jack and jill each had a summer job. jack earned $10.00 per day. jill earned 1 cent on the first day, 2 cents on the second day, 4 cents on the third day, 8 cents on the fourth day, and so on, doubling the amount she makes each day.

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

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a. f(v₁, v₂, v₃) = f₁(v₁) × f₂(v₂) × f₃(v₃) is the  joint pdf of (V₁, V₂, V₃).

b. The marginal pdf of V₂ is 1, indicating that V₂ is uniformly distributed between 0 and 1.

Given that Y₁, Y₂, Y₃, and Y₄ are order statistics of a random sample X₁, X₂, X₃, and X₄ from a uniform distribution U(0, θ), we know that the joint pdf of the order statistics is given by:

f(y₁, y₂, y₃, y₄) = n! / [(k₁ - 1)! × (k₂ - k₁ - 1)! × (k₃ - k₂ - 1)! × (n - k₃)!] × [1 / (θⁿ)],

where n is the sample size (n = 4 in this case), θ is the upper bound of the uniform distribution (θ in U(0, θ)), and k₁, k₂, k₃ are the orders of the order statistics (in ascending order).

Now, we need to determine the values of k₁, k₂, k₃ for the given V₁, V₂, V₃.

k₁ = 1 (as Y₁ is the smallest order statistic)

k₂ = 2 (as Y₂ is the second smallest order statistic)

k₃ = 3 (as Y₃ is the third smallest order statistic)

Now, we can express V₁ = Y₁/Y₂, V₂ = Y₂/Y₃, and V₃ = Y₃/Y₄ in terms of the order statistics:

V₁ = Y₁ / Y₂ = X₁ / X₂

V₂ = Y₂ / Y₃ = X₂ / X₃

V₃ = Y₃ / Y₄ = X₃ / X₄

Since X₁, X₂, X₃, and X₄ are independently and uniformly distributed between 0 and θ, the joint pdf of (V₁, V₂, V₃) can be expressed as the product of their individual pdfs:

f(v₁, v₂, v₃) = f₁(v₁) × f₂(v₂) × f₃(v₃),

where f₁(v₁) is the pdf of V₁, f₂(v₂) is the pdf of V₂, and f₃(v₃) is the pdf of V₃.

(b) To find the marginal pdf of V₂, we integrate the joint pdf f(v₁, v₂, v₃) over v₁ and v₃:

f₂(v₂) = ∫[0, ∞] ∫[0, ∞] f(v₁, v₂, v₃) dv₁ dv₃

Since we know the joint pdf f(v₁, v₂, v₃) is the product of the individual pdfs, we can write:

f₂(v₂) = ∫[0, ∞] ∫[0, ∞] f₁(v₁) × f₂(v₂) × f₃(v₃) dv₁ dv₃

Now, integrate the expression with respect to v₁ and v₃ over their respective domains (0 to ∞):

f₂(v₂) = ∫[0, ∞] f₁(v₁) dv₁ × ∫[0, ∞] f₃(v₃) dv₃

Since V₁ = X₁ / X₂ and V₃ = X₃ / X₄, we can express f₁(v₁) and f₃(v₃) in terms of the pdf of the uniform distribution:

f₁(v₁) = 1 / θ for 0 ≤ v₁ ≤ 1

f₃(v₃) = 1 / θ for 0 ≤ v₃ ≤ 1

Integrating over their respective domains:

∫[0, ∞] f₁(v₁) dv₁ = ∫[0, 1] (1 / θ) dv₁ = 1

∫[0, ∞] f₃(v₃) dv₃ = ∫[0, 1] (1 / θ) dv₃ = 1

Therefore, the marginal pdf of V₂ is:

f₂(v₂) = 1 × 1 = 1.

The marginal pdf of V₂ is a constant 1, indicating that V₂ is uniformly distributed between 0 and 1.

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Let Y₁ ​ ,Y₂ ​ ,Y₃ ​ ,Y₄ ​ be the order statitic of a U(0,θ) random ample X₁ ​, X₂ ​ ,X₃ ​ ,X₄ ​.

(a) Find the joint pdf of (V₁ ,V₂ ​ ,V₃ ​ ) , where V₁ ​ = Y₁/Y₂ ​ ​ ,V₂ ​ =Y₂/Y₃ ​ ​and V₃ ​ = Y₃/Y₄ ​ ​.

(b) Find the marginal pdf of V₂. ​

Answer:

they bought 23 adult tickets and 2 child tickets

Step-by-step explanation:

the explanation is in the screenshot below

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Answer:

766 acres is the difference.

Step-by-step explanation:

2,484 minus 1,718 equals 766 acres.

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Answer:

ranch has a ton of calories

Step-by-step explanation:

The Solution:

Given the linear function below:

So, the slope of the linear function above is the coefficient of x in the given linear function. Therefore, the slope of the given function is 4.6

The interpretation of the slope is 4.6% of the people graduate from college every year after the year 1998.

Answer:

It will take 43.37 mins for the cake to cook off to 90

Step-by-step explanation:

From Newton's law of cooling

\(T_{(t)} = T_{s} + (T_{o} - T_{s})e^{kt}\)

Where

\(t =\) time

\(T_{(t)}\) = Temperature of the given body at time \((t)\)

\(T_{s}\) = Surrounding temperature

\(T_{o}\) = Initial temperature of the body

and \(k\) = constant

From the question,

\(T_{o}\) = 357

\(T_{s}\) = 72

\(T_{o} - T_{s}\) = 357 - 72 = 285

∴ \(T_{(t)} = 72 + 285e^{kt}\)

From the question, the cake cools to 130 after 25 min. Then, we can write that

\(T_{(25)} = 72 + 285e^{k(25)}\)

∴ \(130 = 72 + 285e^{25k}\)

Then,

\(130 - 72 = 285e^{25k}\)

\(58 = 285e^{25k}\)

\(\frac{58}{285} = e^{25k}\)

Take the natural log (ln) of both sides

\(ln^{\frac{58}{285} } =ln^{ e^{25k}}\)

\(-1.5920 = 25k\)

∴ \(k =\frac{-1.5920}{25}\)

\(k = -0.06368\)

Now, to determine how long it take for the cake to cook off to 90

That is,

\(T_{(t)} = 72 + 285e^{kt}\)

\(90 = 72 + 285e^{-0.06368t}\)

\(90 - 72= 285e^{-0.06368t}\)

\(18 = 285e^{-0.06368t}\)

\(\frac{18}{285} = e^{-0.06368t}\)

\(\frac{6}{95} =e^{-0.06368t}\)

Take the natural log (ln) of both sides

\(ln^{\frac{6}{95} } = ln^{e^{-0.06368t}}\)

\(-2.7621 = -0.06368t\\\)

∴ \(t = \frac{-2.7621}{-0.06368}\)

\(t = 43.37 mins\)

Hence, it will take 43.37 mins for the cake to cook off to 90.

The values of p, q, and r are p = 2, q = 5, and r = 3, respectively.

Given that the lowest common multiple (LCM) of A and B is 2250, and the prime factorization of A is A = 2 × p × q¹, and the prime factorization of B is B = 2 × p² × q², we can compare the prime factorizations to determine the values of p, q, and r.

From the prime factorization of 2250 (2 × 3² × 5³), we can observe the following:

The prime factor 2 appears in both A and B.

The prime factor 3 appears in A.

The prime factor 5 appears in A.

Comparing this with the prime factorizations of A and B, we can deduce the following:

The prime factor p appears in both A and B, as it is present in the common factors 2 × p.

The prime factor q appears in both A and B, as it is present in the common factors q¹ × q² = q³.

From the above analysis, we can conclude:

p = 2

q = 5

r = 3.

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The differentiation of the function is -4/t.

Given are two equations x = t², y = 6 - 8t, we need to find \(\mathrm {\frac{dy}{dx} }\).

So,

To find \(\mathrm {\frac{dy}{dx} }\), we can use the chain rule of differentiation.

The chain rule states that if y is a function of u and u is a function of x, then the derivative of y with respect to x \(\mathrm {\frac{dy}{dx} }\) is given by:

\(\mathrm {\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}}\)

Since here the equations are simpler so we will just find the derivatives with respect to t and then divide both the derivates.

In this case, we have x = t² and y = 6 - 8t.

Differentiating x = t² w.r.t. t, we get,

\(\mathrm {\frac{dx}{dt} = 2t}\)

Similarly,

Differentiating y = 6 - 8t w.r.t. t, we get,

\(\mathrm {\frac{dy}{dt} = -8}\)

Now, dividing both the derivates, we get,

\(\mathrm {\frac{dy}{dt} \ \div \mathrm {\frac{dx}{dt} }}\)

\(\mathrm {\frac{dy}{dt} \ \times \mathrm {\frac{dt}{dx} }}\\\\ = \frac{-8}{2\mathrm t} \\\\ = \frac{-4}{t}\)

Hence the differentiation of the function is -4/t.

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Explanation:

For regular tessellations, the types of polygons that we can use are

We can only pick one of those shapes.

Shapes like regular octagons or pentagons will not work on their own because there is gap or overlap if we tried to glue them together. Think of tiles on the floor. There cannot be any gap or overlap when forming a tessellation.

If you wanted to use octagons to tessellate the plane, then you'd need squares to fill in the gaps. At this point, it's not considered a regular tessellation.

Answer:

2f

Step-by-step explanation:

3f-2f+f | Given

1f + f | Subtract 3f and 2f

2f | Add 1f and 1f.

Answer:

260cm²

Step-by-step explanation:

Area of parallelogram = 20 × 13

                                     = 260cm²

Answer: 260 cm^2

Step-by-step explanation: We will be using the same formula as A = b * h for a parallelogram. The base is 20 and the height is 13 (NOT 15 because that is slant height). A = 20 * 13. The answer is 260 cm^2.

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Answer: 205.14

Step-by-step explanation:

Multiply

Add

Insert Decimal Point

205.14

Answer:

205.14

Step-by-step explanation:

Step 1: Multiply without the decimal points, then put the decimal point in the answer:

263x78

Step 2: Line up the numbers:

2 6 3

x 7  8

Step 3: Multipy the top number by the bottom number one digit at a time starting from left to right:

\(\frac{\begin{matrix}\:\:&\:\:&2&6&3\\ \:\:&\times \:&\:\:&7&8\end{matrix}}{\begin{matrix}0&2&1&0&4\\ 1&8&4&1&0\end{matrix}}\)

Step 4: Add:

\(\frac{\begin{matrix}\:\:&\textbf{1}&\:\:&\:\:&\:\:&\:\:\\ \:\:&\textbf{0}&2&1&0&4\\ +&\textbf{1}&8&4&1&0\end{matrix}}{\begin{matrix}\:\:&\textbf{2}&0&5&1&4\end{matrix}}\)

Step 5: Insert Decimal Point:

205.14

Answer:

30 feet and 360 inches

Step-by-step explanation:

10 yards x 36 = 360 inches

10 yards x 3 = 30 feet

The population is growing as the births are more than deaths in an year.

Increases in a population's or a dispersed group's membership are referred to as population growth.

Given:

To find: Is population growing or shrinking?

Finding:

Hence the population is growing as the births are more than deaths in an year.

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1 - C

2 - B

3 - A

Step-by-step explanation:

Therefore, the correct answer is as follows:

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The length of each leg of a right triangle given that one angle is 22° and the length of the hypotenuse is 10 inches are 3.75 and 9.27 inches respectively.

In order to determine the length of the opposite side and adjacent side, we would apply both the cosine and sine trigonometry ratio because the given side lengths represent the hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

By substituting the parameters into the sine trigonometry ratio formula, we have the following;

sin(θ) = Opp/Hyp

sin(22) = y/10

y = 10sin(22)

y = 3.75 inches.

For the adjacent side, we have:

cos(θ) = Adj/Hyp

cos(22) = x/10

x = 10cos(22)

x = 9.27 inches.

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Answer:

18.445

Step-by-step explanation:

Multiply

Answer:

Yes and closed interval

Step-by-step explanation:

The computation is shown below:

For the sum and the reciprocal as small as the possible equation is as follows

\(\(\frac{d}{dx}\left(x+\frac{1}{x}\right)=0.\)\)

Now take out the derivates,

So,

\(\(1-\frac{1}{x^2}=0,\)\)

or we can say that

\(\(x^2-1=0\rightarrow x=\pm1.\)\)

As the only positive number is to be determined i.e

x = 1

So this problem needed the optimization over a closed interval and the same is to be considered.

Answer:

-8x-8

Step-by-step explanation:

Since 16x and -24x have like variables, we can subtract to get -8x.  Then, we can add the constants to get -8.

Step-by-step explanation:

16x-12-24x+4

=16x-24x-12+4

=8x-8

The distance between points A and B is 5 units.

Remember that the distance between two points (a, b) and (c, d) is:

distance = √( (a - c)² + (b - d)²)

In this case the two points are A(7, -4) and B (4, -8), replacing these values in the distance equation we get:

distance = √( (7 - 4)² + (-4 + 8)²) = √(9 + 16) = 5

The distance between the two points is 5 units.

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Answer:

The second one

Step-by-step explanation:

A function is a group of ordered pairs that do not have the same ordered pair. The second one has 2 fives in the x coordinate, therefore the second one is not a function

The area of the polygon is solved to be  1044 squared cm

The area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas

Section 1 has dimensions:

length * width = 46 * 14 = 644

section 2 has dimensions:

length = 46 - 21 = 25

width = 30 - 14 = 16

Area = 25 * 16 = 400

Area of the composite figure

section 1  + section 2

= 644 + 400

= 1044 squared cm

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By means of the law of cosine, the missing side of the triangle has a length of approximately 6.502 units.

Herein we find the case of a triangle with two known side lengths and a known measure of an angle between the two given sides. The measure of the unknown side is determined by the law of cosine, whose definition is shown below:

x² = a² + b² - 2 · a · b · cos θ

If we know that a = 15, b = 12 and θ = 25°, then the equation for the triangle is:

x² = 12² + 15² - 2 · 12 · 15 · cos 25°

Now we proceed to simplify and find the resulting value of x by algebra properties:

x² = 369 - 360 · cos 25°

x² = 369 - 326.271

x² = 42.279

x ≈ 6.502

The length of missing side of the triangle is approximately equal to 6.502 units.

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Using L'Hopital's rule, we can find that the limit is equal to (g(0) - 3)/2.

Since the line tangent to g at (0,3) has slope 2, we know that g(0) - 3 = 2(0) = 0. Therefore, the limit is 0/2 = 0. Based on the given information, we have a twice-differentiable function g(x) and its tangent line at the point (0,3). To find the value of the limit as x approaches 0 for g(x)e^(-x) - 3x^2 - 2x, we can use L'Hopital's rule since it involves indeterminate forms of the type 0/0 or ∞/∞.  Apply L'Hopital's rule twice on the given expression. Then, evaluate the resulting expression at x=0. This will give you the value of the limit for the given expression. Make sure to check if the conditions for using L'Hopital's rule are met before applying it.

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Answer:

7

Step-by-step explanation:

do 8.40 divided by 1.20 which gives you 7

you can double check by multiplying 1.20 by 7

The expected population size be after two generations which has a current size of 150 and λ of 1.2 is 216.

Nt = N₀ × λ^t

Nt = Population size at generation t

N₀ = Current population size

t = Number of generations

λ = Finite rate of increase

λ = 1.2

N₀ = 150

Nt = 150 × 1.2²

Nt = 150 × 1.44

Nt = 216

Population size is defined as the number of individuals present in a designated region. Finite rate of increase is the ratio of population size from increase from one year to the next.

Therefore, the expected population size be after two generations is 216

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