X₁ ~ X / ₁ (c) " k₁ k₁ 2² 2 where Y = X₁ + X₂ (a) Let using the first principle, show 2 X₁ (b) Show the moment generating function of Y ~ X ₁₁+k₂ jf Y = X₁ + X₂ 2 show m m Y=�

Answer:

C there is no solution

Step-by-step explanation:

These 2 equations are the same but equal too different things so they are parralell

hopes this helps

Answer:

Point H is (1,3)

Step-by-step explanation:

The x co - ordinate lies to the right and the y co-ordinate lies above . We are given  H is 3 units above and 1 unit to the right of the origin  so the co-ordinates of H  are ( 1,3).

As this particular order (x,y) is used to represent the the point it is called ordered pair.

The ordered pairs of the other points are

Point A is (4,5)

Point  C is (5,4)

Point H is (1,3)

Point K is (3,1)

Point N is (2,0)

Answer:

\(4(a + 2) - 2(a - 8) = 24 \\ 4a + 8 - 2a + 16 = 24 \\ 2a + 24 = 24 \\ 2a = 24 - 24 \\ a = \frac{0}{2} \\ \\ a = 0\)

I hope I helped you^_^

Answer:

Peter has 6 dollars.

Step-by-step explanation:

The ratio is 1:3, meaning Jane has 3x more money than Peter. Or, Peter has 1/3 as much money as Jane. You know that Jane has 12 dollars more than Peter so you can think of scenarios. Because it is a 1/3 the answer for Peters money has to be 1/3 of Janes, so Peter has 6 dollars, and Jane has 12 more, so Jane has 18 dollars.

here is your answer

if you will not like then you will be ehsanfaramosh

The amount of sales tax is $87.79.

Given a total purchase price of a sofa as $1,254.07 and state taxes of 7%.

We are required to calculate the amount of sales tax.

The amount of sales tax can be calculated by multiplying the purchase price by the sales tax rate.

Let's represent the sales tax rate by `r`.

Therefore, the sales tax formula is expressed as:

Sales tax = r * purchase price

In this case, the rate of the sales tax `r` is 7%.

Therefore, we have:r = 7% = 0.07

Now we substitute the values given into the formula:

Sales tax = 0.07 * $1,254.07= $87.79

Therefore, the amount of sales tax is $87.79.

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Answer:

There is nothing positive or negative about zero. Zero is just zero. It is NEITHER positive NOR negative. To the right of zero on number line are positive numbers and on the left of zero, lie the negative numbers on the number line.

Answer:

Positive numbers are greater than 0 and located to the right of 0 on a number line. Negative numbers are less than 0 and located to the left of 0 on a number line. The number zero is neither positive nor negative.

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Explanation:

1 yard = 3 feet

We'll divide by 3 to convert from feet to yards

The basement is 9*6 = 54 square yards in floor area.

At $32 per square yard, the total cost to carpet the floor is 32*54 = 1728 dollars.

Answer:

x =56

Step-by-step explanation:

1/4 x - 1 =13

Add 1 to each side

1/4x - 1+1 = 13+1

1/4 x = 14

Multiply each side by 4

1/4x * 4 = 14*4

x =56

The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

This can be derived using Chebyshev's inequality, as Chebyshev's inequality and the law of large numbers are different in nature.

Let M_n be the maximum of n independent U(0, 1) random variables.

To derive the exact expression for P(|M_n − 1| > ε), we need to follow the below steps:

First, we determine P(M_n ≤ 1-ε). The probability that all of the n variables are less than 1-ε is (1-ε)^n

So, P(M_n ≤ 1-ε) = (1-ε)^n

Similarly, we determine P(M_n ≥ 1+ε), which is equal to the probability that all the n variables are greater than 1+\epsilon

Hence, P(M_n ≥ 1+ε) = (1-ε)^n

Now we can write P(|M_n-1|>ε)=1-P(M_n≤1-ε)-P(M_n≥1+ε)

P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n.

Thus we have derived the exact expression for P(|M_n − 1| > ε) as P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n

Now, to show that $lim_{n\to\∞}$ P(|M_n - 1| > ε) = 0 , we can use Chebyshev's inequality which states that P(|X-\mu|>ε)≤{Var(X)/ε^2}

Chebyshev's inequality and the law of large numbers are different in nature as Chebyshev's inequality gives the upper bound for the probability of deviation of a random variable from its expected value. On the other hand, the law of large numbers provides information about how the sample mean approaches the population mean as the sample size increases.

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Answer:

  $53

Step-by-step explanation:

You want to know Elijah's initial deposit if his deposits were ...

If x2 is the amount in the bank after the deposit of week 2, the amount deposited in week 3 is 2(x2). The total after that deposit is 477, so we have ...

  x2 +2(x2) = 477

  x2 = 477/3 = 159

Working back another week, we figure ...

If x1 is the amount in the bank after the initial deposit, the amount deposited the following week was 2(x1). Then the total amount in the bank after that deposit is ...

  x1 +2(x1) = 159

  x1 = 159/3 = 53

Elijah put $53 in the bank the first week.

__

Additional comment

We're not asked for the value of x, so the expression 2x+3 doesn't come into play in this problem. (We can see that 2x+3 = 53  ⇒  x = 25.)

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tan= opp/adjacent

tan= 9/3

tan^-1 (9/3) =72°

Answer:

i think so

Step-by-step explanation:

Answer:

i think you are right.. if not sorry! :(

Step-by-step explanation:

The surface area of the prism is 200 cm².

The total surface area of the prism is calculated by applying the formula for total surface area of prism.

S.A = bh + (s₁ + s₂ + s₃)L

where;

The surface area of the prism is calculated as;

S.A = 8 cm (15 cm) + (8 cm + 15 cm + 17 cm) x 2cm

S.A = 120 cm² + 80 cm²

S.A = 200 cm²

Thus, the surface area of the prism is calculated using the formula for surface of right prism.

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Answer:

Step-by-step explanation:

Sides of the triangle:  AB , BC , AC

Angles: ∠A , ∠B , ∠C

Vertices: A , B ,C

It will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.

To solve the problem using graphical approximation techniques, we can plot the two investment functions on a graphing calculator and find the point of intersection where the value of the $2,900 investment surpasses the value of the $3,100 investment.

Let's use the formula \(A = P(1 + i)^n\),

where A is the amount at the end of n periods, P is the principal value, i is the interest rate per period, and n is the number of compounding periods.

For the $2,900 investment at 15% compounded quarterly:

P = $2,900

i = 15% = 0.15/4

= 0.0375 (interest rate per quarter)

For the $3,100 investment at 9% compounded quarterly:

P = $3,100

i = 9% = 0.09/4

= 0.0225 (interest rate per quarter)

Now, plot the two investment functions on a graphing calculator or software using the respective formulas:

Function 1:\(A = 2900(1 + 0.0375)^n\)

Function 2:\(A = 3100(1 + 0.0225)^n\)

Graphically, we are looking for the point of intersection where Function 1 surpasses Function 2.

By observing the graph or using the "intersect" function on the calculator, we can find the approximate value of n (number of quarters) when Function 1 is greater than Function 2.

Let's assume the graph shows the intersection point at n = 15.6 quarters. Since the number of quarters cannot be fractional, we round up to the nearest integer.

Therefore, it will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.

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If you reflect the rectangle across either the horizontal or the vertical line going straight through the middle, you will reflect it onto itself (see image).

The equation for the horizontal line is y = -1. The equation for the vertical line is x = -1.

Two equal-size vectors at right angles to each other have a resultant that is equal to \(\sqrt{2}\) times the magnitude of each individual vector.

The magnitude of the resultant vector of two equal-size vectors at right angles to each other can be determined using the Pythagorean theorem.

Let's assume the magnitude of each vector is represented by "a".

According to the Pythagorean theorem, the magnitude of the resultant vector, denoted as "R", can be calculated as:

R =\(\sqrt{a^2 + a^2}\)

R = (\(\sqrt{2a^{2} )}\)

R = \(\sqrt{2}\) a

Therefore, the magnitude of the resultant vector is equal to \(\sqrt{2}\) times the magnitude of each individual vector.

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Answer:

Step-by-step explanation:

Answer:

r = 6

Step-by-step explanation:

According to the question,

4(r + 4) = 10r - 20

4r + 16 = 10r - 20

16 + 20 = 10r - 4r

6r = 36

r = 36 / 6

r = 6

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

Answer:

The unit rate at HEB is $0.23 per ounce. The unit rate at Fiesta is $0.25 per ounce. So HEB has the better buy for dish soap.

Step-by-step explanation:

To calculate unit rate, you divide the price by the oz.

So for HEB, you should do $2.80/12 oz. This will equal to $0.23 per ounce. For Fiesta, you should do $2.00/8 oz. This will equal to $0.25 per ounce.

To determine which one is the better buy, the lower priced one is better, meaning HEB is the better buy.

The value of the volume of the given prism is 392 cm³

We can calculate the volume of the prism in the following way,

We know the dimensions of the different sides of the prism

Considering the given values we get the following figure of the prism

We will now calculate the volume of the prism using these dimensions

Prism volumes may be calculated by multiplying the area of the base by

B = 1/2 * h(b1+b2), where B is the prism's base area, and H is its height.

Substituting the given values we get,

B = 1/2 * 4 * (2 + 5)

B = 14 cm is the area of the base of the prism

Now calculate the volume of the prism,

The volume of the prism = height * area of the base

volume = 8 * {(5 * 7) + 14}

volume = 8 * {35 + 14}

volume = 8 * 49

volume = 392 cm³

Therefore the volume of the pentagonal-based prism is 392 cm³

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Answer:

r = 11

Step-by-step explanation:

mDG and mGM must add up to mDM

Step 1: Set up equation

mDG + mGM = mDM

r + 5 + 3r - 14 = 35

Step 2: Solve for r

Combine like terms: 4r - 9 = 35

Add 9 to both sides: 4r = 44

Divide both sides by 4: r = 11

Answer:

11

Step-by-step explanation:

\(r+5+3r-14=35\\4r-9=35\\4r=44\\r=11\)

The gravitational potential energy of the vacationers will decrease as they approach the end of the pier.

As the vacationers approach the end of the pier, their gravitational potential energy will decrease.

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It depends on the height of the object and the acceleration due to gravity.

In this scenario, as the vacationers walk out on the horizontal pier, their height above the ground remains constant. Since the height does not change, the gravitational potential energy also remains constant.

However, as they approach the end of the pier, their distance from the center of the Earth decreases. As a result, the gravitational potential energy decreases because it is directly proportional to the distance from the center of the Earth.

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Answer:

A. 25

Step-by-step explanation:

1- See the length of XA

2- Divide length by 2

3- 50 divided by 2 equals 25

Answer:

Freind it's answer is B.25

Step-by-step explanation:

First you have to prove that the triangle XYZ and AYZ are congruent.

There we have YZ in common...

Angles XYZ and AYZ are given congruent...

Also angles XZY and AZY are given 90 degrees.....

Hence, Triangle XYZ is congruent to triangle AYZ....

So,XZ=AZ(Congruent Parts of Congruent Triangle)

Now,we have XZ+AZ=XA

So,XZ+AZ=50cm

=2XZ=50 or 2AZ=50

Hence,AZ=25cm

Here's your answer friend ...

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Answer:

THE ANSWER OF X DGREE MAY BE 95 DEGREE USING THE PROPERTY OF VERTICALLY OPPOSITE ANGLE...