A fence is put around a rectangular plot of land. The perimeter of
the fence is 28 feet. Two of the opposite sides of the fence cost $10
per foot. The other two sides cost $12 per foot. If the total cost of
the fence is $148, what are the dimensions of the fence?
1) 8 by 20
2) 4 by 102
3) 3 by 113
4) 2 by 12
Answers
Let's denote the length of the rectangle as "l" and the width as "w".
From the problem statement, we know that the perimeter of the fence is 28 feet, so:
2l + 2w = 28
Simplifying this equation, we get:
l + w = 14
We also know that two opposite sides cost $10 per foot, and the other two sides cost $12 per foot. This means that the total cost of the fence is:
10(2l) + 12(2w) = 20l + 24w
We are told that the total cost of the fence is $148, so:
20l + 24w = 148
Now we have two equations with two unknowns, which we can solve simultaneously.
We can solve for one variable in terms of the other, and substitute that expression into the other equation. For example, we can solve the first equation for l in terms of w:
l = 14 - w
Substituting this into the second equation, we get:
20(14 - w) + 24w = 148
Simplifying this equation, we get:
280 - 20w + 24w = 148
4w = 132
w = 33
Now that we know the width is 33 feet, we can use the first equation to solve for the length:
l + w = 14
l + 33 = 14
l = -19
This answer doesn't make sense, since the length of the fence can't be negative.
We made an error somewhere, so let's go back and check our work.
We can start by checking our equation for the cost of the fence:
10(2l) + 12(2w) = 20l + 24w
This equation is correct, but we made a mistake when we substituted l = 14 - w into it.
We should have substituted l = 14 - w into the first equation, and solved for w:
l + w = 14
14 - w + w = 14
w = 7
Now we can use this value of w to solve for l:
l + w = 14
l + 7 = 14
l = 7
Therefore, the dimensions of the fence are 7 feet by 7 + 7 + 6 + 6 = 26 feet.
The answer is not
Hopefully this helps ;)
Related Questions
anna walks her dog at a constant rate of 12 blocks in 8 minutes, show the total time it takes to walk 12,24,36, and 48 blocks
Answers
Answer: 8 minutes, 16 minutes, 24 minutes, 32 minutes
Step-by-step explanation: 12x2=24. 8x2=16. 12x3=36. 8x3=24. 12x4=48. 8x4=32.
The total time taken to cover 48 blocks at the same speed will be 32 minutes.
What are work and time?
Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.
Another example of work is that if you have done your food by 1 hour it means your work duration is 1 hour so work is basically the time duration of any task which you have done.
Speed of dog;
Speed = 12 block in 8 minutes ⇒ 12/8 blocks/minutes
Now,
At the same speed
Speed = 48 blocks in T time
So,
12/8 = 48/T
By cross multiplication
T = 48 × 8/12
T = 32
Hence "The total time taken to cover 48 blocks at the same speed will be 32 minutes".
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For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n-65 and p 0.7 O Normal approximation is not suitable O Normal approximation is suitable
Answers
The normal approximation is suitable for the binomial distribution with n = 65 and p = 0.7. This is because the conditions for using the normal approximation, namely having a sufficiently large sample size (n) and a moderate success/failure ratio (np and n(1-p) ≥ 10), are satisfied in this case.
To determine whether the normal distribution can be used as an approximation for the binomial distribution with n = 65 and p = 0.7, we can check the conditions for using the normal approximation to the binomial distribution , which are as follows:
The sample size, n, must be large.The success probability, p, must be not too close to 0 or 1.In this case, n = 65, which is a relatively large sample size. As a rule of thumb, if both np and n(1 - p) are greater than 5, the normal approximation is considered suitable.Calculating np and n(1 - p):
np = 65 × 0.7 = 45.5
n(1 - p) = 65 × (1 - 0.7) = 19.5
Both np and n(1 - p) are greater than 5, which satisfies the condition for the normal approximation.
Therefore, the normal approximation is suitable for the binomial distribution with n = 65 and p = 0.7.
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What is the distance between A(-3, 7)
and
B(3, 7)?
Answers
Answer:
6 units between A and B
Please help me with this. I will appreciate all the help ^^
Answers
Answer:
80 minutes (first one)
Step-by-step explanation:
1/6 of an hour=10 min
3 ppl can go on the ride at the same time
so 24/3=8
leaving 8 more turns before emma's turn
8x10=10
Please help with this question. I don’t get it.
Answers
find the slope of the line that passes through each pair of points. (2,4) and (9,12)
Answers
Considering the expression of a line, the slope of the line that passes through the points (2,4) and (9,12) is 8/7.
What is Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line is calculated as:
m= (y₂ - y₁)÷ (x₂ - x₁)
Slope of the line in this caseIn this case, being (x₁, y₁)= (2,4) and (x₂, y₂)= (9,12), the slope m can be calculated as:
m= (12 -4)÷ (9 -2)
Solving:
m= 8÷ 7= 8/7
Finally, the slope of the line is 8/7.
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Anton surveys 80 students at his school and finds that 55% of them have mobile phones. He also finds that 98% of 50 adults have mobile phones. How many more adults than students have mobile phones?
Answers
Answer:
5 more adults than students have phones.
Step-by-step explanation:
55% of 80 students have phones. This is:
.55 × 80, which is 44 students.
For adults, 98% of 50 is .98 × 50, which is 49.
49 adults have phones. 44 students have phones.
49 - 44 is 5
5 more adults have phones than students.
In a group of 140 students, 65 use Craigslist, 85 use eBay, and 20 use neither. A) how many students use both websites?
Answers
HELP IM BEING TIMEDDDDDDDDDDDDDDDDDDD
Answers
Answer:
- 4
Step-by-step explanation:
5 + -3 = 2
2 - 6 = - 4
Hope this helps! :)
1) Change the rate, 45 miles per 5 gallons to a unit rate per gallon.
Answers
Answer:
9
Step-by-step explanation:
45 mph per 5 gallons
45 ÷ 5
or
45/5
=
9
Unit Rate per Gallon is 9
What is the value of 35−3m, when m = 4?
Answers
Answer:
23
Step-by-step explanation:
Step 1:
35 - 3m Equation
Step 2:
m = 4 Input m into equation
Step 3:
35 - 3 ( 4 ) Add m to the equation
Step 4:
35 - 12 Multiply
Answer:
23
Hope This Helps :)
Alvin's
age Is three times Elga's age. The sum of their ages Is 96. What Is Elga's age?
years old
Answers
Answer: Elga is 16 years old
Step-by-step explanation: so first you divide 96 by 2 and get 48, 48 divided by 3=16,
please mark brainliest if this helps :)
Work Shown:
x = Elga's age
3x = Alvin's age since he is 3 times older
x+3x = 4x = sum of their ages
4x = 96
x = 96/4
x = 24 is Elga's age
3x = 3*24 = 72 is Alvin's age
Check: 24+72 = 96 which confirms the answer.
What is the equation form of the line that is parallel to the line y=-1/3x+4 and passes through the point (6,5)
Answers
Answer: 4
Step-by-step explanation: bc
A cylindrical can of cocoa has the dimensions shown at the right.
What is the approximate area available for the label?
9 2
Answers
Answer:
What are the dementions? 9 and 2?
That would be 9*3.14*4 = 133.04
~ 133.04 units cubed
Step-by-step explanation:
Type the correct answer in the box. Hannah and Leah are running around a circular track. Hannah takes 5 minutes to complete one lap, and Leah takes 6 minutes to complete one lap. If they both start at the same time and from the same point, they will be together at the starting point and then again after minutes.
Answers
Answer:30 min
Step-by-step explanation:
Answer:
1 minute
Step-by-step explanation:
Hannah is 1 minute ahead of Leah. If the start at the same time and it takes Hannah 5 minutes and Leah 6 minutes, they will be together again in 1 minute.
9 and 3/4 As a improper fraction
Answers
Answer:
The improper fraction is 39/4.
Step-by-step explanation:
9 3/4 = 36 + 3 / 4
= 39/4
Thus the improper fraction is 39/4.
Hope I helped!
Answer:
Hi there!
Your answer is:
39/4
Step-by-step explanation:
9 × 4 + 3
36 +3 = 39
An improper fraction is when the numerator has more than the denominator!
Hope this helps!
a crossword game is played by two players. the game has 100 tiles and there is one letter on each tile. the 100 tiles are placed in a bag and mix thoroughly. the first player reaches in the bag and selects seven tiles. how different sets of 7 tiles can the first player choose?
Answers
Therefore, the first player can choose different sets of 7 tiles from 100 tiles, which are 160,075,608.
A crossword game is played by two players.
The game has 100 tiles, and there is one letter on each tile.
The 100 tiles are placed in a bag and mix thoroughly.
The first player reaches in the bag and selects seven tiles.
There are 100 tiles, and the first player selects seven tiles.
The first player can choose different sets of 7 tiles in the following ways:
100 C 7 = 160,075,608.
This is the formula for the combination of 7 items out of 100 items.
Combination: Combination is defined as the way of choosing r things from n different things without considering the order.
The number of possible combinations is given by nCr.
Where nCr is defined as\(\[\frac{n!}{r!(n-r)!}\]n!\) represents factorial, which is the multiplication of all the natural numbers from 1 to n.
A factorial is defined as an integer that is multiplied by all of the positive integers less than.
In mathematics, the factorial of a non-negative integer n is the product of all positive integers less than or equal to n. It is denoted by n!
For example: 5! = 5 × 4 × 3 × 2 × 1
= 1204!
= 4 × 3 × 2 × 1 = 24.
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Which one of the following would be most helpful in strengthening the content validity of a test?
A. Administering a new test and an established test to the same group of students.
B. Calculating the correlation coefficient.
C. Calculating the reliability index.
D. Asking subject matter experts to rate each item in a test.
Answers
Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test
Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test. Content validity refers to the extent to which a test accurately measures the specific content or domain it is intended to assess. By involving subject matter experts, who are knowledgeable and experienced in the domain being tested, in the evaluation of each test item, we can gather expert opinions on the relevance, representativeness, and alignment of the items with the intended content. Their input can help ensure that the items are appropriate and adequately cover the content area being assessed, thus enhancing the content validity of the test.
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Measurement and area maneuvering the middle
Answers
The total surface area of cylinder is 112π units².
What is the formula for surface area of cylinder?The surface area of cylinder is -
A = 2πr(h + r)
Given is a cylinder as shown in the image attached.
We can write the total surface area of cylinder as -
A = 2πr(h + r)
A = 2π x 4 x (10 + 4)
A = 8π x 14
A = 112π
Therefore, the total surface area of cylinder is 112π units².
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Determine the completion time for the following IV. State time in both traditional and military time. Round minutes to the nearest whole number of minutes. (Enter numeric value only.) A liter of D5W is started at 2300 to infuse at 125 mL/hr. Determine the infusion time: a. h
Answers
The infusion time of a liter of D5W at a rate of 125 mL/hr will take 8 hours to complete. The completion time for the IV infusion is 7:00 AM (traditional time). The completion time for the IV infusion is 0700 (military time).
The completion time for the IV infusion is determined by calculating the infusion time and add it to the start time.
a. First, we calculate the infusion time (a):
Infusion rate: 125 mL/hr
Total volume: 1 liter = 1000 mL
Infusion time (a) = Total volume / Infusion rate
= 1000 mL / 125 mL/hr
= 8 hours
The infusion time is 8 hours.
Now, we calculate the completion time:
Start time: 2300 (11:00 PM)
The completion time is calculated by adding the infusion time to the start time.
Completion time = Start time + Infusion time
b. Using traditional time format:
Start time: 11:00 PM
Infusion time: 8 hours
Adding the infusion time to the start time, we get:
Completion time = 11:00 PM + 8 hours
= 7:00 AM
The completion time in traditional time format is 7:00 AM.
c. Using military time format:
Start time: 2300
Infusion time: 8 hours
Adding the infusion time to the start time, we get:
Completion time = 2300 + 8 hours
= 0700
The completion time in military time format is 0700.
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Complete question :
Determine the completion time for the following IV. State time in both traditional and military time. Round minutes to the nearest whole number of minutes. (Enter numeric value only.) A liter of D5W is started at 2300 to infuse at 125 mL/hr.
Determine the infusion time:
a. _____hr
b. Determine the completion time: _____AM (Traditional time)
c. Determine the completion time : _____ (Military time)
Simplify the following expression:(p+q+r+s)(p+ q
ˉ
+r+s) q
ˉ
+r+s p+r+s p+ q
ˉ
+r p+ q
ˉ
+s
Answers
Answer:
Step-by-step explanation:
ok
Grant bought 30 movie tickets for a total of $200. Adult tickets cost $8 each, child tickets cost $3.50
each, and senior tickets cost $6 each. He bought twice the number of adult tickets than the number of
child and senior tickets combined. How many of each type of ticket did Grant buy?
Answers
Answer:
Step-by-step explanation:
Help i will give u brainlest
Erin buys gas at a gas station for $4 a gallon. There is a sale going on at the gas station so that anyone who buys more than 5 gallons of gas only has to pay $3 a gallon for each gallon over 5 gallons. If a person buys more than 10 gallons of gas, each gallon over 10 gallons is only $2 a gallon for every gallon over 10 gallons but less than or equal to 15 gallons.. Erin's tank holds 12 gallons of gas.
Answers
Answer:
39$
Step-by-step explanation:
20+15+4=39$
if 30 houses cost 1.7 billion, how much money will 300 houses cost?
Answers
Answer:
17 billion cause 30*10 300
Answer:
If 30 houses cost 1.7 billion, 300 houses cost 17 billion
Step-by-step explanation:
If you were to make it an equation you would make it
30 = 1.7
Now we were told the 30 would be made 300 so its obvious you multiplied by 10 and whatever you did to one side you do to the other so its
30 x 10 = 1.7 x 10 is 300 = 17
your answer is 17 billion
Could I get the answer don’t understand
Answers
Answer:
DE = 21.4
Step-by-step explanation:
The parallel lines divide the transversals proportionally, that is
\(\frac{DE}{EB}\) = \(\frac{DF}{FC}\) , substitute values
\(\frac{DE}{10.7}\) = \(\frac{32}{16}\) = 2 ( multiply both sides by 10.7 )
DE = 21.4
Simplify the following expression.
X -2/3 . X 6/7
Answers
Answer:
Step-by-step explanation:
Hiiii
Answer:
12/21
Step-by-step explanation:
how you been?
Pls help what is 46743356644 x 5545445555
Answers
Answer: 52.288.802.199
Aroup of 4 friends has a bag of 19 sweets. They want to divide the sweets equally between them. How many sweets would each friend get?
Answers
Each friend would get 4 sweets, and there would be 3 sweets left over that cannot be divided equally among the friends.
If a group of 4 friends wants to divide a bag of 19 sweets equally among them, we need to find the quotient of dividing the total number of sweets by the number of friends.
Dividing 19 sweets by 4 friends gives us a quotient of 4 with a remainder of 3.
Since the remainder represents the sweets that cannot be divided equally, we distribute the quotient of 4 sweets to each friend.
Therefore, each friend would get 4 sweets, and there would be 3 sweets left over that cannot be divided equally among the friends.
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A custom t-shirt company charges a $200 setup fee and $5 per t-shirt. Write an equation that can be used to determine how many t-shirts must be produced so that the total cost per t-shirt is $5.33?
A. (200+5x)/x =5.33
B. (200/x) +x = 5.33
C (200) + 5/x = 5.33
200 + 5x = 5.33/x
Answers
Answer:
its a
plz brainlest
Step-by-step explanation:
MI No E F In the diagram AD is parallel to EG, angle CFD = 40° and triangle BCF is broscles find the value of Angle (67 Angle DUF Le Any (1) find XC 14
Answers
The alternate and same side interior angles theorems indicates;
(i) Angle CBF = 40°
(ii) Angle DCF = 140°
(iii) x = 50°
What are same side interior angles?Same side interior angles are the angles formed on the same side of a two parallel that share a common transversal.
The possible diagram in the figure obtained from a similar figure on the internet indicates;
(i) ∠CFG ≅ ∠FCB (Alternate interior angles theorem)
∠FCB ≅ ∠CBF (Base angles of an isosceles triangle)
∠CBF = ∠FCB = 40° (Definition of congruent angles)
(ii) ∠CFG and ∠DCF are same side interior angles, therefore;
∠CFG + ∠DCF = 180°
40° + m∠DCF = 180°
m∠DCF = 180° - 40° = 140°
The external angle theorem of a triangle indicates that we get;
140° = 2·x + 40°
2·x + 40° = 140°
2·x = 140° - 40° = 100°
x = 100°/2 = 50°
x = 50°
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