171% of x = 3388, Find x and find 500% of x.

.<br> Evaluate the series 1 + 0.1 + 0.01 + . . .

EastWind [94]

We can employ a simple repeated decimal trick:

$x=1.111\ldots$

$0.1x=0.111\ldots$

$\implies x-0.1x=1\implies0.9x=1\implies x=\dfrac1{0.9}=\dfrac{10}9$

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Alternatively, we can compute the partial sum of the series.

$\displaystyle S_n=\sum_{k=0}^n\dfrac1{10^k}$

$S_n=1+0.1+0.01+\cdots+\dfrac1{10^n}$

$0.1S_n=0.1+0.01+0.001+\cdots+\dfrac1{10^{n+1}}$

$\implies S_n-0.1S_n=0.9S_n=1-\dfrac1{10^{n+1}}$

$\implies S_n=\dfrac{10}9-\dfrac9{10^n}$

As $n\to\infty$ , the second term vanishes and we're left with $\dfrac{10}9$ . Notice that this is really just a more formal version of the earlier trick.

6 0

3 years ago

Read 2 more answers

How can you do this

ololo11 [35]

You add up all of the sides and the numbers that are there you pretend that they are on the other side and just add all of them up correctly and you will get your answer.

3 0

3 years ago

Read 2 more answers

Colin buys a tv for £530. It depreciates at a rate of 3% per year. How much will it be worth in 5 years? Give your answer to the

rodikova [14]

Answer: In 5 years it will be worth £455

Step-by-step explanation:

Step 1

Given

The cost of the T.V. for Colin = £530.

The rate of depreciation per year = 3%

Time/ period = 5 years

Formulae to be used

F = P X (1 - r) ^ n

where

F = the future value after depreciation

P = the present value.

r =the interest rate per time period

n = the time/ periods

Step 2--- SOLVING

F = P X (1- r) ^ n

F= 530 x (1-0.03) ^ 5

=530 x 0.858734

=£455.129

Rounding up to the nearest penny where appropriate = £455

3 0

3 years ago

Two cards are drawn with replacement, one after the other, and the outcomes recorded. What is the probability that at least one

babymother [125]

Answer:

The probability is 0.231

Step-by-step explanation:

In this question, we are tasked with calculating the probability that out of two cards drawn with replacement from a pack of cards , at least one of the two is a face card.

In a standard pack of cards, there are 52 cards.

Now let’s calculate the number of face cards we have.

There are 12 face cards in a pack of cards. There are 4 of each of Jack, Queen or King

The probability of drawing a face card is 12/52 = 3/13

Now, we want to calculate the probability of at least one of the cards drawn are face cards.

Mathematically, what we are needing to calculate is

Probability of drawing a single face card or probability of the two being a face card

Now let’s calculate.

The probability of the first card drawn being a face card is 3/13. The probability of the second card not being a face card will be 1-3/13 = 10/13

The joint probability under this first set of condition will be 3/13 * 10/13 = 30/169

Now, for the second condition, here we are considering that both cards drawn are face cards. What we have is 3/13 * 3/13 = 9/169

Now in probabilities, whenever we are having the statement or, we add the probabilities together

Thus, the probability here would be 30/169 + 9/169 = 39/169 = 3/13

In decimal this will be 0.231

8 0

3 years ago

Find the number of sides when:

svp [43]

((n-2)×180)/n = 156
(n-2)×180=156n
24n =360
n =15

360/n =36
n = 10

a)15 b)10

7 0

3 years ago