Presumably, the two dice are fair, so that each face has an equal 1/6 probability of being rolled. We roll 2 dice, so there are 6² = 36 possible outcomes, each with 1/36 probability of occurring.
We have
• P(A) = 2/36 = 1/18, because there are only 2 ways to roll a sum of 3 (1+2 and 2+1)
• P(B) = 6/36 = 1/6, because there are 6 ways of rolling a sum of 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1)
• P(C) = 12/36 = 1/3, because if 1 die shows a 1, then there are 6 possible values for the other die, and vice versa)
(a) By definition of conditional probability,
P(A | C) = P(A and C) / P(C)
A and C only occur together if we had rolled either {1, 2} or {2, 1}, so ultimately
P(A and C) = P(A)
so that
P(A | C) = (1/18) / (1/3) = 3/18 = 1/6
(b) From the definition,
P(B | C) = P(B and C) / P(C)
By the same reasoning as in (a), we have to roll either {1, 6} or {6, 1} to have both B and C occur, so
P(B and C) = (2/36) / (1/3) = 6/36 = 1/6
(c) In order for two events X and Y to be independent, we need to have
P(X and Y) = P(X) P(Y)
or in terms of conditional probability,
P(X | Y) = P(X and Y) / P(Y) = P(X) P(Y) / P(Y) = P(X)
Then it follows that A and C are not independent, while B and C are independent.
Group of answer choices
2
3/2
6
3
it's most likely c but i could be wrong
Find the coordinate of the midpoint of the segment with the given endpoints.
- 2 and 13
The midpoint is ____
(Simplify your answer.)
Answer:
5.5
Step-by-step explanation:
13-(-2) = 15
15 / 2 = 7.5
-2 + 7.5 = 5.5
simplify (x+3)^2 -3 (2x+3)
Answer:
x^2.
Step-by-step explanation:
(x+3)^2 -3 (2x+3)
= (x + 3)(x + 3) - 3(2x + 3)
= x^2 + 3x + 3x + 9 - 6x - 9
= x^2 + 6x + 9 - 6x - 9
= x^2 + 6x - 6x + 9 - 9 Simplify like terms:
= x^2.
Five runners are entered into a competition. Four of the runners have had their turns. Their
completing times are 7.4 s, 7.75 s, 7.09 s, and 7.86 s. What time must the last runner get in order to win
the competition?
Answer:
Just writing anything above these numbers
Step-by-step explanation:
Answer:
let t be winning time t < 7.09 seconds
Step-by-step explanation:
let's first order the times from least to greatest:
7.09, 7.40, 7.75, and 7.86
Now, in order to have the winning time, the last runner must have a time less than the fastest runner so far. So, the winning time is less than 7.09 seconds.
Make sure to add units. I know that my teachers are REALLY picky about that, though yours may not care.
Find the perimeter of a triangle DEF with vertices D (3,2), E (4,2), F (3,-2)
Round the answer to the nearest hundredth please ASAP!!!
Answer:
8.4
Perimeter=a+b+c
3.2+4.2+3.-2
= 8.4
The perimeter of the triangle will be 5 + √17.
What is the perimeter of the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees. The sum of all the sides of the triangle will be known as the perimeter of the triangle.
A triangle DEF with vertices D (3,2), E (4,2), and F (3,-2).
Distance between DE will be
DE² = (4 - 3)² + (2 - 2)²
DE² = 1
DE = 1
Distance between EF will be
EF² = (3 - 4)² + (-2 - 2)²
EF² = 1 + 16
EF = √17
Distance between DF will be
DF² = (3 - 3)² + (-2 - 2)²
DF² = 16
DF = 4
Then the perimeter of the triangle will be
P = DE + EF + DF
P = 1 + √17 + 4
P = 5 + √17
The perimeter of the triangle will be 5 + √17.
More about the perimeter of the triangle link is given below.
https://brainly.com/question/25813512
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Identify the problem with the following study. A local newspaper published the results of a study that claimed "482 people use the public library". The study was produced by using a random sample of 87 people from the town
Answer:
well, only 87 people were asked. How did they get 482?
also, they should have asked the people in the library.
Answer this please ASAP
ans:- 144 inches squared
ur welcome..
Answer:
144
Step-by-step explanation:
12*12=144
squares have all the same sized sides.
what is the value of 45c+28d when c=-5 and d=2
45×(-5) + 28×2
-225 + 56
Ans -169
(-87-12÷3×4) + (37-29) ×4
Answer:
103
Explanation:
Follow BODMAS
BODMAS stands for bracket of division multiplication addition and subtraction.
( 87 - 12 / 3 * 4 ) + ( 37 - 29 ) * 4
( 87 - 4 * 4 ) + ( 8 ) * 4
( 87 - 16 ) + 32
71 + 32
==> 103
Which is best estimate of 90/7 ÷ 1 3/4?
2
6
12
24
Answer:
6
Step-by-step explanation:
90/7 divided by 1 3/4 is 7.34 so the closest one to it is 6
2. The cost of a badger is b pence. A raccoon is 5 pence more expensive than a badger and a beaver three times as expensive as a badger.
a) What is the cost of a raccoon?
b) What is the cost of the beaver?
c) What is the total cost of a raccoon and 8 beavers?
(plz write down a step-by-step explanation)
Answer:
Step-by-step explanation:
A
A raccoon is 5 more pence than a badger.
r = b + 5
B
Let the beaver's price be be.
be = 3*b
C
Total = 5 + b + 8*be
Total = 5+b + 8*3*b
Total = 5 +b + 24b
Total = 25 b + 5
Answer:
a) What is the cost of a raccoon?
b+5
b) What is the cost of the beaver?
b x 3
c) What is the total cost of a raccoon and 8 beavers?
raccoon = b+5
8 beavers = b x 24 (since every beaver is "x3", you do 3x8 beavers)
Step-by-step explanation:
badger = b pence
raccoon = b+5 pence (since it's 5 pence more expensive)
beaver = bx3 (x3 more expensive than a badger.)
I don't know how much "b" is so just fill in the blank.
a+b/c=d/4 solve for a
Answer:
a = d/4 - b/c
Step-by-step explanation:
Subtract b/c from both sides. We can subtract a fraction
so
a = d/4 - b/c
Can someone help me write the equation of this graph?
Answer:
Step-by-step explanation:
The asymtope's equation is y = 3
Just use dy/dx to find the gradient of the curve at this point and sub in y = 3 :)
Please mark as brainliest (I really need it) :)
Simplify:
6 - 2 =
14 14
Answer:
6-2=1414
Step-by-step explanation:
6-2=1414
now
sub 6 from 2
4=1414
now divide 1414 by 4
1414÷4
[tex]1414 \div 4[/tex]
you will get the answer
Step-by-step explanation:
[tex] \frac{6}{14} - \frac{2}{14} \\ have \: same \: denomenator \: so \: we \\ \: can \: substract \: it \: directly \\ \frac{6 - 2}{14} \\ = \frac{4}{14} = \frac{2}{7} \\ thank \: you[/tex]
Solve using elimination
-3x+9y=12
2x-8y=-16
Answer:
x=8 y=4
Step-by-step explanation:
eliminate x: make x of two equation equal to each other
2(-3x+9y=12) : -6x+18y=24 ___[1]
-3(2x-8y=-16) : -6x+24y=48 ___[2]
[2]-[1]= 6y=24
y=4substitute y to any equation;
2x-8y=-16
2x-8(4)= -16
2x= -16+32
2x= 16
x=8Answer:
x=14 and y=6
Step-by-step explanation:
-3x+9y=12.............(i)×2
2x-8y=-16..............(ii)×3
Multiplying equation (i) by 2 and equation (ii) by 3 and adding (i) and (ii)
-6x+18y=12
6x-24y=-48
-----------------
0-6y=-36
or, -6y=-36
So,y=6
From (i)
-3x+9y=12
or,-3x+9×6=12
or,-3x+54=12
or,-3x=12-54
or,-3x=-42
So,x=14
one ball is to be chosen from a box containing red, blue, and green balls. If the probabilitythat
the chosen ball is red 1/5 and the probability that it is blue is 1/3, what is the probability that it
is green?
Answer:
1/4 I think is that answer
If x=1/3 y, show y=135°. Supplementary angle
Answer:
see explanation
Step-by-step explanation:
Supplementary angles sum to 180° , then
x + y = 180 , that is
[tex]\frac{1}{3}[/tex] y + y = 180 ( multiply through by 3 to clear the fraction )
y + 3y = 540
4y = 540 ( divide both sides by 4 )
y = 135°
Bananas cost $3 a bunch and apples cost $0.50 each. If b represents the number of bunches of bananas and a represents the number of apples, which of the following expressions represents the total cost?
-
3b + 0.5a
3.50(b + a)
3.50ab
3.50b + a
3b + 0.5a
the variables b and a are unknown values that represent the number of bananas and apples to be bought. These are next to each of its prices for it to be multiplied once we know the variable.
The costs of the fruits are to be added and you will end up with the total cost of fruits.
TE
The temperature was 4 degrees at midday
Atte
1M
By evening, the temperature was - 6 degrees.
Select all of the calculations below that show how to figure out the
temperature change.
se-
0 4-6
4+ (-6)
(-6) - 4
C (-6) + 4
+6+ (-4)
Answer:
answer is 3 option I believe
is the function in the graph non-linear?
Answer:
yeah, because it doesnt have a constant rate of change - if it did, then it would be linear
Step-by-step explanation:
Solve 3x − x + 2 = 12.
Answer:
is 5Step-by-step explanation:
Move all terms to the left side.
3x−x+2−12=0
Reduce like terms.
2x−10=0
Factor.
2(x−5)=0
Determine the roots from the equation. In this case, x=5 is the only solution to the equation.
Answer:
x = 5
Step-by-step explanation:
hope it is help full
mark me a brainlist
28. Ashton is hosting a banquet. He plans to spend $400, plus/minus $50, at a
cost of $25 per guest,
a. Find the maximum and minimum number of guests.
b. If there can be up to 7 guests per table, what is the minimum number of
tables Ashton should reserve so everyone has a seat?
Answer:
If he can spend $400 +- $50 ($350 or $450) the maximum number of guests at $25 each is 18 and the minimum is 14. If there can be up to 7 guests, he should prepare to have at least 3 tables to ensure everyone gets a seat if he goes with the $450 option.
Step-by-step explanation:
Please mark Brainliest if this helped :)
Division is one of the four fundamental arithmetic operations. The minimum number of tables Ashton should reserve so everyone has a seat is 2.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that Ashton's budget is $400±50. Therefore, the maximum and the minimum budget that Ashton can spend on the banquet are,
Maximum budget = $400 + $50 = $450
Minimum budget = $400 - $50 = $350
A.) Now, the maximum guest will cost the maximum budget, therefore, we can write
Maximum guest = Maximum budget / Budget per guest
= $450 / $25
= 18
Minimum guest = Minimum budget / Budget per guest
= $350 / $25
= 14
B.) Since the minimum number of guests that can come to the banquet is 14, and only 7 people can seat at a table, therefore, the minimum number of tables Ashton should reserve so everyone has a seat is 2.
Learn more about Division here:
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Estimate the quotient using compatible numbers.
2,252 ÷ 7
Choices: 300, 30, 40, 400
Answer:
300
Step-by-step explanation:
2252÷7≈2250÷7
≈300
i need help with atleast 2 of these questions pls
9.
J (0 , -10)
gradient/slope(m) = 2.
We're asked to find K if K is the X- Intercept.
At the x intercept... the corresponding y value is zero. This concept should be pretty clear.
Reason is...
At the Point where the line touches the x axis...If you trace the y value... It will be at point zero(0).
With this Knowledge
We're able to interprete that the points of K is
(x" , 0)
Where x" represents the x coordinate of K
So
J ( 0, - 10)
K ( x" , 0)
m= 2.
Applying the Gradient/Slope Formula
m = y₂ - y₁/x₂ - x₁
x₁ = 0 y₁ = -10
x₂ = x" y₂ = 0
Substituting
2 = 0 - ( -10)/ (x" - 0)
2 = 10/x"
x" = 10/2
x" = 5.
Coordinates of Point K is ( 5 , 0).
THIS IS YOUR ANSWER!.
10.
Total Time Taken = 16secs
10a). We're asked to calculate the rate of speed change for the first 5secs.
This is another way of saying "Calculate Acceleration" in the first 5sec of Motion.
Why?
Acceleration is the rate of change of speed or the rate at which speed changes.
acceleration = v - u/t
where v = Final Speed
u = initial Speed.
Looking at the graph
You see that
Initial speed(u) = 1m/s
Final Speed(v) = 9m/s
t = 5secs
Acceleration = 9 - 1/ 5
a = 8/5
a = 1.6m/s².✅
10b)
We're asked to calc "t" from the graph.
Given that the acceleration at "t" untill 16sec(end of motion) is 2m/s².
This simply means that Constant Acceleration was held from "t" to the end of the Motion.
Do not confuse Constant Acceleration for Constant Velocity.
At Constant Velocity... Acceleration is zero(0)
At Constant Acceleration...Velocity Changes Uniformly or at the same rate each second and this is what we're dealing with in this question.
Taking the same step as we used in calculating acceleration above
Given a= 2m/s²
a = v - u/∆t
Where ∆t means time change or difference.
From "t" to 16
The change in time is 16 - "t"
2 = 21 - 9/( 16 - t)
2 = 12/16-t
16-t = 12/2
16 - t = 6
t = 16 - 6
t = 10secs.✅
Have a great Day!.
Which rule describes the relationship between the input and output pairs in the following table?
Input
Output
10
5
8
3
6
1
Choose 1 answer:
اے
Subtract 5 from the input to get the output.
в)
Multiply the input by 0. Then add 5 to the result to get the output.
Divide the input by 2. Then subtract 1 from the result to get the output.
Answer:
Subtract 5 from input.
Step-by-step explanation:
10-5=5
8-5=3
6-5=1
Note:if you need to ask question let me know about it.
6+3x=7-x. pls solve and i will mark you brainliest
⇛6 + 3x = 7 - x
⇛3x + x = 7 - 6
⇛4x = 1
⇛x = 1/4
Answer:
x=0.25 or 1/4
Step-by-step explanation:
can anyone help me please? 63 over 7-2x3
Answer:
Below,...
Step-by-step explanation:
Your equation:
[tex]\frac{63}{7-(2*3)} =\frac{63}{7-6} =\frac{63}{1}=63[/tex]
Hope it helps,... Chow,...!
Convert 25 30 20" into seconds.
Step-by-step explanation:
ANS is 3.47
ok friend
please like and comments
ok
82.45 × 10a = 82,450, when a =
Answer:
a=100 hope it may help u
Step-by-step explanation:
82.45×10a=82450
824.5a=82450
a=824500/8245
a=100
Triangle ABC translates to triangle ABC describe the translation in terms of X and Y Directions
Answer:
(x + 6, y - 6).
Step-by-step explanation:
6 units to the right and 6 units down =
(x + 6, y - 6).