Probabilities are used to determine how likely it is for an event to happen.
(1) A roll of two dice
Let the dice be A and B. The sample space of each is:
[tex]A = \{1,2,3,4,5,6\}\\B = \{1,2,3,4,5,6\}[/tex]
To get the sample space (S) of the sum of the dice, we simply add up the individual element of both dice. So, we have:
[tex]S = \{(1+1),(1+2),(1+3),(1+4),(1+5),(1+6),.............,(6+1),(6+2),(6+3),(6+4),(6+5),(6+6)\}[/tex]
This gives
[tex]S = \{2,3,4,5,6,7,.............,7,8,9,10,11,12\}[/tex]
The complete sample space is:
[tex]S = \{2,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12\}[/tex]
[tex]n(S) = 36[/tex] --- the total outcomes
The probability of rolling a sum of 7 is:
[tex]P(7) = \frac{n(7)}{n(S)}[/tex]
Where
[tex]n(7) = 6[/tex] ---- number of 7's in the sample space
So, we have:
[tex]P(7) = \frac 6{36}[/tex]
[tex]P(7) = 0.167[/tex]
The probability of rolling a sum of 7 is 0.167
(2) Restaurant
We have:
[tex]Soup = \{A,B,C,D\}[/tex]
[tex]Salads = \{1,2,3\}[/tex]
To get the sample space (S), we simply pick the individual elements of the above data. So, we have:
[tex]S = \{A1, A2, A3,B1, B2, B3,C1, C2, C3,D1, D2, D3\}[/tex]
(3) Disjoint events
Events are said to be disjointed if they cannot happen at the same time. 3 examples are:
Event 1: You are in China. Event 2: You are in NigeriaEvent 1: Heading towards north. Event 2: Heading towards southEven 1: Outcome of even number in a roll of die. Event 2: Outcome of an odd number in the same die(4) Bob and Sarah
Let
[tex]A \to[/tex] Bob gets to work on time
[tex]B \to[/tex] Sarah gets to work on time
[tex]P(A) = 80\% \\ P(B) = 90\%\\P(A\ n\ B) = 72\%[/tex]
The probability that Bob OR Sarah is late for work is represented as:
[tex]P(A'\ or\ B')[/tex]
This is calculated using:
[tex]P(A'\ or\ B') = P(A') + P(B') - P(A'\ n\ B')[/tex]
Where:
[tex]P(A') = 1 - P(A) = 1 - 80\% = 20\%[/tex]
[tex]P(B') = 1 -P(B) = 1 - 90\% =10\%[/tex]
[tex]P(A\ n\ B') = P(A) \times P(B') = 20\% \times 10\% = 2\%[/tex]
So, we have:
[tex]P(A'\ or\ B') = P(A') + P(B') - P(A'\ n\ B')[/tex]
[tex]P(A'\ or\ B') = 20\% + 10\% - 2\%[/tex]
[tex]P(A'\ or\ B') = 28\%[/tex]
[tex]P(A'\ or\ B') = 0.28[/tex]
The probability that Bob OR Sarah is late for work is 0.28
(5) Jake's Pizza
Let
[tex]A \to[/tex] The proportion of time they deliver on time
[tex]B \to[/tex] You get your pizza for free
So:
[tex]P(A) = 92\%[/tex]
You get your pizza for free if they didn't deliver within 30 minutes.
This means that:
[tex]P(B) = 1 - P(A)[/tex] --- Complement rule
So, we have:
[tex]P(B) = 1 - 92\%[/tex]
[tex]P(B) = 0.08[/tex]
The probability that you get your pizza for free is 0.08.
(6) Students and Soccer
Let:
[tex]A \to[/tex] Probability that a student likes soccer
So:
[tex]P(A) = 54\%[/tex]
If all 3 selected students like soccer, the probability is calculated as:
[tex]Pr = P(A) \times P(A) \times P(A)[/tex]
[tex]Pr = P(A)^3[/tex]
[tex]Pr = 54\%^3[/tex]
[tex]Pr = 0.157[/tex]
The probability that all 3 selected students like soccer is 0.157
(7) Students and Soccer
Let:
[tex]A \to[/tex] Probability that a student likes soccer
[tex]B \to[/tex] Probability that a student does not like soccer
So:
[tex]P(A) = 54\%[/tex]
[tex]P(B)= 1 - P(A)= 1 - 54\% = 46\%[/tex] ---- Complement rule
If all 4 selected students do not like soccer, the probability is calculated as:
[tex]Pr = P(B) \times P(B) \times P(B) \times P(B)[/tex]
[tex]Pr = P(B)^4[/tex]
[tex]Pr = 46\%^4[/tex]
[tex]Pr = 0.045[/tex]
The probability that all 4 selected students do not like soccer is 0.045
(8) Marbles
[tex]Blue = 6 \\ Green = 4 \\ Red = 5[/tex]
When the green marble is selected, we are left with
[tex]Blue = 6 \\ Green = 3 \\ Red = 5[/tex]
The probability of selecting a red marble at this point is:
[tex]P(Red) = \frac{Red}{Blue + Green + Red}[/tex]
[tex]P(Red) = \frac{5}{6+3+5}[/tex]
[tex]P(Red) = \frac{5}{14}[/tex]
[tex]P(Red) = 0.357[/tex]
The probability that the next marble you draw is red is 0.357
(9) Studying for test
Let
[tex]A \to[/tex] Students got an A
[tex]B \to[/tex] Students studied for test
So:
[tex]P(A\ n\ B) = 60\% \\ P(B) = 75\%[/tex]
The probability that a student got an A given that they studied for the test is represented as:
[tex]P(A | B)[/tex]
So, we have:
[tex]P(A | B) = \frac{P(A\ n\ B)}{P(B)}[/tex]
[tex]P(A | B) = \frac{60\%}{75\%}[/tex]
[tex]P(A | B) = 0.80[/tex]
The probability that a student got an A given that they studied for the test is 0.80
Read more about probabilities at:
https://brainly.com/question/16693319
The chord of a circle of radius 6 ft is 8 ft long . find the distance if the chord from the center.
Referring to attached figure :
given values : -
radius of the circle = 6 ft measure of chord = 8 ft (AB)construction : -
I actually draw a perpendicular on chord from the centre, and we know that the perpendicular from centre on it bisects the given chord, therefore measure of
AC = BC = 1/2 × ABAC = BC = 4 ftnow, let's apply Pythagoras theorem for triangle OCB,
we get :
OC² + CB² = OB²OC² + 4² = 6²OC² + 16 = 36OC² = 36 - 16OC² = 20OC = [tex] \sqrt{20} [/tex] ft OC = [tex] 2\sqrt{5} [/tex] ftAnd here OC is the distance of chord from its center, therefore required answer is [tex] 2\sqrt{5} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{ \: \: \: TeeNForeveR \: \: \: }}[/tex]
**PLEASE ANSWER THE QUESTION BELOW.**
WILL MARK BRAINLIEST IF YOUR ANSWER IS CORRECT, RELIABLE, AND GOOD. PLEASE ADD DECIMALS, THANK YOU!
Please look at the picture provided below.
NO LINKS OR FALSE ANSWERS.
Answer:
80.5 km/h
Step-by-step explanation:
divide the 426.65 by 5.3 hours to get 80.5/1 hr
Which of these is NOT a terminating decimal?
A) 1.88
B) 1.875
C) 0.88
D) 0.8
Answer:
D
Step-by-step explanation:
find
the selling
price
at the
cost price is
£1 200
and
you make
a
profit
26
[tex]\%[/tex]
Answer:
the selling price = 1512
Step-by-step explanation:
the profit = 1200 × 26/100
= 312
the selling price = profit + the cost
= 1200+ 312 = 1512
Can y’all help me with 17 and 18
Answer:
17 is 35 degrees and 18 is 43 degrees
Answer:
#17 is 35 degrees
#18 is 43 degrees
Step-by-step explanation:
#17. 90-55 = 35
#18. 90 - 47 = 43
Solve the problem, who ever will solve this will be marked as brainliest
Answer:
mark me as brainliest ❤️
Answer:
gain%=8%
hope it helps.stay safe healthy and happy...The linear equation y = −5x − 18 is written in which form?
Kyle has a total of 16 coins in his pocket. All the coins are nickels or quarters, and they have a total value of $2.20. How many nickels does Kyle have?
7 nickels
8 nickels
9 nickels
11 nickels
Answer:
9 nickels
Step-by-step explanation:
Answer:
9 nickels
Step-by-step explanation:
He doesn't have that many coins, and there are 4 choices, so let's use the guess method.
Try 7 nickels.
7 * $0.05 = $0.35
16 - 7 = 9
9 * $0.25 = $2.25
The quarters alone are worth more than $2.20, so this is not the answer. We need more nickels and fewer quarters.
Try 11 nickels.
11 * $0.05 = $0.55
16 - 11 = 5
5 * $0.25 = $1.25
$0.55 + $1.25 = $1.80
The coins are worth too little. We need fewer nickels and more quarters.
Try 9 nickels.
9 * $0.05 = $0.45
16 - 9 = 7
7 * $0.25 = $1.75
$0.45 + $1.75 = $2.20
The coins are worth the correct amount.
Answer: 9 nickels
A box had a volume of 456 cubic inches, with a length of 12 inches and a height of 4 inches l. Determine the width of the box.
abc=1/2; b (;b= solve for b)
Answer:
[tex]abc - \frac{b}{2} = 0[/tex]
Can someone please help <3
Answer:
number (c)
Step-by-step explanation:
I am not sure about this
What would be the equation to you have a part time job. You work for 3h on Friday and 6h on Saturday. You also recieve an allowance of 20 per week. You earn 92 per week how much do you earn per hour at your part time job
What is the equation for this promblem?
Answer:
Step-by-step explanation:
So, to go about your question, we must first ask, how many hours a week is being worked?
In this problem, that is 9 hours per week.
Next, we must question how much per week is made
That is $92 per week
Finally, we must determine if the allowance is occuring many times in the week or just once.
In this problem, that is only occuring once for the week.
So, the equation we must setup is 9x +20 =92.
To solve the equation, we need to subtract 20 on both sides to isolate the variable, x.
9x+20=92
-20 -20
Now our equation is
9x=72
Now, to finally get x by itself or to isolate x, you should divide 9 on both sides to cancel out the 9 being multiplied by the x.
9x=72
9 9
x=8 because of 72/9 is equal to 8.
I hope this helps, and I will answer any questions you have.
WILL GET MARKED THE BRAINIEST
Which logic statement represents this argument?
If it’s a weekend, I exercise. It’s not a weekend. So, I won’t exercise.
Assume that p represents “It’s a weekend” and q represents “I exercise.”
A.
(p q) p
B.
[(p q) p] q
C.
[(p q) p] q
D.
[(p q) p] q
A serving of walnuts is 1/2 of a cup. How many servings are there in a 1 1/2-cup bag of
walnuts?
Answer:
3
Step-by-step explanation:
1/2 a cup makes one serving in 1 1/2 a cup there are 3 servings
Please help probability
Answer:
3/11
There are 11 possibilities and only 3 are even and less than 7.
Help and hurry! Fastest and correct answer gets brainlesst.
No explanation needed
.
Here is a sketch of Noah's bedroom.
He wants to create a scale drawing of his bedroom to show to his designer.
He uses a scale of 1 m = 6 cm to draw his scale drawing.
He draws a 33 cm line to represent wall D.
What is the actual length of wall D according to the above mentioned scale?
Answer:
5.5 m
Step-by-step explanation:
1m = 6cm
x = 33 cm
x = 33 /6
= 5.5 m
A washer and a dryer cost $950 combined. The washer costs $ 100 more than the dryer. What is the cost of the dryer?
Answer:
$850
Step-by-step explanation:
washer + dryer = $950
if washer cost=>$100
Therefore; the value of the dryer should be x
$100+x=$950
x=$850
The dryer cost is =>$850
Answer:
The dryer is $425.
Step-by-step explanation:
Washer = 100 + Dryer
Set up an equation:
Variable x = dryer
x + x + 100 = 950
x + x = 850
2x = 850
x = 425
Dryer = 425
Bonus answer:
Washer = 100 + x
Washer = 100 + 425
Washer = 525
Check your work:
Washer + Dryer = 950
525 + 425 = 950
950 = 950
Correct!
Select the correct answer. Which statement best defines a circle?
A. the set of all points in a plane that are the same distance from each other surrounding a given point called the center
B. the set of all points in a plane that are the same distance from a given point called the center
C. the set of all points that are the same distance from a given point called the center
D. points in a plane that surround a given point called the center
Answer:
A. the set of all points in a plane that are the same distance from each other surrounding a given point called the center. hope this helps
Step-by-step explanation:
- Zombie
The statement best defines a circle is A. the set of all points in a plane that are the same distance from each other surrounding a given point called the center.
What is a circle?A circle is defined as a shape consisting of all points in a plane that are given the same distance from a given point called the center.
A circle can be characterized by its center's location and its radius's length.
The statement best defines a circle is A. the set of all points in a plane that are the same distance from each other surrounding a given point called the center.
Learn more about circle here:
https://brainly.com/question/10165274
#SPJ5
49q²-70q+25 resolve into fractors
Answer:
(7q-5)²
Step-by-step explanation:
= 49q² - 70q + 25
= 49q² -35q -35q + 25
= 7q(7q-5) - 5(7q - 5)
= (7q-5) (7q-5)
= (7q-5)²
CMIIW
Answer:
Step-by-step explanation:
49q² -70q +25 , rewrite the first two terms as squares
(7q)² -70q + 5² , compare with a² - 2ab + b² = (a-b)²
a² - 2ab + b²
(7q)² -2(7q)(5 )+ 5², because 70q = 2*35q = 2*7*5*q
We can see that a = 7q and b=5, therefore
49q² -70q +25 = (7q -5)²
We set the equation equal to 0 to find the roots
7q-5 =0, add 5 to both sides
7q =5 , divide both sides by 7
q = 5/7 ≈ 0.714
A bag contains 8 black marbles, 5 white marbles and 12 red marbles. What is the probability of selecting a red marble, not replacing it, then selecting a white marble?
Answer:
1/10
Step-by-step explanation:
8 black marbles, 5 white marbles and 12 red marbles = 25 marbles
P(red) = red/total = 12/25
Remove the marble
8 black marbles, 5 white marbles and 11 red marbles = 24 marbles
P(white) = white/total = 5/24
P(red, remove,white) = 12/25 * 5/24
=12/24 * 5/25
=1/2 * 1/5
=1/10
Step-by-step explanation:
Total balls = 12 + 5 + 8 = 25 marbles
Probability of getting white marbles = 5/24
Probability of red marbles = 12/24 = 1/2
Now
Probability = 1/2 × 5/24 + 1
Probability = 1/2 × 5/25
Probability = 5/50
Probability = ⅒
x/2 + 1 = 1/4x - 6 solve for x
x=-28......................
Is -15/6 a rational number?
Answer:
Yes it is a rational number
Simplify negative 2 over 3 ÷ negative 7 over 4.
Answer:
[tex]-\frac{2}{3}/-\frac{7}{4}=\frac{8}{21}[/tex]
Step-by-step explanation:
Given: [tex]-\frac{2}{3}/-\frac{7}{4}[/tex]
Take the reciprocal of the divisor: [tex]-\frac{2}{3}/-\frac{4}{7}[/tex]
Multiply the two fractions instead: [tex]-\frac{2}{3}*-\frac{4}{7}[/tex]
Evaluate: [tex]\frac{8}{21}[/tex]
Answer:
8 / 21
Step-by-step explanation:
Find the x- and y-intercepts of the graph of — 2 + 3y = 37. State your answers as
whole numbers or as improper fractions in simplest form.
solve the systems of linear equations using substitution
1.x-4y=-10 2.a-3b=24
2x+y=-11 a+2b=-16
3.4j-5k=27 4.m+n=-3
k=j-7 m-4n=27
Step-by-step explanation:
1 . x - 4y = -10
2x + y = -11
multiply the first equation with 2
2x - 8y = -20
-
2x + y = -11
===============
= 0 - 9y = -9
y = 1
x = -6
-------------------------------------------
2.
a - 3b = 24
-
a + 2b = -16
=============
= 0- 5b = 40
b = - 8
a = 0
and so on
What's the volume of the following is rectangular prism plsssssss will mark brainlist HELPPPP
Answer: 6.75 or 6 3/4
Step-by-step explanation: 3 3/8 x 2 = 6.75 Brainliest please?
Write an exponential model given the two points (8,150) and (9,220).
Answer:
Step-by-step explanation:
The exponential model for the given points is y = 6.88(1.47)ˣ
What is exponential function?In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Given,
points are (8,150) and (9,220)
Exponential function,
y = abˣ --------(A)
for point (8 , 150)
150 = ab⁸ -------(1)
for point (9 , 220)
220 = ab⁹ -------(2)
Dividing equation (2) by equation (1)
220/150 = ab⁹/ab⁸
Simplifying
1.47 = b
Substituting value of b in equation (1)
150 = a(1.47)⁸
150 = a(21.80)
a = 150/21.80
a = 6.88
Substituting value of a and b in equation(A)
y = 6.88(1.47)ˣ
Hence, y = 6.88(1.47)ˣ is the exponential model for given points.
Learn more about exponential function here:
https://brainly.com/question/2456547
#SPJ2
Write a rule in coordinate form for the translation from Triangle EFG to Triangle
E'F'G'.
(x,y)-->(x+2, y-1)
(x,y)-->(x+1, y-2)
(x,y)-->( X-2, y + 1)
(x,y)-->(x+3, y +2)
Answer:
1st option
Step-by-step explanation:
Consider the coordinates of F and F'
F (- 3, 4 ) and F' (- 1, 3 )
To go from - 3 → - 1 in the x- directions , means adding 2
To go from 4 → 3 in the y- direction means subtracting 1
Then translation rule is
(x, y ) → (x + 2, y - 1 )
28 points asap pls PLSSS
Answer:
Its answer is Commutative property
Step-by-step explanation:
Answer will be Commutative property
hope it helps
8x - 5y = 30 + 2x, for x
Answer:
[tex]8x - 5y = 30 + 2x \\ 8x - 2x = 30 + 5y \\ 6x = 30 + 5y \\ \\ x = \frac{30 + 5y}{6} \\ \\ x = \frac{30}{6} + \frac{5y}{6} \\ \\ x = 5 + \frac{5y}{6} [/tex]
I hope I helped you^_^
