Hence, determine the circumstances of the base base of a coffee tin

Answers

Answer 1

Answer:

We can write the diameter and circumferance of base as -

D = 2√(750ρ/πh)

C = 2π√(750ρ/πh)

Step-by-step explanation:

What is function?

A function is a relation between a dependent and independent variable.

Mathematically, we can write → y = f(x) = ax + b.

Given is to find the diameter and height of the tin can.

Assume the density of coffee as {ρ}. We can write the volume of the tin can as -

Volume = mass x density

Volume = 750ρ

We can write -

πr²h = 750ρ

r = √(750ρ/πh)

D = 2r

D = 2√(750ρ/πh)

Now, we can write the circumferance as -

C = 2πr

C = 2π√(750ρ/πh)

Therefore, we can write the diameter and circumferance of base as -

D = 2√(750ρ/πh)

C = 2π√(750ρ/πh)

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Related Questions

f the random walk starts in the center, on average how many steps does it take to return to the center?

Answers

Total number of steps taken by an average man in a year while walking with 7192 steps a day is equals to 2,625,080 steps/year.

Number of steps taken by average man in a day is equals to  7192

Then the total number of steps he takes in a year is equals to,

Calculate it by multiplying the average number of steps per day by the number of days in a year.

There are different ways to define a year,

But assuming a regular calendar year of 365 days, the calculation would be,

Total number of days in a year = 365 days

Total number of steps in a year

= 7192 steps/day x 365 days/year

= 2,625,080 steps/year

Therefore, on average the man would walk about 2,625,080 steps in a year.

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The given question is incomplete, I answer the question in general according to my knowledge:

If a man walks with random steps and the average man takes 7192 steps a day about how many steps does the average man take in a year?

Triangle ABC is similar to triangle DEF. What is AC?

Answers

Answer:

i think side AC is 14 because if you do subtract BC (18) from EF(12) you get 6, so u add 6 to DF(8) and get 14.

if its confusing ask me questions!!

Answer:

12

Step-by-step explanation:

When triangles are similar, their side ratios are the same. The ratio of EF to BC is 18/12, or 3/2. To find the side AC, we would multiply the corresponding part of DEF by 3/2, the same ratio. The corresponding part of DEF would be DF. DF = 8. 8 times 3/2 is 12. So AC is 12.

Let me know if this helped by hitting brainliest! If not, please comment and I'll get back ASAP.

Help please! I have no idea!!!! PLEASEE

Answers

To highlight the line y = 0 on the graph in black/grey, draw a straight line passing through all points whose y-coordinate is 0.

What is graph?

In mathematics, a graph is a visual representation of a set of data, typically as a set of points or lines on a coordinate plane. Graphs are used to represent various types of data, such as numerical values, functions, relationships, and patterns.

Assuming that the graph is a coordinate plane with the x-axis and y-axis, do the following:

To highlight the point (9, 8) on the graph in red, locate the point (9, 8) on the coordinate plane and mark it with a red color.

To highlight the point (20, f(20)) on the graph in green, you need to know the value of f(20) first. Once you have that value, locate the point (20, f(20)) on the coordinate plane and mark it with a green color.

To highlight the line y = 5 on the graph in blue, draw a straight line passing through all points whose y-coordinate is 5. This line should be parallel to the x-axis and should be marked with a blue color.

Therefore To highlight the line y = 0 on the graph in black/grey, draw a straight line passing through all points whose y-coordinate is 0. This line should be parallel to the x-axis and should be marked with a black/grey color.

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how many one-to-one functions are there from a set with five elements to sets with the following number of ele- ments? a) 4 b) 5 c) 6 d) 7

Answers

a) Number of one-to-one functions are equal to the zero, because n< m.

b) Number of one-to-one functions are equal to the ⁵P₅ = 120.

c) Number of one-to-one functions are equal to the ⁶P₅ = 720.

c) Number of one-to-one functions are equal to the ⁷P₅ = 2250.

One to one function is a special form of function that defined from one set to another and maps every element of the range to exactly one element of its domain unique output. As we know a set A has m elements and set B has n elements, then

Number of one-to-one functions from set A to Set B = P(n,m) or ⁿPₘ , n≥ m and number of one-to-one functions from set A to Set B = 0 , n< m.

Now, we have a domain set with five elements, m = 5

a) Here, another set (co-domain) has 4 elements, n = 4. So, Number of one-to-one functions = 0 , n<m.

b) number of elements in another set,n= 5

So, Number of one-to-one functions = ⁵P₅ = 5!/(5 - 5 )! ( permutation formula)

= 5!/0! = 120

c) Number of elements in another set, n= 6

So, Number of one-to-one functions= ⁶P₅

= 6!/(6 - 5)!

= 6!/1! = 720

d) Number of elements in another set, n

= 7

So, Number of one-to-one functions

= ⁷P₅ = 7!(7 - 5)!

= 7!/2! = 2250

Hence, required value is 2250.

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1) Pendant la période des soldes, tous les manteaux d'un magasin sont soldés à 15%.
a. Marjorie a repéré un manteau qui coûtait initialement 78€.
Quel est son prix après réduction ?
b. Mélanie veut acheter un manteau dont le prix après réduction est de 55,25€.
Quel était son prix initial ?
2) Manu affirme que sur les étiquettes suivantes, le pourcentage de réduction appliqué au prix
de la montre est supérieur à celui appliqué aux lunettes. A-t-il raison ?
45€→ 35,55€
Réduction
de 20%

Answers

Answer: Zemāk

Step-by-step explanation:

1)

a. Le prix du manteau après la réduction de 15% est:

78€ - (15/100)*78€ = 66,30€

Le prix du manteau après la réduction est de 66,30€.

b. Soit x le prix initial du manteau.

Le prix du manteau après la réduction de 15% est:

x - (15/100)*x = 55,25€

Simplifions cette équation:

0,85x = 55,25€

x = 65€

Le prix initial du manteau était de 65€.

2)

Pour les lunettes, le prix initial est de 45€ et la réduction appliquée est de 20%:

45€ - (20/100)*45€ = 36€

Pour la montre, le prix initial est de 35,55€ et la réduction appliquée est également de 20%:

35,55€ - (20/100)*35,55€ = 28,44€

On constate que le pourcentage de réduction est le même pour les deux articles, donc Manu a tort.

if the slope of the line joining the points (2,4) and (5,k) is 2. find the value of k

Answers

10 is the value of k of  the slope of the line .

What are slopes called?

Slope, usually referred to as rise over run, is a line's perceived steepness. By dividing the difference between the y-values at two places by the difference between the x-values, we can determine slope.

                                   You may determine a line's slope by looking at how steep it is or how much y grows as x grows. slope categories. When lines are inclined from left to right, they are said to have a positive slope, a negative slope, or a zero slope (when lines are horizontal).

the points  (2,4) and (5,k)

formula from slope of two points

        slope = y₂ - y₁/x₂ - x₁

substitute the values in formula

 slope = 2

 slope =  k - 4/5- 2

   2 =k - 4/3

   6 = k - 4

    k = 6 + 4  

      k = 10

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PLEASE ASAP!!Graph the line 4x+5y=20

Answers

Step-by-step explanation:

Might be a little easier to visualize if yo re-arrange it into y = mx + b form:

4x+ 5y = 20

5y = -4x + 20

y = - 4/5 x + 4         y-axis intercept at y = 4

                                x axis intercept is found by:

                                     0 = -4/5 x + 4

                                             - 4 = -4/5 x

                                                 x = 5

So===> plot the two intercept points ( 0,4)  and  ( 5,0)  and connect the dots

Model the pair of situations with exponential functions f and g. Find the approximate value of x that makes​ f(x) =​ g(x). ​f: initial value of 500 decreasing at a rate of ​6% ​g: initial value of 90 increasing at a rate of ​6%
The value of x that makes ​f(x)​g(x) is x

Answers

Answer:

Step-by-step explanation:

u got this

12. What is the height of the trapezoid in yards? (Hint: Use the formula
A = 1/2h (b 1, + b2,) (Lesson 2)

Answers

Answer:

height = 7 yards

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the 2 parallel bases

here b₁ = 12 , b₂ = 9 and A = 73.5 , then

[tex]\frac{1}{2}[/tex] h(12 + 9) = 73.5 ( multiply both sides by 2 to clear the fraction )

h(21) = 147

21h = 147 ( divide both sides by 21 )

h = 7 yards

123, 185, 143, 137, 192, 185, 129, 143, 154, 165, 143, 138, 187, 176
A bin size ofis most appropriate for the data shown above.
A. 69 B. 2 C. 10 D. 1​

Answers

The answer of the given question based on statistics to find the  most appropriate size of the bin from the data the answer is , the most appropriate bin size for this data set would be A. 69.

What is Statistics?

Statistics is  the practice of collecting, analyzing, and interpreting the data. It involves  use of mathematical tools and techniques to gather insights and knowledge from numerical and categorical information. Statistics is essential in many fields, like  business, medicine, social sciences, and engineering, as it enables researchers to draw conclusions from data and make informed decisions based on evidence.

It includes topics like probability, hypothesis testing, regression analysis, and data visualization. The application of statistical methods can help identify patterns, relationships, and trends in data, allowing researchers to make predictions and solve problems.

To determine the appropriate bin size, we need to consider the range of values in the data. The range is the difference between the largest and smallest values, which in this case is 192 - 123 = 69.

To get the bin size, we divide the range by the number of bins. So the bin size would be 69/4 = 17.25. However, since we can't have a fraction of a unit for bin size, we should round up to the nearest whole number. Therefore, the most appropriate bin size for this data set would be A. 69.

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The answer of the given question based on statistics to find the  most appropriate size of the bin from the data the answer is , the most appropriate bin size for this data set would be A. 69.

What is Statistics?

Statistics is  the practice of collecting, analyzing, and interpreting the data. It involves  use of mathematical tools and techniques to gather insights and knowledge from numerical and categorical information. Statistics is essential in many fields, like  business, medicine, social sciences, and engineering, as it enables researchers to draw conclusions from data and make informed decisions based on evidence.

It includes topics like probability, hypothesis testing, regression analysis, and data visualization. The application of statistical methods can help identify patterns, relationships, and trends in data, allowing researchers to make predictions and solve problems.

To determine the appropriate bin size, we need to consider the range of values in the data. The range is the difference between the largest and smallest values, which in this case is 192 - 123 = 69.

To get the bin size, we divide the range by the number of bins. So the bin size would be 69/4 = 17.25. However, since we can't have a fraction of a unit for bin size, we should round up to the nearest whole number. Therefore, the most appropriate bin size for this data set would be A. 69.

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The complete question is as fpllows:

123, 185, 143, 137, 192, 185, 129, 143, 154, 165, 143, 138, 187, 176

A bin size of is most appropriate for the data shown above.

A. 69

B. 2

C. 10

D. 1​

Find the zeros of the function.
y = (x + 1)(x-2)(x - 5)
The zero(s) of the function are
(Use a comma to separate answers as needed.)

Answers

-1,2,5
Switch the signs to get the zeros in a problem.

What is the slope of the line in the following graph?

Answers

Answer:

1/3

Step-by-step explanation:

using rise over run fron the two dots, we can find 2/6, which simplifies down to 1/3

An instructor is administering a final examination. She tells her class that she with give an A grade to the 10% of the students who earns the highest marks. Past experience with the same examination has yielded grades that are normally distributed with a mean of 70 and a standard deviation of 10. If present class runs true to form, what numerical score would a student need to earn an A grade?

Answers

To earn an A grade, a student needs to score at least 82.8 , calculated using the inverse normal cumulative distribution function with a mean of 70, a standard deviation of 10, and a 10th percentile of 0.10.

Given that the grades are normally distributed with a mean of 70 and a standard deviation of 10.

We need to find the score which is at the 10th percentile of the distribution.

Using the standard normal distribution table, we can find the z-score that corresponds to the 10th percentile.

From the table, we can see that the z-score is approximately -1.28.

Using the formula for standardizing a normal distribution:

z = (x - μ) / σ

where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

Substituting the given values, we have:

-1.28 = (x - 70) / 10

Solving for x, we get:

x = (-1.28 * 10) + 70

x = 82.8

Therefore, a student would need to earn a score of approximately 82.8 to receive an A grade.

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One side of the triangle is 4 cm, and the sum of the other two sides is equal to a whole number of cm. What is the smallest possible perimeter of the triangle?
F. 9 cm
G. 10 cm
H. 11 cm
J. 15 cm
K. 17 cm

Answers

Answer:

9 cm

Step-by-step explanation:

By the Triangle Inequality, any two sides of a triangle must be greater than the remaining side.

In order to minimize the perimeter, we will assume that 4 cm is the longest side.

Thus, the two remaining sides must be greater than 4.

Since we are given that the sum of the two remaining sides is a whole number, the smallest whole number value greater than 4 is 5.

Hence, the smallest perimeter possible 9 cm.

Two cars, one going due east at the rate of 90 km/hr and the other going to south at the rate of 60 km/hr are traveling toward the intersection of two roads. At what rate the two cars approaching each other at the instant when the first car is 0.2 km and the second car is 0.15 km from the intersection ?

Answers

The two cars are approaching each other at a rate of 36 km/hr at the given instant.

We can solve this problem by using the Pythagorean theorem and differentiating with respect to time. Let's call the distance of the first car from the intersection "x" and the distance of the second car from the intersection "y". We want to find the rate at which the two cars are approaching each other, which we'll call "r".

At any moment, the distance between the two cars is the hypotenuse of a right triangle with legs x and y, so we can use the Pythagorean theorem

r^2 = x^2 + y^2

To find the rates of change of x and y, we differentiate both sides of this equation with respect to time

2r(dr/dt) = 2x(dx/dt) + 2y(dy/dt)

Simplifying and plugging in the given values

dr/dt = (x(dx/dt) + y(dy/dt)) / r

dr/dt = (0.2 x 90 + 0.15 x (-60)) / sqrt((0.2)^2 + (0.15)^2)

dr/dt = (18 - 9) / sqrt(0.04 + 0.0225)

dr/dt = 9 / sqrt(0.0625)

dr/dt ≈ 36 km/hr

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the value of the given test statistic lies between the given cutoffs -2.58 and 2.58. it falls in acceptance region.

Answers

Here the values -0.94 and 2.12 falls between the points -2.58 and 2.58. The area between is the acceptance region. So we cannot reject the null hypothesis.

The given is an example for two tailed test. A two tailed test is used to determine whether the value is greater than or less than the mean value of the population. It represents the area under both tails or sides on a normal distribution curve.

Here the value of the test statistic lies between -2.58 and 2.58. So the values less than -2.58 and greater than 2.58 fall in the rejection region, where the null hypothesis can be rejected.

a) -0.94 falls between -2.58 and 2.58. So it is in the acceptance region. So null hypothesis is accepted.

b) 2.12 lies between -2.58 and 2.58. It is also in acceptance region. So null hypothesis is accepted.

So in both cases null hypothesis cannot be rejected.

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The complete question is :

f the cutoffs for a z test are -2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases and explain why:

a. z = −0.94

b. z = 2.12

Suppose we want to choose 5 letters, without replacement, from 15 distinct letters

Answers

[tex]\text{order does not matter}[/tex]

[tex]\text{sample space}= \text{15 letters}[/tex]

[tex]\text{no repetition}[/tex]

[tex]\text{P(A)}= \text{15C5}= \text{3003 ways}[/tex]

The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 30 minutes, what is the probability that X is less than 38 minutes? (Do not round until the final step. Round your answer to 3 decimal places.)

Answers

Answer:

0.718 = 71.8% probability that X is less than 38 minutes

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x)=\mu e^{-\mu x}[/tex]

In which [tex]\mu=\frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X\leq x)=\int\limits^a_0f ({x)} \, dx[/tex]

Which has the following solution:

[tex]P(X\leq x)=1-e^{-\mu x}[/tex]

If X has an average value of 30 minutes

This means that [tex]m=30,\mu=\frac{1}{30}[/tex]

What is the probability that X is less than 38 minutes?

[tex]P(X\leq 38)=1-e^{-\frac{38}{30} }[/tex]

0.718 = 71.8% probability that X is less than 38 minutes

PLEASE HELP MEEE
whoever answers right gets brainliest!!!

Answers

Answer:

 [tex]30\leq x[/tex]  AND [tex]x \leq 106[/tex]

Notice the valid answer is the one with the AND since need to be both at the same time.

Step-by-step explanation:

Is the one is market, you add 6 to each side and you obtain that answer

[tex]24 \leq x-6\leq 100[/tex]

[tex]24 +6\leq x\leq 100+6[/tex]

[tex]30\leq x\leq 106[/tex]

the graph shows the preimage shaded in grey and the image outlined in black. what is the scale factor of the dilation?

Answers

The scale factor of dilation of the shaded in gray to the shaded in black is 3

Calculating the scale factor dilation

Given that

The preimage = shaded in gray

The image = shaded in black

From the graph, we have the following values on the image and the preimage

The preimage = shaded in gray = 4

The image = shaded in black = 12

The scale factor of dilation is then calculated as

Scale factor = shaded in black/shaded in gray

So, we have

Scale factor = 12/4

Evaluate

Scale factor = 3

Hence, the scale factor dilation is 3

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Given the coordinates shown and given that SU = 10, what are the coordinates of U if STUV is a kite?

A) (10, 18)
B) (0, 28)
C) (18, 28)

Answers

The calculated coordinates of U if STUV is a kite is (10, 18)

Calculating the coordinates of U if STUV is a kite?

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

The figute of a kite

Also, we have

S = (0, 18)

And the distance SU to be

SU = 10

If the quadrilateral STUV is a kite, then the coordinates S and U are on the same horizontal level (according to the figure)

So, we have

U = (0 + 10, 18)

Evaluate

U = (10, 18)

Hence, the coordinates of U if STUV is a kite is (10, 18)

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Calculate the following limits?

Answers

The answer of the given question based on the limits the answers are as follows, (a)  lim f(x) = 1 , (b)  lim f(x) = 3 , (c)  lim f(x) = 3.

What is Graph?

A graph is  visual representation of data that shows the relationship between two or more variables. Graphs can be used to display  wide variety of information, including numerical data, functions, and networks. The most common types of graphs like line graphs, bar graphs, scatter plots, and pie charts.

Graphs are widely used in many fields, like science, economics, engineering, and social sciences, to help people understand and analyze complex data. They are  powerful tool for visualizing trends, patterns, and relationships, and are often used to communicate findings to wider audience.

a) The limit of f(x) as x approaches 2 from the left:

We can see from the graph that as x approaches 2 from the left, f(x) approaches 1. Therefore, we can write:

lim f(x) = 1

x→2-

b) The limit of f(x) as x approaches 2 from the right:

Similarly, as x approaches 2 from the right, f(x) approaches 3. Therefore:

lim f(x) = 3

x→2+

c) The limit of f(x) as x approaches 2:

Since the limit from the left and the limit from the right exist and are equal, we can say that the limit of f(x) as x approaches 2 exists and equals the common value of the left and right limits. Therefore:

lim f(x) = 3

x→2

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John plans to practice piano at least 2 hours this weekend.
If he practices 1 hours on Saturday and 14 hours on Sunday, will he meet his goal?

Answers

Answer:

Yes

Step-by-step explanation:

Yes because 1+14=15 hours and that is more than two

If
f(x) = 2x² + 3x - 6, determine the value of f(2).

Answers

Answer:

8

Step-by-step explanation:

2x² + 3x - 6

plug in x with 2

2(2)^2+3(2)-6

2(4)+6-6

8+6-6

14-6

8

If 5 is increased to 9, the increase is what percentage of the original number

Answers

Answer: It's a 80% increase

Step-by-step explanation:

What is the difference between the questionnaire and an interview?

Answers

Answer: Questionnaire refers to a research instrument, in which a series of question, is typed or printed along with the choice of answers, expected to be marked by the respondents, used for survey or statistical study. It consists of aformalisedd set of questions, in a definite order on a form, which are mailed to the respondents or manually delivered to them for answers. The respondents are supposed to read, comprehend and give their responses, in the space provided.

A ‘Pilot Study’ is advised to be conducted to test the questionnaire before using this method. A pilot survey is nothing but a preliminary study or say rehearsal to know the time, cost, efforts, reliability and so forth involved in it.

The interview is a data collection method wherein a direct, in-depth conversation between interviewer and respondent takes place. It is carried out with a purpose like a survey, research, and the like, where both the two parties participate in the one to one interaction. Under this method, oral-verbal stimuli are presented and replied by way of oral-verbal responses.

It is considered as one of the best methods for collecting data because it allows two way exchange of information, the interviewer gets to know about the respondent, and the respondent learns about the interviewer. There are two types of interview:

Personal Interview: A type of interview, wherein there is a face to face question-answer session between the interviewer and interviewee, is conducted.

Telephonic Interview: This method involves contacting the interviewee and asking questions to them on the telephone itself.

A questionnaire is considered a voting type of process while an interview is discussing a topic

The number 0 is an element of the set of natural numbers.
OA. True
B. False
SUBI

Answers

it is false. 0 is not a natural number. it is a whole number

find the closed formula for 3,6,11,18 by relating them to a well known sequence. assume the first term given is

Answers

The closed formula for this particular sequence is an = n² + 2.

Take note that the odd numbers 3, 5, 7, 9, and 11 are separate consecutive terms. This shows that the first n odd numbers can be added to the initial term, az, to get the nth term. Hence, the following is how we may represent the nth term a = az + 1 + 3 + 5 + ... + (2n-3) (2n-3). We may utilize the formula for the sum of an arithmetic series to make the sum of odd integers simpler that is 1 + 3 + 5 + ... + (2n-3) = n².

As a result, we get a = az + n^2 - 1. In conclusion, the equation for the series (an)n21, where a1 = az and an is the result of adding the first n odd numbers to az, is as a = az + n^2 - 1. We have the following for the given series where a1 = az = 3.

So, the closed formula for this particular sequence is an = n² + 2.

To learn more about arithmetic sequences, refer to:

Your question is incomplete. The complete question is:

Find the closed formula for the sequence (an)n21. Assume the first term given is az. an = 3, 6, 11, 18, 27... Hint: Think about the perfect squares.

Mr. Chand is one of the landlords of his town. He buys a land for his daughter spanning over a
area of 480m². He fences the dimensions of the land measuring (x+12) mx (x+16) m. Now he
plans to erect a house with a beautiful garden in the ratio 5:3 respectively. A total of Rs. 5,00,000 is estimated as the budget for the expenses.

1)Give the area of the land purchased in linear polynomial form using algebraic expression

2)Mr. Chand's daughter is ready to share 3/5" of the expenses by her earnings. Express the
fraction in amount.

3)Can you solve the linear equation/polynomial of the area into different factors?

Answers

The required answers are 1) [tex]$$A = x^2 + 28x + 192$$[/tex] 2) 300000 3) [tex]$$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$[/tex].

How to deal with area and fractions?

area of the land purchased is given as 480m², and the dimensions of the land are (x+12)mx(x+16)m. Therefore, the area of the land can be expressed as:

[tex]$$A = (x+12)(x+16)$$[/tex]

Expanding this expression, we get:

[tex]$$A = x^2 + 28x + 192$$[/tex]

Hence, the area of the land purchased is given by the polynomial expression [tex]$x^2 + 28x + 192$[/tex].

The total budget for the expenses is Rs. 5,00,000. If Mr. Chand's daughter is ready to share 3/5 of the expenses, then the fraction of the expenses she will pay is:

[tex]$\frac{3}{5}=\frac{x}{500000}$$[/tex]

Simplifying this expression, we get:

[tex]$x = \frac{3}{5}\times 500000 = 300000$$[/tex]

Therefore, Mr. Chand's daughter will pay Rs. 3,00,000 towards the expenses.

We can solve the polynomial [tex]$x^2 + 28x + 192$[/tex] into different factors by using the quadratic formula:

[tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$[/tex]

Here, the coefficients of the polynomial are:

[tex]$$a = 1, \quad b = 28, \quad c = 192$$[/tex]

Substituting these values in the quadratic formula, we get:

[tex]$x = \frac{-28 \pm \sqrt{28^2 - 4\times 1 \times 192}}{2\times 1}$$[/tex]

Simplifying this expression, we get:

[tex]$$x = -14 \pm 2\sqrt{19}$$[/tex]

Therefore, the polynomial [tex]$x^2 + 28x + 192$[/tex] can be factored as:

[tex]$$x^2 + 28x + 192 = (x - (-14 + 2\sqrt{19}))(x - (-14 - 2\sqrt{19}))$$[/tex]

or

[tex]$$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$[/tex]

So, we have factored the polynomial into two factors.

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A invested Rs 4500 for 3 years at the rate of 8% annual compound interest and B invested the
same amount for same time at the rate of per month per rupee I paisa simple interest. Calculate
(i) The interest received by A. (ii) The interest received by B.

Answers

The calculation of the interest received by Investor A and Investor B is as follows:

Investor A = $1,168.70 (Compound)Investor B = $1,620 (Simple).

What is the difference between compound and simple interest?

Compound interest is based on the system of charging interest on accumulated interest and principal for each period.

Simple interest is charged on only the principal for each period.

A's Investment at 8% Annual Compound Interest:

N (# of periods) = 3 years

I/Y (Interest per year) = 8%

PV (Present Value) = $4,500

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $5,668.70

Total Interest = $1,168.70

B's Investment at Paisa 1 per R1.00 Monthly Simple Interest:

N (# of periods) = 3 years

r = 1 paisa per rupee per month

= 1÷100*100 = 1%

Annually rate =1%*12 = 12%

PV (Present Value) = $4,500

Results:

Total Interest = $1,620 (R4,500 x 12% x 3)

Future Value (FV) = $6,120.

Thus, while Investor A receives $1,168.70 at the end of 3 years, Investor B receives $1,620.

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