2 points) Let Ω=N and A=P(N). Let P:A→[0,1] be a function with the property that for all A,B∈A P(A)=P(B)#A=#B Show that P does not qualify as a probability measure. Hint: Try a proof by contradiction. To this end, assume that P is a probability measure. Define the sets A n
​
:={1,…,n} and use the continuity from below and the additivity of the probability measures to show that the initial assumption leads to a contradiction.
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Answer:

16

Step-by-step explanation:

22-6=16 16+6=22

hope this helps! :)

Answer:

Step-by-step explanation:

56 divided by 42 is your awnser

Using the half life of palladium, mass seven weeks after start was 0.7931 gm.

The half-life is the amount of time it takes for a quantity (of material) to fall to the cost. In nuclear physics, the phrase usually refers to how rapidly neutrons become radioactive atoms or how long stable atoms survive.

The term can also refer to any sort of hyperbolic (or, in rare situations, non-exponential) decay.

The  half life of palladium 100 = 4 days

after 24 days sample has reduced to a mass of 5mg

standard exponential function is

\(P = P_o e^{kt}\)

plugging P = P₀ /2

\(P_o/2 = P_o e^{4k }\)

\(1/2 = e^{4k }\)

ln (1/2) = 4k

k = -0.1733

function becomes

\(P = P_o e^{- 0.1733 t }\)

plugging P = 5 and t = 24

\(5 = P_o e^{( - .1733\times 24 ) }\)

P₀ = 320.10

In the medical sciences, for example, the biological half of drugs and other chemicals in the human body is referred to. The flipside of half-life is doubling time in exponential growth.

For the second part of the problem:

7 weeks = 5 × 7 =49 days

plugging t = 49

\(P = 320.10 e^{(-.1733 * 35 ) }\)

mass 7 weeks after = 0.7431 mg

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The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Answer:

(-3/2, -13/2)

Step-by-step explanation:

To solve the system of equations graphically, we need to plot the two equations on the same set of axes and find the point of intersection.

To plot the first equation y = x - 5, we can start by finding the y-intercept, which is -5. Then, we can use the slope of 1 (since the coefficient of x is 1) to find other points on the line. For example, if we move one unit to the right (in the positive x direction), we will move one unit up (in the positive y direction) and get the point (1, -4). Similarly, if we move two units to the left (in the negative x direction), we will move two units down (in the negative y direction) and get the point (-2, -7). We can plot these points and connect them with a straight line to get the graph of the first equation.

To plot the second equation y = -x - 8, we can follow a similar process. The y-intercept is -8, and the slope is -1 (since the coefficient of x is -1). If we move one unit to the right, we will move one unit down and get the point (1, -9). If we move two units to the left, we will move two units up and get the point (-2, -6). We can plot these points and connect them with a straight line to get the graph of the second equation.

The point of intersection of these two lines is the solution to the system of equations. We can estimate the coordinates of this point by looking at the graph, or we can use algebraic methods to find the exact solution. One way to do this is to set the two equations equal to each other and solve for x:

x - 5 = -x - 8 2x = -3 x = -3/2

Then, we can plug this value of x into either equation to find the corresponding value of y:

y = (-3/2) - 5 y = -13/2

So the solution to the system of equations is (-3/2, -13/2).

we have the equation of curve C

Part a

Find out the gradient, where x=3

To find the gradient, take the derivative of the function with respect to x, then substitute the x-coordinate of the point of interest for the x values in the derivative

so

the first derivative is equal to

Evaluate the first derivative for x=3

Part b

we know that the gradient is equal to 1 at point P

so

equate the first derivative to 1

Find out the possible y-coordinate of point P

For x=2

substitute in the given equation of C

For x=-2

Answer:

y = 3x + 4

Step-by-step explanation:

Given:

Coordinates

(-3 , -5)

Slope m = 3

Find;

Equation of slope

Computation:

Given, x1 = -3 and y1 = -5

Equation of slope = y - y1 = m(x - x1)

Equation of slope = y - (-5) = 3(x + 3)

Equation of slope = y + 5 = 3x + 9

Equation of slope = y = 3x + 9 - 5

Equation of slope = y = 3x + 4

y = 3x + 4

Answer: p = 120 degrees

Step-by-step explanation:

Figure a shows a pentagon. The sum of interior angles in a pentagon is equal to 540 degrees.

1. Subtract the known numerical angle

540 - 60 = 480

All of the remaining angles (represented by the variable p) are equal to one another. Therefore, we can use the expression 4p = 480 to find the value of p.

2. Evaluate the equation to find the value of p.

4p = 480

p = 120

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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Hello !

Answer:

\(\Large \boxed{\sf x=-11}\)

Step-by-step explanation:

We want to find the value of x that satisfies the following equation :

\(\sf 5x+2=4x-9\)

Let's isolate x !

First, substract 4x from both sides :

\(\sf 5x+2-4x=4x-9-4x\\x+2=-9\)

Now let's substract 2 from both sides :

\(\sf x+2-2=-9-2\\\boxed{\sf x=-11}\)

Have a nice day ;)

Hello!

5x + 2 = 4x - 9

5x - 4x = - 9 - 2

x = -11

The tPx = (tPX)^2

Answer: The insurer assumes that the force of mortality of smokers at all ages is twice the force of mortality of non-smokers. Hence, the life insurance policy offers separate rates for smokers and non-smokers. In this regard, the starred function is used to represent smoker's mortality, whereas the unstarred function is used to represent non-smokers' mortality.In insurance, tPx stands for the probability that a person aged x would die within t years. Thus, tPx shows the probability that a person would die within t years considering their smoking habits.The force of mortality of non-smokers is denoted by lx, and the force of mortality of smokers is denoted by lx*. Hence, lx* = 2lx.Taking the life table for smokers and non-smokers, the probability that a person aged x would die within t years can be calculated as follows:tPx* = q[x] + q[x + 1] + q[x + 2] +...+ q[x + t - 1]tPx = q[x]/2 + q[x + 1]/2 + q[x + 2]/2 +...+ q[x + t - 1]/2= (q[x] + q[x + 1] + q[x + 2] +...+ q[x + t - 1])/2= tPx* /2Taking square both sides of the above equation, we gettPx = (tPx*)^2Therefore, it can be concluded that tPx = (tPX)^2.

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Ok here another way.

8×9÷6+2-8.53²+⅖​

= -58.3609

The area of the triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is  13.58

First using distance calculator we derived the length of TV and the length of VU.

Since TV = Height; and

VU = Base

and the triangle is a right triangle,

Then, area is given by 1/2 base x Height

Length of TV usign distance calculator is 6.40312
Lenght of VU using distance calculator is 4.24264

So area = 1/2 * 6.40312 * 4.24264

Area = 13.58

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The statement "the expected value of an unbiased estimator is equal to the parameter whose value is being estimated" is true.

An estimator is a function of the sample data used to estimate the value of a population parameter. An estimator is said to be unbiased if its expected value is equal to the true value of the population parameter. In other words, if we were to repeatedly take samples from the population and calculate the estimator for each sample, the average value of the estimator over all the samples would be equal to the true value of the population parameter. The expected value of an unbiased estimator is a key property because it ensures that the estimator is not systematically overestimating or underestimating the population parameter. Instead, the estimator provides an unbiased estimate of the population parameter on average across all possible samples. It is important to note that not all estimators are unbiased. Biased estimators may systematically overestimate or underestimate the population parameter, leading to incorrect conclusions. Therefore, unbiasedness is a desirable property for an estimator to have.

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Answer:

The answer would be 17

Step-by-step explanation:

You are going to multiply -1 by -5 , that will equal positive 5

So you get 12+5 = 17

Answer:

The given equation is:

It is required to solve for x.

Distribute 6 into the expression in parentheses:

Add 12 to both sides of the equation:

Divide both sides of the equation by 6:

Hence, the correct answer is 3) x=2 2/3.

The correct option is 3.

Answer:

.6239 as a fraction is 6239/10000.

a) The binomial expansion of (1+12x)^1/2 is given by:

(1+12x)^1/2 = 1^1/2 + (1/2)(1^-1/2)(12x) + (1/2)(1^-1/2)(-1/2)*(12x)^2 + ...

Binomial expression: what is it?

A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.

The first four terms, in ascending powers of x, are:

1, (1/2)(12x), (1/8)(12x)^2, (1/16)*(12x)^3

b) To use x=1/36 in the expansion, you would substitute x=1/36 into the expansion, and keep only the terms up to x^3 (the fourth term in the expansion). This will give an approximation of the value of (1+12x)^1/2 when x=1/36.

This will be an approximation of √12 because x=1/36 corresponds to 12x = 1 and the initial value of the expansion is 1 + 12x .

We can use this approximation to approximate square root of 12 and also for other square roots by using appropriate x values.

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Answer:

5.59 times per second.

Step-by-step explanation:

Direct variation is in the form:

\(y=kx\)

Where k is the constant of variation.

Inverse variation is in the form:

\(\displaystyle y=\frac{k}{x}\)

In the given problem, the frequency of a vibrating guitar string varies inversely  as its length. In other words, using f for frequency and l for length:

\(\displaystyle f=\frac{k}{\ell}\)

We can solve for the constant of variation. We know that the frequency f is 4.3 when the length is 0.65 meters long. Thus:

\(\displaystyle 4.3=\frac{k}{0.65}\)

Solve for k:

\(k=4.3(0.65)=2.795\)

So, our equation becomes:

\(\displaystyle f=\frac{2.795}{\ell}\)

Then when the length is 0.5 meters, the frequency will be:

\(\displaystyle f=\frac{2.795}{.5}=5.59\text{ times per second.}\)

The numbers would have to be added to complete the square is x = \(\frac{9+\sqrt{185} }{2}\) and x = \(\frac{9-\sqrt{185} }{2}\)

The quadratic equation is

\(x^2\) - 9x - 26 = 0

Add both side of the equation by 26

\(x^2\) - 9x - 26 + 26 = 26

\(x^2\) - 9x = 26

\(x^2\)  - 2(9/2)x = 26

Take the coefficient of x and take square of the term and add both side of the equation

\(x^2\)  - 2(9/2)x + 81/4 = 81/4 + 26

Add the terms

\(x^2\)  - 2(9/2)x + 81/4 = 185/4

Form the left side of the equation in the form of \((a-b)^2\)

Then the equation will be

\((x-\frac{9}{2} )^2\) = 185/4

x - 9/2 =± \(\frac{\sqrt{185} }{2}\)

x =  \(\frac{\sqrt{185} }{2}\) +  9/2

x = \(\frac{9+\sqrt{185} }{2}\)

Then

x = - \(\frac{\sqrt{185} }{2}\) +  9/2

x = \(\frac{9-\sqrt{185} }{2}\)

Hence, the numbers would have to be added to complete the square is x = \(\frac{9+\sqrt{185} }{2}\) and x = \(\frac{9-\sqrt{185} }{2}\)

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Answer:

pi x radius x 2 x height of the cylinder.

The Mean is 43 and Standard Error of x is 0.7225

What is Statistics?

Statistics is the study of data collection, analysis, presentation, and interpretation. Much of the early push for the subject of statistics came from government demands for census data as well as information about a range of economic operations.

We are provided with the Sample Size (n) = 16

Mean (μ) = 43

Standard Deviation (σ) = 1.7

We need to find:

Standard Error of x

So, to calculate Standard Error of x we need to find variance first

Variance = (Standard Deviation)^2

Variance = 1.7 * 1.7 = 2.89

Standard Error = Variance / √Sample Size

Standard Error = 2.89 / √16

Standard Error = 2.89 / 4

Standard Error of x is 0.7225

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The dimensions of the rectangle are 10 feet (length) and 8 feet (width).

To find the dimensions of the rectangle with an area of 80 square feet and a width that is 2 feet less than the length,

follow these steps:

1. Let the length of the rectangle be L feet and the width be W feet.

2. According to the given information, W = L - 2.

3. The area of a rectangle is calculated by multiplying its length and width: Area = L × W.

4. Substitute the given area and the relationship between L and W into the equation: 80 = L × (L - 2).

5. Solve the quadratic equation: 80 = L² - 2L.

6. Rearrange the equation: L² - 2L - 80 = 0.

7. Factor the equation: (L - 10)(L + 8) = 0.

8. Solve for L: L = 10 or L = -8 (since the length cannot be negative, L = 10).

9. Substitute L back into the equation for W: W = 10 - 2 = 8.

So, the dimensions of the rectangle are 10 feet (length) and 8 feet (width).

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Answer:

The midpoint is ( -1/2, -2)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2

( 1+-2)/2 = -1/2

To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2

( 0+-4)/2 = -4/2=-2

The midpoint is ( -1/2, -2)

Answer:

10%

Step-by-step explanation:

To find the percentage of well-done burgers, we need to divide the number of well-done burgers by the total number of burgers and then multiply by 100%. In this case, we have 1 well-done burger and 10 total burgers, so the percentage of well-done burgers is 1/10 * 100%, or 10%. Therefore, the answer is 10%.

In question 27, the price elasticity of supply for shampoo is given as 20, and the price of shampoo increases by 0.7%. The expected change in the quantity of shampoo supplied can be determined using the concept of price elasticity of supply. However, the specific percentage change in quantity supplied is not provided, so a precise answer cannot be given based on the given information.

In question 20, an inferior good in which the income effect dominates the substitution effect is referred to as a Giffen good. It is not classified as a normal good, luxury good, mass-produced good, or favored good.

In question 30, the cross elasticity of demand measures the responsiveness of the quantity demanded of a particular good to changes in the prices of its substitutes and complements. The correct answer is that the cross elasticity of demand measures the responsiveness to changes in both substitutes and complements.

In question 27, without the specific percentage change in quantity supplied, we cannot determine the exact outcome based on the given information. The price elasticity of supply of 20 suggests that the quantity supplied is highly responsive to changes in price, but the specific percentage change in quantity supplied cannot be calculated without additional data.

In question 28, the relationship between pasta being a Giffen good and other characteristics is not specified. While pasta being a Giffen good indicates that the quantity demanded increases as the price increases, it does not imply whether pasta is a normal good, luxury good, or how price changes affect quantity demanded.

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a. A confidence interval must be used for statistical inference when we want to estimate an unknown population parameter based on a sample of data.

For example, if we want to estimate the average height of all students in a particular school, we could take a random sample of students and use a confidence interval to estimate the true population mean height with a certain degree of certainty.

b. Hypothesis testing must be used for statistical inference when we want to test a specific hypothesis about a population parameter.

For example, we might want to test whether the average salary of male employees in a company is significantly different from the average salary of female employees.

The P-value is the probability of observing a test statistic as extreme as or more extreme than the one calculated from our sample data, assuming the null hypothesis is true. In other words, it represents the likelihood of obtaining the observed result if the null hypothesis is actually true. A small P-value indicates that the observed result is unlikely to have occurred by chance and provides evidence against the null hypothesis.

Hypothesis testing and confidence intervals are closely related. In hypothesis testing, we use a significance level (such as 0.05) to determine whether to reject or fail to reject the null hypothesis based on the P-value. In contrast, a confidence interval gives a range of plausible values for the unknown population parameter based on the sample data, with a specified level of confidence (such as 95%). However, the decision to reject or fail to reject the null hypothesis in a hypothesis test is equivalent to whether the null value (such as zero difference or equality) falls within the confidence interval or not. Therefore, a significant result in a hypothesis test (a small P-value) and a non-overlapping confidence interval both provide evidence against the null hypothesis.

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The volume of the pyramid is approximately 5.9 cm³.

To find the volume of a pyramid with a square base, you can use the formula:

Volume = (1/3) * base area * height

First, let's find the area of the square base. The perimeter of the base is given as 5.7 cm, which means each side of the square has a length of 5.7 cm / 4 = 1.425 cm.

The area of a square is given by the formula:

Area = side length * side length

Substituting the side length, we have:

Area = 1.425 cm * 1.425 cm = 2.030625 cm²

Now, we can calculate the volume of the pyramid:

Volume = (1/3) * base area * height

= (1/3) * 2.030625 cm² * 8.6 cm

= 5.91834375 cm³

Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is approximately 5.9 cm³.

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In triangle STU, with angle U measuring 90° and angle T measuring 26°, and with US measuring 13 feet, we can find the length of ST using trigonometry. By using the sine function, we can determine that ST is approximately 30.8 feet.

In triangle STU, angle U is a right angle, so it measures 90°. Angle T measures 26°. We are given that US has a length of 13 feet. To find the length of ST, we can use trigonometry, specifically the sine function. The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, angle T is opposite side ST, and angle U is opposite side US. So, we can write the sine of angle T as the ratio ST/US.

Using the given information, we can set up the equation sin(T) = ST/US and substitute the known values. Rearranging the equation, we have ST = US * sin(T). Plugging in the values, we get ST = 13 * sin(26°).

Using a calculator to evaluate sin(26°), we find that it is approximately 0.4384. Multiplying this value by 13, we get approximately 5.7. Therefore, the length of ST is approximately 5.7 feet, rounded to the nearest tenth.

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