Four buses carrying 153 high school students arrive to Montreal. The buses carry, respectively, 36, 46, 32, and 39 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying this randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on his bus. Compute the expectations and variances of X and Y: E(X)
Answer:
E(X) = 38.9346
Var(X) = 25.588
E(Y) = 38.25
Var(Y) = 26.1875
Step-by-step explanation:
Given - Four buses carrying 153 high school students arrive to Montreal. The buses carry, respectively, 36, 46, 32, and 39 students. One of the students is randomly selected.One of the 4 bus drivers is also randomly selected.
To find - Compute the expectations and variances of X and Y.
Proof -
Let us assume that,
X be The number of students that were on the bus carrying this randomly selected student.
Y denote the number of students on his bus.
Now,
E(X) = [tex]\frac{36(36) + 46(46) + 32(32) + 39(39)}{153}[/tex]
= [tex]\frac{5957}{153}[/tex]
= 38.9346
⇒E(X) = 38.9346
Now,
E(Y) = [tex]\frac{36 + 46 + 32 + 39}{4}[/tex]
= [tex]\frac{153}{4}[/tex]
= 38.25
⇒E(Y) = 38.25
Now,
Var(X) = [tex]\frac{36(36 - 38.9346)^{2} + 46(46 - 38.9346)^{2} + 32(32 - 38.9346)^{2} + 39(39 - 38.9346)^{2}}{153}[/tex]
= [tex]\frac{310.0276 + 2296.3144 + 1308.5091 + 0.1668}{153}[/tex]
= [tex]\frac{3915.0179}{153}[/tex]
= 25.588
⇒Var(X) = 25.588
Now,
Var(Y) = E(Y²) - [E(Y)]²
= [tex]\frac{36^{2} + 46^{2} + 32^{2} + 39^{2} }{4} - (38.25)^{2}[/tex]
= [tex]\frac{5957}{4} - 1463.0625[/tex]
= 1489.25 - 1463.0625
= 26.1875
⇒Var(Y) = 26.1875
Is this correct?
Answer:
B
Step-by-step explanation:
Yes.
Providing FI is a straight line, then FGH + HGI = 180. The angles are supplementary.
If one of them is 89 then the other one must be 180 - 89 = 91
B is the correct answer.
Find the inverse of g(n) = - 3 - 1
Og-1 (n) = -(n-3)-1
9
9-1 (n) = In
g-1 (n) = (n + 1)3 + 3
Og-1 (n) = 3+n3
Answer:
[tex]g'(n) = -\frac{n+1}{3}[/tex]
Step-by-step explanation:
Given
[tex]g(n) = -3n - 1[/tex]
Required
Determine the inverse
[tex]g(n) = -3n - 1[/tex]
Replace g(n) with y
[tex]y = -3n - 1[/tex]
Swap positions of x and y
[tex]n = -3y - 1[/tex]
Make y the subject
[tex]3y = -n - 1[/tex]
[tex]3y = -(n + 1)[/tex]
[tex]y = -\frac{n+1}{3}[/tex]
Replace y with g'(n)
[tex]g'(n) = -\frac{n+1}{3}[/tex]
gkhoflkhlxrtuu;tdu8rp5[\78u
Answer:
What???
Step-by-step explanation:
Answer:
????
Step-by-step explanation:
Calculate the unit rate. Label your work properly. Show your fraction work.
Math question : eating 3/4 pizza in 5/6 hour
Answer:
(9/10) of a pizza per hour.
Step-by-step explanation:
(3/4)*4=3
(5/6)*4= 3hr 20 mins
[3 (1/3)] / [3 (1/3)]=1
3 / [3 (1/3)]= 0.9
Derek has 2 feet of Tasty Cherry Rope. He plans on splitting it evenly between himself and 5 of his friends. How many inches of Tasty Cherry Rope does Dereck have? *
6 (x + 4) = 48
please help!!
Answer:
x = 4
Step-by-step explanation:
6(+4)=48
6+24=48
6+24=48
6+24−24=48−24
6=24
6=24
6/6=24
...
Look at the graph of the functions. Given the original function, what is a possible equation for the translated function, g(x)?
Answer: c
Step-by-step explanation:
Help me please I’ll give brainliest!!
Answer:
Step-by-step explanation:
Divide the pentagon radially into 5 congruent, isosceles triangles.
Area of one triangle = ½×7.2×4.955 = 17.838 mm²
area of pentagon = 5×17.838 mm ≅ 89.2 mm²
A crew of highway workers paved 9 mile in 20 minutes. If they work at the same rate, what portion of a mile
Will they pave in one hour?
A-1/150
B-2/45
C-2/5
D-5/2
-2/45.
Step-by-step explanation:
9 times 3 gives you 27 miles a hour. We are not done though. Now we have to find the portion of a mile they pave in one hour would be -2/45, which is B.
answer the question in the pic below (math)
Answer:
46.95 in.²
Step-by-step explanation:
Surface area of the kaleidoscope = surface area of a triangular prism = 2(BA) + P*H
Base area (B) = 2(½*bh) = 2(½*1.5*1.3) = 1.95 in.²
Perimeter of base (P) = 1.5 + 1.5 + 1.5 = 4.5 in.
Height of prism (H) = 10 in.
Plug in the values
Surface area = 1.95 + 4.5*10 = 46.95 in.²
Find the value of 3x for x=3
Answer:
9
Step-by-step explanation:
X MULTIPLIED BY 3 EQUALS 9 SINCE X=3
Answer:
9
Step-by-step explanation:
x=3
3*3= 9
so value of 3x = 9
1 1/5 + 3 2/5
fractions
Answer:
4 7/15
Step-by-step explanation:
Hope this helps :)
Find the measure of line segment AB.
Answer:
Measurement of AB = 8.6 units (Approx.)
Step-by-step explanation:
Given:
Coordinate of point A = (3 , 9)
Coordinate of point B = (8 , 2)
Find:
Measurement of AB
Computation:
Distance = √(X1 - X2)² + (Y1 - Y2)²
Measurement of AB = √(3 - 8)² + (9 - 2)²
Measurement of AB = √25 + 49
Measurement of AB = √74
Measurement of AB = 8.6 units (Approx.)
Can someone please help me with this!?
e) que características tienen las gráficas que representan una relación de proporcionalidad directa entre la cantidad de agua en la cisterna y el tiempo del servicio?
f) escriban las expresiones algebraicas de las relaciones que son de proporcionalidad ¿en qué son diferentes?
g) ¿qué representan esas diferencias
Answer:
here is a videos look it up on you tube and it might help
Step-by-step explanation:
search this
Interpreting graphs of proportional relationships
at a sporting event, you can buy 5 hot dogs and 2 drinks and spend $19. you could have also purchased 3 hot dogs and 4 drinks and sprnt $17. How much money did a hot dog cost? how much money did a drink cost?
please help!! I’m failing math and I have no idea what the answer is and if I don’t do my hw and keep failing I might have to repeat the grade! please let me know if you know the answer <3. I provided a photo! but I’ll but it here too
question⬇️⬇️
which expression is equivalent to 5(4x + 3) - 3x
A) 18x + 15
B) 18x + 3
C) 7x + 8
D) 2x + 8
Answer:
A: 18x+15
Step-by-step explanation:
5(4x+3)-2x
Distribute the 5
20x +15 - 2x
Combine like terms
20x-2x +15
18x +15
3x^2+5x-28=0 solve this for me please
Answer:
x= 7/3
x=-4
Step-by-step explanation:
Use the quadratic formula
a= 3, b=5, c=-28
-5± [tex]\sqrt{5^2-4*3(-28)}[/tex]
x= _________________
2.3
Simplfy
[tex]x=\frac{-5+19}{6} \\x=\frac{-5-19}{6}[/tex]
giving brainliest!! *easy*
Answer:
288.68 square millimeters
288.68 square millimeters or 1703.12 square millimeters
Find the measure of a 2.
45 135
62 = [?]
Answer:
45
Step-by-step explanation:
The volume of a cube is 125 inches cubed. What is the length of each side?
Answer:
5
Step-by-step explanation:
Explanation: All the edges of a cube have the same length, and the volume of a cube is the length of an edge taken to the third power. So the length of the edge of a cube with a volume of 125 is 5.
A rectangular prism has a length of 11ft, a height of 4ft, and a width of 3ft. What is its volume, in cubic ft?
Answer:
132 ft³
Step-by-step explanation:
L=11 W=3 H=4
V=LWH
V=(11)(3)(4)
V=132 ft³
Activity 1
Fill in the missing number:
1. 34 533; 35 533 ; 36 533; 37 533; 38 533
2. 6475; 6 490;
3 6 520; 6 235; 6 250.
3. 55 455; 55 470;
Answer:
3 6 520; 6 235; 6 250.
plz help me this work is hard
MUST HELP!!!! (50 POINTS) +BRAINLEST +5 STARS +THANKS ON PROLFILE!!!!
The ratios of the _______________________of the objects is 2.4.
*use the words below to fill in the blank*
Equal, 2.4, point of dilation, Scale factor, perimeters, (7.2,4.8), Enlargement, areas, (4.8, 9.6)
Question 1:
A bag contains 5 black marbles, 7 blue marbles, 3 green marbles, 4 red marbles, and 1 white marble. A marble is selected and then replaced. What is the probability of selecting a black marble?
A 1/5
B 1/4
C 1/20
D 5
Question 2:
Mark has a bag of pink, blue and white gumballs. He randomly selects a gumball from the bag 30 times and records the color of the gumball each time. Before he selects another gumball he replaces the gumball he has already selected. The results are summarized in the table below.
Pink Blue White
Number of Times 8 12 10
Based on these results, determine whether each statement is True or False.
A The experimental probability of pink is 0.8
True
False
B The experimental probability of blue is 0.4
True
False
C It is more likely that Matk will select a blue gumball than a white gumball
True
False
Question 3:
When students line up in the cafeteria, they can choose their main course, drink, and dessert. For the main course students can choose a hot dog, burger, or pizza. For the drink they can choose between water, milk, or soda. And for the dessert they can choose cake or ice cream. The tree diagram shows all possible combinations of meals. Choose two correct answers below.
A The probability of randomly choosing pizza and cake is 3/18
Correct
Incorrect
B The probability of randomly choosing a hot dog, water, and ice cream is 1/3
Correct
Incorrect
C The probability of randomly choosing a burger and water is 1/18
Correct
Incorrect
D The probability of randomly choosing a burger, water, and cake is 1/18
Correct
Incorrect
E The probability of randomly choosing pizza is 1/18
Correct
Incorrect
100 points are awarded to the ones how answer right
Answer:
A 1/5
Step-by-step explanation:
Find the measure of <2.
62 = [?]
Answer:
63°
Step-by-step explanation:
They are corresponding angles.
Helpp me pls ,, 15 points given !!
Answer: The answer is B
Step-by-step explanation:
The average number of people who attended football games at a stadium increased from 8,000 people in the
year 2005 to 12,500 people in the year 2012. By what percentage did the average number of people at the games
increase from 2005 to 2012?
А
56.25%
B
43.75%
C 36%
D 64%