The perimeter of a rectangular field is 60 meters. Its area is 200 square meters. Find its dimensions.
Answers
Answer:
20 m by 10 m
Step-by-step explanation:
let w be width and l be length , then
2(l + w) = 60 ( divide both sides by 2 )
l + w = 30 ( subtract w from both sides )
l = 30 - w → (1)
lw = 200 → (2)
Substitute l = 30 - w into (2)
w(30 - w) = 200 ← distribute parenthesis on left side
30w - w² = 200 ( subtract 200 from both sides )
30w - w² - 200 = 0 ( multiply through by - 1 )
w² - 30w + 200 = 0 ← in standard form
(w - 10)(w - 20) = 0 ← in factored form
Equate each factor to zero and solve for w
w - 10 = 0 ⇒ w = 10
w - 20 = 0 ⇒ w = 20
Substitute these values into (1)
l = 30 - 10 = 20
l = 30 - 20 = 10
dimensions of field is 20 m by 10 m
Answer:
THIS IS THE REPRENTATION :I(LENGTH ),W(WIDTH)
2IW= 200
I,II USE THE SUBSTITUTION METHOD SINCE :I=30-W WE CAN SUBSTITUTE THE LENGTH TO 30
-W TO IW=200
(30-W)W=200
W2 + 30W=200---------------TRANSPOSE -w2
+30w
w2-30w +200 = 0------------------- USE FACTORING
(W-20)(w-10 =0----------------- THEN EQUATE EACH FACTOR TO ZERO
W- 20=0 W-10 =0
W=20 W=10
THEN SUBSTITUTE THE VALUE OF w TO ANY OF THE EQUATIONS TO GET THE VALUE OF I
Iw =200 Iw=200
I(20) =200 I(10)
I(20)/20= 200/20 I(10)/10
=200/10
I=10
SO the answer to the problem are: width = 20 then lenght =10 or width = 10 then lenght =20Related Questions
If RV=w and SU=w–30, what is the value of w?
Answers
Answer:
w = 60
Step-by-step explanation:
the midsegment SU is half the measure of side RV, then
SU = RV , so
w - 30 = w ( multiply through by 2 to clear the fraction )
2w - 60 = w ( subtract w from both sides )
w - 60 = 0 ( add 60 to both sides )
w = 60
The center of circle is on the line y=2x and the line x=1is tangent to the circle at (1,6) find center and radius of the circle?
Answers
Answer:
7898955
Step-by-step explanation:
W212W
The Orchard Cafe has found that about 4% of the diners who make reservations don't show up. If 81 reservations have been made, how many diners can be expected to show up
Answers
The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made
To determine how many diners can be expected to show up at The Orchard Cafe, we can follow these steps:
1. Identify the percentage of diners who actually show up: Since 4% of diners with reservations don't show up, the percentage of diners who do show up is 100% - 4% = 96%.
2. Calculate the expected number of diners who show up: Multiply the total number of reservations (81) by the percentage of diners who show up (96%).
81 reservations x 0.96 (96% as a decimal) = 77.76
Since the number of diners must be a whole number, you can round the result to the nearest whole number.
In this case, 77.76 can be rounded down to 77.
Your answer: The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made.
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Refer to the figure below to answer the following questions: (a) What is the value of "X"? (b) How Given: t|| v many degrees does angle 4 measure? 9x +41\3 4 13r - 15
Answers
Since the angles given by the equation are alternate interior angles the are the same, that is
9x + 41 = 13x - 15
Using this equation, we can find x value
Step 1Rearraging the equation so the terms with the unkown variable x are on the right side and the other ones on the left side:
9x + 41 = 13x - 15
↓ substracting 9x both sides
41 = -9x + 13x - 15
41 = 4x - 15
↓ adding 15 both sides
41 + 15= 4x
56 = 4x
Step 2Solving the equation for x
56 = 4x
↓ dividing by 4 both sides
56/4 = x
14 = x
Answer A: x = 14
Now we want to find angle 4. Since it makes a straight line with the angle given by the expression 13x - 15, then their addition should be equal to 180°:
∡4 + 13x - 15 = 180
We want to find ∡4, and we do know the value for x, so, using the expression we can find it.
Replacing x by 14:
∡4 + 13x - 15 = 180
↓replacing x = 14
∡4 + 13 · 14 - 15 = 180
∡4 + 182 - 15 = 180
∡4 + 167 = 180
We follow the same previous steps to find ∡4
Step 1Rearraging the equation so the terms with the unkown variable ∡4 are on the left side and the other ones on the right side:
∡4 + 167 = 180
↓ substracting 167 both sides
∡4 = - 167 + 180
∡4 = 13°
Step 2:We already found it using step 1 so step 2 is not neccesary to be followed
Answer B: ∡4 = 13°
Which value cannot represent the probability of an event occurring? StartFraction 1 over 100 EndFraction 0. 29 85% Three-half.
Answers
Answer:
29
Step-by-step explanation:
The probability of an event happening is a number from 0 (even will cannot possibly happen) to 1 (event will definitely happen.)
0 ≤ p ≤ 1
1/100, 0, 85% are all numbers from 0 to 1.
29 is not from zero to 1, so the answer is 29.
Every value{0.01, 0.29, 85%} can represent the probability of an event occurring except option d that is 1.5.
Given to us,
a.) \(\dfrac{1}{100}\)
b.) 0.29
c.) 85%
d.) \(\dfrac{3}{2}\)
The probability help us to know about the probability of specific events occurring.
For a sure event, the probability is always 1,
while for an event that will never happen the probability is always 0.
Thus, probability(p), \(\bold{1 \geq p\geq 0}\).
Now looking at the options,
a.) \(\dfrac{1}{100}\) = 0.01
b.) 0.29
c.) 85% = 0.85
d.) \(\dfrac{3}{2}\) = 1.5
Now comparing each option with \(\bold{1 \geq p\geq 0}\).
Therefore, the only option which is not feasible is option d that is 1.5.
Hence, every value{0.01, 0.29, 85%} can represent the probability of an event occurring except option d that is 1.5.
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7m-5m-6
What’s the answer???
Answers
7m-5m-6
Combine like terms
2m-6
hope it helps!
awnser
2•(m- 3)
Step-by-step explanation:
its called google :>
looooooook below
GIVING BRAINLIEST
Answers
Answer:
c
Step-by-step explanation:
Answer:
your answer will be B).60cm
Step-by-step explanation:
have a nice day ^_^
find the volume of a solid obtained by rotating the region calculator
Answers
To find the volume of a solid obtained by rotating a region, you'll need to use the method of disks or washers, depending on the specific problem. The terms "long answer" are not relevant to the calculation.
1. Identify the region you want to rotate and the axis of rotation.
2. Set up an integral using the method of disks or washers, depending on the given problem.
- Disks: Use the formula V = π * ∫[R(x)]^2 dx from x=a to x=b, where R(x) is the radius of the disk and a and b are the bounds of the region.
- Washers: Use the formula V = π * ∫([R(x)]^2 - [r(x)]^2) dx from x=a to x=b, where R(x) is the outer radius and r(x) is the inner radius.
3. Evaluate the integral to find the volume of the solid.
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Charles opened his bank account with $710 and withdrew
$35 a week. Olivia opened her bank account with $500 and
withdrew $25 a week. In how many weeks will they have the
same amount?
Answers
Write the linear equation in standard form.
y - 2 = 1/3(x + 6)
Answers
Answer: y=x/3 + 4
Step-by-step explanation:
distribute 1/3 to the (x+6): x/3 + 2add two to both sides: y=x/3 + 4
what value of x makes the following equation true 4+3x=160
Answers
Answer:
x=52
Step-by-step explanation:
160=4+3x
Subtract 4 from both sides
156=3x
Divide 3 from both sides
x=52
One cubic meter represents a cube shape that measures 1 meter in all three dimensions. how long is each side in centimeters?
Answers
Each side of cube is 100 cm.
What is a cube?In Maths or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.
Given that,
Volume of cube = 1 cubic meter
We know that,
1 m = 100 cm
Also volume of cube = \(a^{3}\)
Then,
Volume of cube = 1000000 cm
\(a^{3}\) = \(100^{3}\)
a = 100 cm
Hence, Each side of cube is 100 cm.
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Il y a 5ans Thomas avait 5 fois l'âge de benoit aujourd'hui Thomas a 3 fois l âge de Benoît quel est l'âge de benoit
Answers
Répondre:
Benoit a 10 ans
Explication étape par étape :
Laisser :
Âge de Thomas = x
Benoit age = y
il y a 5 ans :
x - 5 = 5 (y - 5)
x - 5 = 5y - 25 - - (1)
Aujourd'hui :
x = 3y - - (2)
Mettez x = 3y dans (1)
3 ans - 5 = 5 ans - 25
Recueillir des termes similaires
3 ans - 5 ans = - 25 + 5
-2a = - 20
Diviser les deux côtés par - 2
y = 10
Simplify m^12/(m^8)^3
Answers
Given:
\(\frac{m^{12}}{\mleft(m^8\mright)^3}\)To simplify:
Solving we get,
\(\begin{gathered} \frac{m^{12}}{(m^8)^3}=\frac{m^{12}}{m^{24}^{}} \\ =m^{12-24} \\ =m^{-12} \\ =\frac{1}{m^{12}} \end{gathered}\)Hence, the answer is,
\(\frac{1}{m^{12}}\)a diver makes 2.5 complete revolutions on the way from a 10.4 m high platform to the water. assuming zero initial vertical velocity, find the diver's average angular velocity during the dive.
Answers
The average angular velocity during the dive is 10.78 rad/sec.
Given,
displacement of the diver = 10.4m
as the diver falls freely then the acceleration will be g=9.8 \(m/s^2\)
To find average angular velocity during dive use formula,
\(\omega=\frac{\theta}{t}\)
where, θ=angular displacement and t= time taken to reach water
the diver makes 2.5 revolutions, here 1 revolution is 2π radians then total angular displacement is
θ=2.5* 2π=15.7 radian
To find time taken, use formula \(s=ut+\frac{1}{2}gt^2\)
here u=initial velocity=0
s=displacement of diver=10.4m
\(10.4=0+\frac{1}{2}9.8t^2\\\\10.4=4.9t^2\\\\2.122=t^2\\\\t=1.456 s\)
angular velocity, \(\omega=\frac{15.7}{1.456}=10.78\ rad/sec\)
Thus, the average angular velocity during the dive is 10.78 rad/sec.
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Atticus is examining the equations: 4x + 2y = 10 and y = -2x + 5. He states that the equations are equivalent. Is he correct why or why not?
Answers
Answer:
He is correct
Step-by-step explanation:
Put the first equation into y = mx + b by isolating y:
4x + 2y = 10
2y = -4x + 10
Divide each side by 2:
y = -2x + 5
So, putting the first equation into y = mx + b got us the same equation as the second one, y = -2x + 5.
Since they are the same, the equations are equivalent.
Atticus is correct.
at a certain grocery checkout counter, the average waiting time is 2.5 minutes. suppose the waiting times follow an exponential density function. (a) write the equation for the exponential distribution of waiting times. e(t) = graph the equation and locate the mean waiting time on the graph. webassign plot webassign plot webassign plot webassign plot (b) what is the likelihood that a customer waits less than 1 minutes to check out? (round your answer to one decimal place.) % (c) what is the probability of waiting between 4 and 6 minutes? (round your answer to one decimal place.) % (d) what is the probability of waiting more than 5 minutes to check out? (round your answer to one decimal place.) % need help? read it
Answers
a) The equation for the exponential distribution of waiting times is given by \(f(x) = \lambda e^{-\lambda x}\)
b) The probability of waiting less than 2 minutes to check out is 0.427
c) The probability of waiting between 4 and 6 minutes is 0.242
d) The probability of waiting more than 5 minutes to check out is 0.082
a. The equation for the exponential distribution of waiting times is given by:
\(f(x) = \lambda e^{-\lambda x}\)
where λ is the rate parameter of the distribution, and e is the natural logarithmic constant (approximately equal to 2.71828). The graph of the exponential distribution is a decreasing curve that starts at λ and approaches zero as x approaches infinity. The mean waiting time, denoted by E(X), is equal to 1/λ.
b. To find the probability that a customer waits less than 2 minutes to check out, we need to calculate the area under the exponential distribution curve between zero and 2 minutes. This can be expressed mathematically as:
P(X < 2) = \(\int_0^2 \lambda e^{-\lambda x} dx\)
Solving this integral yields:
P(X < 2) = 1 - \(e^{(-2\lambda)}\)
Substituting the given average waiting time of 2.5 minutes into the formula for the mean waiting time, we can calculate λ as:
E(X) = 1/λ
2.5 = 1/λ
λ = 0.4
Therefore, the probability of waiting less than 2 minutes to check out is:
P(X < 2) = 1 - \(e^{-2*0.4}\)
P(X < 2) ≈ 0.427
c. To find the probability of waiting between 2 and 4 minutes, we need to calculate the area under the exponential distribution curve between 2 and 4 minutes. This can be expressed mathematically as:
P(2 < X < 4) =\(\int_2^4 \lambda e^{(-\lambda x)} dx\)
Solving this integral yields:
P(2 < X < 4) = \(e^{(-2\lambda)} - e^{(-4\lambda)}\)
Substituting the value of λ obtained in part (b), we get:
P(2 < X < 4) = \(e^{(-20.4)} - e^{(-40.4)}\)
P(2 < X < 4) ≈ 0.242
d. To find the probability of waiting more than 5 minutes to check out, we need to calculate the area under the exponential distribution curve to the right of 5 minutes. This can be expressed mathematically as:
P(X > 5) = \(\int_5^{ \infty} \lambda e^{(-\lambda x)} dx\)
Solving this integral yields:
P(X > 5) = \(e^{(-5\lambda)}\)
Substituting the value of λ obtained in part (b), we get:
P(X > 5) = \(e^{(-5*0.4)}\)
P(X > 5) ≈ 0.082
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if the usl is 10, the lsl is 4 and the standard deviation for the process is 2, what is the sigma level? 1 3 5 6
Answers
The sigma level of a process indicates the capability of that process to meet customer specifications. In this case, the sigma level is 1.
In this case, with a USL (Upper Specification Limit) of 10, an LSL (Lower Specification Limit) of 4, and a standard deviation of 2, we can calculate the sigma level. The sigma level is a measure of how many standard deviations fit within the specification limits.
To determine the sigma level, we need to calculate the process capability index, which is defined as (USL - LSL) / (6 * standard deviation). In this case, the process capability index is (10 - 4) / (6 * 2) = 1 / 12 ≈ 0.0833. The sigma level can be derived from the process capability index using statistical tables or calculators.
A process capability index of 0.0833 corresponds to a sigma level of approximately 1. This means that the process is capable of producing within the specification limits, but it has a relatively high probability of producing defects. A higher sigma level indicates better process performance and a lower probability of defects. Therefore, in this case, the sigma level is 1.
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What variable is used to represent slope?
Answers
\(x \: and \: y\)
hope my answer is helpful to you
plz mark me as brainlist
Find the area and perimeter.
Answers
Answer:
Area: 6\(x^{2}\) - 8x
Perimeter: 10x - 8
Step-by-step explanation:
Area:
Multiple the 2 sides together
2x(3x -4) Distribute the 2x
2x(3x)- 2x(4)
6\(x^{2}\) -8x
Perimeter:
Add the four sides together
3x -4 + 3x -4 +2x + 2x Combine like terms
10x - 8
A point goes through the origin and has a slope of 3. What is the equation of the line?
Answers
Answer:
The correct answer is c Y=3x
Step-by-step explanation:
Hope this helps!
Twice a number subtracted from 10 is 14
Answers
Let the number be x
10 - 2x = 14
2x = -4
x = -2
A sum is Rs x. If 2÷3 parts of the sum is Rs 20, find the sum.
Answers
Answer:
30
Step-by-step explanation:
2/3*x=20
2x=20*3
x=60/2
x=30
The product of a number and -7 is greater than 42
Answers
divide by -7
x < -6
Answer:
-7*x>42
Step-by-step explanation:
-7 times any negative number greater than 6 is equal to more than 42
Opening Exercise
Use mental math to solve the following:
Number String
100% of 180 =
25% of 180 =
-75% of 180 =
37.5% of 180 =
Answers
Answer:
100% of 180 = 180
25% of 180 = 45
-75% of 180 = -135
37.5% of 180 = 67.5
Step-by-step explanation:
I looked them up on an app so I hope its right!
A square has side length 4 cm.
a. What is its area?
Answers
Answer:
16cm and a 2 as a exponet
Step-by-step explanation:
Answer:
A=16cm²
Step-by-step explanation:
i think 90% sure that its correct
a) Your friend Faisal is recently hired as a junior engineer by a multinational consulting company working on a Renewable energy project at Gwadar port. Faisal's job description includes the quality control regarding the fatigue life of wind turbine rotors. Most of the components/parts are manufactured locally and have some poor surface finish. Faisal is not sure whether the surface finish and site condition play any role on the fatigue life of the structure. How can you help your friend to improve the fatigue life of the structures at this project?
Answers
Faisal can ensure the best quality of the structures and improve the fatigue life of the wind turbine rotors by following these steps. Surface finish improvement, corrosion protection, and site condition analysis should be the key focus areas to improve the fatigue life of the structures at the project.
As Faisal is recently hired as a junior engineer by a multinational consulting company working on a Renewable energy project at Gwadar port, his job description includes the quality control regarding the fatigue life of wind turbine rotors. Most of the components/parts are manufactured locally and have some poor surface finish.
Faisal is not sure whether the surface finish and site condition play any role on the fatigue life of the structure.To improve the fatigue life of the structures at this project, the following steps can be taken:
Surface Finish Improvement:Faisal can improve the surface finish of components/parts that are manufactured locally. Better surface finish will result in better fatigue life of the structure. This can be achieved by using better techniques of manufacturing, such as grinding or polishing.
Corrosion Protection:Corrosion can cause a significant reduction in fatigue life of the structure. Therefore, corrosion protection measures should be taken to avoid corrosion on the surface of the structure. This can be achieved by using different types of coatings, such as anodizing or galvanizing, depending upon the site condition and type of exposure.
Site Condition Analysis:The site condition analysis should be carried out to identify the possible factors that can affect the fatigue life of the structure.
The analysis should include factors such as wind speed, temperature, humidity, and corrosion environment. Based on the site condition analysis, appropriate measures can be taken to improve the fatigue life of the structure.Main Answer:To improve the fatigue life of the structures at this project, surface finish improvement, corrosion protection, and site condition analysis should be carried out. By following these steps, Faisal can ensure the best quality of the structures and improve the fatigue life of the wind turbine rotors.
Faisal is recently hired as a junior engineer by a multinational consulting company working on a Renewable energy project at Gwadar port. Faisal's job description includes the quality control regarding the fatigue life of wind turbine rotors.
Most of the components/parts are manufactured locally and have some poor surface finish. Faisal is not sure whether the surface finish and site condition play any role on the fatigue life of the structure. To improve the fatigue life of the structures at this project, surface finish improvement, corrosion protection, and site condition analysis should be carried out.
Surface finish improvement can be achieved by using better techniques of manufacturing, such as grinding or polishing. Corrosion protection measures should be taken to avoid corrosion on the surface of the structure. This can be achieved by using different types of coatings, such as anodizing or galvanizing, depending upon the site condition and type of exposure.
The site condition analysis should be carried out to identify the possible factors that can affect the fatigue life of the structure. Based on the site condition analysis, appropriate measures can be taken to improve the fatigue life of the structure
Faisal can ensure the best quality of the structures and improve the fatigue life of the wind turbine rotors by following these steps. Surface finish improvement, corrosion protection, and site condition analysis should be the key focus areas to improve the fatigue life of the structures at the project.
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the letters c, i, r, c, l, and e can be used to form 6-letter strings such as circle or ccirle. using these letters, how many different 6-letter strings can be formed in which the two occurrences of the letter c are separated by at least one other letter?
Answers
To count the number of different 6-letter strings that can be formed using the letters c, i, r, c, l, and e, we can use the permutation formula. There are 6 choices for the first letter, 5 choices for the second letter (since we can't use the same letter twice), and so on, giving us:
6 x 5 x 4 x 3 x 2 x 1 = 720
However, not all of these strings meet the condition that the two occurrences of the letter c are separated by at least one other letter. To count the number of strings that do meet this condition, we can use the complementary counting method.
First, let's count the number of strings in which the two c's are adjacent. There are 5 positions where the two c's could be (the first two, second and third, third and fourth, fourth and fifth, or last two positions), and once we place the c's, we have 4 letters left to fill in the remaining 4 positions. This gives us:
5 x 4 x 3 x 2 x 1 = 120
Now, let's count the total number of 6-letter strings that have at least one pair of adjacents c's. We can use the same method as above, but this time we can place the two c's anywhere in the string, giving us:
6 x 5 x 4 x 3 x 2 x 1 - 5 x 4 x 3 x 2 x 1 = 720 - 120 = 600
Finally, we can subtract this from the total number of 6-letter strings to get the number of strings in which the two c's are separated by at least one other letter:
720 - 600 = 120
Therefore, there are 120 different 6-letter strings that can be formed using the letters c, i, r, c, l, and e in which the two occurrences of the letter c are separated by at least one other letter.
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Prove that ∑i=1[infinity]2i1=1.
Answers
After using the formula for the sum of an infinite geometric series, we conclude that the given infinite series does not converge to 1.
To prove that the infinite series ∑(i=1 to ∞) 2^(i-1) equals 1, we can use the formula for the sum of an infinite geometric series.
The sum of an infinite geometric series with a common ratio r (|r| < 1) is given by the formula:
S = a / (1 - r)
where 'a' is the first term of the series.
In this case, our series is ∑(i=1 to ∞) 2^(i-1), and the first term (a) is 2^0 = 1. The common ratio (r) is 2.
Applying the formula, we have:
S = 1 / (1 - 2)
Simplifying, we get:
S = 1 / (-1)
S = -1
However, we know that the sum of a geometric series should be a positive number when the common ratio is between -1 and 1. Therefore, our result of -1 does not make sense in this context.
Hence, we conclude that the given infinite series does not converge to 1.
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Simplify (pvw)^(pv-w) to p 1. Select a law from the right to apply (pvw)^(pv-w) LawsDistributive (а^ь)v(а^с) = а^(bvc) (avb)^(avc) = av(b^c) Commutative bva = bvaa^b = b^aComplement av-a а^-а Identity а^т avF Double negation - - a
Answers
The simplified proposition, which is not exactly p, but rather:
p + v - w
To simplify the given proposition (pvw)A(pv-w) to p, we will apply the Distributive law:
(pvw)A(pv-w) = (pvw)A(pv) - (pvw)A(w)
Now, apply the Distributive law again to both terms:
= (pA(pv) + vA(pv) + wA(pv)) - (pA(w) + vA(w) + wA(w))
Now, apply the Commutative law and simplify each term:
= (pAp + pAv + pv + vp + vAv + vw + wp + wv + wAw) - (pw + vw + ww)
Notice that pAp = p, vAv = v, and wAw = w due to the Identity law.
Also, ww = w due to the Idempotent law.
So, we have:
= (p + pv + pv + vp + v + vw + wp + wv + w) - (pw + vw + w)
Now, apply the Commutative law again and cancel out similar terms:
= p + pv + vp + v + vw + wp + wv - pw - vw - w
The terms pv, vp, vw, wp, wv, pw, and vw cancel each other out:
= p + v - w
Finally, we reach the simplified proposition, which is not exactly p, but rather:
p + v - w
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