You work at a farm that wants to build three identical rectangular corrals in a row against the side of a barn using 112 ft of fencing. No fence is needed next to the barn itself. What dimensions (for each individual corral) will maximize the corral areas
Answer:
x = 14 ft
y = 56 ft
A(max corral) = 784/3 = 261.33 ft²
Step-by-step explanation:
Let´s call y the side parallel to the barn, then only one y is going to be fenced.
If we are going to divide the area in three identical corrals we need 4 times x ( the other side perpendicular to the barn)
The perimeter of the rectangular area ( divide in three identical corrals)
112 = y + 4*x or y = 112 - 4*x
A (r) = x*y
Area as a function of x is
A(x) = x* ( 112 - 4*x) A(x) = 112*x - 4*x²
Tacking derivatives on both sides of the equation
A´(x) = 112 - 8*x A´(x) = 0 112 - 8*x = 0
x = 112/8
x = 14 ft
And y = 112 - 4*x y = 112 - 56
y = 56 ft
A(max) = 14 * 56 = 784 ft²
A(max corral) = 784/3 = 261.33 ft²
How do we know the area is maximum, tacking the second derivative
A´´(x) = - 8 A´´(x) < 0
Then the function A(x) has a maximum at the point x = 14
Answer:
14ft by 18 2/3 ft
Step-by-step explanation:
A teacher is comparing the quarter grades between two of her classes. She takes a random sample of 8 students from each class and lists the grades as shown. Find the mean for Class A.
Class A: 80, 83, 74, 91, 76, 87, 93, 72
Class B: 90, 75, 82, 86, 73, 85, 79, 94
If the carrier is continental airlines, what is the chance that I will be denied boarding?
Answer:
Sample Answer for Edmentum
Step-by-step explanation:
Answer: 0.0112%
Step-by-step explanation:
What is the Area of the parallelogram?
Answer:
117 sq in
Step-by-step explanation:
Every given minute an ameba is equally likely to do one of 3 things: (1) Die (2) Divide into two (3) Stay the same. If the ameba divides, each of the two cells will continue the above cycle independently. What is the probability that the ameba colony generated from a single cell will eventually die out.
Required:
What is the probability that the ameba colony generated from a single cell will eventually die out?
Answer:
1
Step-by-step explanation:
we have the probability of dyng = 1.3
we have probability of ying =
p0 = p1 = p2 = p3 = 1/3
d = dying
[tex]d=\frac{1}{3} (1+d+d2)[/tex]
we cross multiply from here
3d = 1+d+d2
3d-d = 1+d2
2d = 1 + d2
(d-1)2 = 0
2d - 2 = 0
2d = 2
divide through by 2
d = 1
therefore there is a a confirmed probability that the ameba from a single cell is eventually going to die out.
Solve.
(3- y) (2 y– 9)=0
(If there is more than one solution, separate them with commas.)
Answer:
3 , 9/2
Step-by-step explanation:
(3- y) (2 y– 9)=0
y=3 , y= 9/2
Which of the following tells how to change a measurement from liters to milliliters?
Divide by 100
Multiply by 100
Divide by 1000
Multiply by 1000
Which of the folowing elements represent the whole? a. percentage b. base c. rate d. both a and b
Answer:
The answer is letter D
Explanation:
Hope it helps!
Answer:
D is the right answer ✔
Explanation:
24 boys, 45 girls and 281 adults are the members of a badminton club.
50 more children join the club.
The number of girls is now 18% of the total number of members.
How many of the 50 children were boys?
24+45+281+50=400
(45+n/400)×100=18
45+n=18×4=72
n=72-45=27
50-27=23.
hope it's correct
23 of the 50 children added were boys. The answer is 23 boys
Given that 24 boys, 45 girls and 281 adults are the members of a badminton club.
Total number of people as members of badminton = 24 + 45 + 281 = 350
Percentage of girls = girls/total number x 100
% of girls = 45/350 x 100
% of girls = 12.9%
If 50 more children join the club, and the number of girls is now 18% of the total number of members. Then, the new total number of members will be
New total members = 350 + 50 = 400
Let g = new added girls from the children
Percentage of girls = girls/total number x 100
18 = (g + 45) / 400 x 100
18/100 = (g + 45) / 400
cross multiply
0.18 x 400 = g + 45
72 = g + 45
make g the subject of formula
g = 72 - 45
g = 27 girls
To get the number of boys added, take 27 away from the 50 children. That is,
The number of boys added = 50 - 27 = 23 boys
Therefore, 23 of the 50 children added were boys
Learn more about arithmetic here: https://brainly.com/question/6561461
Find the volume of the following cone. Area of base = 54 cm?
A) 180
B) 422.54
C) 513.33
Answer:
The volume of the cone is of 18h, in which h is the height of the cone.
Step-by-step explanation:
Volume of a cone:
The volume of a cone with base area [tex]A_b[/tex] and height h is given by:
[tex]V = \frac{A_bh}{3}[/tex]
Area of base = 54 cm
This means that [tex]A_b = 54[/tex] and thus:
[tex]V = \frac{54h}{3} = 18h[/tex]
The volume of the cone is of 18h, in which h is the height of the cone.
please help. giving brainliest. 10 points
Answer:
for B based on the information givin the answer would be 8 4/7
hope this helps
Answer:
60/7 or 8 4/7
Step-by-step explanation:
Take the length of one of your rods and multiply by 15.
4/7 x 15/1 = 60/7 or 8 4/7
A sample of radium has a weight of 1.5 mg and decays
by half every 6 years. Circle all of the following
functions that correctly model the amount of radium
f(t) in mg remaining after t years
Answer: [tex](b)[/tex]
Step-by-step explanation:
Given
Initial mass of radium is [tex]A_o=1.5\ mg[/tex]
It decays by half every 6 years i.e. [tex]T_{\frac{1}{2}}=6[/tex]
For radioactive decay, sample at any time is given by
[tex]\Rightarrow A=A_o2^{-\dfrac{t}{T_{\frac{1}{2}}}}[/tex]
Insert the values
[tex]\Rightarrow A=1.5\cdot 2^{\dfrac{-t}{6}}\\\\\Rightarrow A=1.5\cdot \left(\dfrac{1}{2}\right)^{\dfrac{-t}{6}}\\\\\Rightarrow A=1.5\cdot (0.5)^{\dfrac{t}{6}}[/tex]
Thus, option (b) is correct.
hup meh please........
Answer:
the answer is
A..0.248 HOPE IT HELPEDThe wheels on an adult sized 4-wheeler have a radius of 11 inches. What total distance will the wheels travel in one full rotation?
a
34.54 Inches
b
690.80 Inches
c
69.08 Inches
d
379.94 Inches
Answer:
C. 69.08 inches
Step-by-step explanation:
Find the distance the wheels will travel by finding the circumference of the wheel.
Use the circumference formula, C = 2[tex]\pi[/tex]r
Plug in 11 as r in the equation, and 3.14 as pi, then solve:
C = 2[tex]\pi[/tex]r
C = (2)(3.14)(11)
C = 69.08
So, the correct answer is C. 69.08 inches
Answer:
69.08 inches
Step-by-step explanation:
We can plug in the known value into the equation for circumference: [tex]C = 2\pi r[/tex]
Using 3.14 as [tex]\pi[/tex] we get:
[tex]C=69.08[/tex]
Now multiply the circumference by revolutions to get distance:
69.08 x 1 = 69.08
Note that the distance is in inches because the radius is in inches.
3. Solve for each power. 4 to the third power.
Answer:64
Step-by-step explanation:
Answer: 4 to the third power is represented as:
4^3 = 64
Hope this helped!
Could someone please help me because I am rubbish at maths?
15% of £40
the answer of this equation is 6
Answer:
£6.00
Step-by-step explanation:
15/100×40
=£6.00
which point is the vertex of the angle below
Answer:
The answer is K
Answer:
k
Step-by-step explanation:
Which equation can be used to find the length of the missing side x?
The rectangle is rotated 180° about the origin. What are the new coordinates of point D ?
Answer:
The answer is C
Step-by-step explanation:
there is no explanation
Select the correct answer. What are the y-intercept and the slop of the line represented in the graph?
Answer:
B
Step-by-step explanation:
The line crossed the y axis at 4 and the slope is -2. you can do rise/ run to find the slope which is -2/1 or -2
What is the approximate area, rounded to the nearest square inch, of the frame only? Use 3.14 for 1
Answer:
Step-by-step explanation:
area of square=l^2
=12^2
=144 in.^2
9.7 times 10^6 plus 6.7 times 10^5 in scientific notation
Mary is preparing for her college entrance exams. In a practice test, she answered 15 problems in 45 minutes. At this rate, how many problems is she expected to answer in 180 minutes?
(Proportional Reasoning)....
I really need an answer, and it would be great if you answer
Answer:
I'm guessing 60
Step-by-step explanation:
84% sure tho
The sum of a number and twenty-one is sixty-four.
What is the value of the number?
The number equals
Answer:
43
Step-by-step explanation:
64-21= 43 :))))) ez
Answer:
43
Step-by-step explanation:
I hope you pass your test!
EDG2021 <3
Ralph rolls a single die two times in a row. What is
the probability that he will roll a "three" both times?
Answer:
1/18 i think
Step-by-step explanation:
The probability of occurring 3 both times will be 1/36.
What is probability?
The probability of an event occurring is defined by probability.
Probability is also called the chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
Do not take underestimate probability it has several uses in daily life whether forecasts or like that.
Probability of occurring 3 for the first time ⇒
number of outcomes/number of sample
Sample space {1,2,3,4,5,6} and outcome is 3
So,
P = 1/6
Probability of occurring 3 in second time⇒
number of outcomes/number of sample
Sample space {1,2,3,4,5,6} and outcome is 3
So,
P = 1/6
So,
Probability of occurring 3 both times = 1/6 × 1/6 = 1/36
Hence "The probability of occurring 3 both times will be 1/36".
For more information about the probability,
brainly.com/question/11234923
#SPJ2
Which set of three side lengths can be
used to make a right triangle?
39, 49, 59
39, 41, 45
39, 80, 89
39, 49, 59
Answer:
39,80,89
Step-by-step explanation:
Right triangles hypotenuse squared should equal the sum of its other side lengths. A^2+B^2=C^2. The hypotenuse is the longest length (89).
39^2+80^2=89^2
7921=7921
During battling practice, two pop flies are hit from the same location, 2s apart the paths are modeled by the equations h equal negative 16t squared + 56t and h = -16t + 156t - 248 where t is the time that has passed since the first ball was hit
Answer:
Step-by-step explanation:
To find the time at which both balls are at the same height, set the equations equal to each other then solve for t.
h = -16t^2 + 56t
h = -16t^2 + 156t - 248
-16t^2 + 56t = -16t^2 + 156t - 248
You can cancel out the -16t^2's to get
56t = 156t - 248
=> 0 = 100t - 248
=> 248 = 100t
=> 2.48 = t
Using this time value, plug into either equation to find the height.
h = 16(2.48)^2 + 56(2.48)
Final answer:
h = 40.4736
p/o/i/t/s/f/r/e/e/;)
denada
Find the exact value of tan A in simplest radical form.
PLEASE HELP
Answer:
[tex] \tan(A) = \frac{opp}{adj} \\ \tan(A) = \frac{ \sqrt{72} }{3} \\ \tan(A) = \frac{ \sqrt{36 \times 2} }{3} \\ \tan(A) = \frac{6 \sqrt{2} }{3} \\ \tan(A) = 2 \sqrt{2} [/tex]
what is the area of the gray part of the triangle?
Area of complete triangle= 1/2 ×6 ×9 = 27 Sq Unit.
Area of rectangle inside triangle = 2× 5 = 10 sq unit.
area of the gray part of the triangle =Area of triangle - Area of rectangle = 27-10 = 17 Sq unit
Gray area = Big triangle area - white
rectangle area
Gray area = 1/2 × 6 × 9 - 2 × 5
Gray area = 3 × 9 - 10
Gray area = 27 - 10
Gray area = 17