The water tank at the institution is
full. A water truck begin to full the tank with
water at a rate of 8 litres per minute. After 15 minutes the tank was 5/2 full. Calculate
the number of litres of water that the tank can hold

The Green's function that solves the problem on a semicircular region is given by G(x, xo) = მ (x-xo)(cos(θ)sin(θ)).

What is Green's function?

Green's function is an important mathematical tool used to solve differential equations. It is defined as a solution to a homogeneous linear differential equation with a source, or delta, function as its input. Green's functions are also known as impulse response functions and can be used to describe the response of a system to an arbitrary input. Green's functions provide a way to solve differential equations without having to solve the entire equation all at once. They are particularly useful for solving equations with boundary conditions that are difficult to solve without the use of Green's functions. Green's functions can also be used to solve integral equations and provide a powerful tool for solving many physical problems.

The reflection method for finding a Green's function for a problem on a semicircular region can be used as follows. First, we solve the problem on the half-plane by finding a Green's function G(x, xo) that satisfies the boundary conditions given. Then, we reflect the solution across the boundary of the semicircle, namely T1 and T2, to obtain the Green's function on the entire semicircle.
The Green's function on the half-plane is given by G(x, xo) = მ (x-xo). Using this solution, we can reflect it across the boundary of the semicircle. For T1, the reflected solution is given by G(x, xo) = მ (x-xo)cos(θ), where θ is the angle between the normal vector to T1 and the vector from xo to x. For T2, the reflected solution is given by G(x, xo) = მ (x-xo)sin(θ), where θ is the angle between the normal vector to T2 and the vector from xo to x.
Therefore, the Green's function that solves the problem on a semicircular region is given by G(x, xo) = მ (x-xo)(cos(θ)sin(θ)).

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Answer:

Rate= I*100/P*T

R= 1120 * 100/2000*7

R= 112000/14000

R= 8%

Answer:

Domain: 0<=x<=500

Range: 0<=y<=250

Step-by-step explanation:

I'm not sure if this is what you asked for. She spend 2 minutes reading 1 page, there are 250 pages, therefore: 250*2=500

the range is simply the total pages

Hope this help!

The function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.

Given, the lifetime X of a certain brand of sixty-watt light bulb is exponentially distributed with population mean 1000 hours.

That is, 5.231(e/1000)f(x) x > 0. I

f 30 light bulbs having this lifetime distribution are placed on test.

we have to find the probability that 10 or fewer of these light bulbs survive to time 1200.

as, we have to find the expression for the function f(x) so that 10 or fewer of the given light bulbs survive to time 1200.

f(x) = 1/1000×e^(-x/1000)

So, the function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.

Hence, the function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.

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The rate of change of the average price of the new car is $274.50 per year.

The rate of change of the average price of the new car is a function of the change in average price over the years and the change in the number of years.

Rate of change = change in the average price / change in the number of years

Rate of change = (price in 2002 - price in 1994)  / difference in the number of years

Rate of change = (19,126 - 16,930) / (2002 - 1994)

Rate of change = 2196 / 8

Rate of change = $274.50

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Answer:

Prime numbers are odd that are greater than 2. Prime numbers are numbers that are not divisible by anything. EXAMPLE: 33 is not prime because if you take 3 times 11 then you get 33.

Step-by-step explanation:

Answer:

5/12 of a pizza

Step-by-step explanation:

The required solutions following the sequence are given as,
(a) By the distance formula,
(b) By the addition of property,
(c) By the slope formula slopes of parallel lines are equal.

Here,
The coordinates of point D are (4, 5) and the coordinates of point E are (5, 3)
The distance formula is given as,

D = √[[x₂ - x₁]² + [y₂+ - y₁]²]

By distance formula,
DE = √5

Segment DE is half the length of segment AC
AC = DE + DE
AC = 2DE
AC = 2√5

The property used is an addition property.

Segment DE is parallel to segment AC,
By the slope formula slopes of parallel lines are equal.

Thus, the complete reasoning of the solution is shown above.

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The two plans will cost the same when Yolanda has driven 233 miles distance. That is, $70 + (0.30 x 233) = $233 = 0.80 x 233.

To find out how many miles Yolanda needs to drive for the two plans to cost the same, we need to set up an equation. The equation should calculate the total cost of each plan. For the first plan, the total cost is the initial fee plus the cost of the miles driven. For the second plan, the total cost is just the cost of the miles driven. We can then set the two equations equal to each other and solve for the number of miles distance driven. The final result is that Yolanda needs to drive 233 miles for the two plans to cost the same.

Plan 1: C = F + (D × CPM)

Plan 2: C = (D × CPM)

Plan 1 = Plan 2

F + (D × CPM) = (D × CPM)

F = 0

D × CPM = D × CPM

D = 233

Therefore, Yolanda needs to drive 233 miles for the two plans to cost the same.

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The likelihood or the probability is 121, or 8.33%.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.

We must make a table for easier comprehension in order to determine the P(x=4);

Refer to the attachment for table:

There are three different ways that P(x=4) can occur based on the table. Out of 36 possible results (6 x 6 = 36), they are (1,3), (2,2), and (3,1). As a result, the chance of the event is 363; it is then reduced to 121, or 8.33%.

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Answer:

[tex]\log_{10}\sqrt{a} -\dfrac{3}{4}=\dfrac{1}{2}\log_{10}a-\dfrac{3}{4}[/tex]

Step-by-step explanation:

Given:

[tex]x=\dfrac{\sqrt{10a\sqrt{0.1}}}{10}[/tex]

Therefore:

[tex]\implies \log_{10}x=\log_{10}\left(\dfrac{\sqrt{10a\sqrt{0.1}}}{10} \right)[/tex]

[tex]\textsf{Apply the log quotient law}: \quad \log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay[/tex]

[tex]\implies \log_{10}\sqrt{10a\sqrt{0.1}}-\log_{10}10[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies \log_{10}\sqrt{10a\sqrt{0.1}}-1[/tex]

[tex]\textsf{Apply radical rule: $\sqrt{ab}=\sqrt{a}\sqrt{b}$, \quad assuming $a \geq 0,\;b\geq 0$}[/tex]

[tex]\implies \log_{10}\left(\sqrt{10}\sqrt{a}\sqrt{\sqrt{0.1}}}\right)-1[/tex]

[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\implies \log_{10}\sqrt{10} + \log_{10}\sqrt{a} + \log_{10}\sqrt{\sqrt{0.1}}}\right)-1[/tex]

Rewrite the radicals:

[tex]\implies \log_{10} \left(10\right)^{\frac{1}{2}} + \log_{10}\sqrt{a} + \log_{10}\left(0.1\right)^{\frac{1}{4}\right)-1[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies \dfrac{1}{2}\log_{10} 10 + \log_{10}\sqrt{a} + \dfrac{1}{4}\log_{10}0.1-1[/tex]

[tex]\textsf{Apply log laws}: \quad \log_aa=1 \quad \textsf{and} \quad \log_a\dfrac{1}{a}=-1[/tex]

[tex]\implies \dfrac{1}{2}(1) + \log_{10}\sqrt{a} + \dfrac{1}{4}(-1)-1[/tex]

[tex]\implies \dfrac{1}{2}+ \log_{10}\sqrt{a} -\dfrac{1}{4}-1[/tex]

[tex]\implies \log_{10}\sqrt{a} -\dfrac{3}{4}[/tex]

If you want to simplify further:

[tex]\implies \log_{10}\left(a\right)^{\frac{1}{2}} -\dfrac{3}{4}[/tex]

[tex]\implies \dfrac{1}{2}\log_{10}a-\dfrac{3}{4}[/tex]

Answer:

56

Step-by-step explanation: 10a+10 0.1 -=

The 92.5% of confidence interval for the percentage of adults is

(-1.176 ,  1.342).

as per given in the question,

The total number of adults (n) is 649

The number of smokers (x) = 54

the probability of getting a smoker is P =x/n

=> P = 54/649

=> 0.083

not getting a smoker is

1 - P = 1-0.083

=> 0.916

At 92.5% confidence level the Z critical value is ,

[tex]\alpha[/tex] = 1 - 92.5%

=> 1 - 0.925

=> 0.075

[tex]\alpha[/tex] / 2 = 0.075/ 2

=> 0.0375

now,

for the two tail test

Z[tex]\alpha[/tex]/2

= Z(0.0375)

= 1.7805

Margin of error

E = [tex]Z\alpha / 2 * \sqrt{( p * (1 - p) / n)}[/tex]

= 1.780 [tex]\times (\sqrt{((0.083 \times 0.916 ) / 649)}[/tex]

= 1.2596

A 92.5 % confidence interval for population proportion p is ,

P- E < P < P + E

0.083- 1.259 < P < 0.083 + 1.259

-1.176 < p < 1.342

(-1.176 ,  1.342) is the interval

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The probability that we have at least one customer buying 2 or more books before having two customers buying no books is 0.984.

Here is a possible MATLAB code to solve the problem:

%START

% Set the rate of the Poisson process

lambda = 4;

% Set the probabilities of N taking different values

p0 = 0.2;

p1 = 0.4;

p2 = 0.2;

% Compute the probability of having at least one customer buying 2 or more books

% before having two customers buying no books

prob = poisscdf(2-1, lambda*p0) - poisscdf(1-1, lambda*p0);

% Display the result

fprintf('Probability of having at least one customer buying 2 or more books before having two customers buying no books: %.4f\n', prob);

%END

This code uses the poisscdf function to compute the probability of having a certain number of events (customers buying 2 or more books or customers buying no books) in a given time period (one hour), assuming that the events occur according to a Poisson process with the given rate (4 customers per hour).

The probability of having at least one customer buying 2 or more books before having two customers buying no books is then computed as the probability of having 2 or more customers buying 2 or more books minus the probability of having 1 or more customers buying 2 or more books. The result is displayed using the fprintf function.

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Answer:

Step-by-step explanation:

The sum of (2.25 x 10^19) and (6.7 x 10^17) is (2.317 x 10^19).

To find the sum of these two numbers, we first need to line up the decimal points and add the numbers as we would with any other addition problem:

2.25 x 10^19

+ 6.7 x 10^17

Then, we can carry the 1 and add the numbers:

2.25 x 10^19

6.7 x 10^17

2.317 x 10^19

The sum of these two numbers is 2.317 x 10^19, which is equal to choice B.

The number of litres of water the tank can hold is 48 litres

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Volume can be measured in cubic units, litres and gallons.

If the rate of pump is 8minutes per minute, therefore in 15 minutes, 15×8 = 120 litres is in the tank.

120 litres is 5/2 full

the volume of the tank will be 120×2/5

= 240/5

= 48litres

Therefore the volume of the tank is 48litres

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The point of intersection (x,y) is  = (2,23)

Replace every x with 2 and simplify

y = 7x+9

y = 7*2 + 9

y = 14 + 9

y = 23 is the y coordinate

The vertical line x = 2 meets the diagonal line y = 7x+9 at the location (x,y) = (2,23)

What are Coordinates ?

The position of a point or points on a graph or grid is shown by its coordinates. The origin is defined as the point (0, 0). The coordinates are two units to the right in the x-direction and four units up in the y-direction according to the point (2, 4).

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A unit increase in gender will result in decrement of -52.73 in wage provided holding all other parameter constant.

What is parameter?

A parameter is a piece of information that an equation passes on. In terms of statistics, it means something different. In contrast to statistics, which only provide information about a small portion of the population, this value provides information about the entire population.

A parameter is constant because it was determined by surveying everyone (or everything). The average age of the students in your class, for instance, might be of interest to you. Maybe after asking everyone, you discovered that the average age was 25. Given that you polled the entire class, that qualifies as a parameter. Let's say you were curious about the median age of your grade or year.

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The monomials with a GCF of 7x³y with degree 5 are 7x⁴y and 14x³y².

The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.

In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.

As per the given GCF as 7x³y,

The GCF of 14 and 7 is 7.

The GCF of x⁴y and x³y² will be x³y.

Thus,

GCF of 7x⁴y and 14x³y² = 7x³y

So monomials are 7x⁴y and 14x³y².

Hence "The monomials are 7x⁴y and 14x³y²".

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The required simplified value o the given expression is 53.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= 8 - m/n + p²

Now, put m = 8 n = 2 and p = 7

So,
= 8 - 8 / 2 + 7²
= 8 - 4 + 49

= 4 + 49

= 53

Thus, the required simplified value o the given expression is 53.

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Answer:

It does not represent a proportional relationship

Step-by-step explanation:

Answer:

It does not represent a proportional relationship

Step-by-step explanation For a line, the constant of proportionality is a fancy way to say the slope. It makes more sense without the intercept: y=2xclearly, the constant of proportionality is 2.

The point where the boat should be landed is the point 3.4 miles from point P towards the town.

The point where the boat should be landed can be found by expressing

the distance traveled on the boat and walking as a function of time.

Given that x represents the distance from point P to the boat landing point.

Therefore, distance of rowing the boat = √((12 - x)² + 3²)

The total time, t, is, therefore;

[tex]t=\frac{12-x}{4} +\frac{\sqrt{x^2+3^2} }{3}-----------(1)[/tex]

differentiate the above equation we get:

[tex]\frac{dt}{dx} =\frac{d}{dx} (\frac{12-x}{4} +\frac{\sqrt{x^2+3^2} }{3} )\\\\\\=\frac{12.(-3+4*\frac{2x}{2*\sqrt{x^2+9} } )}{144} \\\\\\=\frac{12(-3+4*\frac{2x}{2*\sqrt{x^2+9} }) }{144}\\\\=-\frac{1}{4} +\frac{x}{3*\sqrt{x^2+9} } \\\\\frac{x}{3*\sqrt{x^2+9} }=\frac{1}{4} \\\\cross multiplying both terms we get:\\\\4x=3*\sqrt{x^2+9}[/tex]

squaring on both sides we get:

16x^2=9(X^2+9)

16x^2=9x^2+81

7x^2=81

[tex]x=\frac{9*\sqrt{x} }{7}[/tex]

Approximately,x=3.4 miles.

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The least squares line , y = mx + b form from given data is y = ( -32/100 )x + ( -39/100).

We have an equation of line is

y(x) = mx + b --(1)

given data, (-2, 1), (2, 1),(-1,-1), (0,-2), (2,-2) and (-2, 1)

plugging each point on above equation we get, 1 = -2m + b ; 1 = 2m + b ; -1 = -m + b ; -2 = 0m + b ;

-2 = 2m +b ; 1 = -2m + b

The above equations can be written in matrix form as,

[ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] [ m ; b]

= [ 1 ; 1 ; -1 ; -2 ; -2 ; 1]

AX = B

X = (Aᵀ A)⁻¹ AᵀB where Aᵀ is transpose of matrix A and (Aᵀ A)⁻¹ is inverse of (Aᵀ A).

AᵀA = [ -2 2 -1 0 2 -2 ; 1 1 1 1 1] [ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] = [ 17 -1 ; -1 6 ]

so, X = [ 17 -1 ; -1 6 ] ^-1 [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]

let [ 17 -1 ; -1 6 ] = P

[ 17 -1 ; -1 6 ]⁻¹ = adj.P/det P

det P = 17×6 - 1 = 101

P⁻¹ = 1/101 [ 6 1 ; 1 17 ]

Now, X = 1/101 [ 6 1 ; 1 17 ] [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]

=> X = 1/101[ 6 1 ; 1 17 ] [ -5 ; -2 ]

=> X = 1/101 [ -32 ; -39] = [ -32/100 ; -39/100 ]

=> [ m ; b ] = [ -32/100 ; -39/100 ]

=> m = -32/100 , b = -39/100

then, y = mx + b

=> y = ( -32/100 )x + ( -39/100)

Hence, the required equation is

y = ( -32/100 )x + ( -39/100).

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Answer:

[tex]f(x)=2.6(4)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$f(x)=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given points:

Substitute the given points into the formula to create two equations:

[tex]\implies 10.4=ab[/tex]

[tex]\implies 665.6=ab^4[/tex]

Divide the second equation by the first to eliminate a, then solve for b:

[tex]\implies \dfrac{665.6}{10.4}=\dfrac{ab^4}{ab}[/tex]

[tex]\implies 64=\dfrac{b^4}{b}[/tex]

[tex]\implies 64=b^3[/tex]

[tex]\implies b=\sqrt[3]{64}[/tex]

[tex]\implies b=4[/tex]

Substitute the found value of b into the first equation and solve for a:

[tex]\implies 10.4=4a[/tex]

[tex]\implies a=2.6[/tex]

Therefore, the exponential function is:

[tex]f(x)=2.6(4)^x[/tex]

As per the binomial distribution, the value of var(Y) is 0.00008

What is meant by binomial distribution?

In math, the Binomial distribution counts the number of successes in n trials, where sampling is done with replacement or the probability of success is constant from trial to trial

Here we have given that,  X be a random variable representing the number of rolls of a fair die until we see the first 6. Next, choose with replacement a sample of size X from an urn with 5 red and 4 green balls. Let Y be the number of green balls in the sample.

And we need to find the value of var(Y).

Here we know that the value of n = 6 and the value of x is 4 and the probability is 0.05.

Then as per the binomial distribution formula, it can be calculated as,

By using a calculator, you can enter trials=6, p=0.05, and X=4 into a binomial probability distribution function (PDF). If doing this by hand, apply the binomial probability formula:

=> [6!/4!(6-4)!] x 0.05⁴ x (1- 0.05)⁶⁻⁴

=> 0.00008

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Null Hypothesis: H0: There is an equal distribution of contralateral and ipsilateral tumors in the population.Ha: There is not an equal distribution of contralateral and ipsilateral tumors in the population.

1) Calculate the observed value:

The observed value is 26 out of 41 cases.

2) Calculate the expected value:

The expected value is 20.5 out of 41 cases.

3) Calculate the test statistic:

The test statistic is (26-20.5)/sqrt(20.5) = 2.44

4) State the critical value:

The critical value for a two-sided test with a significance level of 0.05 is 1.96.

5) The test statistic (2.44) is greater than the critical value (1.96), so we reject the null hypothesis and conclude that there is not an equal distribution of contralateral and ipsilateral tumors in the population.

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The correct option is D , as the number of shares issued is 80000.

What is stock ?

In finance, stock consists of all the shares by that possession of an organization or company is split. one share of the stock means that fractional possession of the corporation in proportion to the whole range of shares.

Main body:

as per the information given in the question , Common Stock, $1 par value, $80000 which means  the number of shares issued is 80000.

hence ,correct option is D as the number of shares issued is 80000.

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Answer: Rise over Run

Step-by-step explanation: Take the change in the x coordinates, and divide by the change in y coordinates.

For example, to find slope when given 2 coordinates:

(2,5)     (5, 10)

The change in the x coordinates is 3, because from 2-->5 it moves 3 places to the right. (run)

The change in the y coordinates is 5, because from 5-->10 it moves 5 places upwards. (rise)

Use rise/run.

Rise= 5 (change in y coordinate)

Run = 3 (change in x coordinate)

5/3 is the slope.

On questions like #6, the slope is -3. That is because the equation for slope is y=mx+b.

m is the coefficient of the x, so -3 is the slope.

Likewise, the slope of #2 is 7. The slope of #10 is 3/4.

The probability density function fr(r) of the distance from a uniformly randomly chosen point in the unit disk to the origin is r, and the cumulative distribution function Fr(r) is (r² / 2).

To find the probability density function (PDF) and cumulative distribution function (CDF) of the distance from a uniformly randomly chosen point in the unit disk to the origin, we can first find the area of the unit disk and the area of the annulus centered at the origin and bounded by two circles with radii r and r + dr. The PDF is then the ratio of the area of the annulus to the total area of the unit disk, and the CDF is the ratio of the area of the annulus to the total area of the unit disk up to radius r.

The area of the unit disk is simply the area of a circle with radius 1, which is pi. The area of the annulus centered at the origin and bounded by two circles with radii r and r + dr is equal to the difference between the areas of the two circles, which is pi(r + dr)² - pi(r²). Therefore, the PDF of r is:

fr(r) = [pi(r + dr)² - pi(r²)] / pi = r + dr²

The CDF of r is the sum of the PDFs up to radius r, which is:

Fr(r) = ∫fr(t)dt from 0 to r = ∫(t + dt²)dt from 0 to r = (r² / 2) + (r × dt) + (dt³ / 3)

We can take the limit as dt approaches 0 to get the final expression for the CDF:

Fr(r) = (r² / 2)

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Answer:

16 more blue birds

Step-by-step explanation:

If the total number of blue birds is 48

The total number of red birds is 32

then through simple subtraction we get to know that 16 more blue birds are present in the tree than the red birds

Extra Blue birds = 48-32

= 16