How much would $125 invested at 8% interest compounded continuously be worth after 16 years

Answer:h(13) = 18

Step-by-step explanation:

The CDFs of X and Y agree for all x, and hence X and Y have the same distribution, i.e., P(X = A) = P(Y = A) for all events A.

In mathematics, convergence is the feature of certain infinite series and functions of getting closer to a limit when an input (variable) of the function changes in value or as the number of terms in the series grows.

To prove that limits in distribution are unique, let's assume that (\(X_n\)) converges in distribution to both X and Y. We need to show that the cumulative distribution functions (CDFs) of X and Y agree, i.e., P(X ≤ x) = P(Y ≤ x) for all x.

Let \(F_X\)(x) and F_Y(x) denote the CDFs of X and Y, respectively.

Since (\(X_n\)) converges in distribution to X, we have the following convergence:

lim(n→∞) P(\(X_n\) ≤ x) = P(X ≤ x)

Similarly, since (\(X_n\)) converges in distribution to Y, we have:

lim(n→∞) P(\(X_n\) ≤ x) = P(Y ≤ x)

Therefore, we can write:

lim(n→∞) P(\(X_n\) ≤ x) = P(X ≤ x) = P(Y ≤ x)

Now, let's consider the set S = {x ∈ R: P(X ≤ x) ≠ P(Y ≤ x)}. We want to show that S is empty, which means that the CDFs of X and Y agree for all x.

Assume S is not empty. Since a CDF has at most countably many discontinuities, S is countable.

Now, for each x ∈ S, we can construct a decreasing sequence (\(c_n\)) in R\S such that lim(n→∞) \(c_n\) = x. This is possible because R\S contains infinitely many elements.

Using the fact that (\(X_n\)) converges in distribution to both X and Y, we have:

lim(n→∞) P(X_n ≤ \(c_n\)) = P(X ≤ x)    (1)

lim(n→∞) P(X_n ≤ \(c_n\)) = P(Y ≤ x)    (2)

Taking the limit as n approaches infinity in both equations, we get:

lim(n→∞) P(X ≤ x) = P(X ≤ x)

lim(n→∞) P(Y ≤ x) = P(Y ≤ x)

This implies that P(X ≤ x) = P(Y ≤ x) for all x ∈ S.

However, since S is countable, this implies that P(X ≤ x) = P(Y ≤ x) for all x ∈ R.

Therefore, the CDFs of X and Y agree for all x, and hence X and Y have the same distribution, i.e., P(X = A) = P(Y = A) for all events A.

Hence, we have shown that limits in distribution are unique, as required.

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Step-by-step explanation:

Answer : 5r−4x+5

hope I helped c:

Insta: brianna_editsz

Answer:

ll

Step-by-step explanation:

bye

Answer:

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Pedometer

Answer:

48.3

Step-by-step explanation:

→ See what side is not given

Opposite

→ Find a triangle with out an O in it

Cos = Adjacent / Hypotenuse

→ Make what you want to find the subject

Hypotenuse = Adjacent / Cos

→ Substitute the numbers into the formula

41 / cos (32) = 48.3

Answer:

rate of change = 1.75 over 1 or just 1.75

Step-by-step explanation:

this represents the cost of each cantaloupe. This basically means that each cantaloupe is $1.75.

a. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores. b. The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

(a) To find the probability that the sample mean will be within ±5 of the population mean, we can use the Central Limit Theorem (CLT) and the properties of a normal distribution.

The sample mean, is an unbiased estimator of the population mean, μ. According to the CLT, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

     = 200 / √400

     = 200 / 20

     = 10

To find the probability that the sample mean will be within ±5 of the population mean, we can standardize the interval using the z-score:

For the lower bound (-5), the z-score is (-5 - 0) / 10 = -0.5.

For the upper bound (+5), the z-score is (5 - 0) / 10 = 0.5.

We can now use a standard normal distribution table or technology (such as a calculator or statistical software) to find the probability associated with the z-scores -0.5 and 0.5. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores.

(b) To find the probability that the sample mean will be within ±10 of the population mean, we follow the same steps as in part (a).

The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

Note: Since the question mentions rounding answers to four decimal places, please use the appropriate table or technology to obtain the precise probabilities for parts (a) and (b).

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Answer:

5 in. = 2 mi.

Step-by-step explanation:

2.4mi  = 6in

1 mi = 2.5in

2.5 inches = 1mile

Convert to whole #'s as the question asks

5 in. = 2 mi

-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)

Answer:

3 inches = 1 miles

Step-by-step explanation:

The first scale you get is with the information that is given:

6 inches = 2.4 miles

Then you simplify, dividing both sides by 2.4:

2.5 inches = 1 miles

Rounding up: 3 inches = 1 miles

Hope it helps!

Answer:

p=2/3 mn

p/n=2/3 m(

(3)p/n=2/3(3)m

3p/n=2m

3p/2n=2m/2

3p/2n=m (letter B)

Answer:

$16.5

Step-by-step explanation:

$30-$8-$3.85-$1-$1 = $16.5

Answer: Campbell to Hillsboro to Richmond to Winchester

(Note: Not taking the Washington route)

Step-by-step explanation:

Form Campbell all the way to Richmond have no other choices, From Richmond to Winchester has two choices, 12.2 mi +5.2 mi or 15.7 mi

12.2+5.2=17.4 mi while the other choice is only 15.7 mi

So taking the 15.7 mi option is faster

The age of the decaying sample according to the decay formula is 42,009 years.

The rate of radioactive carbon-14 decay depends on the function

\(A(t) = A_{0} e^{-0.0001216t}\)

where \(A_{0}\) is the quantity found in living plants and animals, t is in years, and is the age.

60% of the carbon-14 of a current-day sample was present in a sample taken from a refuse deposit close to the Strait of Magellan. We need to evaluate the age of the sample,

A = 60 % of \(A_{0}\) = (3/5)\(A_{0}\)

Putting this in the decay equation, we have,

\(\frac{3}{5} A_{0} = A_{0} e^{-0.0001216t}\\\\ 0.6= e^{-0.0001216t}\\ \\ln0.6 = -0.00001216t\\\\-0.51082 = -0.00001216t\\\\t = 42,008.68\)

Thus, the age of the sample is 42,009 years.

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Answer:

730.484397 Hours

Step-by-step explanation:

1 day =24 hours

30 days = 720 hours (30*24)

31 days = 744 hours (31*24)

Answer: (a) Red cars are 5/8 greater than the fraction of blue cars

Step-by-step explanation:

To determine the difference in fractions between the red cars and blue cars in the parking lot, we need to calculate the fraction of red cars and the fraction of blue cars and then find the difference between them.

Given:

(3/4) of the cars are red

(1/8) of the cars are blue

To find the difference between the fractions, subtract the fraction of blue cars from the fraction of red cars:

(3/4) - (1/8)

To subtract fractions, we need a common denominator. In this case, the least common multiple of 4 and 8 is 8.

Rewriting the fractions with a common denominator:

(6/8) - (1/8)

Now we can subtract the numerators:

(6 - 1)/8 = 5/8

Therefore, the fraction of red cars is (5/8) greater than the fraction of blue cars.

So, the answer is (a) (5/8).

Answer:

5/8

Step-by-step explanation:

To find the answer, you should subtract the fraction of the blue cars from that of the red ones.

\( \frac{3}{4} - \frac{1}{8} = \frac{5}{8} \)

The best lower bound for the volume is 24 cm³, and the best upper bound is 120 cm³ and the best lower bound for the surface area is 52 cm², and the best upper bound is 148 cm².

a. To determine the best upper and lower bounds for the volume of the rectangular parallelepiped, we can consider the extreme cases by rounding each side to the nearest centimeter.

Lower bound: If we round each side down to the nearest centimeter, we get a rectangular parallelepiped with sides 2 cm, 3 cm, and 4 cm. The volume of this parallelepiped is 2 cm * 3 cm * 4 cm = 24 cm³.

Upper bound: If we round each side up to the nearest centimeter, we get a rectangular parallelepiped with sides 4 cm, 5 cm, and 6 cm. The volume of this parallelepiped is 4 cm * 5 cm * 6 cm = 120 cm³.

Therefore, the best lower bound for the volume is 24 cm³, and the best upper bound is 120 cm³.

b. Similar to the volume, we can determine the best upper and lower bounds for the surface area of the parallelepiped by considering the extreme cases.

Lower bound: If we round each side down to the nearest centimeter, the dimensions of the parallelepiped become 2 cm, 3 cm, and 4 cm. The surface area is calculated as follows:

2 * (2 cm * 3 cm + 3 cm * 4 cm + 4 cm * 2 cm) = 2 * (6 cm² + 12 cm² + 8 cm²) = 2 * 26 cm² = 52 cm².

Upper bound: If we round each side up to the nearest centimeter, the dimensions become 4 cm, 5 cm, and 6 cm. The surface area is calculated as follows:

2 * (4 cm * 5 cm + 5 cm * 6 cm + 6 cm * 4 cm) = 2 * (20 cm² + 30 cm² + 24 cm²) = 2 * 74 cm² = 148 cm².

Therefore, the best lower bound for the surface area is 52 cm², and the best upper bound is 148 cm².

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The correct expression are

1. 6/9 = 3/9 + 3/9  (fraction as the sum of two equal fractional Parts)

2. 15/4 = 3/4 + 3/4 + 3/4 + 3/4 + 3/4   (fraction as the sum of more then three equal fractional Parts)

Given that,

Each fraction should be written as the addition of two or three equal fractional parts. As a multiplication equation, rewrite each.

We know that,

The fraction are

a. 6/9

b. 15/4

Each fraction is expressed as the sum of two or three equally sized fractional parts;

1) 6/9

⇒ 6/9 = 3/9 + 3/9

2) 15/4

⇒ 15/4 = 3/4 + 3/4 + 3/4 + 3/4 + 3/4

Therefore, The correct expression are

1. 6/9 = 3/9 + 3/9  (fraction as the sum of two equal fractional Parts)

2. 15/4 = 3/4 + 3/4 + 3/4 + 3/4 + 3/4   (fraction as the sum of more then three equal fractional Parts)

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Answer:

Multiply each measurement by 2 then add them together

          OR

Add 7 + 3 and multiply by 2

Step-by-step explanation:

Answer would be 20ft

The answer is would be B.

The trench descends to a depth of -24,997 feet below sea level, representing its remarkable depth below the surface.

The trench reaches a staggering depth of 24,997 feet below sea level, making it the deepest point in the area.

With elevations below sea level indicated by negative numbers, this particular trench plunges deep into the ocean floor.

Its immense depth is a testament to the remarkable geological features that exist beneath the surface of our planet.

The negative elevation signifies the significant extent to which this trench descends below the average sea level, providing an awe-inspiring example of the Earth's dynamic and diverse topography.

This extreme depth underscores the mysterious and captivating nature of our planet's oceans and their hidden wonders.

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The linear function for this problem is defined as follows:

y = x + 50.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph touches the y-axis at y = 50, hence the intercept b is given as follows:

b = 50.

When x increases by 10, y also increases by 10, hence the slope m is given as follows:

m = 10/10

m = 1.

Hence the function is given as follows:

y = x + 50.

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The equations are x - 5 = 7, x - 7 = 5 and x - 4 = 8

The solution to the equation is given as

x = 12

The subtraction property of equality states that if we subtract the same number from both sides of an equation, the equation remains true.

Using the above as a guide, we have the following:

Each of these equations is equivalent to x = 12, since we have simply subtracted the same value from both sides of the equation.

Hence, the solution to each of these equations is x = 12.

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Answer:

A. -3.5, 0.5

Step-by-step explanation:

This is because the coordinates are saying they are located on quadrant ll so the x coordinate has to be a negative and the y coordinate has to be positive

Answer:

$18

Step-by-step explanation:

If she starts with $50 and has $32 left when she's done then. 50-32= 18

So she spent $18 on clothing.

The given system of equations can be solved using Gaussian or Gauss-Jordan elimination. Therefore, the solution to the system of equations is x = 1, y = 2√2, and z = -1.

The solution to the system of equations is x = 1, y = 2√2, and z = -1.

We can start by applying Gaussian elimination to the system of equations:

Row 1: √2x + 2z = 5

Row 2: y + √2y - 3z = 3√2

Row 3: -y + √2z = -3

We can eliminate the √2 term in Row 2 by multiplying Row 2 by √2:

Row 1: √2x + 2z = 5

Row 2: √2y + 2y - 3z = 3√2

Row 3: -y + √2z = -3

Next, we can eliminate the y term in Row 3 by adding Row 2 to Row 3:

Row 1: √2x + 2z = 5

Row 2: √2y + 2y - 3z = 3√2

Row 3: (√2y + 2y - 3z) + (-y + √2z) = (-3√2) + (-3)

Simplifying Row 3, we get:

Row 1: √2x + 2z = 5

Row 2: √2y + 2y - 3z = 3√2

Row 3: √2y + y - 2z = -3√2 - 3

We can further simplify Row 3 by combining like terms:

Row 1: √2x + 2z = 5

Row 2: √2y + 2y - 3z = 3√2

Row 3: (3√2 - 3)y - 2z = -3√2 - 3

Now, we can solve the system using back substitution. From Row 3, we can express y in terms of z:

y = (1/3√2 - 1)z - 1

Substituting the expression for y in Row 2, we can express x in terms of z:

√2x + 2z = 5

x = (5 - 2z)/√2

Therefore, the solution to the system of equations is x = 1, y = 2√2, and z = -1.

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Every polynomial function of odd degree with real coefficients will have at least one real root or zero.

This statement is known as the Fundamental Theorem of Algebra. It states that a polynomial of degree n, where n is a positive odd integer, will have at least one real root or zero.

The reason behind this is that when a polynomial of odd degree is graphed, it exhibits behavior where the graph crosses the x-axis at least once. This implies the existence of at least one real root.

For example, a polynomial function of degree 3 (cubic polynomial) with real coefficients will always have at least one real root. Similarly, a polynomial function of degree 5 (quintic polynomial) with real coefficients will also have at least one real root.

It's important to note that while a polynomial of odd degree is guaranteed to have at least one real root, it may also have additional complex roots.

The Fundamental Theorem of Algebra ensures the existence of at least one real root but does not specify the total number of roots.

In summary, every polynomial function of odd degree with real coefficients will have at least one real root or zero, as guaranteed by the Fundamental Theorem of Algebra.

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