Answer:
a) Probability of ending up wearing 2 blue socks is 1/11.
b) Probability of ending up wearing no grey socks is 7/22.
c) Probability of ending up wearing at least 1 black sock is 5/11.
d) Probability of ending up wearing a green sock is 0.
e) Probability of ending up wearing matching socks is 19/66.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
In your sock drawer, you have 4 blue socks, 5 gray socks, and 3 black ones. Half asleep one morning, you grab 2 socks at random and put them on. Find the probability you end up wearing: a) 2 blue socks. b) no gray socks. c) at least 1 black sock. d) a green sock. e) matching socks.
The explanation of the answer is now given as follows:
The following are given in the question:
n(B) = number of Blue socks = 4
n(G) = number of Gray socks = 5
n(K) = number of black socks = 3
Therefore, we have:
n(T) = Total number of socks = n(B) + n(G) + n(K) = 4 + 5 + 3 = 12
To calculate a probability, the following formula for calculating probability is used:
Probability = Number of favorable outcomes / Number of total possible outcomes ……. (1)
Since this is a without replacement probability, we can now proceed as follows:
a) 2 blue socks
P(B) = Probability of ending up wearing 2 blue socks = ?
Probability of first pick = n(B) / n(T) = 4 / 12 = 1 / 3
Since it is without replacement, we have:
Probability of second pick = (n(B) – 1) / (n(T) – 1) = (4 – 1) / (12 – 1) = 3 / 11
P(B) = Probability of first pick * Probability of second pick = (1 / 3) * (3 / 11) = 1 / 11
b) no gray socks.
Number of favorable outcomes = n(B) + n(K) = 4 + 3 = 7
P(No G) = Probability of ending up wearing no gray socks = ?
Probability of first pick = Number of favorable outcomes / n(T) = 7 / 12
Since it is without replacement, we have:
Probability of second pick = (Number of favorable outcomes – 1) / (n(T) – 1) = (7 – 1) / (12 – 1) = 6 / 11
P(No G) = Probability of first pick * Probability of second pick = (7 / 12) * (6 / 11) = 7 / 22
c) at least 1 black sock.
Probability of at least one black sock = 1 - P(No K)
Number of favorable outcomes = n(B) + n(G) = 4 + 5 = 9
Probability of first pick = Number of favorable outcomes / n(T) = 9 / 12 = 3 /4
Since it is without replacement, we have:
Probability of second pick = (Number of favorable outcomes – 1) / (n(T) – 1) = (9 – 1) / (12 – 1) = 8 / 11
P(No K) = Probability of first pick * Probability of second pick = (3 / 4) * (8 / 11) = 24 / 44 = 6 / 11
Probability of at least one black sock = 1 - (6 / 11) = 5 / 11
d) a green sock.
n(Green) = number of Green socks = 0
Since, n(Green) = 0, it therefore implies that the probability of ending up wearing a green sock is 0.
e) matching socks.
This can be calculated using the following 4 steps:
Step 1: Calculation of the probability of matching blue socks
P(matching blue socks) = P(B) = 1 / 11
Step 2: Calculation of the probability of matching gray socks
P(matching green socks) = Probability of matching gray socks = ?
Probability of first pick = n(G) / n(T) = 5 / 12
Since it is without replacement, we have:
Probability of second pick = (n(G) – 1) / (n(T) – 1) = (5 – 1) / (12 – 1) = 4 / 11
P(matching gray socks = Probability of first pick * Probability of second pick = (5 / 12) * (4 / 11) = 20 / 132 = 5 / 33
Step 3: Calculation of the probability of matching black socks
P(matching black socks) = Probability of matching green socks = ?
Probability of first pick = n(K) / n(T) = 3 / 12 = 1 / 4
Since it is without replacement, we have:
Probability of second pick = (n(K) – 1) / (n(T) – 1) = (3 – 1) / (12 – 1) = 2 / 11
P(matching black socks) = Probability of first pick * Probability of second pick = (1 / 4) * (2 / 11) = 2 / 44 = 1 / 22
Step 4: Calculation of the probability of ending up wearing matching socks
P(matching socks) = Probability of ending up wearing matching socks = ?
P(matching socks) = P(matching blue socks) + P(matching grey socks) + P(matching black socks) = 1/11 + 5/33 + 1/22 = (6 + 10 + 3) / 66 = 19/66
1/8 and 9/5 common denominator and solve the problem
Answer:
Step-by-step explanation:
You haven't stated a problem. Do you want to add the fractions together? Subtract them?
Least common multiple of 8 and 5 is 40.
1/8 = 5/40
9/5 = 72/40
1/8 + 9/5 = 5/40 + 72/40 = 77/40 = 1 37/40
I really need help !!
Answer:
x =44
Step-by-step explanation:
180 - 86 - 50 = 44
for the following exercises, identify the type of data that would be used to describe a response (quantitative discrete, quantitative continuous, or qualitative), and give an example of the data.
14. distance to the closest movie theater
16. number of competing computer spreadsheet software packages
Answer:
14: quantitative continuous
16: quantitative discrete
Step-by-step explanation:
Distance can be any non-negative real number, hence it is continuous.
The number of packages has to be a positive integer, hence is discrete.
a bag contains 6 white marbles and 4 black marbles. a marble is drawn without replacing the first one. what is the probability of drawing a white marble on the first draw, followed by a white marble on the second?
Answer:
30/90 or 1/3
Step-by-step explanation:
This is because we know that 6+4=10. So we know the odds of drawing a white marble first is 6/10. And if we draw one without replacing it. This makes the second time 5/9 for white and 4/9 for black. We can then multiply 6/10 by 5/9 and get 30/90 which is equal to 1/3.
Hope this helps!
Answer:
1/3
Step-by-step explanation:
P=6/10 ×5/9=30/90=1/3
At an assembly 6 out of the first 10 students who entered the gym were carrying a backpack. Based on this information, it 700 students were at the assembly, how many students could be expected to be carrying a backpack? pls give an answer no answer choices ASAP
Answer:
Simple 700/10 is 70 right so multiply 6 by 70 which is 420 so 420 students out of 700. 420/700 ANSWER: 420 hope this is better
Step-by-step explanation:
Which of the values below will make 3+x=21 true
Answer:
x=18
21-3=18
Step-by-step explanation:
[tex]\frac{1}{x {}^{2} - 3 } = \frac{ \sqrt{3} }{x + \sqrt{3} } - \frac{2}{ \sqrt{3} - x } [/tex]
can someone please solve this?
Answer:
[tex]\boxed{\textsf{ The value of x is \textbf{ 8 + 6}$\sqrt{3 }$.}}[/tex]
Step-by-step explanation:
Here we are given a equation which we need today simplify and solve for x .The given equation to us is :-
[tex]\sf\implies \dfrac{1}{x {}^{2} - 3 } = \dfrac{ \sqrt{3} }{x + \sqrt{3} } - \dfrac{2}{ \sqrt{3} - x } [/tex]
Let's simplify the equation :-
[tex]\sf\implies \dfrac{1}{x {}^{2} - 3 } = \dfrac{ \sqrt{3} }{x + \sqrt{3} } - \dfrac{2}{ \sqrt{3} - x } \\\\\sf\implies \dfrac{1}{x^2-3}=\dfrac{\sqrt3}{x+\sqrt3}-\dfrac{2}{-(x-\sqrt3)}\\\\\sf\implies \dfrac{1}{x^2-3}=\dfrac{\sqrt3}{x+\sqrt3}+\dfrac{2}{x-\sqrt3}\\\\\sf\implies \dfrac{1}{x^2-3}=\dfrac{\sqrt3(x-\sqrt3)+2(x+\sqrt3)}{(x+\sqrt3)(x-\sqrt3)}\\\\\sf\implies \dfrac{1}{x^2-3}=\dfrac{\sqrt3x-3+2x+2\sqrt3}{x^2-3}\\\\\sf\implies 1=\sqrt3x-3+2x+2\sqrt3 \\\\\sf\implies \sqrt3x+2x = 4-2\sqrt3\\\\\sf\implies x(\sqrt3 +2)=4-2\sqrt3\\\\\sf\implies x =\dfrac{4-2\sqrt3}{\sqrt3+2}\\\\\sf\implies x =\dfrac{ (4-2\sqrt3)(\sqrt3-2)}{(\sqrt3+2)(\sqrt3-2)}\\\\\sf\implies x =\dfrac{-8-6\sqrt{3}}{3-4}\\\\\sf\implies \boxed{\pink{\sf x =8+6\sqrt3}}[/tex]
Tracy had made a new budget that included all of her necessary expenses. Now she needs to know how much money she has left to spend on entertainment write and solve an inequality be sure to identify your variable
Answer:
t - b >= e
Step-by-step explanation:
There are few actual necessities that a person actually needs in order to survive, everything else is actually a want and not a necessity. Such necessities include food, water, and rent. These can be represented as
Budget = b
We can use them in the following equality. While e would be representing the entertainment and t represents the total money he has.
t - b >= e
You can now plug in the actual values for t and b to find out how much you would have left for entertainment.
Help
Help
Help
Help
Help
Answer:
1.92
Step-by-step explanation:
multipy 8 by .08 to get the sales tax amount
to find the total cost (if you need it) add the sales tax to the original cost
hope it helps
Answer:
1.92
Step-by-step explanation: niueikieoewdn4u
The ladder of a fire truck extends 41 ft. to the top of the
building. If the distance between the wall and the base of the
ladder is 9ft. How tall is the building?
Answer:
Step-by-step explanation:
By the Pythagorean Theorem a^2+b^2=c^2 or the sum of the squared sides is equal to the hypotenuse squared.
41^2=9^2+h^2
h^2=41^2-9^2
h^2=1600
h=40 ft
Express the radical using the imaginary unit I. Express your answer in simplified form
-22
Given:
The radical expression is
[tex]\pm \sqrt{-22}[/tex]
To find:
The simplified form of the given expression by using the imaginary unit i.
Solution:
We have,
[tex]\pm \sqrt{-22}[/tex]
It can be written as
[tex]\pm \sqrt{-22}=\pm \sqrt{22}\sqrt{-1}[/tex] [tex][\because \sqrt{ab}=\sqrt{a}\sqrt{b}][/tex]
[tex]\pm \sqrt{-22}=\pm \sqrt{22}i[/tex] [tex][\because \sqrt{-1}=i][/tex]
Therefore, [tex]\pm \sqrt{-22}=\pm \sqrt{22}i[/tex].
Solve for the variable indicated
-4x-8y=36 solve for x
Answer:
x = -2y - 9
Step-by-step explanation:
First isolate the variable by putting the x on a side by itself.
-4x=36+8y (8y becomes positive when it changes sides)
Then divide the entire equation by -4 to make the x stand alone.
x = -9 -2y
Some teachers prefer the variables at the beginning of the equations so it could also read
x = -2y - 9
Hello there!
Question:-
[tex]-4x-8y=36[/tex]
We need to find the value of x.
Solution:-
[tex]\sf \longmapsto-4x-8y=36[/tex]
Firstly, Add 8y to both sides :-
[tex]\sf \longmapsto \: - 4x - 8y+8y=36+8y[/tex]
On Simplification:-
As (-) and (+) equals to (-),It Will be 8y-8y.Answer would be 0.
[tex]\sf \longmapsto \: - 4x - 0 = 36 + 8y[/tex]
[tex]\sf \longmapsto \: - 4x = 8y + 36[/tex]
Then, Divide both sides by -4:-
[tex]\sf \longmapsto \: \dfrac{4x}{ - 4} = \dfrac{8y + 36}{ - 4} [/tex]
On Simplification:-
[tex]\sf \longmapsto \: x = - 2y - 9[/tex]
______________________________________
Henceforth the value of x is :-
[tex] \boxed{\tt \: x = - 2y - 9}[/tex]
______________________________________
I hope this helps!
Please let me know if you have any questions.
~MisterBrian
andre and Elena are each saving money. Andre starts with $100 in his savings account
nd adds $5 per week. Elena starts with $10 in her savings account and adds $20 each
jeek.
1. Write an equation in y= mx + b form to represent at what rate Elena and Andre are
aving their money.
Y=mx+b
Answer:
Andre y=5x+100
Elena y=20x+10
the rate Elena is 20
the rate Andre is 5
Step-by-step explanation:
The sum of the speeds of two trains is 718.4 miles per hour. If the speed of the first train is 3.6 mph faster than that of the second train, find the speeds of each
Answer:
the answer is 359.7
Step-by-step explanation:
2 9/10 as a decimal number
2 9/10 in decimal form would be,
[tex]2.9[/tex]
if you have any other questions like this,
let me know ill help you!!
Answer:
2 9/10=2.9
Step-by-step explanation:
We know that 9/10 is the same as 9÷10
Therefore:
2 9/10 = 2 + (9÷10)
Then using
Long Division for 9 divided by 10
we have
=2+0.9=2.9
Please give me brainliest because I worked hard on this answer and I am trying to level up
Shannon rode her bike 6 miles in 24 minutes. Find her average rate in miles per hour.
HELP!
Answer:
.25 Mph
Step-by-step explanation:
6 divided by 24
=
0.25
hi im 7th grade and i feel like people think i smell when i do everything to not smell. i wake up take a shower with soap aplly deoderant and brush teeth. any tips
Answer:
Step-by-step explanation:
This might be a hygiene problem. What causes the unpleasant smell is the bacteria that build up on your sweaty skin and react with sweat and oils to grow and multiply when sweat reacts with bacteria on the skin. These bacteria break down proteins and fatty acids, causing body odor in the process. If deodorant isn’t good enough , I recommend perfume, the perfume smell lasts longer than deodorant I would think. But shower everyday, full clean down, but if ur hygiene is ok, I recommend going to the doctor for a checkup. Hopefully your problem will be resolved. Also use lotion.
Can someone help me with this please?
Answer:3:7
Step-by-step explanation:
can you help me in that problem
Answer:
(x - 10, y - 13)
Step-by-step explanation:
We have two shapes on a graph and the question is asking for the translation of rhombus QRST to rhombus Q'R'S'T.
Looking at the graph we can see that not only does the rhombus move backwards, but also downward, this indicates that our answers will be in a subtracting symbol.
So all we have to do is count the amount of spaces rhombus QRST went to get to rhombus Q'R'S'T
The 24/7 Truck Rental Company has been charging an initial rental fee of $29 plus $2.50 per hour for rental of their small trucks. After a change in pricing policy, the new fee will be $19 up front plus $3.25 per hour. After how many hours of renting the truck will the new plan be more expensive than the old plan
Answer:
14 hours
Step-by-step explanation:
Old plan :
Initial fee =. $29
Hourly fee = $2.50
New plan :
Initial fee = $19
Hourly fee = 3.25
Let number of hours = x
When new plan will be more expensive than old plan :
19 + 3.25x > 29 + 2.50x
3.25x - 2.50x > 29 - 19
0.75x > 10
x > 10 / 0.75
x > 13.3333
After 14 hours
14 + 6 + (–2) + (–10) + (–18) + (–26) + (–34) What is the summation notation for the arithmetic series? Enter the correct values for x, y, and z.
x =
y =
z =
Answer:
total -70
Step-by-step explanation:
x =18
y=-28
Z = -60
An Arithmetic series: 14 + 6 + (–2) + (–10) + (–18) + (–26) + (–34)
The Total value is = -70
x = 18
y = -28
Z = -60
Calculation of Arithmetic SeriesAn Arithmetic series: 14 + 6 + (–2) + (–10) + (–18) + (–26) + (–34)
1st an 2nd element difference is = 14 - 6 = 8
2nd and 3rd element difference is = - 6 - 2 = -8
3rd and 4th element difference is = - 2 + 10 = 8
4th and 5th element difference is = -10 + 18 = 8
The difference (x,y and z) is 8 and also it's negative because the series is lowering the previous value.
Now, Proof of x,y and z = - 8
14 - 8 = 6
6 - 8 = - 2
- 2 - 8 = - 10
- 10 - 8 = - 18
- 18 - 8 = - 26
-26 - 8 = -34
Therefore, The value is = total -70
x = 18
y = -28
Z = -60
Find more information about Arithmetic Series here:
https://brainly.com/question/24295771
Can someone help me on this place I will mark brianliest ( also in note if you dont want to help then dont help me and if your going to be rude like saying do it yourself please keep that to yourself and be considerate with your manners thank you ^^
Answer:
That is an entire worksheet. Also just download PhotoMath on your phone and it will give you the answers.
Step-by-step explanation: I'll get you started
1) 1
2) 2
3) 4
4)
5) 20
6) 1
7) 2
8) 20
Answer:
1. 1/2
2. 2/3
3. 4/7
4. 10/25
5. 20/40
6. 1/10
7. 2/6
8. 20/90
9. 27/36
10. 1/6
11. ?
12. 2/5
13. 2/3
14. 11/12
15. 17/25
16. 2/8
17. 6/7
18. 42/70
Step-by-step explanation:
this year a farmer planted 300 acres of corn. this was 1.5 times as many acres as he planted last year. how many acres did he plant this year?
What is a counterexample for 3/4 and 6/8
Answer:
While 3/4 and 6/8 are equivalent fractions, 3/4 and 6/8 of a pizza could represent different amounts.
Which number line model represents the expression -4+7.25
Answer: c
Step-by-step explanation: start at -4 then add 7 to that then .5
HELP! have this assignment due in 30 mins and i dont know how to do this please help i have a D in this class
1 A rectangular playground has a width of 540 feet and a length of 810 feet. Martina makes a scale model of the playground using a scale of 4 cm :
30 ft .What are the dimensions of Martina’s scale model?
A135 cm by 202.5 cm
B72 cm by 108 cm
C54 cm by 81 cm
D18 cm by 27 cm
Answer:
A
Step-by-step explanation:
there are 135 '4cm' segments in 540 feet; 540 ÷ 4
there are 202.5 '4cm' segments in 810 feet; 810 ÷ 4
I am not understanding this topic in math and I have a huge test tomorrow and I need to sleep, I forgot about this assignment and I would really appreciate it if someone could help me out with this!!! ❤️
Answer: (-3,-4)
Step-by-step explanation:
If the any x variable is repeated, it is not a function!
How many gallons of a 15% sugar solution must be mixed with a 5 gallons of a 40% solution to make a 20% solution
Answer:
20 gallons of 15% solution must be mixed with 5 gallons of 40% solution.
Step-by-step explanation:
40% of 5 gallons is 2 gallons of sugar
x represents the number of gallons of solution to be added.
15% of x is sugar.
The total amount of sugar must be equal to 20% of the final mixture.
The end mixture will be x + 5 gallons
Change percent to decimal for the equation:
.2(x +5) = .15x +2
.2x +1 = .15x +2
.2x - .15x = 2 -1
.05x = 1
x = 20
Check:
.2(20 +5) = .15(20) +2
.2(25) = 3 + 2
5 = 5 true
This means that adding 20 gallons of the 15% solution is adding 3 gallons of sugar [along with 17 gallons of water] to the 2 gallons of sugar in the original mixture.
20% of the 25 gallons, 5 gallons, of the final mixture is sugar. 80% [ 3+17 = 20 gallons] is water.
Translate the verbal expression into an algebraic expression
Six more than the quotient of a number and 4.
Answer:
4x+6
Step-by-step explanation:
The quotient of a number and 4 translates to 4x because, "a number" in the expression is x, and it is being multiplied by 4, so you get 4x. six more than would mean adding 6. So the answer would be 4x+6. Thank you! Good Luck!
Please help!! Brainliest for right answer!!
Answer:
(f o g)(x) = 4x^2 - 8
Step-by-step explanation:
(f o g)(x) = f(g(x))
f(x) = x^2 - 8
g(x) = 2x
f(g(x))
f(2x) = (2x)^2 - 8
= 4x^2 - 8
(f o g)(x) = 4x^2 - 8