The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 1995, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the calendar year in which the number of new cases would reach 1282.

The volume of the sphere is 4 π × 3 × h. Option C

To determine the expression, we need to know the formula for volume of a sphere.

The formula that is used for calculating the volume of a sphere is expressed as;

V = 1/3 πr²h

Given that the parameters of the formula are;

Now, substitute the values, we have;

Volume, V= 4/3 × π × 3² × h

Multiply the values, we get;

Volume =4 π × 3² × h/3

Divide the values

Volume =4 π × 3 × h

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The function S(t) = 31,500(1.034)^t approximates the number of digital subscriptions for a large city newspaper after the launch of a new advertising campaign, with an initial number of 31,500 subscriptions and a growth rate of 3.4% per month.

To interpret the parameters of the function S(t) = 31,500(1.034)^t, which approximates the number of digital subscriptions for a large city newspaper after the launch of a new advertising campaign.

1. The initial number of digital subscriptions (S(0)): This is represented by the constant 31,500 in the equation. When t=0 (at the launch of the campaign), the function becomes S(0) = 31,500(1.034)^0 = 31,500. This means that at the start of the advertising campaign, there were 31,500 digital subscriptions.

2. The growth rate of digital subscriptions: This is represented by the factor 1.034 in the equation. The growth rate is 3.4% (since 1.034 = 1 + 0.034).

This means that the number of digital subscriptions is expected to increase by 3.4% each month after the launch of the advertising campaign.

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These values (x4, y4) represent the coordinates of the missing vertex of Lana's square.

To determine the missing vertex of Lana's square, we need to know the location of the three given vertices. Let's assume that Lana plotted the vertices in a clockwise direction, starting from the top left.

If we denote the coordinates of the first vertex as (x1, y1), the second vertex as (x2, y2), and the third vertex as (x3, y3), then the coordinates of the missing vertex can be found as follows:

1. Calculate the distance between the first and second vertices:

d1 = sqrt((x2 - x1)^2 + (y2 - y1)^2)

2. Calculate the distance between the second and third vertices:

d2 = sqrt((x3 - x2)^2 + (y3 - y2)^2)

If the square is regular (i.e., all sides are of equal length), then d1 = d2. Otherwise, the shape is not a square.

3. Calculate the midpoint between the first and second vertices:

xm = (x1 + x2) / 2

ym = (y1 + y2) / 2

4. Calculate the vector that goes from the midpoint to the third vertex:

vx = x3 - xm

vy = y3 - ym

5. Calculate the coordinates of the missing vertex by adding the vector to the midpoint:

x4 = xm + vx

y4 = ym + vy

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Driver's data set that has a mode that is greater than the mean or median is Fabian and a median with the lowest value of the three measures is Kadisha.

Data of Fabian: 7, 12, 11, 23, 13, 23, 30

Mean = sum of all observation / total no. of observation

Mean = (7+ 12+ 11+ 23+ 13+ 23+ 30) / 7

Mean = 17

Mode = most repeating observation

Mode = 23

For median we have to write observation in ascending order

7,11,12,13,23,23,30

Median = (N+1)/2

Where N = No. of observation

Median = (7+1)/2

Median = 4th observation

Median = 13

Here mode that is greater than the mean or median.

similarly for,

Kadisha: 8, 17, 23, 16, 17, 18, 125

Mean = 32

Median = 17

Mode = 17

Here median with the lowest value of the three measures.

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The estimated population proportion is 0.622, with a margin of error of +/- 0.096.

The value of the population proportion of people from Hawaii who exercised for at least 30 minutes a day 3 days a week can be estimated using the sample proportion of 62.2%. However, we need to calculate the margin of error to determine a range in which the true population proportion is likely to fall.

Using the formula for the margin of error:

Margin of error = z*sqrt(p*(1-p)/n)

where z is the z-score for the desired level of confidence (let's use 95% confidence, which corresponds to a z-score of 1.96), p is the sample proportion (0.622), and n is the sample size (100).

Plugging in the values, we get:

Margin of error = 1.96*sqrt(0.622*(1-0.622)/100) = 0.096

So the margin of error is 0.096, meaning that we can be 95% confident that the true population proportion of people from Hawaii who exercise for at least 30 minutes a day 3 days a week falls within a range of 0.622 +/- 0.096.

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a) The height of the tide at low tide is 3.7 feet.

b) The period of the function is 12 hours and it means that the tide goes through a full cycle of high tide.

c) The first time the tide reaches a height of 3 feet is therefore either 23.82 hours or 40.18 hours after high tide.

a. To find the height of the tide at low tide, we need to find the minimum value of the function f(x).

Since cos(π/6 x) has a maximum value of 1 and a minimum value of -1, the minimum value of the entire function occurs when cos(π/6 x) = -1.

This happens when π/6 x = π + 2nπ, where n is any integer.

Solving for x, we get x = 12 + 12n.

Substituting this value of x into the function, we get f(x) = 0 + 3.7 = 3.7 feet.

b. The period of the function is the time it takes for the function to complete one full cycle. Since the period of cos(π/6 x) is 2π/π/6 = 12 hours, the period of the entire function f(x) is also 12 hours. This means that the tide goes through a full cycle of high tide and low tide every 12 hours at this location.

c. To find the first time the tide reaches a height of 3 feet, we need to solve the equation 3 = 3.5 cos (π/6 x) + 3.7 for x.

Subtracting 3.7 from both sides and dividing by 3.5, we get cos(π/6 x) = -0.086.

Taking the inverse cosine of both sides, we get π/6 x = 1.67 + 2nπ or π/6 x = -1.67 + 2nπ, where n is any integer.

Solving for x, we get x = 40.18 + 24n or x = 23.82 + 24n.

The first time the tide reaches a height of 3 feet is therefore either 23.82 hours or 40.18 hours after high tide.

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Answer:

To find (f + g)(x), we need to add the two functions f(x) and g(x), and then evaluate the sum at x.

So, we have:

(f + g)(x) = f(x) + g(x)

Substituting the given functions, we get:

(f + g)(x) = (2x + 3) + (3x + 2)

Simplifying the expression, we get:

(f + g)(x) = 5x + 5

Therefore, (f + g)(x) is equal to 5x + 5.

The faster pipe can fill and drain the pool at a rate of 640.34 cubic feet per hour.

Reese is installing a rectangular pool in her backyard that is 30 feet long, 14 feet wide, and has an average depth of 8 feet. To fill and drain the pool, she is using two pipes. Let's call the slower pipe's rate of filling and draining the pool "r" (in units of volume per hour). Then, according to the problem, the faster pipe's rate is 2r+1 (since it is "1 more than 2 times faster" than the slower pipe).
If both pipes are open and working properly, we know it will take 3.5 hours to fill the pool. That means the total volume of the pool is:
V = length x width x depth
V = 30 ft x 14 ft x 8 ft
V = 3,360 cubic feet
We also know that when both pipes are open, they can fill the pool in 3.5 hours. That means the combined rate of filling the pool is:
V / t = (r + 2r+1)
3360 / 3.5 = 3r+1
960 = 3r+1
959 = 3r
r = 319.67 cubic feet per hour
So the slower pipe can fill and drain the pool at a rate of 319.67 cubic feet per hour. To find the rate of the faster pipe, we just need to substitute this value into our equation for the faster pipe's rate:
2r+1 = 2(319.67) + 1
2r+1 = 640.34
Therefore, the faster pipe can fill and drain the pool at a rate of 640.34 cubic feet per hour.

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Answer

Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?

To find the mean, we add up all the values and divide by the number of values:

Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10

Mean = 36.7 / 10

Mean = 3.67

To find the median, we need to put the values in order:

2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4

The middle number is the median, which is 3.35 in this case.

To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.

To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:

2.5, 2.6, 2.8, 3.1, 3.2

The median of this lower half is 2.8, so Q1 = 2.8.

To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:

3.7, 3.8, 4.1, 9.4

The median of this upper half is 3.95, so Q3 = 3.95.

To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

IQR = 3.95 - 2.8

IQR = 1.15

1.5 times the IQR is 1.5 * 1.15 = 1.725.

The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.

Answer

To find the perimeter of a regular polygon with n sides, we can use the formula:

Perimeter = n * s

where s is the length of each side. To find s, we can use trigonometry to find the length of one of the sides and then multiply by the number of sides.

In a regular polygon with n sides, the interior angle at each vertex is given by:

Interior angle = (n - 2) * 180 degrees / n

In a 15-sided polygon, the interior angle at each vertex is:

(15 - 2) * 180 degrees / 15 = 156 degrees

If we draw a line from the center of the polygon to a vertex, we form a right triangle with the side of the polygon as the hypotenuse, the distance from the center to the vertex as one leg, and half of the side length as the other leg. Using trigonometry, we can find the length of half of the side:

sin(78 degrees) = 12 / (1/2 * s)

s = 2 * 12 / sin(78 degrees)

s ≈ 2.17 inches

Finally, we can find the perimeter of the polygon:

Perimeter = 15 * s

Perimeter ≈ 32.55 inches

Rounding this to the nearest whole number, we get that the best approximation for the perimeter is 33 inches. Therefore, the closest option is (1) 68 inches.

By calculations, Colleen's photo is smaller than Ali's photo

From the question, we have the following parameters that can be used in our computation:

Area of Ali's photo = 91 square inches.

For Colleen's photo, we have

9 inches by 7 inches

This means that

Area of Colleen's photo = 9 * 7 square inches.

Evaluate

Area of Colleen's photo = 63 square inches.

63 square inches is lesser than 91 square inches

This means that Colleen's photo is smaller than Ali's photo

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Distribution that results in all the data intervals that have the same frequency is called D)frequency distribution

A frequency distribution is a way of summarizing and displaying a dataset by showing the number of times each value or range of values appears in the data.

When all the intervals in a frequency distribution have the same frequency, it means that the data is evenly distributed across those intervals. This type of distribution is useful when analyzing data that falls into discrete categories or groups, such as survey responses or test scores.

By organizing the data into intervals with equal or same frequencies, patterns in the data can become more apparent and it can be easier to draw conclusions or make predictions.

Overall, a frequency distribution is a helpful tool for understanding the distribution of data and can provide valuable insights into the characteristics of a dataset.

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To find the general expression for the elasticity of demand (e_p), we need to differentiate the demand function with respect to price (p) and multiply it by the ratio of price to quantity (p/q). The elasticity of demand measures the responsiveness of quantity demanded to changes in price.

The general expression for elasticity of demand (e_p) can be calculated as:

e_p = (dQ/dp) * (p/Q)

Where dQ/dp represents the derivative of the demand function with respect to price, and Q represents the quantity demanded.

The elasticity of demand helps us understand how sensitive the quantity demanded is to changes in price. If e_p is greater than 1, demand is considered elastic, meaning that quantity demanded is highly responsive to price changes. If e_p is less than 1, demand is inelastic, indicating that quantity demanded is less responsive to price changes.

In conclusion, the general expression for the elasticity of demand (e_p) is calculated by taking the derivative of the demand function with respect to price and multiplying it by the ratio of price to quantity. This measure helps determine the responsiveness of quantity demanded to changes in price.

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Lamar can spend at most $3.01 on a single pair of socks to stay within his budget.

a. The total cost of the socks and shorts can be represented by the expression:

Total cost = Cost of shorts + Cost of 5 pairs of socks

= $19.95 + 5x

where x is the price of one pair of socks.

b. To write an equation that says Lamar spent exactly $35 on the socks and shorts, we can equate the total cost expression to $35:

$19.95 + 5x = $35

To solve for x, we can first subtract $19.95 from both sides:

5x = $15.05

Then, divide both sides by 5:

x = $3.01

So, Lamar spent $19.95 + 5($3.01) = $35 on the socks and shorts.

c. Other possible prices for the socks that would still allow Lamar to stay within his budget of $35 can be found by plugging in values of x that satisfy the inequality:

Cost of 5 pairs of socks = 5x ≤ $15.05

For example, if the socks cost $2.99 per pair, then the total cost would be:

$19.95 + 5($2.99) = $34.90

which is within Lamar's budget.

d. We can write an inequality to represent the amount Lamar can spend on a single pair of socks as:

x ≤ (35 - 19.95)/5

This simplifies to:

x ≤ $3.01

So, Lamar can spend at most $3.01 on a single pair of socks to stay within his budget.

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At the point P(2,2), the unit vector for the direction of steepest ascent is  (-i + j)/√2, and the unit vector for the direction of steepest descent is (i - j)/√2. A vector that points in the direction of no change in the function at P is (2e^(-1/3)/49) i + (2e^(-1/3)/49) j + (2/7) k.

To find the unit vectors that give the direction of steepest ascent and steepest descent at P, we need to find the gradient of F at P and normalize it to obtain a unit vector.

First, we find the partial derivatives of F with respect to x and y

Fx = -2x e^(-x^2/(16-y^2))/((16-y^2)^2)

Fy = 2y e^(-x^2/(16-y^2))/((16-y^2)^2)

Plugging in the coordinates of P, we get

Fx(2,2) = -2e^(-1/3)/49

Fy(2,2) = 2e^(-1/3)/49

Therefore, the gradient of F at P is

∇F(2,2) = (-2e^(-1/3)/49) i + (2e^(-1/3)/49) j

To obtain the unit vector in the direction of steepest ascent, we normalize the gradient

u = (∇F(2,2))/||∇F(2,2)|| = (-i + j)/√2

To obtain the unit vector in the direction of steepest descent, we take the negative of u

v = -u = (i - j)/√2

To find a vector that points in a direction of no change in the function at P, we need to find a vector orthogonal to the gradient of F at P. One way to do this is to take the cross product of the gradient with the vector k in the z-direction

w = ∇F(2,2) x k = (2e^(-1/3)/49) i + (2e^(-1/3)/49) j + (2/7) k

Therefore, the vector that points in a direction of no change in the function at P is

(2e^(-1/3)/49) i + (2e^(-1/3)/49) j + (2/7) k

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The test score of the student who joined the class is 55.

To find the test score of the student who joined the class, we can use the formula for calculating the mean:

Mean = (Sum of all values) / (Number of values)

We know that the mean test score of the original 12 students was 42. This means that the sum of their test scores was:

Sum of scores = Mean x Number of students = 42 x 12 = 504

Now, when the new student joins the class, the mean test score becomes 43. This means that the sum of all 13 students' test scores is:

Sum of scores = Mean x Number of students = 43 x 13 = 559

We can subtract the sum of the original 12 students' test scores from the sum of all 13 students' test scores to find the test score of the student who joined the class:

Test score of new student = Sum of all scores - Sum of original scores
Test score of new student = 559 - 504
Test score of new student = 55

Therefore, the test score of the student who joined the class is 55.

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The critical value t Subscript c for a confidence level of 0.90 and sample size of 26 is 1.708. A t-value greater than or less than 1.708 in absolute value would lead to rejection of the null hypothesis at the 0.10 level of significance.

To find the critical value t Subscript c for the confidence level c=0.90 and sample size n=26, we can use a t-distribution table or calculator.

Since we have a sample size of n=26, we have n-1 = 25 degrees of freedom. Using a t-distribution table or calculator with 25 degrees of freedom and a confidence level of 0.90, we get

t Subscript c = 1.708

Therefore, the critical value t Subscript c for the confidence level c=0.90 and sample size n=26 is 1.708. This means that if we calculate the t-value from our sample data and it is greater than or less than 1.708 in absolute value, we can reject the null hypothesis at the 0.10 level of significance.

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Among the given options, the square is a rectangle.

To determine which of these is a rectangle, we will consider the properties of a rectangle and compare them with the properties of a pentagon, trapezoid, square, and rhombus.

A rectangle is a quadrilateral with four right angles and opposite sides equal in length.

1. Pentagon: A pentagon has five sides and cannot be a rectangle since a rectangle must have four sides.

2. Trapezoid: A trapezoid has one pair of parallel sides, but it does not have four right angles, so it cannot be a rectangle.

3. Square: A square has four equal sides and four right angles, making it a special type of rectangle. Therefore, a square is a rectangle.

4. Rhombus: A rhombus has four equal sides but does not necessarily have four right angles, so it is not a rectangle.

In conclusion, among the given options, the square is a rectangle.

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the determinant of the matrix is e1e4-e3e2

The determinant of a matrix is a scalar value that is a function of the entries. It characterizes some properties of the matrix and the linear map represented by it. The determinant is nonzero if and only if the matrix is invertible and an isomorphism exists.

Determinants are only defined for square matrices and encode certain properties of the matrices.

The determinant of a matrix is defined by the difference betweern the product of the right diagonal to the the product of the left diagonal

From the given question. the determinant of the matrix is e1*e4 -e3-e2 = e1e4-e3e2

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Answer:the radius of the hemisphere with a volume of 324 ft³ is approximately 6.3 feet (to the nearest tenth).

Step-by-step explanation:

The formula for the volume of a hemisphere is:

V = (2/3) × π × r³, where V is the volume and r is the radius of the hemisphere.

We have been given the volume of the hemisphere as 324 ft³, so we can substitute this into the formula:324 = (2/3) × π × r³

To find the radius r, we need to solve for it. Dividing both sides by (2/3) × π gives:r³ = (324 / ((2/3) × π))r³ = (324 × 3) / (2 × π)r³ = 486 / π

Taking the cube root of both sides gives:r = (486 / π)^(1/3)

Using a calculator to evaluate this expression, we get:r ≈ 6.3

The depreciation for the first year of the truck's useful life is $7,467 by the straight-line method and $2,720 by the units-of-output method.

Depreciation per year = (Cost - Salvage value) / Useful life

Depreciation per year = (40,000 - 5,000) / 5 = $7,000

Depreciation for the first year = (16,000 / 15,000) x $7,000 = $7,467

Depreciation per mile = (Cost - Salvage value) / Total miles expected to be driven

Depreciation per mile = (40,000 - 5,000) / (5 x 15,000) = $0.17/mile

Depreciation for the first year = 16,000 x $0.17 = $2,720

Therefore, the depreciation for the first year of the truck's useful life is $7,467 by the straight-line method and $2,720 by the units-of-output method.

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The zeros for this quadratic equation is [-1, 0].

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Next, we would solve the quadratic function by using the factorization method as follows;

y = x² + 2x + 1

x² + 2x + 1 = 0

x² + x + x + 1 = 0

x(x + 1) + 1(x + 1) = 0

(x + 1)(x + 1) = 0

x = -1.

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Two balloons A and B apart 150km with given angle of elevation represents observer A is at a distance of  122.5 km approximately from balloon.

Number of observers = 2

Distance between two observers A and B = 150km

Angles of elevation are 42° and 76°.

Let us consider 'h' be the height of the balloon

Let the distance from observer A to the balloon x.

Use trigonometry to find the value of x.

From observer A, the angle of elevation to the balloon is 42°.

This means that the height of the balloon above observer A is ,

h = x ×  tan(42°)

From observer B,

The angle of elevation to the balloon is 76°.

This means that the height of the balloon above observer B is ,

h = (150 - x) × tan(76°)

Since both expressions give the same value for h, set them equal to each other,

⇒ x × tan(42°) = (150 - x) × tan(76°)

Simplifying this equation, we get,

⇒ x × (0.9004 ) = (150 - x) × 4.0107

⇒ 0.9004x = 601.605 - 4.0107x

⇒ 4.9111x = 601.605

⇒ x ≈ 122.5 km

Therefore, the distance from observer A to the balloon as per given angle of elevation is approximately 98.3 km.

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Answer: 2,506 people

Step-by-step explanation:

786 + 908 + 812 = 2,506 people

Step-by-step explanation:

x = sqrt (y-9)     square both sides

x^2 = y-9           add 9 to both sides

y = x^2 + 9        <====== this parabola has a POSITIVE x^2 coefficient ( +1)...

                                      so it is bowl shaped and opens UPWARD

The equation of the quadratic function in the stretch part is f(x) = x² + 4x - 11

From the question, we have the following parameters that can be used in our computation:

Zeros: -2 ± √15

This means that

Zeros: -2 - √15 and -2 + √15

The equation of the function is calculated as

f(x) = product of (x - zeros)

So, we have

f(x) = (x - (-2 -√15)) * (x - (-2 + √15))

When expanded, we have

f(x) = (x + 2 + √15)) * (x + 2 - √15))

Evaluate the products

f(x) = x² + 4x - 11

Hence, the function is f(x) = x² + 4x - 11

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The equation of the ellipse is x^2/9 + y^2/6.75 = 1

To find the equation of an ellipse, we need to know the center, the major and minor axis, and the foci.

Since we are given the eccentricity and foci, we can use the following formula:

c = (1/2)a

Since the foci are (0, +/-3), the center is at (0, 0). We know that c = 3/2, so we can find a:

c = (1/2)a

3/2 = (1/2)a

a = 3

The distance from the center to the end of the minor axis is b, which can be found using the formula:

b = √(a^2 - c^2)

b = √(3^2 - (3/2)^2)

b = √6.75

So the equation of the ellipse is:

x^2/a^2 + y^2/b^2 = 1

Plugging in the values we found, we get:

x^2/3^2 + y^2/6.75 = 1

Simplifying:

x^2/9 + y^2/6.75 = 1

Therefore, the equation of the ellipse is x^2/9 + y^2/6.75 = 1

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Answer: -10.57

Step-by-step explanation:

Answer:

0.25 years

Step-by-step explanation:

Penelope invested $89,000 in an account paying an interest rate of 6⅜% compounded continuously.

To calculate the time it would take Penelope's money to double, use the continuous compounding interest formula.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Interest Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

As the principal amount is doubled, then A = 2P.

Given interest rate:

Substitute A = 2P and r = 0.06375 into the continuous compounding interest formula and solve for t:

[tex]\implies 2P=Pe^{0.06375t}[/tex]

[tex]\implies 2=e^{0.06375t}[/tex]

[tex]\implies \ln 2=\ln e^{0.06375t}[/tex]

[tex]\implies \ln 2=0.06375t\ln e[/tex]

[tex]\implies \ln 2=0.06375t(1)[/tex]

[tex]\implies \ln 2=0.06375t[/tex]

[tex]\implies t=\dfrac{\ln 2}{0.06375}[/tex]

[tex]\implies t=10.872896949...[/tex]

Therefore, it will take 10.87 years for Penelope's investment to double.

[tex]\hrulefill[/tex]

Samir invested $89,000 in an account paying an interest rate of 6¹/₄% compounded monthly.

To calculate the time it would take Samir's money to double, use the compound interest formula.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

As the principal amount is doubled, then A = 2P.

Given values:

Substitute the values into the formula and solve for t:

[tex]\implies 2P=P\left(1+\dfrac{0.0625}{12}\right)^{12t}[/tex]

[tex]\implies 2=\left(1+\dfrac{0.0625}{12}\right)^{12t}[/tex]

[tex]\implies 2=\left(1+0.005208333...\right)^{12t}[/tex]

[tex]\implies 2=\left(1.005208333...\right)^{12t}[/tex]

[tex]\implies \ln 2=\ln \left(1.005208333...\right)^{12t}[/tex]

[tex]\implies \ln 2=12t \ln \left(1.005208333...\right)[/tex]

[tex]\implies t=\dfrac{\ln 2}{12 \ln \left(1.005208333...\right)}[/tex]

[tex]\implies t=11.1192110...[/tex]

Therefore, it will take 11.12 years for Samir's investment to double.

[tex]\hrulefill[/tex]

To calculate how much longer it would take for Samir's money to double than for Penelope's money to double, subtract the value of t for Penelope from the value of t for Samir:

[tex]\begin{aligned}\implies t_{\sf Samir}-t_{\sf Penelope}&=11.1192110......-10.872896949...\\&= 0.246314066...\\&=0.25\; \sf years\;(nearest\;hundredth)\end{aligned}[/tex]

Therefore, it would take 0.25 years longer for Samir's money to double than for Penelope's money to double.

Thus, the amount after the compounding is found to be $14,683.82.

Compound interest is, to put it simply, interest that is earned on interest. Compound interest is interest that is earned on both the initial principal and interest that builds up over time in a savings account.

There may be a difference in the timing of when interest is paid out and compounded. For instance, interest on a savings account may be paid monthly but compounded daily.

Given data:

principal P: $5,000,

annual interest r: 6%,

n interest periods: 12,

number of years t : 18

Formula:

A = P[tex](1 + r/n)^{nt}[/tex]

Put the values:

A = 5000[tex](1 + 0.06/12)^{12*18}[/tex]

A = 5000*2.93

A = 14,683.82

Thus, the amount after the compounding is found to be $14,683.82.

Know more about the compound interest:

https://brainly.com/question/30364118

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Complete question:

principal: $5,000, annual interest: 6%, interest periods: 12, number of years: 18

After 18 years, the investment compounded what will be worth $___.?

The volume of the smaller cone is approximately [tex]5.5 cm^3[/tex], rounded to the nearest tenth

If the cones are similar, then the ratio of the corresponding dimensions of the cones is the same.

Let's denote the height and radius of the smaller cone as h and r, respectively. Then, the height and radius of the larger cone are 3h and 2r, respectively.

Since the volumes of the cones are proportional to the cube of their radii and heights, we can write:

(volume of smaller cone) / (volume of larger cone) = [tex](r^2 * h) / ((2r)^2 * 3h)[/tex]

Simplifying this expression, we get:

(volume of smaller cone) / (volume of larger cone) = 1/12

Since we are given that the volume of the larger cone is [tex]66 cm^3[/tex], we can solve for the volume of the smaller cone as follows:

(volume of smaller cone) =[tex](1/12) * (66 cm^3) = 5.5 cm^3[/tex]

To know more about cones  refer here

https://brainly.com/question/1142336#

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