sets, without any repetition of elements, is known as a universal set (often symbolised by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.

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Answer:

make sure you have a good understanding of the subject you are translating, and that the translation is for that subject

To find the surface area of the part of the paraboloid y = x^2 + z^2 that lies inside the cylinder x^2 + z^2 = 16, we can use a surface area integral.

The surface area integral for a surface defined by the function f(x, y, z) = 0 is given by:

Surface Area = ∬S √(1 + (∂f/∂x)^2 + (∂f/∂y)^2 + (∂f/∂z)^2) dA

For the paraboloid y = x^2 + z^2, we can rewrite it as f(x, y, z) = y - x^2 - z^2 = 0.

To find the limits of integration, we need to consider the region of the paraboloid that lies inside the cylinder x^2 + z^2 = 16. This cylinder is a circular disk with radius 4 in the xz-plane.

Since the paraboloid is symmetric about the y-axis, we can consider only the region in the first quadrant, where x ≥ 0 and z ≥ 0.

The limits of integration are:

0 ≤ x ≤ 4

0 ≤ z ≤ √(16 - x^2)

Now, let's calculate the partial derivatives of f(x, y, z) with respect to x, y, and z:

∂f/∂x = -2x

∂f/∂y = 1

∂f/∂z = -2z

Substituting these values into the surface area integral formula, we have:

Surface Area = ∬S √(1 + (-2x)^2 + 1 + (-2z)^2) dA

Surface Area = ∬S √(1 + 4x^2 + 1 + 4z^2) dA

Surface Area = ∬S √(2 + 4x^2 + 4z^2) dA

To evaluate this integral, we need to convert it to polar coordinates because of the circular symmetry of the region.

In polar coordinates, we have:

x = r cos(θ)

z = r sin(θ)

dA = r dr dθ

The limits of integration in polar coordinates are:

0 ≤ r ≤ 4

0 ≤ θ ≤ π/2

Now, let's express the surface area integral in polar coordinates:

Surface Area = ∫₀^(π/2) ∫₀⁴ √(2 + 4r^2 cos^2(θ) + 4r^2 sin^2(θ)) r dr dθ

Surface Area = ∫₀^(π/2) ∫₀⁴ √(2 + 4r^2) r dr dθ

We can now evaluate this integral to find the surface area.

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Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

```

A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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| x

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-------------

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B

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

The expected value of the sum of the numbers that come up on four spinners is equal to the average of the possible outcomes of each spinner, which is (m + n + p + q)/4.

To find the expected value of the sum of the numbers that come up on four spinners, we need to first find the possible outcomes and their probabilities.

Since each spinner has equally likely outcomes, we can represent each spinner with a uniform probability distribution, where the probability of each outcome is 1 divided by the number of possible outcomes. Assuming that spinner 1 has m possible outcomes, spinner 2 has n possible outcomes, spinner 3 has p possible outcomes, and spinner 4 has q possible outcomes, the total number of possible outcomes for all four spinners is m x n x p x q.

Now, we need to find the sum of all possible outcomes and their probabilities. The expected value of the sum of the numbers that come up on four spinners is the sum of the products of each outcome and its probability. Mathematically, we can express this as:

Expected value = (1/m) x (1/n) x (1/p) x (1/q) x Σ(i=1 to m) Σ(j=1 to n) Σ(k=1 to p) Σ(l=1 to q) (i + j + k + l)

where Σ denotes the summation symbol, and i, j, k, and l represent the possible outcomes of each spinner.

Simplifying this expression, we get:

Expected value = (m + n + p + q)/4

Therefore, the expected value of the sum of the numbers that come up on four spinners is equal to the average of the possible outcomes of each spinner, which is (m + n + p + q)/4.

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Answer:

Slope = 6

Step-by-step explanation:

Taking two points on line l to find its slope: (0, 3) and (6, 2).

Slope of line l =

We know that the slope of a line which is perpendicular to another line has a slope which is a negative reciprocal of the other line.

Therefore, the slope of the line which is perpendicular to line l will have a slope of 6.  

MARK BRAINLIEST PLS

Answer:748cm^2

Step-by-step explanation:

The probability that a player will be asked a math question and then a music question is 0.03125

The size of the sections are given as:

Music = 0.5

Sport = 0.5

Others = 1

So, the total size is:

Total = 0.5 + 0.5 + 1 + 1 + 1

Evaluate

Total = 4

The probability of asking a math question is:

P(Math) = 1/4 = 0.25

The probability of asking a music question is:

P(Music) = 0.5/4 = 0.125

The required probability is:

P(Math and Music) = P(Math) * P(Music)

This gives

P(Math and Music) = 0.25 * 0.125

Evaluate

P(Math and Music) = 0.03125

Hence, the probability that a player will be asked a math question and then a music question is 0.03125

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Answer: B

Step-by-step explanation:

Answer:

0.93 km

Step-by-step explanation:

The White Chuck Glacier lost 70% of its area between 1958 and 2002, which means that its area was reduced by 70/100 = <<70/100=0.7>>0.7.

Since the glacier-covered 3.1 km. in 1958, its area was reduced by 0.7 * 3.1 km? = <<0.7*3.1=2.17>>2.17 km.

Therefore, the area of the White Chuck Glacier in 2002 was 3.1 km. - 2.17 km? = <<3.1-2.17=0.93>>0.93 km.

Answer:

2 years

Step-by-step explanation:

If it is annunal I think it would be 2 years

5 x annual year (year) =2

Answer:

x = 66°

∠MON = 57°

x = 13°

Step-by-step explanation:

To tired to explain, just take my word for it...

Answer:

1.

X=66

2.

57

3.

13

Step-by-step explanation:

Good luck .

Answer:

13.6 is the distance of BC

a) the solution to the differential equation y' + ycos(x) = 0 is given by y(x) = \(Ke^{(-sin(x))\), where K is an arbitrary constant.

b) he solution to the differential equation dy/dx = (x + 1)e⁻ˣy² is given by:

y(x) = 1 / [(x + 1)e⁻ˣ + e⁻ˣ - C]

c) the solution to the differential equation y' + 6y = 2e⁻ˣ is given by:

y(x) = (2x + C) / e⁶ˣ

a) To solve the differential equation y' + ycos(x) = 0, we can use the method of separating variables.

First, let's rewrite the equation in the following form:

y' = -ycos(x).

Now, we'll separate the variables by moving all the terms involving y to one side and the terms involving x to the other side:

y' / y = -cos(x).

Next, we'll integrate both sides with respect to x:

∫ (y' / y) dx = ∫ -cos(x) dx.

Integrating the left side gives us:

ln|y| = -sin(x) + C,

where C is the constant of integration.

To solve for y, we'll exponentiate both sides:

|y| = \(e^{(-sin(x) + C)\).

Using the properties of logarithms, we can rewrite this as:

|y| = \(e^C / e^{sin(x)\).

Since \(e^C\) is a positive constant, we can simplify the absolute value to remove the modulus:

y = ±( \(e^C / e^{sin(x)\)).

Combining the constant, we can write this as:

y = \(Ke^{(-sin(x))\),

where K is a constant, and we have dropped the absolute value since \(e^C\) is always positive.

Therefore, the solution to the differential equation y' + ycos(x) = 0 is given by y(x) = \(Ke^{(-sin(x))\), where K is an arbitrary constant.

b) To solve the differential equation dy/dx = (x + 1)e⁻ˣy², we can use separation of variables.

First, let's rewrite the equation in a more convenient form:

dy/y² = (x + 1)e⁻ˣdx.

Now, we'll separate the variables by moving the terms involving y to one side and the terms involving x to the other side:

y⁻²dy = (x + 1)e⁻ˣdx.

Next, we'll integrate both sides with respect to their respective variables:

∫y⁻²dy = ∫(x + 1)e⁻ˣdx.

For the left-hand side integral, we can use the power rule of integration:

∫y⁻²dy = -y^(-1).

For the right-hand side integral, we can integrate by parts. Let's choose u = x + 1 and dv = e⁻ˣ dx. Then, du = dx and v = -e⁻ˣ:

∫(x + 1)e⁻ˣdx = -e⁻ˣ (x + 1) - ∫(-e⁻ˣ)dx

                = -(x + 1)e⁻ˣ + ∫e⁻ˣdx

                = -(x + 1)e⁻ˣ - e⁻ˣ + C,

where C is the constant of integration.

Now, we'll substitute these results back into the original equation:

-y⁻¹ = -(x + 1)e⁻ˣ - e⁻ˣ + C.

To solve for y, we'll multiply through by -1 to get rid of the negative sign:

y⁻¹ = (x + 1)e⁻ˣ + e⁻ˣ - C.

Taking the reciprocal of both sides gives:

y = (1 / [(x + 1)e⁻ˣ + e⁻ˣ - C]).

Therefore, the solution to the differential equation dy/dx = (x + 1)e⁻ˣy² is given by:

y(x) = 1 / [(x + 1)e⁻ˣ + e⁻ˣ - C],

where C is an arbitrary constant.

c) To solve the differential equation y' + 6y = 2e⁻ˣ, we can use an integrating factor.

First, let's rewrite the equation in the standard form:

y' + 6y = 2e⁻ˣ

The integrating factor (IF) is given by the exponential of the integral of the coefficient of y, which in this case is 6:

IF = \(e^{\int6dx\) = e⁶ˣ

Now, we multiply the entire equation by the integrating factor:

e⁶ˣy' + 6e⁶ˣy = 2e⁶ˣe⁻ˣ.

Simplifying the right side:

e⁶ˣy' + 6e⁶ˣy = 2.

Notice that the left side is a derivative of the product of y and e⁶ˣ with respect to x:

(e⁶ˣy)' = 2.

Now, we can integrate both sides with respect to x:

∫ (e⁶ˣy)' dx = ∫ 2 dx.

Integrating the right side gives us:

e⁶ˣy = 2x + C,

where C is the constant of integration.

Now, we solve for y by dividing both sides by e⁶ˣ:

y = (2x + C) / e⁶ˣ

Therefore, the solution to the differential equation y' + 6y = 2e⁻ˣ is given by:

y(x) = (2x + C) / e⁶ˣ

where C is an arbitrary constant.

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Answer:

graph #x

Step-by-step explanation:

where are the graphs

According to the given statement Beth would walk approximately 8 blocks if she worked at the same rate for an hour.

To find out how many blocks Beth would walk if she worked at the same rate for an hour, we need to determine the number of blocks she walks in one minute.
Given that the person walks two blocks in 15 minutes, we can calculate the number of blocks walked in one minute by dividing 2 by 15:
2 blocks / 15 minutes = 0.1333 blocks/minute
Now, we can find out how many blocks Beth would walk in an hour by multiplying the blocks walked in one minute by 60 (the number of minutes in an hour):
0.1333 blocks/minute * 60 minutes/hour = 7.998 blocks/hour
Therefore, Beth would walk approximately 8 blocks if she worked at the same rate for an hour.

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The actual distance between M and μ is measured by the numerator of the z-score test statistic.

The distribution of the z-score test is normally distributed under the null hypothesis, making it a statistical test. The mean is tested for a known standard deviation using this method. The z score (z), which is determined by the following equation, is the difference between the sample mean and the population mean in units of standard error. The distribution of the z-score test is normally distributed under the null hypothesis, making it a statistical test. The mean is tested for a known standard deviation using this method. The z score (z), which is determined by the following equation, is the difference between the sample mean and the population mean in units of standard error. The equation is z = M - μ / σ/√n, where n is the number of samples in the population, is the mean, o is the standard deviation, and σ/√n is the standard error. The sample mean's (μ) distance from the population mean serves as the z score's numerator (M).

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