Answer:
The expected value of the sum of three numbers chosen out of 10 numbers will be 16.5.
Step-by-step explanation:
Felicia has a stack of 10 cards with number 1,2,3,4,5,6,7,8,9,10
Selecting 3 cards out of 10
10C3 = 120
Now she picks three cards to look at their numbers and sum it up
The possible three numbers are
(1 2 3), (1 3 2), (2 1 3) ,(2 3 1), (3 1 2), (3 2 1) ,(1 2 4), (1 4 2), (2 1 4), (2 4 1),
(4 1 2)│(4 2 1), (1 2 5), (1 5 2)│(2 1 5), (2 5 1) ,(5 1 2), (5 2 1), (1 2 6), (1 6 2), (2 1 6), (2 6 1), (6 1 2) ,(6 2 1) ,(1 2 7), (1 7 2) ,(2 1 7), (2 7 1), (7 1 2), (7 2 1), (1 2 8), (1 8 2), (2 1 8) ,(2 8 1), (8 1 2) ,(8 2 1), (1 2 9), (1 9 2), (2 1 9), (2 9 1), (9 1 2), (9 2 1),
(1 2... …, (6 10 8), (8 6 10), (8 10 6), (10 6 8), (10 8 6), (6 9 10), (6 10 9), (9 6 10),
(9 10 6), (10 6 9), (10 9 6), (7 8 9), (7 9 8), (8 7 9), (8 9 7), (9 7 8), (9 8 7), (7 8 10),
(7 10 8), (8 7 10), (8 10 7), (10 7 8), (10 8 7), (7 9 10), (7 10 9), (9 7 10), (9 10 7),
(10 7 9), (10 9 7) , (8 9 10), (8 10 9), (9 8 10), (9 10 8), (10 8 9), (10 9 8)
Now we sum it all up so minimum sum can be 1+2+3 = 6 andthe maximum can be 8+9+10 = 27
Let S denote the sum of the three numbers that are chosen and P(S=k) denotes its probability
P(S=6)=1/120
P(S=7)=1/120
P(S=8)=1/60
P(S=9)=1/40
P(S=10)=1/30
P(S=11)=1/24
P(S=12)=7/120
P(S=13)=1/15
P(S=14)=3/40
P(S=15)=1/12
P(S=16)=1/12
P(S=17)=1/12
P(S=18)=1/12
P(S=19)=3/40
P(S=20)=1/15
P(S=21)=7/120
P(S=22)=1/24
P(S=23)=1/30
P(S=24)=1/40
P(S=25)=1/60
P(S=26)=1/120
P(S=27)=1/120
Now adding all the sum in order to get the expected value
∑(K=6 to 27) k*P(S=k) = 33/2 = 16.5
Therefore the expected value of the sum is 16.5.
3. Which is equivalent to the expression below?
4.5m + 8 - 2.3m - 3.5
A.6.7m
B. 6.8m + 4.5
C 2.2m + 11.5
D. 2.2m + 4.5
Answer:
D. 2.2m + 4.5
Step-by-step explanation:
What is 4(2 + a) = 24
a=
Answer:
2/5
Step-by-step explanation:
Rearrange terms:
4(2 + a) = 24a
4(a + 2) = 24a
Distrbute:
4(a + 2) = 24a
4a + 8 = 24a
Subtract 8 from both sides of the equation:
4a + 8 = 24a
4a + 8-8 = 24a-8
Simplify:
4a = 24a - 8
Subtract 24a from both sides of the equation:
4a = 24a - 8
4a - 24a = 24a - 8 - 24a
Combine like terms:
-20a = -8
Divide both sides of the equation by the same term:
-20a = -8
-20a/-20 = -8/-20
Simplify:
Cancel terms that are in both the numerator and denominator
Divide the numbers
a = 2/5
I hope that helps! :D
By 27leejaeyat the zoo,the ratio of monkeys to gorillas is 5:1
Answer:
thats a statement
Step-by-step explanation:
Which inquality is graft below?
Answer:
Option C - 2x + y > 2
Step-by-step explanation:
We don’t have to do some serious math here. We can already eliminate half of the options just looking at it, because the graph has a dotted line, which means it does not include those values.
So, choses A and B are eliminated because the inequality shows the ≥ and ≤ symbol, which means that it does include those values. It’s either C or D because they have the > and < symbol, which means that the inequality does not include those values.
To have a better look at the inequalities, write them in slope-intercept form, which is y=mx+b:
Option C: y > -2x + 2
Option D: y < -2x +2
Just looking at the inequlaity symbol, we can tell that Option C is the correct one because it shows that all the y-values are greater than -2x + 2. Which is true because it’s shaded above the line. When it’s shaded above the line, it means that the y-values are greater.
To make sure my answer was correct, I graphed Option C. The image below shows Option C (2x + y > 2) graphed.
Hope this helps! :)
Slope, m = 3, y-intercept, b = 5
Answer:
I can't help if I don't have enough to answer sorry
Step-by-step explanation:
Question:
Find the limit
x2 – 3x – 28/x-7
lim 7
See attachment for math work and answer.
A pet store sells dog treats and the prices are represented
in the graph
X = number of treats
y = cost (in dollars)
Select the true statement.
Select one
Each treat costs $0.50
Each treat costs $3
Each treat costs $2
Each treat costs 51
Answer: 1$
Step-by-step explanation:
The ratio of employees who own a red car to employees who own a black car is
1:5. If there are 6 employees who own a red car, how many employees own a
black car? *
Answer:
There would be 30 black cars.
Since the ratio is 1:5
And we know that there are 6 red cars,
we basically just input it in our ratio
so it would look like 6:x
Now, we just have to plug in for x.
To do that, you have to multiply 6 by 5
To match the ratio.
So that would give us 6:30
And if we divide by 5 we should get our original ratio.
I know this seems confusing haha, but I hope you get it, it's not as hard as it looks !!
A store orders 22 boxes of light bulbs. Each box has 148 bulbs.
Which is the best estimate of the total number of bulbs the store orders?
plzzz answer.
Answer:
estimate, 3000. exact answer 3256
Step-by-step explanation:
hope this helps
Which point is a solution to this system of inequalities?
y 6
A) (7,-8)
B) (2,-3)
C) (5,-2)
D) (4,1)
Answer:
h
Step-by-step explanation:
Answer:
the answer is c
Step-by-step explanation:
What are the missing angles?
12 hungry friends see 8 cupcakes sitting b.
on the table. If they split the cupcakes
equally, how many does friend each get?
12 other friends are told they can eat 0.8 cupcakes each. How many total cupcakes do these 12 friends eat?
I already got the answer for the first question, but i only want to know how to do the next question, I do NOT want the answer. Thanks!
Answer: a. 1 1/2 b. 9.6
Step-by-step explanation:
The stock of Company A gained $1.86 throughout the day and ended at a value of $94.86. By what percentage did the stock rise
Answer:
tTe answer is 1.96%
Step-by-step explanation:
given data
change in price/gain= $1.86
the closing price = $94.86
Required.
The percent rise.
Step two:
The formula for the percent rise is
=change/close price*100
substitute our given data
= 1.86/94.86*100
=0.0196*100
=1.96%
are any of these equivalent to 3/8 ?
2/7
8/3
9/24
5/18
Answer:
9/24 is
Step-by-step explanation:
Yup
-BaconSoup the scientist LOL
Answer:
9/24
Step-by-step explanation:
[tex]\frac{2}{7}= 0.28571428571\\\\\frac{3}{8}= 0.375\\\\\frac{2}{7}\neq \frac{3}{8}\\\\ \frac{8}{3}= 2.666...\\\\\frac{8}{3} \neq \frac{3}{8}\\\\\frac{9}{24}=\frac{9/3}{24/3} =\boxed{\frac{3}{8}}\\\\ \boxed{\frac{9}{24}=\frac{3}{8}}\\\\\frac{5}{18}= 0.27777...\\\\\frac{5}{18} \neq \frac{3}{8}[/tex]
Hope this helps.
Find the coordinates of the midpoint of a segment with endpoints A(-3,7) and B(8,-2)
Answer:
the midpoint is (2.5, 2.5)
How to find the radius of a cylinder with only knowing it's height and diagonal thing here
HEY YOU! can you help me ?❤️
What is |-8|?
-16
-8
08
16
Answer:
it's 8
Step-by-step explanation:
lol girl I did this in the first day of school in 6th and I got the same answer , -8 is a negative, your supposed to put it back to a non negative when something is negative change it back to positive it's 8!
This is Amy's box of candies.
She has already eaten 6 of them.
What fraction of the candies has Amy eaten?
Answer:
[tex] \frac{6}{9} [/tex]
or
[tex] \frac{2}{3} [/tex]
Step-by-step explanation:
There are nine in total and she has eaten 6, so the fraction would be 6/9.
If you need to simplify it it would be 2/3.
Solve the system, enter ur answer as an ordered triple.
Answer:
x = 1, y = -1, z = 3
Step-by-step explanation:
x - 2y + 2z = 9
y + 2z = 5
z = 3
According to the last equation, z is equal to 3 so we can plug that in and our new 2 equations will be:
x - 2y + 6 = 9
y + 6 = 5
We can subtract 6 from both sides of the second equation to end up with:
y = -1
Now plugging this into the first equation, we have:
x + 2 + 6 = 9
x + 8 = 9
Subtract 8 from both sides
x = 1
I really need help please help me
Answer:
top right
Step-by-step explanation:
If you imagine yourself building with that model you can see its that one
Pls I need answer quick, pls
Answer:
its a hope this helps
Step-by-step explanation:
3, -9, 27, -81.......
Neither
Arithmetic
Geometric
Answer:
Geometric
Step-by-step explanation:
sorry if I am wrong just let me know please
Find the domain of the vector function. (Enter your answer in interval notation.) r(t) = t − 2 t + 2 i + sin(t)j + ln(36 − t2)k
Answer:
The domain of the vector function is : ( -6, -2) ∪ ( -2, 6)
Step-by-step explanation:
The given vector function can be correctly expressed as:
[tex]r(t) = \dfrac{t-2}{t+2}i + sin \ tj + In(36-t^2) k[/tex]
The domain of the given function can be determined by finding the domain of each respective component.
To start with [tex]\dfrac{t-2}{t+2}[/tex]
Not defined, t = -2
Thus, the domain of the first component of the vector = [tex]( - \infty , -2) \cup ( 2, \infty )[/tex]
The 2nd component = sin t
No restriction on t
The 3rd component of the function is ㏑(36 - t²)
Let recall that natural is defined for +ve numbers,
i.e.
36 - t² > 0
(6 + t) (6 - t) > 0
Thus, it satisfies the inequality -6 < t < 6
The third domain = (-6,6)
Overall;
The domain of the vector function is : ( -6, -2) ∪ ( -2, 6)
Domain of a function is the set all possible inputs for that function.The domain of the given vector function is,
[tex](-6, -2) \cap (-2,6)[/tex]
What is domain?
Domain of a function is the set all possible inputs for that function.
Given information-
The vector function given in the problem is,
[tex]r(t)=\dfrac{t-1}{t+2} \hat i++sin(t)\hat j+ln(49-t^2)\hat k[/tex]
To find the domain of the above vector function, we need to find the domain of each function of vector quantity.
Lets find the domain of [tex]\hat i[/tex] first which is given by,
[tex]\dfrac{t-2}{t+2}[/tex]
This function is defined at all values except, t equals to -2 as the function is not defined at,
[tex]t=-2[/tex]
Hence the domain of component [tex]\hat i[/tex] is,
[tex](-\infty, -2) \cap (\infty,2)\\[/tex]
Lets find the domain of [tex]\hat j[/tex] first which is given by,
[tex]\sin(t)[/tex]
Two trigonometry function sine and cosine defined for all real number.
This function is defined at all real numbers. Hence the domain of component [tex]\hat j[/tex] is
Lets find the domain of [tex]\hat k[/tex] first which is given by,
[tex]\ln(36-t^2)[/tex]
Set the above argument greater than zero to find where the expression is defined.Thus,
[tex](36-t^2)>0\\(6+t)(6-t)>0[/tex]
Therefore,
The domain of it should be [tex](-6,6)[/tex]
Hence the domain of the given vector function is,
[tex](-6, -2) \cap (-2,6)[/tex]
Learn more about the domain here;
https://brainly.com/question/10197594
Are x and 1/x like terms?
Answer:
no
Step-by-step explanation:
we'll say x=5
5 does not equal 1/5
HELLLLLPPPPPPPP MY SISTER HAS LATE HOMEWORKKKKK she need help with number 4. the empty space is the part where She need to show how She got her answer so if someone could help that would mean the world to me and her
Answer:
13
Step-by-step explanation:
13x4=52 that would be in the check section or whatever but she did really good
Answer:
Your sister did the equation perfectly. That's exactly how I would work it, and the answer is 13.
there are 8 dinner rolls in a package. how many packages will be needed to feed 88 people if each person has 2 dinner rolls
Answer:
22
Step-by-step explanation:
8 times 10= 80 +8=88. now thats 11 packages. 11 times 2=22
The pottery store can make 176 coffee mugs in an 8 hour day. How many mugs can they make in one hour
Watch your units!
Answer:
22 per hour
Step-by-step explanation:
8 divided by 176 lol Hope I did it right tho ;-;
Answer:
they can make 22 in one hour.
solve each system by graphing.
The vertices of ΔMNO are M (1, 3), N (4, 9), and O (7, 3). The vertices of ΔPQR are P (3, 0), Q (4, 2), and R (5, 0). Which conclusion is true about the triangles?
The ratio of their corresponding sides is 1:2.
The ratio of their corresponding angles is 1:2.
They are similar by the definition of similarity in terms of a dilation.
They are congruent by the definition of congruence in terms of rigid motions.
C. They are similar by the definition of similarity in terms of a dilation.
The conclusion about the triangles is (c) they are similar by the definition of similarity in terms of a dilation.
The coordinates are given as:
[tex]M = (1,3)[/tex]
[tex]N = (4,9)[/tex]
[tex]O = (7,3)[/tex]
[tex]P =(3,0)[/tex]
[tex]Q = (4,2)[/tex]
[tex]R = (5,0)[/tex]
Start by calculating the lengths of the triangles using the following distance formula
[tex]d = \sqrt{(x_1-x_2)^2 + (y_1 -y_2)^2}[/tex]
So, we have:
[tex]MN = \sqrt{(1 -4)^2 + (3 - 9)^2}[/tex]
[tex]MN = \sqrt{45}[/tex]
[tex]MO = \sqrt{(1 -7)^2 + (3 - 3)^2}[/tex]
[tex]MO = 6[/tex]
[tex]NO = \sqrt{(4 -7)^2 + (9 - 3)^2}[/tex]
[tex]NO = \sqrt{45}[/tex]
[tex]PQ = \sqrt{(3 -4)^2 + (0 - 2)^2}[/tex]
[tex]PQ = \sqrt{5}[/tex]
[tex]PR = \sqrt{(3 -5)^2 + (0 - 0)^2}[/tex]
[tex]PR = 2[/tex]
[tex]QR = \sqrt{(4 -5)^2 + (2 - 0)^2}[/tex]
[tex]QR = \sqrt{5}[/tex]
So, we have:
[tex]MN = \sqrt{45}[/tex] [tex]PQ = \sqrt{5}[/tex]
[tex]MO = 6[/tex] [tex]PR = 2[/tex]
[tex]NO = \sqrt{45}[/tex] [tex]QR = \sqrt{5}[/tex]
The above means that the triangles are not congruent.
So, we determine if they are similar by dividing the corresponding sides
[tex]k = \frac{MN}{PQ} = \sqrt{\frac{45}{5}} = 3[/tex]
[tex]k = \frac{MO}{PR} = \frac{6}{2} = 3[/tex]
[tex]k = \frac{NO}{QR} = \sqrt{\frac{45}{5}} = 3[/tex]
The scale factor is 3.
Hence, the triangles are similar
Read more about similar triangles at:
https://brainly.com/question/14285697