Find the dimensions of a rectangle with perimeter 108 m whose area is as large as possible. (If both values are the same number, enter it into both blanks.) m (smaller value) m (larger value)

Answers

Answer 1

Answer:

27 by 27

Step-by-step explanation:

Let the sides be x and y. The problem is essentially asking:

Given 2(x+y)=108, maximize xy.

We know that x+y=54. By the Arithmetic Mean - Geometric Mean inequality, we can see that [tex]\frac{x+y}{2} \ge \sqrt{xy[/tex]. Substituting in x+y=54, we get [tex]27\ge\sqrt{xy}[/tex], meaning that [tex]729 \ge xy[/tex]. Equality will only be obtained when x=y (in this case it will generate the maximum for xy), so setting x = y, we can see that x = y = 27. Hence, 27 is the answer you are looking for.


Related Questions

What is the volume of a pyramid below?



600 cm^3

750 cm^3

900 cm^3

1800 cm^3

Answers

Answer: 600 cm³

Step-by-step explanation:

Volume of square pyramid = (1/3) · b² · h

b = base edge length = 10 cmh = height = 18 cm

Therefore, the volume can be calculated as

[tex]\frac{1}{3} *10^{2}*18=\frac{1}{3}*100*18=\frac{1}{3}*1800=\frac{1800}{3}=600[/tex]

Answer

900

Step-by-step explanation:

it is pyramid and finding its volume we use the 3 components that is length, with and the height

1/2 base x width x height

5 x 18 x 10 = 900cm³

E
Homework: Practice
Exam 3
Question 7
Find the standard deviation for the group of data items.
14, 15, 16, 16, 17, 18
The standard deviation is
(Simplify your answer. Round to two decimal places as needed.)
9

Answers

Answer:

Step-by-step explanation:

I need helpppp please I don’t understand this question at alll

Answers

Answer:

17000

Step-by-step explanation:

17^1 * 10^3

17 * 10*10*10

17*1000

17000

the answer is 17,000

the exponent shows how many times you multiply the number by itself

here is an image for an explanation

hope I helped ❤

Leena is arranging 3 different books in a row on a shelf. Create a sample space for the arrangement of a detective story (D), a mystery story (M), and a comic book (C).

Source
StylesNormal

Answers

There are 6 DIFFERENT POSSIBLE arrangements as obtained using the factorial method and they are :

DMC, CMD, DCM, MDC, CDM, MCD

Given :

DETECTIVE STORY = D

MYSTERY STORY = M

COMIC BOOK = C

To use the factorial method, we find the factorial value of the number of books to be arranged

Number of different possible arrangements = (number of books)!

Number of books = 3

Hence, 3! = 3 * 2 * 1 = 6 ways

The sample space :

DMC

CMD

DCM

MDC

CDM

MCD

THEREFORE, there are 6 different samples on the SAMPLE SPACE.

learn more :

https://brainly.com/question/13041664

The Demand function for a product is given by:

D(q) = - 0.0003q^2 - 0.04q + 23.56

where q is the number of units sold and D(q) is the corresponding price per unit, in dollars. What is the average rate of change of Demand between 40 and 175 units sold?

Answers

Answer:

The average rate of change of Demand between 40 and 175 units sold is of -0.1045.

Step-by-step explanation:

Average rate of change:

The average rate of a function f(x) in an interval [a,b] is given by:

[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]

In this question:

[tex]D(q) = -0.0003q^2 - 0.04q + 23.56[/tex]

What is the average rate of change of Demand between 40 and 175 units sold?

[tex]a = 40, b = 175[/tex]. So

[tex]D(40) = -0.0003*40^2 - 0.04*40 + 23.56 = 21.48[/tex]

[tex]D(175) = -0.0003*175^2 - 0.04*175 + 23.56 = 7.3725[/tex]

So

[tex]A = \frac{f(b) - f(a)}{b - a} = \frac{7.3725 - 21.48}{175 - 40} = -0.1045[/tex]

The average rate of change of Demand between 40 and 175 units sold is of -0.1045.

I NEED HELP ON MATH PLS

Answers

Answer:

5/2 or 2½ or 2.5

Step-by-step explanation:

20/8 = 2.5

10/4 = 2.5

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.74. (a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 19 specimens from the seam was 4.85. (Round your answers to

Answers

Answer:

The answer is "(4.518, 5.182)"

Step-by-step explanation:

[tex]\sigma = 0.74[/tex]

The aveage porosity for a sample of [tex]n = 19[/tex] specimens is

[tex]\bar{x}=4.85[/tex]

Thus, the[tex]95\%[/tex] confidence interval for the true mean is

[tex]=\bar{x}\pm Z_{\frac{0.05}{2}} \frac{\sigma}{\sqrt{n}}\\\\=4.85\pm 1.96 \frac{0.74}{\sqrt{19}}\\\\=4.85\pm 0.332\\\\=(4.518, 5.182)[/tex]

Therefore, one can state that the true average porosity will lie  between 4.518 and 5.182 with the 95\% confidence.

When is it appropriate to use the​ two-sample t-methods instead of the one sample​ t-methods? Choose the correct answer below. A. Use the​ two-sample t-methods when a sample was taken from each of two populations​ (i.e. two groups being​ compared) and the population standard deviations are not known. Use the​ one-sample t-methods when a sample was taken from one population. B. Use the​ two-sample t-methods when a random sample was not taken. Use the​ one-sample t-methods when a random sample was taken. C. Use the​ two-sample t-methods when the conditions for inference using the​ one-sample t-methods​ aren't satisfied. D. Use the​ two-sample t-methods when the population standard deviation is known. Use the​ one-sample t-methods when the population standard deviation is not known.

Answers

Answer:

A. Use the​ two-sample t-methods when a sample was taken from each of two populations​ (i.e. two groups being​ compared) and the population standard deviations are not known.

Step-by-step explanation:

T-distribution:

When the population standard deviation is not known, the t-distribution is used.

If a sample was taken from one population, we use the one-sample method, while if there is a comparison of two populations, the two-sample method is used, and thus, the correct answer is given by option A.

find two ordered pairs for x-4y=2

Answers

Answer:

x-4y=2 can be written as y=(x-2)/4

(2,0) when x=2, y=0 and (6,1) when x=6, y=1

Water is flowing into a tank at a rate of 20 cm3/min. At the start, there is 250 cm3 of water in the tank.
(i) How much water will be in the tank after 30 minutes?
(ii) Find the time when there is 1210 cm3 of water in the tank.

Answers

Answer:

i) 410 cm³

ii) 48 min

Step-by-step explanation:

we start with 250 cm³.

and then we fill in 20 cm³ per minute.

i)

after 30 minutes we have

250 + 8×20 = 250 + 160 = 410 cm³

ii)

how long (how many minutes) does it take to reach 1210 cm³ in the tank ?

well, first we subtract the start amount (250).

and then we see how often 20 cm³ will "fit" into the remainder. and then we know how many minutes the water has to run.

1210 - 250 = 960 cm³

so, the incoming water needs to reach 960 cm³ to have a total of 1210 cm³.

and

960 cm³ / (20 cm³ / min) = 960 cm³ min / 20 cm³ =

= 960 min / 20 = 48 min

Question 3 (5 points)
Draw a right isosceles triangle.

Answers

I drew it so here’s an example

Answer:

Step-by-step explanation:

Vẽ góc vuông. - Trên hai canh góc vuô dùng thước thước có chia khoảng vẽ hai đoạn thẳng bằng nhau có chung một điểm và nối hai điểm còn lại.

A son is 8 years old. his father is 5 times as old. How old will the father be when he is twice as old as his son?

Answers

The father would be 64 years old

7. Solve for x: x/6 - y/3 = 1

Please give steps! ❤️

Answers

[tex]\\ \sf\longmapsto \frac{x}{6} - \frac{y}{3} = 1 \\ \\ \sf\longmapsto \frac{x - 2y}{6} = 1 \\ \\ \sf\longmapsto x - 2y = 6 \\ \\ \sf\longmapsto x = 6 + 2y[/tex]

Tuition. The tuition at a community college increased from $2,500 to $2,650 per semester. What was the percent of increase in the tuition?​

Answers

Answer:

6 percent increase

Step-by-step explanation:

2650 divided by 2500 gives you 1.06 which means if 2500 is 100 percent 2650 would be 106 percent so the answer is a 6 percent increase

Answer:

6%

Step-by-step explanation:

another way of doing this type of calculation is...

NEW-OLD  =  2650-2500  = 150     = .06 = 6%

   OLD                2500            2500

One time Maria took 27 minutes to walk 1.8km to school. She left home at 07:48 . Write down the time Maria arrived at school

Answers

Answer:

8:15

Step-by-step explanation:

the time would be 8:15 7:48 + 27 = 8:15

HELP ME PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

9514 1404 393

Answer:

  D. 72 heads in 100 flips

Step-by-step explanation:

A probability calculator will tell you the probabilities of the given outcome with a fair coin are ...

  A: 0.0625

  B: 0.04395

  C: 0.15498

  D: 3.9×10^-6

__

It is "improbable" that a fair coin will give 72 heads in 100 flips. So, it is reasonable to assume the coin is not fair if that is the result.

A local church holds an annual raffle to raise money for a new roof. They sell only 500 tickets at $50 each. This year's prizes include: $3,000 in cash, four $100 Amazon gift cards, and two $75 Visa gift cards. You buy one ticket. What is your mathematical expectation for this game

Answers

Answer:

The expectation for an event with outcomes:

{x₁, x₂, ..., xₙ}

Each one with probability:

{p₁, p₂, ..., pₙ}

Is:

Ev = x₁*p₁ + ... + xₙ*pₙ

There are 500 tickets sold.

1 of these, wins $3,000  (this is the event x₁)

4 of these, wins $100     (this is the event x₂)

2 of these, wins $75        (this is the event x₃)

The others do not have a prize.

So the probability of winning the $3000 is equal to the quotient between the number of tickets with that prize (1) and the total number of tickets (500)

p₁ = 1/500

Similarly, the probability of winning $100 will be:

p₂ = 4/500

And for the $75 prize:

p₃ = 2/500

Then the probability of not winning is:

p₄ = 493/500

Then the expected value for a single ticket is:

Ev = $0*493/500 + $75*2/500 + $100*4/500 + $3000*1/500

Ev = $7.1

If you take in account that you pay $50 for the ticket, the actual expectation should be:

E = $7.10 - $50 = -$42.90

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
[infinity]Σ n =1 (-1)^n - 1/n√n

Answers

Answer: hello your question is poorly written attached below is the complete question

answer:

The series is absolutely convergent

Step-by-step explanation:

To determine whether the series is absolutely or conditionally  convergent or divergent. apply the Root Test

The series is absolutely convergent

attached below is the solution

The number line shows the record low temperatures for four states.. what is the difference, between the low temperature in Hawaii and the low temperatures In south Dakota
A -70°F
B -46°F
C 46°F
D 70°F​

Answers

Answer:

D 70°F

Step-by-step explanation:

Difference between temperature in Hawaii and in South Dakota is 12°F - (-58°F) = 12°F + 58°F = 70 °F

Adam runs 13 miles in 143 minutes. How many minutes does it take him to run one mile? Adam runs at a rate of minutes per mile.

Answers

Answer:

Adam runs at a rate of 11 minutes per mile.

Step-by-step explanation:

Take 143 minutes and divide by 13 miles and you will get the answer of 11 minutes.

PLEASE MARK ME BRAINEIST.

Answer:

it would take him 11 minuets to run a mile

Step-by-step

143 divided by 13 is 11 which means each mile takes 11

you can also check the answer by multiplying 13 times 11 which is 143

I need help finding what U stand for

Answers

Answer:

u = 18

Step-by-step explanation:

The two angles 3u and u+36 are equal so

3u = u+36

Subtract u from each side

3u -u = u+36-u

2u = 38

Divide by 2

2u/2 = 36/2

u = 18

Find the Z scores for which 5% of the distributions area lies between negative Z & Z

Answers

Answer:

0.475: Z = -0.062706778

0.525: Z = 0.062706778

Step-by-step explanation:

Write the standard form of the equation of the circle with radius 3 and center (−4,−10)

Answers

Answer:

(x + 4)² + (y + 10)² = 9

Step-by-step explanation:

The standard equation of a circle is written as seen below

(x - h)² + (y - k)² = r²

Where (h,k) is at the center and r is the radius

We want to find the standard equation of a circle that has a radius of 3 and a center at (-4,-10)

Remember r = radius so r = 3

and (h,k) is at center so h = -4 and k = -10

Now to find the standard equation of the circle we simply plug in the values of the variables (h,k and r) into the standard equation of a circle formula.

Equation of a circle: (x - h)² + (y - k)² = r²

r = 3, h = -4 and k = -10

Plug in values

(x - (-4))² + (y - (-10))² = 3²

Simplify

(x + 4)² + (y + 10)² = 9

And we are done!

Which expression is equivalent to: 16x - 16
4(2x - 2)
4(4x - 16)
4(4x - 4)​

Answers

Answer:

4(4x-16)

Step-by-step explanation:

If you like my answer than please mark me as brainliest

It’s 4(4x-4)
Using the distributive property you would take the 4 outside of the parentheses, and multiply it by the 4x and then by the -4 inside the parentheses. 4•4x=16x. 4•-4=16 (remembering that a negative times a positive is still a negative)

Savannah used 2 quarts of paint on a summer project. She still had 5.
quarts of paint left when she was finished. How much paint did Savannah
have at first?
la cloud

Answers

Answer:

7 quarts

Step-by-step explanation:

total paint = paint used + paint left

total paint = 2 +5

total paint 7

5 quarts left +2 quarts used = 7 so the answer is 7 yw

whats the value of 5 in the product of 6,541 x 100

Answers

Answer:

50,000

Step-by-step explanation:

The product would be 654,100. Replace the other numbers to find the value of 5. The value of 5 is 050,000 or 50,000.

I hope this helps!

Please help brainliest will be given

Complete the equation describing how
x and y are related.
x
-1
5
0 1 2 3 4
3 8
V 2
13
18
23
28
y = 5x + [?]
Enter the answer that belongs in [?].

Answers

Answer:

y = 5x + 3

Step-by-step explanation:

When x = 0 y = 3 so the y-intercept will be 3

And the equation is y = 5x + 3 where the slope is 5

please help answer question

Answers

Answer:

Mark me brainlist please please please please

Answer:

Step-by-step explanation:

two cars started to move towards each other at the same time. the speed of the first car was twice the speed of the second car. they met in two hours. if the distance traveled altogether was 300 km find the rates of the cars.

Answers

Answer:

Step-by-step explanation:

Let v be the speed of the slower car

2v is the speed of the faster car

In 2 hrs, the slower car travels a distance of

2 hr(v km/hr) = 2v km

In 2 hrs, the faster car travels a distance of

2 hr(2v km/hr) = 4v km

2v + 4v = 300

6v = 300

 v = 50 km/hr

2v = 100 km/hr

What is the solution to this system of equations?

a - b + c = -6
b - c = 5
2a - 2c = 4

A) 2

B) -1

C) -3

D) 1

Answers

(-1;2;-3)

а, b, c

~~~~~~

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