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3 years ago

The circumference of a circle measures 15.7 centimeters. What is the measure of its diameter?

Mathematics

2 answers:

SVETLANKA909090 [29]3 years ago

8 0

A. 12 cm

there you go

IceJOKER [234]3 years ago

4 0

Answer:

Step-by-step explanation:

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What is the sum of the first 51 consecutive odd positive integers?

Angelina_Jolie [31]

We call:

$a_{n}$ as the set of the first 51 consecutive odd positive integers, so:

 $a_{n} = \{1, 3, 5, 7, 9...\}$

Where:
$a_{1} = 1$
$a_{2} = 3$
$a_{3} = 5$
$a_{4} = 7$
$a_{5} = 9$
and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:

 $a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\}$

Then:

 $a_{n} = a_{1} + (n-1)d$

So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

 $S_{k} = ( \frac{a_{1} + a_{k}}{2} ).k$

Therefore, we need to find:
 $a_{k} = a_{51}$

Given that $a_{1} = 1$ , then:

$a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1$

Thus:
$a_{k} = a_{51} = 2(51)-1 = 101$

Lastly:

$S_{51} = ( \frac{1 + 101}{2} ).51 = 2601$

4 0

3 years ago

Which student has a greater median test score? **Will mark brainliest **¿?

vivado [14]

Amy I think

Explanation

3 0

4 years ago

The nth term of a sequence is 3−2n Work out the 8th term of the sequence

seraphim [82]

Answer:

-13

Step-by-step explanation:

3-2n

3-2×8

3-16

-13

7 0

3 years ago

Tim goes on a car journey

irinina [24]

Answer:

vroom vroom he keeps driving

4 0

3 years ago

You invested $20,000 in two accounts paying 7% and 8% annual interest, respectively. If the total interest earned for the year

sasho [114]

Answer:

$7,000 at 7%; $13,000 at 8%

Step-by-step explanation

x: the amount invested at 7%

y: the amount invested at 8%

x + y = 20,000

7%.x + 8%.y = 1,530

⇒ x =7,000

y = 13,000

5 0

3 years ago