let x and y be two continuous random variables, with the same joint probability density function as in exercise 9.10. find the probability p(x < y) that x is smaller than y.

The length of a taut belt around the two pulleys is 79.3 cm.

The length of a taut belt around the two pulleys is calculated as follows;

Shapes formed within the two circles of the pulley.

From top to bottom, a rectangle, a right triangle and a trapezium.

The height of the right triangle is equal to length of the rectangle

base of the right triangle = radius of big circle - radius of small circle

base of the right triangle = (0.5 x 12 cm) - (0.5 x 6 cm) = 3 cm

tan α = height/base

tan (72.54)  = h/3

h = 3 tan(72.54)

h = 9.54 cm

The length of the trapezium at bottom is equal to length of rectangle at top, L = h = 9.54 cm

Portion of belt in contact with circumference of small circle is subtended by an angle = 2 × 72.54 = 145.08°

Length of belt in contact with circumference of smaller circle

= 2πr (θ/360)

= (2 x 6 cm)π x (145.08/360)

= 15.19 cm

Portion of belt in contact with circumference of big circle is subtended by an angle = 360 - 145.08° = 214.92⁰

Length of belt in contact with circumference of smaller circle

= 2πr (θ/360)

= (2 x 12 cm)π x (214.92 / 360)

= 45.01 cm

= 9.54 cm + 9.54 cm + 15.19 cm + 45.01 cm

= 79.28 cm

= 79.3 cm

Thus, the length of a taut belt around the two pulleys is 79.3 cm.

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Answer: a is more than 1 but less than 2

Step-by-step explanation:

b > 1

0 < [tex]\frac{1}{b}[/tex] < 1

0 + 1 < 1 + [tex]\frac{1}{b}[/tex] < 1 + 1

1 < 1 + [tex]\frac{1}{b}[/tex] < 2

So 1 < a < 2

Answer:

288pi in^3 , which is 904.78 in^3 to nearest hundredth.

Step-by-step explanation:

V = 4/3 pi r^3

  = 4/3 pi * 6*3

   = 288pi in^3

   = 904.7786842 in^3

The solution to the expression [tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18}[/tex] gives (x + 4)/2

An equation is an expression that shows the relationship between two or more number and variables.

[tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18} \\\\=\frac{(x +3)(x +4)}{x-3} .\frac{(x-3)(x-3)}{2(x+3)(x-3)} =\frac{x+4}{2}[/tex]

The solution to the expression [tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18}[/tex] gives (x + 4)/2

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The length of BD is √182

The given parameters are:

AD = 7

DC = 26

BD = x

The side lengths are represented by the following ratio:

7 : x = x : 26

Express as fraction

7/x = x/26

Cross multiply

x^2 = 182

Take the square roots

x = √182

Hence, the length of BD is √182

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Answer:

The length of BD is √182

hope this helps :)

Answer:

3x+2=2190

3x=2190-2

3x=2188

x=2188÷3

x=729

The perimeter of the garden is 46 units.

To calculate for the perimeter of the garden, we have to solve for the measures of each of the sides of the four-sided polygon. That is calculated by getting the distances between consecutive points.

The equation for the distance is:

d = sqrt ((x₂ - x₁)² + (y₂ - y₁)²)

Distance from G and A,

d = sqrt ((4 - -8)² + (8 - 3)²)

d = 13

Distance from A to R,

d = sqrt ((10 - 4)² + (0 - 8)²)

d = 10

Distance from R to D,

d = sqrt ((-2 - 10)² + (-5 - 0)²

d = 13

Distance from D to G,

d = sqrt ((-8 --2)² + (-5 -3)²)

d = 10

Summing up all the four calculated distances will give us an answer of 46.

Thus, the perimeter of the garden is 46 units.

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Answer: 46 meters.

Step-by-step explanation: I just did it on edge 2023. Hope this helps!

Answer:

2

Step-by-step explanation:

Given the area of the rectangular community garden, the length and width of the garden are 30ft and 10ft respectively.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

Area of a rectangle is expressed as;

A = length × Width

Given the data in the question;

We substitute the values into the equation

A = length × breadth

300 = 3x × x

300 = 3x²

Divide both sides by 3

x² = 100

Take the square root of both sides

x = ±√100

x = 10, -10

Since, dimension of a rectangle cannot be Negative.

x = 10

Hence;

Width w = x = 10ft

Length = 3Width = 3x = 3( 10 ) = 30ft

Given the area of the rectangular community garden, the length and width of the garden are 30ft and 10ft respectively.

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The logarithmic equation of 8^x = 64 is [tex]x = \log_8(64)[/tex]

The exponential equation is given as:

8^x = 64

Take the logarithm of both sides

xlog(8) = log(64)

Divide both sides by log(8)

x = log(64)/log(8)

Apply the change of base rule

[tex]x = \log_8(64)[/tex]

Hence, the logarithmic equation of 8^x = 64 is [tex]x = \log_8(64)[/tex]

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The equation of a line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0 is y = -1/2x + 1

A line is the shortest distance between two points. The equation of a line in point-slope form and perpendicular to a line is given as;

y - y1 = -1/m(x-x1)

where

m is the slope

(x1, y1) is the intercept

Given the following

Point = (4, -1)

Line: 2x-y - 7 = 0

Determine the slope

-y = -2x + 7

y= 2x - 7

Slope = 2

Substitute

y+1 = -1/2(x -4)

Write in slope-intercept form

2(y + 1) = -(x - 4)

2y+2 = -x + 4

2y = -x + 2

y = -1/2 + 1

Hence the equation of a line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0 is y = -1/2x + 1

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Answer:

y = - (1/2) x + 1

Answer:

it depends.

Step-by-step explanation:

A perfect square is a number that can be expressed as the product of an interger by itself or as the second exponent of an interger. For example, 25 is a perfect square because it is the product of interger 5 by itself, 5 × 5 =25.

Answer:

11

Step-by-step explanation:

if the some of a number is an restrocal is 122 upon 11 find the integers value of x let the number bees two values of x i e 11 and 1 upon 11 are possible hence required in future value of x is 11

The measure of the ∠1 is 35 degrees.

it is important to know that the measure of an angle with its vertex outside the circle is half the difference of the intercepted arcs.

Also, the angle subtended by the arc at the center of the circle is the angle of the arc

From the diagram, we have

m ∠ of external angle = half of the difference of arc angles

The arc angles are

m ∠ of external angle = ∠ 1

Let's substitute the angles

∠1 = [tex]\frac{106 - 36}{2}[/tex]

∠ 1 = [tex]\frac{70}{2}[/tex]

∠ 1 = 35°

We can see that the external angle 1 measures 35 degrees.

Note that the complete image is added.

Thus, the measure of the ∠1 is 35 degrees.

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The equations of the transformed graphs are [tex]y = \tan(\frac{\pi}{4}x) + 3[/tex] and [tex]y = -\frac34\sin(2x)[/tex]

The tangent function

The parent function is:

y = Atan(Bx) + k

It has a period of 4.

So, we have:

[tex]\frac{\pi}{B} = 4[/tex]

Make B the subject

[tex]B = \frac{\pi}{4}[/tex]

It is shifted vertically up by 3 units.

So, we have:

k = 3

Substitute these values in y = Atan(Bx) + k and remove A

[tex]y = \tan(\frac{\pi}{4}x) + 3[/tex]

Hence, the equation of the transformed graph is [tex]y = \tan(\frac{\pi}{4}x) + 3[/tex]

The sine function

The parent function is:

y = Asin(Bx) + k

It has a period of [tex]\pi[/tex]

So, we have:

[tex]\frac{2\pi}{B} = \pi[/tex]

Make B the subject

B = 2

It has an amplitude of 3/4

So, we have:

A = 3/4

It is flipped across the x-axis

So, we have:

A = -3/4

Substitute these values in y = Asin(Bx) + k and remove k

[tex]y = -\frac34\sin(2x)[/tex]

Hence, the equation of the transformed graph is [tex]y = -\frac34\sin(2x)[/tex]

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The equation of distance traveled by the car is d(t) = 60 · t, for t ≥ 0.

In accordance with the statement, car travels in a straight line at constant speed. The distance traveled (d), in miles, is equal to the product of the speed (v), in miles per hour, and time (t), in hours:

d(t) = v · t     (1)

If we know that v = 60 mi/h, then the equation of distance traveled by the car is d(t) = 60 · t, for t ≥ 0.

The statement is incomplete and complete form cannot be found. Then, we decided to complete the statement by asking for the equation that describes the distance of the car.

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The tiger population loses 3/5 of its size every 2.94 decades

The given equation is:

[tex]N(t)=710(\frac{8}{125} )^t[/tex]

Find the derivative of the given function

[tex]\frac{dN}{dt} =710(0.064)^tln(0.064)\\\\\frac{dN}{dt} =-1951.7(0.064)^t[/tex]

When the tiger loses 3/5 of its population

dN/dt = 3/5

Solve for t

[tex]\frac{3}{5} =-1951.7(0.064)^t\\\\-0.0003=(0.064)^t[/tex]

Take the natural logarithm of both sides

[tex]ln(-0.0003)=t(ln0.064)\\\\-8.087=-2.75t\\\\t=\frac{-8.087}{-2.75} \\\\t=2.94[/tex]

The tiger population loses 3/5 of its size every 2.94 decades

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The slope of a line shows the distance of that line. This means it tells us how far the line moves each time you move over one unit on the x-axis for that line.

The slope of a line can be defined a number that describes the direction and steepness of the line.

It is also known as gradient

It is denoted by the letter 'm'

Thus, the slope of a line shows the distance of that line. This means it tells us how far the line moves each time you move over one unit on the x-axis for that line.

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Answer:

10 eggs

Step-by-step explanation:

We need to work out the price per unit :

12 eggs = rs 192

1 egg = rs 192÷12

1 egg = rs 16

? egg = rs 160

16×? = 160

? = 160÷16

? = 10

So our final answer will be 10 eggs

Answer:

10

Step-by-step explanation:

Using the law of cosines, it is found that the length of side AB is of AB = 13.

The law of cosines states that we can find the angle C of a triangle as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

in which:

For this problem, the parameters are:

C = 120, a = 8, b = 7.

Hence:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

[tex]c^2 = 8^2 + 7^2 - 2(8)(7)\cos{120^\circ}[/tex]

[tex]c^2 = 169[/tex]

[tex]c = \sqrt{169}[/tex]

c = 13.

Hence AB = 13.

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The largest interval of x-values where the function is increasing is (-1, 1)

The table of values is added as an attachment

From the table, the function f(x) decreases from x = -3 to x = -1 and x = 1 and x = 2

So, we make use of the intervals

x = -1, 0 and 1

From the table,

From x = -1 to 0, the change is 3

From x =  0 to 1, the change is 3

From x =  -1 to 1, the change is 6

Using the above highlights, the largest increasing interval is (-1, 1)

Hence, the largest interval of x-values where the function is increasing is (-1, 1)

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Answer:

25%

Step-by-step explanation:

When you simple 6 out of 24 you get a quarter.

A quarter us equivalent to 25%

Step-by-step explanation:

[tex]algenbraic[/tex]

The equation of the parabola graphed is given as follows:

y = a(x + 1)² - 4.

What is parabola and examples?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the vertex given, we have that h = -1, k = -4, hence the equation is:

y = a(x + 1)² - 4

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Answer: B) 1/13

Step-by-step explanation:

There are 52 cards. So, there are 52/4 = 13 cards of each amount of hearts, diamonds, clubs and spades. In this case, we're looking for the probability of picking a club. Since there are 13 club cards and we want to know the probability of picking ONE, our answer is b) 1/13.

Considering the definition of probability, the correct answer is option d): if one card is picked at random from the deck, the probability that it is a club is 1/4.

The higher or lower possibility that a particular event will occur is known as the probability. This is, the probability establishes a relationship between quantity of favorable events and the total quantity of possible events.

The ratio of favorable situations (the number of cases in which event A may or may not occur) to all possible cases is used to calculate the the probability of any event A. This is called Laplace's Law:

probability= number of favorable cases÷ total number of possible cases

In this case, you know:

Replacing in the definition of probability:

probability= 13÷ 52

Solving:

porbability= 1/4

Finally, if one card is picked at random from the deck, the probability that it is a club is 1/4.

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Answer:

The box is 8 feet long.

Step-by-step explanation:

1 inch = 2 feet.

Multiply 4 by 2.

4×2=8

I multiplied 4 by 2 because 1-inch equals 2 feet, which means if we multiply both terms by 4, you will get 4 inch = 8 feet.

Hope this helps!

Answer:

  18π cm² ≈ 56.5 cm²

Step-by-step explanation:

The area of the sector can be found using an appropriate area formula.

When the sector central angle is given in radians, the formula for the area of that sector is ...

  A = 1/2r²θ . . . . . . where θ is the central angle, and r is the radius

When the angle is in degrees, the formula will include a factor to convert it to radians:

  A = 1/2r²θ(π/180) . . . . where angle θ is in degrees

  A = (πθ/360)r² . . . . simplified slightly

The figure shows r=9 cm, and θ=80°. Using these values in the formula gives an area of ...

  A = π(80/360)(9 cm)² = 18π cm² ≈ 56.5 cm²

Answer:

$1995.97.

Step-by-step explanation:

Amount in bank after 20 days =

18000(1 + 0.05/365)^20

= $18049.38

So H = 18049.38 - 16093.41

        =  $1995.97.

Answer:

sum

Step-by-step explanation:

example

2+3=5