I'll use the method of transformations.
If [tex]f_X(x)[/tex] denotes the PDF of [tex]X[/tex], and [tex]y=g(x)=x^3 \iff x=g^{-1}(y) = y^{1/3}[/tex], we have
[tex]f_Y(y) = f_X\left(g^{-1}(y)\right) \left|\dfrac{dg^{-1}}{dy}\right|[/tex]
[tex]\dfrac{dg^{-1}}{dy} = \dfrac13 y^{-2/3}[/tex]
[tex]\implies f_Y(y) = f_X\left(y^{1/3}\right) \left|\dfrac13 y^{-2/3}\right| = \boxed{\begin{cases} \dfrac53 y^{2/3} & \text{if } 0 \le y \le 1 \\ 0 & \text{otherwise} \end{cases}}[/tex]
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QUESTION 5 1 POINT
Tickets for a basketball game cost $5 for students and $8 for adults. The number of students was 7 less than 11 times the
number of adults. The total amount of money from ticket sales was $3682. How many of each ticket were sold?
Provide your answer below:
FEEDBACK
adult tickets, student tickets
FEED-BACK
Answer:
Adult: 59 tickets, Student: 642 tickets
Step-by-step explanation:
$5 = ticket per student (s)
$8 = ticket per adult (a)
$3682 = total money made
# of s = 11a-7 (7 less than 11 times the adults)
We can use this information to create a systems of equations.
5s + 8a = 3682
*price of a ticket times the number of students or adults equals total*
where s = 11a-7
Now we substitute in:
5(11a-7) + 8a = 3682
55a - 35 + 8a = 3682
63a - 35 = 3682
63a = 3717
a = 59
so 59 adult tickets were sold, now we can use this information to solve for student tickets.
s = 11(59)-7
s = 642
So 59 adult tickets, and 642 student tickets were sold.
What algebraic expression is a product with a factor of 5
Answer:
y=5x
Step-by-step explanation:
A product means multiplication, and you need to multiply x by 5 in order to make the product have a factor of 5.
PLEASE PLEASEEEEEEE HELPPPPPP!! 100 POINTSSSS :)
A Ferris wheel, called the Atlanta Skyview, recently opened in Centennial Olympic Park in the Atlanta, GA area. The diameter of this Atlanta attraction is 200 feet and has 42 gondolas evenly spaced out along the circle. Each sector starts and ends at the point at which the gondola is attached to the Ferris wheel circle.
Answer the following questions about this Ferris wheel. Be sure to show and explain all work for each problem.
a. Area of the wheel?
b. measure the central angle in degrees
c. Measure of a central angle in radians
d. Arc length between two gondolas
e. Area of each sector.
The area of the wheel is 31415.9 ft².
The Central angle in degrees is 34.29°
Measure of a central angle in radians is 0.5984 radians
How to calculate the area and central angle of a circle?
A) The image shows an example of this Ferris wheel.
We are given;
Diameter; d = 200 ft
Radius; r = 100 ft
Number of gondolas = 42
Area of the circle wheel = πr²
Area = π * 100²
Area = 31415.9 ft²
B) Now, the sum of angles in a circle is 360°.
Since there are 42 gondola's, then;
Each angle = 360/42 = 60/7°
The central angle will be an angle with its vertex at the center of a circle and with sides that are radii of the circle. From the image, we see that it covers approximately 4 gondola's. Thus;
Central angle = 4 * 60/7° = 34.29°
C) Central Angle in radians will be converted as 0.5984 rad.
D) Arc length between two gondolas is;
S = rθ
S = 100 * 0.5984
S = 59.84 radians
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What is the area of the rectangle below
Answer:
130 sq. units
Step-by-step explanation:
Any number multiplied by 10 is the same number with a 0 added at the end.
Answer:
1300
Step-by-step explanation:
1. calculator
2.putreef Iub numbers
3 solve
Suppose you just purchased a digital music player and put 6 tracks on it. After listening to it you decide you only like 2 songs. With the random feature on the player, each of the 6 songs is played once in random order. Find the probability that among the first 2 songs played
A. You like both of them
B. You like neither of them
C. You like exactly 1
The probability that among the first 2 songs played ;a) 6% , not unusual b) 40% and c) 48.4%
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
We have the following information from the statement:
n = 6, r = 2
a)
P (like both of them) = P (like first song) x P (like second song)
P = 2/6 x 1/5
P = 0.06 = 6%
The probability that among the first 2 songs played and You like both of them is 6%.
b)
P (like neither) = P (not like first song) x P (not like second song)
P = 4/6 x 3/5
P = 0.4 = 40%
c) P (like exactly one of them) = P (first song liked) x P (second song not liked) + P (first song not liked) x P (second song liked)
P = ( 2/6 x 1/5) + (4/6 x 3/5)
P = 0.484 = 48.4%
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5x -9=2y por suma y resta ecuacion
2. Find the LCM of the following numbers by division method. (a) 16 and 28 (b) 36 and 44 (c) 45 and 120 (d) 10, 15 and 30 (e) 52 and 128 (f) 20, 60 and 80
(a):112
(b):396
(c):360
(d):30
(e):1664
(f):240
Steve bought a new car for $22,000 but paid 93% of the list price. How much was the list price
Answer:
approximately $23,655.91 (rounded to the nearest hundredths place)
Step-by-step explanation:
[tex]22,000=0.93x\\x=23,655.91[/tex]
Students in a fitness class each completed a one-mile walk or run. The list shows the time it took each person to complete the mile. Each time is rounded to the nearest half-minute.
5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5
Which statements are true about a histogram with one-minute increments representing the data? Select three options.
A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes.
The histogram will have a shape that is left-skewed.
The histogram will show that the mean time is greater than the median time of 7.4 minutes.
The shape of the histogram can be approximated with a normal curve.
The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
The histogram will have a shape that is left-skewed. Then the correct option is B.
What is a histogram?A diagram is made up of rectangles whose size is related to a variable's frequency and whose width is comparable to the training sample.
Students in a fitness class each completed a one-mile walk or run. The list shows the time it took each person to complete the mile. Each time is rounded to the nearest half-minute.
5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5
Then the mean will be
Mean = (5.5 + 6 + ..... + 6.5 + 5.5) / 15
Mean = 111.5/12
Mean = 7.4333
Then the median will be
Median = 7.5
The histogram will have a shape that is left-skewed.
Then the correct option is B.
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Answer:
The histogram will have a shape that is left-skewed.
The shape of the histogram can be approximated with a normal curve.
The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
Step-by-step explanation:
B/2, D/4, E/5
A soccer league has 160 players. Of those players 50% are boys. How many boys are in the soccer league?
Answer:
80 boys
Step-by-step explanation:
160 total players
50% are boys
50% of 160 is 80
I need help in this problem
Step-by-step explanation:
this is first an arithmetic sequence with the first term A1=3(1)+1=4 And the 12th term A12=3(12)+1=37. Then use this formula
S12=12/2 ×(4+37)
=6×41
=246
Evaluate:
10
Σ¹0 4(1)n-1 = [?]
Round to the nearest hundredth.
Enter
Answer:
Using the formula of geometric progression, we get 5.3333333. After rounding off to the nearest hundredth or to the two digit place after the decimal, we get 5.33.
Step-by-step explanation:
Concept: Given expression means that [tex]4(\frac{1}{4} )^{n-1}[/tex] is a series that starts from n = 1 and ends at n = 10. Or we can say that the given expression is a summation from n = 1 to n = 10. This will make a geometric progression. Use the formula of geometric progression to find the answer.
[tex]4(\frac{1}{4})^{0} + 4(\frac{1}{4})^{1} + 4(\frac{1}{4})^{2} +...+ 4(\frac{1}{4})^{10}\\4\frac{-(\frac{1}{4} )^{11} +1}{-\frac{1}{4} +1} \\4\frac{1}{\frac{3}{4} } \\\frac{16}{3} \\5.33333333\\[/tex]
Now, we want the answer to the nearest hundredth. This means that the answer should have two digits after the point.
The answer, to the nearest hundredth is 5.3333333
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This year Rafael has 60 regular customers which is 150 percent of the 40 regular customers he had last year.
The base is 60, the part is 40 and the rate is 150%.
How to depict the information?The base is the whole quantity or amount that the problem is about.
The part is referred to as the percentage is the portion of the base. The rate is the number with the percentage.
In this case, the base is 60, the part is 40 and the rate is 150%.
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A country's population in 1991 was 103 million, in 1999 it was 108 million. estimate the total population in 2013
Answer:
117
Step-by-step explanation:
The total population is 117 million
aron bought an almirah for $1520 and sold it at a profit of 12 1/2% what is the selling price
Answer:
$1710
Step-by-step explanation:
let me know if you want an explanation :))
Factor the polynomial function.
G(v) - 196v² + 100
Answer:
4(49v²+25)
Step-by-step explanation:
[tex]196 {v}^{2} + 100[/tex]
[tex]4(49 {v}^{2} + 25)[/tex]
Help my son please!!!
Answer:
that makes no sence at all i read it over 3 times and still font understand a word of it
sorry :(
12x² + 9x² =
A. 21x²²
B. 21x
C. 22x²
D. 22xA
Answer:
21x²
Step-by-step explanation:
hopefully A is a typo
Answer: A (if it's just a typo) or [tex]21x^{2}[/tex]
Step-by-step explanation:
Since it's the same variable and same exponent, you just need to add the whole numbers and put the same variable and exponent.
12 + 9 = 21
[tex]21x^{2}[/tex]
can someone please help walk me through the steps to solve number 79? i’m lost
Answer: 70/29
Step-by-step explanation:
[tex]S=\theta r\\\\35=14.5 \theta\\\\\theta=\frac{35}{14.5}=\boxed{\frac{70}{29}}[/tex]
what is golden ratio, and explain it's history
Answer:
The golden ratio is a proper term in the field of mathematics, but it finally covers more than the research in the field of mathematics. According to the current literature discussion, we can say that the discovery of the Golden ratio and how it evolved is still a mystery. But studies have shown that the Pythagorean school of ancient Greece in the 6th century BC studied the formation of regular 5-sided and regular 10-sided plots, leading modern mathematicians to conclude that the Pythagorean school had touched on and even mastered some of the rules of the golden ratio and also discovered irrational numbers. It focuses on the relationship from mathematics, to explore the principle of beauty and that beauty is harmony and proportion, according to the proportional relationship can form beautiful patterns, this is actually a digital proportional relations, the line is divided into two parts, a long and a short period of the ratio of the equal to the ratio of length to a long, their proportion is around 1.618:1, This mathematical principle is also embodied in the famous Frederikian sequence, in which everything in this proportion shows the harmony and balance of its internal relations.
In the 4th century BC, the Greek mathematician Eudoxus was the first to systematically study this problem and establish the theory of proportion. Around 300 BC, Euclid absorbed the research results of Eudoxus in writing The Elements of Geometry and further systematically discussed the Golden Section, which became the earliest treatise on the golden Section (i.e. the middle and the end ratio) [5].
After the Middle Ages, the golden ratio was shrouded in mystery. Italian mathematician Luca Pacioli called the middle and the end of the ratio sacred and wrote a book about it. The German astronomer Johannes Kepler called the divine ratio the Golden Ratio. Golden in the 19th century the name only gradually, and the evidence is that German mathematician Martin Ohm (English: Martin Ohm) wrote the second edition of the basic pure mathematics annotation wrote about the interpretation of the golden ratio: "people used to put any straight line along the way will be divided into two parts, the method of known as the golden mean". And in the ninth edition of the Encyclopaedia Britannica, published in 1875, Sully notes: "The interesting, experimental and strong idea put forward by Frederick... proclaimed the supposed superiority of the 'golden Section' in visual proportion." So the Golden Section was already popular. In the 20th century, American mathematician Mark Barr gave it the name Phi. The Golden Section has many interesting properties and has been widely used by humans to make it famous today. The most famous example is the golden ratio or 0.618 method in optimization, which is first proposed in 1953 by Jack Kiefer (English: Jack Kiefer), an American mathematician, and is promoted in China in 1970s.
Any help will do! Thank you!
Let's take this problem step-by-step:
First let's set up the equation for the cost for one week of renting the car
agency charges $230 per week[tex]charge = 230[/tex]
agency charges $0.25 per mile (lets set the number of miles as 'x')[tex]charge = 230 + 0.25x[/tex]
The total cost was 415, therefore:
[tex]415 =230 + 0.25x\\185 = 0.25x\\x = 740[/tex]
Therefore, you traveled 740 miles
Answer: 740 miles
Hope that helps!
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what is the value of x
let's name the vertices of the triangle as A B C and D as the image shown above
In triangle ABC
sin 60° = AB/AC
√3/2 = 8√2/ AC
AC = 16√2/√3
In triangle ACD
sin 45° = AC/AD
1/√2 = 16√2/ 3 AD
AD = 16/3 x = 16/3. Find the general solution to
d²y/dx²= 49y. Enter your answer as an equation y = ..
Note: d²y/dx²=k^2y
The given differential equation is linear with constant coefficients,
[tex]\dfrac{d^2y}{dx^2} - 49y = 0[/tex]
with characteristic equation
[tex]r^2 - 49 = 0[/tex]
and hence characteristic roots [tex]r=\pm7[/tex]. This means the general solution to the ODE is
[tex]y = C_1 e^{7x} + C_2 e^{-7x}[/tex]
In fact, you're given the solution already,
[tex]y = C_1 e^{kx} + C_2 e^{-kx}[/tex]
and you've determined that
[tex]\dfrac{d^2y}{dx^2} = k^2 (C_1 e^{kx} + C_2 e^{-kx}) = k^2 y[/tex]
Comparing this to the given ODE, it's obvious that [tex]k=7[/tex], so you can just replace [tex]k[/tex] with 7 in the given template solution.
For the given equation, find the values of a, b, and c, determine the direction in which
and determine the y-intercept. Decide which table best illustrates these values for the equation
f(x) = -9x² +7x
Answer: Table D
Step-by-step explanation:
The coefficient of x^2 is -9, the coefficient of x is 7, and the constant is 0, so we know a = -9, b = 7, c = 0.
This eliminates tables A, B, and C.Thus, table D is the answer.
Urgent please help!!!!!!!!!!
—————————-
What is the solution to system of equations question?
Answer:
The correct answer is B, the second option
Step-by-step explanation:
(-2, 5/3)
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Indicate the equation of the given line in standard form. Show all of your work for full credit.
The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5).
Answer: 24 sq units is the area of triangle.
Step-by-step explanation:
Given , (x1 , y1) = (-1, 1), (x2 , y2) = (3, 5) , (x3, y3) = (5, -5)
Using the Formula :
Area of triangle = [tex]\[\frac{1}{2}(x1(y2-y3) + x2(y3-y1) + x3(y1 -y2))\][/tex]
[tex]\[=\frac{1}{2}(-1(5-(-5)) + 3(-5-1) + 5(1-5)) \\=\frac{1}{2}(-10 -1 8 -20) \\=\frac{1}{2}(-48) = -24\][/tex]
Area cannot be negative. We only consider the numerical value of answer. Therefore, area of triangle = 24 sq units.
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Which statements about the location of the point are
true? Select three options.
The point is in the first octant.
The point lies behind the yz-plane.
The x-coordinate is -3.
The y-coordinate is positive.
The point lies to the left of the xz-plane.
Answer:
Step-by-step explanation:
Assuming that Hamid’s revenue is found by multiplying the book price by the number of copies sold, create an equation (in standard form) to model his revenue.
An equation of Hamid’s revenue by multiplying the book price by the number of copies sold is x = ny.
What is an equation?The process of equating one thing with another.
Let Hamid’s revenue is $x and the price of book is $y.
If he sold n number of copies.
Then, the general equation will be x = n * y.
Therefore, an equation of Hamid's revenue will be x = ny.
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4x + 2y=4 and 3x -y= -7
Answer:
y = 4
x = -1
Step-by-step explanation:
4x + 2y = 4 Eq. 1
3x - y = -7 Eq. 2
from the Eq. 2
3x = y - 7
3x + 7 = y Eq. 3
Replacing the value of the Eq. 3 in the Eq. 1
4x + 2(3x+7) = 4
4x + (2*3x + 2*7) = 4
4x + (6x + 14) = 4
10x + 14 = 4
10x = 4 - 14
10x = - 10
x = -10/10
x = -1
from the Eq. 3
3x + 7 = y
3*-1 + 7 = y
-3 + 7 = y
4 = y
Check:
from the Eq. 1
4x + 2y = 4
4*-1 + 2*4 = 4
-4 + 8 = 4
f(x) = 3x² + 5x - 2
g(x) = 5x³-4x² + 4
Find (f + g)(x)
Answer: [tex]5x^3 - x^2 + 5x+2[/tex]
Step-by-step explanation:
[tex](f+g)(x)=(3x^2 + 5x-2)+(5x^3 - 4x^2 +4)=3x^2 + 5x-2+5x^3 - 4x^2 +4=\boxed{5x^3 - x^2 + 5x+2}[/tex]
