Answer:
Step-by-step explanation:
Answer: it will take 17.5 years to double his money in the account.
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = $500
A = 500 × 2 = $1000
r = 4% = 4/100 = 0.04
n = 4 because it was compounded 3 times in a year.
Therefore,.
1000 = 500(1 + 0.04/4)^4 × t
1000/500 = (1 + 0.01)^4t
2 = (1.01)^4t
Taking log of both sides, it becomes
Log2 = 4tlog 1.01
0.301 = 4t × 0.0043 = 0.0172t
t = 0.301/0.0172
t = 17.5 years
Answer:
a) marked-down price = $6.00
b) with-tax cost = $6.06
Step-by-step explanation:
a) The amount of the markdown is ...
0.20 × $7.50 = $1.50
so the marked-down price is ...
$7.50 - 1.50 = $6.00
__
b) The sales tax is ...
0.01 × $6.00 = $0.06
so the total cost with tax is ...
$6.00 + 0.06 = $6.06
_____
Of course, you know that 20% = 20/100 = 0.20, and 1% = 1/100 = 0.01.
Answer:
$8.75
Step-by-step explanation:
To calculate this you could use two methods. The first method is to find out what 10% is and multiply it by 5. The second method is to calculate 50% using the formula.
<u>Method 1:</u>
To work this out you would simply divide 17.50 by 10, which is 1.75. This is because percentages are out of 100 and so by dividing by 10 we are finding out what 10% is. Then you would multiply 1.75 by 5, which is 8.75. Then you would minus 8.75 from 17.50, which is 8.75.
<u></u>
1) Divide 17.50 by 10.

2) Multiply 1.75 by 5.

3) Minus 8.75 from 17.50.

4) The new price is $8.75
<u>Method 2:</u>
<u></u>
The formula for percentages is.

<u></u>
To work this out you would first divide 50 by 100, which gives you 0.5. Then you would multiply 0.5 by 17.50, which is 8.75. Then you would minus 8.75 from 17.50, which is 8.75.
1) Divide 50 by 100.

2) Multiply 0.5 by 17.50.

3) Minus 8.75 from 17.50.

4) The new price is $8.75.
For this case we have the following expression:

We follow the steps below:
We subtract 4x on both sides of the equation:

We subtract 10 from both sides of the equation:

Now, we must complete squares.
When we have an equation of the form:
, if we want to complete squares we must subtract c on both sides of the equation obtaining:

The square is completed by adding to both sides of the equation: 
So, we have left:

In the given expression we have:

And to complete the square we have:

Rewriting we have:

We factor the left side of the equation, that is, we look for two numbers that when added together result in -8 and when multiplied as a result 16. We have:

So, we have:

Answer:
The intermediate step is to complete squares

Answer:
I put the numbers first because it was easier for me to do but if it confuses you I can redo it
1. C
2. D
3. F
4. B
5. E
6. A