what is a 500 doller diposet for 20 years witha intrest rate of 2%

Choose a row or column and perform Gaussian Elimination to reduce the matrix to row/column echelon form.Once the matrix is in row/column echelon form, the determinant can be found by multiplying the diagonal elements.

Let's take the matrix

A =

[1, 2, 3]

[4, 5, 6]

[7, 8, 9]

Choose the first column and perform Gaussian Elimination to reduce the matrix to row echelon form:

A =

[1, 2, 3]

[0, -3, -6]

[0, -6, -12]

The determinant of the matrix is found by multiplying the diagonal elements, which in this case is (1)(-3)(-12) = 36.

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If f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0.

What is a function?

In mathematics, a function is a rule that assigns a unique output to each input in a set. A function is continuous if the output value changes smoothly as the input value changes, without any sudden jumps or breaks.

To prove that if f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0, we can use the intermediate value theorem.

The intermediate value theorem states that if a function f is continuous on a closed interval [a,b], and if y is any value between f(a) and f(b), then there exists at least one x in the interval [a,b] such that f(x) = y.

In our case, f is a function from [0,1] to R, which is a closed interval, and f is continuous on this interval. Therefore, the intermediate value theorem applies to f.

To prove that there exists an x in [0,1] such that f(x) = 0, we can use the intermediate value theorem with y = 0. Since 0 is between f(0) and f(1), the intermediate value theorem guarantees that there exists at least one x in [0,1] such that f(x) = 0.

Hence, if f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0.

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(a) The height of the slide is 34.64 feet .

(b) The angle of depression is θ = tan⁻¹(34.64/d)

(c) The interval for which the rider travels horizontally is (60 , 74.3) .

In the question ,

it is given that ,

the length of the ladder is = 40 feet .

the angle of elevation is 60° .

From the figure given below.

Part(a) :

Let the height of the slide be = h.

From the triangle ABC ,

Sin(60°) = h/l

So , h = 40×0.8660

h = 34.64 feet .

Part(b) :

let θ be the angle of depression .

So , From the triangle DEF ;

tanθ = DF/DE

tanθ = h/d

So , θ = tan⁻¹(34.64/d)

Part(c) :

Safety restrictions require the angle of depression of the slide to be no less than 25 and no more than 30° .

let  θ = 25° , then

tanθ = 34.64/d

So , tan25° = 34.64/d

d = 34.64/tan25°

d = 34.64/0.4663

Simplifying further ,

we get ,

d = 74.3 feet .

and θ = 30° , then

tan30° = 34.64/d

d = 34.64/tan30°

d = 34.64/0.5773

So , d = 60 feet .

So , the interval for which the rider travels horizontally is (60 , 74.3) .

Therefore , (a) The required height is 34.64 feet , (b) angle of depression is tan⁻¹(34.64/d) and (c) the interval is (60 , 74.3) .

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The possible values of B in the number line are option A, C, D and E

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically. As we move towards the right side of a horizontal number line, the numbers increase; as we move towards the left, the numbers decrease.

In this problem, the value of B is between 3 and 2 since B is located between them.

Checking the given options;

A = 2.5

This is possible because B can be at the middle between 2 and 3

B = 2/5

This fraction isn't possible because the value of B is greater than this.

C = 5 / 2

This fraction is possible because the decimal value is 2.5 which is the same as option A

D = 25 / 10

This fraction is also possible because the decimal value is 2.5 which is same as option A and C

E = 2.49

This is also a likely possibility as this can be approximated to 2.5

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Al's AGI is  $126,500.

What is gross income?

Before any deductions or taxes, gross income is the total of all wages, salaries, profits, interest payments, rentals, and other sources of income. It differs from net income, which is calculated as gross income less any applicable taxes and other deductions.

Here, we have

Given

Gross income of $140,000

Fewer Deductible expenses :

Alimony ($20,000)

Contribution to a traditional IRA ($6,000)

Expenses paid on rental property ($7,500)

AGI = Gross income - Contribution to a traditional IRA- Expenses paid on rental property

AGI = $140,000 - $6,000 - $7,500

AGI = $126,500.

Hence, Al's AGI is  $126,500.

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Answer:

Step-by-step explanation:

ok

alr

Answer:

below

Step-by-step explanation:

Largest angle = largest opposite side  ,  smallest angle = smallest opposite side

EF < ED <DF

Answer:

Step-by-step explanation:

You want to rewrite f(x) and differentiate it for f(x) = 6·ln(8/x).

The log of a ratio is the difference of logs:

  ln(a/b) = ln(a) -ln(b)

Using this to rewrite f(x), we have ...

  f(x) = 6ln(8/x) = 6(ln(8) -ln(x))

  f(x) = 6·ln(8) -6·ln(x)

The derivative of the constant is zero, so ...

  f'(x) = -6/x

The critical values for the following sample are ±2.0064.

Here it is given that α = 0.05,

To calculate the critical values we will use the t-statistic.

Here n₁ = 25 and n₂ = 30

Hence, the degrees of freedom

d.f = n₁ + n₂ - 2           [Since it's a 2-sample test]

= 25 + 30 - 2

= 53

Now our significance level is  α = 0.05,

To know the critical value we will make use of a t-distribution table and look up the value corresponding to a 0.05 significance level and 53 degrees of freedom.

Here we will get the critical values ±2.0064

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The function represents f ( x ) is f ( x ) = 32 ( 3x - 1 )

Given :

The table represents some points on the graph of linear function f.

Table :

x        -2         1        5       10

f ( x ) -224   64     448   928

take two points ( 5 , 448 ) and ( 1 , 64 )

slope m = 64 - ( 448 ) / 1 - ( 5 )

= 64 - 448 / 1 - 5

= -384 / -4

= 384 / 4

= 192 / 2

= 96

( 1 , 64 ) on

y -  64 = 96 ( x - 1 )

y - 64 = 96x - 96

y = 96x - 96 + 64

y = 96x - 32

take 32 as common

= 32 ( 3x - 1 )

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The value of f(2000 , 20) is $6640.24   and the interpretation is "if 2000 was invested initially then $6640.24 will be the amount after 20 years"  .

In the question ,

it is given that,

the future value (S) on investment earning is compounded continuously at 6% .

the function of the principal P and the length of time t that the principal has been invested is given by

S = f(P, t) = P×[tex]e^{0.06 \times t}[/tex]

to find f(2000 , 20) ,

we substitute P = 2000 and t = 20 ,

we get ,

f(2000 , 20) = 2000×[tex]e^{0.06 \times 20}[/tex]

Simplifying further ,

we get ,

= 6640.2338

≈ 6640.24

Its interpretation is "if 2000 was invested initially then $6640.24 will be the amount after 20 years .

Therefore , the value of f(2000 , 20) is $6640.24  .

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The monthly payment required into the annuity with an APR of 8.0% compounded annually and you wish to reach your savings goal in 30 years is $156.19.

The monthly payment is required for 360 months (30 years x 12).

We can compute this periodic payment using an online finance calculator by inputting the parameters below:

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 8%

PV (Present Value) = $0

FV (Future Value) = $220,000

P/Y (# of periods per year) = 12

C/Y (# of times interest compound per year) = 1

Results:

Monthly Payments (PMT) = $156.19

Sum of all periodic payments = $56,228.40

Total Interest = $163,771.60

Thus, to reach a future value of $220,000, the monthly annuity deposit should be $156.19 for 30 years at 8%.

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Assuming no employees are subject to ceilings for their earnings IS $7,450

The computation of Salaries Payable is shown below:-

Gross Payroll $10,000

Less:

Federal income tax withheld $1,800

Social security rate at 6% -$600

Medicare rate at 1.5% -$150

Total deduction -$2,550

Salary Payable $7,450

We simply deduct three above taxes from the gross payroll so that we get to know for the salary payable amount

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The tanθ  for the angle θ that lies in Quadrant III is √35

Trigonometry simply means the branch of mathematics that is concerned with functions of angles as well as their applications to calculation. It also deals with the relationship between ratios and their angles.

Given: The angle θ lies in Quadrant III

cosθ= −1/6 (adjacent/hypotenuse)

adjacent = -1 and hypotenuse = 6

We can draw the position of the angle as shown in the image attached.

Using Pythagoras' theorem:

opposite = √6²-(-1)² = √35

tanθ = (-√35) / (-1) = √35       (tanθ = opposite/adjacent)

Note: opposite in  Quadrant III is negative

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The answer to this integration is - [tex]\frac{u^{7} }{28} + c[/tex] .

u = 3 + x⁴

differentiate both sides,

⇒ du = 0 + 4x³ dx

⇒ du = 4x³ dx

⇒[tex]dx = \frac{du}{4x^{3} }[/tex]   ..........(1)

The integration is :

[tex]\int x^{3} ( 3 +x^{4} )^{6} dx[/tex]

Substitute the values from equation (1)

= [tex]\int x^{3} u^{6} \frac{du}{4x^{3} }[/tex]

= [tex]\frac{1}{4} \int u^{6} du[/tex]

=[tex]\frac{1}{4} . \frac{u^{7} }{7} + c[/tex] ( c = integration constant )

= [tex]\frac{u^{7} }{28} + c[/tex]

Hence, the answer to this integration is - [tex]\frac{u^{7} }{28} + c[/tex] .

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If x and y be  i.i.d. unif(0, 1), then the covariance of x + y and x - y is zero

Here  x and y be i.i.d. unif(0, 1)

The i.i.d stands for independent and identically distributed

unif means that the uniformly distributed

Here x and y are i.i.d unif (0,1)

The covariance is defined as the relationship between the two random variables . Therefore, variance of one variable is equal to the change in another variable

Here we have to find the covariance of x + y and x - y

According to the properties of covariance

Cov(x+ y, x - y) = Cov (x, x) + Cov(y, x) - Cov(x, y) - Cov(y, y) = 0

Because Cov(x, x) = Cov (y, y)

Cov(y, x) = Cov(x, y)

Therefore, the covariance of x+y and x - y is 0

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capital accumulation is 3,973,910.14.

To evaluate the definite integral, we will have to find the indefinite integral. We use integral by substitution to find the indefinite integral.

Capital Accumulation = ∫ dI/dt dt

= ∫ 16,000t (t^2 + 2)^2dt

If u = t^2 + 2 then du = 2t dt so the integral is

Capital accumulation = ∫ 16,000t (t^2 + 2)^2 dt

= ∫ 16,000 × (u - 2) × u^2 du/2

= ∫ 16,000u^3 - 64,000u^2 + 64,000udu/2

= 8,000u^4/4 - 32,000u^3/3 + 32,000u^2/2 + C

= 2,000u^4 - 10,667.7u^3 + 16,000u^2 + C

Substituting u again gives us:

Capital Accumulation = 2,000(t^2 + 2)^4 - 10,667.7(t^2 + 2)^3 + 16,000(t^2 + 2)^2 + C

To evaluate the definite integral, we need to find the values ​​of this expression at t=0 and t=5 and subtract the two.

Capital Accumulation = [2,000(5^2 + 2)^4 - 10,667.7(5^2 + 2)^3 + 16,000(5^2 + 2)^2] - [2,000(0^2 + 2)^4 - 10,667.7(0^2 + 2)^3 + 16,000(0^2 + 2)^2]

= [2000(27)^4 - 10667.7(27)^3 + 16000(27)^2] - [2000(2)^4 - 10667.7(2)^3 + 16000(2)^2]

= 4,607,143.47 - 1,333,333.33 + 691,200

= 3,973,910.14

Therefore, the five-year capital accumulation is 3,973,910.14.

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Answer:

60% because the total should be 100% and if you take 40% away you should be left with 60%

The value of each company's product sold price is given as follows:

The values of each company's product sold price is obtained using a system of equations, for which the variables are defined as follows:

The sold sum of both the two companies salaries are $44,000,000, hence:

x + y = 44000000.

The sold price of company x is 1000 more than the other, hence:

x = 1000 + y.

Then the sold price of company y can be found replacing the second equation into the first, as follows:

1000 + y + y = 44000000

2y = 44000000 - 1000

y = (44000000 - 1000)/2

y = $21,999,500.

The sold price for company x is then calculated as follows:

x = 1000 + y = 1000 + 21999500 = $22,000,500.

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Answer:

Step-by-step explanation:

probability ≤|1|

or -1≤ probability ≤1

Answer:

No

Step-by-step explanation:

The sum of the probabilities in a probability distribution is always 1.

If the perimeter of the rectangle is 48 cm, its length and width is equal to 16 cm and 8 cm respectively.

Mathematically, the perimeter of a rectangle can be calculated by using this equation;

P = 2(L + W)

Where:

Since the length is twice the​ width, we have;

L = 2W

Substituting the given parameters into the perimeter formula, we have;

48 = 2(2W + W)

48 = 6W

W = 48/6

Width, W = 8 cm.

For the length of this rectangle, we have;

L = 2W

L = 2(8)

L = 16 cm.

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They sold $479 in ticket sales and they had a total of 297 tickets sold, so they must have sold $479/297 = $<<479/297=1.61>>1.61 per ticket.

There are two types of tickets, adult tickets and student tickets, and adult tickets are $3, so the student tickets are $1.61 - $3 = $<<1.61-3=-1.39>>-1.39.

However, a ticket cannot be negative so we know that all of the tickets must have been adult tickets and they sold 297 tickets for $479, so they sold 297 tickets * $3/ticket = $<<297*3=891>>891 worth of adult tickets. Answer: \boxed{891}.

The interval containing the middle-most76% of sample means  [tex]102.836 < \mathrm{x} < 137.164[/tex].

As per the data given in the above question,

A distribution of values is normal with a mean of [tex]\mu=120[/tex].

A standard deviation of [tex]\sigma=21[/tex].

Drawing samples of size n=13.

The middle-most76% of sample means.

Find the interval containing the middle-most76% of sample means?

[tex]\mathrm{P}(-\mathrm{z} < \mathrm{x} < \mathrm{z})=0.76\\\mathrm{P}(\mathrm{x} < \mathrm{z})-\mathrm{P}(\mathrm{x} < -\mathrm{z})=0.76\\[/tex]

Further

[tex]\mathrm{P}(\mathrm{x} < -\mathrm{z})=\mathrm{P}(\mathrm{x} > \mathrm{z})[/tex]

[tex]\mathrm{P}(\mathrm{X} < \mathrm{Z})-\mathrm{P}(\mathrm{X} > \mathrm{Z})=0.76\\\mathrm{P}(\mathrm{X} < \mathrm{Z})-1+\mathrm{P}(\mathrm{X} < \mathrm{Z})=0.46\\2 \mathrm{P}(\mathrm{X} < \mathrm{Z})=1.76\\\mathrm{P}(\mathrm{X} < \mathrm{Z})=0.88[/tex]

[tex]= NORMSINV (0.73)\\\mathrm{Z}=0.613[/tex]

[tex]& \mathrm{X}=\mathrm{z} \sigma+\mu \\& \mathrm{X}=0.613 \times 28+120 \\& \mathrm{X}=137.164-\mathrm{x} & =\mu-\mathrm{z} \sigma \\-\mathrm{x} & =120-0.613 \times 28 \\-\mathrm{x} & =102.836[/tex]

Now the interval sample is as follow,

[tex]102.836 < \mathrm{x} < 137.164[/tex]

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0.2019 is a fraction of the toasters that can be expected to fail during the fourth year of use  for  the given statistical studies

As it is the fraction of toasters that can be expected to fail during the fourth year of use. This is determined from a statistical study, which indicates that the fraction of electric toasters manufactured by a certain company that is still in working condition after t years of use is approximately 0.3012. To calculate the fraction of toasters expected to fail during the fourth year of use, we simply subtract 0.3012 from 1, which gives us 0.2019. This means that, according to the statistical study, approximately 20% of the electric toasters manufactured by the company can be expected to fail during the fourth year of use.

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Answer:

19 and 20

Step-by-step explanation:

Take the square root of 389

[tex]\sqrt{389} = 19.723...[/tex]

The median represents here as, Option B; More  than half the police officers wrote this number of tickets.

Given,

A police department collected the statistics for the number of tickets police officers wrote each day over the last 6 weeks.

Mean =5.23

Median =3

Mode =2

We have to find the representation of median in this situation;

Median;-

The value that, when a dataset is arranged, falls exactly in the middle is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.

Here,

The median 3 represents that, More than half the police officers wrote this number of tickets.

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Evaluation of the integral is  [tex]\frac{81}{16}[/tex]

In mathematics, an integral is either a definite value representing the region under a function's graph for a certain interval or a new function whose derivative represents the original function (indefinite integral). The fact that a definite integral of any function that can be integrated may be found using the indefinite integral and a corollary to the calculus fundamental theorem connects these two interpretations.

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There is an imbalance between males and females, with a ratio of 1.5 men to every woman in the population.

Which age structure diagram represents a population's ages the best?

Hence, there is an imbalance between males and females, with a ratio of 1.5 men to every woman in the population.

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decision tree and neutral network

What is decision tree?

The most effective and well-liked technique for categorization and prediction is the decision tree. A decision tree is a type of tree structure that resembles a flowchart, where each internal node represents a test on an attribute, each branch a test result, and each leaf node (terminal node) a class label.

A model is an automatic flexible non linear regression model not interpretable and retains all predictor variables although it may limit the effect of some decision tree

A model is handles outliers well handle many potential predictor variable easy and short through predictor variables repeatedly to divide the data into group to best determine the response variable is  neutral network

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a) Six-week learning and memory test: Both groups had a six-week learning and memory test.

b) According to Table A, the first five ginkgo trees are 103, 105, 107, 108, and 109.

(A) By randomly allocating people to treatment & control groups, randomized controlled trials are a form of experimental investigation that seeks to reduce bias. In this instance, the treatment group took tablets containing ginkgo extract, whereas the control group took pills containing a placebo. Prior to the initiation of therapy & again after six weeks, both groups underwent memory and learning tests.

The experiment's design may be summarized as follows:

Choosing the research population is folks over 60 who are in good health

Calculate the sample size: 230 people

Place individuals in control and treatment groups at random: The ginkgo group received half of the participants, while the placebo group received the other half.

Administering care: Pills containing ginkgo extract were given to the ginkgo group, whereas placebo pills were given to the placebo group.

Prior to starting therapy, both groups had their learning and memory skills tested.

Both groups underwent learning and memory ability tests six weeks later.

(b) According to the basic random sample applet, the first 20 members of the ginkgo Biloba subpopulation are:

11, 13, 15, 16, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35

first 20 subjects using a placebo Those that participated are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 23, 31, 36, 37, 38, 39, and 40. 

5 people: 103, 105, 107, 108, and 109

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