a farmer has a piece of land measuring 140 m by 936 m he divides it into square plots of equal size find the maximum area of one plot
WORTH 20 POINTS
Answers
Area of each plot be 16 square units.
What do you mean by GCD?
The greatest common divisor (gcd) of two or more numbers is the greatest common divisor that divides them exactly. This is also known as the highest common factor (HCF).
If a and b are two numbers, the greatest common divisor of both numbers is given by gcd(a, b). To find the gcd of a number, we need to list all divisors of the number and find the greatest common divisor.
It is given that a farmer has a piece of land measuring 140 m by 936 m he divides it into square plots of equal size.
140 = 2 × 2 × 5 × 7
936 = 2 × 2 × 2 × 3 × 3 × 13
GCD = 2 × 2 = 4
Area = 4 × 4 = 16 square units.
Therefore, area of each plot be 16 square units.
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Related Questions
you want to buy a car which will cost you $10,000. You do not have sufficient funds to purchase the car. You do not expect the price of the car to change in the foreseeable future. You can either save money or borrow money to buy the car.
Plan 1: You decide to open a bank account and start saving money. You will purchase the car when you have sufficient savings. The nominal interest rate for the bank account is 6% per annum compounded monthly.
a) You will make regular deposits in your bank account at the start of each month for the next 2.5 years. Calculate the minimum required monthly savings to be deposited into the bank such that you would have sufficient funds to purchase the car in 2.5 years.
b) You will make regular deposits in your bank account at the start of each week for the next 2.5 years. Calculate the minimum required weekly savings to be deposited into the bank such that you would have sufficient funds to purchase the car in 2.5 years.
c) You will make regular deposits of $2,000 at the end of each year. Calculate how long will it take for you to have sufficient funds to purchase the car.
Plan 2: You decide to borrow $13,000 from the bank and purchase the car now, as well as cover some other expenses. The bank offers two options for the structure of the repayments.
- Option 1: The first repayment will not start until you graduate from university. Therefore, no month-end-instalments will be made for the first 36 months. Then, commencing at the end of the 37th month, a total of 30 month-end-instalments of $X will be made over the life of the loan. The nominal interest rate is 6% per annum compounded monthly.
d) Calculate X.
e) Your parents agree to help you repay the loan by contributing a lump sum of $1,800 when you successfully graduate from university. Calculate the new value of X.
- Option 2: For the first 36 months (while you are still studying), you will be making month-end-instalments of $Y. Then, commencing at the end of the 37th month (when you graduate from university), you will double the amount of monthly repayment for the remaining 30 month-end-instalments. The nominal interest rate is 6% per annum compounded monthly.
f) Calculate the value of Y.
Answers
a) To save enough funds to purchase the car in 2.5 years, monthly deposits of $373.69 are required, while weekly deposits of $86.21 are needed.
b) With annual deposits of $2,000, it will take approximately 5 years to accumulate sufficient funds to purchase the car. For borrowing options, under Option 1, the monthly installment amount is $349.56, which reduces to $291.55 with a $1,800 lump sum contribution from parents. Under Option 2, the monthly installment amount is $237.63 for the first 36 months, doubling thereafter.
a) To calculate the minimum required monthly savings, we use the future value formula with monthly compounding: \($10,000 = PMT * ((1 + 0.06/12)^(2.5*12) - 1) / (0.06/12)\). Solving for PMT, the monthly deposit required is approximately $373.69.
b) Similarly, for weekly deposits, we use the future value formula with weekly compounding: \($10,000 = PMT * ((1 + 0.06/52)^(2.5*52) - 1) / (0.06/52)\). Solving for PMT, the weekly deposit required is approximately $86.21.
c) Using the future value formula for annual deposits: \($10,000 = $2,000 * ((1 + 0.06)^t - 1) / 0.06\). Solving for t, the time required to accumulate $10,000, we find it will take approximately 5 years.
d) For Option 1, the monthly installment amount can be calculated using the present value formula: \($13,000 = X * (1 - (1 + 0.06/12)^-30) / (0.06/12).\) Solving for X, the monthly installment amount is approximately $349.56.
e) With a lump sum contribution of $1,800, the remaining loan amount becomes $13,000 - $1,800 = $11,200. Using the same formula as in (d), the new monthly installment amount is approximately $291.55.
f) For Option 2, the monthly installment amount during the first 36 months is $Y. After 36 months, the monthly installment amount doubles. Using the present value formula: \($13,000 = Y * (1 - (1 + 0.06/12)^-36) / (0.06/12) + 2Y * (1 - (1 + 0.06/12)^-30) / (0.06/12)\). Solving for Y, the monthly installment amount is approximately $237.63.
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8+3(4x-2) anyone know how to solve?
Answers
Answer:
x = -1/6
Step-by-step explanation:
Firstly, you need to expand the brackets. So this would give, 8 + 12x - 6.
Then you collect like terms to give, 12x + 2. After this, we solve for x. To do this we need to assume that all this is = 0. Then it's easy to solve:
12x + 2 = 0
12x = -2
x = -2/12
x = -1/6
Priscilla is 24 inches tall. There are 2.54 centimeters in 1 inch. What is Priscilla's height in centimeters?
Answers
Priscilla is 24 inches tall.
24 x 2.54cm = 60.96cm
Therefore, Priscilla is 60.96cm tall
The members of the sales team at the car dealership earn 9% commission on any car sales and earn a weekly base salary of $500. A member of the sales team sold a car this week for $25,000. What was his pay for this week, including his base pay and commission from the sale?
Enter your answer in the box.
Answers
Answer:
2,750
Step-by-step explanation:
Answer:
2,750
Step-by-step explanation:
9% of 25,000= 2,250
2,250+500=2,750
THEOREM 5 If A is an invertible n x n matrix, then for each b in R", the equation Ax = b has the unique solution x = A-'b.
PROOF Take any b in R" A solution exists because if A-lb is substituted for x, then AX = A(A-1b) = (AA-))b = Ib = b. So A-1b is a solution. To prove that the solution is unique, show that if u is any solution, then u, in fact, must be A-'b. Indeed, if Au = b, we can multiply both sides by A- and obtain
A- Au = A-'b, Tu= A-'b, and u=A-'b
The Invertible Matrix Theorem
Let A be a square n x n matrix. Then the following statements are equivalent. That is, for a given A, the statements are either all true or all false.
a. A is an invertible matrix.
b. A is row equivalent to the n x n identity matrix.
c. A has n pivot positions. d. The equation Ax = 0 has only the trivial solution.
e. The columns of A form a linearly independent set.
f. The linear transformation x H Ax is one-to-one.
g. The equation Ax = b has at least one solution for each b in R".
h. The columns of A span R".
i. The linear transformation x # Ax maps R" onto R".
j. There is an n x n matrix C such that CA = I.
k. There is an n x n matrix D such that AD = I.
l. AT is an invertible matrix.
Because of Theorem 5 in Section 2.2, statement (g) in Theorem 8 could also be written as "The equation Ax = b has a unique solution for each b in R" " This statement certainly implies (b) and hence implies that A is invertible.
These are in David C. Lay's Linear Algebra fifth edition.
My question is: Why (g) and Theorem 5 are equivalent? I think (g) also include the infinite solutions case and unique solution case. So they are not equivalent.
Answers
(g) and Theorem 5 are not equivalent.
Are (g) and Theorem 5 equivalent?
You are correct. Statement (g) in Theorem 8, which states that the equation Ax = b has at least one solution for each b in R", includes both the case of a unique solution and the case of infinitely many solutions.
Therefore, (g) is not equivalent to Theorem 5, which specifically states that the equation Ax = b has a unique solution x = A^(-1)b when A is an invertible matrix. The equivalence mentioned in the text seems to be an error or a misinterpretation.
The correct interpretation is that Theorem 5 implies statement (g) in Theorem 8, but the converse is not necessarily true.
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Review the diagram.
Awagon is being pulled by a force of 15 pounds. How
much work is done in moving the wagon 50 feet if the
handle makes an angle of 40° with the ground?
O 11.49 foot-pounds
O 38.30 foot-pounds
O 574.53 foot-pounds
O 750.00 foot-pounds
Answers
Answer:
C) 574.53 foot-pounds
Step-by-step explanation:
got it right on edge :)
Awagon is being pulled by a force of 15 pounds. the required work done is 574.53 to pull the wagon So, Option C) is correct work done = 574.53.
What is work done?The work done is product of force and cosine of displacement.
Given; Awagon is being pulled by a force of 15 pounds. We need to find How much work is done in moving the wagon 50 feet if the handle makes an angle of 40° with the ground.
Force = 15 pounds
distance = 50 feet
Ф = 40°
We can calculate the work done as;
work done = force x displacement x cosФ
work done = 15 x 50 x cos40
work done = 15 x 50 x 0.76
work done = 574.53
Therefore, the required work done is 574.53 to pull the wagon.
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please need help asap
Answers
Answer:
90
Step-by-step explanation:
Answer:
i dont know..
Step-by-step explanation:
Find the value of x.
Answers
Answer:
60 = x
Step-by-step explanation:
180-144 = 36
36+84 = 120
180-120 = 60
Answer:
Value of x is 60°.
Step-by-step explanation:
According to the theorum,
The exterior angle is equal to the sum of the opposite two interior angles.
Exterior angle is 144°. The interior angles are 84° and x°
\(\longrightarrow\) x° + 84° = 144°
\(\longrightarrow\) x° = 144° - 84°
\(\longrightarrow\) x° = 60°
Value of x is 60°.
Which inequality represents the following number line?
+
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Select one:
a. x < -6
b.X > -6
C.XS-6
d. x > -6
Answers
Answer:
b. x > -6
Step-by-step explanation:
> [greater than], and < [less than] inequalities are not filled in because the value is not included, but is only greater or less than.
≥ [greater than or equal to], and ≤ [less than or equal to] inequalities are filled in because the value is included, and it is greater than or less than.
Given that there is an empty circle with an arrow moving in the positive direction from -6, the inequality must be a greater than, and since the value is -6, x > -6.
Divide and simplify -1/6 divided by 2/6
Answers
Answer:
-1/2
Step-by-step explanation:
\(-\frac{1}{6}\) ÷ \(\frac{2}{6}= -\frac{1}{6}\) x \(\frac{6}{2} \\\) = \(\frac{-6}{-12} =- \frac{1}{2}\)
Evaluate the expression 2b^3 + 5 = 2 (?)^3 + 5
Answers
To evaluate the expression 2b^3 + 5, we substitute the value of "?" that satisfies the equation 2(?)^3 + 5.
Without any specific information or context, it is not possible to determine the value of "?" that satisfies the equation. The expression 2b^3 + 5 represents a cubic polynomial, and the value of "?" depends on the specific value assigned to the variable "b" or any additional constraints given in the problem or context. Please provide more information or any specific values assigned to "b" in order to find the value of "?".
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average linkage is a measure of calculating dissimilarity between two clusters by . a. finding the distance between the two closest observations in the two clusters b. finding the distance between the two most dissimilar observations in the two clusters c. computing the average distance between every pair of observations between two clusters d. computing the distance between the cluster centroids
Answers
The correct answer will be c. computing the average distance between every pair of observations between two clusters
What is Cluster Analysis?
Grouping "things" into "similar" groups is one of the most fundamental, straightforward, and frequently overlooked techniques (or processes) of comprehending and learning, on which cluster analysis is based. To create clusters of a particular type, this process uses a variety of different algorithms and techniques. It is also a component of data management in statistical analysis.
A multivariate data mining technique called cluster analysis aims to group things (such goods, responders, or other entities) based on a set of user-selected features or characteristics. Data compression, machine learning, pattern recognition, information retrieval, and other areas all use this essential and crucial phase of data mining, which is also a widely used method for statistical data analysis.
Here as per the given question, there are two clusters given.
Hence, computing the average distance between every pair of observations between two clusters.
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PLS HELP! THE THING IS IN THE PHOTO!!!!!!!!!! I WILL GIVE YOU BRAINLIEST IF U GIVE ME THE RIGHT ANSWER!!!!!
Answers
An exponential model best describes this set of data.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.For the value in this problem, which is the output, it has a constant ratio, as:
21093.75/28125 = 28125/37500 = 37500/50000 = 0.75.
Hence an exponential model best describes this set of data.
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what is the probability that 356 randomly selected children will have a proportion of nearsightedness of at least 9% ?
Answers
The accurate solution is that the probability of the proportion of nearsightedness of at least 0.09 is approximately 0.0324 or 3.24%.
There are a few steps to answer this question about probability with the proportion of nearsightedness:
1. Define the variable: Let p be the true proportion of children with nearsightedness.
2. Check the conditions for using the normal approximation to the binomial distribution: np = 356 × 0.09 = 32.04 and n(1 - p) = 356 × 0.91 = 323.96, both greater than or equal to 10.
3. Calculate the z-score using the formula: z = (x - np) / √(np(1 - p)), where x = 0.09 × 356 = 32.04.
4. Find the probability using a calculator.
The probability that 356 randomly selected children will have a proportion of nearsightedness of at least 9% is approximately 0.0324, or 3.24%.
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Please help! WILL GIVE BRAINLIEST
Answers
The triangle base is 5, height is 14
1/2 x 5 x 14= 35
Next is is the square 2 x 2=4
Next is the rectangle 8 x 4= 32
Now add them all 35 +4+32=71
71 square feet is your answer
Answer:
71
Step-by-step explanation:
I found the area by spliting the figure into the triangle, square, and rectangle
triangle = .5(14*5)=35
square = 2*2=4
rectangle = 8*4=32
35+4+32=71
hope this is right:)
-2 1/5 (10x - 4.4) - 0.32
Answers
I think !!
Please help and explain will try to give the brainiest if two people answer. Really need your help
Answers
Is 39,052 divisible by 3?
Answers
Answer:
39052 ends in 2, hence it is divisible by 2. But (3+9+0+5+2) = 19, which is not divisible by 3.
Answer:
Step-by-step explanation:
to check a number is divisible by 3. add all the numbers and check whether it is divisible by 3
=3+9+5+2
=19
so it is not divisible
How do you solve this need help
38°
(5x + 2)°?
Answers
1. According to the rule of angles in a triangle, the value of x is 28.
2. the value of x is 47.
3. the value of x is 46.
What is right angle?It is an angle that measures 90 degrees and forms a square corner. It is the most common type of angle and is found in all shapes and sizes.
1. In the given question, a right angle has been bisected into two angles of 38 degree and (5x+2) degree. According to the rule of angles in a triangle, the sum of all the angles of a triangle is 180 degree.
So, 38 + (5x+2) = 180
=> 5x + 40 = 180
=> 5x = 140
=> x = 28
2. In this question, a right angle has been bisected into two angles of 39 degree and 3x degree.
So, 39 + 3x = 180
=> 3x = 141
=> x = 47
3. In this question, an exterior angle of a right angle has been bisected into two angles of 42 degree and 3x degree.
So, 42 + 3x = 180
=> 3x = 138
=> x = 46
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pagina 32 de libri de tercero de secundaria
Answers
Answer:
Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation
Step-by-step explanation:
Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation hi
Aaron started at a height of 43 feet in the air. He jumped feet first from the cliff into the water below. The total
distance he traveled was 52 feet. How far underwater did Aaron travel?
Answers
Answer:
Aaron travelled about 9 feet underwater
Step-by-step explanation:
We need to work with the information we are given in the question.
there are two stages of Aaron's travel. the first distance was in the air, and the second distance was in the water.
We are given both the total distance travelled and the distance travelled in the air.
To get the distance travelled in water, we subtract the distance travelled in the air from the total distance.
This will be 52 feet - 43 feet = 9 feet
Hence Aaron travelled about 9 feet underwater
what is r-0.2r when r equals the regular price of a cd player, which is equalivent to this expression.
(please answer step by step)
0.1r
0.8r
0.9r
1.2r
please
help
Answers
Answer:
0.8r
Step-by-step explanation:
r - 0.2r = 1r - 0.2r = (1 - 0.2)r = 0.8r
Answer:
0.8r
Step-by-step ex
took test
In the equation x + y = 6, find the value of x if y = 2
A. 2
B. 4
C. 6
D. 12
Answers
Answer: B
Step-by-step explanation:
(m-2)-5=8-2(m-4) ?
Answers
Answer:
m=\(\frac{23}{3}\) simplest form if you need it as a decimal its m=7.6
Step-by-step explanation:
please see attached screenshot. thanks!
Answers
Answer:
10
Step-by-step explanation:
4+4/4*(5+1)=
4+1(6)=
4+6=
10
3 = b + 12
I need work and answer
Answers
Answer:
b= -9
Step-by-step explanation:
Plug in -9 for b.
3= -9+12
Solve.
3=3
Since both sides are equal, the answer is -9
I hope this helped you ;)
Carpets Plus has five square carpet remnants. Two of the remnants measure 8 feet on a side, and three of the remnants
measure 10 feet on a side. Which expression represents the total square footage of the five carpet remnants?
O 12 * 102) + (382)
82 +10%
5(8 + 10)2
O (2*82) + (3 x 102
Answers
Answer:I don’t understand what you are asking so I am going to answer it my way sorry if it wrong oki think that it is 10 x 4 = 40 but I just did what I think sorry it most likely wrong but yea ..,
Step-by-step explanation:
If S is comapct and x0 ∈/ S, then prove that Infx∈Sd(x, x0) >
0
Answers
We get inf {d(x, x0) : x is an element of S} > 0, because for any p > 0, we can find some x in S such that, d(x, x0) < p.
Given:
Let S be a compact subset of a metric space (M, d). x0 is a point in M \ S which is the complement of S in M.
To Prove: inf {d(x, x0): x is an element of S} > 0.
Solution:
For every y in S, let d(y, x0) = r(y) > 0.
Then we have {B(y, r(y)/2) : y is an element of S} is an open cover of S.
Therefore, S is compact, so there exists a finite sub-cover, i.e., {B(y1, r(y1)/2), B(y2, r(y2)/2),..., B(yk, r(yk)/2)}
where y1, y2, ..., yk belong to S.
We assume without loss of generality that
r(y1)/2 <= r(y2)/2 <= ... <= r(yk)/2.
Then for every x in S, we have x belongs to some B(yj, r(yj)/2) for some j from 1 to k.
Therefore, we have d(x, x0) >= d(yj, x0) - d(x, yj) > r(yj)/2.
From this, we get inf {d(x, x0) : x is an element of S} > 0, because for any p > 0, we can find some x in S such that
d(x, x0) < p.
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Use a tree diagram to find the sample space and the total number of possible outcomes Birthday Party Miniature golf, Laser tag, Activity Roller skating Time 1:00 P.M.-3:00 P.M., 6:00 P.M.-8:00 P.M.
Answers
Therefore, the sample space has 8 possible outcomes.
In order to use a tree diagram to find the sample space and the total number of possible outcomes, you can follow the steps mentioned below:
Step 1: Identify the branches that represent each activity (birthday party, miniature golf, laser tag, and roller skating).
Step 2: Next, list the possible time slots for each activity.
Step 3: Draw a tree diagram and organize the activities by category.
Step 4: Then, label each branch with the time slot for that activity.
Step 5: Count the total number of branches in each activity category and multiply those numbers to determine the total number of possible outcomes.Sample space represents the collection of all possible outcomes. Here, the given activities are Birthday Party, Miniature golf, Laser tag, and Activity Roller skating and the given time slots are 1:00 P.M.-3:00 P.M. and 6:00 P.M.-8:00 P.M.
Now, we will use a tree diagram to find the sample space and the total number of possible outcomes.
The tree diagram can be represented as follows: \(\begin{array}{|c|c|c|}\hline & 1:00-3:00 & 6:00-8:00 \\\hline \text{Birthday Party} & & \\ \hline \text{Miniature Golf} & & \\ \hline \text{Laser Tag} & & \\ \hline \text{Roller Skating} & & \\ \hline \end{array}\)The total number of possible outcomes is the product of the number of time slots and the number of activities. Thus, the number of possible outcomes can be calculated as follows:Total number of possible outcomes = Number of activities × Number of time slots= 4 × 2 = 8
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Select the non−linear function from the list of the following:
Select one:
a.
xy + 1 / x = 7
b.
5x + 6y = − 2 / 3
c.
x + 3y = − 2
d.
− 4x − 5y = − 3
Answers
Answer:
a. xy + 1/x = 7
Step-by-step explanation:
The first equation has terms with degrees 2 and -1. A linear equation has variable terms only with degree 1.
The nonlinear equation is ...
xy + 1/x = 7