an architect designs a rectangular flower garden such that the width is exactly two thirds of the length if 320 ft of the antique picket fencing are to be used to enclose the garden find the dimensions of the garden
Answers
what's the width? well, w = (2/3)l.
The dimensions of the garden where 320 ft of the antique picket fencing are to be used to enclose the garden are 96 feet and 64 feet.
Given that:
A garden is in rectangular shape.
The length of the antique picket fencing used to enclose the garden is 320 feet.
The perimeter defines the enclosing length.
So, the perimeter is 320 feet.
Let P = 320.
Let l represent the length and w represents the width of the garden.
The width is exactly two-thirds of the length.
So, [tex]w=\frac{2}{3} l[/tex].
The perimeter of the garden is:
P = 2(l + w)
= 2 (l + [tex]\frac{2}{3} l[/tex])
= [tex]\frac{10}{3} l[/tex]
So, substitute P = 320.
[tex]\frac{10}{3} l=320[/tex]
Simplifying,
l = 96 feet
So, w = 64 feet
Hence, the dimensions are 96 feet and 64 feet.
Learn more about Perimeter here :
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Related Questions
A _____ is the composition of a translation and a reflection across a line parallel to the direction of translation. glide reflection tessellation rotation dilation
Answers
Answer:
Glide reflection
Step-by-step explanation:
A glide reflection is a composition of a translation and a reflection across a line parallel to the direction of translation. A glide reflection requires a translation on a figure, which is then reflected over a line. This is a symmetry operation that requires a translation rule and a line to reflect over. A common example of this are footsteps in the sand.
The Darnells are having a swimming pool installed. The pool has a radius of 14 feet and a height of 4 feet. What is the volume of the pool? Use 3.14 for pi .
Answers
volume = pi x r^2 x h
3.14 x 4 x 14^2 = 2461.76 cubic feet
Fixed the typo I had in my answer.
Answer:
So volume of the swimming pool is 2461.76 feet³.
Step-by-step explanation:
The Darnells are having a swimming pool installed.
The pool has a radius of 14 feet and height of 4 feet.
Since pool is in the form of a cylinder so volume of cylinder
= πr²h
= π (14)² × 4
= (3.14) (196) × 4
= 2461.76 cubic feet.
So volume of the swimming pool is 2461.76 feet³.
A can in the shape of a right cylinder is filled with 10W-40 oil. The weight of 10W-40 oil is 0.857 gram per cubic centimeter. If the cylinder has a radius of length 5 cm and a height of 10 cm, calculate the weight of the oil (in grams) in the can. Round your answer to the nearest tenth. Use 3.14 for pi
Answers
A.833B.117C.704D.647
Answer: Weight of the oil is 672.74 grams.
Step-by-step explanation:
Since we have given that
Radius of cylinder = 5 cm
Height of cylinder = 10 cm
Volume of cylinder would be
[tex]\pi r^2h\\\\=3.14\times 5\times 5\times 10\\\\=785\ cm^3[/tex]
Weight of 10W-40 oil = 0.857 grams per cubic cm
So, Weight of the oil in the can would be
Volume × Weight per cm³
[tex]=785.71\times 0.857\\\\=672.74\ grams[/tex]
Hence, Weight of the oil is 672.74 grams.
A triangle is dilated by a scale factor of n = 1/3 . Which statement is true regarding the dilation?
It is a reduction because n > 1.
It is a reduction because 0 < n < 1.
It is an enlargement because n > 1.
It is an enlargement because 0 > n > 1
Answers
Answer: The second statement is true. It is a reduction because 0 < n < 1.
Step-by-step explanation:
Given: A triangle is dilated by a scale factor of n = 1/3 .
as n is less than 1 but greater than 0.
A dilation is a rigid transformation that forms an image that is the same shape as of the original figure, but with a different size. A dilation transform a figure by scalar factor 'n' about the center of dilation is a fixed point in the plane which never change.
A dilation that forms a larger image is known as enlargement. A dilation that forms a smaller image is known as reduction.
• If n is greater than 1, then the image is an enlargement.
• If n is between 0 and 1, then the image is a reduction .
• If n is 1, the figure and then the image are exactly same.
Answer:
2nd statement
Step-by-step explanation:
I need help with a homework assignment:
Write each series in summation notation beginning with k = 1.
1/2 + 2/3 + 3/4 + 4/5 + 5/6
−11 + 12 − 13 + 14 − 15 + 16
9 − 16 + 25 − 36 + 49 − 64
3 + (3/2) + 1 + (3/4) + (3/5)
I get the numbers that go under and on top of the sigma, I need help deriving the explicit value for the sequence that goes on the right of the sigma.
Thanks
Answers
[tex]\bf -------------------------------\\\\ \begin{array}{lllllllllll} 3&,&\frac{3}{2}&,&1&,&\frac{3}{4}&,&\frac{3}{5}\\\\ \frac{3}{1}&,&\frac{3}{2}&,&\frac{3}{3}&,&\frac{3}{4}&,&\frac{3}{5} \end{array}\qquad \sum\limits_{k=1}^5\ \cfrac{3}{k}[/tex]
05.01)A company makes triangular plates for individual slices of pizza. For each plate, the base is 5 inches and the height is 16 inches. The area of the top of the plate is ____ inches squared
Answers
Answer: 40 inches squared
Step-by-step explanation:
1. first, you multiply, do 5*16 what does that give you? (80)
2. then, divide your answer by 2 what do you get? (40)
3. lastly, it should look like this: 5*16=(answer)/2=(answer)
hope this helps
Lebron scored a basket 72 times out of 150 shots. what percent of his shots did he score?
a. 42%
b. 50%
c. 48%
d. 63%
Answers
Solve for x.
X=48, i.e. 48%
The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. if you select a random sample of 9 tennis balls, what is the probability that the sample mean is between 2.62 and 2.64 inches
Answers
Final answer:
The probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%, calculated using the Central Limit Theorem to find the standard error and z-scores.
Explanation:
To calculate the probability that the sample mean diameter of the tennis balls is between 2.62 and 2.64 inches, we can use the Central Limit Theorem since we are dealing with a sample of tennis balls rather than just one. The Central Limit Theorem tells us that the sampling distribution of the sample mean will be normally distributed with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation (σ) divided by the square root of the sample size (n), which is called the standard error (SE).
Given that the population mean (μ) is 2.63 inches, the population standard deviation (σ) is 0.03 inch, and the sample size (n) is 9, we first calculate the standard error (SE) as follows:
SE = σ / √n = 0.03 / √9 = 0.03 / 3 = 0.01 inch.
Next, we convert the sample mean range (2.62, 2.64) to z-scores, which are measures of how many standard deviations an element is from the mean.
Z for 2.62 = (2.62 - μ) / SE = (2.62 - 2.63) / 0.01 = -0.01 / 0.01 = -1
Z for 2.64 = (2.64 - μ) / SE = (2.64 - 2.63) / 0.01 = 0.01 / 0.01 = 1
Using a standard normal distribution table or calculator, we find the probabilities corresponding to these z-scores. The probability of a z-score being between -1 and 1 is approximately 0.6827 (68.27%).
Therefore, the probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%.
Which is a correct first step for solving this equation?
2x−1(5−3x)=4x+2
Answers
2x-5+3x=4x+2
(combine like terms)
5x-5=4x+2
(move the x to the left side of the equation by subtraction)
x-5=2
(then of course we isolate the x by adding the 5 to the right side)
x=7
then you can check your work by replacing all of the x's with 7
2(7)-1(5-3(7))=4(7)+2
14-1(-16)=28+2
14+16=30
30=30
hope this helps!
A triangle has an area of 56 square units its height is 14 units what is the length of its base
Answers
area=56
height= 14
A=1/2 bh
56=1/2 b(14)
56=b(14)/2
8=b
Let f(x) = -10x-18 and g(x) = -3x, find (f-g)(x)
Answers
How many ounces are there in a gallon?
and how would I come about solving this?..
Answers
But 159 should be accurate enough.
What is the length of a diagonal of a square with a side length of 6?
Answers
d^2=x^2+y^2, where x and y are the dimensions of the rectangle, however this is just a square, so x=y=s so
d^2=s^2+s^2
d^2=2s^2, and we are told that s=6 so
d^2=2(6^2)
d^2=2(36)
d=√(2(36))
d=6√2 units
d≈8.49 units (to nearest hundredth of a unit)
I- - - - - - - - - - - - I
I I
I d I a
I I
I I
I- - - - - - - - - - - - I
what number is 115% of 73.8?
Answers
how to write 293,805 in standard and expanded form
Answers
1) standard form : 293805
2) expanded form : 200000 + 90000 + 3000 + 800 + 5
Hope it helped!
Ellen has $75 in her savings account. She deposits $25 every week. Her father also deposits $35 into the account every time Ellen mows the lawn. Her savings account balance can be shown with the following expression: 75 + 25w + 35m Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points) Part B: If Ellen saves for 8 weeks and mows the lawn 2 times, how much will she have in her account? Show your work to receive full credit. (4 points) Part C: If Ellen had $95 in her savings account, would the coefficient, variable, or constant in the expression change? Why?
Answers
A. 75 = constant, since it's a deposit not related to any transaction
w and m are 2 variables
25 and 35 are 2 coefficient to w and m respectively
B. Saving = 75 + 25(8) + 35(2)
Saving = $345
C. If Ellen had $95 instead of $75, we will just replace $75 with $98, this will NOT AT ALL AFFECT neither the duration (number of weeks) nor the number of times she mows the loan. Only previously said ONLY The Coefficient will change
A coefficient is the '25' in 25m
A variable is the 'm' in 35m <-------- Part A
A constant is the 75.
-----------------------------------------
8x25=200
35x2=70 <----------- Part B
200+70=270+75=345
Ellen will have $345.
-----------------------------------------
Yes, but only the constant would change.
The new expression would be: 95+25w+35m. <----- Part C
The coefficient and variable wouldn't change because she still
deposits $25 a week and gets $35 every time she mows the lawn.
A computer printer can print a 800-word document in 32 seconds. At this rate, how many seconds are required to print a document that contains 880 words?
Answers
880w(32sec/800w)=35.2 seconds
A parachutist's rate during a free fall reaches 165 feet per second. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 5 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
Answers
Answer: [tex]250\ m[/tex]
Step-by-step explanation:
Assuming that:
[tex]1\ m=3.3\ ft[/tex]
We can make the conversion from feet per second to meters per second with this procedure:
[tex](165\ \frac{ft}{s})(\frac{1\ m}{3.3\ ft})=50\ \frac{m}{s}[/tex]
Let be "x" the amount of meters the parachutist will fall during 5 seconds of free fall
Knowing that in 1 second the parachutist falls 50 meters, we can calculate "x" by solving the following multiplication:
[tex]x=(50\ \frac{m}{s})(5\ s)\\\\x=250\ m[/tex]
The parachutist's rate of free fall is 165 feet per second, which is equivalent to 50 meters per second. The parachutist will fall approximately 250 meters during 5 seconds of free fall.
Explanation:To convert the rate of 165 feet per second to meters per second, we need to use the conversion factor of 1 meter equals 3.3 feet. So, the rate in meters per second is 165 feet per second divided by 3.3 feet per meter, which equals 50 meters per second.
To find how many meters the parachutist will fall during 5 seconds of free fall, we can multiply the rate of 50 meters per second by the time of 5 seconds. This gives us 250 meters of free fall during 5 seconds.
1 gallon of paint pour the paint into a paint tray that measures 10 inch wide 10 inch long and 7 cm deep what will happen
Answers
1 gallon = 231 cubic inches
7cm = 2.75591 inches ( round to 2.76 )
10 x 10 x 2.76 = 276 cubic inches
there will be more than enough room for the gallon of paint
276-231 = 45 cubic inches of space left over
Simplify 2(f^4)^2 f^3 divided by 6f^9
Answers
pertinent rules of exponents:
(a^b)^c=a^(b*c), (a^b)(a^c)=a^(b+c), and (a^b)/(a^c)=a^(b-c) so
(2f^(4*2)*f^3)/(6f^9)
(2f^8*f^3)/(6f^9)
(2f^(8+3))/(6f^9)
(2f^11)/(6f^9)
(2/6)(f^11/f^9)
(1/3)(f^(11-9)
(1/3)(f^2)
(f^2)/3
Final answer:
The expression 2(f^4)^2 f^3 divided by 6f^9 simplifies to 1/3 f^2, after applying the properties of exponents and dividing coefficients.
Explanation:
To simplify the expression 2(f^4)^2 f^3 divided by 6f^9, we need to use the properties of exponents. First, we simplify (f^4)^2 by multiplying the exponents, which gives us f^8.
Then, we multiply f^8 by f^3 to get f^11. Next, we divide our new expression 2f^11 by 6f^9. This can be done by dividing the coefficients (2 divided by 6) and subtracting the exponents of f (11 minus 9), resulting in f^2 over 3, or 1/3 f^2.
The assembly department started the month with 17,500 units in its beginning work in process inventory. an additional 288,000 units were transferred in from the prior department during the month to begin processing in the assembly department. there were 29,250 units in the ending work in process inventory of the assembly department. how many units were transferred to the next processing department during the month?
Answers
Units completed and transferred out=17,500+288,000−29,250
=276,250
Y=0, what is x when y=x^2-6x+9
Answers
x = ?
y= x^2 -6x +9
0 = x^2 - 6x +9
(x -3)
(x -3)
(x-3)(x-3)
x = 3
y = 3^2 - 6(3) + 9
y = 9 - 18 + 9
y = 18
Answer
x= 3, y = 18
hope this helps :D
If the odds of the steelers beating the chiefs are 7 to 4, what is the probability of this event happening?
Answers
Probability of the event = ( Number of ways it can happen ) : ( Total number of outcomes )
If the odds are 7 to 4:
- number of ways it can happen: 7.
- total number of outcomes : 7 + 4 = 11
Probability = 7 : 11 = 7/11 = 0.6364
Answer: The probability of this event is 0.6364 or 63.64%.
3x+17-5x=12-(6x+3) can someone help
Answers
-2x+17=12-6x-3
-2x+17=9-6x
17=9-4x
8=-4x
x=-2
-2x17=12-6x+3
-2x+17=9-6x
2x+6x=9-17
4x=-8
x=-2
If Q is directly proportional to P and Q = 28 when P = 4
i) express Q in terms of P
ii) find the value of Q when P=5
iii) calculate the value of P when Q = 42
Answers
Answer:
May be !
i> Q = 7P
ii> when p =5 then from above eqn we can find Q = 7p and = 7×5=35
iii> from eqn i we can write p = Q/7 So when Q=42 then P=Q/7=42/7=6
Question part points submissions used use a power series to approximate the definite integral, i, to six decimal places. 0.3 ln(1 + x4) dx 0
Answers
[tex]\implies\ln(1+x^4)=\displaystyle-\sum_{n=1}^\infty\frac{(-x^4)^n}n[/tex]
[tex]\displaystyle-\int_0^{0.3}\sum_{n=1}^\infty\frac{(-x^4)^n}n\,\mathrm dx[/tex]
[tex]=\displaystyle\sum_{n=1}^\infty\frac{(-1)^{n+1}}n\int_0^{0.3}x^{4n}\,\mathrm dx[/tex]
[tex]=\displaystyle\sum_{n=1}^\infty\frac{(-1)^{n+1}}n\dfrac{x^{4n+1}}{4n+1}\bigg|_0^{0.3}[/tex]
[tex]=\displaystyle\sum_{n=1}^\infty\frac{(-1)^{n+1}(0.3)^{4n+1}}{n(4n+1)}[/tex]
[tex]\approx0.000485[/tex]
A 8.5
B 8.1
C 12.5
D 12.9
Answers
Put 36 into a fancy calculator with one of those cos() things. You get about 0.81.
So that's the ratio between x and 10.
So basically x/10 = 0.81, or 0.81 * 10 = x.
8.1 = x
If a pitcher strikes out 5 batters in 4 innings how many batters is it likely he will strike out in, 9 innings round to the nearest whole number
Answers
solve for "x".
karens penny bank is 1/5 full. after she adds 280 pennies it is now 7/10 full how many pennies can karens bank hold?
Answers
7/10-1/5 = 7/10-2/10 = 5/10 = 1/2
so 280 pennies fills 1/2 of her piggy bank
so 280*2 = 560
her piggy bank can hold 560 pennies
Add (11a + 4b) + (a +4b - 2)
A) 12a + 8b - 2
B) 12a - 2
C) 11a - 2
D) 11a + 8b - 2