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Rus_ich [418]
3 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]3 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

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Researchers fed mice a specific amount of Toxaphene, a poisonous pesticide, and studied their nervous systems to find out why To
Mkey [24]

Answer:

a. The mean refractory period= 1.85 and the standard error = 0.06455

b.  90% confidence interval for the mean absolute refractory period for all mice when subjected to the same treatment = 1.6981, 2.0019

c. Yes, the data give good evidence to support this theory

Step-by-step explanation:

a.  The table below shows the calculations:

                 X                (X-mean)^2

                1.7             0.0225

                1.8                 0.0025

                1.9                 0.0025

                2.0                 0.0225

Total        7.4                  0.05

Sample size: n=4

The mean is:  \bar{x} = \frac{7.4}{4} = 1.85

The sample standard deviation, s = \sqrt{\frac{\sum \left ( x-\bar{x} \right )^{2}}{n-1}}=0.1291

The standard error, se= \frac{s}{\sqrt{n}}=\frac{0.1291}{2} = 0.06455

b. Degree of freedom: df = n-1 = 3

Critical value of t for 90% confidence interval is: 2.3534

The confidence interval is  \bar{x}\pm t_{c}se = 1.85\pm 2.3534\cdot 0.06455=1.85\pm 0.1519 = (1.6981, 2.0019)

c. The Hypotheses are:

H_{0}:\mu=1.3,H_{1}:\mu>1.3

So the test statistics will be

t=\frac{\bar{x}-\mu}{s/\sqrt{n}}=8.52

The p-value is: 0.0017

We reject the null hypothesis because p-value is less than 0.05 . This indicates that the data gave good evidence to support this theory.

4 0
3 years ago
Find the<br>simple interest:<br>Princpd $6000<br>Interest Rate 5%<br>Time: 6 months<br>Start​
sattari [20]

Answer: The interest is: $150.00

The formula we'll use for this is the simple interest formula, or:

Where:

   P is the principal amount, $6000.00.

   r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.

   t is the time involved, 6....month(s) time periods.

   Since your interest rate is "per year" and you gave your time interval in "month(s)" we need to convert your time interval into "year" as well.

       Do this by dividing your time, 6- month(s), by 12, since there's 12 months in 1 year.

   So, t is 0.5....year time periods.

To find the simple interest, we multiply 6000 × 0.05 × 0.5 to get that:

The interest is: $150.00

8 0
3 years ago
Why do people keep adding links instead of answering my? question
Svet_ta [14]

I know! It's kind if annoying tbh...

7 0
3 years ago
Loretta and her family are going on vacation. Their destination is 610 miles from their home. Loretta is going to share some of
alexandr402 [8]
Loretta:
Average driving speed = 55 mph
Time = 4 hours
Distance traveled = 55*4 = 220 miles

Dad:
Average driving speed = 65 mph
Let x =  hours driven
Distance traveled = 65x miles

The length of the trip is 610 miles, therefore
65x + 220 = 610
65x = 390
x = 6  hours

Answer: Loretta's dad drove for 6 hours.
7 0
3 years ago
PPPPPPPPPPLLLLLLLLLLZZZZZZ HELP!<br><br> A.<br> B.<br> C.<br> D.
dangina [55]

Answer:

B

Step-by-step explanation:

The square root of 21 will be halfway between 4 and 5. 4.58 ~ 4.6

The square root of 17 will be closer to 4 than 5. 4.12 ~ 4.1

3Pi/2 will beclose to 5 than 4. 4.71 ~ 4.7

4.1, 4.6, 4.7

That is B.

4 0
3 years ago
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