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anzhelika [568]
3 years ago
15

On the 1st of January 2014, Carol invested some money in a bank account. The account pays 2.5% compound interest per year. On th

e 1st of January 2015, Carol withdrew £1000 from the account. On the 1st of January 2016, she had £23 517.60 in the account. Work out how much Carol originally invested in the account?
Mathematics
1 answer:
cluponka [151]3 years ago
5 0
She started with x.
After 1 year, she had 1.025x.
She withdrew <span>£1000, so now she has 1.025x - 1000.
Then it earned interest for 1 year and ended up as </span>1.025(1.025x - 1000).
The actual amount of money was £23 517.60.
Therefore,

<span>1.025(1.025x - 1000) = 23517.60

1.025x - 1000 = 22 944

1.025x = 23 944

x = 23 360

Her original deposit was </span><span>£23 360</span>
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One third of a birds eggs hatched if 2 eggs hatched, how many eggs did the bird lay.
irinina [24]

Answer:

6 eggs

Step-by-step explanation:

given

one third (i.e 1/3 ) ---> equivalent to 2 eggs

total number of eggs

= three-thirds

= 3 x (1/3) -----------> equivalent to 3 x 2 eggs = 6 eggs

4 0
3 years ago
Any help with an explanation would be appreciated!
Lilit [14]

Problem 1

We'll use the product rule to say

h(x) = f(x)*g(x)

h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)

Then plug in x = 2 and use the table to fill in the rest

h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)

h ' (2) = f ' (2)*g(2) + f(2)*g ' (2)

h ' (2) = 2*3 + 2*4

h ' (2) = 6 + 8

h ' (2) = 14

<h3>Answer: 14</h3>

============================================================

Problem 2

Now we'll use the quotient rule

h(x) = \frac{f(x)}{g(x)}\\\\h'(x) = \frac{f'(x)*g(x)-f(x)*g'(x)}{(g(x))^2}\\\\h'(2) = \frac{f'(2)*g(2)-f(2)*g'(2)}{(g(2))^2}\\\\h'(2) = \frac{2*3-2*4}{(3)^2}\\\\h'(2) = \frac{6-8}{9}\\\\h'(2) = -\frac{2}{9}\\\\

<h3>Answer:  -2/9</h3>

============================================================

Problem 3

Use the chain rule

h(x) = f(g(x))\\\\h'(x) = f'(g(x))*g'(x)\\\\h'(2) = f'(g(2))*g'(2)\\\\h'(2) = f'(3)*g'(2)\\\\h'(2) = 3*4\\\\h'(2) = 12\\\\

<h3>Answer:  12</h3>
5 0
2 years ago
5.) 49 : 7x4 + 3 whats the answer? plzzz help me i rlly need it im gonna pass this in friday​
vitfil [10]

Answer:

31

Step-by-step explanation:

7x4+3

7x4=28

28+3=31

3 0
3 years ago
At a store, sales tax is changed at &amp; rare of
Softa [21]

Answer:

$3.60

Step-by-step explanation:

Convert the percentage to a decimal.

2% = 0.02

Multiply the cost of the dress by the decimal to find the sales tax.

$180 × 0.02 = $3.60

The sales tax $3.60.

7 0
3 years ago
Read 2 more answers
The Super Lotto Plus game consists of a player selecting five different numbers from 1 to 47 and a mega number from 1 to 27 (the
Gnesinka [82]

Answer:

1/41416353 probability of all five numbers and the mega number matching the winning numbers

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the order of the numbers is not important. So we use the combinations formula to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

Probability of the five numbers matching:

Desired outcomes: 1 -> the matching numbers

Total outcomes: 5 from a set of 47. So

T = C_{47,5} = \frac{47!}{5!(47-5)!} = 1533939

Probability:

p_{S} = \frac{1}{1533939}

Probability of the mega number matching:

1 from a set of 27. So

p_M = \frac{1}{27}

Probability of both matching:

Independent events, so we multiply the probabilities:

p = p_S*p_M = \frac{1}{1533939}*\frac{1}{27} = \frac{1}{41416353}

1/41416353 probability of all five numbers and the mega number matching the winning numbers

7 0
3 years ago
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