Let X and Y be continuous random variables with joint probability density function
fX,Y (x,y) =2(x^2)y/81 , 0 ≤x ≤3, 0 ≤y ≤3
0, otherwise.
Find P(X > 3Y ) and P(X + Y > 3).

Answer:

y≤-2x=+1

Step-by-step explanation:

this will definitely on coordinate plan.

Kindly completed your question as it seem unfinished

Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

a) To determine values of h and k such that the system x1 + hx2 = 2, 4x1 + 8x2 = k has (a) no solution, set the determinant of the system equal to zero: h*8 - 4*2 = 0. Solving for h yields h = 8/2 = 4, and setting k equal to 8 yields a no solution.

b) To determine values of h and k such that the system x1 + hx2 = 2, 4x1 + 8x2 = k has (b) a unique solution, set the determinant of the system not equal to zero: h*8 - 4*2 ≠ 0. Solving for h yields h ≠ 4, and setting k equal to 8 yields a unique solution of x1 = 1 and x2 = 1.

c) To determine values of h and k such that the system x1 + hx2 = 2, 4x1 + 8x2 = k has (c) infinitely many solutions, set the determinant of the system equal to zero: h*8 - 4*2 = 0. Solving for h yields h = 4, and setting k equal to 8 yields infinitely many solutions of the form x1 = k1, x2 = k2, where k1 and k2 are any real numbers.

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For the given function f(x), x-intercepts are 1,2 and 6 and the y-intercept is -12

Given :

\(f(x) = x^{3} -9x^{2} +20x -12 \\\)

One of the factors of f(x) is (x-6)

Dividing f(x) by (x-6), we get :
\(\frac{x^{3} -9x^{2} +20x -12 \\}{x-6} = x^{2} -3x +2\)

Now expanding, \(x^{2} -3x +2\)

\(x^{2} -3x +2 = x^{2} -2x -x +2 =x(x-2) -(x-2) = (x-2)(x-1)\)

Hence, \(x^{3} -9x^{2} +20x -12 = (x-6)(x-1)(x-2)\)

For x-intercept, f(x) = 0 . Then

(x-6)(x-1)(x-2) =0

x = 1,2 and 6

For y-intercept, x=0 in f(x)

f(0) = -12

Hence, the x-intercepts are 1,2, and 6 and the y-intercept is -12.

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answer

measure of o is 75

and n is same as o as the sides are same

hope this helps you

Answer:

177

Step-by-step explanation:

Answer: a_10 = 177147/65536. Write the general term through the pattern:: a_n = 36 3/4 n - 1 Substitute and calculate:: a_10 = 177.

Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.

In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.

Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.

A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).

Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.

Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).

Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.

By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.

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Answer:

540 degrees (interior angles)

Step-by-step explanation:

Answer:

The answer is 52 cm

Step-by-step explanation:

Answer: 52 cm

Step-by-step explanation:

For the given right triangle, we can see that:

UV = 2√11

TV = √33

mU = 60°

Here we can see a right triangle where we know one angle and the opposite cathetus, first we can find the hypotenuse using:

sin(angle) = (opposite cathetus)/hypotenuse.

Replacing the values that we know, we will get:

sin(30°) = √11/UV

Then:

UV = √11/sin(30°) = 2√11

For TV we can use the tangent function:

tan(30°) = √11/TV

TV = √11/tan(30°) = √11*√3 = √33

Finally, for the measure of U, we know that the sum of the 3 interior angles must be 180°, and one measures 90° and one 30°, then:

30 + 90 + U = 180

U = 180 - 30 - 90

U = 60

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Step-by-step explanation:

6 I think that is the answer I hop you get it right

Answer:

A

Step-by-step explanation:

The answer is a because essentially what it's asking for is the y intercept.

it gives us what the value of y = 1 so all we have to do is find the constant rate of change which is 3 and subtract that from 8

8-3=5 so your answer is A

Answer:

16

Step-by-step explanation:

im pretty sure

We would expect to see approximately 4.2 defects in total if two containers are inspected.

If the number of visible defects on a product container follows a Poisson distribution with a mean of 2.1, then the probability of having x defects on a single container is given by:

P(X = x) = \(e^(-2.1) * (2.1)^x / x!\)

where e is the mathematical constant approximately equal to 2.71828.

To find the expected number of defects in two containers, we can use the linearity of expectation, which states that the expected value of a sum of random variables is equal to the sum of their expected values. Therefore, the expected number of defects in the two containers is:

E(X1 + X2) = E(X1) + E(X2)

Since the Poisson distribution is memoryless, the expected number of defects in one container is equal to the mean, which is 2.1. Therefore:

E(X1 + X2) = E(X1) + E(X2) = 2.1 + 2.1 = 4.2

So, we would expect to see approximately 4.2 defects in total if two containers are inspected.

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Answer:

Step-by-step explanation:

A. 2 + -1 - 1^2 = 1 - 1 = 0

B. 2^3 - -1 + 1 = 8 + 1 + 1 = 10.

C. 2 - -1 - 1 = 2 + 1 - 1 = 2.

=2+(-1-1)^2

=1-1

=0

2^3-(-1+1)

=8+1+1

= 10

2-(-1-1)

=2+1-1

=2

Answer:

I believe 72

Step-by-step explanation:

The ratio between the time and charge is 2:3 and which defines their proportionality.

Proportion is explained majorly based on ratio and fractions. A fraction, represented in the form of a/b, while ratio a:b, then a proportion states that two ratios are equal. Here, a and b are any two integers. Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

In the table given, we can find the proportion between time and charge.

When time (t) = 0.5, the charge = $2.25

This can be written as 0.5 : 2.25 = 2 : 3

When time = 1, the charge = 1.5

When time = 1 1/2 = 1.5, the charge = 2.25

When time = 2, the charge = 3

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By induction, the formula 1+2+3+…+(n−1)+n= 2n(n+1) is true for any n∈N.

To prove the formula 1+2+3+…+(n−1)+n= 2n(n+1) by induction, we need to first establish the base case and then show that the formula holds for any n∈N by assuming it is true for n=k and then proving it is true for n=k+1.

Base case: n=1
1= 2(1)(1+1)
1= 2(2)
1= 4
This is true, so the base case holds.

Inductive step:
Assume the formula is true for n=k, that is:
1+2+3+…+(k−1)+k= 2k(k+1)

Now we need to show that the formula is true for n=k+1:
1+2+3+…+(k−1)+k+(k+1)= 2(k+1)(k+1+1)

We can use the assumption that the formula is true for n=k and substitute it into the left side of the equation:
2k(k+1)+(k+1)= 2(k+1)(k+1+1)

Distributing the 2 on the left side of the equation:
2k^2+2k+k+1= 2(k+1)(k+2)

Simplifying:
2k^2+3k+1= 2(k^2+3k+2)

Distributing the 2 on the right side of the equation:
2k^2+3k+1= 2k^2+6k+4

Subtracting 2k^2+3k+1 from both sides of the equation:
0= 3k+3

Dividing by 3:
0= k+1

This is true for any k∈N, so the formula holds for n=k+1. Therefore, by induction, the formula 1+2+3+…+(n−1)+n= 2n(n+1) is true for any n∈N.

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Answer:

43, 52, 61

(adding nine each time)

When b is 3, the value of the expression \(2b^3 + 5\) is 59.

To evaluate the expression\(2b^3 + 5\) when b is 3, we substitute the value of b into the expression and perform the necessary calculations.

Given that b = 3, we substitute this value into the expression:

\(2(3)^3 + 5\)

First, we evaluate the exponent, which is 3 raised to the power of 3:

2(27) + 5

Next, we perform the multiplication:

54 + 5

Finally, we add the two terms:

59

Therefore, when b is 3, the value of the expression \(2b^3 + 5\) is 59.

In summary, by substituting b = 3 into the expression \(2b^3 + 5\), we find that the value of the expression is 59.

It's important to note that the provided equation has multiple possible solutions for x, but when b is specifically given as 3, the value of x is approximately 3.78.

It's important to note that in this equation, we substituted the value of b and solved for x, resulting in a specific value for x. However, if we wanted to solve for b given a specific value of x, we would follow the same steps but rearrange the equation accordingly.

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Answer:

434433444444444446666%$"$$$

Answer:

0 and 1123

Step-by-step explanation:

The car with the speed of 50 Km/h travels the fastest.

We have given with three choices for selecting the fastest speed from them. The three choices are

First choice is 50 Km/h.

Second Choice is  car b travels a distance of d kilometers in h hours, based on the equation 55 h = d , h, equals, d.. So from this be can conclude that this car is moving with the speed of (1/55)km/h.

Third choice is  car c travels 135 kilometers in 3 hours. So from this be can conclude that this car is moving with the speed of (135/3) Km/h i.e., 45 Km/h.

So, from the given choices we can conclude that the car with the speed of 50 Km/h travels the fastest.

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Answer:

Step-by-step explanation:

Your y= -x2 -10x +1 should be written as y = -x^2 -10x +1.  This is a quadratic function.  Because the coefficient (-1) of the x^2 term is negative, we know immediately that the graph (a parabola) opens down, and thus has a maximum.

There are 46 different ways in which a set of 10 coins can have a total value of 59 cents.

To find the number of different ways, we can use a systematic approach. Let's consider the five types of coins: pennies (1 cent), nickels (5 cents), dimes (10 cents), quarters (25 cents), and half-dollars (50 cents).

Since we need a total value of 59 cents, we can start by using as many half-dollars as possible. The maximum number of half-dollars that can be used is one since two half-dollars would already exceed the required total.

Next, we can iterate through the remaining values and combinations of the remaining coins (quarters, dimes, nickels, and pennies) to find all possible ways to reach 59 cents. We can use nested loops to generate all the combinations. By trying different combinations, we find that there are 46 different ways to achieve a total value of 59 cents using 10 coins.

There are 46 different ways in which a set of 10 coins can have a total value of 59 cents. This calculation takes into account all possible combinations of pennies, nickels, dimes, quarters, and half-dollars.

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The sample variance using the computing formula is S² = 2.24.

The sample standard deviation is S ≈ 1.496.

To calculate the sample variance, s², using the definition formula, you need to follow these steps:

1. Find the mean (average) of the measurements:

Mean (x-bar) = (5 + 3 + 5 + 3 + 1) / 5 = 17 / 5 = 3.4

2. Calculate the deviation of each measurement from the mean:

Deviation = measurement - mean

Deviation = (5 - 3.4), (3 - 3.4), (5 - 3.4), (3 - 3.4), (1 - 3.4)

= 1.6, -0.4, 1.6, -0.4, -2.4

3. Square each deviation:

Deviation squared = (1.6)², (-0.4)², (1.6)², (-0.4)², (-2.4)²

= 2.56, 0.16, 2.56, 0.16, 5.76

4. Calculate the sum of the squared deviations:

Sum of squared deviations = 2.56 + 0.16 + 2.56 + 0.16 + 5.76

= 11.2

5. Divide the sum of squared deviations by (n-1), where n is the number of measurements:

Sample variance (s²) = Sum of squared deviations / (n-1)

= 11.2 / (5-1)

= 11.2 / 4

= 2.8

Therefore, the sample variance using the definition formula is s^2 = 2.8.

To calculate the sample variance, s², using the computing formula, you can follow these steps:

1. Find the mean (average) of the measurements (x-bar) as calculated previously:

Mean (x-bar) = 3.4

2. Calculate the squared deviation of each measurement from the mean:

Squared deviation = (measurement - mean)^2

= (5 - 3.4)², (3 - 3.4)², (5 - 3.4)², (3 - 3.4)², (1 - 3.4)²

= 1.6², -0.4², 1.6², -0.4², -2.4²

= 2.56, 0.16, 2.56, 0.16, 5.76

3. Calculate the sum of the squared deviations:

Sum of squared deviations = 2.56 + 0.16 + 2.56 + 0.16 + 5.76

= 11.2

4. Divide the sum of squared deviations by (n), where n is the number of measurements:

Sample variance (s²) = Sum of squared deviations / n

= 11.2 / 5

= 2.24

Therefore, the sample variance using the computing formula is S² = 2.24.

To calculate the sample standard deviation, s, you need to take the square root of the sample variance (s²):

s = √(s²)

= √(2.24)

≈ 1.496 (rounded to three decimal places)

Therefore, the sample standard deviation is S ≈ 1.496.

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Answer:

False

Step-by-step explanation:

It has two parts that is separated by a minus.

The correct similarity of the triangles are JMK ~ LMK ~ JLM (option D)

Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles and equal scale factors. Equal scale factors mean that the lengths of their corresponding sides have a matching ratio.

Given that, there are 3 right triangles in the drawing given. They are all similar. we need to identify the correct similarity,

So, from the figure, if we separate each triangle,

We will get,

Triangles JLM, JMK and LMK

If we check,

They are showing true similarity by their figure (refer to diagram attached)

Hence, the correct similarity of the triangles are JMK ~ LMK ~ JLM (correct option is D)

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Your investment of $10000 compounded continuously at 6% p.a. would be worth $14,366.00 after 6 years.

If you invest $10000 compounded continuously at 6% p.a., the formula for calculating the value of your investment after 6 years would be:

A = Pe^(rt)

Where A is the final amount, P is the principal investment amount, e is Euler's number (approximately 2.718), r is the interest rate (in decimal form), and t is the time period (in years).

Plugging in the given values, we get:

A = 10000e^(0.06*6)

A = 10000e^(0.36)

A = 10000*1.4366

A = $14,366.00

Therefore, your investment of $10000 compounded continuously at 6% p.a. would be worth $14,366.00 after 6 years.

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Answer:

6x=-60

Step-by-step explanation: