You are using 1000 feet of fence to create a rectangular enclosure. Let X represents length of the rectangle. Please use proper unit in each answer. A rectangle drawing could help. 1. Express the width of the rectangle in terms of the length X. 2. Express the surface area of the rectangle in terms of X. 3. What value of X gives the maximum surface area. 4. What is the maximum surface area?
Answer:
1. Express the width of the rectangle in terms of the length X.
width = 500 - X
2. Express the surface area of the rectangle in terms of X.
area = -X² + 500X
3. What value of X gives the maximum surface area?
maximum surface area results from the rectangle being a square, so 1,000 ÷ 4 = 250
X = 250 ft
4. What is the maximum surface area?
maximum surface area = X² = 250² = 62,500 ft²
Step-by-step explanation:
since the perimeter = 1,000
1,000 = 2X + 2W
500 = X + W
W = 500 - X
area = X · W = X · (500 - X) = 500X - X² or -X² + 500X
The area of a shape is the amount of space it occupies.
The width in terms of x is 500 - xThe surface area in terms of x is x(500 - x)The value of x that gives maximum surface area is 250 feetThe maximum area is 62500 square feetThe length is represented as x.
Let the width be y.
So, we have:
[tex]\mathbf{Perimeter =2(x + y)}[/tex]
This gives
[tex]\mathbf{2(x + y) = 1000}[/tex]
Divide both sides by 2
[tex]\mathbf{x + y = 500}[/tex]
Make y the subject
[tex]\mathbf{y = 500 -x}[/tex]
So, the width in terms of x is 500 - x
The surface area is calculated as:
[tex]\mathbf{A = xy}[/tex]
Substitute [tex]\mathbf{y = 500 -x}[/tex]
[tex]\mathbf{A = x(500 - x)}[/tex]
So, the surface area in terms of x is x(500 - x)
Expand [tex]\mathbf{A = x(500 - x)}[/tex]
[tex]\mathbf{A = 500x - x^2}[/tex]
Differentiate
[tex]\mathbf{A' = 500- 2x}[/tex]
Equate to 0
[tex]\mathbf{500- 2x = 0}[/tex]
Rewrite as:
[tex]\mathbf{2x = 500}[/tex]
Divide both sides by 2
[tex]\mathbf{x = 250}[/tex]
So, the value of x that gives maximum surface area is 250
Substitute 250 for x in [tex]\mathbf{A = x(500 - x)}[/tex]
[tex]\mathbf{A = 250 \times (500 - 250)}[/tex]
[tex]\mathbf{A = 250 \times 250}[/tex]
[tex]\mathbf{A = 62500}[/tex]
Hence, the maximum area is 62500
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What is the slope of the linear table below?
Answer:
A
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 8) and (x₂, y₂ ) = (0, 10) ← 2 ordered pairs from the table
m = [tex]\frac{10-8}{0+3}[/tex] = [tex]\frac{2}{3}[/tex] → A
4n+7-2 pls in really need help;-;
Answer:
4n + 5
Step-by-step explanation:
This equation cannot be simplified further
Unless you meant 4n + 7 = 2
Then the answer would be -1.25
Answer:
4n+5 hope this helps
Step-by-step explanation:
4n+7-2
4n+5
What is the slope of the line in this graph?
y 10
9
18
17
6
4
3
12
1
X
4
5
6
7
8
9
10
Answer : 5/7 for sure is the answer
Find all the factor pairs for 84 and complete the equations.
84 =
X 84
84 = 2 x
84 = 3 x
84 = 4 x
84 = 6 x
84 =
X 12
Please help! I need the answer quick. The picture attached ^
Answer:
[tex]6p+4q=r\\\\4q = r-6p[/tex]
[tex]q = \frac{r}{4} -\frac{6}{4}p \\\\q = \frac{r}{4} -\frac{3}{2}p[/tex]
A student wants to determine if different types of soil, A and B, affect the propagation of African violets. One hundred leaves from the same variety of African violet were selected. The leaves were then randomly assigned to 50 pots with type A soil and the remaining leaves were put into the 50 pots with type B soil. All of the pots were given the same amount of water and arranged in 10 rows of 10 pots near a window for light. The 50 pots with type A soil were placed closest to the window. At the end of two months, the pots with type A soil had the greatest number of pots with new growth, so the student concluded that soil type A was more effective that soil type B.
Is this a valid conclusion?
Yes, because the leaves were randomly assigned, this evenly distributed the variability in the leaves; therefore, type A soil is more effective than type B soil.
Yes, because the amount of water and light were controlled, this may have reduced the variability in the response; therefore, type A soil is more effective than type B soil.
No, because the pots with type A soil were closest to the window, they received more light, which may have led to the new growth.
No, because only African violets were used, replication was not properly implemented; therefore, we cannot conclude that type A soil was more effective.
Answer:
C
Step-by-step explanation:
No, because the pots with type A soil were closest to the window, they received more light, which may have led to the new growth. Option C is correct.
Given that,
A statement is given we have to justify which among the option is the correct reason.
The statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
The pots with type A soil received more light because they were closer to the window, which may have resulted in new growth.
So, the valid conclusion is mentioned in option C.
Thus, Option C is correct.
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Determine if each pair of ratios or rates are equivalent.
16 points scored in 4 games.
48 points scored in 8 games.
Answer:
it is not the same
Step-by-step explanation:
16x4=64 & 48x8=394
Which of the following statements are reasons for why we get electrical energy from a
battery. Select all that apply.
A device runs until either of two comonents fails, at which point the device stops running. The joint density function of the lifetimes of the two components, both measured in hours, is f(x,y) = x + y/8 for 0 < x < 2 and 0 < y < 2Calculate the probability that the device fails during its first hour of operation.
Answer:
The probability that the device fails during its first hour of operation is 0.625.
Step-by-step explanation:
The joint density function of the lifetimes of the two components, both measured in hours, is:
[tex]f(x,y)=\frac{x+y}{8};\ 0<x<2,\ 0<y<2[/tex]
Compute the probability that the device fails during its first hour of operation as follows:
[tex]P[(X<1)\cup (Y<1)]=1-\int\limits^{2}_{1} {\int\limits^{2}_{1} {\frac{x+y}{8}} \, dx } \, dy[/tex]
[tex]=1-\int\limits^{2}_{1} {\frac{x^{2}+2xy}{16}}|^{2}_{1} \, dy\\\\=1- \int\limits^{2}_{1}[{\frac{4+4y}{16}-\frac{1+2y}{16}}] \, dy\\\\=1-\int\limits^{2}_{1}{\frac{3+2y}{16}}\, dy\\\\=1-[\frac{3y+y^{2}}{16}]^{2}_{1}\\\\=1-0.375\\\\=0.625[/tex]
Thus, the probability that the device fails during its first hour of operation is 0.625.
There are 33 students in your class. Yesterday, 9 students were absent. What decimal represents the students were absent? *
Answer:
27.27% of the class was absent
Step-by-step explanation
On average, Seattle gets 38 inches of rain each year. How many centimeters of rain do they get each year?
I'll give brainiest!
Answer:
88.9
Step-by-step explanation:
A baseball is 1.75 times the size of a golf ball. If the golf ball is 1.68 inches in
diameter, what is the diameter of the baseball?
Answer:
2.94 in
Step-by-step explanation:
from 12 teachers to 48 teachers rounded to the nearest percent
Answer:
20%
Step-by-step explanation:
i don't know if this it what you want bc there isn't enough info. 12+48=60
12/60=1/5
1/5=.2
.2=20%
Witch expression converts 100 inches per minute to feet per minute
What is 8x to the power of 3, divided by 2x to the power of 9?
Answer:
first we have divide
8x/2x their power going to sub 3-9
4xpower-6
we have to keep than 1/4power sign going to plus
1/4 power 6
Sharon has a square picture frame with an area
of 400 inches squared. She wants to decorate
one side of the frame with ribbon. What is the
amount of ribbon she needs?
Answer:
200 inches of ribbon
Step-by-step explanation:
if the formula to finding an area is s²
and we already know that the area is 400, so we divide the area by 1/2 to get the length of each side
where can I find about slopes in homework 5 unit 3
Answer:
idk
Step-by-step explanation: sorry im in unit 6 in science im working on rn
baiiii
At the carnival, the ratio of people who won the ring toss game to lost it was 8 : 5. If 56
people won, how many people would have lost?
Answer:
The answer is 35
Step-by-step explanation:
First of all, note that 56 is the same as 56/1 since 56 divided by 1 is 56. Therefore, start by setting up the problem like this:
Step 1: 56/1 x 8/5 =
Step 2: Multiply the numerators together (56 x 8 = 448) and multiply the denominators together (1 x 5 = 5) and make it into one fraction like so 448/5 Step 3: Convert the improper fraction above to a mixed number to get the answer: 89 3/5
That's it! Now you know how to calculate 56 times 8:5.
Answer:
35
Step-by-step explanation:
A total of six and x is less than 20
Answer:
x+6<20
x<14
Step-by-step explanation:
Answer:
20-6+x
Step-by-step explanation:
you would add six and x and then subtract it from twenty becouse less than means to subract
The weighted voting systems for the voters A, B, C, ... are given in the form q: w1, w2, w3, w4, ..., wn . The weight of voter A is w1, the weight of voter B is w2, the weight of voter C is w3, and so on. Calculate, if possible, the Banzhaf power index for each voter. Round to the nearest hundredth. (If not possible, enter IMPOSSIBLE.) {76: 52, 39, 31, 25, 9}
Answer:
Banzhaf power index for each voter
Voter A = 3/4 = 0.75
Voter B = 0/4 = impossible
Voter C = 1/4 = 0.25
Step-by-step explanation:
using the Banzhaf power index for each voter
{76: 52, 39, 31, 25, 9}
Voter A = 52
Voter B = 39
Voter C = 31
Voter D = 25
Voter E = 9
lets calculate the Banzhaf power index for Voters A to C
A B = 52 + 39 ≥ 76
B C = 39 + 31 ≤ 76
A C = 52 + 31 ≥ 76
A B C = 52 + 39 + 31 ≥ 76
Lets consider critical
A B : A is critical because without A the sum < 76
B C : B is not critical because without B the sum is still < 76
A C : C is critical because without C the sum < 76
A B C : A is critical as B + C < 76
B is not critical as A + C ≥ 76
C is not critical as A + B ≥ 76
Number of times critical : For A = 3, For B = 0 , For C = 1
Banzhaf power index for each voter
Voter A = 3/4 = 0.75
Voter B = 0/4 = impossible
Voter C = 1/4 = 0.25
Which weighs more a backpack that weighs 9.5 kg grams or a case of water that weighs 16 pounds
Answer:
The backpack weighs more
Step-by-step explanation:
9.5kg = 20.94391 lbs
Answer:
a backpack that weighs 9.5kg
Step-by-step explanation:
kilogram (kg) is stated to be 2.2 times heavier than a pound
3(2e + 5) + 8(1 - e) = 1
ILL MARK BRAINLIST HELP !!!
Answer:
11 (positive)
Step-by-step explanation:
Answer:
e=11
Step-by-step explanation:
3(2e+5)+8(1-e)=1
6e+15+8-8e=1
-2e+23=1
-2e=-22
e=11
What rule can you write about where the numbers in an inequality with a greater than symbol lie in relation to each other on the horizontal number line?
Answer:
For inequalities with a less than sign (<), the first number is always to the left of the second number on the horizontal number line.
Step-by-step explanation: I had it as a question.
The first number is always to the left of the second number in inequalities with a less-than sign ().
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let's assume an inequality,
y < x
Which represents that x has a greater value than y, and also on the horizontal number line, the first number is always to the left of the second number in inequalities with a less-than sign ().
Thus, The first number is always to the left of the second number in inequalities with a less-than sign ().
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Peter needs 20 meters of wood for his backyard. The nursery only sells
wood by the foot. Which is closest to the number of feet of wood Peter
needs?
1 meter = 3.28 feet
A 66 feet
B 6 feet
C. 17 feet
D. 60 feet
Answer:
A
Step-by-step explanation: 20 x 3.28 is 65.6 round it up its 66
A ball has a diameter
8 inches what is the surface area
Answer:
diameter ÷ 2 = 8 ÷ 2 = 4
Step-by-step explanation:
Ken prepared 12 kilograms of dough after working 2 hours. How many hours did Ken work if he prepared 36 kilograms of dough? Assume the relationship is directly proportional.
Answer:
36 Kilograms of Dough in 6 hours
Step-by-step explanation:
Each hour Ken prepares 6 kilograms of dough, and every 2 hours Ken prepare 12 kilograms of dough.
what is 4(x-1)^2+2=10
Answer:
Answer below
Step-by-step explanation:
4(x−1)
2
=10−2
4(x−1)
2
=8
(x−1)
2
=
4
8
(x−1)
2
=2
x −1=±√
2
x−1=√
2
x-1=-\sqrt{2}x−1=−√
2
x=√
2
+1
x=−√
2
+1
x=√
2
+1,−√
2
+1
Solve the equation 4(2x + 1) = 6x - 12
x=-13/2
x = -8
x = 8
X=11/2
3x^2+5x+2=0
Find what x is for both
Answer:
x = -2/3 and -1
Step-by-step explanation:
3x²+5x+2 = 0
3x²+3x+2x+2=0
3x(x+1) + 2(x+1) =0
(3x + 2) (x + 1) = 0
x = -2/3 and -1
Answer:
Exact form:
x = - 2/3, -1
Decimal Form:
x = -0.6repeated, -1
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.