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3 years ago

The mean of 9, 6, 5, 64, 7, 4, 2

Mathematics

2 answers:

Georgia [21]3 years ago

4 0

Answer:

The mean is 11.25

Step-by-step explanation:

to get the mean youll first add all the numbers together and divide them by the amount of numbers that you have then you get your avarage. Once you have your avarage then you subtract it from all your numbers , add up what you get and divide again by the amont of numbers you have

swat323 years ago

4 0

The mean of this number is 11.45

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X^5/x^-3 Multiply or divide.

Inessa05 [86]

The answer to the question is x^8.

3 0

3 years ago

SOLUTION We observe that f '(x) = -1 / (1 + x2) and find the required series by integrating the power series for -1 / (1 + x2).

Ann [662]

Answer:

Required series is:

$\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

Step-by-step explanation:

Given that

$f'(x) = -\frac{1}{1 + x^{2}}$ ---(1)

We know that:

$\frac{d}{dx}(tan^{-1}x)=\frac{1}{1+x^{2}}$ ---(2)

Comparing (1) and (2)

$f'(x)=-(tan^{-1}x)$ ---- (3)

Using power series expansion for $tan^{-1}x$

$f'(x)=-tan^{-1}x=-\int {\frac{1}{1+x^{2}} \, dx$

$= -\int{ \sum\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx$

$= -\sum{ \int\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx$

$=-[c+\sum\limits^{ \infty}_{n=0} (-1)^{n}\frac{x^{2n+1}}{2n+1}]$

$=C+\sum\limits^{ \infty}_{n=0} (-1)^{n+1}\frac{x^{2n+1}}{2n+1}$

$=C-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

$tan^{-1}(0)=0 \implies C=0$

Hence,

$\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

7 0

3 years ago

A firefighter sees a woman trapped in a building 47 feet up from the bottom floor. If the firefighter is parked 43 feet away fro

Airida [17]

Answer:

48 degrees

Step-by-step explanation:

4 0

2 years ago

Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction. Samuel traveled 3km/h fa

12345 [234]

Samuel was going with 40 km/h and Heather was going with 37 km/h

Step-by-step explanation:

Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction

Samuel traveled 3 km/h faster than Heather
After 3.5 h Samuel stopped for a half-hour break, but Heather kept going
Heather was 8 km ahead of Samuel

We need to find how fast each was going

Assume that Heather's speed is x km/h

∵ Heather's speed = x km/h

∵ Samuel traveled 3 km/h faster than Heather

∴ Samuel's speed = x + 3 km/h

The formula of the distance is distance = speed × time

∵ Samuel travel for 3.5 hours

- Find the distance that Samuel traveled in 3.5 h

∴ Samuel distance = (x + 3) × 3.5

- Multiply the bracket by 3.5 to simplify

∴ Samuel distance = 3.5x + 10.5

∵ Samuel took a break for half hour

∵ Heather kept going

∵ At the end of the break, Heather was 8 km ahead of Samuel

- That means Heather was going for 4 hours (3.5 + 0.5), and her

distance is longer than Samuel distance by 8 km

∴ Heather distance = x × 4 = 4x

- Subtract the distance of Samuel from the distance of Heather

and equate the difference by 8

∵ 4x - (3x + 10.5) = 8

∴ 4x - 3x - 10.5 = 8

- Add the like terms in the left hand side

∴ 0.5x - 10.5 = 8

- Add 10.5 to both sides

∴ 0.5x = 18.5

- Divide both sides by 0.5

∴ x = 37

∵ x represents Heather's speed

∴ Heather's speed = 37 km/h

∵ x + 3 represents Samuel's speed

∴ Samuel's speed = 37 + 3 = 40 km/h

Samuel was going with 40 km/h and Heather was going with 37 km/h

Learn more:

You can learn more about the equation of motion in brainly.com/question/568302

#LearnwithBrainly

3 0

3 years ago

Ella grew 3 over 4 of an inch last year. Ben grew 2 over 3 of an inch last year. How much more did Ella grow than Ben last year?

IrinaK [193]

Answer:

Ella grew $\frac{1}{12}$ of an inch more

Step-by-step explanation:

For this problem, you want to subtract Ben's growth from Ella's.

This expression would be $\frac{3}{4}$ - $\frac{2}{3}$ .

To work these out, they must have the same denominator (which should be the lowest common multiple or LCM).

In this case, the LCM is 12, so you want to multiply each side so the denominator is 12. This means the first fraction should be multiplied by $\frac{3}{3}$ and the second by $\frac{4}{4}$ .

This makes the expression $\frac{9}{12}$ - $\frac{8}{12}$ , which equals $\frac{1}{12}$ .

**This content involves adding and subtracting fractions, which you may want to revise. I'm always happy to help!

7 0

3 years ago