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3 years ago

A sum of money is invested at 12% compounded quarterly. About how long will it take for the amount of money to double?

Mathematics

1 answer:

kompoz [17]3 years ago

8 0

Answer:

5.9 years

Step-by-step explanation:

We believe a better representation of the compound interest formula is ...

$V(t)=P(1+\dfrac{r}{n})^{nt}$

We want to find the value of t for P=1 and V(t)=2. We are told n=4, so the formula becomes ...

$2=(1+\dfrac{.12}{4})^{4t}\\\\\log{(2)}=4t\log{(1.03)}\quad\text{take logs}\\\\t=\dfrac{\log{2}}{4\log{1.03}}\approx\boxed{5.9\quad\text{years}}$

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What is the angle of rotation counterclockwise about the spinner's center that maps label g to label B?

gizmo_the_mogwai [7]

Answer:

The answer is:

The angle of rotation counterclockwise about the spinner's center that maps label g to label B is 180° .

Step-by-step explanation:

The angle of rotation counterclockwise about the spinner's center that maps label g to label B is 180° .

Look at the attached picture of a spinner:

We know that the angle formed by a straight line is equal to 180°

So, in order to map label g to label B we have to set the needle of the spinner straight. Hence the angle formed by the needle is 180° ....

4 0

2 years ago

Read 2 more answers

I arrive at a bus stop at a time that is normally distributed with mean 08:00 and SD 2 minutes. My bus arrives at the stop at an

Nimfa-mama [501]

Answer:

0.0485 = 4.85% probability that you miss the bus.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When two normal distributions are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

In this question:

We have to find the distribution for the difference in times between when you arrive and when the bus arrives.

You arrive at 8, so we consider the mean 0. The bus arrives at 8:05, 5 minutes later, so we consider mean 5. This means that the mean is:

$\mu = 0 - 5 = -5$

The standard deviation of your arrival time is of 2 minutes, while for the bus it is 3. So

$\sigma = \sqrt{2^2 + 3^2} = \sqrt{13}$

The bus remains at the stop for 1 minute and then leaves. What is the chance that I miss the bus?

You will miss the bus if the difference is larger than 1. So this probability is 1 subtracted by the pvalue of Z when X = 1.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1 - (-5)}{\sqrt{13}}$

$Z = \frac{6}{\sqrt{13}}$

$Z = 1.66$

$Z = 1.66$ has a pvalue of 0.9515

1 - 0.9515 = 0.0485

0.0485 = 4.85% probability that you miss the bus.

5 0

3 years ago

The high for a winter day in Sitka,

m_a_m_a [10]

Answer:

The maximum temperature will be -10°C, then if T represents the temperature, we can write this as:

T ≤ -10°C

And the minimum temperature will be -25°C, then we must have that:

T ≥ -25°C

if we use both conditions, we will have:

-25°C ≤ T ≤ -10°C

We can write this range:

[-25°C, -10°C]

Where the [] symbols mean that the extremes are possible temperatures.

The length of the range will be:

-10°C - 25°C = 15°C.

3 0

3 years ago

Distance measured in miles distance measured in yards 1 5

insens350 [35]

You can use ruler and stuff and yea

4 0

3 years ago

Find the total paid on a $65,000 loan with 6% simple interest for 4 years

zubka84 [21]

Answer:

**If the interest is by year then this should work

The interest is $15600 and the amount is $80600.

Step-by-step explanation:

Problem

You deposit $65000 into a bank account paying 6% simple interest per year. You left the money in for 4 years. Find the interest earned and the amount at the end of those 4 years?

Result:

The interest is $15600 and the amount is $80600.

5 0

3 years ago