Ernesto plans to build a pen for his pet iguana. Think about these two different questions. What is the area of the largest rectangular pen that he can make with 400 meters of fencing? What is the area of the largest circular pen he can make with the 400 meters of fencing?
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.
How many inches did the height of the plant increase between weeks 3 and 4
What is twenty percent of 30
Miss Valens withdrew $525 from her savings account over a period of 14 days. Which ratio represents the daily change in her account balance?
(multi choice picture below)
It says that she withdrew 525 dollars from a saving account over a total period of 14 days.
As this amount is debited from her account, so it would be a negative number in her passbook i.e. -525 dollars.
To find the average change in the account balance, we can divide the total amount withdrawn from the account by the total number of days.
Average change in account balance = [tex]\frac{debited \;amount}{total \;time \;period}[/tex] .
Average change = [tex]\frac{-525}{14}[/tex]
Hence, option A is correct i.e. [tex]\frac{-525}{14}[/tex].
write the equation of the line that passes through the points (-2,3) and (-2,5)
triangle with base 12.5m and height 2.4m
What is the surface area of the cube?
A. 64 mm^2
B. 192 mm ^2
C. 384 mm ^2
D. 512 mm ^2
if i I wanted to be precise, how can I express the exact circumference for the circumference given the diameter
When was Louisville cooler, in December - 3/5F or in January -9/2F?
Answer: Louisville was cooler in January (-9/2 F) than in December
(-3.5 F).
Step-by-step explanation: PLATO
Write the letter in the box that correctly describes the three dimensional figure.
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]
Evaluate the expression, mn if m=6 and n=4. A. 24 B. 64 C. 1,296 D.4,096
To solve for the expression mn with m=6 and n=4, the values are multiplied to get 6 × 4 = 24. Therefore, the answer is 24, which corresponds to Option A.
Explanation:To evaluate the expression mn when m=6 and n=4, you simply multiply the values of m and n together.
The calculation is as follows:
m × n = 6 × 4Therefore, the value of mn is 24.
So, the correct answer is Option A: 24.
The correct answer is A. 24. The expression, mn is 24.
To evaluate the expression [tex]\( mn \)[/tex] when [tex]\( m = 6 \)[/tex] and [tex]\( n = 4 \)[/tex], we simply multiply the two numbers together:
[tex]\( mn = (6)(4) \).[/tex]
Now, let's perform the multiplication:
[tex]\( 6 \times 4 = 24 \)[/tex].
Therefore, the value of [tex]\( mn \)[/tex] when [tex]\( m = 6 \)[/tex] and [tex]\( n = 4 \)[/tex] is 24.
The other options provided in the question are incorrect because they do not result from the multiplication of [tex]\( m \)[/tex] and [tex]\( n \)[/tex] as given:
B. [tex]\( 64 \) is \( 4^3 \) or \( 2^6 \)[/tex], which is not the product of [tex]\( m \)[/tex] and [tex]\( n \)[/tex].
C. [tex]\( 1,296 \) is \( 6^4 \) or \( 2^{10} \)[/tex], which is also not the product of [tex]\( m \)[/tex] and [tex]\( n \)[/tex].
D.[tex]\( 4,096 \) is \( 4^6 \) or \( 2^{12} \)[/tex], which again is not the product of [tex]\( m \)[/tex] and [tex]\( n \)[/tex].
The only correct answer is A. [tex]\( 24 \)[/tex], which is the result of multiplying [tex]\( m \)[/tex] by [tex]\( n \)[/tex].
How do you subtract mixed numbers
Graph y+2 ≤ 1/4x-1 I GIVE BRAINLIEST
The shaded region represents the solution to the inequality y + 2 ≤ (1/4)x - 1. Graph A represent the inequality.
To graph the inequality y + 2 ≤ (1/4)x - 1, we need to first plot the corresponding boundary line, which is the equation y + 2 = (1/4)x - 1. Then, we'll determine the region of the graph that satisfies the inequality.
Step 1: Plot the boundary line:
To graph the line y + 2 = (1/4)x - 1, we'll first rewrite it in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
y + 2 = (1/4)x - 1
Subtract 2 from both sides:
y = (1/4)x - 3
Now, we can see that the slope (m) is 1/4, and the y-intercept (b) is -3.
Step 2: Plot the y-intercept and use the slope to find additional points:
Plot the y-intercept, which is -3, on the graph. Then, use the slope (1/4) to find other points. The slope of 1/4 means that for every increase of 1 unit in the x-direction, y increases by 1/4 units.
Let's find a few more points:
- If x = 0, y = (1/4) * 0 - 3 = -3 (giving us another point on the line).
- If x = 4, y = (1/4) * 4 - 3 = -2 (giving us another point on the line).
- If x = -4, y = (1/4) * (-4) - 3 = -4 (giving us another point on the line).
Step 3: Connect the points to draw the line:
Now, draw a straight line passing through all the points you've plotted. The line represents the boundary of the inequality.
Step 4: Determine the region that satisfies the inequality:
Since the inequality is y + 2 ≤ (1/4)x - 1, we need to determine which side of the line satisfies this inequality. One way to do this is to pick a test point that is not on the line (like the origin (0,0)), and check if it satisfies the inequality.
For (0, 0):
0 + 2 ≤ (1/4) * 0 - 1
2 ≤ -1
Since 2 is not less than or equal to -1, the region containing the origin (0,0) does not satisfy the inequality. Thus, we shade the other side of the line.
Step 5: Shade the region that satisfies the inequality:
Shade the region on the graph that is below the line y + 2 = (1/4)x - 1. This shaded region represents the solution to the inequality y + 2 ≤ (1/4)x - 1.
Graph A represent the inequality.
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Which of the following measures can be determined by analyzing a dot plot? Select all that apply.
range
median
mode
mean
All of the statistical measures are used to analyze a dot plot.
What is the mean?In mathematics and statistics, the term "mean" refers to the average of a set of variables. There are various ways to determine the mean, including geometric means, harmonic means, and simple arithmetic means (putting the numbers together and dividing the result by the quantity of observations).
All of the following measures can be determined by analyzing a dot plot:
Range: The difference between the highest and lowest values.
Median: The middle value when the data is arranged in order.
Mode: The value that appears most frequently in the data set.
Mean The average of all the values in the data set.
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The awnser I’m really have trouble finding a awnser
If the area of a circle is 58 square feet find the circumference
ANSWER BOTH QUESTIONS FOR BRAIN
PLEASE HELP!!!!!!!!!!! Kim wants to know if the number of words on a page in her math book is generally more than the number of words on a page in her poetry book. She takes a random sample of 25 pages in each book, then calculates the mean, median, and mean absolute deviation for the 25 samples of each book.
Book Mean Median Mean absolute deviation
Math 49.9 43 10.2
Poetry 41.5 42 1.1
Kim claims that because the mean number of words on each page in the math book is greater than the mean number of words on each page in the poetry book, the math book has more words per page. Based on the data, is this a valid inference? (5 points)
Yes, because the mean is larger in the math book
No, because the mean is larger in the math book
No, because there is a lot of variability in the math book data
Yes, because there is a lot of variability in the math book data
YOU WILL GET BRAINIEST
It's D, because the mean doesn't matter as much if it's only taken in a small variability. The mean was selected from 25 random pages in the book, that is why it is right.
Answer:
Yes, because the mean is larger in the math book.Step-by-step explanation:
According to Kim's calculations
The mean of the Math Book is 49.9, this means there are 49.9 per page.The mean of the Poetry Book is 41.5, which means there are 41.5 per page.Remember that a mean is defined as the quotient between the sum of all elements and the total number.
According to this calculations, the Math Book has more words per page, based on its greater mean.
Therefore, the right answer is the first choice.
how do i simplify 40 15×40 2
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
Evaluate the expression. Write your answer in scientific notation. (9×10^−3)+(2.4×10^−5)÷0.0012
The given expression (9×10^−3)+(2.4×10^−5)÷0.0012 equals 2.9x10^-2 in scientific notation. The division operation was performed first and added to 9x10^-3, demonstrating the usefulness of scientific notation in simplifying arithmetic.
Explanation:In order to evaluate the given expression (9×10^−3)+(2.4×10^−5)÷0.0012, you first need to perform the operations in parentheses which is the standard form of the expression to simplify it. Next, we must remember the order of mathematical operations, also known as BIDMAS or PEMDAS in mathematics: Brackets (or Parentheses), Indices (or Exponents), Division, Multiplication, Addition, and Subtraction.
However, in this expression we only have addition and a division to perform. The division operation takes precedence over addition, thus we first divide 2.4×10^−5 by 0.0012. The result of this can then be added to 9×10^−3. Let's perform these calculations:
2.4×10^−5 ÷ 0.0012 = 2×10^−2(9×10^−3)+(2×10^−2)= 0.029 or 2.9x10^-2 in scientific notationSo, the evaluated expression equals 2.9x10^-2 in scientific notation. This is a simplification of arithmetic using scientific notation, which helps to easily handle very large or very small numbers.
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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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which choice shows three lengths that cannot be the lengths of the three sides of a triangle
Give the equation y=35(0.57)^x.
Evaluate for x=5
West and Company uses the LIFO method to calculate inventory values. Their beginning inventory consisted of 200 units at a cost of $9.00 each. Purchases include 300 units at $10.00 each on February 18; 400 units at $11.00 each on July 16; and 100 units at $12.00 each on December 5. If there were 300 units remaining in imventory at the end of the year, what was the cost of goods sold?
Trisha noticed that three copies of a certain triangle could be arranged in a way that the three angles of the triangle form a straight line. what can she conclude from this observation
a. that each interior angle of the triangle must measure 60*
b.exterior must measure 60*
c.sum of interior angles must be 180*
d.sum of exterior angles must be 180*
show work please and i need it desperately
Trisha's observation that three copies of a certain triangle can be arranged to form a straight line suggests that each interior angle of the triangle measures 60 degrees. This is because a straight line measures 180 degrees, which implies that the sum of the three angles is 180 degrees. Therefore, each angle must measure 60 degrees.
Explanation:In this case, Trisha was able to arrange three copies of the triangle in such a way that their angles form a straight line. That straight line, or 180 degrees, is, in fact, the sum of all interior angles in a triangle. Hence, it can be inferred that the sum of the angles of each triangle she had must be 60 degrees, implying that each triangle is an equilateral triangle. Therefore the correct answer is: a. each interior angle of the triangle must measure 60*.
Step-by-step explanation: If you consider a straight line, it measures 180 degrees. If Trisha's three triangles are forming such a line, it implies that the three angles are combining to give 180 degrees. Assuming each angle is the same (because they are copies of the same triangle), then each angle in the triangle is 60 degrees (since 180/3 = 60).
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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?
quick I need help quick Morgan rode her bike. 2 kilometers from her house to her friend's house from her friend's house she rode 600m in all going to and from the library then she rode back home how many meters did Morgan like in all
Morgan rode her bike a total of 4600 meters after combining the distances from her house to her friend's, to and from the library, and back to her house.
To determine how many meters Morgan cycled in total, we first need to convert all distances into the same unit. Morgan rode 2 kilometers from her house to her friend's house, which is equal to 2000 meters. Then, she rode 600 meters in total going to and from the library. Since she needs to return home, she would ride the initial 2000 meters back. Therefore, the total distance Morgan cycled is the sum of these three distances.
Calculation
Distance from home to friend's house: 2000 meters
Traveling to and from the library: 600 meters
Distance from friend's house back to home: 2000 meters
Adding these distances gives us the total distance Morgan rode:
Total Distance = 2000m + 600m + 2000m = 4600 meters.
Need some help! Find the area of this shape.