1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ser-zykov [4K]
3 years ago
5

A family wants to save for college tuition for their daughter. What continuous yearly interest rate r% is needed in their saving

s account if their deposits of $4700 per year are to grow to $110,000 in 14 years? Assume that they make deposits continuously throughout the year.
Mathematics
1 answer:
sergey [27]3 years ago
4 0

Answer:

The continuous yearly interest is  22.5% per year.

Step-by-step explanation:

Continuous yearly interest:

Continuous yearly interest is defined as the sum of the interest comes from principle and the interest comes from interest.

The formula for continuous interest yearly is

A=Pe^{rt}

where A = The final amount =$110,000

P= principle =$4,700

r= rate of interest

t= time (in year)= 14 years

\therefore 110,000= 4,700e^{r\times 14}

\Rightarrow e^{14r}= \frac{110,000}{4,700}

Taking ln both sides

\Rightarrow ln e^{14r}= ln(\frac{110,000}{4,700})

\Rightarrow {14r}= ln(\frac{1100}{47})

\Rightarrow r=\frac{ln( \frac{1100}{47})}{14}

\Rightarrow r = 0.225  (approx)

The continuous yearly interest is 0.225 = 22.5% per year.

You might be interested in
A homeowner compared his electric bill from the last four months. In January, his bill was up $30; in February it was up another
kipiarov [429]
B: because she gained and didn’t decrease








Explanation:
A: 30
B:36
C:11
D: -5





So b is correct because it’s Greater
7 0
2 years ago
Read 2 more answers
Find the slope of the line containing the points (1, 4) and (3, 7).
irina1246 [14]

Answer: 3/2

Step-by-step explanation:

the formula to find slope is:

m = rise/run = \frac{y2-y1}{x2-x1}

In this case:

m = 3/2 = \frac{7-4}{3-1}

6 0
2 years ago
There are 8 competitors in each ring for a tae kwon do tournament. If there are 96 competitors in the tournament, how many rings
Marysya12 [62]
All you need to do is divide 96 by 8 and you get 12 as your answer
5 0
3 years ago
Read 2 more answers
g A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is cha
leva [86]

Answer:

Null hypothesis:p_{1} = p_{2}    

Alternative hypothesis:p_{1} \neq p_{2}  

z=\frac{0.410-0.35}{\sqrt{0.385(1-0.385)(\frac{1}{1000}+\frac{1}{700})}}=2.502    

p_v =2*P(Z>2.502)= 0.0123    

Comparing the p value with the significance level assumed \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.    

Step-by-step explanation:

Data given and notation    

X_{1}=410 represent the number of people indicating that their financial security was more than fair for the recent year

X_{2}=245 represent the number of people indicating that their financial security was more than fair for the year before

n_{1}=1000 sample 1 selected  

n_{2}=700 sample 2 selected  

p_{1}=\frac{410}{1000}=0.410 represent the proportion estimated of indicating that their financial security was more than fair this year

p_{2}=\frac{245}{700}=0.35 represent the proportion estimated of indicating that their financial security was more than fair the year before

\hat p represent the pooled estimate of p

z would represent the statistic (variable of interest)    

p_v represent the value for the test (variable of interest)  

\alpha significance level given  

Concepts and formulas to use    

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:    

Null hypothesis:p_{1} = p_{2}    

Alternative hypothesis:p_{1} \neq p_{2}    

We need to apply a z test to compare proportions, and the statistic is given by:    

z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}   (1)  

Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{410+245}{1000+700}=0.385  

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.    

Calculate the statistic  

Replacing in formula (1) the values obtained we got this:    

z=\frac{0.410-0.35}{\sqrt{0.385(1-0.385)(\frac{1}{1000}+\frac{1}{700})}}=2.502    

Statistical decision  

Since is a two sided test the p value would be:    

p_v =2*P(Z>2.502)= 0.0123    

Comparing the p value with the significance level assumed \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.    

7 0
3 years ago
The distance between the cities Chicago and Toronto is 540 miles. A motorcycle's speed is 48 mph. For a car, it takes 2.25 hours
serious [3.7K]

Answer:

5 hours

Step-by-step explanation:

given :

Distance between the cities = 540 miles

Speed of motorcycle =48 mph

TO CALCULATE THE TIME TAKEN BY MOTORCYCLE TO COVER THE TOTAL DISTANCE WE USE THE FORMULA :

\frac{DISTANCE}{SPEED}

By putting given values in the formula we get :

\frac{540}{48}

= 11.25 hours

Now, We are given that for a car to cover the same distance it takes 2.25 hours less than the time taken by motorcycle

⇒ 11.25 hours - 2.25 hours

⇒ 9 hours

Thus , Time taken by car to cover the same distance is 9 hours .

Now to calculate speed of car by using formula:

\frac{distance}{time}

\frac{540}{9}

= 60 mph

Let t be the time taken to meet if they start moving towards each other.

So distance covered by motorcycle in t hours is

speed\times time

= 48t miles

Distance covered by car in t hours is

speed\times time

= 60t miles

⇒ 60t + 48t =540

⇒ 108t = 540

⇒ t= 5 hours

Therefore, time taken to meet if they start moving towards each other is 5 hours.





7 0
3 years ago
Other questions:
  • Someone help pls!!! Idk what it is
    5·1 answer
  • Need help with #12 ASAP. What is the equation of a line that is perpendicular to the line y= -1/2x+7 and passes through the poin
    13·1 answer
  • The Triangle Shirtwaist fire: a. resulted in laws that banned all manufacturing in New York. b. occurred during the Uprising of
    11·1 answer
  • What is the result of converting 1250 yards into miles
    11·2 answers
  • If three X equal to 216 then find the value of 3 X - 2 ​
    12·1 answer
  • Please help me asap!
    6·1 answer
  • Plz help me solve this
    6·2 answers
  • The power is the probability that the assembly process is not stopped when it should be because a high number of defective items
    8·1 answer
  • Elena needs 1/4 meter of ribbon to decorate the border of a photo frame.
    12·1 answer
  • |(2,9)<br> J (79)<br> 00 -<br> H(25)
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!