There is given a 2D joint probability density function + 163,0) ={(2x+y ) +ž) if 0 Find:
1) Coefficient a
2) Marginal p.d.f. of X, marginal p.d.f. of Y
3) E(X), E(Y), E (XY)
4) Var(X), Var(Y)
5) 0(X), (Y)
6) Cov(X,Y)
7) Corr(X,Y).

Step-by-step explanation:

so u could see that the yellow cab that will take Emma to airport is much more cheaper even though the entry price is a bit expensive .

The length of the missing side is 3 units

Using the Pythagorean theorem, we have that;

Square of the hypotenuse is equal to the sum of the squares of the other two sides.

This is written as;

a² = b² + c²

Now, for the larger triangle, substitute the values, we have;

9² = 6² + c²

find the squares

c²= 81 - 36

add the values

c² = 45

c = √45

c = 6, 7 units

For the smaller triangle

6.7² - 6² = x²

x² = 45 - 36

x² = 9

Find the square root

x = 3

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The number of pounds of durian needed to produce 216 pounds of durian-flavored chocolate bars is 50 pounds.

We have,

To determine the amount of durian needed to produce 216 pounds of durian-flavored chocolate bars, we need to calculate the cost and compare it to the budget constraint.

Let's assume x represents the number of pounds of durian needed.

The cost of plain chocolate per pound is $3.50, so the cost of x pounds of plain chocolate is 3.50x dollars.

The cost of durian per pound is $15.75, so the cost of x pounds of durian is 15.75x dollars.

To ensure the cost does not exceed $4.50 per pound, we set up the inequality:

3.50x + 15.75x ≤ 4.50 x 216.

Combining like terms:

19.25x ≤ 972.

Dividing both sides by 19.25:

x ≤ 50.45.

Since we cannot have a fraction of a pound, we round down to the nearest whole number.

Therefore,

The number of pounds of durian needed to produce 216 pounds of durian-flavored chocolate bars is 50 pounds.

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a. False
b. True
c. False
d. False

In order to answer this question, it is important to understand the definitions of each of the terms:
- True or False: this is a type of question that requires the student to choose between two possible answers, True or False.
- Normal Distribution: this is a type of data distribution in which the data is symmetrically distributed around the mean, and the probability of occurrence is equal for all values.
- Standard Deviation: this is a measure of how spread out a set of data is from the mean. It is calculated by taking the square root of the variance of the data set.
- Median: this is the middle value in a data set when the values are arranged in ascending or descending order.
- Quartile: this is a type of quartile division in which a data set is divided into four equal parts, each containing 25% of the data.
- Mode: this is the most frequently occurring value in a data set.
- Population Standard Deviation: this is a measure of the spread of the population, and it is calculated by taking the square root of the variance of the population.

Therefore, the correct answer to the given question is:
a. False
b. True
c. False
d. False

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By 12.57 feet the circumference of outer circle greater than the circumference of the inner​ circle

The circle's boundary is the length of the circle's circumference, sometimes referred to as its perimeter. whereas the size of a circle determines the space it occupies.

The formula for calculating a circle's circumference is written as

Circumference = πD

where D stands for the circle's diameter.

The inner circle is 44 feet in diameter. It means that

22/7 × D = 44

22D = 7 × 44 = 308

D = 308/22

D = 14 ft

The inner circle and the outer circle are separated by 2 feet. This implies that the outer circle's diameter would be

14 + 2 + 2 = 18 ft

Circumference of the outer circle is

22/7 × 18 = 56.57 ft

The distance in feet that the circumference of the outer circle exceeds that of the inner circle is

56.57 - 44 = 12.57 feet

Hence, By 12.57 feet the circumference of outer circle greater than the circumference of the inner​ circle

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Domain of function is 0 ≤ x < ∞ , range of function is 0 ≤ y < ∞

A function's domain  is the set of values ​​that can be put into the function. This set is the x-values ​​of a function like f(x). A function's range is the set of values ​​that the function takes on. This set is the value that the function outputs after inserting the x value.

Given,

graph of the function is drawn as a ray,

ray is starting from origin and extends to infinity on first quadrant

domain of the function

0 ≤ x < ∞

interval notation

Domain = [0, ∞)

range of the function

0 ≤ y < ∞

interval notation

Range = [0, ∞)

Hence, Domain and range of the function are 0 ≤ x < ∞ and 0 ≤ y < ∞ respectively.

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The quadrilateral whose vertices are A(2, 3); B(4, -2);C(-1,-4); D(-3, 1) is a square.

Quadrilaterals are four sided polygons which also have four vertices and four angles.

Sum of all the interior angles of a quadrilateral is 360 degrees.

Given A(2, 3); B(4, -2);C(-1,-4); D(-3, 1)

Length of AB = [tex]\sqrt{(4-2)^2+(-2-3)^2}[/tex] = √29 units

Length of BC = [tex]\sqrt{(-1-4)^2+(-4--2)^2}[/tex] = √29 units

Adjacent sides are equal.

So the quadrilateral must be square or rhombus.

Now, find the length of diagonals.

If the diagonals are equal, then it is square. If they are not equal, then it is rhombus.

AC = [tex]\sqrt{(-1-2)^2+ (-4-3)^2}[/tex] = √58 units

BD = [tex]\sqrt{(-3-4)^2+(1--2)^2}[/tex] = √58 units

Diagonals are equal.

So it is a square.

Hence the quadrilateral is a square.

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Answer: a. Here is a sketch of the situation described above:

 80 +                       .           July (x = 7)

      |                      .

      |                     .

      |                     .

 60 +           .               .

      |                .

      |                    .

      |                        .

 40 +          .                   .     .

      |                              .

      |                               .

      |                                .

 20 +   .         . . . . . . . . . . . . . .

      |                                      .

      |                                          .

 0  +_______________________________________________

     1   2   3   4   5   6   7   8   9   10  11  12

                          January                 December

b. One possible trigonometric equation that models the temperature throughout the year is:

T(x) = (36cos((2π/12)(x-7))) + 41

where T(x) represents the average temperature in degrees Fahrenheit for month x (with January corresponding to x=1), and the constant term of 41 is added to shift the curve up to match the lowest average temperature recorded.

c. To find the average monthly temperature for the month of March, we simply plug in x=3 into the equation above:

T(3) = (36cos((2π/12)(3-7))) + 41

= (36*cos(-π/3)) + 41

≈ 51.4°F

So the average monthly temperature for the month of March is approximately 51.4 degrees Fahrenheit.

d. To find the period of time during which the average temperature is less than 41°F, we need to solve the inequality:

T(x) < 41

Substituting the equation for T(x) from part b, we get:

(36cos((2π/12)(x-7))) + 41 < 41

Simplifying this inequality, we get:

cos((2π/12)*(x-7)) < 0

We can solve this inequality by finding the values of x for which the cosine function is negative. The cosine function is negative in the second and third quadrants of the unit circle, so we have:

(2π/12)*(x-7) ∈ (π, 2π) ∪ (3π, 4π)

Simplifying this expression, we get:

π/6 < x-7 < π/2 or 5π/6 < x-7 < 2π/3

Adding 7 to both sides of each inequality, we get:

7 + π/6 < x < 7 + π/2 or 7 + 5π/6 < x < 7 + 2π/3

Simplifying these expressions, we get:

7.524 < x < 8.571 or 11.286 < x < 11.857

Therefore, the average temperature is less than 41°F during the period of time from approximately November 24th to December 19th, and from approximately February 15th to March 20th.

Step-by-step explanation:

The simplified expression is -4x + 44/3.

An exponent is a numerical value that indicates how many times a number, variable, or expression is to be multiplied by itself. It is usually written as a superscript to the right of the base, such as in the expression 3², where 3 is the base and 2 is the exponent.

The exponent indicates that 3 is to be multiplied by itself 2 times, resulting in a value of 9. Exponents are used in many areas of mathematics, including algebra, calculus, and geometry, and are an important concept for understanding mathematical operations and functions.

To simplify the expression, we need to follow the order of operations and combine like terms where possible:

2/3(3x - 1) + 4x + 3² - 10x + 5

First, simplify the expression inside the parentheses:

2/3(3x - 1) = 2x - 2/3

Next, simplify the squared term:

3² = 9

Now, combine the like terms:

2x - 2/3 + 4x - 10x + 9 + 5 = -4x + 14 + 2/3

Finally, we can rewrite the expression with the fractional coefficient as a mixed number:

-4x + 14 + 2/3 = -4x + 44/3

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Answer:

$211 if rounding to nearest whole number (this may be what looking for)

$211.20 if rounding to nearest tenth

Step-by-step explanation:

The answer depends on what precision of rounding is done so i am providing 2 answers

Rounding to the nearest whole number:
14,49 rounded = 14
68.64 rounded = 69
128.05 rounded = 128

$14.49 + $68.64 + $128.05 =  14 + 69 + 128

= $211

Rounding to the tenths:

14,49 rounded = 14.5

68.64 rounded = 68.6

128.05 rounded = 128.1

$14.49 + $68.64 + $128.05= 14.5 + 68.6 + 128.1 = $211.20

Answer:

78

Step-by-step explanation:

The exact value of cos(2a) is 7/25 and the exact value of sin a/2 is √10/10. Remember to consider which sign is appropriate when using the trigonometric identities.

Given tan a = 3/4, and sin a = -3/5, we can find the exact value of cos(2a) and sin a/2 by using the appropriate trigonometric identities.

a) cos(2a) = 1 - 2sin^2(a) = 1 - 2(-3/5)^2 = 1 - 18/25 = 7/25

b) sin a/2 = √[(1 - cos a)/2] = √[(1 - (4/5))/2] = √[(1/5)/2] = √(1/10) = 1/√10 = √10/10

Therefore, the exact value of cos(2a) is 7/25 and the exact value of sin a/2 is √10/10. Remember to consider which sign is appropriate when using the trigonometric identities.

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Answer:

79° , 65° , 144°

Step-by-step explanation:

65° , x° and 36° lie on a straight line and sum to 180° , that is

65° + x° + 36° = 180°

101° + x° = 180 ( subtract 101° from both sides )

x= 79°

y + 10 and 65° are alternate angles and are congruent , then

y + 10 = 65°

z and 36° are same- side interior angles and sum to 180° , that is

z + 36° = 180° ( subtract 36° from both sides )

z = 144°

Answer:

6

hope this helps! :)

the number that is not in the solution set of x + 8 > 15 is 6

The difference quotient for the function f(x) = 4x^2 + 1 is 8x

The difference quotient is a formula used to find the average rate of change of a function over an interval. It is represented by the formula: (f(x+h) - f(x))/h. In this case, we are asked to evaluate the difference quotient for the function f(x) = 4x^2 + 1.

Step 1: Substitute the function into the difference quotient formula:
(f(x+h) - f(x))/h = ((4(x+h)^2 + 1) - (4x^2 + 1))/h

Step 2: Simplify the expression:
= ((4x^2 + 8xh + 4h^2 + 1) - (4x^2 + 1))/h
= (8xh + 4h^2)/h

Step 3: Factor out h from the numerator:
= h(8x + 4h)/h

Step 4: Cancel out the h terms:
= 8x + 4h

Step 5: Substitute h = 0 to find the final answer:
= 8x + 4(0)
= 8x

Therefore, the difference quotient for the function f(x) = 4x^2 + 1 is 8x. This is the final answer for this Assignment. Remember to always show all work when evaluating the difference quotient.

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The polynomial g(x)=x^(3)+3x^(2)-x-3 is a cubic polynomial with 4 terms.

To prove its degree using successive differences, we first need to find the successive differences of the polynomial's y-values for consecutive x-values. We can do this by substituting x-values into the polynomial and finding the differences between the resulting y-values.

For x=0, g(x)=0^(3)+3(0^(2))-0-3=-3
For x=1, g(x)=1^(3)+3(1^(2))-1-3=0
For x=2, g(x)=2^(3)+3(2^(2))-2-3=11
For x=3, g(x)=3^(3)+3(3^(2))-3-3=30

The first successive difference is 0-(-3)=3
The second successive difference is 11-0=11
The third successive difference is 30-11=19

Since the successive differences are not constant, we need to find the successive differences of the successive differences.

The first successive difference of the successive differences is 11-3=8
The second successive difference of the successive differences is 19-11=8

Since the successive differences of the successive differences are constant, the degree of the polynomial is 3, which is one less than the number of times we had to find successive differences. This confirms that g(x)=x^(3)+3x^(2)-x-3 is a cubic polynomial.

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In linear equation, 2000 pupils are there in the school.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Ax+By=C is the typical form for linear equations involving two variables. Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.

= 540/27%

= 54000/27

= 2000

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Answer:

181.74

Step-by-step explanation:

I hope you meant the paycheck was $1398.. if not then this is wrong.

So you take 1398 and multiply it by 0.13 and then you get 181.74. So Jim donated 181.74 this month.

We have the following response after answering the given question: As a result, the following are the answers to the equation: [tex]x = 4 + 6 = 10[/tex] and [tex]x = 4 - 6 = -2[/tex]

In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.

We may use the completing the square method to solve the equation x2 - 8x + 5 = 25 by doing the following steps:

[tex]x^2 - 8x + 5 - 25 = 0\\x^2 - 8x - 20 = 0\\(-8/2)^2 = c\\16 = c\\x^2 - 8x + 16 - 16 - 20 = 0\\(x - 4)^2 - 36 = 0\\(x - 4)^2 = 36\\x - 4 = +6\\x = 4 + 6[/tex]

As a result, the following are the answers to the equation:

[tex]x = 4 + 6 = 10[/tex]

[tex]x = 4 - 6 = -2[/tex]

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The correct way to name the figure shown is PQ. This figure consists of two perpendicular lines, P and Q, which intersect at a point. The lines are labeled P and Q, so the correct name for the figure is PQ.

Perpendicular lines are those two lines that intersect each other at a 90 degree angle. These lines are also known as orthogonal lines. When two lines intersect at a 90 degree angle, they are said to be perpendicular.

The figure is a basic geometric shape and is used to illustrate the concept of perpendicular lines. In the figure shown, the angle formed by the intersection of the two lines is a right angle, so the lines are perpendicular.

The figure can also be used to illustrate the concept of a transversal. A transversal is a line that intersects two other lines at different points. In the figure, the line PQ is a transversal intersecting the two lines P and Q.

In conclusion, the correct way to name the figure shown is PQ. This figure is used to illustrate the concepts of perpendicular lines, line segments, and transversals.

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The product of these two matrices is a 3x3 matrix, AB.
AB = [[-9, -7, -1]
     [-9, -42, -7]
     [63, -42, 7]]

To determine AB, we need to multiply matrix A and matrix B. The dimensions of matrix A are 3x1 and the dimensions of matrix B are 1x3. Since the number of columns in matrix A is equal to the number of rows in matrix B, we can multiply these matrices. The resulting matrix will have the dimensions of the number of rows in matrix A and the number of columns in matrix B, which is 3x3.

To multiply the matrices, we take the dot product of each row in matrix A with each column in matrix B. The dot product is the sum of the products of the corresponding entries in the row and column.

AB = [[(-1)(-9) + (-6)(-7) + (7)(-1)], [(-1)(-9) + (-6)(-7) + (7)(-1)], [(-1)(-9) + (-6)(-7) + (7)(-1)]]
AB = [[-9, -7, -1]
     [-9, -42, -7]
     [63, -42, 7]]

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Scheme procedure to generate a list of all subsets of a set:

(define (subsets set)

 (if (null? set)

     '(())

     (let ((rest (subsets (cdr set))))

       (append rest (map (lambda (x) (cons (car set) x)) rest))))))

The subsets procedure takes a set as input and checks if the set is empty. If the set is empty, it returns a list with an empty set as its only element. Otherwise, it calls the subsets procedure recursively on the rest of the set (without the first element) and stores the result in a variable called rest.

It then appends the rest list to the result of mapping a lambda function over the rest list. The lambda function takes an element x from the rest list and conses the first element of the original set to it to create a new subset. This results in a list of all subsets of the original set.

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The experimental probability of spinning a number less than 3 is given as follows:

0.38.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the experimental probability of spinning a number less than 3 is given as follows:

p = 38/100

p = 0.38.

The bars are given as follows:

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Answer: A quarter or 1/4 rotation is 90°.

Step-by-step explanation:

A full rotation is 360 degrees, usually written as 360°. Half a rotation is then 180° and a quarter rotation is 90°.

Answer:

Mother: £200, Sister: £80, Mary: £120

Step-by-step explanation:

Mary has a total of £400 to start off with.

In order to calculate the amount she gives to her mother, we must multiply 400 by .5 (the decimal equivalent of 50%), which leaves us with £200 to her mother.

Do the same with her sister; multiply 400 by .2 (the decimal equivalent of 20%), which leaves us with £80.

To figure out what she is left with,  £400 - 200 - 80 = £120. Mary is left with £120.

Mary will have £120 with her, her mother will have £200 and her sister will have £80.

Percentages are fractions with 100 as the denominator. It is the relation between part and whole where the value of whole is always taken as 100.

Given that, Mary won £400.

She gave 50% to her mother, 20% to her sister and rest she kept with herself,

So,

The amount her mother got =

50% of £400 = 1/2 × 400 = 200

Therefore, her mother got £200.

The amount her sister got =

20% of £400 = 1/5 × 400 = 80

Therefore, her sister got £80.

The amount Mary have = 400 - (200+80) = 400 - 280 = £120

Hence Mary will have £120 with her.

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I is both an ideal of k[x] and a principle ideal.

Let k be a field. The ideal of k, I = {p(x) ∈ k[x] : p(0) = 0}, is an ideal of k[x] because it satisfies the following properties:

1) Closure under addition: If p(x) and q(x) are both in I, then p(x) + q(x) is also in I. This is because p(0) + q(0) = 0 + 0 = 0, so (p + q)(0) = 0.

2) Closure under multiplication by elements of k[x]: If p(x) is in I and r(x) is any polynomial in k[x], then r(x)p(x) is also in I. This is because r(0)p(0) = 0, so (rp)(0) = 0.

Additionally, I is a principle ideal because it can be generated by a single element. In this case, the principle idea is the polynomial x, since any polynomial in I can be written as a multiple of x. For example, if p(x) = x^2 + 2x, then p(x) = x(x + 2), so p(x) is a multiple of x and is therefore in the ideal generated by x.

Therefore, I is both an ideal of k[x] and a principle ideal.

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The function h(x) can be expressed as f(g(x)) where g(x) = (x-7) and f(x) = x.

The function h(x) = (x-7)1 can be expressed in the form f(g(x)) where g(x) = (x-7) and f(x) is defined as f(x) = x1.

To find f(x), we need to isolate x on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of 1, which is 1.

f(x) = x1 * 11 = x

Therefore, the function h(x) can be expressed as f(g(x)) where g(x) = (x-7) and f(x) = x.

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Answer:

it’s 159 sorry

Step-by-step explanation:

10 to the second power is 10x10 which is 100 then 8 to the second power is 8x8 which is 64. 164-5 is 159, I apologize.

If there are 360 students in the school, we can expect 108 students in the school to have a pet cat.

We can use proportion to solve the problem.

If 6 out of 20 students have a pet cat, then we can write:

6/20 = x/360

where;

x is the number of students in the school who have a pet cat.

To solve for x, we can cross-multiply:

20x = 6*360

20x = 2160

x = 108

Therefore, 108 students  are expected to have a pet cat in the school

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Answer:

-11

Step-by-step explanation:

*The sum of all three angles of a triangle is 180*

So,

80+60

140 + (x + 51) = 180

-140 -140

x + 51 = 40

- 51 - 51

x = - 11

HOPE this helped