QUESTION 5 - 1 POINT
An investment of $32,000 is worth $38,302 after being compounded monthly at 3%. How many years was the investment
for? (Round to the nearest whole year).

Answers

Answer 1

9514 1404 393

Answer:

  6

Step-by-step explanation:

The compound interest formula tells you the future value of principal P invested at annual rate r compounded n times per year for t years is ...

  A = P(1 +r/n)^(nt)

Solving for t, we get ...

  t = log(A/P)/(n·log(1 +r/n))

Using the given values, we find t to be ...

  t = log(38302/32000)/(12·log(1 +0.03/12)) ≈ 5.9997

The investment was for 6 years.


Related Questions

there are 10 crates of eggs stacked in the corner. each crate of eggs holds 20 eggs. If there is only 1 broken egg in the entire stack of crates, what percent of the crates have broken eggs in them?

Answers

Answer: 5%

Step-by-step explanation: If there is one broken egg in each crate (1/20), you would change that to5%

And if there are ten crates, then you see how many eggs there a re total.

(10 × 20 = 200)

If there are 200 eggs and for every 20 eggs there is on broken one, then there will be 10 broken eggs total. or 10/200

convert the fraction to a decimal ( 10 ÷ 200 = .05)

then convert the decimal to a percent. .05 is equal to 5%

PLEAZE RATE BRAINLIEST!!!

Do 8 plz find OS thanks​

Answers

Answer:

OS = 10

Step-by-step explanation:

We can use a ratio to solve

QP     PR

-----  = ------

QO     OS

14          7

-----   = -------

14+6      OS

14          7

-----   = -------

20        OS

Using cross products

14 * OS = 7*20

14 OS = 140

Divide by 14

OS = 140/14

OS = 10

The answer above should be Cortes you

Plz help me find sides M and N round to the nearest tenth​

Answers

Answer:

44

Step-by-step explanation:

gradpoint

Describe the domain and range of the graph

Answers

Domain={-5,4}

Range={-3,4}

A jar of gumballs contains 4 reds, 2 greens, and 6 blues. What is the probability of getting two blues in a row without replacement?

Select one:
a. 3/4
b. 1/2
c. 5/22
d. 5/11

Answers

Answer:

C

Step-by-step explanation:

Hypergeometric distribution

[tex]\frac{{6\choose2}}{{12\choose2}}=\frac{15}{66}= \frac{5}{22}[/tex]

Use the hyper geometric distribution to get your answer but the answer is c. 5/11

Consider the sequence {an}={3n+13n−3n3n+1}. Graph this sequence and use your graph to help you answer the following questions.

Answers

Part 1: You can simplify [tex]a_n[/tex] to

[tex]\dfrac{3n+1}{3n}-\dfrac{3n}{3n+1} = \dfrac1{3n}+\dfrac1{3n+1}[/tex]

Presumably, the sequence starts at n = 1. It's easy to see that the sequence is strictly decreasing, since larger values of n make either fraction smaller.

(a) So, the sequence is bounded above by its first value,

[tex]|a_n| \le a_1 = \dfrac13+\dfrac14 = \boxed{\dfrac7{12}}[/tex]

(b) And because both fractions in [tex]a_n[/tex] converge to 0, while remaining positive for any natural number n, the sequence is bounded below by 0,

[tex]|a_n| \ge \boxed{0}[/tex]

(c) Finally, [tex]a_n[/tex] is bounded above and below, so it is a bounded sequence.

Part 2: Yes, [tex]a_n[/tex] is monotonic and strictly decreasing.

Part 3:

(a) I assume the choices are between convergent and divergent. Any monotonic and bounded sequence is convergent.

(b) Since [tex]a_n[/tex] is decreasing and bounded below by 0, its limit as n goes to infinity is 0.

Part 4:

(a) We have

[tex]\displaystyle \lim_{n\to\infty} \frac{10n^2+1}{n^2+n} = \lim_{n\to\infty}10+\frac1{n^2}}{1+\frac1n} = 10[/tex]

and the (-1)ⁿ makes this limit alternate between -10 and 10. So the sequence is bounded but clearly not monotonic, and hence divergent.

(b) Taking the limit gives

[tex]\displaystyle\lim_{n\to\infty}\frac{10n^3+1}{n^2+n} = \lim_{n\to\infty}\frac{10+\frac1{n^3}}{\frac1n+\frac1{n^2}} = \infty[/tex]

so the sequence is unbounded and divergent. It should also be easy to see or establish that the sequence is strictly increasing and thus monotonic.

For the next three, I'm guessing the options here are something to the effect of "does", "may", or "does not".

(c) may : the sequence in (a) demonstrates that a bounded sequence need not converge

(d) does not : a monotonic sequence has to be bounded in order to converge, otherwise it grows to ± infinity.

(e) does : this is true and is known as the monotone convergence theorem.

In a class there are 400 students. 250 of them studying Mathematics, 150 of them studying English, 100 of them studying Biology, 100 of them studying both Mathematics and English, 60 of them studying both Mathematics and Biology, 40 of them studying both English and Biology, 30 of them studying all Mathematics, English and Biology. Find
a) The number of students who are studying only Mathematics.
b) The number of students who are studying only English.
c) The number of students who are studying only Biology.
d) The number of students who are studying none of Mathematics, English and Biology.​

Answers

I hope this helps and sorry if it's wrong

how to work this problem 736.5 x .78

Answers

Answer=. 736.5 x .78 =574.47

!!!!!!!!PLEASE HELP NOW !!!!!!!!!!!!!!!!!!
What is the following product?
45 47 47.45
4(977)
O AN
74
7

Answers

Answer:

7

Step-by-step explanation:

You can convert the fourth square roots to [tex]7^{\frac{1}{4}}} * 7^{\frac{1}{4}}} * 7^{\frac{1}{4}}} * 7^{\frac{1}{4}}}[/tex]. Using the product of powers rule, we can add the four terms' exponents, resulting in [tex]7^1[/tex], which is 7.

The distance, y, in miles, traveled by a car in a certain amount of time, x, in hours, is shown in the graph below:

A graph titled Motion of Car is shown with Time in hours labeled on x-axis and Distance from Starting Point in miles labeled on y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, and the scale on the y-axis shows the numbers 0, 14, 28, 42, 56, 70, 84. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 3, 42. The second straight line joins 3,42 and 4,42 and the third straight line joins ordered pair 4,42 with the ordered pair 5,56.

Which of the following best describes the motion of the car shown?

It travels for 2 hours, then stops for 1 hour, and finally travels again for 5 hours.
It travels for 3 hours, then stops for 1 hour, and finally travels again for 1 hour.
It travels for 3 hours, then stops for 4 hours, and finally travels again for 5 hours.
It travels for 2 hours, then stops for 2 hours, and finally travels again for 1 hour.

Answers

Answer:

The last choice

Step-by-step explanation:

:)

please answer all the questions and get 15 pts

Answers

Answer:

Here you go

Ans is in pictures.

The entire graph of the function g is shown in the figure below.
Write the domain and range of g as intervals or unions of intervals.

Answers

Step-by-step explanation:

here's the answer to your question

What is the vertex of the graph of y = 2(x + 5)2 - 2?

Answers

Answer:

The vertex is (-5, -2)

Step-by-step explanation:

y = 2(x + 5)^2 - 2

The vertex form of a parabola is

y =a(x-h)^2 +k  where (h,k) is the vertex

y = 2(x  -  -5)^2 - 2

The vertex is (-5, -2)

(0,18) might be correct

The jury pool for the upcoming murder trial of a celebrity actor contains the names of 100,000 individuals in the population who may be called for jury duty. The proportion of the available jurors on the population list who are Hispanic is .40. A jury of size 12 is selected at random from the population list of available jurors. Let X = the number of Hispanics selected to be jurors for this jury.

a. What is the expected number of hispanic jurors being on the jury?
b. What is the expected value (or theoretical mean) of a great earthquake off the coast of Oregon in two years?
c. Use the poisson distribution to appropriate the probability that there will be at least one major earthquake in the next two years.

Answers

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Have a Spanish Jury possibility[tex]= 0.40[/tex]

Jury member No. to be chosen[tex]= n= 12[/tex]

Hispanic Juror Expected [tex]= np = 12\times 0.40 = 4.8[/tex]

The jury group will be constituted by Hispanic Jurors [tex]4.8[/tex]

OR

The binomial distribution defines the behavior of a count variable X, provided:

There are a set number of data points n.

Set [tex]n=12[/tex]

Each perception is independent. This will not affect others if your first juror is selected

One of two results is that each observation ("success" or "failure"). English or not

Each result has the same chance of "success" p. for every [tex]p=0.40[/tex]

Well by the binomial distribution. Mean[tex]=E(x)=np=4.8[/tex]

Find x please step by step explanation need it

Answers

Answer:

37.3

Step-by-step explanation:

19tan(63) = x = 37.289... = 37.3

The radius of a circular disk is given as 26 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (Round your answer to two decimal places.) cm2 (b) What is the relative error

Answers

Answer:

(a) Hence the maximum error in the calculated area of the disk is 32.67[tex]cm^{2}[/tex].

(b) Hence the relative error is 1.54%.

Step-by-step explanation:

Here the given are,

The Radius of the circle r = 26cm.

The maximum error in measurement dr = 0.2 cm.

Answer:

(a) [tex]A =(4245.28\pm32.66) cm^2[/tex]

(b) [tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]

Step-by-step explanation:

radius, r = 26 cm

error = 0.2 cm

(a) The area of the disc is given by

[tex]A = \pi r^2\\\\dA = 2\pi r dr\\\\dA = 2 \times 3.14\times 26\times 0.2= 32.66[/tex]

Now

A = 3.14 x r x r = 3.14 x 26 x 26 = 4245.28 cm^2

So, the area with error is given by

[tex]A =(4245.28\pm32.66) cm^2[/tex]

(b) The relative error is

[tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]

If angle ACB is congruent, and angle BAC=3x-10, angle ECD=45 and angle EDC=2x+10 what is x?

Answers

Answer:

x=20

Step-by-step explanation:

Since BAC and EDC are the same (ACB and DCE are congruent), 2x+10=3x-10, x=20



A student writes
2
pages of a report in
2
an hour. What is her unit
rate in pages per hour?

Answers

Answer:

1 page of a report per hour

Step-by-step explanation:

2/2= 1 page per hour

A student rights 2 pages of report in 2 an half hour

Lets find unit rate

[tex]\\ \sf\longmapsto \dfrac{2\dfrac{1}{2}}{2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{5}{2}\div 2[/tex]

[tex]\\ \sf\longmapsto \dfrac{5}{4}[/tex]

[tex]\\ \sf\longmapsto 1.2pages/hour[/tex]

ASAP!!!!!! SHOW WORK!!!! Thank you

Answers

Answer:

y = -6

Step-by-step explanation:

If the three points are collinear, the slopes of RS and ST are same:

m(RS) = (4 - 8)/(1 + 1) = -4/2 = -2m(ST) = (y - 4)/(6 - 1) = (y - 4)/5

Since the sloes are equal we have the following equation:

(y - 4)/5 = -2y - 4 = -10y = -10 + 4y = -6

Slopes must be equal

slope of RS

m=4-8/1+1m=-4/2m=-2

Now

Slope of ST=-2

y-4/6-1=-2y-4/5=-2y-4=-10y=-10+4y=-6

Diane bought new headphones originally listed for $70.99. They are 25% off. Which equation can be used to find the amount Diane will save?

Answers

Step-by-step explanation:

100% = $70.99

there is a discount of 25%.

that means 75% (100 - 25) of the original price remains.

the equation to get any x% amount of a 100% total is simply

x% amount = 100% total amount × x/100

25% = 70.99 × 25/100 = $17.75

What are the x-intercepts of this quadratic function?
g(x) = -2(x - 4)(x + 1)

Answers

Answer:

4 and -1

Step-by-step explanation:

A quadratic function is given to us and we need to find the x Intercepts of the given function . The function is ,

[tex]\bf \implies g(x) = -2( x -4)(x+1)[/tex]

Step 1 : Equate the function with 0,

[tex]\bf \implies -2( x -4)(x+1) = 0 [/tex]

Step 2: Equating with 0 :-

Now equate each factors seperately with 0 , to get the x Intercepts.

Step 3: Finding the intercepts :-

[tex]\bf \implies x - 4 = 0 \\\\\implies\boxed{\bf\blue{ x = 4 }} [/tex]

Again ,

[tex]\bf \implies x + 1 = 0 \\\\\implies\boxed{ \blue{\bf x = -1}} [/tex]

Hence the x intercepts are 4 and -1 .

Answer:D (4,0) and (-1,0)

Step-by-step explanation:

I’m so confused. Need the help

Answers

1.621 kN

Step-by-step explanation:

Let the centerline of the canal be the x-axis. Because the forces exerted by the horses are symmetric to the centerline, only the x-components of these forces contribute to the resultant force on the barge, i.e., the y-components cancel out. Each x-component is equal to [tex]F_x = 839\cos 15[/tex] = 810.4 N. Therefore, the resultant force on the barge is twice this:

[tex]F_{net} = 2(839\:\text{N})\cos 15 = 1620.8\:\text{N}[/tex]

[tex]= 1.621\:\text{kN}[/tex]

a family has two children. what is the probability that both are girls, given that at least one is a boy

Answers

Answer: The probability would be zero

Step-by-step explanation:

There are two children and one is a boy, so the probability of both being girls is a zero

3/4 divided by 1/2

multiple choices
2/3
1 1/4
1 1/2
3

please hurry and choose between those

Answers

Answer:

Step-by-step explanation:

Will give brainliest answer

Answers

Answer:

Step-by-step explanation:

A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.​

Answers

Try the answer vertex

A line has a slope of -5 and
passes through the point
(0, -7). What is its equation in
slope-intercept form?
Write your answer using integers,
proper fractions, and improper
fractions in simplest form.

Answers

Answer:

y = -5x - 7

Step-by-step explanation:

All the information is given in the question lol

Help please :c
What is the probability that a randomly selected student from your group is a 9th grader?
What is the probability that a randomly selected student from your group prefers comedy?
What is the probability that a randomly selected student does not prefer action?
What is the probability that a student prefers comedy, given that the student is in the 10th grade?
What is the probability that a student does not prefer action, given that the student is in 9th grade?

Answers

Answer:

1/4

3/8

5/8

2/5

Step-by-step explanation:

From the table :

1.)

P(9th grade) = (9th grade total / total) = 4 / 16 = 1/4

2.)

P(comedy) = (comedy total / total) = 6 / 16 = 3/8

3.)

P(not action) = 1 - P(action) = 1 - (action total / total) = (1 - 6/16) = 1 - 3/8 = 5/8

4.)

P(comefy | 10th grade) = P(comedy n 10th grade) / P(10th grade) = 2 / 5

Answer:

The answer is 12

Step-by-step explanation:

help with num 9 please. thanks​

Answers

Answer:

See Below.

Step-by-step explanation:

We want to show that the function:

[tex]f(x) = e^x - e^{-x}[/tex]

Increases for all values of x.

A function is increasing whenever its derivative is positive.

So, find the derivative of our function:

[tex]\displaystyle f'(x) = \frac{d}{dx}\left[e^x - e^{-x}\right][/tex]

Differentiate:

[tex]\displaystyle f'(x) = e^x - (-e^{-x})[/tex]

Simplify:

[tex]f'(x) = e^x+e^{-x}[/tex]

Since eˣ is always greater than zero and e⁻ˣ is also always greater than zero, f'(x) is always positive. Hence, the original function increases for all values of x.

Now suppose that not every player can play in every position. The outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch. Suppose a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers.
How many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled?

Answers

Answer:

The team can assign field positions to 9 of the 19 players in 181,440 different ways.

Step-by-step explanation:

Since the outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch, supposing a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers, to determine how many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled, the following calculation must be performed:

3 x 7 x 6 x 5 x 4 x 3 x 4 x 3 x 2 = X

21 x 30 x 12 x 24 = X

630 x 12 x 24 = X

181,440 = X

Therefore, the team can assign field positions to 9 of the 19 players in 181,440 different ways.

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