need more help, have to multuply all of them

a. The matrices whose entries are all greater than or equal to 0: Yes, it is a subspace.

b. The matrices with trace (the sum of diagonal entries): No, it is not a subspace.

c. The matrices with all zeros in the third row: Yes, it is a subspace.

d. The matrices of rank 3: No, it is not a subspace.

e. The non-invertible matrices: No, it is not a subspace.

f. The matrices such that the vector [1, 2, 3] is in the kernel: Yes, it is a subspace.

What is matrix?

A matrix is a rectangular array of numbers or elements arranged in rows and columns. It is a fundamental concept in linear algebra and has various applications in mathematics, science, engineering, and computer science.

Let's analyze each subset and determine whether they are subspaces of the set of matrices.

a. The matrices whose entries are all greater than or equal to 0:

This subset is a subspace of the set of matrices since it satisfies the three conditions for being a subspace: closure under addition, closure under scalar multiplication, and containing the zero vector.

b. The matrices with trace (the sum of diagonal entries):

This subset is not a subspace of the set of matrices because it does not satisfy closure under scalar multiplication. Multiplying a matrix by a scalar will change the diagonal entries and, thus, the trace.

c. The matrices with all zeros in the third row:

This subset is a subspace of the set of matrices since it satisfies the three conditions for being a subspace: closure under addition, closure under scalar multiplication, and containing the zero vector.

d. The matrices of rank 3:

This subset is not a subspace of the set of matrices because it does not satisfy closure under addition. Adding two matrices of rank 3 may result in a matrix with a rank less than 3.

e. The non-invertible matrices:

This subset is not a subspace of the set of matrices because it does not satisfy closure under scalar multiplication. Multiplying a non-invertible matrix by a non-zero scalar will result in a matrix that may be invertible.

f. The matrices such that the vector [1, 2, 3] is in the kernel:

This subset is a subspace of the set of matrices since it satisfies the three conditions for being a subspace: closure under addition, closure under scalar multiplication, and containing the zero vector (which makes the vector [1, 2, 3] in the kernel).

In summary:

a. Yes, it is a subspace.

b. No, it is not a subspace.

c. Yes, it is a subspace.

d. No, it is not a subspace.

e. No, it is not a subspace.

f. Yes, it is a subspace.

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To cover the candle, Madeline will need around 150.72 square inches of wrapping paper.

To determine how much wrapping paper Madeline will use, we must first determine the surface area of the candle's correct circular cylinder shape. This comprises the top, bottom, and curving side areas.

To begin, we must determine the radius of the candle. Given that the diameter is 4 inches, the radius is half that, or 2 inches.

The area of the top and bottom of the candle may then be calculated. A = is the formula for calculating the area of a circle. As a result, the area of the top and bottom is:

A = inch square

To calculate the area of the curved side, take the circumference of the cylinder's circle (base) and multiply it by the height of the cylinder. C = is the formula for calculating the circumference of a circle. As a result, the circle's circumference is:

12.56 inches = C

Finally, we can calculate the area of the curved side by multiplying the circumference by the cylinder's height:

A is equal to 12.56 x 10 = 125.6 square inches.

To get the total quantity of wrapping paper required for Madeline, multiply the area of the top and bottom by the area of the curved side:

150.72 square inches = 12.56 + 12.56 + 125.6

To cover the candle, Madeline will need around 150.72 square inches of wrapping paper.

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If it is determined that Ray failed to exercise the appropriate level of care by not inspecting the ladder for defects and was therefore negligent, he could be held legally liable for the injuries Claude sustained due to the loose rung on the ladder.

The question involves the legal concepts of negligence, duty of care, and liability. Claude borrows an extension ladder from his neighbor, Ray, to use while painting his house. Ray is not aware that one of the rungs on the ladder is loose. Because of the loose rung, Claude falls while climbing the ladder and breaks his leg.

1. Negligence: This occurs when someone fails to exercise the level of care that a reasonable person would have exercised in a similar situation. In this case, Ray may be considered negligent if a reasonable person would have checked the ladder for defects before lending it to Claude.

2. Duty of care: This is a legal obligation that one person owes to another to exercise a reasonable level of care to avoid causing harm. As the owner of the ladder, Ray has a duty of care to ensure that the ladder is safe for Claude to use.

3. Liability: This refers to the legal responsibility for the consequences of one's actions. If Ray is found to be negligent in not ensuring the safety of the ladder, he may be held liable for Claude's injuries.

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The value of N in the quadrilateral is 9.

We are given that;

Angle z is 75degree angle x=105degree and angle w=90degree y=90degree ZW=4 WX=4 XY=under root N

Now,

we can use the fact that angle Z is 75 degrees and angle X is 105 degrees to find angle YZ. Since the sum of the angles in a quadrilateral is 360 degrees, we have:

Z+X+W+Y=360

Substituting the given values, we get:

75+105+90+YZ=360

Solving for YZ, we get:

YZ=90

Since angle YZ is 90 degrees, we can use the trigonometric ratio of tangent to find ZY. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. That is:

tanθ=adjacent/opposite​

Applying this to angle YZ, we get:

tan YZ =ZWZY​

Substituting the given values, we get:

tan90=4ZY​

Solving for ZY, we get:

ZY=4tan90

Therefore, by the quadrilateral the answer will be 9.

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332 square inches is the area of the octagon, rounded to the nearest square inch.

To find the area of the octagon, we can use the formula:

Area = (1/2) * apothem * perimeter

In this case, the apothem is given as 10 inches and the perimeter is given as 66.3 inches.

Substituting the values into the formula, we have:

Area = (1/2) * 10 * 66.3

Area = 5 * 66.3

Area = 331.5 square inches

Rounded to the nearest square inch, the area of the octagon is:

332 square inches

Therefore, the correct answer is:

332 in.²

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Depending on the accounting method used, the expense shown on the income and expense statement for the year would either be $150 or $500.

When purchasing a $500 stereo on an installment plan, the expense recorded on the income and expense statement for the year will depend on the accounting method used.

1. Cash Basis Accounting:

Under cash premise bookkeeping, costs are recorded when money is paid. In this case, since you made two payments of $75 each during the year, the expense recorded would be the total amount of cash paid, which is $75 x 2 = $150.

2. Accrual Basis Accounting:

Under accrual basis accounting, expenses are recorded when they are incurred, regardless of when the cash is paid. In this case, the expense recorded would be the total cost of the stereo, which is $500. The payments made during the year would be recorded as a reduction in the accounts payable liability associated with the stereo purchase.

Therefore, depending on the accounting method used, the expense shown on the income and expense statement for the year would either be $150 (cash basis accounting) or $500 (accrual basis accounting). It's important to note that the chosen accounting method should align with the accounting principles and regulations applicable to your situation.

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Answer:

a) £6200

b) £450

Step-by-step explanation:

cost = 12(monthly payment) + deposit

cost = c

monthly payment = m

deposit = d

a) c = 12m + d

m = 350

d = 2000

c = 12(350) + 2000 = 6200

The cost of a car is £6200

b) c = 12m + d

c = 8000

d = 2600

8000 = 12m + 2600

12m = 5400

m = 450

The monthly payment is £450

The solutions to the right triangle in this problem are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle A is given as follows:

m < A + 50 + 90 = 180

m < A = 180 - 140

m < A = 40º.

Side b is opposite to the angle of 50º, while 21 is the adjacent side to the angle of 50º, hence:

tan(50º) = b/21

b = 21 x tangent of 50 degrees

b = 25.

The hypotenuse c is then obtained as follows:

sin(50º) = b/c

c = 25/sine of 50 degrees

c = 32.6.

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The given statement "A beverage manufacturer enters the snack food business with the purchase of a popular potato chip company. This is an example of diversification." is true because the company to expand its product portfolio, enter a new market segment, reduce risk, and potentially increase its overall profitability.

In the case of the beverage manufacturer, their original business focused solely on beverages. This concentration poses a risk because if the beverage market experiences a downturn or faces intense competition, the company's profitability could be adversely affected.

This diversification strategy offers several advantages. First, it reduces the company's reliance on a single market, spreading the risk across different product categories. If the beverage market declines, the snack food business can potentially offset the losses. Second, by entering the snack food industry, the beverage manufacturer can benefit from economies of scope.

They can leverage their existing distribution networks, marketing expertise, and customer base to promote and sell their newly acquired potato chip products. This cross-promotion and synergy can enhance their overall competitiveness and profitability.

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[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]-36y=x^2\implies \stackrel{ 4p }{-36}(y-0)=(x-0)^2 \\\\\\ \stackrel{\textit{so we can say}}{4p=-36}\implies p=\cfrac{-36}{4}\implies p=-9[/tex]

now, the "p" distance is negative, meaning the parabola is clearly opening downwards like a camel's hump, that also means that the directrix is above it, and since the vertex is at the origin, Check the picture below.

The statement when setting up a new group item, you should enter the name, quantity, and sale price of each item in the group is true .

When setting up a new group item, it is important to enter the name, quantity, and sale price of each item in the group. This information allows for accurate tracking of inventory and sales, as well as proper pricing and calculation of profits or losses. By including the name, quantity, and sale price for each item in the group, you ensure that the group item is properly defined and can be managed effectively .

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The aspects of a written report would Malcom most likely prioritize over some of his millennial reports are specific work environment, industry, or personal inclinations.

Traditionalists generally appreciate reports that rely on factual information and data to support arguments and conclusions. Malcolm may prioritize reports that provide evidence-based analysis, statistical data, and logical reasoning. He might expect the inclusion of citations or references to reputable sources when presenting facts, figures, or external information. This focus on concrete evidence helps establish credibility and supports decision-making processes.

Given Malcolm's traditionalist tendencies, he might prioritize reports that demonstrate a keen eye for detail and accuracy. He may expect information to be well-researched, double-checked for accuracy, and presented in a meticulous manner. Spelling errors, typos, or incorrect information may be seen as indications of carelessness or lack of professionalism, which might impact his perception of the report's quality.

Furthermore, individuals' preferences may also be influenced by their specific work environment, industry, or personal inclinations. Effective communication and understanding between Malcolm and his millennial team members would involve considering their perspectives and finding a balance that satisfies everyone's needs and preferences while maintaining the standards required by the organization.

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Answer:

[tex]\phi=1080 \textdegree}[/tex]

Step-by-step explanation:

To tackle these types of problems it is only a matter of memorizing the proper conversion formula that I have posted below.

[tex]\text{Conversions:}\\\\\boxed{\left\begin{array}{ccc}\text{\underline{Degrees to Radians:}}\\\\ \text{Number of degrees} \times\frac{\pi}{180 \textdegree} \end{array}\right} \ \ \boxed{\left\begin{array}{ccc}\text{\underline{Radians to Degrees:}}\\\\ \text{Number of radians} \times\frac{180 \textdegree}{\pi} \end{array}\right}[/tex]

Given the angle 6π in radians, convert it to degrees.

[tex]\text{Number of radians} \times\frac{180 \textdegree}{\pi} \\\\\Longrightarrow \phi=6\pi\times\frac{180 \textdegree}{\pi}\\\\\Longrightarrow \phi=6\times180 \textdegree\\\\\therefore \boxed{\boxed{\phi=1080 \textdegree}}[/tex]

Thus, the problem is solved.

The minimum distance the annihilation event could have occurred from the center of the machine is approximately 98.94 nanometers.

To determine the minimum distance the annihilation event could have occurred from the center of the machine, we can use the speed of light as a constant and the time difference between the collisions of the gamma rays.

The speed of light in a vacuum is approximately 299,792,458 meters per second (m/s).

Since the time difference between the collisions of the gamma rays is given as 0.33 nanoseconds, we need to convert this time to seconds. One nanosecond is equal to 1 × 10⁻⁹seconds.

0.33 nanoseconds is equal to 0.33 × 10⁻⁹ seconds.

Now, we can calculate the minimum distance using the equation:

Distance = Speed of light × Time

Distance = 299,792,458 m/s × 0.33 × 10⁻⁹ seconds

Distance ≈ 98.94 nanometers

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The profit from selling the call option with an exercise price of $40 will approximately be $6.82,

To determine the profit from selling the call option with an exercise price of $40, we need to consider the difference between the premium received and the potential payout.

When selling a call option, the maximum profit is equal to the premium received. In this case, the premium received for selling the call option with an exercise price of $40 is $6.82.

The profit from selling the call option with an exercise price of $40 will be positive as long as the price of the underlying IBM stock remains below the exercise price of $40. If the stock price exceeds $40, the seller of the call option may face losses.

It's important to note that the profit from the option trade can be realized only if the option is not exercised by the buyer. If the buyer decides to exercise the option, the seller will have to fulfill their obligation and sell the stock at the exercise price, which may result in potential losses.

In summary, the profit from selling the call option with an exercise price of $40 is $6.82, assuming the option is not exercised by the buyer.

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The statement is false. It is not legal to directly instantiate an abstract class, whether or not it is initialized.

An abstract class is a class that cannot be instantiated directly. It serves as a blueprint for its subclasses and is meant to be extended and implemented by its derived classes. Abstract classes are designed to be partially or fully implemented by their subclasses, and they often contain abstract methods that must be overridden by the subclasses.

Attempting to instantiate an abstract class directly will result in a compilation error. The purpose of an abstract class is to provide a common interface and define common behavior for its subclasses. Therefore, it is not intended to be instantiated on its own.

To use the functionality of an abstract class, you need to create a concrete subclass that extends the abstract class and implements any necessary abstract methods. Instances of the concrete subclass can then be created and utilized.

Therefore, Incorrect. It is not permissible to directly create an instance of an abstract class, regardless of whether it is initialized or not.

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The scenario described involves walking across a carpet and experiencing shock upon touching an object. In this case, the object you touched is most likely a(n) electrostatic discharge (ESD) source.

When you walk across a carpet, friction between your shoes and the carpet generates static electricity. This process is known as triboelectric charging, and it results in a buildup of electrostatic charges on your body. As you continue walking, your body accumulates more and more of these charges.

When you touch an object, like a doorknob or a metal surface, the electrostatic charges on your body are transferred to the object, causing a sudden discharge of electricity. This discharge is what you feel as a shock, and it's known as an electrostatic discharge (ESD).

When you walk across a carpet and touch an object, experiencing a shock, the object you touched is most likely an electrostatic discharge (ESD) source. The process of accumulating charges on your body is called triboelectric charging, and the shock you feel is the result of the sudden discharge of electricity from your body to the object.

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The graph of the functions indicates that the intervals over which the functions are increasing are;

The function f is increasing over the interval 0 ≤ x < ∞

The function g is increasing over the interval -∞ < x < ∞

A function is a rule or definition that maps an input element to an output element, such that each input has exactly one output.

The values on the graph of the functions indicates;

The vertex of the function f is; (0, 2)

The function f is decreasing from -∞ < x ≤ 0

The function f is increasing from 0 ≤ x ≤ -∞

The function g is increasing over the interval -∞ < x < ∞

The correct options are therefore;

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Step-by-step explanation:

Using the given formula, we can substitute x = 1 and solve for y:

y = 5 x 2^x

y = 5 x 2^1 (substitute x = 1)

y = 5 x 2

y = 10

Therefore, when x = 1, y = 10.

Answer:

y = 10

Step-by-step explanation:

Chlorine has two stable isotopes , Cl-35 and Cl-37 with atomic masses 34.968 u and 36.956 u respectively. If the average atomic mass is 35.453 u.

The requested function, `outputvals()`, takes two integer parameters and prints all integers starting with the first parameter and ending with the second parameter, each multiplied by 100 and followed by a newline. There is no value returned by the function

Here is the implementation of the `outputvals()` function in Python:

```python

def outputvals(start, end):

print(i * 100)

# Example usage

outputvals(1, 5)

```

The `outputvals()` function takes two parameters, `start` and `end`, representing the starting and ending values for the sequence. It uses a `for` loop to iterate over the range from `start` to `end + 1` (inclusive). Inside the loop, each value is multiplied by 100, and then printed to the console followed by a newline.

For example, when `outputvals(1, 5)` is called, the function will iterate from 1 to 5 (inclusive) and print the values 100, 200, 300, 400, and 500, each on a separate line.

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Josh's paycheck can be calculated by finding three-fourths of the total amount he spent on the TV and then adding $100 to that amount. By subtracting this total from the cost of the TV, we can determine the value of his paycheck.

Let's assume Josh's paycheck is represented by the variable "P." According to the information given, Josh used one hundred dollars less than three-fourths of his paycheck to buy the new TV, which cost $488.

To find out how much Josh spent on the TV, we can set up an equation. Three-fourths of his paycheck is represented by (3/4)P, and since he spent $100 less than that amount, the equation becomes (3/4)P - $100 = $488.

To solve for P, we need to isolate the variable. Adding $100 to both sides of the equation, we have (3/4)P = $588. Next, we can multiply both sides of the equation by the reciprocal of (3/4), which is 4/3, to cancel out the fraction. This yields P = ($588) * (4/3) = $784.

Therefore, Josh's paycheck was $784.

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Russell and Dantzel Nelson immediately started studying Mandarin Chinese.

This information is specific to Russell and Dantzel Nelson and their personal response to President Kimball's challenge. It is not mentioned in the question why they chose Mandarin Chinese specifically, but it can be assumed that they had their own reasons for selecting that language. It is worth noting that Mandarin Chinese is one of the most widely spoken languages in the world, and learning it would have been beneficial for missionary work in areas where Mandarin is spoken. Russell M. Nelson, who later became the President of The Church of Jesus Christ of Latter-day Saints, had significant international experience and worked extensively with various cultures and interest, further emphasizing the importance of language learning for missionary service.

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Symantec Certified Specialist (SCS) certifications primarily emphasize troubleshooting skills related to Symantec solutions.

The statement highlights the core focus of Symantec Certified Specialist (SCS) certifications, which is troubleshooting Symantec solutions. Symantec, a well-known cybersecurity company, offers a range of products and solutions to protect against various threats and ensure data security. SCS certifications are designed to equip individuals with the knowledge and skills necessary to effectively troubleshoot issues that may arise while using Symantec solutions.

These certifications provide professionals with in-depth training and expertise in identifying and resolving technical problems, optimizing performance, and ensuring the smooth operation of Symantec software and systems. By specializing in troubleshooting, SCS-certified individuals are well-prepared to handle challenges related to installation, configuration, integration, and maintenance of Symantec products.

The emphasis on troubleshooting skills in SCS certifications underscores the importance of effectively resolving issues and providing technical support to users of Symantec solutions. This ensures that organizations can rely on these certified specialists to troubleshoot and rectify any problems that may arise, ultimately enhancing the overall effectiveness and performance of Symantec solutions in safeguarding against cybersecurity threats.

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The original volume is 6.3 cubic inches, on increase in height it is 9.4 and 14.1 inches³ on increase in diameter. The dependency on square of radius increases the volume more compared to height.

The volume of cone is calculated using the formula -

V = πr²h/3, where V is volume of cone, r is the radius and h is the height of cone.

Radius = Diameter/2

Radius = 2/2

Radius = 1 inch

Firstly finding the original cone volume

V = π×1²×6/3

V = 2π

V = 6.3 inches³

Increasing the height now -

Height = 6 + 3

Height = 9

Volume = π×1² × 9/3

Volume = 3π

Volume = 9.4 inches³

Increasing the diameter now -

Diameter = 2 + 1

Diameter = 3 inches

Radius = 3/2 inches

Volume = π×(3/2)² × 6/3

Volume = π × 9/2

Volume = 9π/2

Volume = 4.5π

Volume = 14.1 inches³

Hence, the increase in diameter will increase the volume more as the volume is directly proportional to square of radius.

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To adjust the length of the pendulum, we need to make it 9.7922 times longer than its current length.

To adjust the length of the pendulum, we can use the formula for the period of pendulum, which is T = 2π√(L/g), where T is the period (time it takes for one swing), L is the length of the pendulum, and g is the acceleration due to gravity.

Since we don't know the exact value of g, we can use the fact that the clock loses 27 s per day, which means it runs at a rate of (24 hours - 27 s)/(24 hours) = 0.9990625 times the actual time. This means that the period of the clock is 0.9990625 times the actual period.

Setting the period of the clock equal to 0.9990625 times the actual period, we get:
0.9990625 T = 2π√(L/g)
Squaring both sides and rearranging, we get:
L = (g/4π^2) (0.9990625 T)²
Substituting T = 24 hours = 86400 s and solving for L, we get:
L = (g/4π²) (0.9990625 x 86400 s)²
L = (g/4π²) (86338.13 s)²
L = 9.7922(g) m

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The height of the cylinder is 0.955 meters, according to the stated volume and radius.

The volume of the cylinder is calculated using the formula -

V = πr²h, where V represents volume, r represents radius and h is the height of cylinder. Keep the values in formula to find the height

300 = π×10²× h

Keep the value of pi as 3.14 in the equation

h =

[tex] \frac{ {300} }{3.14 \times 100} [/tex]

Performing multiplication in denominator

h = 300/314

Performing division on Right Hand Side of the equation

h = 0.955 meters

Thus, the height of the cylinder is 0.955 meters.

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The complete question is -

The volume of a cylinder is 300 m^3. The radius of the cylinder is 10 m. Find the height of the cylinder

There are approximately 265 bottles in the first group, 285 bottles in the second group, 570 bottles in the third group, and 580 bottles in the fourth group.

Let's solve this problem step by step to determine the number of bottles in each group.

Let's assume:

First group: x bottles

Second group: x + 20 bottles (20 more than the first group)

Third group: 2(x + 20) bottles (twice as many as the second group)

Fourth group: 2(x + 20) + 10 bottles (10 more than the third group)

Now, let's sum up the number of bottles in all the groups:

x + (x + 20) + 2(x + 20) + 2(x + 20) + 10 = 1700

Simplifying the equation:

x + x + 20 + 2x + 40 + 2x + 40 + 10 = 1700

6x + 110 = 1700

Subtracting 110 from both sides of the equation:

6x = 1590

Dividing both sides by 6:

x = 1590 / 6

x ≈ 265

Therefore, the first group has approximately 265 bottles.

Now, let's find the number of bottles in the other groups:

Second group: x + 20 ≈ 265 + 20 ≈ 285 bottles

Third group: 2(x + 20) ≈ 2(285) ≈ 570 bottles

Fourth group: 2(x + 20) + 10 ≈ 570 + 10 ≈ 580 bottles

To summarize:

First group: approximately 265 bottles

Second group: approximately 285 bottles

Third group: approximately 570 bottles

Fourth group: approximately 580 bottles

Thus, there are approximately 265 bottles in the first group, 285 bottles in the second group, 570 bottles in the third group, and 580 bottles in the fourth group.

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True, analysts use trend and comparative analyses to help "interpret the numbers.

What is Ratio Analysis?

a) Ratio analysis is a financial analysis tool that helps to evaluate the financial performance and health of a business by comparing different financial figures

b) There are three categories of ratios in ratio analysis: liquidity ratios, profitability ratios, and solvency ratios.

c) Ratio analysis is important because it helps to provide a quick snapshot of a company's financial health and performance.

In ratio analysis, a single value may not provide sufficient context or insight into a company's financial performance.

To draw meaningful conclusions, analysts use trend and comparative analysis to effectively interpret numbers.

Trend analysis involves examining financial ratios over multiple periods to identify patterns and determine whether performance is improving, deteriorating, or remaining stable over time.

This helps identify potential trends or anomalies that may affect decision making. Benchmarking, on the other hand, involves comparing a company's ratios to industry standards, competitor performance, or historical data to assess its relative performance and identify areas of strength or weakness.

By comparing ratios over different time periods or with external benchmarks, analysts gain a more comprehensive picture of a company's financial health and can make more informed judgments and recommendations.

Trend and comparative analyzes are therefore essential tools for analysts to effectively interpret ratio analysis and gain valuable insights into a company's financial performance.

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Answer:

x = 8√2

Step-by-step explanation:

The ratio of sides of 45-45-90 right angle triangle is:-  1 : 1 : √2

The legs of this 45-45-90 triangle are equal.

     ⇒ y = 8

The longest side is the hypotenuse, and it is opposite to 90°.

The hypotenuse = x  = y√2

                                  = 8√2    

Shanna should have multiplied by f(x) rather than have it as an exponent.

Here the given sequence,

2, 5, 12.5, 31.25,........

Since,

5/2 = 12.5 / 5 = 31.25/12.5 = 2.5

Hence, The given sequence is a G.P. having the first term 2 and common ratio of 2.5,

If f(x) represents a term of this g.p. then f(x+1) will show the next term,

By the above sequence, Next term = 2.5 × Previous term,

⇒ f(x+1) = 2.5 × f(x)

Which is the formula represents the above sequence,

But, the formula written by her,

⇒ f(x+1) = 2.5 × f(x)

Hence, Shanna should have multiplied by f(x) rather than have it as an exponent.

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