Answer:
60
Step-by-step explanation:
Let's call the number A.
We are told that:
(2/3)A - 8 = 32
Multiply both sides by 3 and rearrange:
3*[(2/3)A - 8 = 32]
2A - 24 = 96
2A = 120
A = 60
CHECK:
Does (2/3) of 60 minus 8 equal 32?
(2/3)*(60) = 40
40 - 8 = 32
YES
The number is 60
Explain the difference between SAS similiarity and SAS congruency.
Answer:
In the SAS congruence criterion, you must show that two pairs of sides are equal and their included angles are equal as well. But In the SAS similarity criterion, you must show that two pairs of sides are proportional and their included angles are equal.
Step-by-step explanation:
Solution: In the SAS congruence criterion, you must show that two pairs of sides are equal and their included angles are equal as well. But In the SAS similarity criterion, you must show that two pairs of sides are proportional and their included angles are equal.
Sherrie's biology class is studying the ability of a certain microbe to dissipate oil spilled in seawater. to be effective the population of microbes must grow exponentially. she has recorded the microbe population growth as follows: # days after march 1st 0, 1, 5, 10 population 57, 95, 700, 8525 a. using sherrie's data, find the best exponential equation for this growth using the substitution method. must show work. b. using the same data get an equation using calculator's regression feature. then estimate the microbe population on march 21st
The exponential equation for the growth is f(x)=57[tex]e^{0.51x}[/tex] where x is the number of days and the population on 21st march is 2069983.5 of microbes.
Given:
Days population
0 57
1 95
5 700
10 8525
We have to form exponential equation which shows the growth of microbes.
We know that exponential equation which shows the sum is as under:
f(x)=P[tex]e^{rt}[/tex] where r is the rate of growth and x is the number of days, months or years depending on how things grows.
In the question when x=0 population is 57.
f(0)=57
P[tex]e^{0}[/tex]=57
P=57
When x=1, population is 95.
f(1)=95
P[tex]e^{r}[/tex]=95
57 [tex]e^{r}[/tex]=95
57=95/[tex]e^{r}[/tex]----1
when x=5,population is 700.
f(5)=700
P[tex]e^{5r}[/tex]=700
57[tex]e^{5r}[/tex]=700
57=700/[tex]e^{5r}[/tex]-----2
Equating 1&2
95/[tex]e^{r}[/tex]=700/[tex]e^{5r}[/tex]
[tex]e^{5x} /e^{x} =700/95[/tex]
[tex]e^{5r-r}[/tex]=7.36
[tex]e^{4r}[/tex]=7.36
[tex](2.7182)^{4r}[/tex]=[tex](2.7182)^{2}[/tex]
equating both sides
4r=2
r=0.5
put the value of t=21 in the exponential equation
f(21)=57[tex]e^{0.5*21}[/tex]
=57[tex]e^{10.5}[/tex]
=57*36315.5
=2069983.5
Hence the population on 21st march is 2069983.5.
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options.
18 x minus 15 = 72
50 x minus 25 = 72
18 x minus 9 = 72
3 (6 x minus 3) = 72
x = 4.5
The equivalent equations to [tex]\frac{3}{5}(30x - 15) = 72[/tex] are given as follows:
18 x - 9 = 723(6x - 3) = 72x = 4.5.What are equivalent equations?Equivalent equations are equations that have the same solution.
First, we have to check the solution to [tex]\frac{3}{5}(30x - 15) = 72[/tex], hence:
[tex]\frac{3}{5}(30x - 15) = 72[/tex]
Applying the fraction:
18x - 9 = 72 -> first equivalent equation
Simplifying by 3:
3(6x - 3) = 72 -> second equivalent equation
The solution is:
18x - 9 = 72
18x = 81
x = 81/18
x = 4.5 -> third equivalent equation.
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PLEASE HEELPPPPPP
in circle A, AT = AE =7cm & BR= 48 CM
FIND AS
Answer:
Step-by-step explanation:
Comments
AE = AT = 7 Given
AT is a perpendicular bisector of OS Property of a circle
AE is a perpendicular bisector of BR Property of a circle
ER = 1/2 BR = 48/2 = 24 Property of a bisector
TS = ER Property of a bisector and chord
TS = 24 ER = 24 so TS = 24
AS^2 = TS^2 + TA^2 Pythagorean Theorem + rt angle
AS^2 = 24^2 + 7^2 Substitute values
AS^2 = 576 + 49 Combine
AS^2 = 625 Take sqrt of both sides
√AS^2 = √625
AS = 25
Answer
AS = 25
PLEASE HELP URGENT!!!!
Answer:
(d) y≥-5
Step-by-step explanation:
first, we find the equation for the blue line:
a doesn't work as it goes diagonally, so as b, e, or f.
so it must be y≥-5 or y<-5
since the graph is shaded above the line, it must be greater than or greater than or equal to, so it must be D) y≥-5.
You can tell it must be D as greater or less than is dotted while greater equal or less equal would be a solid line.
The ratio of winning tickets to tickets sold is 2 to 5. If 3,500,000 are sold, how many tickets are winners?
Answer:
1400000
Step-by-step explanation:
This is very simple,
multiply the total tickets with this fraction which is
= 2/5x 3500000
= 1400000
Answer:
14,000,000.
Step-by-step explanation:
2 out 5 tickets are winners.
So number of winning tickets = 3,500,000 * 2/5
= 2 * 7,000,000
= 14,000,000
how did the temperature change if it decreased by 60% and then increased by 80%
Answer:
The temperature decreased by 28%
Step-by-step explanation:
How did the temperature change if :
At first it decreased by 60%
Then increased by 80%
Assume that the temperature before decreasing is 100%
∵ The temperature before decreasing = 100%
∵ It decreased by 60%
→ Before decreasing : decreasing : after decreasing
→ 100% : 60% : 100% - 60% = 40%
∴ The temperature after decreasing = 40%
Assume that the temperature after decreasing is 100%
∵ The temperature after decreasing = 100%
∵ It increased by 80%
By using the ratio method
→ After decreasing : increasing : after increasing
→ 100% : 80% : 100% + 80% = 180%
→ 40% : : x%
By using cross multiplication
∴ 100% × x% = 40% × 180%
- Divide both sides by 100%
∴ x% =
∴ x% = 72%
∵ At first the temperature = 100%
∵ At last the temperature = 72%
∵ The first the temperature > the last the temperature
∴ The decreasing in temperature = 100% - 72% = 28%
choosing a spade, not replacing it, then choosing a jack
Answer:
Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.
The higher or lesser the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2.
please help! i will give u 20 points I need the answer with the method
Answer:
6 mm
Step-by-step explanation:
So, the area he needs to fill isn't really important, you don't need to calculate it. What is necessary is the individual dimensions of that area (width/length). The width and the length must be divisible by the lengths of the tiles. This is so you don't need to cut anything. For example let's say the area needed to be filled was 15 mm (width) by 10 mm (length). If I chose 3mm square tiles, it could perfectly fill up the width, but when it came to the length there would be a small 1 mm gap. And you would need to cut one of the square tiles, so it would have a length of 1 mm. In this case the 15mm was divisible by 3, but the 10 mm wasn't. So using this logic, it can't be the 4 mm square tile since 150mm / 4 mm = 37.5. It can be the 6m since 150mm / 6mm = 25 and 180 mm / 6mm = 30. It can't be the 8 mm since 150 mm / 8mm = 18.75 mm
Use the drawing tools to form the correct answers on the graph.
Consider this linear function:
y =
x + 1.
Plot all ordered pairs for the values in the domain.
D: (-8, -4, 0, 2, 6}
Drawing Tools
Select
Point
Click on the Graph to
place a Point
Click on a tool to begin drawing.
-10 -9 -8
+7 -6
-5
H
-3
-2
10
9
8-
7-
6
5
4
3-
2
Delete
3
4
5
6
Undo
7 8
Reset
9 10
The function y = x + 1 has a slope (rate of change) of 1 as well as an y intercept of 1.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard form for a linear function is:
y = mx + b
Where m is the slope and b is the y intercept.
Given the function y = x + 1
The function y = x + 1 has a slope (rate of change) of 1 as well as an y intercept of 1.
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Find x if 2x - 9 = 0
Answer:
2x-9=0
2x-9+9=0+9.add the inverse of subtraction /addition/ (+9)
2x=9....then divide by 2
x=9/2
x=4.5. will the final answer
A sock drawer contains 5 different colors of socks. it has 20 white, 10 black, 6 red, and 4 purple. if you reach into the drawer and choose a sock randomly, what is the probability you will get a a black sock? (write your final answer as a fraction.)
The probability of selecting a black sock is 1/4.
What is the required probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. It is more likely that an event will occur if its probability is higher.
Number of white socks=20
Number of black socks=10
Number of red socks=6
Number of purple socks=4
Total number of socks=20+10+6+4
=40
Probability of getting a black sock=Number of black socks/Total number of socks
=10/40
=1/4
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how to get the answers?
By inclusion/exclusion,
[tex]n(P' \cup Q) = n(P') + n(Q) - n(P' \cap Q)[/tex]
We have
[tex]n(\xi) = n(P) + n(P') \implies n(P') = 28 - n(P)[/tex]
so that
[tex]n(P' \cup Q) = (28 - n(P)) + n(Q) - 2n(P) = 28 - 3n(P) + n(Q)[/tex]
Now,
[tex]n(\xi) = 28 \implies n(P \cup Q) = 28 - 7 = 21[/tex]
and by inclusion/exclusion,
[tex]n(P \cup Q) = n(P) + n(Q) - n(P \cap Q)[/tex]
Decompose [tex]Q[/tex] into the union of two disjoint sets:
[tex]Q = (P \cap Q) \cup (P' \cap Q)[/tex]
Since they're disjoint,
[tex]n(Q) = n(P\cap Q) + n(P'\cap Q) \implies n(Q) = n(P\cap Q) + 2n(P)[/tex]
[tex]\implies n(P \cup Q) = n(P) + (n(P\cap Q) + 2n(P)) - n(P \cap Q)[/tex]
[tex]\implies 21 = 3n(P)[/tex]
[tex]\implies n(P) = 7[/tex]
From the Venn diagram, we see there are 3 elements unique to [tex]P[/tex] - by the way, this is the set [tex]P \cap Q'[/tex] - so [tex]n(P\cap Q) = 7-3 = 4[/tex], and it follows that
[tex]n(Q) = n(P\cap Q) + 2n(P) = 4 + 2\times7 = 18[/tex]
Finally, we get for (a)
[tex]n(P' \cup Q) = 28 - 3n(P) + n(Q) = 28 - 3\times7 + 18 = \boxed{25}[/tex]
For (b), we have by inclusion/exclusion that
[tex]n(P \cup Q') = n(P) + n(Q) - n(P \cap Q') = 7 + 18 - 3 = \boxed{22}[/tex]
Which is the equivalent expression of 78?
2 × (10 × 3 + 32)
2 × (13 + 32)
(10 × 3 + 32)
2 × (10 × 3 + 3)
None of the expressions is equivalent to 78
How to determine the equivalent expression?The number is given as:
Number = 78
Next, we evaluate the expressions in the options using a calculator
2 × (10 × 3 + 32) = 124
2 × (13 + 32) = 90
(10 × 3 + 32) =62
2 × (10 × 3 + 3) = 66
None of the options equals 78
Hence, none of the expressions is equivalent to 78
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In the diagram below, ΔPQR ≅ ΔSTR. Complete the statement RQ⎯⎯⎯⎯⎯⎯⎯⎯≅ R Q ¯ ≅ ___
Based on the CPCTC theorem, the complete statement is: RQ ≅ RT.
What is the CPCTC Theorem?According to the CPCTC theorem, if two triangles are said to be congruent, then all the corresponding parts of both triangles are congruent.
Given that ΔPQR ≅ ΔSTR, RQ corresponds to RT. Therefore, both sides are congruent to each other.
Thus, the complete statement is: RQ ≅ RT.
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The speed that a tsunami can travel is modeled by the equation , where s is the speed in kilometers per hour and d is the average depth of the water in kilometers. What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?.
The approximate depth of water for a tsunami traveling at 200 kilometers per hour, given the equation S=356√d, where S is the speed in kilometers per hour and d is the average depth of the water in kilometers, is 0.32 km. Hence, option A is the correct choice.
To solve for the average depth of water, when the water is traveling at 200 kilometers per hour, we substitute speed S = 200, in the relation S = 356√d.
This will be solved in the following way:
S = 356√d,
or, 200 = 356√d {Substituting S = 200},
or, 200/356 = (356√d)/356 {Dividing both sides by 356},
or, √d = 0.5618 {Simplifying},
or, d = 0.32 kilometers.
Therefore, the approximate depth of water for a tsunami traveling at 200 kilometers per hour, given the equation S=356√d, where S is the speed in kilometers per hour and d is the average depth of the water in kilometers, is 0.32 km. Hence, option A is the correct choice.
The provided question is incomplete.
The complete question is:
"The speed that a tsunami can travel is modeled by the equation S=356√d, where S is the speed in kilometers per hour and d is the average depth of the water in kilometers. What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?
A. 0.32 km
B. 0.75 km
C. 1.12 km
D. 3.17 km"
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Please help, i already tried and couldn't get it right
Answer:
3072
Step-by-step explanation:
General form of a geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termr is the common ratioGiven values:
first term, a = 3common ratio, r = 4Substitute the given values into the formula to create an equation for the nth term:
[tex]\implies a_n=3(4)^{n-1}[/tex]
To find the 6th term, substitute n = 6 into the equation:
[tex]\implies a_6=3(4)^{6-1}[/tex]
[tex]\implies a_6=3(4)^{5}[/tex]
[tex]\implies a_6=3(1024)[/tex]
[tex]\implies a_6=3072[/tex]
Therefore, the 6th term of a geometric sequence whose 1st term is 3 and whose common ratio is 4 is 3072.
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given cos data = 0.7620, approximate the acute angle to the following
a. the nearest 0.01
The acute angle is 40.40 degrees
How to determine the acute angle?The cosine of the angle is given as:
cos(x) = 0.7620
Take the arc cos of both sides
[tex]x = \cos^{-1}(0.7620)[/tex]
Evaluate the arc cos
x = 40.359
Approximate
x = 40.40
Hence, the acute angle is 40.40 degrees
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Susan's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Susan $5.45 per pound, and type B coffee
costs $4.05 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $633.60. How
many pounds of type A coffee were used?
The amount in pounds of Type A coffee used is 36 pounds.
Using equation to find the number of pounds?Type A coffee costs Susan $5.45 per pound, and type B coffee
costs $4.05 per pound.
Therefore,
Let x = the number of pounds of Type A coffee.
total pounds = x + 3x
total cost = 5.45(x) + 3x(4.05)
633.60 = 5.45(x) + 3x(4.05)
633.60 = 5.45x + 12.15x
633.60 = 17.6x
divide both sides by 17.6
x = 633.60 / 17.6
x = 36
Pounds of Type A coffee used = 36 pounds
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if ace had 6 grapes and he gave 3 to mason how many will he have left
Answer:
its 3 grapes
Step-by-step explanation:
6-3=3 therefore the answer is 3
Answer:
3 grapes are left
Step-by-step explanation:
if you subtract 3 from 6 (6 - 3) you will find the answer you need to find how many grapes you have left.
Geometry question I need help with this one
First part;
Following the transformation (x, y) → (3•x, 2•y), the images are;
A'(9, 10), B'(15, 6), C'(6, 4)
Second part;
The distance between points A and B is 2•√2 which is different from the distance between the image A' and B' which indicates that the transformation is a non rigid transformation.
How can the images and the type of transformation be found?First part;
The given points are;
A(3, 5), B(5, 3), C(2, 2)The given transformation is presented as follows;
(x, y) → (3•x, 2•y)
Therefore, the images are;
A(3, 5) → A'(3 × 3, 2 × 5) = A'(9, 10)
B(5, 3) → B'(3 × 5, 2 × 3) = B'(15, 6)
C(2, 2) → C'(3 × 2, 2 × 2) = C'(6, 4)
A(3, 5) → A'(9, 10)B(5, 3) → B'(15, 6)C(2, 2) → C'(6, 4)Second part;
Length of AB = √((5-3)² + (3-5)²) = 2•√2
Length of A'B' = √((15-9)² + (6-10)²) = 2•√13
2•√2 ≠ 2•√13AB ≠ A'B'Given that the length of AB ≠ the length of A'B' then we have;
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The points of the image are (9, 10), (15, 6) and (6, 4) and the resulting image is a nonrigid motion.
How to determine the image of the points?The points are given as:
A = (3, 5)
B = (5, 3)
C = (2, 2)
The transformation is given as:
(x, y) ⇒ (3x, 2y)
So, we have:
A' = (9, 10)
B' = (15, 6)
C' = (6, 4)
Hence, the image of the transformation is (9, 10), (15, 6) and (6, 4)
See attachment for the image
Also, the resulting image is a nonrigid motion.
This is so because the lengths of the image and the preimage are not equal
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Riddle-if you solve it i will delete your answer and you have to post the riddle. Riddle-you enter a room. 2 dogs, 4 horses, 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground? don’t play if you’re not to continue.
Answer:
28
Step-by-step explanation:
Triangle H L I is shown. Line segment J K is drawn near point L to create triangle J L K.
If △HLI ~ △JLK by the SSS similarity theorem, then StartFraction H L Over J L EndFraction = StartFraction I L Over K L EndFraction is also equal to which ratio?
StartFraction H I Over J K EndFraction
StartFraction H J Over J L EndFraction
StartFraction I K Over K L EndFraction
StartFraction J K Over H I EndFraction
The correct option is to show that the ratios HL/JL = IL/KL = HI/JK are equivalent. Option A is correct.
Similarity theorem of trianglesFor two triangles to be similar, the ratio of the measure of similar sides of the triangle must be equal to a constant known as a scale factor.
From the given figures, the expression that can be used to prove that the triangles are similar is as shown;
HL/JL = IL/KL = HI/JK
Hence the correct option is to show that the ratios HL/JL = IL/KL = HI/JK are equivalent
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I can Confirm A is correct
Step-by-step explanation:
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=21 miles and c=75 miles, what is b? If necessary, round to the nearest tenth.
Answer:
C = 29.7
Step-by-step explanation:
Remember to use a^2 + b^2 = c^2
21^2+ 21^2 = c^2
441 + 441 = c^2
882 = c^2
you square root both sides
c= 29.6984
Round it
C = 29.7
Dylan examines 10 different brands of yogurt. He lists the amount of yogurt in one container of each brand to the nearest 18 of a cup. The results are recorded in this frequency table. Create a line plot to display the data. To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
The attached graph represents the line plot of the dataset
How to create the line plot?The frequency table is given as:
Amount 3 3.5 4 4.5 5
Frequency 1 2 3 3 1
To create the line plot, we represent the frequency by dots.
Take for instance:
The amount 3 will be represented by 1 dot because it has a frequency of 1The amount 3.5 will be represented by 2 dots because it has a frequency of 2See attachment for the line plot
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The point-slope form of the equation of of the line that passes through (-4, -3) and (12, 1) is y - 1 = 1/4(x - 12). What
is the standard form of the equation for this line?
O x- 4y = 8
O x-4y=2
O 4x-y= 8
O 4x-y=2
Answer: [tex]\frac{1}{4}[/tex]x - y = 2
Step-by-step explanation:
Standard form is Ax + By = C where A, B, and C, are integers.
Given:
y - 1 = 1/4(x - 12)
Distribute:
y - 1 = [tex]\frac{1}{4}[/tex]x - 3
Add 3 to both sides of the equation:
y + 2 = [tex]\frac{1}{4}[/tex]x
Subtract y from both sides of the equation:
2 = [tex]\frac{1}{4}[/tex]x - y
Apply the reflexive property:
[tex]\frac{1}{4}[/tex]x - y = 2
is 4(2r-1)=-2(3r+16) a no solution or infinite solutions
Answer: Infinite
Step-by-step explanation:
Answer:
one solution, r = - 2
Step-by-step explanation:
4(2r - 1) = - 2(3r + 16) ← distribute parenthesis on both sides
8r - 4 = - 6r - 32 ( add 6r to both sides )
14r - 4 = - 32 ( add 4 to both sides )
14r = - 28 ( divide both sides by 14 )
r = - 2
The concession stand at a local high school sells nachos for $4 each and popcorn for $2 each. At the next event, the manager of the stand expects sales of a minimum of 100 items, totaling at least $225. Let x represent the number of nachos sold and let y represent the number of popcorn sold. Which of the following systems correctly represents the scenario?
The system of inequalities that correctly represents this scenario is given by:
[tex]x + y \geq 100[/tex].[tex]4x + 2y \geq 225[/tex].What is a system of inequalities?A system of inequalities is when two or more variables are related, and inequalities are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: number of nachos sold.Variable y: number of popcorn sold.The manager of the stand expects sales of a minimum of 100 items, hence:
[tex]x + y \geq 100[/tex].
The concession stand at a local high school sells nachos for $4 each and popcorn for $2 each. The manager wants a total of at least $225, hence:
[tex]4x + 2y \geq 225[/tex]
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NEED HELP IMMEDIATELY PLS!
Answer:c
Step-by-step explanation:
c
Answer:
D.
Step-by-step explanation:
The equation must be true to have a proportion.
12/20 = 0.6
21/34 = 0.62
A. No
10/15 = 0.666666...
34/60 = 0.566666...
B. No
13/23 = 0.565217...
26/56 = 0.46428...
C. No
25/15 = 1.6666...
85/51 = 1.6666...
D. Yes
Answer: D
A man is dealt 4 spade cards from an ordinary deck of 52 cards. If he is given five more, what is the probability that none of them are spades
The probability that none of them are spades is c(39,5) / c(48,5).
Probability is without a doubt how probable something is to show up. whenever we are uncertain about the final results of an occasion, we can talk about the possibilities of sure outcomes and how probable they are. The analysis of events governed by opportunity is referred to as records.
A chain of moves in which the results are usually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a cube. occasion. it is a single final result of an experiment. Getting a Head whilst tossing a coin is an event.
Simple chance is the calculation of an outcome or the chance of an event ever taking place. Coverage companies use possibility statistics to determine the possibility of having to pay out a declaration. A simple chance is calculated by way of dividing a particular outcome by all of the feasible outcomes.
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