A perimeter of 24 feet is achieved in this optimal scenario.
For an area of 36 square feet, we can factor this into pairs: (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6). Since we are looking for the minimum perimeter, the closest factors will yield the smallest perimeter, which in this case is the pair (6, 6). Therefore, a rectangle with the dimensions 6 feet by 6 feet will not only satisfy the area requirement of 36 square feet but will also have the minimum perimeter, which is 24 feet.
The perimeter (P) of a rectangle is calculated by the formula P = 2(l + w), where 'l' is the length and 'w' is the width. Given our dimensions, P = 2(6 + 6) = 24 feet. The square shape of the rectangle, which is a special case where the length and width are equal, is what minimizes the perimeter for a given area.
The rectangle with an area of 36 square feet that has minimal perimeter is actually a square with dimensions of 6 feet by 6 feet.
To find the length and width of a rectangle with an area of 36 square feet that has the minimum perimeter, we need to follow these steps:
Assume the length is l and the width is w. The area equation becomes: l × w = 36 sq ftExpress one variable in terms of the other: l = 36 / wUse the perimeter formula: P = 2l + 2w. Substitute l = 36 / w into this formula: P = 2(36 / w) + 2wTo find the minimum perimeter, take the derivative of P with respect to w and set it to zero: P'(w) = -72/w² + 2 = 0Solve for w: 2 = 72/w² gives w² = 36, so w = 6 ftThen, find l using l = 36 / w, giving l = 6 ftThus, the dimensions that yield the minimum perimeter are 6 feet by 6 feet. This results in a square having the smallest possible perimeter for the given area.
You flipped a coin 70 times and recorded 23 heads. What is the experimental probability of flipping tails?
ANY HELP IS APPRECIATED!
Please show work
There are 5 cars to be displayed in 5 parking spaces, with all the cars facing the same direction. of the 5 cars, 3 are red, 1 is blue, and 1 is yellow. if the cars are identical except for color, how many different display arrangements of the 5 cars are possible?
The question relates to combinatorial mathematics and asks for possible arrangements of 5 cars of three different colors. Treating identical colors as one entity, we find that there are 6 ways to arrange the color groups and another 6 ways to arrange the red cars among themselves, resulting in 36 possible arrangements.
Explanation:The subject of this question is combinatorial mathematics. We're asked how many different arrangements there are if we have 5 cars to be displayed in 5 parking spaces, with the condition that the cars are identical besides their color; 3 of them are red, 1 is blue, and 1 is yellow.
Since three cars are identical (red ones), we treat them as one. So initially, we have three 'entities' to arrange: the red group (of 3 cars), the blue car, and the yellow car. These can be arranged in 3! (which means 3 factorial, or 3 * 2 * 1) = 6 ways.
However, within the red group, those 3 red cars can be arranged amongst themselves in 3! = 6 ways.
Therefore, to get the total number of arrangements, we multiply these results together, giving us: 6 * 6 = 36 different arrangements.
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10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!! ALL PARTS A, B, C, D, E
A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base, as shown below.
What is the vertical clearance 7 m from the edge of the tunnel?
What do the graphs of sine and cosine have in common with the swinging you see?
Which reasons did you think of?
Answer:
The high and low points repeat in a pattern.
The cycle repeats at equal time intervals.
The swinging motion is smooth, unabrupt.
The graphs of sine and cosine functions have similarities with the swinging motion such as repeating patterns at equal time intervals and smoothness.
Explanation:The graphs of sine and cosine functions have several similarities with the swinging motion you observe:
Both the high and low points in the graphs of sine and cosine functions repeat in a pattern, just like the motion of a swing repeating from its highest to lowest points.The cycle of both graphs repeats at equal time intervals, just like the swinging motion of a swing that takes the same amount of time to swing back and forth.The swinging motion of a swing is smooth and uninterrupted, just like the graphs of sine and cosine functions.These similarities are because simple harmonic motion, which includes swinging, is closely related to sine and cosine waves.
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Algebra question ( Matrices and Determinants ) 20 points
Isabel is purshing a 5 pound bag of dog food.how many 8- ounce servings can she feed her dog (1lb=16oz
A number cube is rolled 120 times. The number 4 comes up 47 times. What is the experimental probability of rolling a 4? What is the theoretical probability of rolling a 4?
A. 47/120; 1/30
B. 47/120; 1/6 ******
C. 4/47; 1/6
D. 1/6; 47/120
Am I Correct?
A number cube is rolled 120 times. The number 4 comes up 47 times.
We have to determine the experimental probability of rolling a 4.
The formula to evaluate probability of an event is given by:
Probability = [tex] \frac{Favourable outcomes}{Total outcomes} [/tex]
So, Probability of rolling a 4 = [tex] \frac{ Total number of times when 4 appears}{Total number of times number cube rolled} [/tex]
= [tex] \frac{47}{120} [/tex]
Now, we have to find the theoretical probability of rolling a 4.
Total number of outcomes of number cube = {1,2,3,4,5,6}
Probability of rolling a 4 = [tex] \frac{1}{6} [/tex]
So, Option B is the correct answer.
An irregularly shaped stone was lowered into a graduated cylinder holding a volume of water equal to 20mL. The height of the water rose to 30.2mL. If the mass of the stone was 25g what was its density?
To find the density of the stone, subtract the initial volume of water from the final volume, then divide the mass of the stone by the volume. The density of the stone is 2.45 g/cm³.
Explanation:In order to find the density of the stone, we first need to calculate its volume. The volume can be determined by subtracting the initial volume of water in the graduated cylinder from the final volume with the stone submerged. In this case, the volume of the stone is 30.2 mL - 20 mL = 10.2 mL.
Next, we can use the formula for density: density = mass/volume. Plugging in the given values, we have density = 25 g/10.2 mL.
Since density is mass divided by volume, we need to convert mL to g/cm³. 1 mL is equal to 1 g/cm³. Therefore, the density of the stone is 25 g/10.2 mL = 2.45 g/cm³.
What is EC if AC = 12, BC = 5, and DC = 4?
A. 30
B. 9
C. 15
D. 7
Find the slope of the line graphed below
The slope of the line is 2/3
To find the slope of the line, first choose two points that are on the line. For this example we'll use (0, -4) and (6, 0). Now use the slope formula with these two points to find the slope.
m(slope) = (y2 - y1)/(x2 - x1)
m = (0 - -4)/(6 - 0)
m = (0 + 4)/(6 - 0)
m = 4/6
m = 2/3
What constant term should be used to complete the square? x 2 - 5x + _____ = 7
Madeline is financing $321,800 to purchase a house. How much money will she save over the life of a 20 year fixed rate loan by buying five points with the rate of 4.23% instead of not buying points with the rate of 5.18%? Round to the nearest dollar. (show work)
A= $39,984
B= $23,894
C= $36,697
D= $36,766
"the placement test for a college has scores that are normally distributed with a mean of 600 and a standard deviation of 60.if the college accepts only the top 1% of examinees, what is the cutoff score on the test for admission?"
When i am divided into 22, the remained is one. when i am added to 5, the answer is an even number. what number am i? * 5 7 9 10 4 2/5?
Answer:
Number is 23.
Step-by-step explanation:
We have been given the information when a number is divided by 22 the remainder is 1.
And when it is added to 5 it will give us an even number.
So, the number 23 if we take when divided by 22 it will give the remainder 1.
And when added to 5 it will give 23+5=28 which is an even number.
So, the number is 23.
HELP PLEASE Simplify the rational expression. State any excluded values. x^2-12x+35/x^2-3x-10
Which kind of function best models the data in the table? Use differences or ratios.
A. linear
B. quadratic
C. exponential
D. none of the above
Aubrey has a new art box in the shape of a rectangular prism. The box is 5 inches, by 8 inches, by 2 inches. How much volume is not take-up by the eraser if the dimension of the eraser is 5.5 inches^3
volume of the rectangular prism = base area * height
base area = length * breadth
volume of the rectangular prism = length * breadth * height
volume of the rectangular prism = 5*8*2 = 80 inches ^3
volume of taken up by the eraser = 5.5 inches^3
volume that is not take-up by the eraser = 80-5.5 = 74.5 inches^3
Simplify: x+2/x2-6x-16 ÷ 1/9x
Will give brainliest! pts to the correct answer! Are quadratic equations already in rectangular form? I'm asked to eliminate the parameter t from these two questions to get it into the rectangular equation with x and y. Is it possible?
x(t) = 0.5t^2+0.4t-87.30
y(t)= 0.4t^2+0.1t +29.44
Brian wants to build a ramp that leads to a storeroom 5 meters above the ground. He wants the ramp to be 10 meters long. What should the angle of elevation of the ramp be?
15°
30°
45°
60°
Answer:
It would be 30
Step-by-step explanation:
I did it on plato
Write the expression in complete factored form 5(y-7)+b(y-7)
A toy company produces two kites whose shapes are geomaetrically similar. Find the length of the missing size of similar kite.
Anyone know the answer?
The window is 60 inches wide. What is the width of the window in feet.
I would appreciate it if someone could please check my work on this calculus problem! My steps/answers are in green.
Identify the values that create ordered pairs that are solutions to the equation 3x - 5y = 20.
(5,y) (x,2)
Which graph shows the same end behavior as the graph of f(x) = 2x6 – 2x2 – 5?
[tex]Given \ function : \ f(x) = 2x^6-2x^2-5[/tex]
In order to find the end behavior of the graph, we need to find the degree of the given function and the leading coefficent.
Degree of the given function is the highest power of the variable.
We have variable x there.
Highest power of x is 6.
So, we can say:
Degree = 6 ( an even degree)
And leading coefficent is the coefficent of highest power term.
We have highest power term is 2x^6.
So, the leading coefficent is : 2 (Positive number)
For even degree and positive leading coefficent, end behaviour is
x --> ∞ f(x) = +∞
x-->-∞ f(x) = +∞
Answer:
The answer is A on edg
Step-by-step explanation:
just took the test
Need help please asap.
What does the underlined conjunction connect in the sentence? The family enjoyed fishing, but they loved hiking during their trip. A. sentences B. predicates C. subjects D. direct objects