Final answer:
Given 400 meters of fencing, constructing a square pen would result in an area of 10,000 square meters, while a circular pen would yield approximately 12,732 square meters, making the circular pen the larger option.
Explanation:
Ernesto wants to construct the largest possible pen for his iguana using 400 meters of fencing. To determine the maximum area of a rectangular pen, we can use the principle that a square will always provide the largest area for a given perimeter. In the case of a rectangular enclosure, we form a square with each side being one-fourth of the total available fencing, here being L/4 where L is 400 meters. Thus, each side of the square would be 400/4 = 100 meters. The area of such a square would be side × side = 100 m × 100 m = 10,000 square meters.
For the circular pen, the entire length of fencing would be the circumference of the circle. Given the formula for circumference is C = 2πr, where r is the radius, we set 400 = 2πr to solve for r, which is approximately 63.66 meters. The area of a circle is given by A = πr², which would then be approximately π(63.66)^2 ≈ 12,732 square meters. Therefore, a circular pen would provide a larger enclosed area compared to a square one given the same amount of fencing.
Julia has two children who are four years apart in age. Julia is four times older than her youngest child. The sum of the ages of Julia and her children is 76 years. How old is Julia and each of her children?
Answer:
c
Step-by-step explanation:
The linear function graphed below represents Tim’s age in the years since he was married. Which of these statements is correct?
A(The initial value is 22, and the rate of change is 1.
B(The initial value is 22, and the rate of change is 15.
C(The initial value is 32, and the rate of change is 1.
D(The initial value is 32, and the rate of change is 15.
Answer:
B) The initial value is 22, and the rate of change is 15.
Step-by-step explanation:
The first point is located at (22, 54). This means the initial value is 22.
The rate of change is found using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the first two points, we have
[tex]m=\frac{69-54}{37-22}\\\\=\frac{15}{15}=1[/tex]
Choose the correct simplification of the expression (7m3 n) 2. 14m5n3 14m6n2 49m5n3 49m6n2
what is the approximate volume of a cylinder with the radius of 4 cm and height of 5 cm
x^2-7×+10 solve for quadratic formula.
wich one is the solution???: 4(2x-1)=-3x+32
i dont understand this thing....
Jasmine works in Lower Beauvale and arrives at the station at 5.20 p.m. If she catches the next available train to Common Top, what time will she arrive?
Answer:18:19
Step-by-step explanation:
If the area of a circle is 58 square feet find the circumference
I need help with #8 & #9
How many inches did the height of the plant increase between weeks 3 and 4
a cookie factory uses 1/4 of a barrel of oatmeal in each batch of cookies. The factory used 1/2 of a barrel of oatmeal yesterday. How many batches of cookies did the factory make yesterday?
Answer: 2 BATCHES
Step-by-step explanation: to produce one batch it takes 1/4 of oatmeal
Now the factory uses 1/2 batch of oatmeal
1=1/4 OATMEAL
X=1/2 OATMEAL
X=(1/2*1)/1/4
=1/2*4/1
=4/2
=2
Alana tosses 2 number cubes. She wins if she rolls double sixes. Find p(Alana wins)
x^2+13x+30=0 in quadratic formula
On which of the following lines does the point (7, 1) lie?
A.) y = 5x + 4
B.) y = -x + 8
C.) y = x - 10
D.) y = -4x + 3
Please help, personal finance question
Dave has a life insurance policy with $2.2 million benefit. If this money was put into an account with a 3.4% interest rate, how much income can his beneficiaries expect i case Dave dies?
A $74, 800
B $20, 600
C. $60, 000
D $40, 000
Answer:
Step-by-step explanation:
The maximum value can reach $74, 800 if Dave Dies.
What is Exponential GrowthInsofar as they use compound interest, life insurance premiums are equivalent to bank interest rates. We may use the exponential growth formula to get the insurance policy payout because they are compound interests. Those being the following,
Given:
T = [tex]a(1+r)^t[/tex]
Where:
T is the final payout, a is the initial amount, r is the interest rate in decimal form and t is the time.
So, T = [tex]2200000(1+ 0.034)^t[/tex]
let Dave dies after 2 years of buying his life insurance the beneficiaries will get the following payout.
T = [tex]2200000(1+ 0.034)^2[/tex]
T= 2200000 ( 1.069156)
T = $23,52,143.2
So, the maximum value can reach $74, 800.
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A certain college randomly selected 30 freshman students who completed college algebra during their first semester. Fifteen students were chosen from students who took the course at night and 15 students were chosen from students who took the course during the day. The following statistical information was calculated from their final grades.
Day Night
Mean 76 68
Median 68 72
Mode 64 72
Range 38 53
Based on these samples, what generalization can be made? (Assume that a score of 70 or greater is a passing score.)
A.
The mean score for the night students was higher than the mean score for the day students.
B.
The median score for the day students was higher than the median score for the night students.
C.
The mean score for the day students was higher than the mean score for the night students.
D.
The range of scores was larger for the day students than for the night students.
It's C because if you look at the day and night students, the mean score for the day students was actually higher then the mean score for the night student.
Answer: C
Step-by-step explanation:
Staci is attending a music festival. The ticket to the festival costs $87.96. Staci plans to purchase $30.00 t-shirt from the event for close friends. she is taking $200.00 to the festival. what is the maximum number of t-shirts can purchase?
After purchasing the festival ticket, Staci has $112.04 remaining from her $200 budget. Each T-shirt costs $30, so she can buy a maximum of 3 T-shirts.
Explanation:The student asked how many
T-shirts Staci can purchase at a music festival considering she has a budget of $200, and she also needs to buy a ticket and possibly T-shirts for her friends.
First, we need to subtract the cost of the festival ticket from Staci's total budget which is $200.00 - $87.96 = $112.04 remaining. Now, if each T-shirt costs $30.00, we can find the maximum number of T-shirts she can purchase by dividing the remaining money by the cost of one T-shirt.
$112.04 / $30.00 = 3.734.
Since Staci cannot buy a fraction of a T-shirt, she can purchase a maximum of 3 T-shirts with the remaining budget.
A circle has a center at (1,-2) and radius of 4. Does the point (3.4,1.2) lie on the circle? Justify your answer.
The point (3.4, 1.2) lies on the circle with center at (1, -2) and radius of 4, as the distance from the point to the circle's center is exactly equal to the circle's radius.
The question asks if the point (3.4, 1.2) lies on a circle with a center at (1, -2) and a radius of 4. To determine this, we can use the distance formula, which calculates the distance between two points in a coordinate plane. The distance formula is √((x_2 - x_1)^2 + (y_2 - y_1)^2), where (x_1, y_1) and (x_2, y_2) are the coordinates of the two points. In this case, the center of the circle is (1, -2) and the point in question is (3.4, 1.2).
To see if the point lies on the circle, we check if the distance from the point to the center equals the circle's radius. Calculating: √((3.4 - 1)^2 + (1.2 - (-2))^2) = √((2.4)^2 + (3.2)^2) = √(5.76 + 10.24) = √16 = 4. Since this distance is exactly 4, which is the circle's radius, the point (3.4, 1.2) does indeed lie on the circle.
Plz tell me the aswer and how you worked it out. A tree grows to a height of 13.75m over 5 1/2 years. What is the average annual growth rate in metres per year?
Michael has 225 milliliters of a liquid. To find out the number of grams of calcium in this liquid, Michael multiplies the volume by 0.015. When he writes the number representing the amount of calcium in the liquid, how many significant digits will the number have?
Answer:the answer is 2 trust me it had 2 significant digits
Step-by-step explanation:
The reason why is because the number 0.015 only has 2 significant digits is because until a number that is not 0 comes up then it doesn’t count as a significant digit so in this case the number 1 is the number that does start with a zero so thats 1 significant digit and then after that is 5 so they’re is the second significant digit so the 2 other zeros don’t count cause in order for the zero to be a significant digit it has to be to the left of a other number thats not 0 so there’s your answer mark me brailiest pls and have a good day .-. :)
Which story problems could be solved using the given equation? Choose exactly two answers that are correct. A. Bo is carrying a bag of topsoil that is full. He drops the bag and of the soil pours out onto the ground. How much of the bag of soil poured onto the ground? B. The city park has an area of square kilometer. The width of the park is kilometer. What is the length of the park? C. Julia has a bucket that contains gallon of water. She wants to pour the water to fill some dog bowls. Each bowl holds gallon of liquid. How many dog bowls can Julia fill with water? D. Kai has a rope that is meter long. Kai cuts off a piece that is of the length of the rope. How long, in meters, is the piece of rope that Kai cut off?
what is the exact volume of a sphere with a diameter of 6 ft
Help asap thank you....
What is a 4:1 ratio? Is it equivalent to 75% to 25%?
April wants to know what the probability is that a card drawn randomly from a deck will be a heart. Her sample space includes all 52 cards in a standard deck. Which of these outcomes composes the event?
(This question was not multiple choice)
There is a 1/4 chance.
In decimal 0.25
In percentage 25%
Ik the other guy answered it but I figured why don't I answer it as well :)
ANSWER BOTH QUESTIONS FOR BRAIN
All the answers please on paper and work
Sue used the equation y=10x to calculate how much money, y, she would make for babysitting x hours. How many hours did Sue babysit for if she made $260?
George is playing a board game and hopes to roll a sum of 5 he tosses a pair of number cubes what is the probability that the sum of the numbers tossed will be five
The probability of rolling a sum of 5 with two dice is 1/9, as there are 4 favorable outcomes out of the 36 possible outcomes when rolling two dice.
The student asked about the probability of rolling a sum of 5 using two fair, six-sided dice (also known as number cubes). To find this probability, we need to consider all possible outcomes that result in a sum of 5 and divide it by the total number of possible outcomes when rolling two dice.
By examining the possible ways to get a sum of 5, we have the following pairs: (1,4), (2,3), (3,2), and (4,1). There are 4 favorable outcomes. Since each die has 6 faces, there are a total of 6 x 6 = 36 possible outcomes when rolling two dice. Thus, the probability of rolling a sum of 5 is 4/36, which reduces to 1/9.
To conclude, the probability to roll a sum of 5 on two dice is 1/9.
a cylinder and a cone have the same base and height.The cylinder can hold about 4,712 cm3 of sand .Jared says that the cone can hold about 1,178 cm3 of sand.Which explains where Jared is correct
Jared is correct because the volume of a cone that has the same base and height as a cylinder is one-third the volume of the cylinder. This is due to the 1/3 factor in the formula for the volume of a cone. Therefore, the cone would indeed hold about 1,178 cm³ of sand.
Explanation:Jared is indeed correct in his statement. The volume of a cone is found by using the formula 1/3 * base area * height, while the volume of a cylinder is found by using the formula base area * height. In this case, both the cone and the cylinder have the same base and height. However, the key difference lies in the 1/3 factor of the formula for a cone. This means that a cone with the same base and height as a cylinder would hold only one-third the volume of the cylinder.
In this case, the cylinder can hold about 4,712 cm³ of sand. As the cone is one third the size of the cylinder, it can hold about 1,178 cm³, which is precisely one third of the cylinder's volume, thus Jared's statement is correct.
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