To find the shortest total length of fence needed, divide the field into 3 equal areas. Use the area formula and differentiate to find the value of L that minimizes the perimeter. The shortest total length of fence needed is approximately 64.26m.
Explanation:To find the shortest total length of fence needed, we need to divide the field into 3 equal areas. Since the total area is 800m², each area will be 800m² ÷ 3 = 266.67m².
Now, let's find the dimensions of each area. Let the length of the rectangle be L and the width be W.
Since the areas are equal, we have LW = 266.67m². We are also given that the field is rectangular, so the perimeter is given by 2L + 2W.
To minimize the perimeter, we can use the formula 2L + 2W = P, and solve for L or W. Using the area formula and substituting, we have 2L + 2(266.67m²/L) = P.
Differentiating with respect to L and equating to zero, we can find the value of L that minimizes the perimeter. Solving the equation gives L ≈ 15.65m.
Therefore, the shortest total length of fence needed is approximately 2L + 2W ≈ 2(15.65m) + 2(266.67m²/15.65m) ≈ 64.26m.
For a rectangular field with a total area of 800 m², divided into three equal areas, the optimal solution is a square field with a side length of approximately 28.28 m. The shortest total length of fence needed is approximately 113.14 m.
Let's go through the step-by-step calculation:
1. **Given Information:**
- Total area of the rectangular field: [tex]\(800 \, \text{m}^2\).[/tex]
- The field is divided into 3 equal areas.
2. **Calculate the area of each section:**
[tex]\[ \text{Area of each section} = \frac{\text{Total area}}{\text{Number of sections}} = \frac{800 \, \text{m}^2}{3} \approx 266.67 \, \text{m}^2 \][/tex]
3. **Assume a square field:**
Let [tex]\(a\)[/tex] be the side length of the square field.
4. **Express the total area in terms of side length [tex](\(a\))[/tex]:**
[tex]\[ a^2 = 800 \, \text{m}^2 \][/tex]
5. **Calculate the side length [tex](\(a\))[/tex] :**
[tex]\[ a = \sqrt{800} \approx 28.28 \, \text{m} \][/tex]
6. **Calculate the total length of the fence (perimeter of the square):**
[tex]\[ \text{Perimeter} = 4a = 4 \times 28.28 \, \text{m} \approx 113.14 \, \text{m} \][/tex]
f(x)=x^4+7x^3+13x^2-3x-18
How many 1/4 teaspoon doses are im 7/8 teaspoon of medicine
Find the volume of a right circular cone that has a radius of 4 inches and a height of 12 inches.
A) 36π in. ^ 3
B) 48π in. ^ 3
C) 52π in. ^ 3
D) 64π in. ^ 3
What are the diminshens of a cube with the volume of 216?
A sequence is defined by the recursive formula f(n+1)=f(n)-2. If f(1)=18,what is f(5)?
The answer is for this problem is 10
Using the heaviside function write down the piecewise function that is 0 for t < 0 , t2 for t in [0,1] and t for t > 1 .
Final answer:
The piecewise function, using the Heaviside function, is defined as 0 for t < 0, t^2 for t in [0, 1], and t for t > 1.
Explanation:
The piecewise function can be defined using the Heaviside function.
We know that the Heaviside function, H(x), is defined as:
H(x) = 0 for x < 0
H(x) = 1 for x ≥ 0
Using the Heaviside function, the piecewise function can be written as:
f(t) = 0 for t < 0
f(t) = t2 for t ∈ [0, 1]
f(t) = t for t ≥ 1
Peppermint Patty is very discouraged about her chances on a 10-item true-false quiz. If she randomly answers each question, what is her probability of getting a grade of at least 50% on the following? (Enter an exact number as an integer, fraction, or decimal.)
three-item quiz
four-item quiz
five-item quiz
We can solve this problem using the binomial probability equation:
P = [n! / (n – r)! r!] p^r q^(n – r)
where the variables are:
n = total number of questions = 10
r = number of correct = at least 5
p = probability of success = 0.5
q = probability of failure = 0.5
So what we have to do is to calculate for P for r = 5 to 10
when r = 5
P = [10! / (10 – 5)! 5!] 0.5^5 0.5^(10 – 5)
P = 0.246
when r = 6
P = [10! / (10 – 6)! 6!] 0.5^6 0.5^(10 – 6)
P = 0.205
when r = 7
P = [10! / (10 – 7)! 7!] 0.5^7 0.5^(10 – 7)
P = 0.117
when r = 8
P = [10! / (10 – 8)! 8!] 0.5^8 0.5^(10 – 8)
P = 0.044
when r = 9
P = [10! / (10 – 9)! 9!] 0.5^9 0.5^(10 – 9)
P = 9.766 x 10^-3
when r = 10
P = [10! / (10 – 10)! 10!] 0.5^10 0.5^(10 – 10)
P = 9.766 x 10^-4
So the probability that her score will be at least 5 is:
P (r≥5) = 0.246 + 0.205 + 0.117 + 0.044 + 9.766 x 10^-3 + 9.766 x 10^-4
P (r≥5) = 0.623
So about 62.3% chance.
You can do the same for the other item quiz, just set the value of n
Final answer:
When randomly guessing on true-false quizzes, the probability of getting at least a 50% grade on a three-item quiz is 0.5, on a four-item quiz is 0.6875, and on a five-item quiz is also 0.5.
Explanation:
Calculating the probability of getting at least 50% on a true-false quiz when randomly guessing involves understanding the binomial probability distribution. For a true-false quiz, each question has two possible outcomes, from which we can calculate the likelihood of each score.
For a three-item quiz, to get at least a 50% grade, Peppermint Patty needs to get at least 2 questions correct. Since each question has a 1/2 chance of being answered correctly when guessing, the probability of getting exactly two questions right is: P(X=2) = 3C2 * (1/2)² * (1/2)¹ = 3/8, and the probability of getting all three correct is P(X=3) = 1/8. So, the total probability of getting at least 50% is P(X>=2) = P(X=2) + P(X=3) = 3/8 + 1/8 = 1/2 or 0.5.For a four-item quiz, getting at least 50% means 2 or more questions correct. The probabilities are: P(X=2) = 6/16, P(X=3) = 4/16, P(X=4) = 1/16. Therefore, P(X>=2) = 6/16 + 4/16 + 1/16 = 11/16 or 0.6875.For a five-item quiz, 50% means at least 3 questions correct. The probabilities are: P(X=3) = 10/32, P(X=4) = 5/32, P(X=5) = 1/32. Hence, P(X>=3) = 10/32 + 5/32 + 1/32 = 16/32 or 0.5.Jose is now six years older than John. In two years, Jose will be twice as old as John. How old is John now?
x + 6 =y
8 =2y ........ y = 8/2 = 4
4+6 =10
John is four & Jose is 10
A Rectangular prisim is completely packed with 200 cubes of edge length 1/5in without any gap or overlap. Which of these best describes the volume of this rectangular prism?
The volume of the rectangular prism completely packed with 200 cubes of edge length 1/5in is approximately 1600 cubic inches.
Explanation:The volume of a rectangular prism can be found by multiplying the length, width, and height of the prism. In this case, the prism is completely packed with cubes of edge length 1/5in. Since there are 200 cubes, the length, width, and height of the prism would be the number of cubes in each respective direction. Therefore, the volume of the rectangular prism is:
(200 cubes in length) x (200 cubes in width) x (200 cubes in height) x (1/5in cube)^3
To simplify the calculation, we can express the volume in terms of the number of cubes:
200 x 200 x 200 x (1/5)^3 in³
Converting the units, we find that the volume of the rectangular prism is approximately 1600 cubic inches.
Suppose your opponent reraises all-in before the flop, and you know that she would do this with 90% probability if she had aa, kk, or qq. if she had any suited connectors, she would do this with 20% probability. with any other hand, the probability that she would reraise all-in is 0. given that she reraises all-in, what is the probability that she has suited connectors?
In this problem, y = 1/(x2 +
c.is a one-parameter family of solutions of the first-order de y' + 2xy2 = 0. find a solution of the first-order ivp consisting of this differential equation and the given initial condition. y(4) = 1/15
solve 20p−60 using GCF
State restrictions on the variable.
What is 43,000 rounded to the nearest thousand
Translate the following problem to an equation. Do not solve.
55 times what number is 1265?
Choose the correct equation.
A) 55 dot x=1265
B) 23
C) 55/ x=1265
D) 55 dot 1265= x
The translation of the statement '55 times what number is 1265?' into an equation is '55 * x = 1265', which, with 'dot' finding use as multiplication, matches with the provided option A) 55 dot x = 1265.
Explanation:The question asks for the translation of the problem statement into an equation. The phrase '55 times what number is 1265?' implies multiplication. Specifically, 55 is being multiplied by an unknown number (which we can denote by 'x'), and the result of this multiplication is 1265. Therefore, the correct translation of this problem into an equation would be 55 * x = 1265 or in the provided options A) 55 dot x = 1265 where 'dot' indicates multiplication.
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The number of gallons of coffee a mathematician drinks on any given day is inversely proportional to how much sleep he gets the night before. On Monday, he got 9 hours of sleep and drank 2 gallons of coffee. On Tuesday, he got 6 hours of sleep. How many gallons of coffee did he drink?
Calculate the probability of getting exactly 50 heads and 50 tails after flipping a fair coin 100 times.
The u.s. per capita chicken consumption for 2007 was 90.6 pounds. assume this consumption is normally distributed with a standard deviation of 17.2 pounds. assume n infinite. what is the probability that a sample taken of 100 individuals shows an average consumption of less than 90 pounds of chicken?
To solve this, we need to use the z statistic. The formula for z score is:
z = (x – u) / s
where x is sample value = less than 90, u is the sample mean = 90.6, s is the standard deviation = 17.2
z = (90 – 90.6) / 17.2
z = -0.035
From the standard distribution tables:
P (z = -0.035) = 0.4860
Therefore there is about 48.60 % chance that it will be less than 90 pounds
a certain game involves tossing 3 fair coins. it pays 28 cents for 3 heads, 16 cents for 2 heads, and 4 cents for 1 head. what is a fair price to play this game?
Final answer:
The fair price to play this game is 10.5 cents.
Explanation:
To find the fair price to play this game, we need to calculate the expected value. The expected value is calculated by multiplying each outcome by its probability and summing them up.
Let's calculate the expected value:
Probability of getting 3 heads: 1/8 (since there are 8 possible outcomes)Payout for 3 heads: 28 centsProbability of getting 2 heads: 3/8Payout for 2 heads: 16 centsProbability of getting 1 head: 3/8Payout for 1 head: 4 centsNow, we calculate the expected value:
(1/8) * 28 + (3/8) * 16 + (3/8) * 4 = 3.5 + 6 + 1 = 10.5 cents
Therefore, the fair price to play this game is 10.5 cents.
What effect does increasing the sample size have on a distribution of sample means?
If the number of samples is increased, this actually leads to a reduction in error of the distribution. This is because of the relationship between variation and sample size which has the formula of:
σx = σ / sqrt (n)
So from the formula we can actually see that the variation and sample size is inversely proportional.
Which means that increasing the sample size results in a reduction of variation.
Answer:
It will have less variation
Increasing the sample size causes the confidence interval to narrow, decreases the standard deviation, and makes the sample mean distribution more normal. This leads to more accurate and reliable estimates of the population parameters.
Explanation:The effect of increasing the sample size in a distribution of sample means primarily involves the confidence interval, the standard deviation, and the progress towards a normal distribution.
Firstly, increasing the sample size reduces the error bound, leading to a narrower confidence interval. This means that the calculated mean is likely to be more accurate representation of the true population mean.
Secondly, as the sample size increases, the standard deviation, which is a measure of spread or dispersion in the data, decreases. So, larger sample sizes result in lesser variability.
Finally, per the central limit theorem, an increased sample size makes the distribution of sample means get closer to a normal distribution, regardless of the population's initial distribution. This property is valid as long as the sample size is large enough (generally taken as 30 or more).
Thus, larger sample sizes tend to provide more accurate and reliable estimates of the population parameters.
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An unordered list can use one of four different bullet options: disc, square, circle, or triangle.
Final answer:
The question involves creating unordered lists with various bullet options such as disc, square, circle, and triangle. While disc, square, and circle are commonly available, the triangle may need to be created as a custom bullet option in advanced editors. The process includes selecting the Bullets icon in the Paragraph section and choosing or customizing the bullet style.
Explanation:
The question refers to the process of creating unordered lists in document editing or web development environments, where you have the option to format lists using different types of bullets. When you want to organize information without a specific order of importance, an unordered list can be used. These lists are often formatted with bullet points to improve readability and structure.
Steps to Create an Unordered List with Different Bullet Options:
Go to the Home menu item.
In the Paragraph section, select the Bullets icon for unordered lists.
To choose a different bullet format, select the arrow beside the icon.
Select a format from the format Library that appears in the drop-down menu. Common bullet styles include disc, square, and circle. However, the question mentions 'triangle' which is not a standard option in most document editors but can be created as a custom bullet in some advanced editing tools.
Using different bullet styles like disc, square, and circle can help distinguish or organize your content more effectively. While the 'triangle' option might not be directly available, it represents the possibility to define new custom bullets, adding a unique aspect to your document's design.
Factorise 2b squared - 2b
Find the sum of 2x 2 + 3x - 4, 8 - 3x, and -5x 2 + 2
(2x² +3x -4) + (8 -3x) + (-5x² +2)
= x²(2 -5) +x(3 -3) +(-4 +8 +2)
= -3x² +6
_____
The process here is called "collecting terms", which means you add the coefficients of "like" terms. Terms are "like terms" when they have the same constellation of variables. Here, there are three different kinds of like terms:
• x² terms
• x terms
• constants
This process is an application of the distributive property, as you can see on the second line of the solution above.
Dan earns $8.25 an hour and works 20 hours a week. How much will he earn in three weeks?
Answer:
Step-by-step explanation:
Okay. So first 8.25 * 20 = 165. Then you multiply 165 by 3 (165*3). 165 * 3 = 495.
Dan will earn $495 in three weeks.
Start at 5. Create a pattern that multiplies each number by 3 and subtracts 2. Stop when you have 5 numbers.
Answer: The required pattern is 13, 37, 109, 325, 973
Step-by-step explanation:
Since, each number in the sequence follows the following rule,
2 less than the 3 times of the previous number.
If we start from 5,
Then first number of the sequence = 3×5 - 2 = 15 - 2 = 13
Second number = 3× 13 - 2 = 39 - 2 = 37
Third number = 3× 37 - 2 = 111 - 2 = 109
Fourth number = 3×109 - 2 = 327 - 2 = 325
Fifth number = 3× 325 - 2 = 975 - 2 = 973
Hence, The required sequence is,
13, 37, 109, 325, 973
2005 months = how many liters
Find A ∩ B if A = {3, 6, 9, 12} and B = {2, 4, 6, 8, 10, 12}.
Ø
{6, 12}
{2, 3, 4, 6, 8, 9, 10, 12}
Find A ∩ B is any numbers that are in both sets
they booth have 6 & 12 so the answer is: {6, 12}
Answer:
6,12
Step-by-step explanation:
Find the parabola of the form y = ax2 + b which best fits the points (1, 0), (3, 2), (4, 4) by minimizing the sum of squares, s, given by
Give the angle measure represented by 2 rotations clockwise
the answer to Give the angle measure represented by 2 rotations clockwise. it's A. -720 on edge
Which rational number is equivalent to the expression 69 2/9 - 31 1/9 - ( -12 4/9) ?
The rational number equivalent to the given expression is 50 5/9.
The given expression is [tex]69\frac{2}{9} -31\frac{1}{9} -(-12\frac{4}{9} )[/tex].
How do add and subtract rational numbers?To add or subtract two rational expressions with the same denominator, we simply add or subtract the numerators and write the result over the common denominator.
Now, [tex]69\frac{2}{9} -31\frac{1}{9} +12\frac{4}{9}[/tex]
[tex]=(69-31+12)(\frac{2}{9}-\frac{1}{9}+\frac{4}{9})[/tex]
=50 5/9
Therefore, the rational number equivalent to the given expression is 50 5/9.
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