An account with an initial balance of $1250 earns interest that is compounded quarterly. If no other deposits or withdrawals are made, the account will have a balance of $1406.08 after 9 months. Find the annual interest rate.

The set of all first components of the ordered pairs of a function are called the Independent Variable.

In a function, the first component of the ordered pairs is known as the independent variable, which is the input value of the function. The second component of the ordered pairs is known as the dependent variable, which is the output value of the function. The set of all first components is also called the domain of the function, while the set of all second components is called the range of the function.

Therefore, the correct term to complete the statement is the Independent Variable.

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There does not exist a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}.

(a) To show that NG(H) = G, we need to show that every element of G normalizes H. Let g ∈ G, and let h ∈ H. Since H = ker(φ), we know that φ(h) = 1. Now, we need to show that ghg⁻¹ ∈ H. Using the properties of a homomorphism, we can write:

φ(ghg⁻¹) = φ(g)φ(h)φ(g⁻¹) = φ(g)1φ(g⁻¹) = φ(g)φ(g⁻¹) = φ(gg⁻¹) = φ(1) = 1

Therefore, ghg⁻¹ ∈ H, and so g normalizes H. Since this is true for any g ∈ G, we can conclude that NG(H) = G.

(b) Suppose there exists a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}. Since s ∈ ker(φ), we know that φ(s) = 1. However, we also know that rs = sr⁻¹, and so φ(rs) = φ(sr⁻¹). Using the properties of a homomorphism, we can write:

φ(r)φ(s) = φ(s)φ(r⁻¹) = φ(s)φ(r)⁻¹

Since φ(s) = 1, this simplifies to:

φ(r) = φ(r)⁻¹

But this means that φ(r) is its own inverse, and so φ(r)² = 1. However, we also know that rn = 1, and so φ(rn) = 1. Using the properties of a homomorphism, we can write:

φ(rn) = φ(r)ⁿ = (φ(r)²)ⁿ/2 = 1ⁿ/2 = 1

But this means that n/2 must be an integer, which contradicts the fact that n > 2. Therefore, there does not exist a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}.

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Answer: 2783 minutes

Step-by-step explanation:

Answer:

2783

Step-by-step explanation:

Since there is 11 episodes in each season and there is 23 seasons we multiply and get 253 so 253 episodes and each one has 11 minutes so 11 x 253 which is 2783

The equation for the relationship between the net profit and the number of tickets sold is Y= 70x - 1500.

We are aware that the group charges $70 for each ticket and that after selling 10 tickets, there was a net loss of $800. Thus, the sum of the proceeds from the sale of the ten tickets was:

10 tickets sold for $70 each will bring in a total of $700.

The total production expenses must have been: Given that the net loss was $800:

Costs of production in total are $700 + $800 = $1500.

Let x be the number of purchased tickets. The sum of the sales of x tickets is:

Selling x tickets will bring in a total of $70.

The sum of the revenue less the sum of the production costs is the net profit:

All revenue minus all costs of production equals net profit.

[tex]Y = x × $70 - $1500[/tex]

Thus, the following equation represents the connection between the net profit and the number of tickets sold:

Y = 70x - 1500

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The critical numbers of f''(x) are 5 and 4.5.

To find the critical numbers of f(x), we need to first find the derivative of f(x) and then set it equal to zero. The derivative of f(x) is f'(x) = 4x3 - 57x2 + 270x. Setting this equal to zero gives us:

4x3 - 57x2 + 270x = 0

Factoring out an x gives us:

x(4x2 - 57x + 270) = 0

Using the quadratic formula, we can find the values of x that make this equation true:

x = (-(-57) ± √((-57)2 - 4(4)(270)))/(2(4))

x = (57 ± √(3249 - 4320))/8

x = (57 ± √(-1071))/8

x = (57 ± i√1071)/8

Since the values of x are complex, there are no real critical numbers of f(x).

The second derivative of f(x) is f''(x) = 12x2 - 114x + 270. Setting this equal to zero gives us:

12x2 - 114x + 270 = 0

Using the quadratic formula, we can find the values of x that make this equation true:

x = (-( -114) ± √((-114)2 - 4(12)(270)))/(2(12))

x = (114 ± √(12996 - 12960))/24

x = (114 ± √36)/24

x = (114 ± 6)/24

x = 5 or x = 4.5

The table below shows the critical numbers of f(x) and f''(x) in ascending order:

| Critical Number | f(x) | f''(x) |
|-----------------|------|--------|
| 4.5             | N/A  | 0      |
| 5               | N/A  | 0      |

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Therefore, the jar can hold 75.36 cubic inches of peanut butter.

The answer is B) 75.36 in3.

An inch is a unit of measurement that is commonly used in the United States, United Kingdom, and other countries that follow the Imperial system of measurement. It is defined as 1/12th of a foot or 2.54 centimeters. In other words, there are 12 inches in a foot. The inch is often used to measure the length or width of small objects or to express the size of computer screens, TVs, and other electronic displays.

Given by the question.

The volume of a cylinder can be calculated using the formula: V = πr^2h, where r is the radius of the base of the cylinder and h is its height.

In this case, the jar has a diameter of 4 inches, which means the radius is 2 inches (diameter = 2 × radius). The height is given as 6 inches. So, we can calculate the volume of peanut butter that the jar can hold as follows:

V = π[tex]r^{2}[/tex]h

V = 3.14 × [tex]2^{2}[/tex] × 6

V = 3.14 × 4 × 6

V = 75.36 cubic inches

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slope of HI = 6, slope of IJ = -1/6, slope of HJ = 5/7, length of HI = √37, length of IJ = √37, length of HJ = √74, Triangle HIJ is isosceles

The slope of a line is found by the formula (y2-y1)/(x2-x1). The length of a line is found by the formula √((x2-x1)²+(y2-y1)²).

Slope of HI = (1-(-5))/(8-7) = 6/1 = 6
Slope of IJ = (-5-(-4))/(7-1) = -1/6
Slope of HJ = (1-(-4))/(8-1) = 5/7

Length of HI = √((8-7)²+(1-(-5))²) = √(1²+6²) = √(1+36) = √37
Length of IJ = √((7-1)²+(-5-(-4))²) = √(6²+(-1)²) = √(36+1) = √37
Length of HJ = √((8-1)²+(1-(-4))²) = √(7²+5²) = √(49+25) = √74

Triangle HIJ is isosceles because it has two sides with the same length (HI and IJ).

- slope of HI = 6
- slope of IJ = -1/6
- slope of HJ = 5/7
- length of HI = √37
- length of IJ = √37
- length of HJ = √74
Triangle HIJ is isosceles

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The quotient is -6x^2-2x-2 and the remainder is -4.

To find the quotient and remainder for the given expression, we can use long division.

First, we divide the first term of the dividend (-6x^3) by the first term of the divisor (x) to get -6x^2. This is the first term of the quotient.

Next, we multiply the first term of the quotient (-6x^2) by the divisor (x-1) to get -6x^3+6x^2. We subtract this from the dividend to get -2x^2-2.

We repeat this process with the new dividend (-2x^2-2) and the same divisor (x-1). We divide the first term of the new dividend (-2x^2) by the first term of the divisor (x) to get -2x. This is the second term of the quotient.

We multiply the second term of the quotient (-2x) by the divisor (x-1) to get -2x^2+2x. We subtract this from the new dividend to get -2x-2.

We repeat this process one more time with the new dividend (-2x-2) and the same divisor (x-1). We divide the first term of the new dividend (-2x) by the first term of the divisor (x) to get -2. This is the third term of the quotient.

We multiply the third term of the quotient (-2) by the divisor (x-1) to get -2x+2. We subtract this from the new dividend to get -4. This is the remainder.

So, the quotient is -6x^2-2x-2 and the remainder is -4.

We can check our work by verifying that

(Quotient)(Divisor) + Remainder = Dividend:

(-6x^2-2x-2)(x-1) + (-4) = -6x^3+6x^2-2x^2+2x+2x-2-4 = -6x^3+4x^2-2

Therefore, our answer is correct.

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coefficient of correlation is 0.82

a) (i) The scatter plot of the data given is:



(ii) The scatter plot suggests that there is a positive linear relationship between x and y, as the data points move in an upward trend.

b) (i) The fitted line of the regression model is: y = 2.06 + 0.68x

(ii) When x = 250, the predicted value of y is 165.0

(iii) Missing values A, B, C, D, and E in the table are:

A = 3410, B = 5, C = 1, D = 5, E = 6.59

(iv) An estimate of the variance σ2 is 5.98

c) (i) The F-value for the F-test is 6.59, and the p-value is 0.02. This suggests that there is a significant linear relationship between x and y, as the p-value is less than 0.05.

(ii) The percentage of variation in y explained by x is 68.1%.

(iii) The coefficient of correlation is 0.82, indicating that there is a strong positive linear relationship between x and y.

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Given sin θ = -12/13 and θ is in the 4th quadrant, we can use the double angle identities to find sin 2θ and cos 2θ. The double angle identities are:

sin 2θ = 2sin θcos θ

cos 2θ = cos^2 θ - sin^2 θ

First, we need to find cos θ. Since θ is in the 4th quadrant, we know that cos θ is positive. Using the Pythagorean identity, we can find cos θ:

sin^2 θ + cos^2 θ = 1

(-12/13)^2 + cos^2 θ = 1

144/169 + cos^2 θ = 1

cos^2 θ = 25/169

cos θ = 5/13

Now, we can use the double angle identities to find sin 2θ and cos 2θ:

sin 2θ = 2sin θcos θ = 2(-12/13)(5/13) = -120/169

cos 2θ = cos^2 θ - sin^2 θ = (5/13)^2 - (-12/13)^2 = -119/169

Therefore, the answers are:

a. sin 2θ = -120/169

b. cos 2θ = -119/169

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In answering the question above, the solution is Yet it's obvious that this function isn't the right response. As a result, the question or the possible answers might be wrong.

Mathematicians investigate the relationships between numbers, equations, and related structures, as well as the locations of forms and possible placements for these items. A set of inputs and their corresponding outputs are referred to as a "function" in this context. If each input results in a single, unique output, the relationship between the inputs and outputs is known as a function. Each function has its own domain, codomain, or scope. A common way to denote functions is with the letter f. (x). is an x for entry. One-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.

We must work out the equation c(n)/n = 1.3, where c(n)/n is the average cost per part, in order to get the value of n. When we replace the provided cost function, we obtain:

103n/n = 1.3

By condensing, we obtain: 103 = 1.3n.

The result of dividing both sides by 1.3 is: n 79.23

In order for the typical part to cost $1.3 million, around 79 pieces must be produced. The closest option is (d) 10 pieces because this isn't one of the available options. Yet it's obvious that this isn't the right response. As a result, the question or the possible answers might be wrong.

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Answer:

Try out

Step-by-step explanation:

1/4

1/2

1

1 1/2

Answer: 360 degrees

So basically when you spin around you make 360 degrees lol.

The value of 'x' and 'y' in the given circle and triangle are 30 and 12 respectively.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

From the given information we can form,

x² = 18² + 24². (As tangent is always perpendicular to the radius).

x² = 900.

x = 30.

Now, y = x - radius.

y = 30 - 18.

y = 12.

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a) sin B = y/r = -1/5sqrt(2) and cos B = x/r = 7/5sqrt(2) (b) Since sin B is positive and cos B is negative, we found that angle B belongs in Quadrant II.

Given that cot a = 7, we know that tan a = 1/7. Since tan a = y/x, we can let x = 7 and y = -1 (since a is in Quadrant III and both x and y values are negative in this quadrant).

Using the Pythagorean Theorem, we can find r:
r = sqrt(x^2 + y^2) = sqrt(7^2 + (-1)^2) = sqrt(50) = 5sqrt(2)
Now we can find sin B and cos B:
sin B = y/r = -1/5sqrt(2)
cos B = x/r = 7/5sqrt(2)

We can use the double angle formulas for sine and cosine, sin B and cos B: sin B = sin(Phi - a) = sin Phi cos a - cos Phi sin a = (0)(-7/25) - (1)(-24/25) = 24/25 cos B = cos(Phi - a) = cos Phi cos a + sin Phi sin a = (1)(-7/25) + (0)(-24/25) = -7/25.

Since sin B is positive and cos B is negative, we know that angle B is in Quadrant II.

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Knowing the functions f(x) and g(x) we have:

To find the sum, difference, product, and quotient of two functions, we simply perform the corresponding operations on the expressions for each function.

For (f+g)(x), we add the expressions for f(x) and g(x):

(f+g)(x) = (x² + 3x + 1) + (x^2) = 2x² + 3x + 1

For (f-g)(x), we subtract the expression for g(x) from the expression for f(x):

(f-g)(x) = (x² + 3x + 1) - (x²) = 3x + 1

For (f·g)(x), we multiply the expressions for f(x) and g(x):

(f·g)(x) = (x² + 3x + 1) · (x²) = x⁴ + 3x³ + x²

For (f/g)(x), we divide the expression for f(x) by the expression for g(x):

(f/g)(x) = (x² + 3x + 1) / (x²) = 1 + 3x/x² + 1/x² = 1 + 3/x + 1/x²

So, the final answers are:

(f+g)(x) = 2x² + 3x + 1

(f-g)(x) = 3x + 1

(f·g)(x) = x⁴ + 3x³ + x²

(f/g)(x) = 1 + 3/x + 1/x²

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Answer:

x = -2.

Step-by-step explanation:

9.9 = 3.1 - 3.4x

9.9 - 3.1 = -3.4x

6.8 = -3.4

6.8 /-3.4 = -3.4/-3.4

-2 = x

In a triangle EAC, F is the centroid and two medians, then the required expressions are 10x² + 2y , 5x² +y respectively.

The centroid is the centre point of the object. It is a point at which three medians of a triangle meet. Properties :

We have a triangle AEC, with centroid point F. Here, two medians of triangle AEC. Here, AD = 15x² + 3y, we have to determine the expression for bigger and smaller parts of median. As we know, centroid point F, divides median into ratio, 2: 1, i.e., bigger divided part/smaller divided part = 2/1

First expression for bigger divided part of median = (2/3) (15x² + 3y)

= 10x² + 2y

second expression for smaller divided part of median = (1/3) ( 15x² + 3y)

= 5x² + y

Hence, required expression are 10x² + 2y and 5x² + y.

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Answer:

2g) Letty cannot use the factors 4 and 12 to simplify the square root of 48 using the Product Property of Square Roots because 4 is a perfect square, but 12 is not. The Product Property of Square Roots only applies to factors that are both perfect squares.

2h) A better choice to simplify the square root of 48 would be to use the factors 16 and 3. This is because 16 is a perfect square and is a factor of 48, which means it can be taken out of the radical completely. The remaining factor is 3, which cannot be simplified any further since it is not a perfect square. Therefore, the square root of 48 can be simplified to 4 times the square root of 3. It is important to choose 16 and 3 as the factors and not any other pair because 16 is the largest perfect square factor of 48, and 3 is the remaining factor after taking out 16 that cannot be simplified any further.

2g) These factors (4 and 12) are not the best choice to simplify the square root of 48 because 4 is a perfect square, but 12 is not.

2h) a better choice to simplify the square root of 48 would be to use the factors 16 and 3. This is because 16 is the largest perfect square factor of 48, which simplifies the radical the most.

Now, Using the Product Property of Square Roots, we can simplify the square root of 48 as :

√48 = √(4 x 12)

However, these factors (4 and 12) are not the best choice to simplify the square root of 48 because 4 is a perfect square, but 12 is not.

Hence, We want to simplify the radical by finding the largest perfect square that is a factor of 48.

For this, we can break down 48 into its prime factors:

48 = 2 x 2 x 2 x 2 x 3

Then, we group the prime factors into pairs of the same number:

48 = (2 x 2) x (2 x 2) x 3

This gives us two perfect squares, 4 and 16.

Hence, We can simplify the square root of 48 by using the largest perfect square factor, which is 16:

√48 = √(16 x 3)

√48 = √16 x √3

√48 = 4√3

Therefore, a better choice to simplify the square root of 48 would be to use the factors 16 and 3.

This is because 16 is the largest perfect square factor of 48, which simplifies the radical the most.

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The solution to the compound inequality 3u-2<=-14 or 4u+4<28 is u<=-4 or u<6.

A compound inequality is an equation that combines two inequalities with the word "and" or "or".

To solve a compound inequality, we need to solve each inequality separately and then combine the solutions.

For the compound inequality 3u-2<=-14 or 4u+4<28, we will solve each inequality separately.

First, we will solve 3u-2<=-14: 3u-2<=-14 3u<=-14+2 3u<=-12 u<=-4

Next, we will solve 4u+4<28:

4u+4<28 4u<28-4 4u<24 u<6

Now, we will combine the solutions.

Since the word "or" is used in the compound inequality, the solution is the union of the two solutions. This means that the solution is any value of u that satisfies either inequality.

The solution is u<=-4 or u<6. This can also be written in interval notation as (-∞,-4] U (-∞,6).

So, the solution to the compound inequality 3u-2<=-14 or 4u+4<28 is u<=-4 or u<6.

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Answer:

Please review the trigonometric proof below

Step-by-step explanation:

Given

[tex]\csc x -\sin x=\cos x \cot x[/tex]

Apply the reciprocal identity to [tex]\csc x[/tex].

[tex]\frac{1}{\sin x} -\sin x=\cos x \cot x[/tex]

Write [tex]-\sin x[/tex] as a fraction then multiply by [tex]\frac{\sin x}{\sin x}[/tex].

[tex]\frac{1}{\sin x} + \frac{-\sin x}{1} =\cos x \cot x[/tex]

[tex]\frac{1}{\sin x} + \frac{-\sin x}{1} *\frac{\sin x}{\sin x}=\cos x \cot x[/tex]

[tex]\frac{1}{\sin x} + \frac{-\sin x\sin x}{\sin x}=\cos x \cot x[/tex]

Combine the numerators over the common denominator.

[tex]\frac{1-\sin x\sin x}{\sin x}=\cos x \cot x[/tex]

Multiply [tex]\sin x[/tex] by [tex]\sin x[/tex].

[tex]\frac{1-\sin^2 x}{\sin x}=\cos x \cot x[/tex]

Apply the Pythagorean identity [tex]1-\sin^2 x=\cos^2 x[/tex]

[tex]\frac{\cos^2 x}{\sin x}=\cos x \cot x[/tex]

Factor [tex]\cos x[/tex] out of [tex]\cos^2 x[/tex].

[tex]\frac{\cos x\cos x}{\sin x}=\cos x \cot x[/tex]

Separate into two fractions.

[tex]\frac{\cos x}{1} *\frac{\cos x}{\sin x}=\cos x \cot x[/tex]

Apply the quotient identity [tex]\frac{\cos x}{\sin x}=\cot x[/tex].

[tex]\frac{\cos x}{1} *\cot x=\cos x \cot x[/tex]

Anything over 1 is just itself.

[tex]\cos x\cot x=\cos x \cot x[/tex]

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, = space

Answer:

csc x − sin x

= [tex]\frac{1}{sin, x}[/tex] - sin x

= [tex]\frac{1 - sin^{2}, x }{sin, x}[/tex]

= [tex]\frac{cos^{2}, x }{sin, x}[/tex]

= [tex]\frac{cos, x}{sin, x}[/tex] * cos x

= cot x cos x

∴csc x - sin x - cot x cos xQED

It is the most " explanation " I can think of.

Thus the answer is shown above..

The integers are 16.8 and 26.8. To find the integers, we need to use a system of equations. Let's call the first integer x and the second integer y. We know that one integer is 10 more than another, so we can write the first equation as: x = y + 10. We also know that their product is 375, so we can write the second equation as: xy = 375.

Now we can substitute the first equation into the second equation to solve for one of the integers.

y(y + 10) = 375

y^2 + 10y - 375 = 0

Using the quadratic formula, we can find the value of y:

y = (-10 ± √(10^2 - 4(1)(-375)))/2(1)

y = (-10 ± √1900)/2

y = (-10 ± 43.6)/2

y = 16.8 or y = -26.8

Since y has to be an integer, we can only use the value of 16.8.

So, y = 16.8 and x = 16.8 + 10 = 26.8.

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a + 26 = 180 (linear pair)

a = 180 - 26

a = 154°

The length of Diagonal is 14.73 unit.

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

Given:

l = 9, w= 10 and h= 6

The Formula for Diagonal length of Prism is:

d =√l² + w² + h²

Here, d = length of the diagonal, l = length of the rectangular base of the prism, w = width of the rectangular base of the prism, and h = height of the prism.

Substitute the value in the equation,

d =√9² + 10² + 6²

d =√81+ 100 + 36

d = √217

d =  14.73 units

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Based on the sample of the 48 South African households collected from the Census At School survey project, the mean number of people living in a household will be 6.208, and the standard deviation is 2.576.

However, it is important to note that this sample only represents a small fraction of the total number of the households in South Africa, so we cannot make definitive conclusions about the entire population based on this sample alone.

To get a more accurate estimate of the number of people living in the South African households, a larger and the more representative sample would need to be collected.

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O(n

A brute force algorithm for the 3-center problem would involve trying every combination of three points in the set of given points, calculating the cost for each combination using Equation (1), and then returning the combination with the minimum cost. The algorithm can be expressed as follows:

The computational complexity of this algorithm is O(n

combinations of three points from a set of n points.

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The solution to the compound inequality 4v + 3 <= 23 and 3v + 4 < 1 is v in the interval (-1, 5].

To solve the compound inequality, we need to solve each inequality separately and then find the intersection of the two solutions.

First, let's solve the inequality 4v+3<=23:
4v+3<=23
4v<=20
v<=5

Next, let's solve the inequality 3v+4<1:
3v+4<1
3v<-3
v<-1

Now, we need to find the intersection of the two solutions, which is the solution that satisfies both inequalities. The intersection of v<=5 and v<-1 is the interval (-1, 5].

So, the solution to the compound inequality is v in the interval (-1, 5]. In interval notation, this is written as (-1, 5].

Therefore, the solution to the compound inequality 4v+3<=23 and 3v+4<1 is v in the interval (-1, 5].

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The value of Y is not independent of the value of X, and so X and Y are not independent.

Let X be a random variable with EXP <∞ and let Y = [X]. Since X has a Lebesgue density symmetric about 0, we know that E[X] = 0. Therefore, E[XY] = E[X[X]] = E[X²] = Var[X] + E[X]² = Var[X].

Since X and Y are uncorrelated, we have E[XY] - E[X]E[Y] = 0, which implies that E[XY] = E[X]E[Y] = 0*E[Y] = 0. Therefore, X and Y are uncorrelated.

However, X and Y are not independent because the value of Y depends on the value of X. For example, if X = 1.5, then Y = 1, but if X = -1.5, then Y = -2. Therefore, the value of Y is not independent of the value of X, and so X and Y are not independent.

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Answer: 4 bracelets per hour

Step-by-step explanation:

You're basically finding the amount made in one hour instead of 5, so we just use an equation:

20 = 5x

x = 4

4 are made in an hour. Hope this helps!

Answer: 50in^2

Remember the formula for finding the area of a rectangle is:

A = (base)(height)

In this problem you find the area like so:

A = (12[tex]\frac{1}{2}[/tex])(4)

= ([tex]\frac{25}{2}[/tex])([tex]\frac{4}{1}[/tex])

= ([tex]\frac{25}{1}[/tex])([tex]\frac{2}{1}[/tex])

= 50in^2

In the given question, 1 British pound will be equal to AU$2.00.

Algebra is a common thread that runs through almost all of mathematics. It is the study of variables and the principles for manipulating them in formulas. Since all mathematical uses involve manipulating variables as though they were numbers, elementary algebra is a prerequisite.

The area of mathematics known as algebra aids in the representation of situations or issues as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z along with mathematical processes like addition, subtraction, multiplication, and division.

A homogeneous relation R over the set A, which includes the elements x, y, and z, is what mathematicians refer to as a transitive relation. If R relates x to y and y to z, then R also relates x to z.

In this question,

1£ = US$1.40             (Equation 1)

AU$1 = US$0.70      (Equation 2)

Multiplying equation 2 by 2, we get

AU$2 = US$1.40

Using equation 1, we can say that,

1£ = AU$2

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