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kirill115 [55]
3 years ago
13

Sabena invests $250 in an account that earns 2.4% interest per year compounded continuously. How many years will it take the acc

ount to have a value of $300?
Mathematics
1 answer:
g100num [7]3 years ago
6 0

Answer:

It'll take 7.5967 years to have $300 on that account.

Step-by-step explanation:

This problem involves a compounded interest compounded continuously, so in order to solve it we must use the formula for those cases as shown below:

M = C*e^(i*t)

Where M is the final value, C is the initial capital, i is the interest rate and t is the total time. We have:

300 = 250*e^(0.024*t)

e^(0.024*t) = 300/250

e^(0.024*t) = 1.2

0.024*t = ln(1.2)

t = ln(1.2)/0.024 = 7.5967

It'll take 7.5967 years to have $300 on that account.

You might be interested in
Mini made a recipe that yields 4 and 1 over 2 cups. If each serving is 1 over 2 cup, which expression will help Mini determine t
Olenka [21]

Answer:

1/2x = 4 1/2

Where x = Number of servings = 9 servings

Step-by-step explanation:

Mini made a recipe that yields 4 and 1 over 2 cups.

1 recipe = 4 1/2 cups

1 serving = 1/2 cups

1/2 cups = 1 servings

4 1/2 cups = x servings

Cross Multiply

1/2 × x = 4 1/2

x = 4 1/2 ÷ 1/2

x = 9/2 ÷ 1/2

x = 9/2 × 2

x = 9 servings.

Therefore, the expression tha will help Mini to determine the number of servings her recipe will yield is

1/2x = 4 1/2

Where x = Number of servings = 9 servings

4 0
3 years ago
What is the slope and y intercept of (-3,0),(2,-3)?
irina1246 [14]
So the pattern is x,y so the left is x and the right is y. Just graph it
4 0
3 years ago
The following data were collected from 12 rain gauges in a park. Build a 95% CI for the mean rainfall at the park.
dybincka [34]

Answer:

Critical values:t_{\alpha/2}=-2.201 t_{1-\alpha/2}=2.201

95% confidence interval would be given by (3.646;4.472)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The data is:

4.65 3.89 2.73 4.35 3.80 4.86 4.33 4.37 4.76 4.05 3.05 3.87

2) Compute the sample mean and sample standard deviation.

In order to calculate the mean and the sample deviation we need to have on mind the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n}

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}

=AVERAGE(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

On this case the average is \bar X= 4.059

=STDEV.S(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

The sample standard deviation obtained was s=0.6503

3) Find the critical value t* Use the formula for a CI to find upper and lower endpoints

In order to find the critical value we need to take in count that our sample size n =12 <30 and on this case we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. The degrees of freedom are given by:

df=n-1=12-1=11

We can find the critical values in excel using the following formulas:

"=T.INV(0.025,11)" for t_{\alpha/2}=-2.201

"=T.INV(1-0.025,11)" for t_{1-\alpha/2}=2.201

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}  

And we can use Excel to calculate the limits for the interval

Lower interval : "=4.059 -2.201*(0.6503/SQRT(12))" =3.646

Upper interval :  "=4.059 +2.201*(0.6503/SQRT(12))" =4.472

So the 95% confidence interval would be given by (3.646;4.472)

8 0
3 years ago
Leona purchased a $1,000 bond having a quoted price of 99.875. She had to pay a 5.5% brokerage fee (of the selling price). What
iogann1982 [59]

Answer:

None of these choices are correct.

Step-by-step explanation:

If a bond is quoted at 99.875, it means that it is sold at 99.875%  of the face value;

Face value = 1000

Therefore, Price = 0.99875 * 1000

Price = $998.75

If Leona pays  5.5% of the selling price, it means that she is paying additional cost which will make the total cost more than the quoted price;

5.5% of 998.75 is;

0.055*998.75 = $54.93

The total cost = $998.75 +$54.93

= $1053.68

Therefore, none of the given choices is correct.

4 0
3 years ago
Read 2 more answers
WILL MARK BRANLIEST TO ACCURATE ANSWER. URGENT ANSWER REQUIRED. ANSWER NOW.
ICE Princess25 [194]

Answer:

It’s D. 4

Step-by-step explanation:

GOOD LUCK HOMIE AND USE A CALCULATO ;)

7 0
3 years ago
Read 2 more answers
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