I would like to know the answer

1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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Answer:

JL = 70

Step-by-step explanation:

Since K is the midpoint of JL then JK = KL and

JL = JK + KL = 9x - 1 + 2x + 27 = 11x + 26

solve for x using JK = KL

9x - 1 = 2x + 27 ( subtract 2x from both sides )

7x - 1 = 27 ( add 1 to both sides )

7x = 28 ( divide both sides by 7 )

x = 4, hence

JL = 11x + 26 = (11 × 4 ) + 26 = 44 + 26 = 70

Answer:

XZ = 2.5 BD

Step-by-step explanation:

Comparing the two triangles,

\(\frac{BD}{BC}\) = \(\frac{XZ}{XY}\)

\(\frac{6}{8}\) = \(\frac{XZ}{20}\)

⇒ XZ = \(\frac{20*6}{8}\)

         = 15

XZ = 15

So that,

BD:XZ = 6:15

           = 1:2.5

Therefore, the relationship between BD and XZ is XZ = 2.5 BD.

Answer:

$3.039

Step-by-step explanation:

Step 1

They bought 2 pounds of paper hearts at $ 3.42 per pound

1 pound = $3.42

2 pounds =

2 × $3.42

= $6.84

2 pounds of sparkling stars for $ 3.93 per pound

1 pound of sparking stars = $3.93

2 pounds =

$3.93 × 2

= $7.86

5 pounds of shiny coils for $ 2.53 per pound.

1 pounds of shiny coils = $2.53

5 pounds =

5 × $2.53

= $12.65

Step 2

We find the total cost of the materials

Total cost of Materials that make up the confetti = Cost of paper heart + Cost of sparkling stars + Cost of shiny coils.

= $6.84 + $7.86 + $12.65

= $27.35

Step 3

Total pounds of materials bought = 2 pounds + 2 pounds + 5 pounds

= 9 pounds

Step 4

The cost per pound of confetti = Total cost of the materials bought/ Total pounds of materials

= $27.35/9

= $3.0388888889

Approximately ≈ $3.039

The cost per pound of the confetti = $3.039

The cost per pound of the confetti is  $3.04

Given that, they bought 2 pounds of paper hearts at $ 3.42 per pound.

The cost of 2 pounds of paper hearts is, \(=2 *3.42=6.84\)

the 2 pounds of sparkling stars for $ 3.93 per pound

The cost of 2 pounds of sparkling stars is, \(=$3.93 * 2=7.86\)

the 5 pounds of shiny coils for $ 2.53 per pound.

The cost of 5 pounds of  shiny coils is, \(=5 * $2.53=12.65\)

Total cost of confetti is,

                         \(= $6.84 + $7.86 + $12.65=27.35\)

Total pounds of materials bought ,

                          \(=2+2+5=9pounds\)

The cost per pound of confetti is,

                         \(=\frac{27.35}{9}=3.04\)

The cost per pound of the confetti  is $3.039

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The distribution does not represent a probability distribution. The correct option is b.

A probability distribution should satisfy two main conditions: (1) the sum of the probabilities for all possible outcomes should be equal to 1, and (2) the probabilities for each outcome should be between 0 and 1 (inclusive).

In this distribution, the probabilities for the outcomes are 0.3, 0.4, 0.3, and 0.1 for the values of X as 3, 6, 9, and 0, respectively. However, the sum of these probabilities is 1.1, which violates the first condition of a probability distribution.

Therefore, this distribution does not meet the requirements of a probability distribution and is not a valid probability distribution. The correct answer is option b.

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The time taken to travel the distance 70 Km/h is 11 hours.

Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took.

The formula can be rearranged in three ways:

Given:

time = 9 hours

speed = 85 Km/h

Now, distance

=speed * time

=85 * 9

= 765 km

As, the speed is 70 km/h

time = distance/ speed

time = 765 / 70

time = 10.92

time= 11 hours

Hence, the time taken to travel the distance 70 Km/h is 11 hours.

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The translation of the question is:

A car takes 9 hours to travel a distance with a speed of 85km/h, how long will it take to travel the same distance at 70km/h?

The sum of the series 2 + 4 + 6 + 58 can be expressed using sigma notation as Σ(i = 1 to 4) 2i, which simplifies to 20.

The first term of the series is 2, the second term is obtained by adding 2 to the first term (2 + 2 = 4), the third term is obtained by adding 2 to the second term (4 + 2 = 6), and so on. Finally, the last term of the series is 58.

Now, let's express this series using sigma notation:

Σ(i = 1 to n) 2i

In the above notation, the Greek letter sigma (Σ) represents the sum. The variable i is the index of summation, which starts at 1 and goes up to n. In this case, n represents the number of terms in the series.

The expression 2i represents the terms of the series. As i increases from 1 to n, the value of 2i increases accordingly. For example, when i = 1, 2i = 2. When i = 2, 2i = 4, and so on.

To find the sum of the series using sigma notation, we substitute the values of the index of summation into the expression 2i and add up the terms:

Σ(i = 1 to n) 2i = 2(1) + 2(2) + 2(3) + ... + 2(n)

For our specific series, we have:

Σ(i = 1 to 4) 2i = 2(1) + 2(2) + 2(3) + 2(4)

Simplifying this expression, we get:

2 + 4 + 6 + 8 = 20

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Based on the data from the recent sample of customers, there is evidence to suggest that the percentages of people applying for Silver, Gold, and Platinum cards have changed at a significance level of 0.01.

To determine if there is evidence to suggest that the percentages of people applying for Silver, Gold, and Platinum credit cards have changed, we can conduct a hypothesis test using the chi-square goodness-of-fit test.

Null Hypothesis: The percentages of people applying for Silver, Gold, and Platinum cards are still 60%, 30%, and 10% respectively.

Alternative Hypothesis (Ha): The percentages of people applying for Silver, Gold, and Platinum cards have changed.

We will use a significance level (α) of 0.01.

To conduct the chi-square goodness-of-fit test, we need to calculate the expected frequencies under the assumption of the null hypothesis.

Expected Frequencies:

For Silver: 60% of the total sample size

Expected frequency for Silver = 0.60 * (110 + 55 + 35)

For Gold: 30% of the total sample size

Expected frequency for Gold = 0.30 * (110 + 55 + 35)

For Platinum: 10% of the total sample size

Expected frequency for Platinum = 0.10 * (110 + 55 + 35)

Expected frequency for Silver = 0.60 * (200) = 120

Expected frequency for Gold = 0.30 * (200) = 60

Expected frequency for Platinum = 0.10 * (200) = 20

Now we can set up the chi-square test statistic:

χ² = Σ [(Observed Frequency - Expected Frequency)² / Expected Frequency]

Calculating the chi-square test statistic:

χ² = [(110 - 120)² / 120] + [(55 - 60)² / 60] + [(35 - 20)² / 20]

χ² = [(-10)² / 120] + [(-5)² / 60] + [(15)² / 20]

   = 100/120 + 25/60 + 225/20

   = 0.833 + 0.417 + 11.25

   = 12.50

Next, we need to determine the degrees of freedom for the test. In this case, there are three categories (Silver, Gold, Platinum), so the degrees of freedom (df) is (number of categories - 1) = 3 - 1 = 2.

Using a chi-square distribution table or statistical software, we can find the critical chi-square value for α = 0.01 with df = 2. The critical value is approximately 9.210.

Comparing the calculated chi-square value (12.50) with the critical chi-square value (9.210), we can make a decision.

Since the calculated chi-square value (12.50) is greater than the critical chi-square value (9.210), we reject the null hypothesis.

Therefore, based on the data from the recent sample of customers, there is evidence to suggest that the percentages of people applying for Silver, Gold, and Platinum credit cards have changed at a significance level of 0.01.

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Answer:

  3.85 minutes

Step-by-step explanation:

You want to know the time it takes for taxis traveling 33 mph and 45 mph toward each other to meet if they start 5 miles apart.

The speed at which the taxis approach each other is (33 mph +45 mph) = 78 mph. The time it takes to close the 5-mile gap is ...

  time = distance/speed

  time = (5 mi)/(78 mi/h) = 5/78 h ≈ 0.0641 h

In minutes, the time is ...

  (5/78 h)(60 min/h) = 300/78 min ≈ 3.85 minutes

__

Additional comment

That's about 3 minutes 50.8 seconds.

The value of dz is given by (cd(cz - 5))/(-cz + 5). Let us consider that the line cx passes through the intersection of cd and xz. By the alternate interior angle theorem, angle dcz is equal to the angle cxz.

Therefore, triangles cdz and cxz are similar.Using the fact that triangles cdz and cxz are similar, we can write:

cd/cz = cx/cz (corresponding sides of similar triangles are proportional)

cd/(cz + dz) = cx/cz (using the fact that cz + dz = xz)

cd/(cz + dz) = 5/cz (since cx = 5)

cz(cd + dz) = 5(cd + dz)

cz*cd + cz*dz = 5*cd + 5*dz

cz*dz = 5*cd - cz*cd + 5*dz

cz*dz = cd(5 - cz) + 5*dz

dz = (cd(5 - cz))/(5 - cz)

Now, substituting the given value of cx = 5 in the above equation we get,

dz = (cd(5 - cz))/(5 - cz) = (cd(cz - 5))/(-cz + 5)

Therefore, the value of dz is given by (cd(cz - 5))/(-cz + 5).

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Frequency and wavelength are related by the equation f=cλ, where c is the speed of light in a vacuum. The speed of light in a vacuum is 2.9979×108 m/s. Wavelength must be converted from kilometers to meters, then the values can be plugged into the equation. f=2.9979×108 m/s5,700 m=52,594 Hz. The resulting frequency is 52,594 Hz or 5.3×104 Hz when rounded to the correct number of significant figures.

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In a simple linear regression model, the coefficient of the independent variable (x) in the estimated sample regression equation indicates the change in the predicted value of the dependent variable (y) when x increases by one unit. This coefficient is also known as the slope of the regression line. Therefore, to calculate the predicted value of y, we multiply the coefficient by the value of x and add the intercept.

In a simple linear regression model, the coefficient that indicates the change in the predicted value of y when x increases by one unit is the "slope coefficient" or the "regression coefficient" (usually denoted as b1). This coefficient represents the relationship between the independent variable x and the dependent variable y.

The linear regression equation is given as:

y = b0 + b1 * x

Where:
- y is the predicted value of the dependent variable
- b0 is the intercept coefficient (where the line intersects the y-axis)
- b1 is the slope coefficient (the change in y when x increases by one unit)
- x is the independent variable

In this equation, b1 indicates the change in the predicted value of y when x increases by one unit.

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In the video game Unicorn Quest, Brianna earned 56 points for completing 2 levels.

To find out how many points she will earn for completing 4 levels, we can determine the equivalent ratio between the number of levels and the points earned.

We can set up a proportion to find the equivalent ratio. Let's represent the number of levels as "L" and the number of points as "P." The given information states that when completing 2 levels, Brianna earned 56 points, so we have the ratio 2/56. To find the equivalent ratio for 4 levels, we can set up the proportion as (2/56) = (4/P).

To solve this proportion, we can cross-multiply: 2P = 4 * 56. Simplifying the right side, we have 2P = 224. Dividing both sides by 2, we find P = 112.

Therefore, Brianna will earn 112 points for completing 4 levels in the game Unicorn Quest.

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Answer:olution:. Given data:. Answer:. sum_(n=4)^10 15(3/10)^(n-1)= sum_(n=4)^10 15(0.3)^(n-1) = 15 [(0.3)^3 + (0.3)^4 + (0.3)^5+ (0.3)^6 + (0.3)^7+ (0.3)^8 + ...

Doesn’t include: 0.58 ‎b ‎1.92 ‎c ‎6.42 ‎d ‎9.43

Evaluate: summation from n equals 4 to 10 of 15 times 3 tenths to the n minus 1 power period Round to the nearest hundredth.

Step-by-step explanation:Example

Evaluate X

4

r=1

r

3

.

Solution

This is the sum of all the r

3

terms from r = 1 to r = 4. So we take each value of r, work out

r

3

in each case, and add the results. Therefore

X

4

r=1

r

3 = 13 + 23 + 33 + 43

= 1 + 8 + 27 + 64

= 100 .

Example

Evaluate X

5

n=2

n

2

.

Solution

In this example we have used the letter n to represent the variable in the sum, rather than r.

Any letter can be used, and we find the answer in the same way as before:

X

5

n=2

n

2 = 22 + 32 + 42 + 52

= 4 + 9 + 16 + 25

= 54 .

Example

Evaluate X

5

k=0

2

k

.

The change in kinetic energy of a body can be calculated by multiplying the force applied to the body by the distance it moves. In this case, a body of mass 20 kg is subjected to a force of 40 N for 5 seconds.

The change in kinetic energy (ΔKE) can be calculated using the formula ΔKE = F * d, where F is the force applied and d is the distance covered by the body. However, in this case, we are only given the force and the time (5 seconds), but not the distance.

To calculate the change in kinetic energy, we need to consider the relationship between force, mass, acceleration, and distance covered. According to Newton's second law of motion (F = m * a), we can determine the acceleration (a) experienced by the body by dividing the force by the mass: a = F / m.

Once we have the acceleration, we can use the kinematic equation v = u + at, where v is the final velocity, u is the initial velocity (which is zero since the body is initially at rest), a is the acceleration, and t is the time. Solving for v, we get v = a * t.

Since the body starts from rest, the initial kinetic energy is zero. The final kinetic energy can be calculated using the formula KE = (1/2) * m * \(v^2\), where m is the mass and v is the final velocity obtained from the previous step.

Therefore, to find the change in kinetic energy, we subtract the initial kinetic energy (zero) from the final kinetic energy calculated.

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Answer: D. The membership increases by 50 members in each of the six warmest months and decreases by 50 members in each of the other six months.

Step-by-step explanation: Because it is a linear function it needs to fluctuate so by using process of elimination D is the only answer that would look like a linear function by having that curved line we are looking for in a function.

Answer:

length = 3x - 1

Step-by-step explanation:

Area of a rectangle = length x width

or using l = length, w = width and A = area

A = l x w

or

l = A/w

Given
A = 18x² - 6x
w = 6x

l = 18x²- 6x/6x

= 18x²/6x - 6x/6x

= 3x - 1

Answer:

3x - 1

Step-by-step explanation:

Area of the Rectangle:

18x^2 - 6x

6x (3x - 1)

Width = 6x

Length =?

Area of Rectangle = Length *  Width

Length = Area/breadth

6x (3x -1) / 6x cross out 6x

Thus, Length of Rectangle = 3x - 1

Answer:0.0625

Step-by-step explanation:

Answer:

1/16.

Step-by-step explanation:

4 ^-2 = 1 / 4^2

= 1/16.

The probability of no one getting a hole in one on the sixth hole during the 1989 U.S. Open golf tournament is 0.95431 and the probability of exactly one golfer getting a hole in one on the sixth hole is 0.04478.

The probability of an event occurring is the number of favorable outcomes divided by the number of possible outcomes. In this case, the probability of a professional golfer making a hole in one is 1/3,709.

a. To find the probability that no one gets a hole in one on the sixth hole, we need to find the probability that each of the 174 golfers does not get a hole in one. The probability of not getting a hole in one is 1 - (1/3,709) = 3,708/3,709. The probability that no one gets a hole in one is (3,708/3,709)^174 = 0.95431. Therefore, the probability that no one gets a hole in one on the sixth hole is 0.95431.

b. To find the probability that exactly one golfer gets a hole in one on the sixth hole, we need to find the probability that one golfer gets a hole in one and the rest do not. The probability of one golfer getting a hole in one is 1/3,709 and the probability of the rest not getting a hole in one is (3,708/3,709)^173. There are 174 ways this can happen, so the probability is 174 * (1/3,709) * (3,708/3,709)^173 = 0.04478. Therefore, the probability that exactly one golfer gets a hole in one on the sixth hole is 0.04478.

In conclusion, the probability of no one getting a hole in one on the sixth hole during the 1989 U.S. Open golf tournament is 0.95431 and the probability of exactly one golfer getting a hole in one on the sixth hole is 0.04478.

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Answer:

n/4

Step-by-step explanation:

Answer:

Give the domain

Step-by-step explanation:

Answer:

Celsius = 100c

Fahrenheit = 212f

the The Solution:

Step 1:

We shall split the triangular pyramid into its component surfaces.

3 triangles + 1 triangle.

Step 2:

We shall find the area of the triangle in fig 1., by using Heron's formula.

Step 3:

We shall state the formula for calculating the total surface area of the triangular pyramid.

Step 4:

We shall substitute the above values into the formula.

Step 4:

The presentation of the Answer.

The slant height is 11.4 centimeters.

Thus, the correct answer is 11.4 centimeters.

Answer:

W = - 6

Step-by-step explanation:

-3(-8w+1) - w = 5(w-1) - 1 -> (Original equation)

24w - 3 - w = 5w - 5 - 1 -> (Expanded version)

23w - 3 = 5w - 6 -> (Simplified version)

18w - 3 = - 6 -> (Subtract 5w from both sides)

18w = - 3 -> (Add 3 to both sides)

w = 18/-3 which is - 6 -> (Doing 18/-3)