The probability that x is smaller than y is 1.
In Exercise 9.10, we are given the joint probability density function of two continuous random variables as:
f(x,y) = 2, for 0 ≤ x ≤ y ≤ 1
f(x,y) = 0, otherwise
To find the probability that x is smaller than y, we need to integrate the joint probability density function over the region where x is less than y:
p(x < y) = ∫∫R f(x,y) dA
where R is the region where x is less than y, which is the triangular region with vertices at (0,0), (1,0), and (1,1).
Therefore, the probability can be computed as:
p(x < y) = ∫∫R f(x,y) dA
= ∫0^1 ∫x^1 2 dy dx (using the limits of integration for R)
= ∫0^1 (2-2x) dx
= 2x - x^2 |0^1
= 1 - 0 - (2(0) - 0^2)
= 1
Hence, the probability that x is smaller than y is 1.
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A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 18, 3, 0, 3, 6, 3.
Using only the values given in the table for the function f(x) = –x3 + 4x + 3, what is the largest interval of x-values where the function is increasing?
(
,
)
The largest interval of x-values where the function is increasing is (-1, 1)
How to determine the largest increasing interval?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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The sum of a number and its reciprocal is 122/11. Find the
number.
O -11
09
O 11
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
Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative one and negative two.
The equation of the parabola graphed is given as follows:
y = a(x + 1)² - 4.
What is parabola and examples?
A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. Terms related to Parabola.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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help....
delta math questions...
The length of BD is √182
How to solve for x?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 :)
What is the equation of the line described below written in slope-iWhat is the equation of the line described below written in slope-intercept form?
the line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0
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
Equation of a lineA 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
6 out of 24 as a percentage
Answer:
25%
Step-by-step explanation:
When you simple 6 out of 24 you get a quarter.
A quarter us equivalent to 25%
4. If a = 1+ 1/b where b>1, find the value of a ?
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
3. The slope of a line shows the___
for 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 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.
What is the slope of a 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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Expand the following using the Binomial Theorem and Pascal’s Triangle. Show your work
2. (x-4)^4
3. (2x+3)^5
4. (2x-3y)^4
Answer:
2
Step-by-step explanation:
Pls help with b
The diameters of two circular pulleys are 6cm and 12 cm, and their centres
are 10cm apart.
a. Angle a = 72.54 degrees
b. Hence find, in centimetres correct to one decimal place, the length of a
taut belt around the two pulleys
The length of a taut belt around the two pulleys is 79.3 cm.
Length around the pulley
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.
Length of the rectangleThe 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
Length of trapezium at bottomThe length of the trapezium at bottom is equal to length of rectangle at top, L = h = 9.54 cm
Angles and length of belt in each circlePortion 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
Length of a taut belt around the two pulleys= 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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A deck of 52 cards contains an equal amount of hearts, diamonds, clubs, and spades. If one card is picked at random from the deck, the probability that it is a club is:
a)1/52
b)1/13
c) 1/10
d) 1/4
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.
Definition of probabilityThe 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
Probability that the picked card is a clubIn this case, you know:
Total number of cards = 52 (number of possible cases)The deck of cards contains an equal amount of hearts, diamonds, clubs, and spades.Total number of cards that are clubs= 52÷4= 13 (number of favorable cases)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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Jason deposited $18 000 in a bank that offers an interest rate of 5% per annum compounded
daily.
He kept the money in the bank for 20 days, before withdrawing an amount, H.
Given that, the balance in the bank after another 20 days is $16 093.41, find H.
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.
A car travels at a constant speed of 60 miles per hour. The distance, d, the car travels in miles is a function of time, t, in hours given by d(t)
The equation of distance traveled by the car is d(t) = 60 · t, for t ≥ 0.
What is the equation of the distance travelled by a car?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.
RemarkThe 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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Need it solved correctly for khan academy
The tiger population loses 3/5 of its size every 2.94 decades
Rate of change using differential calculus
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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Find the area of the shaded region.
Answer:
18π cm² ≈ 56.5 cm²
Step-by-step explanation:
The area of the sector can be found using an appropriate area formula.
Sector areaWhen 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
Lamont is making a blue print of his shoebox. He made a drawing of how he would like to make the box. If the drawing is 4 inches long and the scale of the drawing is 1 inch = 2 feet, how long is the box?
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!
Write the equation of the transformed graphs of each trigonometric function
The equations of the transformed graphs are [tex]y = \tan(\frac{\pi}{4}x) + 3[/tex] and [tex]y = -\frac34\sin(2x)[/tex]
How to transform the functions?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 ____ of two numbers is greater than or equal to the numbers
Answer:
sum
Step-by-step explanation:
example
2+3=5
This is greater than the two numberswitch is a value of a perfect square
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.
if price of 12 eggs is rs 192 , how many eggs can be bought for rs 160
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:
What is the equation of the line through the origin and (-2,3)?
Step-by-step explanation:
[tex]algenbraic[/tex]
Surface area=
Volume =
Help me please thanks
Can someone help me out on this problem and show work please !!
Given the area of the rectangular community garden, the length and width of the garden are 30ft and 10ft respectively.
What is the length and width of the garden?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;
Area of the rectangular community garden A = 300ft²Let width w = xLength = three times width = 3xWe 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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Circle C is shown. 2 secants intersect at a point outside of the circle to form angle 1. The first arc formed is 36 degrees, and the second arc formed is 106 degrees.
In the diagram of circle C, what is the measure of ∠1?
17°
35°
70°
71°
The measure of the ∠1 is 35 degrees.
How to determine the angleit 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
106°36°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 sum of 3 consecutive integers is 2190. what is the value of the smallest integer?
Answer:
3x+2=2190
3x=2190-2
3x=2188
x=2188÷3
x=729
Simplify the expression
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
What is an equation?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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On a coordinate plane, quadrilateral D G A R is shown. Point G is at (negative 8, 3), point A is (4, 8), point R is at (10, 0), and point (negative 2, negative 5).
A grid map marks the plot of Harold’s garden in meters. The coordinates of the quadrilateral-shaped property are G(–8, 3), A(4, 8), R(10, 0), and D(–2, –5). He wants to build a short fence around the garden.
The perimeter of his garden is
meters.
The perimeter of the garden is 46 units.
How to calculate the perimeter?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!
what is the volume of a sphere with a radius of 6 inches
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
See picture to answer!
Using the law of cosines, it is found that the length of side AB is of AB = 13.
What is the law of cosines?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:
c is the length of the side opposite to angle C.a and b are the lengths of the other sides.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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Which logarithmic equation correctly rewrites this exponential equation? 8x = 64
The logarithmic equation of 8^x = 64 is [tex]x = \log_8(64)[/tex]
How to determine the logarithmic equation?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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