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.
measure at least pairs of corresponding angles in XJYN and ZSCH using a protractor. Record your measurements to the nearest 5. what do you notice?
Answer:
any file to have a reference?
A sum of Rs 105 is divided into two parts.if two times the greater part is 15 less than three times the smaller part, find the parts of the sum.
Answer:
Step-by-step explanation:
Let the greater part = x
Smaller part = 105 - x
2*(greater part) = (3*smaller part) - 15
2*x = 3*(105 -x) - 15
Use distributive property
2x = 3*105 - 3*x - 15
2x = 315 - 3x - 15
2x = 300 - 3x
Add 3x to both sides
2x +3x = 300
5x = 300
Divide both sides by 5
x = 300/5
x =60
Smaller part = 105 - 60 = 45
Greater part = Rs. 60
Smaller part = Rs. 45
-6, 20, 4.3, 159/-9
Order from least to greatest
Jonathon can jog 2 2/7 miles in 2/8 hour. Find his average speed of miles per hour.
Answer:
9.14 miles an hour
Step-by-step explanation:
-8=x+ll/-2 solve for x step by step and answer
Answer:
x=(-5)/2
Step-by-step explanation:
-8×(-2)=-2x+11
16-11=(-2x)
x=(-5)/2
Compare and order the numbers below from least to greatest.
4.6, 2.8, V7, V17,
Answer:
2.8, 4.6, V7, V17
i hope it help n im sorry i can't explain
what is 2x-9=5x+12 with the step by step
Answer:
x = -7
Step-by-step explanation:
Please view the detailed answer in the image attached
Answer:
[tex]2x - 9 = 5x + 12 \\ - 3x = 21 \\ x = - 7[/tex]
Step-by-step explanation:
x = -7
Robert wants to buy a digital piano at a yard sale. He makes a scale drawing of his living room. He uses a scale of 1cm in the drawing to 6 inches in the actual room. The width of the digital piano is 54 inches will it fit along the wal. Next to the bookshelf ?
Answer:
It’s 48 just do 8*6=48 I don’t know how I got that answer but Ik it’s right lol
Write a proof. Given x - 2 = 3(x - 4) Prove x = 5
x=5
Step-by-step explanation:
x-2=3(x-4)
x-2=3x-12
12-2=3x-x
10=2x
x=10/2
x=5
Answer:
x = 5
Step-by-step explanation:
x - 2 = 3(x - 4)
x - 2 = 3x - 12
-2x - 2 = -12
-2x = -10
x = 5
Find the perimeter, in units, of the polygon with the given vertices. Plot the points.
Round to the nearest tenth.
5. A(8,0), B(-3, 2), C(10, 2)
6. A(4, -3), B(7, 10), C(-8, 2)
7. A(-5,5), B(5, -5), C(-5, -5)
8. A(4, -3), B(7,10), C(-8, 2), D(-1, -5)
9. A(-4, -8), B(4, -8), C(4, 0), D(0, 3), E(-4, 0)
Answer: 9
Step-by-step explanation:
Plot the points
Find the distance of each side
add the three numbers
9
Answer:
5. 27
6. 43
7. 47
Step-by-step explanation:
dentify the error in finding the distance between A(6,2) and B(1,−4).
What is the answer ?
Answer:
70 seconds
Step-by-step explanation:
first we'll divide seconds by shirts 28/2 to find out how long it takes to do one shirt. it takes Jonah 14 seconds to do 1 shirt so we can then multiply that by 5 shirts to get 70 seconds
Which expression has a value of 48?
A . (16−8)×(2+4)
B . 16−(8×2+4)
C . 16−8×(2+4)
D . (16−8)×2+4
Step-by-step explanation:
(16-8)x(2+4)
= 8x(6)
= 8x6
= 48
if (x+30°) and (180°-2x) are vertically opposite angles . Find the value of x .
Answer:
50
Step-by-step explanation:
x + 30 = 180 - 2x [vertically opposite angles]
x = 180 - 30 - 2x
x = 150 - 2x
x + 2x = 150
3x = 150
x = 150/3
x = 50
PLEASE HELP FAST!! I CANNOT GET THIS WRONG!!!!
Makayla and David work at a furniture store. Makayla is paid $230 per week plus 7.5% of her total sales in dollars, x, which can be represented by g(x)=230+0.075x. David is paid $321 per week plus 4% of his total sales in dollars, x, which can be represented by f(x)=321+0.04x. Determine the value of x, in dollars, that will make their weekly pay the same.
Answer:
6
Step-by-step explanation:
you kna mean?
put the following equation of a line into slope intercept form simplifying all fractions 5x + 2y = -6
Answer:
The general equation of a slope-intercept form is as below;
[tex]y = mx + c[/tex]
m » slope / gradient
c » y - intercept
x » x - intercept
Since our equation is 5x + 2y = -6, make y the subject:
[tex]5x + 2y = - 6 [/tex]
subtract 5x from either sides:
[tex](5x + 2y) - 5x = - 6 - 5x \\ 2y = - 5x - 6[/tex]
apply the division rule of equality:
[tex] \frac{2y}{2} = \frac{ - 5x}{2} - \frac{6}{2} \\ \\ { \boxed{ \boxed{answer : \: y = - \frac{5}{2} x - 3}}}[/tex]
slope » -5/2
y - intetcept » -3
Factoring binomials with the difference of squares
Answer:
Step-by-step explanation:
Find the equation of the line that contains the point (1,-5) and has a slope that is undefined. Express the equation using either the general form or the slope-intercept form of the equation of a line.
The equation of the line is
Answer:
x=1
Step-by-step explanation:
Since the slope is undefined, it's of the form x=a and since it passes through (1,-5) the equation is x=1
The equation of the vertical line in slope-intercept form is: x = 1.
What is the Equation of a Vertical Line?A vertical line has an undefined slope and therefore has no y-intercept. the equation of a vertical line is therefore expressed as, x = a, where a is the x-intercept, which is the value of x of the point where the vertical line intersects the x-axis..
Given the point (1, -5), since the line has an undefined slope, the equation in slope-intercept form would be: x = 1.
Learn more about equation of a vertical line on:
https://brainly.com/question/9050446
#SPJ6
where does 0.5 goes on a real number line
Use the distributive property to write an equivalent expression.
8(3v+3w-2)
Answer:
8(3v+3w-2)=(8×3v+8×3w-8×2)
Step-by-step explanation:
8×3v=24v.
8×3w=24w. [24v+24w-16]=(8×3v+8×3w-2×8)
8×(-2)=-16.
Please help me I’ll give a brainliest! Even if you are only able to do one of them it help because I don’t understand how to do it!!!
Answer:
The x which is not in the domain of the function is the root of the denominator
6) x+3=0, x=-3 is the x which is not in the domain of the function
7) |2x+5|=0, x=-5/2 is the x which is not in the domain of the function
8) x^2-16=0, x=±4 are the x which are not in the domain of the function
Whats the answer and the steps
2(3x-4)
Answer:
-24
Step-by-step explanation:
2(3x-4)
6x-8
Which variable is dependent temperature or time of day? Which variable is independent?
Answer:
The temperature depends on the time.
The independent variable is the variable the experimenter manipulates or changes.
Hope it helps you.Lauren bought snacks for her team's practice. She bought a bag of popcorn for $2.37 and a 6-pack of juice bottles. The total cost before tax was $15.45. How much was each bottle of juice?
Answer:
$2.18
$15.45-$2.37=$13.08
$13.08/6
$2.18
A group of 20 people are going to run a race. The top 6 finishers advance to the finals. In how many different ways can they advance?
What is 10% of a number whose square
is 81
Answer: 0.9
Step-by-step explanation:
Let x be the number
Determine the value of the number
x² = 81
√x² = √81
x = 9
Find the 10% of the number
Final number = rate of percentage × original number
Final number = 10% × 9
Final number = [tex]\boxed{0.9}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
HELPPPPPP MEEEE PLESDEEEE
Answer:
7, 5, 1, 3
Step-by-step explanation:
Hope this Helps!
Please mark me Brainliest
write each expression as a single power of 10
Answer:
[tex]{ \underline{ \sf{it \: is \: {10}^{9} }}}[/tex]
Step-by-step explanation:
[tex](10 {}^{4} ). \frac{ {10}^{12} }{ {10}^{7} } = ( {10}^{4} ). {10}^{(12 - 7)} \\ \\ = ( {10}^{4} ). {10}^{5} \\ = {10}^{(4 + 5)} \\ = {10}^{9} [/tex]
Answer:
[tex]10^{9}[/tex]
Step-by-step explanation:
I. [tex]10^{4} * 10^{12-7}[/tex]
= [tex]10^{4} * 10^{5}[/tex]
= [tex]10^{4 + 5}[/tex]
= [tex]10^{9}[/tex]
y-3 = 2(x+1)
fiind the missing value ?
Step by step process:
Let's solve for x.
y−3=2(x+1)
Step 1: Flip the equation.
2x+2=y−3
Step 2: Add -2 to both sides.
2x+2+−2=y−3+−2
2x=y−5
Step 3: Divide both sides by 2.
2x/2=y−5/2
x=1/2y+(−5/2)
Answer: x=1/2y+(−5/2)
Let's solve for y.
y−3=2(x+1)
Step 1: Add 3 to both sides.
y−3+3=2x+2+3
y=2x+5
Answer:
y=2x+5
PLEASE HELP! it's due today
Answer:
[tex]thank \: you[/tex]
