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The number a has to be greater than or equal to 1000.

As per the given data we have to determine that how large the number a has to be so that [tex]$$\int_a^{\infty} \frac{1}{1+x^2} \cdot d x < 0.001$$[/tex]

[tex]$$\Rightarrow \quad\left[\tan ^{-1}(x)\right]_a^{\infty} < 0.001$$[/tex]

[tex]$\Rightarrow \quad \tan ^{-1}(x)-\tan ^{-1}(a) < 0.001$[/tex]

[tex]$$\begin{array}{ll}\Rightarrow & \frac{\pi}{2}-0.001 < \tan ^{-1}(a) \\\\\Rightarrow & 1.5698 < \tan ^{-1}(a)\end{array}$$[/tex]

[tex]$$\begin{aligned}& \Rightarrow \quad \tan ^{-1}(a) > 1.5698 \\& \Rightarrow \quad a > \tan (1.5698)\end{aligned}$$[/tex]

[tex]$$\begin{aligned}& \Rightarrow \quad a > 999.999 \\& \Rightarrow \quad a \geqslant 1000\end{aligned}$$[/tex]

Therefore the answer is [tex]\quad a \geqslant 1000[/tex]

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The value of y in the given inequality 4y + 1/5 ≤ 4/5 is: y ≤ 3/20.

To solve any inequalities, apply the same knowledge used to solve a normal algebraic equation by isolating the value of the variable.

The given inequality is 4y + 1/5 ≤ 4/5. To solve for the value of y, follow the steps below:

4y + 1/5 ≤ 4/5 [given]

Subtract 1/5 from both sides of the inequality:

4y ≤ 4/5 - 1/5 [subtraction property of equality]

4y ≤ 3/5

Multiply both sides by 1/4:

4y × 1/4 ≤ 3/5 × 1/4

y ≤ (3 × 1) / (5 × 4)

y ≤ 3/20

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Monica was wrong she will get less interest than Paul as Paul has invested a higher Principal amount than Monica.

What is simple interest?

Simple interest is based on the principal amount of a loan or the first deposit in a savings account.

                         [tex]A = P (1 + rt)\\\\A $ = final amount$\\P $ = initial principal balance$\\r $ = annual interest rate$\\t $ = time (in years)$[/tex]

Given that:

For Monica:

Principal (p) = $400

Rate (r) = 4.3% = 0.043

Year (t) = 1 year

Deposit Paul:

Principal = $500

Rate (r) = 4.2%  = 0.042

Year (t) = 1 year

Now calculate the interest amount for Monica and Paul, we get

For Monica:

             A = P(1 + rt)

             A = 400(1 + (0.043 × 1))

             A = 417.2

             A = $417.20

Now for Monica, Interest will be

           I = A - P

             = 417.20 - 400

           I = 17.20 dollars -----------(II)

For Paul:

             A = P(1 + rt)

             A = 500(1 + (0.042 × 1))

             A = 521

             A = $521 dollars

Now for Paul, Interest will be

           I = A - P

             = 521 - 500

           I = 21 dollars ---------------(II)

From (I) and (II), we can say that Paul will earn more interest than Monica.

Hence, Monica was wrong she will get less interest than Paul as Paul has invested a higher Principal amount than Monica.

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After 8 years, the amount of money which Carl would have in the bank account is equal to $620.

Mathematically, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have the following;

S.I = 500 × 3/100 × 8

S.I = $120.

Now, we can calculate the future value (A) as follows;

Future value (A) = P + S.1

Future value (A) = 500 + 120

Future value (A) = $620.

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Answer: 170678

Step-by-step explanation:

try it and you'll see.

Thus ,the statement about overhead expenses which is true is option (B). .

In the business world, an ongoing expense of operating a business is known as overhead or an overhead charge .In contrast to operating costs like raw material and labor, overheads are expenses that cannot easily be connected to or associated with any one revenue unit.

Here,

the statement about overhead expenses  which is true is option (B).

Explanation :The costs of operating a firm that aren't directly connected to providing an item or service are referred to as overhead. These expenses might be either fixed, like rent, or variable, like transportation expenditures. Additionally, they may be semi-variable, like utilities. Thus contribute directly to the running of a business.

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If the regular box has dimensions l, w, and h, then the dimensions of the family value box would be 1.25l, 1.25w, and 1.25h. This means that the volume of the family value box would be 1.25 * 1.25 * 1.25 = 1.953125 times the volume of the regular box. Since the family value box is 25% larger in each dimension, its volume is nearly double the volume of the regular box.

The number of possible outcomes that do not show 1 on the first spinner and 4 on the second spinner is 2.

It is the total number of possible outcomes from a given set.

We have,

The sample space for when both the spinners are spun once.

S = {(1, 2, 3) x (3, 4, 5, 6)}

S = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 4), (3, 5), (3, 6)}

Now,

The number of total outcomes = 12

The number of outcomes that do not show 1 on the first spinner and 4 on the second spinner.

= {(2, 4), (3, 4)}

= 2

Thus,

The number of required possible outcomes is 2.

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Answer:

d=c/pi

Step-by-step explanation

divide by pi then d=c/pi

Answer:

C / pi = d

Step-by-step explanation:

The formula for circumference is

C = pi * d

To solve for d, divide each side by pi

C / pi = d

Step-by-step explanation:

5. the most significant challenge that small businesses face is financial problems.

In the early 1900s, many people in the United States were concerned that drinking alcoholic beverages was causing many problems in society. This concern led to the passage of the Eighteenth Amendment.

An unintended effect of the enactment of this amendment was an increase in The amount of organized crime.

The temperance movement, which believed that prohibiting the sale of alcohol would help alleviate poverty and other societal issues, worked for decades to create the Eighteenth Amendment.

Sadly, there was an unintended effect with the Eighteenth Amendment which was a rise in organized crime. This was because criminal gangs became obscenely rich and powerful from the sale of alcohol on the Black Market.

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The required value of y is obtained as -2.

The given system of equation can either have a unique solution, more than one solutions or no solution.

On this basis they are divided into two parts consistent and inconsistent.

A consistent system has one or more solutions while for an inconsistent system there are no solutions.

The given system of equations is as below,

4x - y = 10             (1)

x - 4 = y               (2)

Substitute the value of y from equation (2) into equation (1) to get,

4x - (x - 4) = 10

=> 3x + 4 = 10

=> 3x = 6

=> x = 2

Then, substitute x = 2 in  x - 4 = y  to get,

y = 2 - 4  = -2

Hence, the value of y for the given system of equations is -2.

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The dimension of the eigenspace corresponding to an eigenvalue is the number of linearly independent eigenvectors associated with that eigenvalue

What is Eigen Value?

Eigenvalues are a unique set of scalar values connected to a set of linear equations that are most likely seen in matrix equations. The characteristic roots are another name for the eigenvectors. It is a non-zero vector that, after applying linear transformations, can only be altered by its scalar factor.

It is not possible to determine the eigenvalues, their multiplicities, and the dimensions of the corresponding eigenspaces of the matrix g without more information about the matrix itself.

In order to find the eigenvalues of a matrix, you need to determine the values of the variables in the matrix and then solve the characteristic equation, which is obtained by setting the determinant of the matrix equal to zero.

The eigenvalues are the roots of the characteristic equation, and the multiplicity of an eigenvalue is the number of times it appears as a root.

The dimension of the eigenspace corresponding to an eigenvalue is the number of linearly independent eigenvectors associated with that eigenvalue.

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The population percentage of candies that are red: (0.141,0.447)

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The formula for the population proportion's confidence interval is: pz/2[p (1-p)/n]

Given:

- Number of samples: 34

10 red candies total.

The formula for the population proportion's confidence interval is: pz/2[p (1-p)/n]

Given:

- Number of samples: 34

10 red candies total.

Red candy prevalence in sample: p = 10/340.294

Level of significance: =1-0.95=0.05

Critical value: 1.96 for z / 2

The population percentage of red candies will now have the following 95% confidence interval estimate: 0.294 (1.96) [0.294(1-0.294)/34] 0.294 0.153, 0.294+0.153) (0.141.0. 447)

The population percentage of candies that are red: (0.141,0.447)

The complete question is : The data given to the right includes data from 34 ​candies, and 10 of them are red. The company that makes the candy claims that 29​% of its candies are red. Use the sample data to construct a 95​% confidence interval estimate of the percentage of red candies. What do you conclude about the claim of 29​%? Construct a 95 % confidence interval estimate of the population percentage of candies that are red.

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The required explanation of probability distribution that has a mean of 0 and a standard deviation of 1 is describe below.

Probability distributions help to show our reality, empowering us to get evaluations of the likelihood that a specific occasion might happen, or gauge the inconstancy of event. They are a typical method for depicting, and potentially foresee, the likelihood of an occasion

The mean of the z-scores is dependably 0. The standard deviation of the z-scores is dependably 1. The chart of the z-score dissemination generally has a similar shape as the first conveyance of test values. The amount of the squared z-scores is dependably equivalent to the quantity of z-score values.

Thus, it is dependable.

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Correct question:

A normal probability distribution can have any value of the mean or must have a standard deviation of 1 and a mean of 0?

ΔLMJ and ΔLKN are congruent by SAS congruence postulate.

What is SAS and ASA congruence rule for triangles?

SAS : If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

ASA : If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

According to the given question:

The pair of overlapping congruent triangles in the diagram are:

ΔLMJ and ΔLKN

Now,

LM ≅ LK (Given)

LN ≅ LJ (Given)

∠LJM = ∠LNK (Angles opposite to equal sides are equal)

∴ ΔLMJ ≅ ΔLKN by SAS congruence of triangles

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The number of sides of Alexandra's regular polygon is 12.

The number of sides of Maris's regular polygon is 15.

What is a regulars polygon?

A regular polygon is denoted a area. The area bounded by equal length of arms. The angel between any two consecutive arms will same any other pair of consecutive arms.

The number of line of symmetry of a polygon is the same is the number of arm or sides of that polygon.

Thus the number of sides of a polygon that has 12 lines of symmetry is 12.

The angle of rotational symmetry of a polygon is 360°/n, where n is the number of arms.

Therefore,

Angle of rotational symmetry = 360°/n

Putting Angle of rotational symmetry = 24°:

24° = 360°/n

Multiply both sides by n

24n = 360

Divide both sides by 24:

n = 360/24

n = 15

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Answer:

it would be C

hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that $6000 is deposited into an account earning 5.9% compounded quarterly, you want the values of P, r, n used in the future-value formula, and you want the value after 9 years.

The problem statement tells you the values:

  amount deposited = P = 6000

  interest rate = r = 5.9% = 0.059

  compounding periods in a year = n = 4

Using these numbers in the formula, you find (with t=9) ...

  S(9) = 6000(1 +0.059/4)^(4·9) ≈ $10164.30

By solving a system of equations we will see that they sold 35 advanced tickets and 30 same-day ones.

Let's define the variables we will be using for this problem, these are:

x = number of same advance tickets.

y = number of same-day tickets.

With the given information we can write a system of equations:

x*$25 + y*$20 =  $1,450

x + y = 65

To solve the system we can isolate x on the second equation:

x = 65 - y

Now let's replace that in the other equation:

(65 - y)*$25 + y*$20 =  $1,450

$1,625 - y*$5 =  $1,450

$1,625 - $1,450 = $5*y

$175/$5 = y

35 = y

Then the value of x is:

x = 65 - 35 = 30

So they sold 35 advanced tickets and 30 same-day ones.

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Answer:

117.12

Step-by-step explanation:

43.78+21.05 = 64.83

64.83+52.29 = 117.12

PA BRAINLIEST

Answer:

Step-by-step explanation:

To calculate the original price of the sweater, we first need to determine the amount of the discount. Since the sweater was 40% off, the discount was 40/100 * $21 = $8.40.

To find the original price of the sweater, we then need to subtract the discount from the sales price. Since the sales price was $21 and the discount was $8.40, the original price of the sweater was $21 - $8.40 = $<<21-8.4=12.60>>12.60.

However, since the problem states that the original price of the sweater was $35, we can conclude that the calculation above must be incorrect. To find the correct original price of the sweater, we need to divide the sales price by the discount percentage, rather than subtracting the discount amount from the sales price.

Using this method, we can calculate the original price of the sweater by dividing the sales price of $21 by the discount percentage of 40/100, which gives us $21 / (40/100) = $35. This is the correct original price of the sweater

The area of circle when π is 3.14 is 1017.36 inches².

What is the area of circle?

Area of the circle = πr²

= 3.14 * 18 * 18

= 3.14 * 324

= 1017.36 inches²

Hence, the area of circle when π is 3.14 is 1017.36 inches².

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Answer:

Savings Account

Investment Account

Since ,the amount is same in both jobs as valet and waiter thus the total amount of money he made is $538.9

Equation: a claim that two expressions with variable- and/or number-filled expressions are equivalent. Mathematical development has been sparked by the desire to find solutions to equations, which are really just questions.

Here,

Part A:

Jamal works as a valet made $10.25 an hour and an additional $50.10 in tips,

Thus number of hours be x

equation : 10.25x + 50.10 =0

or

Jamal works as a waiter made $6.75 an hour and an additional $125 in tips

equation : 6.75x + 125 = 0

Part B:

The total amount he made when both paychecks are same

=> 6.75x + 125 = 10.25x + 50.10

=> 10.25x-6.75x = 125-50.10

=>3.5x = 74.9

=>x=74.9/3.5 =21.4

Thus the total amount he made

10.25(21.4) + 50.1 = 269.45

and

Total amount = 2* 269.45=538.9

Since ,the amount is same in both jobs as valet and waiter thus the total amount of money he made is $538.9

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The reason why simple random sampling will be a good way to do the selection of bad books is; Option C: He will have a more representative sample if he chooses randomly

A simple random sample is defined as a randomly selected subset of a particular population. In this method of sampling, it will be noticed that each member of the population has an exactly equal chance of being selected.

The importance of simple random sampling is that it removes every form of bias as every member has an equal chance of being selected. Thus, it will give a good representation of what we want to research.

Now, in this case, since the librarian wants to check a sample of books from the library to get an idea of how many need replacing, it means that a random sampling method is good because;

He will have a more representative sample if he selects randomly as the definition earlier stated makes clear.

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Answer:

24 sides

Step-by-step explanation:

The interior angles of a polygon add up to 180(n-2) degrees, where n is the number of sides the polygon has. This means that to find the number of sides a polygon has, we can set up the following equation:

180(n-2) = 4320

Solving for n, we get:

n = (4320 + 360) / 180 = 24

Therefore, the polygon has 24 sides.

The sales price for the shirts in different countries are the following

Country. Price of shirt

4. European Union, is the best market for Mariee Josee’s shirts and this country also gives her most revenue.

We have given that,

Marie Josee makes famous custom shirts and sold it in Canada. The currency of Canada , CAD.

The price of shirt = $45 CAD

Now, we should find out the price of shirt in different countries.

Country Currency

Canada CAD

European Union EUR

Japan JPY

Australia AUD

1. one CAD = 1.3882 EUR

=> price of shirt in European Union = 45× 1.3882

= 62.469 EUR

2. one CAD = 0.0106 JPY

=> price of shirt in Japan = 45× 0.0106 =0.477 JPY

3. one CAD = 0.9314 AUD

=> price of shirt in Australia = 45× 0.9314

= 41.913 AUD

4. The country Currency which gives highest price of shirt in above list is better option for selling it. So, we see that the European Union country would it be the best market for Mariee Josee’s shirts. It gives best selling price for shirt

i.e 62.469 EUR.

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f(x)=-25x^4+3x^2+2 = f'(x)=-100x^3+6x

Take derivation

f'(x)=d/dx(-25x^4+3x^2+2)

Formula

f'(x)=d/dx(-25x^4)+d/dx(3x^2)+d/dx(2)

Formula

f'(x)=-25(4x^3)+3(2x)+0

f'(x)=-100x^3+6x

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