Answer:
[tex]k = 1[/tex]
[tex]P(x > 3y) = \frac{2}{3}[/tex]
Step-by-step explanation:
Given
[tex]f \left(x,y \right) = \left{ \begin{array} { l l } { k , } & { 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x } & { \text 0, { elsewhere. } } \end{array} \right.[/tex]
Solving (a):
Find k
To solve for k, we use the definition of joint probability function:
[tex]\int\limits^a_b \int\limits^a_b {f(x,y)} \, = 1[/tex]
Where
[tex]{ 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x }[/tex]
Substitute values for the interval of x and y respectively
So, we have:
[tex]\int\limits^2_{0} \int\limits^{x/2}_{0} {k\ dy\ dx} \, = 1[/tex]
Isolate k
[tex]k \int\limits^2_{0} \int\limits^{x/2}_{0} {dy\ dx} \, = 1[/tex]
Integrate y, leave x:
[tex]k \int\limits^2_{0} y {dx} \, [0,x/2]= 1[/tex]
Substitute 0 and x/2 for y
[tex]k \int\limits^2_{0} (x/2 - 0) {dx} \,= 1[/tex]
[tex]k \int\limits^2_{0} \frac{x}{2} {dx} \,= 1[/tex]
Integrate x
[tex]k * \frac{x^2}{2*2} [0,2]= 1[/tex]
[tex]k * \frac{x^2}{4} [0,2]= 1[/tex]
Substitute 0 and 2 for x
[tex]k *[ \frac{2^2}{4} - \frac{0^2}{4} ]= 1[/tex]
[tex]k *[ \frac{4}{4} - \frac{0}{4} ]= 1[/tex]
[tex]k *[ 1-0 ]= 1[/tex]
[tex]k *[ 1]= 1[/tex]
[tex]k = 1[/tex]
Solving (b): [tex]P(x > 3y)[/tex]
We have:
[tex]f(x,y) = k[/tex]
Where [tex]k = 1[/tex]
[tex]f(x,y) = 1[/tex]
To find [tex]P(x > 3y)[/tex], we use:
[tex]\int\limits^a_b \int\limits^a_b {f(x,y)}[/tex]
So, we have:
[tex]P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {f(x,y)} dxdy[/tex]
[tex]P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {1} dxdy[/tex]
[tex]P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 dxdy[/tex]
Integrate x leave y
[tex]P(x > 3y) = \int\limits^2_0 x [0,y/3]dy[/tex]
Substitute 0 and y/3 for x
[tex]P(x > 3y) = \int\limits^2_0 [y/3 - 0]dy[/tex]
[tex]P(x > 3y) = \int\limits^2_0 y/3\ dy[/tex]
Integrate
[tex]P(x > 3y) = \frac{y^2}{2*3} [0,2][/tex]
[tex]P(x > 3y) = \frac{y^2}{6} [0,2]\\[/tex]
Substitute 0 and 2 for y
[tex]P(x > 3y) = \frac{2^2}{6} -\frac{0^2}{6}[/tex]
[tex]P(x > 3y) = \frac{4}{6} -\frac{0}{6}[/tex]
[tex]P(x > 3y) = \frac{4}{6}[/tex]
[tex]P(x > 3y) = \frac{2}{3}[/tex]
1 point
Every five years in March, the population of a certain town is recorded. In
1995, the town had a population of 4500 people. From 1995 to 2000, the
population increased by 15%. From 2000 to 2005, the population
decreased by 4%. What was the town's population in 2005? *
4527
4968
4995
5382
Answer:
So, the town had a population on 4,500 people in 1995. Then from 1995 to 2000, the population increased by 15%.
Convert 15% to a decimal by dividing it by 100. Then, the population in 1995 by this decimal.
15% ÷ 100 = 0.15
4,500 × 0.15 = 675
Now, add this to the population in 1995.
4,500 + 675 = 5,175
This means that the town had a population of 5,175 people in 2000.
To calculate the town's population in 2005, repeat the same steps we took to find the population in 2000, except this time we will subtract instead of add since the population DECREASED.
4% ÷ 100 = 0.4
5,175 × 0.4 = 207
5,175 - 207 = 4,968
FINAL ANSWER:
The town had a population of 4,968 in 2005.
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Step-by-step explanation:
What is a decimal that is equivalent to the fraction 44/100
Answer:
0.44
Step-by-step explanation:
44/100 as a decimal is 0.44.
Hope this helped!!!
The decimal equivalent to the fraction 44/100 is 0.44.
We have,
To find a decimal equivalent to the fraction 44/100, we can simply divide the numerator (44) by the denominator (100):
44 ÷ 100 = 0.44
The concept used to find the decimal equivalent of a fraction is division.
By dividing the numerator by the denominator, we obtain the decimal representation of the fraction.
Therefore,
The decimal equivalent to the fraction 44/100 is 0.44.
Learn more about expressions here:
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Least to greatest - 1.8 , 1 , 1 2/5 , 1 9/10 , -1.25
Answer:
-1.25, 1, 1 2/5, 1.8, 1 9/10
Step-by-step explanation:
Answer:
-1.25, 1, 1 2/5, 1.8, 1 9/10
Step-by-step explanation:
someone help me pls before i cry okay okay
Answer:
22%
Step-by-step explanation:
First, determine the total: 2392 total surveys.
Next, determine the number of people who prefer Italian: 526
Solve:
526/2392 (This is will determine the percentage of people who prefer Italian food according to the pie chart)
= 0.2198...
Round
= 22%
Answer:
I'm going to say that it is 28% or 22%
Step-by-step explanation:
so they surveyed 2392 people and only 526 of them said that they would eat Italian food so you would do
2392- 526= 1866 then 526/1866=28%
but if that is wrong then you would just do
526/2392=22%
Construye una fórmula que permita calcular el dinero recaudado en un autobús en función de los billetes vendidos, sabiendo que cada uno cuesta 1,2 euros. Represéntala. ¿Se pueden unir los puntos?
Answer:
1.2X = $
Step-by-step explanation:
Para construir una fórmula que permita calcular el dinero recaudado en un autobús en función de los billetes vendidos, sabiendo que cada uno cuesta 1,2 euros, se debe realizar el siguiente razonamiento lógico matemático:
1.2(variable fija) x X (número de billetes vendidos) = $ (Dinero recaudado)
1.2X = $
Por lo tanto, si por ejemplo se hubiesen vendido 100 billetes, la ecuación operaría de la siguiente manera:
1.2 x 100 = $
120 = $
It costs $90 720 to stay in a
hotel for 7 days. How much does it
cost to stay for 3 days?
Answer:
$38 880
Step-by-step explanation:
So for 7 days it costs $90 720
First we need to find what 1 day cost
So you will divide $90 720 by 7
90 720÷7= $12 960
To find the cost for 3 days your gonna multiply $12 960 by 3
12 960×3= $38 880
Write down the integer values satisfied by the diagram
Answer:
{0, 1, 2, 3}Step-by-step explanation:
The diagram includes the interval:
(-1, 3]The integer values in the given interval are:
{0, 1, 2, 3}The figure is a ____.
1. Square
2. Rectangle
3. Triangle
The figure has _____ sides.
1. Three
2. Four
3. Five
The figure has the dimensions of _____.
1. Length, Width, and height
2. Length, Width, Base, and height
3. Length and Width
(also ignore my mouse)
The figure is a rectangle.
The figure has Four sides.
The figure has the dimensions of Length and Width.
Sorry if its wrong, I have bad memory
What is the probability of choosing a king from a deck of cards? Type your answer as a fraction.
Answer:
4/52 or 1/13
Step-by-step explanation:
there are only 4 kings; diamond, Heart, Spades and Clubs.
You are buying shoes online. The selling price is $29.99. The sales tax is 6.5% What is the total cost? Round to the nearest penny, if necessary.
Answer:
$31.94
Step-by-step explanation:
29.99 x 0.065 = 1.95
29.99 + 1.95= 31.94 :)
Answer:
$31.94
Step-by-step explanation:
find the area of the triangle
Answer:
133
Step-by-step explanation:
14 times 19 is 266 divided by 2 is 133
Area of a triangle is 1/2 x base x height
Base is given as 19 ft and height is given as 14 ft
Area = 1/2 x 19 x 14 = 133 square ft
Please help me with this ASAP ASAP please please help
Answer:
4ㅈr² is formula
so
4 × ㅈ× (16)²
= 1024ㅈ cm²
Miss Potter wants to send thank-you cards to 132 students. The cards are sold in packages of 30. How many packages does Miss Potter need to buy?
Answer:
The answer i got it 4.4
Step-by-step explanation:
Answer:
worng it is five
Step-by-step explanation:
sorry if you got it worng because I got it worng to from that answer and it said it is five
Simplify (6x2 - 4x + 7) - (8x2 - 2x + 5) =
Answer:
−2x 2−2+2
Step-by-step explanation:
A school sold tickets to a musical. The school received $6.50 per ticket sold.
Select the ordered pairs that represent possible combinations of the number of tickets sold and the corresponding total amount of money the school would have received from selling the tickets, if this relatioship was graphed on a Coordinate Plane.
Select all that apply.
A.) 0, 0.00
B.) 2, 13.00
C.) 4, 24.00
D.) 10, 65.00
E.) 12, 68.00
No links plz
Answer:
A B D
Step-by-step explanation:
Answer:
B and D
Step-by-step explanation:
hope this helps :))))
Installment Loan
Principal
$1500.00
Term Length
4 years
How much of the first
payment for the
installment loan
6% shown in the table will
go towards interest?
Interest Rate
Monthly Payment
$35.00
A. $27.50
B. $7.50
C. $2.10
D. $32.90
The amount of the first payment that will go towards interest is $7.50.
The answer is B. $7.50.
To calculate the amount of the first payment that will go towards interest for an installment loan, we need to consider the principal, term length, and interest rate.
Given:
Principal: $1500.00
Term Length: 4 years
Interest Rate: 6%
Monthly Payment: $35.00
To find the amount of interest paid in the first payment, we'll first calculate the total interest paid over the entire term and then divide it by the number of payments.
Calculate the total interest paid over the term.
Total Interest = Principal × Interest Rate × Term Length
Total Interest = $1500.00 × 6% × 4 = $360.00
Divide the total interest by the number of payments.
Interest in the First Payment = Total Interest / Number of Payments
Interest in the First Payment = $360.00 / (4 years × 12 months per year)
Interest in the First Payment = $360.00 / 48
Interest in the First Payment = $7.50
Therefore, the amount of the first payment that will go towards interest is $7.50.
The answer is B. $7.50.
for such more question on interest
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Can someone help me with this, please!!!
Answer:
The answer is C
Step-by-step explanation:
Both triangles are very similar
Make frequency tables for the following data sets. Include columns for relative frequency. Also, make a bar graph for the frequency
Final grades of 30 students in a math class: AAAAAABBBBBBCCCCCCCCCCFFF
Can someone explain me this
Answer:
area of circle - area of hexagon
Step-by-step explanation:
can you please help me with the question below
Nancy uses her $10 allowance to buy a dress. She got $2 bills and 2quarters in change. what was the price of the dress???
Answer:cdjbskbbN
Step-by-step explanation:2 2/4
Answer:
$7.50
Step-by-step explanation:
10 - 2.50 = 7.50
in an office building,92 offices are currently being rented. This represents 80% of the total units. How many offices are in the building?
Answer:
Number of offices in the building = 115
Step-by-step explanation:
Let x be the total number of offices.
Then 80% x= 92 or 80/100 * x =92
Hence, x = 92*100/80 = 9200/80= 115
The terminal side of an angle in standard position passes through P(15,-8). What is the value of sin e?
Express the relation in a table:(2,1),(4,5),(3,3),(1,(2)
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Once the data is entered into a spreadsheet, it is convenient to sort the table by the input values. The relation is unchanged, but it may be easier to work with that way.
The table is shown below.
Help please I’ll mark brainlist
I really needs help pls
Answer:
Step-by-step explanation:
base of 5 = 5 + 4 + 3 + 2 + 1 = 15
base of 10 = [tex]n^{2}[/tex]/2 + n/2 = 100/2 + 10/2 = 55
formula = [tex]n^{2}[/tex]/2 + n/2
where n is the number of base boxes
Can someone solve this?
Answer:
The answer is A.
Step-by-step explanation:
Because if you compare the two "y" section on both graphs you will notice that the "Speedy Delivery" charges way more than the "Lightning Delivery ."
Hope this helps ,have a good day.
Is it True or false??
Answer:
I think it's false.
Step-by-step explanation:
Gino wants to leave at least 20% tip on his restaurant bill of $197.40. Approximately how much tip should he add to the bill?
what is the unit price of 12 cupcakes for 25 dollars
Answer:
Unit price of 12 cupcakes for 25 dollars = 25/12
= 2.08 dollars
Answer:
The unit price would be $2.08 for a cupcake because if you divide 12 and 25, you would get 2.08.
Step-by-step explanation:
Allen has a piece of wood that is 10.5 feet long. He decides to cut it into 3 equal pieces to repair his deck. How long should he cut each piece?
Answer:
3.5 feet
I think is right