When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events. The correct options are A and B.
Which pair of events are called independent events?When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.
Symbolically, we have:
Two events A and B are said to be independent iff we have:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Comparing it with chain rule will give
[tex]P(A|B) = P(A)\\P(B|A) = P(B)[/tex]
Thus, showing that whether one occurred or not, the other one doesn't care about it (independence).
Two events are known to be independent even if the result of one event does not affect the result of the second event.
Rolling a dice in an independent event and choosing a blue marble is another independent event. The two events are independent and the result of one does not affect the other.
Thus, A is correct.
Rolling a dice in an independent event, and rolling it again won't affect the result of the second roll. Therefore, rolling a dice twice or for n number of times is an independent event.
Thus, B is correct.
Hence, the correct options are A and B.
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In an oblique drawing, which surface is shown in its true size and shape and is parallel to the horizon?
top
side
bottom
front
In an oblique drawing, the surface that is shown in its true size and shape and is parallel to the horizon is the front.
What is the drawing about?The Position of an object in a drawing is known to be parallel to the plane of projection and the circular shape is true in front plane of the oblique view.
The measurements on the front and oblique faces are known to have all its lengths to be true.
Note also that A pictorial drawing that has the front view of an object parallel to the projection plane and shown its true size and shape is known to be Oblique Drawing.
Therefore, In an oblique drawing, the surface that is shown in its true size and shape and is parallel to the horizon is the front and as such, option d is correct.
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Automobile insurance with the split limits 200/300/400 will cover up to how much in bodily injury per person?
Automobile insurance with the split limits 200/300/400 will cover up to $200,000 in bodily injury per person.
What is Insurance?This is a form of protection from financial loss and is used as a means of risk management.
$200,000 medical bodily injury coverage per person, $300,000 bodily injury coverage for the entire accident and $400,000 total property damage limits.
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Find the median of the following data : 9, 15, 17, 18,6, 20, 8, 5, 18, 18, 10, 5, 14, 12, 10, 7
A. 15
B. 18
C. 12
D. 11
Answer:
The median is 11.
Explanation:
Add the middle values to calculate the mean, then divide this by 2. That gives you 11.
solve for K
7K-6
2K+14
How many times larger than (6 - 4) is (6 - 4) × 5?
Answer:
5 times bigger
Step-by-step explanation:
(6-4) = 2
(6-4) x 5 = 10
the table below shows the results from a spinner experiment find the probability of spinning a number greater than 2
Answer:
29/48
Step-by-step explanation:
Total number of spins: 8 + 11 + 17 + 12 = 48
Total number of spins greater than 2: 17 + 12 = 29
p(greater than 2) = 29/48
a cone has a base with a diameter of 60 cm. the height of the cone is 24 cm. what is the approximate volume of the cone? use 3.14 or pi.
Answer:
22619.47
Step-by-step explanation:
V=π[tex]r^{2}[/tex][tex]\frac{h}{3}[/tex]
=π·30^2·24/3
≈22619.46711
The following box plot shows the number of years during which 24 schools have participated in an interschool swimming meet:
At least how many schools have participated for 1 year or less? (5 points)
6 schools
8 schools
12 schools
14 schools
The number of schools have participated for 1 year or less are below the first quartile, which is: A. 6 schools.
What is the First Quartile in A Box Plot?The first quartile marks the 25th data point of a data distribution (1/4) and is represented at the beginning of the edge of the rectangular box in a box plot.
Using the box plot given, 1 year is the first quartile mark on the box plot. So, the schools that participated for 1 year or less is 1/4 of the total schools. That is:
1/4 × 24 = 6 schools.
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whitch of the following is closest to 8 62 61 65 66
Answer:
If the question is which is closest to 8, the answer is 61
Step-by-step explanation:
Find the value of h(-7) for the function below.
h(x) = 5.7 −19x
A.
0.67
B.
-138.7
C.
-127.3
D.
138.7
The input value of the function h(-7) for h(x) = 5.7 - 19x is -26.6.
How to find the input value of a Function?We are given the function;
h(x) = 5.7 - 19x
Thus;
h(-7) = 5.7 - 19(1.7)
h(-7) = 5.7 - 32.3
h(-7) = -26.6
Thus, we conclude that the input value of the function h(-7) is -26.6.
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help marking brainliest
Answer:
9-pack
Step-by-step explanation:
Price per roll for 4-pack = Pack price / Number of rolls in pack
= 2.25 / 4
= £0.56 (rounded off to nearest cent)
Price per roll for 9-pack = Pack price / Number of rolls in pack
= 4.50 / 9
= £0.50
From here, we can see the 9-pack is of better value.
Please help! This is reflections in geometry! Thank you.
If these coordinates reflected over y = -1, the resulting coordinate will be:
P = (-4, -6)
Q = (-2,-8)
R = (1, -4)
Reflection of coordinatesA reflected coordinates are mirror images of each other. From the given diagram, the coordinate points are;
P = (-4, -3)
Q = (-2,-4)
R = (1, -2)
If these coordinates reflected over y = -1, the resulting coordinate will be:
P = (-4, -6)
Q = (-2,-8)
R = (1, -4)
The y coordinates are multiplied by a factor of 2
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What is the slope of the line that contains the points (-2, 2) and (3, 4)?
A -2/5
B 2/5
C 5/2
D -5/2
Answer:
[tex]B) ~\dfrac 25[/tex]
Step-by-step explanation:
[tex]\text{Given that,} ~ (x_1,y_1) = (-2,2)~ \text{and}~ (x_2 ,y_2) = (3,4)\\\\\text{Slope},~ m = \dfrac{y_2 - y_1}{x_2 -x_1}\\\\\\~~~~~~~~~~~~~=\dfrac{4-2}{3+2}\\\\\\~~~~~~~~~~~~~=\dfrac 25[/tex]
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the slope of the line that contains the points (-2, 2) and (3, 4).
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Use the slope formula, which is given below:[tex]\star~\mathrm{\cfrac{y2-y1}{x2-x1}}[/tex]
Where
y2 and y1 are y-coordinates
x2 and x1 are x-coordinates
Substitute the values:
[tex]\star~\mathrm{\cfrac{4-2}{3-(-2)}}[/tex]
Simplify!
[tex]\star~\mathrm{\cfrac{2}{5}}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
student can work no more than 23 hours
per week.
2. The tutoring center requires that each
tutor spend at least two hours per week
tutoring.
3. The tutoring center requires that each
tutor spend no more than seven hours pers
week tutoring.
Answer:
See below ~
Step-by-step explanation:
We need to represent the situations as inequalities.
===============================================================
Students can work no more than 23 hours per week
⇒ Let the hours per week be x
⇒ 'no more than' refers to less than or equal to (≤)
⇒ x ≤ 23
=============================================================
Tutors are required to spend at least 2 hours per week
⇒ At least refers to greater than or equal to (≥)
⇒ x ≥ 2
============================================================
Tutors should spend no more than 7 hours per week
⇒ As mentioned before, no more than refers to less than or equal to (≤)
⇒ x ≤ 7
ae need inequalities
#1
No more than means maximum
h≤23#2
At least means minimum
h≥2#3
No more than is maximum
h≤7
12345678910111213141516
Step-by-step explanation:
oh, come on. you can just use common sense.
a local minimum is a point where the curve goes down to, and then turns around and starts to go up again. that point in the middle, where it turns around and does not go down any further, is the minimum.
for the maximum the same thing applies, just in the other direction (the curve goes up and turns around to go back down again).
a)
the local minimum values (y) are
-2, -1
b)
the values of x where it had these minimum values are
-1, +3
Jessica has a penny and a nickel. She flipped both coins. What are the chances that both coins land on tails?
Answer:
Step-by-step explanation:
Here is a list of possible outcomes.
Penny nickel
Heads heads
Heads tails
tails Heads
tails tails
Since there are four ways the two coins can land, the chances of getting tails - tails is 1 chance in 4.
Answer: The answer is C 1/4
Pls helpDetermine the area, in square units, of rectangle ABCD.
Enter the area of rectangle ABCD.
The area of the rectangle, as shown in the image given is calculated as: 48 square units.
What is the Area of a Rectangle?The area of a rectangle = length × width.
Find the length and width of the rectangle:
Length (BC) = 8 unitsWidth (AB) = 6 unitsArea of rectangle ABCD = 8 × 6 = 48 square units.
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what is the coordinate of the vertex for the following prabola: (x-10)^2 = 12(y+2)
Answer:
Hi,
Step-by-step explanation:
[tex](x-10)^2=12(y+2)\\y=\dfrac{(x-10)^2}{12}-2\\y'=0 == > 2(x-10)/12=0 == > x=10 == > y=-2\\\\Vertex\ is\ (10,-2)\\[/tex]
The ocean was a magnet pulling me closer to it.
Group of answer choices
1:hyperbole
2:simile
3:metaphor
Answer:
Metaphor
Step-by-step explanation:
This is a comparison between the ocean and a magnet, but it did not use like or as, so it is a metaphor.
Answer: The correct answer is 3. metaphor.
Step-by-step explanation:
A hyperbole is an exagerration.
A simile is a comparison used with like or as.
A metaphor is a comparison used without like or as.
Therefore, "The ocean was a magnet pulling me closer to it." includes a metaphor.
The graph of y=x is shifted up 2 units and 3 units to the left. Which is the equation of the translated function?
Check the picture below.
[tex]y = x\implies y = \stackrel{A}{1}(\stackrel{B}{1}x+\stackrel{C}{0})+\stackrel{D}{0} \\\\\\ \begin{cases} \stackrel{\textit{2 units up}}{D=+2}\\\\ \stackrel{\textit{3 units left}}{C=+3}\\ B=1 \end{cases}\qquad \implies y = \stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{+3})\stackrel{D}{+2}\qquad \implies y=(x+3)+2[/tex]
the sum of interior angle of a regular Pentagon in 540 degree find the interior angle
Answer:
108°Step-by-step explanation:
A regular pentagon has five interior angles of the same measure.
Then
An interior angle has a measure of :
540/5 = 108°
Hello, the answer should be [tex]108^o[/tex].
The interior angle of any shape formula, if the geometric shape is regular and the sum of interior angle is known, can be written as;
[tex]Interior=\frac{Sum(angles)}{Side}[/tex]
Regular pentagon has 5 sides.
The sum of interior angles of regular pentagon is [tex]540^o[/tex].
[tex]Result=\frac{540^o}{5}=108^o[/tex]
Good luck! If you have any question(s), then feel free to ask in comments.
Ariel has a salary of $100,000 in the year 2003 and got a raise of 3.32 % every year. How much money in total will Ariel earn up through the year 2007, to the nearest dollar?
What is the measure of angle ACB
What is the measure of the arc from A to B not passing through C?
solve the equation
(x+1)(x+8)=0
Answer:
x²+9x+8
Step-by-step explanation:
(x)(x+8)+(1)(x+8)
x²+8x + ×+8
x²+9x+8
Hey there!
Answer :x = -1 or x = -8 ✅
Explanation :To solve this equation, you have to use the zero product property.
↳ Ifa product of factors is zero, then at least one of its factors is zero.
Which means that either x + 1 = 0 or x + 8 = 0
⇒ x + 1 = 0
Subtract 1 from both sides :
⇒ x + 1 - 1 = 0 - 1
⇒ x = -1
OR
⇒x + 8 = 0
Subtract 8 from both sides :
⇒x + 8 - 8 = 0 - 8
⇒x = -8
Therefore, x = -1 or x = -8.
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Follow the directions to solve the system of equations by elimination.
8x + 7y = 39
4x – 14y = –68
Multiply the first equation to enable the elimination of the y-term.
Add the equations to eliminate the y-terms.
Solve the new equation for the x-value.
Substitute the x-value back into either original equation to find the y-value.
Check the solution.
The solution to the system of equations is?
Answer:
X= 1/2 Y= 5
Step-by-step explanation:
8x+7y=39-------------(1)--------×2
4x-14y= -68-----------(2)-------×1
16X + 14Y = 78--------(3)
4X- 14Y = -68----------(4)
Addy equation (4) and (3)
20X = 10
dividing bothsides by 20
20X/20= 10/20
X = 1/2
substitute the value of X into equation (1)
8X+7Y = 39
8(1/2)+7Y= 39
4+7Y = 39
7Y = 39-4
7Y = 35
dividing bothsides 7
7Y= 35/7
Y = 5
What is the velocity (speed) of a car (in kilometres per hour) if it goes 40 kilometres in 35 minutes?
A: 70.27 km/hr
B: 67.52 km/hr
C: 68.57 km/hour
D: 69.88 km/hr
speed = distance / time
35 minutes / 60 minutes = 0.583 hours
speed = 49 km / 0.583 hours
Speed = 68.57 km/hr
answer: C. 68.57 km/hour
If anyone know how to solve this please help!!
this my last slide to finish
solve this please!!
Answer:
Area=18ft^3 Surface Area=44ft^2
Step-by-step explanation:
The formula for area of a rectangular prism is A=lwh. So you just plus that in
Answer:
Volume = 18 cubic feet
Surface Area = 44 square feet
Double width = Double the space
Step-by-step explanation:
Please see attached explanations.
Surface area is the area (one side multiplied by another) of every side of the storage box, added together.
I have labeled each unique pair of sides as a, b, and c. That is top and bottom, left and right side, and front and back side.
Volume is the length multiplied by the width multiplied by the height.
By doubling the width, you are doubling the size of the box in that given direction. You can prove this mathematically by making the width twice of what it was and finding volume again.
yx^-4*(x^2y^4)^-2
Simplify,
Please show work
I’ll give Brainliest
I am thinking of a secret number. 12 is a factor of my number. Suggest three other factors of my number.
Answer:
Let us assume your secret number is 12, and we can simply write down ALL the factors of 12:
1, 12
2, 6
3, 4
Question 4 of 25
Which of these could be the graph of F(x) = In x + 1?
51
51
5.
H
5
-5
-5-
B
A
5
-5
D
5
Answer:
fx 8
Step-by-step explanation:
ao the answer ia fx 8 do times