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3 years ago

Oscar has received a $4,000 gift and is looking for a bank to start a savings account. Which option

Mathematics

1 answer:

hoa [83]3 years ago

4 0

Answer:

The best option for him would be a real interest rate of 5%.

Step-by-step explanation:

The nominal interest rate is the one that represents the percentage of increase of the money that is in a certain investment, without discounting the depreciation due to inflation or the payment of taxes.

On the other hand, the real interest rate is the one that represents the real increase in the money invested, after discounting inflation and any taxes to be paid.

Therefore, the best option for Oscar would be to invest his $ 4,000 in a savings account with a real interest rate of 5% per year.

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The longer leg of a right triangle is 4cm longer than the shorter leg. the hypotenuse is 8cm longer than the shorter leg. find t

Alexeev081 [22]

Longer leg = x + 4

Shorter leg = x

Hypotenuse = x + 8

Using Pythagorean Theorem:

a^2 + b^2 = c^2

(x + 4)^2 + x^2 = (x + 8)^2

x^2 + 8x + 16 + x^2 = x^2 + 16x + 64

2x^2 + 8x + 16 = x^2 + 16x + 64

2x^2 +8x = x^2 + 16x + 48

2x^2 - 8x = x^2 + 48

x^2 - 8x = 48

x^2 - 8x - 48 = 0

You can complete the square from here or use the quadratic formula.

Completing the square:

x^2 - 8x = 48

x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2

x^2 - 8x + 16 = 48 + 16

(x - 4)(x - 4) = 64 or (x - 4)^2 = 64

x - 4 = +√64 OR x - 4 = -√64

x - 4 = +8 OR x - 4 = -8

x = 12 OR x = -4

However, you can't use negative 4 as a length because your length needs to be a positive.

So x will be 12.

Shorter leg: 12

Longer leg: 12 + 4

Hypotenuse: 12 + 8

8 0

3 years ago

Consider a binomial distribution of 200 trials with expected value 80 and standard deviation of about 6.9. Use the criterion tha

mote1985 [20]

Answer:

The correct answer is option 'a' : 120 is more than 2.5 standard deviations above the expected value.

Step-by-step explanation:

For an exponential distribution we have

The expected value μ = 80

No of trails n = 200

Thus we have

$p=\frac{80}{200}=0.4$

The deviation is related to expected value and probability as

$\sigma =\sqrt{np(1-p)}\\\\\therefore \sigma =\sqrt{200\cdot 0.4\cdot (1-0.4)}=6.9$

Thus the values between the given deviation is

$x_{1}=80-2.5\times 6.9=62.75\\\\x_{2}=80+6.9\times 2.5=97.25$

Now since 120 successes are out of the range of [62.75,97.25] thus 120 is more than the expected value.

5 0

3 years ago

An investment company pays 8% compounded semiannually. You want to have $12,000 in the future. (A) How much should you deposit

Leno4ka [110]

Before we start answering the question, let's define the compound interest formula:
$A = P(1+ \frac{r}{n}) ^{nt}$
Where:
'A' is the amount of money in dollars
'P' is the principal amount of money in dollars
'r' is the interest rate (decimal)
'n' is the number of times interest is compounded per year
't' is the time in years

(A) Find Principal Amount
Given:
A = 12,000
P = ?
r = 0.08
n = 2 (semiannually)
t = 5
Now we plug our values in and solve:
$12,000 = P(1+ \frac{0.08}{2}) ^{(2)(5)}$
$12,000 = P(1.04) ^{10}$
$P = 8106.77$
∴ You would have to deposit $8106.77 in order to have $12,000 in 5 years from now.

(B) Find Principal Amount
Same given values as above, with the exception of 't' which is now 10 instead of 5.
$12,000 = P(1+ \frac{0.08}{2}) ^{(2)(10)}$
$12,000 = P(1.04) ^{20}$
$P = 5476.64$
∴ You would have to deposit $5476.64 in order to have $12,000 in 10 years from now.

Hope this helps!

4 0

4 years ago

Find the length of side a

velikii [3]

Answer:

Step-by-step explanation:

Hope this helps

5 0

3 years ago

Read 2 more answers

what are all the square numbers

jok3333 [9.3K]

Answer: So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.

hope this helps

8 0

2 years ago