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3 years ago

(1+1/1)(1+1/2)(1+1/3)......(1+1/n)=n+1

Mathematics

2 answers:

s2008m [1.1K]3 years ago

7 0

Answer:

Step-by-step explanation:

(2/1 )(3/2)(4/3)...(n-1/n-2)(n/n-1)(n+1/n) = n + 1

n + 1 = n + 1

1 = 1 ( Fact )

podryga [215]3 years ago

6 0

(2/1 )(3/2)(4/3)...(n-1/n-2)(n/n-1)(n+1/n) = n + 1

n + 1 = n + 1

1 = 1 ( Fact )

Thus it is not importent what the value of n is at all because the equation is always have the equal number ( which is 1 ) in both sides .

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The ages of 11 students enrolled in an on-line macroeconomics course are given in the following steam-and-leaf display:

blsea [12.9K]

Answer:

The standard deviation of the age distribution is 6.2899 years.

Step-by-step explanation:

The formula to compute the standard deviation is:

$SD=\sqrt{\frac{1}{n}\sum\limits^{n}_{i=1}{(x_{i}-\bar x)^{2}}}$

The data provided is:

X = {19, 19, 21, 25, 25, 28, 29, 30, 31, 32, 40}

Compute the mean of the data as follows:

$\bar x=\frac{1}{n}\sum\limits^{n}_{i=1}{x_{i}}$

$=\frac{1}{11}\times [19+19+21+...+40]\\\\=\frac{299}{11}\\\\=27.182$

Compute the standard deviation as follows:

$SD=\sqrt{\frac{1}{n}\sum\limits^{n}_{i=1}{(x_{i}-\bar x)^{2}}}$

$=\sqrt{\frac{1}{11-1}\times [(19-27.182)^{2}+(19-27.182)^{2}+...+(40-27.182)^{2}]}}\\\\=\sqrt{\frac{395.6364}{10}}\\\\=6.28996\\\\\approx 6.2899$

Thus, the standard deviation of the age distribution is 6.2899 years.

7 0

3 years ago

Jan needed to empty 18 gallons of water from a tub into jugs that hold 0.5 gallons of water. How many jugs did Jan need?

Ilia_Sergeevich [38]

So you would do,
18 gallons of water divided by 0.5 gallons of water
if you did that correctly you should have gotten... 36 jugs

8 0

3 years ago

What does -22 belong to

Len [333]

Answer:

it's part of the real number system

it's a rational number

it's an integer

Step-by-step explanation:

6 0

2 years ago

PLEASE HELP ME I MIGHT FAIL <br> What is the area of the shaded region?<br><br> square centimeters

scoray [572]

Answer:

98 square centimeters

Step-by-step explanation:

first find the area of the non shaded area

8x4=32

next find the area of the rectangle around it

13x10=130

and last you need to subtract the non shaded area from the rectangle around it to find the area of the shaded area

130-32=98

4 0

3 years ago

A lighthouse is built on an exposed reef, 4.5 miles off-shore. The shoreline is perfectly straight, and a town is located 6 mile

Alisiya [41]

Answer: 3.94 hours

Step-by-step explanation:

From the question, the following parameters are given:

Distance offshore = 4.5 miles

Distance downshore = 6 miles

Speed when running = 3.4 mph

Speed with boat = 1.8 mph

distance of boat rowing = sqrt(4.5^2 + x^2)

Where

Speed = distance/time

Time = distance/speed

Time = distance of boat rowing/1.8

distance of running = 6 - x

Time = (6-x)/3.4

total travel time

t = sqrt(4.5^2 + x^2)/1.8 + (6 - x)/3.4

dt/dx = x/(1.8×sqrt(4.5^2 + x^2) - 1/3.4

d^2t/dx^2 = +ve at any x

x is at its minimum when dt/dx=0

x/(1.8×sqrt(4.5^2 + x^2) = 1/3.4

x = 6/sqrt(253) × 4.5 = 1.697 miles

Substitute x in

t = sqrt(4.5^2 + x^2)/1.8 + (6 - x)/3.4

We obtaine

t = sqrt(4.5^2 + 1.697^2)/1.8 + (6 - 1.69)/3.4

t = 2.672+ 1.266 = 3.94 hours

7 0

3 years ago