Find the time required for an investment to double in value if invested in an account paying 3% compounded quarterly.

Answers

Answer 1

Answer: [tex]6.12\ \text{years}[/tex]

Step-by-step explanation:

Given

Rate of interest is [tex]r=3\%[/tex] compounded quarterly

So, annually it is [tex]r=12\%[/tex]

Suppose [tex]P[/tex] is the Principal and A is the amount after certain time period.

Amount in Compound interest is given by

[tex]\Rightarrow A=P[1+r\%]^t[/tex]

for given conditions

[tex]\Rightarrow 2P=P[1+0.12]^t\\\Rightarrow 2=(1.12)^t\\\\\Rightarrow t=\dfrac{\ln (2)}{\ln (1.12)}\\\\\Rightarrow t=6.116\approx 6.12\ \text{years}[/tex]

It take [tex]6.12\ \text{years}[/tex] to double the invested amount.


Related Questions

Multiply:

2 × (–21) × 7


A)

294

B)

–273

C)

–7

D)

–294

Answers

Answer:

[tex]2\times \left(-21\right)\times \:7[/tex]

PEMDAS order of operations:

[tex]2\times \left(-21\right)=-2\times \:21=-42[/tex]

[tex]=-42\times \:7[/tex]

[tex]=-294[/tex]

D) -294 is your answer

OAmalOHopeO

Use pemdas order & that’ll get you to your answer which is D) -294

7+4i+1-3i simplify as much as possible

Answers

Answer:

8+i

Step-by-step explanation:

7+4i+1-3i

Combine like terms.

8+i

I hope this helps!

pls ❤ and give brainliest pls

A data set includes data from student evaluations of courses. The summary statistics are n=89​, x=3.44​, s=0.67. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative​ hypotheses?
A.
H0​: μ=3.50
H1​: μ>3.50
B.
H0​: μ=3.50
H1​: μ<3.50
C.
H0​: μ≠3.50
H1​: μ=3.50
D.
H0​: μ=3.50
H1​: μ≠
(I also need the test statistic and p-value) thank you so much in advance :)

Answers

We're told that "the claim that the population of student course evaluations has a mean equal to 3.50". So this means μ=3.50 makes up the null H0

The alternative would be H1: μ ≠ 3.50 since it's the opposite of the claim made in the null.

We go with answer choice D to form the null and alternative hypotheses.

The sign ≠ in the alternative hypothesis tell us that we have a two tail test.

---------------------------------------

Let's compute the test statistic

z = (xbar - mu)/(s/sqrt(n))

z = (3.44 - 3.50)/(0.67/sqrt(89))

z = -0.84483413122896

z = -0.84

The test statistic is roughly -0.84

---------------------------------------

Despite not knowing what sigma is (aka the population standard deviation), we can see that n > 30 is the case. So we can use the Z distribution. This is the standard normal distribution. When n > 30, the T distribution is fairly approximately the same as the Z distribution.

Use a calculator or a Z table to determine that

P(Z < -0.84) = 0.2005

which is approximate

Because we're doing a two-tail test, this means we double that result to get 2*0.2005 = 0.401

The p-value is roughly 0.401

-----------------------------------------

Since the p-value is larger than alpha = 0.05, we don't have enough evidence to reject the null. So you can say that we fail to reject the null, or we accept the null.

The conclusion based on that means that μ=3.50  must be true (unless other evidence comes along to disprove this). In other words, the mean evaluation score from students appears to be 3.50

Lesson 9.6: Steady-State Analysis.) Consider a particular data set of 100,000 stationary waiting times obtained from a large queueing system. Suppose your goal is to get a confidence interval for the unknown mean. Would you rather use (a) 50 batches of 2000 observations or (b) 10000 batches of 10 observations each?

Answers

Answer:

I would rather use:

(b) 10,000 batches of 10 observations each.

Step-by-step explanation:

It is easier to have 10,000 batches of 10 observations each than to have 50 batches of 2,000 observations.  Human errors are reduced with fewer observations. For example, Hadoop, a framework used for storing and processing big data, relies on batch processing.  Using batch processing that divides the 100,000 stationary waiting times into 10 observations with 10,000 batches each is more efficient than having 2,000 observations with 50 batches each.

If f(x)=x-2 and g(x)=2x-6, then g(4)/f(3)

Answers

Answer:

2

Step-by-step explanation:

g(x) = 2x - 6

g(4) = 2*4 - 6

g(4) = 2

f(x) = x - 2

f(3) = 3 - 2

f(3) = 1

Thus g (4) / f (3) = 2 / 1 = 2

The value of the function g (4) / f (3) is 2.

What is a function?

Function is a type of relation, or rule, that maps one input to specific single output.

We are given the function as;

f(x)=x-2 and g(x)=2x-6, then we need to find g(4)/f(3)

Therefore, g(x) = 2x - 6

g(4) = 2*4 - 6

g(4) = 2

Similalry,

f(x) = x - 2

f(3) = 3 - 2

f(3) = 1

Thus we have the value of function as

g (4) / f (3) = 2 / 1

g (4) / f (3) = 2

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For an ordered pair left parenthesis x comma y right parenthesis in a relation, the x element represents the

Answers

Answer:

the x éléments représente the domain

x represents the value on the x-axis and the coordinate is also known as abscissa.

What is coordinate geometry?

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

For an ordered pair left parenthesis x comma y right parenthesis in a relation that is (x, y).

Here x represents the value on the x-axis and the coordinate is also known as abscissa.

More about the coordinate geometry link is given below.

https://brainly.com/question/1601567

17. what is the value of x?

18. what is the value of z?

please help me fast!!

Answers

for x ,

8x + 10x = 180°

[sum of linear pair is equal to 180°]

or, 18x = 180°

or, x = 180/18

therefore, x = 10°……

for z,

10z =8x

[ being corresponding angles are equal ]

or, 10z = 8 × 10°

( replacing x by 10°)

or, 10z = 80°

or, z = 80/10

thus z = 8°…………

The correlation between a student’s shoe size and their score on a final exam is −0.79.What conclusions can be drawn based on the correlation coefficient? Select all that apply.



There is a relationship between a student’s shoe size and their final exam score.Big shoe sizes correlate to low exam scores.Large shoe sizes cause students to do poorly on the final exam.As the shoe size decreases, the final exam score increases.Small shoe sizes cause students to do well on the final exam.

(1,2,4) (A,B,D)

Answers

Answer:

The first one, the second, and fourth one are correct.

Select A,B, and D.

ED2021

Answer:

A, B, and C

Step-by-step explanation:

I got it right ;)

3)
Write an inequality for the graph below. If necessary, use
<= for < or >= for.



Kinda stuck and running out of time

Answers

Answer:

Step-by-step explanation:

A scientist is studying the growth and development of an epidemic virus with a growth rate of 9% per month that has infected 3,124 people. If this rate continues, what will be the number of infected people in another 9 months? Round your answer to the nearest whole number.

Answers

Answer:

About 6,785 people will be infected about nine months.

Step-by-step explanation:

We can write an exponential function to represent the situation. The standard exponential function is given by:

[tex]\displaystyle f(x) = a(r)^x[/tex]

Where a is the initial value, r is the rate, and x, in this case, is the time that has passed in months.

3,124 people have already been infected. Thus, our initial value a = 3124.

And an additional 9% will be infected per month. Therefore, our rate r will be 1 + 9% or 1.09.

Hence, our function is:

[tex]\displaystyle f(x) = 3124(1.09)^x[/tex]

Then after nine months, the total amount of infected people will be f(9):

[tex]\displaystyle f(9) = 3124(1.09)^{(9)}[/tex]

Use a calculator:

[tex]\displaystyle f(9) \approx 6785[/tex]

About 6,785 people will be infected about nine months.

Answer:

7,022

Step-by-step explanation:

please help me with this question!

Answers

I am un able to see the photo please re try so I can help

Mr. Howe ate 1/3 of a pizza and then Mr. Kurt ate 1/8 of the same pizza. How
much of the pizza has been eaten? *

Answers

12/24

Step One: We need to convert 1/3 and 1/8 so both have the same denominator, so we need to find the a number that is able to be multiply by 3 and 8 for the process.

Step Two: 1/3 x 8= 8/24 and 1/8x3= 3/24

Step Three: Add our new fractions: 3/24+8/24= 12/24

Step Four: Subtract 12 by 24: 24-12= 12; our answer is 12/24 or half the pizza was eaten

I hope I've help!

Find the remainder when f(x) = –2x3 + x2 - 4x + 1 is divided by x + 3.

Answers

Answer:

Step-by-step explanation:

The remainder when f(x) is divided by x + 3 would be 76.

What is remainder theorem for polynomials?

If there is a polynomial p(x), and a constant number 'a', then

[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]

where g(x) is a factor of p(x).

We have been given a function;

[tex]f(x) = -2x^3 + x^2 - 4x + 1[/tex]

We need to find the remainder when f(x) is divided by x + 3.

So, Let p(x) = x + 3

p(x) = 0

x + 3 = 0

x = -3

Substitute in the given function f(x);

[tex]f(x) = -2x^3 + x^2 - 4x + 1\\\\f(-3) = -2(-3)^3 + (-3)^2 - 4(-3) + 1\\\\f(-3) = 54 + 9 + 12 + 1\\\\f(-3) = 76[/tex]

Thus, the remainder when f(x) is divided by x + 3 would be 76.

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What is the minimum perimeter of a rectangle with an area of 625 mm^2

Answers

130 mm^2 your welcome

a test has 10 multiple-choice questions with 6 choices each, followed by 35 true/false questions. if a student guesses on each equation, how many ways can he answer the questions on the test

Answers

Answer:

6¹⁰×2³⁵

Step-by-step explanation:

he has 6 choices for the first multiple choice question.

and for each of those he had again 6 more choices to answer the second question. 6×6 = 36

so, for all 10 multiple choice questions he answer in

6¹⁰ different ways = 60466176 ways

then there are 35 true/false questions, which are Bausch again multiple choice questions but with only 2 options instead of 6.

so we get 2³⁵ different possibilities. a huge number.

and they're possible for each of the 60466176 ways of the multiple choice part.

so, in total we have

6¹⁰×2³⁵ different answer possibilities.

Express 18 hours to 2 days in its lowest term

Answers

Answer:

1 : 3

Step-by-step explanation:

We know that 1 days is 24 hours

2 days = 2*24 = 48 hours

16 hours : 48 hours

Divide each by 16

16/16 : 48/16

1 : 3

Answer:

[tex]3 : 8[/tex]

Step-by-step explanation:

[tex]18h : 2d \\ 18h : 2 \times 24h \\ 18 :48 \\ 3 : 8[/tex]

Hi I need help :( I can’t figure these out

Answers

Step-by-step explanation:

I do don't either ok wjshjddshsj

Answer:

Part A: A scatter diagram (Also known as scatter plot, scatter graph, and correlation chart) is a tool for analyzing relationships between two variables for determining how closely the two variables are related. One variable is plotted on the horizontal axis and the other is plotted on the vertical axis. The dots in a scatter plot not only report the values of individual data points, but also patterns when the data are taken as a whole. Identification of correlational relationships are common with scatter plots.

Part B: There are three types of correlation: positive, negative, and none (no correlation).

Part C: A scatter plot is a graph of points that show the relationship between two different pieces of data, while a line graph is a graph that shows information via a connected line.

Please mark me brainliest:))

True or false? The polynomial 3xy + 4z - 8 is a trinomial.

Answers

Answer:

False is the answer.

Step-by-step explanation:

answer is False.

Answer:

True.

Step-by-step explanation:

A trinomial is an algebraic expression consisting of 3 terms. The terms in this instance are: 3xy, 4z, and -8.

10 times as much as 9

Answers

Answer:

90

Step-by-step explanation:

10 x 9

=> 90

10 times 9 is 90.

Ken needs a total of $410 to buy a new bicycle. He has $35 saved. He earns $15 each week delivering newspapers. How many weeks will Ken have to deliver papers to have enough money to buy the bicycle?

Thanks so much! :D

Answers

25 weeks he’ll have all $410 :)

Answer:

25 weeks

Step-by-step explanation:

Since we already know that he has $35 buck-a-roons saved, we can just subtract that from the cost of the bicycle to find the actual price—which would be 375. Then, we know that for every week, he gains $15 bucks. Therefore we know that 15 would be our variable so we can create the following equation:

15x + 35 = 410

15x = 375

15x/15 = 375/15

x = 25

After 25 weeks, Ken will have enough money to buy the bicycle.

A telephone call arrived at a switchboard at random within a one-minute interval. The switch board was fully busy for 10 seconds into this one-minute period. What is the probability that the call arrived when the switchboard was not fully busy

Answers

Answer:

50/60 = .8333=  83.33%

Step-by-step explanation:

The probability that the call arrived when the switchboard was not fully busy is 0.75.

What is Normal Distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

Given:

Here X follows uniform distribution with parameter a and b.

Where,

a = 0 and b = 1.

Then,

The density function of Y is given by:

P( 15 < Y ≤ 60)

or, P( 0.25 < Y ≤ 1)

So,  P( 0.25 < Y ≤ 1) = [tex]\int\limits^{1}_{0.25}{f(y) \, dy[/tex]

                                = [tex][y]^1 _ {0.25}[/tex]

                                = (1- 0.25)

                                = 0.75

Hence, The probability that the call arrived when the switchboard was not fully busy is 0.75.

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Which expression is equivalent to sqrt of (6x^5 z)^3/ 4x^4 z^2

Answers

Answer:

[tex]\frac{(6x^{5}z) ^{3} }{4x^{4} {z}^{2} } = \frac{216 {x}^{15}z^{3} }{4 {x}^{4} {z}^{2} } = \frac{4x ^{4} {z}^{2} (54x ^{11}z) }{4 {x}^{4} {z}^{2} } = 54 {x}^{11} z[/tex]

I hope I helped you^_^

How much state tax is withheld from $36,200 if the tax rate is 4%?

Answers

Answer:

$1448

Step-by-step explanation:

Tax=rate*amount=(4/100)*36200=1448

In a certain year Congress debated a bill. A poll of 1000 Americans indicated 401 opposed 293 favored 306 not sure. What is the probability that random person was in favor

Answers

So actually you have 100%
401 + 239 + 306 = 1000

Now 293 from the 1000 is favored,
So in pregnant is 293/1000 = 0.293
That’s also the probability to random person is favor (or 29.3% chance)

Which polynomial function is best represented by the graph?

ƒ(x) = –x(x – 1)4
ƒ(x) = x2(x + 1)3
ƒ(x) = x2(x – 1)3
ƒ(x) = x(x – 1)4

Answers

Answer: ƒ(x) = x2(x – 1)3

can anyone heelp me







b

Answers

Answer:

B. suggest that you and your boss schedule regular check-ins at lunchtime and at the end of the day

Step-by-step explanation:

It allows you to be ontask at your role (which you are hired for) while at the same time helps your boss know that you are on top of everything. It is the most polite option since you are setting professional boundaries but not complaining and showing frustrations.

(also so that your boss isn't micro-checking on you)

An employee makes $11.20 per hour but is getting a 6.5% increase. What is his new wage per hour to the nearest cent? His new wage per hour is?​

Answers

Answer:

11.93

Step-by-step explanation:

First find the amount of increase

11.20 *6.5%

11.20 *.065

0.728

Rounding to the nearest cent

.73

Add this to the original wage

11.20+.73

11.93

Determine the coordinates of the ordered pairs on the coordinate grid.

Answers

Answer:

A = (5,7)

B = (0, -1)

C = (-8, -3)

D = (5, -8)

Step-by-step explanation:

Answer:

A = (5, 7)

B = (0, -1)

C = (-8, -3)

D = (5, -8)

To do these problems, trace along in a straight line from the coordinate to the x- axis line and then to the y-axis line. Whatever number you reach will be part of the coordinate.

Hope this helped.

find the two intersection points

(x+1)^2 +(y+2)^2 = 16

3x+ 4y = 1
Show your steps please

Answers

Answer:

Our two intersection points are:

[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]

Step-by-step explanation:

We want to find where the two graphs given by the equations:

[tex]\displaystyle (x+1)^2+(y+2)^2 = 16\text{ and } 3x+4y=1[/tex]

Intersect.

When they intersect, their x- and y-values are equivalent. So, we can solve one equation for y and substitute it into the other and solve for x.

Since the linear equation is easier to solve, solve it for y:

[tex]\displaystyle y = -\frac{3}{4} x + \frac{1}{4}[/tex]

Substitute this into the first equation:

[tex]\displaystyle (x+1)^2 + \left(\left(-\frac{3}{4}x + \frac{1}{4}\right) +2\right)^2 = 16[/tex]

Simplify:

[tex]\displaystyle (x+1)^2 + \left(-\frac{3}{4} x + \frac{9}{4}\right)^2 = 16[/tex]

Square. We can use the perfect square trinomial pattern:

[tex]\displaystyle \underbrace{(x^2 + 2x+1)}_{(a+b)^2=a^2+2ab+b^2} + \underbrace{\left(\frac{9}{16}x^2-\frac{27}{8}x+\frac{81}{16}\right)}_{(a+b)^2=a^2+2ab+b^2} = 16[/tex]

Multiply both sides by 16:

[tex](16x^2+32x+16)+(9x^2-54x+81) = 256[/tex]

Combine like terms:

[tex]25x^2+-22x+97=256[/tex]

Isolate the equation:

[tex]\displaystyle 25x^2 - 22x -159=0[/tex]

We can use the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 25, b = -22, and c = -159. Substitute:

[tex]\displaystyle x = \frac{-(-22)\pm\sqrt{(-22)^2-4(25)(-159)}}{2(25)}[/tex]

Evaluate:

[tex]\displaystyle \begin{aligned} x &= \frac{22\pm\sqrt{16384}}{50} \\ \\ &= \frac{22\pm 128}{50}\\ \\ &=\frac{11\pm 64}{25}\end{aligned}[/tex]

Hence, our two solutions are:

[tex]\displaystyle x_1 = \frac{11+64}{25} = 3\text{ and } x_2 = \frac{11-64}{25} =-\frac{53}{25}[/tex]

We have our two x-coordinates.

To find the y-coordinates, we can simply substitute it into the linear equation and evaluate. Thus:

[tex]\displaystyle y_1 = -\frac{3}{4}(3)+\frac{1}{4} = -2[/tex]

And:

[tex]\displaystyle y _2 = -\frac{3}{4}\left(-\frac{53}{25}\right) +\frac{1}{4} = \frac{46}{25}[/tex]

Thus, our two intersection points are:

[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]

How many real solutions does this system of equations have? x2 +3 = y
3х — у+1 = 0

Answers

Answer:

Step-by-step explanation:

y = x²+3

y = 3x+1

x² + 3 = 3x +1

x² - 3x + 2 = 0

(x-2)(x-1) = 0

x = 2, 1

Two solutions

(2,7) and (1,4)

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