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cricket20 [7]
3 years ago
6

What is the sum of the first five terms of a geometric series with a1 = 6 and r = 1/3? Express your answer as an improper fracti

on in lowest terms without using spaces.
Mathematics
1 answer:
Likurg_2 [28]3 years ago
5 0

Answer:

  242/27

Step-by-step explanation:

Using the formula for the sum, you can fill in the given values and do the arithmetic.

  Sn = a1·(r^n -1)/(r -1)

  S5 = 6·((1/3)^5 -1)/(1/3 -1) = 6(-242/243)/(-2/3) = 6·(121/81)

  S5 = 242/27

_____

Or, you can write the terms and add them up. The sum is ...

  6 + 2 + 2/3 + 2/9 + 2/27 = (162 +54 +18 +6 +2)/27 = 242/27

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James has a bag 77 of nickels and dimes. The total value of coins is $6.60. How many dimes does James have?
tatuchka [14]

James has 55 dimes in the bag

Step-by-step explanation:

The given is:

  • James has in a bag 77 of nickels and dimes
  • The total value of coins is $6.60

We need to find how many dimes James has

Assume that the number of nickels is x and the number of

dimes is y in the bag

∵ There are x nickels in the bag

∵ There are y dimes in the bag

∵ There are 77 coins in the bag

∴ x + y = 77 ⇒ (1)

∵ 1 nickel = 5 cents

∴ The value of nickles in the bag = 5x cents

∵ 1 dime = 10 cents

∴ The value of dimes in the bag = 10y cents

∵ The total value of coins is $6.60

∵ 1 dollar = 100 cents

∴ $6.60 = 6.60 × 100 = 660 cents

∴ 5x + 10y = 660 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -10 to eliminate y

∵ -10x - 10y = -770 ⇒ (3)

- Add equations (2) and (3)

∴ -5x = -110

- Divide both sides by -5

∴ x = 22

Substitute the value of x in equation (2) to find y

∵ 22 + y = 77

- Subtract 22 from both sides

∴ y = 55

∴ The number of dimes is 55

James has 55 dimes in the bag

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

#LearnwithBrainly

6 0
3 years ago
Please help is due at 8:00 pm
tester [92]

Answer:

Answer is C

Step-by-step explanation:

Please mark brainliest if I helped!

3 0
3 years ago
Pat has nine cards. Frank has two more cards than Steve. Steve has 3 cards how many more cards does Pat have than Frank?
n200080 [17]
4. Pat 9. Frank 5. Steve 3. 9-5=4.
4 0
3 years ago
Read 2 more answers
You have a map of Southern California. If the distance between
Rudiy27

9514 1404 393

Answer:

  18 miles

Step-by-step explanation:

The map distance and ground distance are proportional.

  (distance to school)/(3 in) = (12 miles)/(2 in)

Multiplying by 3 in gives ...

  distance to school = (12 miles)(3/2) = 18 miles

4 0
3 years ago
A paper container in the shape of a right circular cone has a radius of 3 inches and a height of 8 inches. Determine and state t
Scrat [10]

Given:

Radius of the cone = 3 inches

Height of the cone = 8 inches

To find:

The volume of the cone, in terms of  π.​

Solution:

We know that, the volume of a cone is:

V=\dfrac{1}{3}\pi r^2h

Putting r=3,h=8, we get

V=\dfrac{1}{3}\pi (3)^2(8)

V=\dfrac{1}{3}\pi (9)(8)

V=\dfrac{72}{3}\pi

V=24\pi

Therefore, the volume of the cone is 24\pi.

7 0
2 years ago
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