The dimensions of a rectangle with an area 2,197 m² whose perimeter is as small as possible are 46.9m by 46.9m
What is area?The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Here,
The area of a rectangle is expressed as A = xy
Perimeter of the rectangle = 2(x + y)
Since A = 2,197m²
xy = 2197..............1
2(x+y) = Minimum ....................2
From 1,
x = 2197/y
Substitute into equation 2,
2(2197/y + y) = minimum
4394/y + 2y = P(y)
If the perimeter is at minimum, hence dP/dy = 0
-4394/y² + 2 = 0
-4394/y² = -2
2y² = 4394
y² = 2197
y =√2197
y = 46.9m
Since xy = 2197
x = 2197/y
x = 2197/46.9
x = 46.9m
Hence the dimensions of a rectangle with an area 2,197 m² whose perimeter is as small as possible are 46.9m by 46.9m
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HELP ME PLEASE THANKS GOOD NIGHT☺️
Answer:
y= -2x+6
Step-by-step explanation:
y=mx+b
b is the y intercept (what is y when x is 0) in this case it is positive 6
m is slope which is rise/run, in this case down 2 and over 1 so that would be -2/1 which is the same as -2
y = -2x+6
I WILL GIVE BRANLIEST PLS HELP
What is the contrapositive of the following conditional statement?
"If it is summer, then it is sunny."
If it is not sunny, then it is not summer.
If it is sunny, then it is summer.
If it is not summer, then it is not sunny.
It is summer if and only if it is sunny.
Answer:
The contrapositive of the given conditional statement "If it is summer, then it is sunny" is "If it is not sunny, then it is not summer."
Step-by-step explanation:
In logic, a conditional statement takes the form "if p then q", where p is the hypothesis or antecedent, and q is the conclusion or consequent. The contrapositive of a conditional statement involves negating both the hypothesis and conclusion and reversing their order. So, the contrapositive of "if p then q" is "if not q then not p".
In the given conditional statement "If it is summer, then it is sunny", the hypothesis is "it is summer", and the conclusion is "it is sunny". The negation of the hypothesis is "it is not summer", and the negation of the conclusion is "it is not sunny". Therefore, the contrapositive of the given conditional statement is "If it is not sunny, then it is not summer".
h. How many yards are there in 255ft? (3 ft = 1 yd)
Answer:
85
Step-by-step explanation:
Answer:
85 yards
Step-by-step explanation:
You just go online to find the answer.
plsss helpp meeee!!!!!!!
Answer:
is that geometry
Step-by-step explanation:
A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 31 batteries of each type. (a) How many ways can a total inventory of 31 batteries be distributed among the eight different types
Answer: 12,620,256
Step-by-step explanation:
Given: The camera shop socks eight different types of batteries and there re at least 31 batteries of each type.
Here we want to select r= 31 batteries from n= 8 kinds of batteries, then formula we use to find number of ways is \(^{n+r-1}C_r=\ ^{31+8-1}C_{31}\)
\(=^{38}C_{31}=\dfrac{38!}{31!(38-31)!}\\\\=\dfrac{38!}{31!7!}\\\\=\dfrac{38\times37\times36\times35\times34\times33\times32\times31!}{31!\times5040}\\\\=12620256\)
Hence, the number of ways can a total inventory of 31 batteries be distributed among the eight different types = 12,620,256
Which of the following titles is most likely a compare-and-contrast essay?
A. Living on the West Coast and Why I Like It
B. East Meets West: Natives’ Perspectives
C. Traveling on the West Coast
D. Problems with Living on the East Coast
B. East Meets West: Natives’ Perspectives is most likely a compare-and-contrast essay because it is directly comparing the perspectives of people from the East and West coasts. The other titles are more descriptive or subjective in nature, rather than focused on comparing and contrasting two different things.
On the map below, 1 cam represents 50 km. The distance between sommerwile and Linden is 2.5 cm.
Answer:
125
Step-by-step explanation:
Answer: I think it's D
Step-by-step explanation: I say the answer is (B) because in the full question, it's asking how much would 2.5 means, therefore, you're multiplying, to get 125.
If 1cm=50km Then 2.5 is 50km, 50km, 25
50+50+25=125, or simply just multiply. 25 is half of 50, so with the 2.5 there, doesn't make it a whole number, therefore, making the 25 in it's place, because of the 2.5.
HELP PLEASE!!!!
The 10 largest soccer and football stadiums have a capacity of at least of 1 x 105 people. Each stadium has 8 events each year for 10 years.
How many total people attended these events if every event was seated to capacity? Select ALL that apply
A
at least 80,000,000 people
B
at least 800,000,000 people
С
at least 0.8 x 107 people
D
at least 8 x 107
people
E
at least 80 x 107 people
Draw the image of triangle △ABC under a dilation whose center is P and scale factor is 1/3.
Answer:
Here you gooooo
Step-by-step explanation:
Answer:
khan
Step-by-step explanation:
a variable has a normal distribution with a mean of 100 and a standard deviation of 15. what percent of the data is less than 105? round to the nearest 10th of a percent.
Rounding to the nearest tenth of a percent, we find that approximately 65.5% of the data is less than 105.
To find the percentage of the data that is less than 105 in a normal distribution with a mean of 100 and a standard deviation of 15, we can use the standard normal distribution table or a statistical calculator.
Using a standard normal distribution table, we need to calculate the z-score for the value 105, which represents the number of standard deviations away from the mean:
z = (x - μ) / σ,
where x is the value (105), μ is the mean (100), and σ is the standard deviation (15).
Substituting the values:
z = (105 - 100) / 15 = 5 / 15 = 1/3.
Looking up the z-score of 1/3 in the standard normal distribution table, we find that it corresponds to approximately 0.6293.
The percentage of the data that is less than 105 can be calculated by converting the z-score to a percentile:
Percentile = (0.5 + 0.5 * erf(z / √2)) * 100,
where erf is the error function.
Substituting the z-score into the formula:
Percentile = (0.5 + 0.5 * erf(1/3 / √2)) * 100 = (0.5 + 0.5 * erf(1/3 / 1.414)) * 100.
Calculating this value gives us approximately 65.48.
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f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6
where c is constant
The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.
Given a function:
f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6
where c is a constant.
The solution to the question is shown below.
Step 1: We have given a function:
f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6
We have to find the number of words we have to write to express this function in words.
Step 2: Solution
f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶
Where,
et5+4t = exponential function
ln(t²+3c)⁷ = natural logarithmic function
te-1 = linear function
e⁶ = exponential function
Therefore, f(t) can be expressed in words as:
The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.
Step 3: Conclusion
Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.
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5 pts! (Yall I really need help) How much does a video game cost per in:
America
Great Britain
Japan
Answer:
there are millions of video games, ranging from all different prices, so it all depends on what game.
Step-by-step explanation:
is 7-y=5x+11 a linear equation
Yes. As long as it is y = mx+b.
In geriatrics, why is it MOST important not to be too focused on one aspect of care?
The patient may have multiple medical problems.
The family may not want to focus on the illness.
The patient may want to talk about other things.
There may not be a good chance for a recovery
In geriatrics, it is crucial not to be overly focused on one aspect of care because elderly patients often have multiple medical problems. By taking a holistic approach to care, healthcare providers can address the comprehensive needs of the patient and improve overall well-being.
Elderly patients frequently experience various health conditions concurrently, such as chronic illnesses, cognitive impairment, and physical limitations. Focusing solely on one aspect of care may neglect other critical issues, leading to inadequate treatment and potentially worsening the patient's overall health status.
Furthermore, being too narrowly focused on one aspect of care may not align with the preferences and priorities of the patient and their family. It is essential to engage in open communication and consider the patient's desires, allowing them to express their thoughts and concerns. This person-centered approach ensures that care is tailored to their individual needs and preferences.
Lastly, geriatric patients may have limited chances for a complete recovery due to the presence of chronic conditions or age-related decline. Instead of aiming for cure or complete reversal of the illness, the focus should shift towards improving quality of life, managing symptoms, and providing comfort and support.
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Find the total surface area of a cylinder. Use 3.14 for pi
1. 228.49 ft
2. 1,005.9 ft
3. 954 ft
4. 847.80 ft
5. 610.11 ft
6. 740.96 ft
Answer:
it is 847.80 ft
i done the quiz
what is this answer?
Choose the graph that represents the following set.
the whole numbers greater than 3
Answer:
The last graph or
Graph C
Step-by-step explanation:
what number is a solution of the inequality 3<3x-15
Answer:
x > 6
{7, 8, 9, 10...}
Step-by-step explanation:
\(3<3x-15\\\\3x-15>3\\\\3x-15+15>3+15\\\\3x>18\\\\\frac{3x>18}{3}\\\\\boxed{x>6}\)
Any number will be a solution if it's value is greater than 6.
Hope this helps.
( help me please ) ….
Answer:
The slope is 6/5, ;)))))))
The speed at which a ball bits the ground is proportional to the
height to which the ball rebounds. If the ball hits the ground at
a speed of 20 miles per hour and rebounds to a height of 10 feet,
then how fast must it be traveling (in miles per hour) to rebound
to a height of 15 feet?
Answer:
30 mph
Step-by-step explanation:
let s represent speed and h represent rebound.
Given that s is proportional to h then the equation relating them is
s = kh ← k is the constant of proportion
To find k use the condition s = 20, h = 10, then
20 = 10k ( divide both sides by 10 )
2 = k
s = 2h ← equation of proportionality
When h = 15 , then
s = 2 × 15 = 30 mph
Convert fraction to equaivlent
17
__
6
Answer:
\(\frac{34}{12}\) , \(\frac{51}{18}\) , \(\frac{68}{24}\) , \(\frac{85}{30}\)
some equivalent fraction examples of \(\frac{17}{6}\):
\(\dfrac{17}{6} *\dfrac{2}{2} = \dfrac{34}{12}\)\(\dfrac{17}{6} *\dfrac{3}{3} = \dfrac{51}{18}\)\(\dfrac{17}{6} *\dfrac{4}{4} = \dfrac{68}{24}\)\(\dfrac{17}{6} *\dfrac{5}{5} = \dfrac{85}{30}\)Therefore the equivalent fractions are \(\frac{34}{12}\) , \(\frac{51}{18}\) , \(\frac{68}{24}\) , \(\frac{85}{30}\)
A group of friends are going to see a movie. The admission cost is $8 per person. The table below represents the number of friends and the total cost. Movie Costs Number of Friends, (x) 2 3 4 5 Total Cost in Dollars, (y) Which set of ordered pairs can be written from the table? (2, 10), (3, 11), (4, 12), (5, 13) (2, 16), (3, 24), (4, 32), (5, 40) (10, 2), (11, 3), (12, 4), (13, 5) (16, 2), (24, 3), (32, 4), (40, 5)
Answer:
B) (2, 16), (3, 24), (4, 32), (5, 40)
Step-by-step explanation:
1 ticket costs $8. 8 x 2 = 16, so 2 tickets cost $16. 8 x 3 = 24, so 3 tickets cost $24. The same thing goes for 4 tickets, and 5 tickets.
Answer:
It should be (b) on edge 2020.
Step-by-step explanation:
Use the Intermediate Value Theorem to show that at least one zero lies in the given interval for the given polynomial. f (x) = x^3 - 6x + 1, between x = 2 and x = 3 Substitute x = 2 and x = 3 into the function and simplify. f (2) = f (3) = Interpret the results using the Intermediate Value Theorem. Because f is a polynomial function and since f (2) it and f (3) is, there is at least one real zero between x = 2 and x =
Proved that at least one zero lies in the interval x = 1 and x = 2 for the given polynomial
The polynomial is given by
f(x) = \(x^3\) - 6x + 1
We have to show that at least one zero lies in the given interval for the given polynomial using the intermediate value theorem
When the value of x = 2
Substitute the value of x in the polynomial
f(2) = (2)^3 - 6(2) + 1
= 8 - 12 + 1
= -3
When the value of x = 3
Substitute the value of x in the polynomial
f(3) = (3)^3 - 6(3) + 1
= 27 - 18 + 1
= 10
Here the value of f(2) is negative and the value of f(3) is positive therefore there is at least one real zero between x = 1and x = 2
Hence, proved that at least one zero lies in the interval x = 1 and x = 2 for the given polynomial
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Marie transforms △TZP to create △VQK. She translates △TZP 1 inch down and 1.5 inches to the right. She then dilates △TZP using a scale factor of ⁹⁄₅. Select the true statements below regarding the dimensions of △VQK.
The true statements regarding the dimensions of △VQK, the transformation of △TZP, are as follows:
△VQK is translated 1 inch down and 1.5 inches to the right compared to △TZP.
The side lengths of △VQK are not equal to the corresponding side lengths of △TZP.
The corresponding angles of △VQK and △TZP are congruent.
△VQK is larger or smaller in size compared to △TZP due to the dilation.
Explanation:
The transformation of △TZP to △VQK involves a translation and a dilation. Firstly, △TZP is translated 1 inch down and 1.5 inches to the right. This means that every point of △TZP is moved 1 inch downwards and 1.5 inches to the right to obtain the corresponding points in △VQK. The translation affects the position of the vertices, but it does not alter the shape or size of the triangle.
Secondly, △TZP is dilated using a scale factor of ⁹⁄₅. This means that every side length of △TZP is multiplied by ⁹⁄₅ to obtain the corresponding side lengths in △VQK. The dilation changes the size of the triangle, making it larger or smaller depending on the scale factor.
Based on these transformations, we can conclude the following true statements:
△VQK is translated 1 inch down and 1.5 inches to the right compared to △TZP.
The side lengths of △VQK are not equal to the corresponding side lengths of △TZP due to the dilation.
The corresponding angles of △VQK and △TZP are congruent, as angles are preserved under both translation and dilation.
△VQK is larger or smaller in size compared to △TZP due to the dilation.
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15 of the 25 students Brought their own lunch. What percent of the students brought their own lunch?
Answer:
60%
Step-by-step explanation:
1: 15 divided by 25 to get 0.6
2: multiple 0.6 by 100 to get 60%
john cleans the house for two hours more than jane. if they work together they clean the house for 2 hours and 24 minutes. for how many hours does john clean the house? can you write the solution as well
John will clean the house for 5/2 = 2.5 hours.
What is quadratic equation?
The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:
ax² + bx + c = 0
where x is the unknown variable and a, b and c are the constant terms.
Given, that John cleans the house 2 hours more than Jane.
Let x be the time taken by the Jane and x +2 be the time taken by John.
Total they work for 2 hours 24 minutes
first we will convert minutes into hours, 24/60
= 2.4 hours
Let time taken by John = 1/x+2
time taken by Jane = x
1/x + 1/(x+2) = 2.4
Taking lcm,
x+x+2 = 2.4(x)(x+2)
2x +2 = 2.4\(x^{2}\) +4.8x
2.4x\(x^{2}\)+2.8x -2 = 0
On solving it,
x = \(\frac{b-\sqrt{b^{2-4ac} } }{2a}\)
x = 1/2 and x = -5/3
only x = 1/2 is possible value.
Time taken by John = 1+1/2
=5/2
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Which number is bigger 25% or 0.025
50%
The website told me
how many solutions are there to square root x =9
Answer:
There are 2 solutions to square root x = 9
They are 3, and -3
Step-by-step explanation:
The square root of x=9 has 2 solutions,
The square root means, for a given number, (in our case 9) what number times itself equals the given number,
Or, squaring (i.e multiplying with itself) what number would give the given number,
so, we have to find the solutions to \(\sqrt{9}\)
since we know that,
\((3)(3) = 9\\and,\\(-3)(-3) = 9\)
hence if we square either 3 or -3, we get 9
Hence the solutions are 3, and -3
Nina can ride her bike 63,360 feet in 3,400 seconds, how fast is she going?
Answer:
18.64 ft/s
Step-by-step explanation:
Use the formula for speed, speed = distance/time or s = d/t
Here, Distance = 63,360 Feet and Time = 3400 Seconds
Therefore, using the formula with these specifications we get speed = 63360/3400 = 18.64 ft/s
Nina Travels at 18.64 ft/s
Which graph shows the fastest rate of change in the velocity of Ross' car?
Change in Velocity
1234
Time (seconds)
Change in Velocity
1234S
Time (seconds)
Change in Velocity
12345
Time (seconds)
Change in Velocity
12345
Time (seconds)
Velocity
(leet per second)
Velocity
(feet per second)
Velocity
(feet per second)
Velocity
BOT
...
Answer:
B
i’m not 100 percent sure but i think it’s b