All categories

2 years ago

Find S for the given geometric series. Round answers to the nearest hundredth, if necessary.

Mathematics

2 answers:

mash [69]2 years ago

6 0

Answer:

Step-by-step explanation:

Sum of the first n terms of a geometric series is:

S = a₁ (1 - r^n) / (1 - r)

Here, a₁ = 0.2, r = 6, and n = 5.

S = 0.2 (1 - 6^5) / (1 - 6)

S = 311

inn [45]2 years ago

4 0

Answer:

Option A

Step-by-step explanation:

For the given geometric series

a₁ = 0.2

a₅ = 259.2

r = 6

Then we have to find the sum of initial 5 terms of this series

$S_{n} =\frac{a_1(r^4-1)}{(r-1)}=\frac{0.2(6^3-1)}{(6-1)}$

$=\frac{0.2(7776-1)}{5}$

$\frac{0.2\times 7775}{5}$

= 311

Option A is the answer.

You might be interested in

Let f(t) be the the number of units produced by a company t years after opening in 2005. What is the correct interpretation of f

Crazy boy [7]

Answer:

In 2011, 44,500 units are produced

Step-by-step explanation:

Let

t ----> the number of years after 2005

f(t) ----> the number of units produced by a company

we have

f(6)=44,500

For t=6, f(t)=44,500

That means

The number of units produced by a company is equal to 44,500 units six years after 2005

six years after 2005 is the year 2011

therefore

In 2011, 44,500 units are produced

4 0

2 years ago

You want to purchase a new car in 55

Tanzania [10]

Answer:

Ans. you should deposit each month to end up with $38,000 the amount of $533.33 every month for 5 years at a APR of 6.5%

Step-by-step explanation:

Hi, first we have to convert all the data to monthly basis, that is, 5 years (5*12=60 months) and the rate of 6.5% APR offered by the bank (Monthly rate = 0.065/12=0,005666667 or 0.5667% monthly)

With that in mind, we need to solve for "A" the following equation.

$FV=\frac{A((1+r)^{n}-1) }{r}$

Where:

FV = Future value of the car

r = rate of return offered by the bank

n = number of periods that you are going to make the monthly deposit

That is:

$38,000=\frac{A((1+0,005667)^{60}-1) }{0,005667}$

$38,000=\frac{A(0,403599896)}{0,005667}$

$38,000=A(71,22351103)$

$A= 533,53$

Best of luck.

5 0

2 years ago

Identify two ANGLES that are marked congruent to each other on the diagram below

Blababa [14]

Answer:

Angle J is congruent to Angle G

7 0

2 years ago

Read 2 more answers

Which property is best to use when determining the strength of an ionic bond in a solid?

Shtirlitz [24]

I think the best property to use is electronegativity since that is how much it attracts/wants electrons. The larger the difference in electronegativity is between two atoms, the stronger the ionic bond will be. This is also why two atoms need to have a minimum difference between the electronegativity to be considered ionic and not covalent.

6 0

2 years ago

A circle has a diameter of 25cm. How far from the centre of this circle is a chord 16cm long? Draw a picture before you start.

yan [13]

Answer:

The cord is 9.6 cm away from the centre of the circle.

Step-by-step explanation:

See The Image First

The image below shows a picture of everything that’s given, labeled, and drawn in the circle.

Description of the Picture:

You can use the Pythagorean to find the what the distance (the length b) the cord is from the center. You can use the radius as the hypotenuse. The radius is half of the diameter, and the diameter is 25. So the radius is 12.5, which means that 12.5 is the hypotenuse of the triangle (also known as side c). The whole length of the cord is 16cm long, and we can use half of the cord, which is 8cm, for the triangle. So we know two sides already: the hypotenuse (the radius) and the length a of the triangle (half of the length of the cord).

To Solve (variables a, b, and c, are in italics so you don’t get confused):

⇒ Use the formula of the Pythagorean Theorem ( $a^{2}+b^{2}=c^{2}$ ), where b is the length of the distance from the cord to the centre of the circle (what we need to find out), a is the length of the side of the triangle (half of the cord size – 8cm), and c is the hypotenuse (the radius – 12.5cm). So plug the given values of b and c into the formula: