AMOUNT ALREADY APPROVED R9 000,00 Cash already approved YOUR LOAN OFFER 1. EXPIRY DATE: 28 February 2023 . Payable over 48 months Monthly instalments = R 318,92 R 9 000,00 Calculate the TOTAL amount that Theo has to payback if s the loan. Why, do you think, do banks and other financial institutions cash loans to people that did not apply for it? Theo decides to take the loan and wants to invest the mon. he following options. Option 1: The R9 000 invested at 8% p.a. simple interest f Option 2: The R9 000 invested at 7% p.a. compound interest
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Angles AOB and BOC are complimentary angles if AOC is a right angle. Let's use x to represent the angle BOC's size. Next, we have: Angle AOB plus Angle BOC equals 90° (definition of complementary angles).

BOC/AOB angle equals 2/3 (given) Angle AOB may be expressed in terms of angle BOC using the second equation: (3/2) × angle BOC, where angle AOB (multiplying both sides by angle AOB)    Angle BOC plus angle (3/2) equals 90 degrees. When we simplify this equation, we obtain: BOC angle (5/2) times equals 90 degrees. By multiplying both sides by 5, we obtain: BOC angle = (2/5) x 90 degrees BOC angle is 36 degrees. Hence, the angle's size Substituting this expression into the first equation, we get: (3/2) x angle BOC + angle BOC = 90 degrees Simplifying this equation, we get: (5/2) x angle BOC = 90 degrees.

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Using binomial theorem we can expand the equation but We are not given the value of a or n, so we cannot determine c exactly.

Integers are real numbers that only comprise positive and negative whole integers as well as natural numbers. Because of rational and irrational numbers, real numbers may include fractions, whereas integers cannot.

A real number is a quantity in mathematics that may be expressed as an infinite decimal expansion. Real numbers, as opposed to natural numbers such as 1, 2, 3,..., which are generated from counting, are used in measures of continually changing quantities such as size and time.

by applying the binomial theorem:

[tex](1 + ax)^n = C(n, 0) + C(n, 1)(ax) + C(n, 2)(ax)^2 + C(n, 3)(ax)^3 + ...[/tex]

where C(n, k) is the binomial coefficient, which equals[tex]n!/(k!(n-k)!).[/tex]

The first few terms of this expansion are:

[tex](1 + ax)^n = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]

Comparing with the given expression [1 - 20x + 150x^2 + cx^3], we have:

[tex]1 - 20x + 150x^2 + cx^3 = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]

Equating coefficients of [tex]x^3[/tex] on both sides, we get:

[tex]c = n(n-1)(n-2)(a^3/6)[/tex]

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Answer: x=211/1296

Step-by-step explanation:

The height of the triangle is 1.12 units (rounded to two decimal places).

The height of a triangle is the perpendicular distance from the base of the triangle to the opposite vertex. In other words, it is the length of the line segment that is perpendicular to the base and passes through the opposite vertex.

We can use the formula for the area of a triangle:

Area = (1/2) * base * height

And since we know the values of the base (b) and the area (a), we can rearrange the formula to solve for the height (h):

h = (2a) / b

Plugging in the values of a and b:

h = (2 * 14) / 25

h = 28 / 25

Therefore, the height of the triangle is 1.12 units (rounded to two decimal places).

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Answer:

AD=4

Step-by-step explanation:

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The length of AD in the triangular prism is 9.8 cm.

The length of AD in the triangular prism can be found using Pythagoras' theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The base of the prism is a right triangle, so:

AD² = AE² + ED²

AD² = 4² + 9²

AD² = √97

AD = √97

AD = 9.8 cm (rounded to 1 decimal)

Therefore, the length of AD in the triangular prism is 9.8 cm.

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Complete Question:

Use Pythagoras' theorem to work out the length of AD in this triangular prism. Give your answer in centimeters (cm) to 1 decimal point.

Thus, the total cost of gas for fill the tank of car tank is $40.23.

Finding the sum of the values of one unit and then multiplying its amount by the sum of the values of one unit to get the value of even more or fewer units is the unitary method's formula.  In this illustration, the "unit" represents the quantity of books, and the "value" is their purchase price.

When we visit the market to purchase any item, we inquire about the item's pricing from the shopkeeper. The term for this is unit price.

For the stated question:

Capacity of car = 13.5 gallons of gas.

Gas cost = $2.98 per gallon

So, cost to fill the tank:

Total cost = gas costs per gallon * Capacity of car

Total cost = $2.98 * 13.5

Total cost = $40.23

Thus, the total cost of gas for fill the tank of car tank is $40.23.

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Answer:

A. x = -2 or x = 8

Good luck!!

Step-by-step explanation:

(x - 3) - 10 = -5

x - 3 = - 5 + 10

x - 3 = 5

x = 5 + 3

x = 8

Answer:

  -10/11

Step-by-step explanation:

You want the average rate of change of f(x) on the interval [-6, 5].

The average rate of change of function f(x) on the interval [a, b] is ...

  AROC = (f(b) -f(a))/(b -a)

  = (f(5) -f(-6))/(5 -(-6))

  = (-20 -(-10))/5 +6 = (-20 +10)/(5 +6)

  AROC = -10/11

The average rate of change on the interval is -10/11.

Answer:

How to solve a ratio problem:

Add together the parts of the ratio to find the total number of shares.

Divide the total amount by the total number of shares.

Multiply by the number of shares required.

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I often see myself represented in the media as a strong, independent woman who lives fearlessly and passionately. I'm a black woman, and I'm proud to be a part of the diverse range of people in our society.

Passionately is an adjective that describes a person who is filled with intense emotion and enthusiasm. This can be expressed through action or behavior. When someone is passionate about something, they often feel an overwhelming urge to pursue it with great intensity. Being passionate about something is often associated with seeking to make a difference or make an impact on the world.

My representation in the media is not always positive, however. I've been depicted as being too opinionated, too outspoken, or too headstrong. I'm often seen as a stereotype, or as someone who doesn't fit into the roles that society has determined for me.

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I see myself represented in the media by characters who are strong, independent, and confident.

Media is the broad term used to describe any form of communication that can be used to disseminate information to a large group of people. Media includes traditional media such as newspapers, magazines, radio, and television, as well as more modern forms such as digital media, including websites, social media, and online streaming.

They may have had a difficult start, but they don't let it define them. They are determined to make something of themselves, regardless of the odds. They are resilient and are not afraid to stand up for what they believe in. Through these characters, I can relate to and identify with the struggles and successes of the journey.
My own writer's voice is often reflective and contemplative. I strive to be thoughtful and honest in my writing, and often use metaphors and imagery to make a point. For example, I might write, "Her journey was like a rollercoaster, with highs and lows along the way, but she kept her eyes on the horizon, never losing sight of her goals." Here, I am using an analogy to convey the idea of how a person's path might not always be easy, but they can remain focused on the end result.
The author of the essay used rhetorical questions to emphasize their points and express their opinion. I have also adopted this technique in my writing. For example, I might write, "Do we ever really know how our stories will unfold? Or what it takes to get there?" The use of rhetorical questions captures the reader's attention and sparks their imagination.
Overall, I feel that my writer's voice is distinct and I am confident in my use of literary devices. By incorporating the use of rhetorical questions and analogies, I am able to effectively convey my opinion and perspective in a unique way.

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To solve this inequality, we must first isolate the absolute value on one side of the equation.

Step 1: Add 5 to both sides of the equation.

−2x−5 + 5 ≤ 5 + 5

Step 2: Simplify the left side.

−2x ≤ 10

Step 3: Divide both sides by -2.

x ≥ -5

Step 4: Graph the solution on a number line.

The solution set is {x | x ≥ -5}

Here, QRS represents the proportion of longest triangle to middle-length sides. 26/36 = 13/18 QUT: 12/16 = ¾ ≠ 13/18

Students should be taught that whereas a triangle can have many various side lengths and angles, a square must have all of its sides be the same length and all of its angles must be right angles.

Hence, a square cover must contain a minimum of 4 corner-power points. Nevertheless, each triangles may include one corners in its inside or twin vertex on edges (score of 1) for a not more than one point. Three triangles only cover a square with a maximum of three corner-power points.

[tex]QRS: 26/36 = 13/18[/tex]

[tex]QUT: 12/16 = 3/4 not equal 13/18[/tex]

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5) By AAA congruency rule, ΔVWU ≅ ΔMNU.

6) By SAS congruency rule, ΔCAB ≅ ΔUAV

If any twο sides and the angle included between the sides οf οne triangle are equivalent tο the cοrrespοnding twο sides and the angle between the sides οf the secοnd triangle, then the twο triangles are said tο be cοngruent by SAS rule.

5) ∠V ≅ ∠V = 36°

∠VUW ≅ ∠NUM

then according to angle sum property

∠VWU ≅ ∠MNU

Then,

ΔVWU ≅ ΔMNU

By AAA congruency rule, ΔVWU ≅ ΔMNU.

6) 77 ≅ 66 (common side)

42 ≅ 36 (common side)

∠CAB ≅ ∠UAV (common angle)

Then,

ΔCAB ≅ ΔUAV

By SAS congruency rule, ΔCAB ≅ ΔUAV

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The set of all possible y-values for the function h constitutes its range. The range is therefore [-3, 0].

The collection of all feasible output values (dependent variable) of a function is known as the range in mathematics. It is the totality of all possible numbers that the function can accept as input (an independent variable) and output. On the number line, the range is frequently represented by an interval or group of intervals. For instance, the range can be written as [-3, 3] if the domain of a function f(x) is [-2, 2] and its output numbers fall within [-3, 3].

given

The collection of all x-values for which h(x) is specified is the domain of the function h.

The graph's [-2, 4] domain can be determined by looking at the graph, which shows that it begins at x=-2 and concludes at x=4.

The set of all possible y-values for the function h constitutes its range. Looking at the graph, we can see that it takes all values between y=-3 and y=0, and that it begins at y=-3.

The range is therefore [-3, 0].

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The complete question is :-  The entire graph of the function h is shown in the figure below. Write the domain and range of h as intervals or unions of intervals.

-2

-3-

4-

domain =

range =

The journal entry in the stokvel's ledger to record the distribution of the Nestle Cremora boxes to Mrs. Bosoga would be as follows:

Date Account Debit Credit

Dec 2022 Nestle Cremora ZAR 3,750

Dec 2022 Mrs. Bosoga  ZAR 3,750

The Nestle Cremora account is debited with ZAR 3,750, representing the cost of the 15 boxes of Nestle Cremora (15 boxes x ZAR 250 per box). The Mrs. Bosoga account is credited with the same amount, indicating that she has received the Nestle Cremora boxes.

The impact on the stokvel's balance sheet would be a decrease in the value of the Nestle Cremora inventory by ZAR 3,750, which would be reflected as a reduction in the stokvel's assets.

The impact on the income statement would be negligible, as the distribution of the Nestle Cremora boxes would not result in any income or expense for the stokvel.

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Mrs. Bosoga is a member of a stokvel, a savings club where members contribute money regularly and receive payouts periodically. During December 2022, Mrs. Bosoga received a share of 15 boxes of Nestle Cremora from the stokvel. The market value of each box of Nestle Cremora at the time was ZAR 250. The stokvel keeps track of its transactions using a ledger. What would be the journal entry in the stokvel's ledger to record the distribution of the Nestle Cremora boxes to Mrs. Bosoga? Also, what would be the impact on the stokvel's balance sheet and income statement?

We have that, based on the system of the module, by sending Nelson 2ec (mod n), Eve can use her system to find m without ever sending him c.

Naive Nelson's RSA system works using the equation c = me (mod n), where c is the recorded text, m is the message, e is the recorded exponent, and n is the public modulus. Therefore, to find m, Eve needs to solve the equation 2ec = me2 (mod n). Since 2e and m2 are known values, Eve can calculate more:

m = 2ec / m2 (module n)

So by sending Nelson 2ec (mod n), Eve can use her system to find m without ever sending him c.

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the variance of X is 9. b) Determine E [2X² - 20X +5]:

Using linearity of expectation, we can find E [2X² - 20X +5] as:

E [2X² - 20X +5] = 2E[X²] - 20E[X] + 5

by the question.

The number of ways to select the first 2 white chips is given by:

Number of ways = (6C2) (5C0) (3C0) = 15

The number of ways to select the third chip as blue given that the first 2 chips were white is given by:

Number of ways = (3C1) = 3

Therefore, the probability of selecting the third chip as blue given that the first 2 chips were white is:

P(The third chip is blue the first 2 were white) = Number of ways / Total number of ways = 3 / 350 = 0.0086 (rounded to 4 decimal places)

c) P(The fourth chip is blue the first 2 were white):

The number of ways to select the first 2 white chips is given by:

Number of ways = (6C2) (5C0) (3C0) = 15

The number of ways to select the third chip as non-white given that the first 2 chips were white is given by:

Number of ways = (8C1) = 8

The number of ways to select the fourth chip as blue given that the first 2 chips were white, and the third chip was non-white is given by:

Number of ways = (3C1) = 3

Therefore, the probability of selecting the fourth chip as blue given that the first 2 chips were white is:

P(The fourth chip is blue the first 2 were white) = Number of ways / Total number of ways = 8*3 / 350 = 0.0686 (rounded to 4 decimal places)

Suppose we have a random variable X such that E[X]= 7 and E[X²] =58.

a) Determine the variance of X:

The variance of X is given by:

Var[X] = E[X²] - (E[X]) ²

Substituting the given values, we get:

Var[X] = 58 - (7) ² = 9

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Answer:

To find the average distance away from the mean, we need to first find the mean distance from the mean. To do this, we need to find the mean of the distances from the mean:

|32 - 33| = 1

|45 - 33| = 12

|23 - 33| = 10

|35 - 33| = 2

|30 - 33| = 3

Mean distance from the mean = (1 + 12 + 10 + 2 + 3) / 5 = 6. However, the question asks for the average distance away from the mean, so we need to take the absolute value of this result:

Average distance away from the mean = |6| = 6

To find the mean absolute deviation, we first need to find the deviations from the mean:

12.7 - 15.2 = -2.5

22 - 15.2 = 6.8

23.5 - 15.2 = 8.3

24 - 15.2 = 8.8

11 - 15.2 = -4.2

22 - 15.2 = 6.8

Next, we need to take the absolute value of each deviation:

|-2.5| = 2.5

|6.8| = 6.8

|8.3| = 8.3

|8.8| = 8.8

|-4.2| = 4.2

|6.8| = 6.8

The sum of these absolute deviations is:

2.5 + 6.8 + 8.3 + 8.8 + 4.2 + 6.8 = 37.4

To find the mean absolute deviation, we divide this sum by the number of data points:

Mean absolute deviation = 37.4 / 6 = 6.23

Therefore, the answer is not listed among the choices given.

Answer:

B. 33

Step-by-step explanation:

1) Find the mean

32+45+23+35+30/5

165/5

=33

Answer:

Step-by-step explanation:

1. add 14 to 24

2. ur done!

The volume of the frustum is 970 cm².

What is frustum?

In geometry, a frustum is a three-dimensional solid that is created by cutting a larger solid, such as a cone or pyramid, with a plane parallel to its base, and then removing the smaller solid that lies above the plane. The resulting solid has two parallel bases of different sizes, and its sides are trapezoidal in shape.

We know that, volume of frustum is given by

                       V = (1/3) * h * (A + B + sqrt(A * B))

where V is the volume of the frustum, h is the height of the frustum, A is the area of the rectangular base, and B is the area of the rectangular top.

So, A = base × height = 8 × 16

                                    = 128 cm²

Similarly, B = base × height =  3 × 6

                                             = 18 cm²

and, given height of frustum = 15 cm

Now, putting all values into the formula:

So,  V = (1/3)× h × (A + B + sqrt(A×B))

          = 1/3 × 15 × ( 128+18 + √(128×18))

          = 5 × ( 146 + 48 )

          = 970 cm²

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Answer:

Step-by-step explanation: In the problem, they tell us that

dL / dt = 7 cm/s (the rate at which the length is changing) and

dw / dt = 8 cm/s (the rate at which the width is changing)

Want dA/dt (the rate at which the area is changing) when L = 7 cm and w = 5 cm

The equation for the area of a rectangle is:

A = L·w, so will need the product rule when taking the derivative.

dA/dt = L (dw/dt) + w (dL/dt)

Now just plug in all of the given numbers:

dA/dt = (7)(7) + (5)(8) = 49+40 = 89  cm²/s

Answer:

(-∝, 0)

Step-by-step explanation

f(x) will extend from negative infinity and approach but never reach the point where x = 0.

So the solution is  x > -infinity and < 0.

Thus, a 0.1271 area under the standard normal curve corresponds to a z-score of roughly -1.14.

The degree of variance or dispersion in a set of data values is measured by standard deviation. It computes the deviation of each data point from the mean (average) of the data. While a high standard deviation suggests that the data points are dispersed throughout a broader range of values, a low standard deviation suggests that the data points tend to be close to the mean. In statistics, the standard deviation is frequently used to evaluate the level of variability or dispersion within a data collection.

given

Using a normal distribution function on a calculator or a standard normal distribution table, we can determine the z-score that corresponds to an area of 0.1271 under the standard normal curve.

We can enter the following data into a calculator equipped with a normal distribution function:

Area = 0.1271

Mean = 0 (because we are using the usual normal distribution) (since we are using the standard normal distribution)

Standard deviation equals one (since we are using the standard normal distribution)

Calculating this, we obtain:

Z is equal to invNorm(0.1271, 0, 1) = -1.14.

Thus, a 0.1271 area under the standard normal curve corresponds to a z-score of roughly -1.14.

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Answer:

it is -1.14

Step-by-step explanation:

I took the k12 quiz

(a) Starting with the 75% estimate for Italians, the sample you must collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence is n = 51.

(b) The sample size required if you made no assumptions about the value of the proportion who could taste PTC is n = 68.

(a) To estimate the sample size needed to find the proportion of PTC tasters within ± 0.1 with 90% confidence, we will use the formula for sample size estimation in proportion problems:
n = (Z² * p * (1-p)) / E²

Where n is the sample size, Z is the Z-score corresponding to the desired confidence level (1.645 for 90% confidence), p is the proportion of PTC tasters (0.75), and E is the margin of error (0.1).

n = (1.645² * 0.75 * (1-0.75)) / 0.1²
n = (2.706 * 0.75 * 0.25) / 0.01
n ≈ 50.74

Since we need a whole number, we round up to the nearest whole number:
n = 51

(b) If no assumptions were made about the proportion of PTC tasters, we would use the worst-case scenario, which is p = 0.5 (maximum variance):

n = (1.645² * 0.5 * (1-0.5)) / 0.1²
n = (2.706 * 0.5 * 0.5) / 0.01
n ≈ 67.65

Again, rounding up to the nearest whole number:
n = 68

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The length, in feet, of BC is the square root of  √242 and, The length, in feet, of CF is the square root of √363

Cube:

In geometry, a cube is a three-dimensional solid object bounded by six faces, facets, or square sides, with three points of intersection at each vertex. Seen from a certain angle, it is a hexagon and its canvas is often represented by a cross.

Cube is the only regular hexahedron and one of the five Platonic solids. It has 6 faces, 12 edges and 8 vertices. Cube is also a cube, an equilateral cuboid, a rhombus and a 3-sonohedron.

Three orientations are square prisms and four orientations are triangular trapezoids. A cube is twice as large as an octahedron. It has cubic or octahedral symmetry. Cube is the only convex polyhedron whose faces are square.

Then the length CB is given by the Pythagorean theorem as:

CB = √(AC² +AB²)

     = √{(2 cm)² + (√2 cm)²}

     = √(4 +2) cm

CB = √6 cm

Now,

The length, in feet, of BC is the square root of  

√242

And,

The length, in feet, of CF is the square root of  

√363

Complete Question:

A cube. The top face has points C, A, B, D and the bottom face has points G, E, F, H. Diagonals are drawn from B to C and from C to F. Side B F is 11 feet.

What are the exact lengths of BC and CF?

The length, in feet, of BC is the square root of

The length, in feet, of CF is the square root of

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Answer:

The length, in feet, of BC is the square root of

✔ 242

The length, in feet, of CF is the square root of

✔ 363

Step-by-step explanation:

If the hypothesis test is performed to determine if the proportion of all six packs of seltzers sold in a particular grocery store near a college campus that are alcoholic exceeds 50% Then complement of the P-value gives the probability that the null hypothesis is true, which is 1 minus 0.0047, or 0.9953.

The probability the null hypothesis is true is 1-0.0047 = 0.9953 because ,

The given P-value is 0.0047,

which is the probability of observing a test statistic as extreme as 2.60 or more extreme if the null hypothesis is true. Since this P-value is less than the significance level of 0.05 (assuming a typical significance level), we reject the null hypothesis and conclude that the proportion of all six packs of seltzers sold in the grocery store that are alcoholic exceeds 50%.

Therefore, statement (a) is true and all the other statements are incorrect. The complement of the P-value gives the probability that the null hypothesis is true, which is 1 minus 0.0047, or 0.9953.

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Answer:

Step-by-step explanation:

To graph the line with slope 3 passing through the point (1,-5), we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is a point on the line.

Substituting the given values, we get:

y - (-5) = 3(x - 1)

Simplifying the equation, we get:

y + 5 = 3x - 3

Subtracting 5 from both sides, we get:

y = 3x - 8

Now we have the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Comparing this equation to the one we just found, we can see that the slope is 3 and the y-intercept is -8.

To graph the line, we can plot the y-intercept at (0,-8) and then use the slope to find other points on the line. Since the slope is 3, we can go up 3 units and to the right 1 unit to find another point on the line. We can repeat this process to find more points on the line, and then connect them to graph the line.

Therefore, in about 15 years and 2 months, the senior class will have about 100 students.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).

Then, we can write the following equation to represent the situation:

P[tex](1-r)^{n}[/tex] = 100

We know that the current population of the senior class is 320, so we can substitute these values into the equation:

320[tex](1-0.07)^{n}[/tex] = 100

Simplifying the equation, we get:

[tex]0.93^{n}[/tex] = 0.3125

Taking the natural logarithm of both sides, we get:

n ln (0.93) = ln (0.3125)

Dividing both sides by ln (0.93), we get:

n = ln (0.3125) / ln (0.93)

Using a calculator, we find that n is approximately equal to 15.21 years.

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