1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Katen [24]
3 years ago
12

What is the sum of a common geometric series if the first term is 8 and the common ratio is 1/2?

Mathematics
1 answer:
stealth61 [152]3 years ago
6 0

Answer:  A

Step-by-step explanation:

The sum to infinity of a geometric series is

S (∞ ) = \frac{a}{1-r} ( - 1 < r < 1 )

where a is the first term 8 and r is the common ratio, hence

S(∞ ) = {8}{1-\{1}{2} } = {8}{1}{2} } = 16

You might be interested in
A store sells flower arrangements at a cost of $28 each. Which statements are true regarding the price of the arrangements? Chec
Maru [420]

Let's check each case to determine the solution to the problem.

we know that

The cost of each flower  arrangements is \$28

Statements

<u>case A)</u> If the price is marked down by 10 percent, the new price will be \$25.20

we know that

If the price is marked down by 10 percent

then

the new price will be

10\%= \frac{10}{100} =0.10  

(1-0.10)*\$28=0.90*\$28 \\= \$25.20

\$25.20=\$25.20

therefore

The statement case A) is True

<u>case B)</u> If the price is marked down by 25 percent, the new price will be \$21

we know that

If the price is marked down by 25 percent

then

the new price will be

25\%= \frac{25}{100} =0.25  

(1-0.25)*\$28=0.75*\$28 \\= \$21

\$21=\$21

therefore

The statement case B) is True

<u>case C)</u> If the price is marked down by 50 percent, the new price will be \$19

we know that

If the price is marked down by 50 percent

then

the new price will be

50\%= \frac{50}{100} =0.50  

(1-0.50)*\$28=0.50*\$28 \\= \$14

\$14 \neq \$19

therefore

The statement case C) is False

<u>case D)</u> If the price is marked down by 35 percent, the new price will be \$18.20

we know that

If the price is marked down by 35 percent

then

the new price will be

35\%= \frac{35}{100} =0.35  

(1-0.35)*\$28=0.65*\$28 \\= \$18.20

\$18.20=\$18.20

therefore

The statement case D) is True

<u>case E)</u> If the price is marked down by 40 percent, the new price will be \$29.80

we know that

If the price is marked down by 40 percent

then

the new price will be

40\%= \frac{40}{100} =0.40  

(1-0.40)*\$28=0.60*\$28 \\= \$16.80

\$16.80 \neq \$29.80

therefore

The statement case E) is False


7 0
3 years ago
Read 2 more answers
How do you write 30.0 in scientific notation? ____× 10^_____
Pie

Answer:

It's written as

3 \times  {10}^{1}

Hope this helps you

8 0
3 years ago
Read 2 more answers
In a square with side length of 6, what is the distance between the center of the square and the center of the largest equilater
Vanyuwa [196]
Place the right angle at the origin. Short leg on x-axis.
The forth corner of the square is the point on the hypotenuse where the line y = x intersects. (Draw a diagram!)
In this case the hypotenuse is y = -4x/3 + 8
x = -4x/3 + 8
7x/3 = 8
7x = 24
x = 3.428571429
8 0
3 years ago
A five​-digit number starts with a number between 4​-9 in the first​ position, with no restrictions on the remaining 4 digits. a
Maurinko [17]

Answer:

(a) Pr = 0.3024

(b) Pr = 0.6976

(c) Pr = \frac{^9P_{n-1}}{10^{n-1}}

Step-by-step explanation:

Given

Start = \{5,6,7,8\} i.e. between 4 and 9

n(Start) =4

Digits = 5

Solving (a): Probability that each of the 5 digit are different

Since there is no restriction;

The total possible selection is as follows:

First\ digit = 4 (i.e. any of the 4 start digits)

Second\ digit = 10\\ (i.e. any of the 10 digits 0 - 9)

Third\ digit = 10 (i.e. any of the 10 digits 0 - 9)

Fourth\ digit = 10 (i.e. any of the 10 digits 0 - 9)

Fifth\ digit = 10 (i.e. any of the 10 digits 0 - 9)

So, the total is:

Total = 4 * 10 * 10 * 10 * 10

Total = 40000

For selection that all digits are different, the selection is:

First\ digit = 4 (i.e. any of the 4 start digits)

Second\ digit = 9 (i.e. any of the remaining 9)

Third\ digit = 8 (i.e. any of the remaining 8)

Fourth\ digit = 7 (i.e. any of the remaining 7)

Fifth\ digit = 6 (i.e. any of the remaining 6)

So:

Selection =4 * 9 * 8 * 7 * 6

Selection =12096

So, the probability is:

Pr = \frac{Selection}{Total}

Pr = \frac{12096}{40000}

Pr = 0.3024

Solving (b): At least 1 repeated digit

The probability calculated in (a) is the all digits are different i.e. P(None)

So, using laws of complement

We have:

P(At\ least\ 1) = 1 - P(None)

So, we have:

Pr= 1 - 0.3024

Pr = 0.6976

Solving (c): An expression to model the probability.

<em>Using (a) as a point of reference, we have;</em>

Pr = \frac{Selection}{Total}

Where

Selection =4 * 9 * 8 * 7 * 6 ---- for selection of 5 i.e. n = 5

Total = 4 * 10 * 10 * 10 * 10

Selection =4 * 9 * 8 * 7 * 6

This can be rewritten as:

Selection = 4 * ^9P_4

4 can be expressed as: 5 - 1

So, we have:

Selection = (5-1) *^9P_{5-1}

Substitute n for 5

Selection = (n-1) *^9P_{n-1}

Selection = (n-1)^9P_{n-1}

Total = 4 * 10 * 10 * 10 * 10

This can be rewritten as:

Total = 4 * 10^4

Total = (5-1) * 10^{5-1}

Total = (n-1) * 10^{n-1}

Total = (n-1) 10^{n-1}

So, the expression is:

Pr = \frac{(n-1)^9P_{n-1}}{(n-1)10^{n-1}}

Pr = \frac{^9P_{n-1}}{10^{n-1}}

<em>Where n represents the digit number</em>

5 0
3 years ago
Robin can run 1.71 kilometers in 10 minutes. How far can she run in 1.5 hours?
Flura [38]

Answer:

I think is 15.39 kilometers

Step-by-step explanation:

1 hour=60 minutes +.5 hours =90 minutes = 9 x 1.71 = 15.39

7 0
2 years ago
Other questions:
  • Suppose Charli D'Amelio posted 42 videos to TikTok. If the ratio of dance trend videos to all other videos is 2:5, how many of t
    9·1 answer
  • find the slope and y-intercept of the line. y equals seven fourths x minus 10. a. 10; seven fourths b. four sevenths; 10 c. nega
    13·1 answer
  • Which description best describes the data in the frequency table .
    5·1 answer
  • What is the slope of the line that passes through the points (4, -9) and (-10, 18)?
    14·1 answer
  • Solvex2 - 8x + 12 =0 for x.<br> The solutions for x are<br> and
    5·1 answer
  • A manufacturer of matches randomly and independently puts 22 matches in each box of matches produced. The company knows that one
    15·1 answer
  • Devin has a change jar that contain only half dollars and pennies. He has 93 coins which add up to a total of $23.96. How many o
    5·2 answers
  • X+ 1<br> If g(x) =<br> x-2 and h(x) = 4 – X, what is the value of (905)(-3)?
    11·1 answer
  • If I look in my closet before I go to school, I have 5 pants
    12·1 answer
  • Geometry Unit 3-2 Parallel and Perpendicular lines on the coordinate plane
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!