Refer to the diagram below. If m

The numbers of teams remaining in each round of a single-elimination tennis tournament represent a geometric sequence where an i

Anit [1.1K]

Answer:

$a_n = 128\bigg(\dfrac{1}{2}\bigg)^{n-1}$

Step-by-step explanation:

We are given the following in the question:

The numbers of teams remaining in each round follows a geometric sequence.

Let a be the first the of the geometric sequence and r be the common ration.

The $n^{th}$ term of geometric sequence is given by:

$a_n = ar^{n-1}$

$a_4 = 16 = ar^3\\a_6 = 4 = ar^5$

Dividing the two equations, we get,

$\dfrac{16}{4} = \dfrac{ar^3}{ar^5}\\\\4}=\dfrac{1}{r^2}\\\\\Rightarrow r^2 = \dfrac{1}{4}\\\Rightarrow r = \dfrac{1}{2}$

the first term can be calculated as:

$16=a(\dfrac{1}{2})^3\\\\a = 16\times 6\\a = 128$

Thus, the required geometric sequence is

$a_n = 128\bigg(\dfrac{1}{2}\bigg)^{n-1}$

4 0

3 years ago

Sarah Jones earns $640 per week selling life insurance for Farmer’s Insurance plus 5% of sales over $5,750. Sarah’s sales this m

Alex_Xolod [135]

Answer:

$2560+$1100=$3660

Step-by-step explanation:

$640×4=$2560 if the month is over and she is due a payment

5%×$22000=$1100 of sales if they are to be considerred and paid every month

3 0

3 years ago

An electric bulb is sold in a box measuring 5 cm by 4 cm by 4 cm. If the shopkeeper receives them in a carton measuring 50 cm by

katen-ka-za [31]

Answer:

250

Step-by-step explanation:

Bulb box and carton both are of cuboidal shape.

For bulb box the dimensions are:

l = 5 cm, w = 4 cm, h = 4 cm

$V_{Bulb\: box} =lwh$

$\implies V_{Bulb\: box} =5(4)(4)$

$\implies V_{Bulb\: box} =80\: cm^3$

For Carton the dimensions are:

l = 50 cm, w = 20 cm, h = 20 cm

$V_{Carton} =lwh$

$\implies V_{Carton} =50(20)(20)$

$\implies V_{Bulb\: box} =20,000\: cm^3$

To find the number of bulbs packed in the carton, divide the $V_{Carton}$ by $V_{Bulb\: box}$

$Number \:of \:bulbs =\frac{V_{Carton}}{V_{Bulb\: box}}$

$\implies Number \:of \:bulbs =\frac{20,000}{80}$

$\implies Number \:of \:bulbs = 250$

So, 250 bulbs will be packed in one carton.

3 0

2 years ago

Cornelia cut equal lengths of ribbon each 7/10 ft long. The ribbon was 3 1/2 ft long.How many pieces did Cornelia cut?

Ilya [14]

she cut two and two thirds 2 2/3

6 0

3 years ago

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What is the length if a right triangle with a leg that measures 16 and a hypotenuse of 20

Genrish500 [490]

Answer:

It would be 12.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers