1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Rus_ich [418]
2 years ago
14

Robert has available 400 yards of fencing and wishes to enclose a rectangular area. Express the areaAof the rectangle as a funct

ion of the widthwof the rectangle. For what value ofwis the arealargest? What is the maximum area?
Mathematics
1 answer:
solong [7]2 years ago
7 0

Answer:

The answer is below

Step-by-step explanation:

a)Given that the length of fencing available is 400 yards. This means that the perimeter of the rectangle is 400 yards.

the perimeter of a rectangle is given as:

Perimeter = 2(length + width) = 2(l + w)

Hence;

400 = 2(l + w)

200 = l + w

l = 200 - w

The area of a rectangle is given as:

Area = length × width

Area = (200 - w) × w

Area = 200w - w²

b) For a quadratic equation y = ax² + bx + c. it has a maximum at x = -b/2a

Hence, for the area = 200w - w² a=-1, b = 200, the maximum width is at:

w = -b/2a = -200/2(-1) = -200/-2 = 100

A width of 100 yard has the largest area

c) l = 200 - w = 200 - 100 = 100 yards

Area = l × w = 100 × 100 = 10000 yd²

The maximum area is 10000 yd²

You might be interested in
ASAP GIVING GOOD AMOUNT OF POINTS. I cannot fail my class or I will be sent to school again
svlad2 [7]

Answer

- 3/2

Step-by-step explanation:

Hope this helps:) if you need anynore help lmk!

6 0
2 years ago
Solve for w.<br> 5W + 9z = 2z + 3W<br> What is the answer
andreyandreev [35.5K]

Answer:

−7z/2

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
How are angles 1,2,3,4 related in the trapezoid
Alex

Answer:

The degree measure of the four add up to 360 degrees. This is actually true of any quadrilateral. Let lower case letter a,b,c and d represent the angle of trapezoid ABCD. Then a+b+c+d= 360 degreees.

5 0
3 years ago
A candy store has ten giant pieces of candy! Find the probability of each event. There are 4 gumdrops, 3 lolipops, 2 jellybeans,
AveGali [126]

Answer:

1. P = 9/90 = 1/10

2. P = 16/90 = 8/45

3. P = 10/90 = 1/9

4. P = 4/90 = 2/45

Step-by-step explanation:

Total no. of candy = 10

No. of Gumdrops = 4

No. of Lollipops = 3

No. of Jellybeans = 2

No. of Peppermint = 1

1. To find the probability that the child will pick a peppermint or jellybean, we will add the probabilities of both the candies.

P(Peppermint) = No. of Peppermint/Total no. of candy

                        = 1/10

P(Jellybean) = No. of Jellybean/Total no. of candy

                    = 2/10

P(Peppermint or Jellybean) = 1/10 + 2/10

P(Peppermint or Jellybean) = 3/10

Then, the child picks a lollipop. Note that after picking a peppermint or a jellybean, the number of candies left are 9. So,

P(Lollipop) = No. of Lollipops/Total no. of candy

P(Lollipop) = 3/9

To compute the probability that the child will pick a peppermint or a jellybean and then a lollipop,

P = P(Peppermint or Jellybean) x P(Lollipop)

  = 3/10 x 3/9

P = 9/90 = 1/10

2. Probability that a child will pick a lollipop or peppermint:

P(Lollipop or Peppermint) = P(lollipop) + P(peppermint)

                                          = 3/10 + 1/10

P(Lollipop or Peppermint) = 4/10

Then the child picks a gumdrop. Note that the number of candies remaining are 9. So,

P(Gumdrop) = 4/9

The probability that the child picks a lollipop or peppermint and then a gumdrop:

P = P(Lollipop or Peppermint) x P(Gumdrop)

  = 4/10 x 4/9

P = 16/90 = 8/45

3. Probability that a child will pick a jellybean:

P(Jellybean) = No. of Jellybeans/Total no. of candy

P(Jellybean) = 2/10

Then the child picks a peppermint or a gumdrop. Note that one candy has been picked out so there are 9 candies left in total.

P(Peppermint or Gumdrop) = P(peppermint) + P(Gumdrop)

                                              = 1/9 + 4/9

P(Peppermint or Gumdrop) = 5/9

The probability that a child picks a jellybean then a peppermint or a gumdrop is:

P = P(Jellybean) x P(Peppermint or Gumdrop)

  = 2/10 x 5/9

P = 10/90 = 1/9

4. P(peppermint) = 1/10

Then the child picks a gumdrop. (remaining candies are 9)

P(Gumdrop) = 4/9

Probability that a child will pick a peppermint then a gumdrop:

P = P(peppermint) x P(gumdrop)

  = 1/10 x 4/9

P = 4/90 = 2/45

5 0
3 years ago
If x is a normal random variable with a standard deviation of 10, then 3x has a standard deviation equal to:
kicyunya [14]
Standard deviation(σ_{x}) = √V(X) = 10
Therefore, variance of X. V(X) = 10² = 100

Variance of aX is given by,
V(aX) = a²V(X)

Therefore, variance of 3X will be,
V(3X) = 3²V(X) = 9(100) = 900

Therefore, standard deviation of 3X is,

σ_{3x} = √V(3X) = √900 = 30
4 0
3 years ago
Other questions:
  • If M is the midpoint of segment XY, find the coordinates of point X if M is at
    9·1 answer
  • Algebraic expression that best describes the sequence 2,4,8,16,32,...?
    10·2 answers
  • Which of these descriptions matches the graph?
    7·2 answers
  • Haley buys 9 pounds of apples for $3. How many pounds of apples can she buy for $1?
    8·1 answer
  • Use the distributive property to remove the parentheses. -6(11 - 2)​
    8·1 answer
  • Does 1/6, -3, V7, -6/5 or 4.5 come first when the numbers are listed from least to greatest? Explain.
    5·2 answers
  • Help plsss thank youuuu
    5·1 answer
  • Vanilla: 36 Chocolate: 26 Strawberry: 18 <br><br> What percent of customers chose Vanilla ice cream?
    9·2 answers
  • A box contains 512 grams of cereal. one serving is 56 grams. how many servings of cereal dose the box contain?​ GETS BRAINLIEST
    8·2 answers
  • Which of the following ordered pair is the solution to the system of equations?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!