Compute the probability that the sum of X and Y exceeds 1.
Let (X, Y) be random variables with joint density Jxy xy if 0≤x≤ 2, 0 ≤ y ≤ 1 fx,y(2,y) = = 0 otherwise

Answer:

$14.45

Step-by-step explanation:

To make the equation easier you would have to make the percent decimal and to do that move it twice to the left. So it would be 0.17 x 85 which is 14.45 and add that dollar sign there. :)

The conversion of 70°F is equal to 21.1°C.

A temperature unit developed from the SI (International System of Units) is Celsius (symbol: °C).

Prior to the adoption of the metric system, Fahrenheit (symbol: °F) was a commonly used measurement of temperature.

To convert 70°F (degrees Fahrenheit) to Celsius (°C), you can use the following formula:

°C = (°F - 32) / 1.8

Substituting 70°F for °F in the formula, we get:

°C = (70 - 32) / 1.8

Simplifying the calculation, we get:

°C = 38 / 1.8

°C ≈ 21.1

Therefore, the conversion of 70°F is nearly equal to 21.1°C.

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Answer:

300 is the answer

Step-by-step explanation:

area of triangle-BxH/2

area of square- LxW

10x10=100/2=50

50x4=200

+100

=300

Answer:

Th answer is 220

Step-by-step explanation:

The value of r at which the rate of change of A with respect to t is equal to the rate of change of C with respect to t is r = 1.

None of the options are correct.

We have,

To find the value of r at which the rate of change of the area A with respect to t is equal to the rate of change of the circumference C with respect to t, we need to equate their derivatives.

Given:

A = πr²

C = 2πr

Let's differentiate both equations with respect to t:

dA/dt = d(πr²)/dt

dC/dt = d(2πr)/dt

Using the power rule of differentiation, we get:

dA/dt = 2πr(dr/dt)

dC/dt = 2π(dr/dt)

Now, we can equate the two expressions:

2πr(dr/dt) = 2π(dr/dt)

Canceling out the common factor of 2π and (dr/dt), we get:

r = 1

Therefore,

The value of r at which the rate of change of A with respect to t is equal to the rate of change of C with respect to t is r = 1.

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Answer:

20 days

Step-by-step explanation:

Number of books sold each day for 40 days :

The first quartile (Q1) = 2

For the 25% of the days = 2 books were sold

Hence 0.25 * 40 = 10 days, 2 books or less were sold

The upper quartile (Q3) = 12 books

For up to 75% of the days = 0.75 * 40 = 30 days ; 12 books or less were sold

To obtain the number of books sold between 2 and 12 ; we subtract :

(30 days - 10 days) = 20 days

Answer:

20

Step-by-step explanation:

Answer:

59.6°

Step-by-step explanation:

Answer:

x^2 - 2x - 15 = 0.

Step-by-step explanation:

x^2 - 2x - 3 = 0

(x - 3)(x + 1) = 0

So alpha and beta are -1 and 3.

So the roots of the required equation are 2(-1)-1 and 2(3) - 1

= -3, 5.

So the equation is

(x - 5)(x + 3) = 0

-that is x^2 - 2x - 15 = 0

Answer:

19.

Step-by-step explanation:

7 + |2 + (-5)| x |-5| - 3

= 7 + |-3| x 5 - 3                  The | | indicate the absolute value so |-5| = 5.

= 7 + 3 x 5 - 3                     The multiplication is done first:  

=  7 + 15 - 3

= 22 -3

= 19.              

Answer:

The surface area of the similar prism is 56 square inches

Step-by-step explanation:

Given surface area of prism, A = 224 square inches

The total surface area of a triangular prism = 2 x Area of triangle + ph

Area of triangle = ¹/₂bh

Where;

b is the base of the prism

h is the height of the prism

p is the perimeter of lateral surfaces

Area of prism involves the product of the dimensions, if the new dimensions is 1/4 the original dimensions;

Product of original dimensions = 224 square inches

1/4 of the product of original dimensions = 1/4 x 224 square inches

= 56 square inches

The surface area of the similar prism = 56 square inches

Thus, the surface area of the similar prism is 56 square inches

Answer:

The slope is 6. For the first line you could do y=6x+7, and the line parallel to that could be y= 6x+3

Step-by-step explanation:

For it to be parallel the slopes have to be the same and the y intercepts (b) have to be different. And I found the slope by doing y-y/x-x

plug in you numbers 19-7/5-3= 12/2 = 6

Step-by-step explanation:

A. b x 30 = 7E. b x 7 =30C. b = 30 + 7

Answer:

1 exactly iam genius

₩¥₩

Answer:

PO = 7

PM = 7

MJ = 11

∠PJO = 32°

∠KJL = 64°

PL ≈ 18.385

OL = 17

∠PLO = 22°

∠NLO = 44°

∠JKL = 72°

∠MKP = 36°

∠NKP = 36°

∠PKN = 36°

KN = 10

PL ≈ 13.04

PK ≈ 12.21

JL = 28

JK = 21

LK = 27

Step-by-step explanation:

The given parameters are;

The point representing the incenter of the triangle = P

Therefore PO = PM = PN = 7

tan(32°) = PM/JM = 7/JM

∴JM = 7/(tan(32°)) ≈ 11.2

∠PJO = tan⁻¹(7/11)≈ 32.47°

∠PJO = ∠PJM = 32° similar triangles

∠KJL = ∠KJP + ∠PJO = 32 + 32 = 64°

∠KJL ≈ 64°

PL = √(7² + 17²) ≈ 18.385

OL = NL = 17 similar triangles

∠PLO = sin⁻¹(7/18.385) ≈ 22.380°

∠PLO = ∠PLN = 22°

∠NLO = ∠PNL + ∠OLP ≈ 22° + 22° ≈ 44°

∠NLO ≈ 44.380°

∠JKL = 180 - (∠KJL + ∠NLO)

∠JKL = 180° - (64° + 44°) ≈ 72°

∠JKL  ≈ 72°

∠MKP = ∠NKP = 72°/2 = 36°

∠MKP = 36°

∠NKP = 36°

∠PKN = ∠JKL - ∠MKP = 72° - 36° ≈ 36°

∠PKN  ≈ 36°

KN = KM = 10

MJ = OJ = 11

PL = √(7² + 11²) ≈ 13.04

PK = √(7² + 10²) ≈ 12.21

JL = JO + OL = 11 + 17 = 28

JK = JM + MK = 11 + 10 = 21

LK = LN + NK = 17 + 10 = 27

  By using the property of incenter, measures of the sides and the angles will be,

JK = 21.2 units

KL = 26.63 units

JL = 28.33 units

m∠K = 36°

 By the property of incenter,

PM = PN = PO = 7 units

∠MJP = ∠OJP = 32°

∠NLP = ∠OLP = 22°

 By the triangle sum theorem,

m∠JKL + m∠KLJ + m∠LJK = 180°

2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°

2(m∠NKP) + 2(22°) + 2(32°) = 180°

2(m∠NKP) = 180° - 108°

m∠NKP = 36°

From ΔJMP,

tan(32°) = \(\frac{MP}{MJ}\)

tan(32°) = \(\frac{7}{MJ}\)

MJ = \(\frac{7}{\text{tan}(32)^\circ}\)

MJ = 11.20

From ΔPOL,

tan(22°) = \(\frac{OP}{OL}\)

tan(22°) = \(\frac{7}{OL}\)

OL = 17.33

From ΔKNP,

tan(36°) = \(\frac{NP}{KN}\)

tan(36°) = \(\frac{7}{KN}\)

KN = 9.63

Therefore, JK = MJ + MK = 21.2 units

KL = LN + KN = 26.63 units

JL = JO + OL = 28.33 units

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The mathematical expression y(x,t) = Asin(kx)sin(wt) provides a way to describe the behavior of a standing wave in terms of its amplitude, frequency, and location along the string.

At time t=0,

the standing wave can be mathematically expressed as

y(x,0) = Asin(kx)sin(w*0) = Asin(kx)sin(0) = 0.

This means that the displacement of the string is zero at time t=0.

However, it is important to note that this does not mean that the string is not moving at all. Rather, it means that the string is in a state of equilibrium at time t=0, with the maximum transverse displacement being A.

As time progresses, the standing wave will oscillate between the maximum positive and negative transverse displacement values, creating a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).

The wave number k and angular frequency w are both constants that are dependent on the physical properties of the string and the conditions under which the wave is being produced.

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a. i. There are 27,040,000 different passwords are possible if repetition of digits and letters is allowed and passwords are not case sensitive  (so 123AB is the same as 123aB)

ii. There will be 99,532,800  different passwords are possible if repetition of digits and letters is not allowed and the passwords are case-sensitive

b. i. The probability that all 4 randomly selected students were math majors is  0.520

ii. There are 4,725 different pairs of math majors that could be chosen for the committee.

a. i) There are 10 choices for each of the first 3 digits, and 26 choices for each of the last 2 letters. Since the password is not case sensitive, we can choose either uppercase or lowercase letters, so there are 26 + 26 = 52 choices in total for each letter. Therefore, the total number of different passwords is:

10 x 10 x 10 x 52 x 52 = 27,040,000

ii) There are 10 choices for the first digit, 9 choices for the second digit (since we can't repeat the first digit), 8 choices for the third digit (since we can't repeat the first two digits), and 52 choices for the first letter. For the second letter, there are 51 choices left (since we can't repeat the first letter), but we need to distinguish between uppercase and lowercase letters, so there are 52 x 51 = 2,652 choices for the two letters in total. Therefore, the total number of different passwords is:

10 x 9 x 8 x 52 x 2,652 = 99,532,800

b) i) The total number of ways to select a 4-student committee from 20 students is:

20 choose 4 = 4,845

The number of ways to select a committee consisting of 4 math majors is:

10 choose 4 = 2,520

Therefore, the probability that all 4 randomly selected students were math majors is:

2,520 / 4,845 = 0.520

ii) The number of ways to select a 4-student committee with exactly two math majors is:

(10 choose 2) x (10 choose 2) x (15 choose 0) = 4,725

(We choose 2 math majors from 10, and 2 non-math majors from 15, since there are 5 biology majors and 5 music majors to choose from.)

Therefore, there are 4,725 different pairs of math majors that could be chosen for the committee.

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The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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A) The probability that you will share in the first prize pool is calculated to be 0.000000049.

B)The probability that you will share n the second or in the third prize pool is calculated to be 0.0625.

It is given that 6 numbers are drawn from a set of numbers containing a set of 1 to 52 numbers.

The number of possibilities of selecting 6 numbers from a set of 52 is,

n(s) = 52C₆ = 52!/(46! × 6!) = 20358520

Let E represent the likelihood of getting the prize.

Number of possibility of winning first prize is only 1.

n(E) = 1

So, the probability of winning first prize is n(E)/n(s) = 1/20358520 = 0.000000049

B) If four or five of the six numbers are drawn in the second or third prize pool,

n(s) = 6C₅ + 6C₄ = 1 + 15 = 16

The probability that you will share in the second or third in the third prize pool is,

n(E) = 1 (As it is second or third prize and not both at once)

n(s) = 16

So, the probability of winning second or third prize is n(E)/n(s) = 1/16 = 0.0625

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Answer:

v <−1/2 or v >4

Answer: B 10.6

Explanation:

We would assume that the stock tank is cylindrical. We would calculate the volume by applying the formula,

Volume = πr^h

where

π = 3.14

r is the radius of the cylinder

h is the height of the cylinder

From the information given,

diameter = 3

radius = diameter/2 = 3/2

r = 1.5

h = 1.5

Volume = 3.14 x 1.5^2 x 1.5 = 10.5975 cubic meters

By rounding to the nearest tenth,

Volume = 10.6 cubic meters

The length of third side is 4 cm. This can be solved using the concept of right angled triangle.

Three straight sides and three angles make up a triangle, a two-dimensional form. Three vertices, three angles, and three sides define a triangle. In a triangle, the lengths of its two longest sides are always bigger than its third side's length.

A triangle seems to be a three-sided polygon with three vertices. There is a 180-degree angle created inside the triangle. In other words, a triangle's internal angles add up to 180 degrees.

Triangles can be categorized into one of three groups, namely Scalene, Isosceles, or Equilateral, depending on how long their sides are.

the triangle given is Right Angled Triangle because to find a third side provided two sides are given is only possible in a right angled triangle.

We know that the right-angled triangle follows Pythagoras Theorem

According to Pythagoras Theorem, the sum of squares of two sides is equal to the square of the third side:

(Perpendicular)² + (Base)² = (Hypotenuse)²

or, (2√3)² + (2)² = (Hypotenuse)²

or, 12 + 4 = (Hypotenuse)²

or, (Hypotenuse)² = 16

or, Hypotenuse = √16

or, Hypotenuse = 4 cm

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(i) In order to prove that A, B and C lie on a straight line, we can show that the vector AB and the vector BC are parallel. The vector AB is given by: AB = B − A= (5i + 7j + 4k) − (2i + j + k)= 3i + 6j + 3kThe vector BC is given by: BC = C − B= (i − j) − (5i + 7j + 4k)= −4i − 8j − 4k

To show that these vectors are parallel, we can take their cross product and check if it is equal to the zero vector: AB × BC = (3i + 6j + 3k) × (−4i − 8j − 4k)= −30i − 6j + 18k

Since this is not equal to the zero vector, AB and BC are not parallel, and therefore points A, B, and C do not lie on a straight line. So we cannot prove that points A, B, and C lie on a straight line.

(ii) Let's start by finding the vector OD and then find its magnitude.

OD = D - O= 2i + j - 3k - (0i + 0j + 0k)= 2i + j - 3k|OD| = √(2² + 1² + (−3)²) = √14

Now we can find the unit vector in the direction of OD: uOD = OD / |OD|= (2/√14)i + (1/√14)j − (3/√14)k

To find the cosine of the acute angle between u and line OD, we need to take their dot product:

cosθ = uOD · u= ((2/√14)i + (1/√14)j − (3/√14)k) · (1i + 0j + 0k)= 2/√14

Therefore, the cosine of the acute angle between / and line OD is 2/√14.

(iii) Since OE is perpendicular to OD, we know that the vector OE is orthogonal to the unit vector uOD.

This means that OE lies in the plane that is perpendicular to uOD, which is the plane that contains the line I and the point O.

Therefore, in order to prove that E lies on I, we need to show that the vector OE is a scalar multiple of the vector AB.

To do this, we can find the projection of OE onto AB: proj AB OE = (OE · AB / |AB|²) AB= ((−3j − k) · (3i + 6j + 3k) / (3² + 6² + 3²)) (3i + 6j + 3k)= (−27/54) (3i + 6j + 3k)= −(1/2) (3i + 6j + 3k)

Now we can check if the vector OE is equal to this projection: OE = −(1/2) (3i + 6j + 3k)= −(3/2)i − 3j − (3/2)k

This is a scalar multiple of AB, since we can write: AB = 3i + 6j + 3k= −2(−(3/2)i − 3j − (3/2)k)

Therefore, E lies on the line I.

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Factoring the sum or difference of cubes involves using specific formulas to simplify expressions.

The sum of cubes formula, a^3 + b^3 = (a + b)(a^2 - ab + b^2), and the difference of cubes formula, a^3 - b^3 = (a - b)(a^2 + ab + b^2), allow us to break down these expressions into more manageable factors.

To factor the sum or difference of cubes, you can use the following formulas:

Sum of Cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Cube difference: (a - b)(a - b)(a - b)(a - b)(a - b)

Sum of Cubes:

The sum of cubes formula states that the sum of two cubes, a^3 + b^3, can be factored into (a + b) multiplied by the quadratic expression a^2 - ab + b^2.

For example, let's factorize 8x^3 + 27:

We can identify a = 2x and b = 3, so using the sum of cubes formula:

8x^3 + 27 = (2x + 3)(4x^2 - 6x + 9)

Difference of Cubes:

The difference of cubes formula states that the difference between two cubes, a^3 - b^3, can be factored into (a - b) multiplied by the quadratic expression a^2 + ab + b^2.

For example, let's factorize 64y^3 - 125:

We can identify a = 4y and b = 5, so using the difference of cubes formula:

64y^3 - 125 = (4y - 5)(16y^2 + 20y + 25)

Factoring the sum or difference of cubes involves using specific formulas to simplify expressions. The sum of cubes formula, a^3 + b^3 = (a + b)(a^2 - ab + b^2), and the difference of cubes formula, a^3 - b^3 = (a - b)(a^2 + ab + b^2), allow us to break down these expressions into more manageable factors. Factoring such expressions can be useful in various algebraic calculations and simplifications.

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Answer:

Your statement is true

Step-by-step explanation:

:|

Answer:

x₁(2x₁x₂² - x₂ - 3) - 3x₂

Step-by-step explanation:

The expression you provided is a polynomial in two variables, x₁ and x₂. Let's simplify it step by step:

2x₁²x₂² - x₁x₂ - 3x₁ - 3x₂

To simplify, we can look for common terms that can be factored out:

x₁(2x₁x₂² - x₂ - 3) - 3x₂

Now let's simplify the expression inside the parentheses:

2x₁x₂² - x₂ - 3

F(11) means to replace x in the equation with 11

12(11) + 5

12 x 11 = 132

Now you have 132 + 5 = 137

F(11) = 137

A time lag exists between the columns of birth (B) and death (D) sequences. The length of the time lag needs to be provided to further analyze the reasons behind its existence.

In order to determine the length of the time lag and the reasons behind it, we need specific information regarding the recorded columns of birth and death sequences. The time lag refers to a shift in the start of the sequence between the two columns, indicating a delay or gap between births and deaths.

To identify the time lag and understand its causes, we would need to compare the specific data points in the birth and death columns and analyze the chronological order of events. By examining the sequence of births and deaths, we can observe any differences or delays in the occurrence of these events and determine the length of the time lag.

Without the actual data or specific information about the columns of birth and death, it is not possible to provide an accurate length of the time lag or the reasons behind its existence.

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Answer:

Area of the plot of the land is 4840 square units.

Step-by-step explanation:

Let's draw the rectangle approximately on an x y plane. That would help us to find the length and width of the rectangle.

Answer: 4,480yd^2

Step-by-step explanation:

You have the x and y coordinates of the vertices (10, 10), (10,90), (70.5,90),  and (70.5, 10) you have the coordinates: x and y as the first two which are the ones in bold. From that you do 70.5-10= 60.5.

Then you subtract the x and y coordinates again, which are underlined. From that do 90-10=80

Last you do 60.5x80=4,840 yards squared

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A decrease in the ratio 4:5 implies that :

New quantity:Old quantity = 4:5

Let the new quantity be \( \bf \: x\)

\( \bf∴ x : 40 = 4:5\)

\( = > \bf \frac{x}{40} = \frac{4}{5} \)

\( \bf = > 40 \times \frac{x}{40} = 40 \times \frac{4}{5} \)

\( \bf = > x = 8 \times 4\)

\( \bf = > x = 32\)

So, the new quantity is 32