Random variables X and Y have the following joint probability distribution. Find the marginal probability distributions f1(x) and f2(y).
f(x,y) x
1 2 3
y 1 0.1 0.1 0.15
2 0.05 0.05 0.2
3 0.15 0.1 0.1

Answer:

x=42°

Step-by-step explanation:

All sides of a triangle equals 180. so 56+82= 138. 180-138 equals 42

1) The figure shows a translation.

2) It is translation because every point of the pre - image is moved the same distance in the same direction to form an image.

3) Point A from the pre - image corresponds with Point D on the image.

We have to given that,

There are transformation of triangles are shown.

Now, From figure all the coordinates are,

A = (- 5, 3)

B = (- 4, 7)

C = (- 1, 3)

D = (- 1, - 2)

E = (0, 1)

F = (3, - 2)

Hence, We get;

1) The figure shows a translation.

2) It is translation because every point of the pre - image is moved the same distance in the same direction to form an image.

3) Point A from the pre - image corresponds with Point D on the image.

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Answer: sorry if this is wrong I tried.

Physical factors such as terrain, climate, soil, water bodies, and mineral resources. These factors affect the availability of resources, the suitability of land for agriculture, the accessibility of transportation, and the attractiveness of living conditions.

Human factors such as industries, urbanization, transport, culture, history, and politics. These factors affect the type and scale of economic activities, the availability of services and amenities, the migration patterns and preferences of people, and the distribution of power and wealth.

These factors vary according to the scale of analysis because different regions may have different combinations and interactions of these factors that influence their population distribution. For example, at a global scale, climate may be a major factor that determines where people live, but at a local scale, urbanization may be more important.

Step-by-step explanation:

Answer:

y = 1/2x - 4

Step-by-step explanation:

If you plot the first three coordinates you find the slope that is one half and your y-intercept is -4.

You can also figure it out without plotting it by finding the slope between the first two coordinates by finding the change of Y over the change of x and simplify it and you will get 1/2.

Answer:

134 questions

Step-by-step explanation:

150 x 0.89 = 133.5

If Francine adds 8.0 ml of 3.0 m KOH to 4.0 ml of 6.0 m HBr, then the resulting mixture will be neutral in nature.

To determine whether the mixture is acidic, basic or neutral, litmus test is done or some other tests can also be performed. However, the mathematical calculations help in understanding the reason behind the result of litmus test.

In the given problem, the volume and molarity of the solutions are given, so number of moles can be easily calculated.

Number of moles of KOH = (8.0 mL) x (3.0 mol/L) / 1000 mL/L = 0.024 mol

Number of moles of HBr = (4.0 mL) x (6.0 mol/L) / 1000 mL/L = 0.024 mol

Considering the chemical reaction between KOH (which is a strong base) and HBr ( which is a strong acid), the resulting product will be a salt along with water (in the form of vapors).

KOH + HBr → KBr + H2O

Since, the number of moles of KOH and HBr is same, therefore the resultant solution will have salt with neutral pH.

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Conditioning is much more likely when the CS and the US are presented together on every trial. The answer is option (2).

Classical conditioning is a type of learning that occurs through association. In classical conditioning, a neutral stimulus (NS) is repeatedly paired with an unconditioned stimulus (US) to elicit a conditioned response (CR). The most effective way to establish this association is by presenting the NS and the US together on every trial. In contrast, if the US occurs without the CS, or if the US is not presented after the CS in some trials, the association between the NS and the US is weakened, making conditioning less likely to occur.

Hence, option (2) is the correct answer.

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Answer:

Step-by-step explanation:

x-intercept (x,0) , y intercept (0,y)

10: -3x-4y=12

x=0 , -3(0)-4y=12

-4y=12 , ⇒ y=12/-4 ⇒ y=-3

y=0 : -3x-4(0)=12

-3x=12 ⇒ x=12/-3 ⇒ x=-4

-9x+4y=-36

x=0 , 4y=-36 , y=-36/4 , y=-9  

y=0 , -9x=-36 , x=-36/-9 , x=4

5x-3y=-15

x=0 , -3y=-15 , y=-15/-3 , y=5

y=0 , 5x=-15 , x=-15/5 , x=-3

Answer:

I got 7%

Step-by-step explanation:

110 x .15 = 16.5

110-16.5=93.5

93.5 x .10 = 9.35

93.5 + 9.35= $102.82

Thats the discount price

110 - 102.82 + 7.18

7.18/102 = .0698

.0698 x 100 = 6.98

7%

I have this on my middle school test and it's my first time doing it so yea. I hope it helps even if it's already too late.

I had to edit it beforee

The primary role of a control in an experiment is not to prove that a hypothesis is correct but rather to provide a baseline for comparison and ensure the validity and reliability of the experimental results. The statement attributed to Rachel Carson is about the concern regarding pesticides. Among the given categories of thinking (critical, creative, analytical, reflective, logical), there is no single category that is above all others. Each category has its own significance and contributes to different aspects of thinking.

The primary role of a control in an experiment is to provide a standard or baseline against which the experimental group is compared. It helps researchers assess the effect of the independent variable by isolating it from other potential variables. The purpose is not to prove the hypothesis correct but rather to ensure that any observed changes or effects can be attributed to the independent variable and not to other factors.

The statement about pesticides eating and drinking chemicals is attributed to Rachel Carson, who was an influential environmentalist and author known for her book "Silent Spring" which highlighted the harmful effects of pesticides on the environment and human health.

Regarding the categories of thinking, critical, creative, analytical, reflective, and logical thinking are all important and serve different purposes. Critical thinking involves evaluating and analyzing information, creative thinking involves generating new ideas, analytical thinking involves breaking down complex problems, reflective thinking involves introspection and learning from past experiences, and logical thinking involves reasoning and making logical connections. Each category of thinking has its own value and is applicable in different contexts, and there is no single category that can be considered above all others as they are all important in their own right.

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Answer:

C. -1

Step-by-step explanation:

Slope is: \(m=\frac{y_2-y_1}{x_2-x_1}\)

We are given the points (1,7) and (3,5).

\(m=\frac{5-7}{3-1} =\frac{-2}{2} =-1\)

The slope is -1, and therefore, Option C should be the correct answer.

Answer:

7

Step-by-step explanation:

the answer is 7 because it is a 1 to three ratio.

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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Answer:

Area= 2000 feet^2

Step-by-step explanation:

Know how to find the perimeter and the area of a rectangle

area=length*width

perimeter= 2*length + 2*width

Draw a rectangle

The question states that the pasture is 50 feet long

So the length of the rectangle pasture should be 50. We can label the 2 lengths of the rectangle to be 50 feet long

Since the farmer only has 160 feet of fence, we can say that because the pasture is a rectangle, we can label the width as 40 because 2*50+2*40=160

Now that we know the length and width, we can find the area by multiplying those 2 values together to get 2000

=========================================================

Work Shown:

SA = surface area of the rectangular prism (aka block or box)

SA = 2*(LW + LH + WH)

SA = 2*(8*3 + 8*1 + 3*1)

SA = 2*(24 + 8 + 3)

SA = 2*(35)

SA = 70 square feet

This is the amount of wrapping paper you would need to cover all six sides of the box. This assumes that there are no gaps or overlaps.

Answer:

It doesnt

Step-by-step explanation:

Answer:

There are 7 fewer people.

Step-by-step explanation:

This can be calculated just via simple adition and subtraction.

10 people got off the bus, so that is a negative 10 with a positive 7 afterwards as people got on the bus:

-10 + 7 = -3

Now another 4 people got off the bus:

-3 -4 = -7

Therefore there are 7 fewer people on the bus after the second stop when compared to the stop at 2:30.

Hope this helps!

Answer:

LALLALA IS

Step-by-step explanation:

Answer:

Option (2)

Step-by-step explanation:

To get the transformation applied in triangle ABC to map triangle DEF we will apply the following rules.

If a point A of triangle ABC maps the point D of triangle DEF,

Coordinates of point A → (-4, -5)

Coordinates of point D → (2, 6)

First point A is shifted to quadrant (4) from quadrant (3),

Rule for the translation,

A(x, y) → A'(x + 6, y - 1)

A(-4, -5) → A'(2, -6)

Followed by reflection across x-axis (y = 0)

A'(x, y) → D(x, -y)

A'(2, -6) → D(2, 6)

Therefore, Option (2) will be the answer.

The company can maximize its revenue by charging the price of $73 per phone.

Changing the price and monitoring how many phones are sold in reaction to the price change allows for trial-and-error in determining accuracy.

With 520 phones sold each week at $73, the corporation will make a total of $38,160 in revenue. There are 20 more phones than when it was charging $75, thus the business will make an additional $1,500 every week.

Due to the increased number of phones sold, the corporation may increase revenue by merely $2 by lowering the price, leading to an increase in both total revenue and profit.

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Answer:

d = 10 degrees

Step-by-step explanation:

You need to set the two equations equal to each other to solve this question:

(40 + 7) = (5d - 3)

(47) = (5d - 3)

47 = 5d - 3

50 = 5d

10 = d

d = 10 degrees

Image is attached below.

If the sum of the digits its divisible by 9,

then the original number is divisible by 9.

Since 18 (the sum of the digits) is divisible by 9,

the number 540,171 is also divisible by 9.

Answer:

Yes, The number is divisible by 9

Step-by-step explanation:

If you divide the number by 9 you will get 60019. Also if we add the numbers we will get 18 which is also divisible by 9.

Hope this helps.

Answer:

The sample included only those people who chose to complete the survey.

Step-by-step explanation:

In triangle XYZ, m∠Z > m∠X + m∠Y, the term which is true about △XYZ is m∠X + m∠Z < 90° option A.

Three vertices, three sides, and three angles make up a closed triangle. PQR serves as the symbol for a triangle having the vertices P, Q, and R. Triangle-shaped items are most commonly found in sandwiches and signboards.

A closed triangle has three angles, three vertices, and three sides. PQR is the algebraic notation for a triangle with three vertices. The shapes of triangles that are most common are those on sandwiches and signboards.

We know that XYZ is a triangle.

We must choose which choice best describes XYZ.

The total of all a triangle's internal angles is always equal to 180 degrees according to the triangle's angle sum characteristic.

Therefore, ∠X + ∠Y + ∠Z = 180°

Assuming, mZ > mX + mY.

This suggests that Z is larger than the product of angles X and Y.

As a result, X + Y must not be 90 degrees.

Hence, X + Y = 90°.

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Complete question:

In triangle XYZ, m∠Z > m∠X + m∠Y. Which must be true about △XYZ?

m∠X + m∠Z < 90°

m∠Y > 90°

∠X and∠Y are complementary

m∠X + m∠Y < 90°

The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.

The formula for the volume of a cylinder is \(V = \pi r^2h,\) where V is the volume, r is the radius, and h is the height.

Let's assume that the cone and cylinder have a radius of 'r' and a height of 'h'.

The volume of the cylinder is given by \(= \pi r^2h.\)

The volume of the cone is given by V_cone = \((1/3)\pi r^2h.\)

Since the cone and cylinder have the same base and height, their radius and height are the same.

Therefore, we can simplify the volumes as V_cylinder = \(\pi r^2h\) and V_cone = \((1/3)\pi r^2h.\)

The ratio of the volume of the cone to the volume of the cylinder is then:

V_cone/V_cylinder = \(((1/3)\pi r^2h) / (\pi r^2h) = (1/3) / 1 = 1/3\)

So, the volume of the cone is one-third of the volume of the cylinder.

Alternatively, we can write this as the ratio of the volume of the cone to the volume of the cylinder being 1:2, since the volume of the cylinder is twice the volume of the cone.

Therefore,The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.

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Answer:

C. d(t) = 2.37t; 14.22 ft

Step-by-step explanation:

2.37 per minute is multiplication so A and B are definitely wrong

Another way to check is 2.37*6=14.22 so the answer is C

Answer:

D. d(t) = 6t; 14.22 ft

Step-by-step explanation:

d(t)= 2.37t; 14.22 ft

d(t)= 2.37t; 14.22 ft

Answer:

a. f(t)=2.37t

b.  14.22 feet

Step-by-step explanation:

We are given that:

A snail travels at a rate of 2.37 feet per minute.

a. write a rule to describe a function.

Let t describe the time and f(t) be a function how far snail travels

then,     f(t)=2.37×t

where the unit of t is in minutes and that of f(t) is feet

b. how far will the snail travel in 6 minutes

we have to find f(t) at t=6

f(6)= 2.37×6

  = 14.22 feet

Hence, snail traveled 14.22 feet in 6 minutes

2.37/minute

14.22 feet in six minutes

Answer:

Rule for Distance is f(t) = 2.37t and distance covered in 6 minutes is 14.22 feet.

Step-by-step explanation:

Speed of Snail = 2.37 feet per minute

To write the rule we use relation of Speed, Distance and time

Distance = Speed × Time

So, Distance cover by snail in t minutes is given by f(t) = 2.37 × t

⇒ f(t) = 2.37t

Distance traveled by Snail in 6 minutes , f(6) = 2.37 × 6 = 14.22 feet

Therefore, Rule for Distance is f(t) = 2.37t and distance covered in 6 minutes is 14.22 feet.

The area of the roof is 1984 sq. ft. 1984 square feet of roofing is needed for the roof of a building that is 32 ft wide and 62 ft long.

Given, the length of the roof is 62 ft long and the width of the roof is 32 ft wide. Therefore, the area of the roof is length * width.

Area of the roof = length of the roof * width of the roof

Area = 62 ft * 32 ft

Area = 1984 sq. ft

Here, also given the slope of the roof is 1:2 which indicates the ratio of rise and run.

Slope of the roof = Rise / Run = 1 / 2

Then, the slope factor is \(\frac{\sqrt{\frac{ 1^{2} }{2 ^{2} } }}{12}\) = \(\frac{1}{24}\) = 0.04167

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The right question is:

How many square feet of roofing is needed for the roof of a building that is 32 ft wide and 62 ft long?

Answer:

1.05

Step-by-step explanation:

3.5x.30=1.05

Answer:

1.05

Step-by-step explanation:

You will have to multiply if you are trying to find the amount of water in total. So, 0.30*3.5=1.05. So, that would be your answer for the amount of rainfall.

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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The updated solution is x1 = 5/2, x2 = 9/4, and x3 = 0.

To apply the Simple Active-Set Method to the given problem, we first write the Lagrangian function as:

L(x, λ) = x1^2 + 2x2^2 + 3x3^2 - λ(x1 + x2 + x3 - 1)

where λ is the Lagrange multiplier.

At each iteration, we need to identify the active set of constraints and solve a subproblem to find the search direction. We start with the initial guess x0 = (5, 9, 2)^T and assume that all constraints are inactive.

Step 1: Check Optimality

We calculate the gradient of the Lagrangian as:

∇L(x, λ) = [2x1 - λ, 4x2 - λ, 6x3 - λ, -(x1 + x2 + x3 - 1)]

Setting this gradient to zero, we get:

x1 = λ/2

x2 = λ/4

x3 = λ/6

x1 + x2 + x3 = 1

Substituting these values into the constraint inequalities, we get:

λ/2 ≥ 0

λ/4 ≥ 0

λ/6 ≥ 0

These conditions imply that λ ≥ 0. Since the objective function is strictly convex, the point x0 = (5, 9, 2)^T is not optimal.

Step 2: Identify Active Constraints

Since λ ≥ 0, the first two inequality constraints are inactive. The third inequality constraint is active, i.e., x3 = 0.

Substituting x3 = 0 into the objective function and the remaining constraints, we get:

minimize f(x) = x1^2 + 2x2^2

subject to x1 + x2 ≥ 1

x1 ≥ 0

x2 ≥ 0

The active-set subproblem is to minimize the above objective function subject to the given constraints.

Step 3: Solve Active-Set Subproblem

We use a reduced Newton method to solve the active-set subproblem. The reduced Hessian is given by:

H = [2  0]

[0  4]

At the current point x0 = (5, 9, 0)^T, we have:

∇f(x0) = [10, 36]^T

Solving the equation HΔx = -∇f(x0), we get:

Δx = [-5/2, -9/4]^T

Step 4: Update Solution

The search direction Δx is in the direction of decreasing f(x). However, we need to ensure that the constraints are satisfied after taking the step Δx. In particular, we need to check if any previously inactive constraints have become active or any previously active constraints have become inactive.

In this case, the only active constraint is x1 + x2 ≥ 1. We can take the full step Δx = [-5/2, -9/4]^T since it satisfies the constraint x1 + x2 ≥ 1.

Therefore, the updated solution is x1 = 5/2, x2 = 9/4, and x3 = 0.

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Answer:

__

0.45

__

__ means it's on-going, so 0.45454545