Answer: r = 11
Step-by-step explanation:
We know that the point (-2, r) lies on the graph of:
2*x + y = 7.
Then, if we that point is on the graph of the equation, we can replace the values and we will have:
2*(-2) + r = 7
and now we solve this for r-
-4 + r = 7
r = 7 + 4 = 11
r = 11
Give the domain and range of each relation using set notation
Answer:
See below.
Step-by-step explanation:
First, recall the meanings of the domain and range.
The domain is the span of x-values covered by the graph.
And the range is the span of y-values covered by the graph.
1)
So, we have here an absolute value function.
As we can see, the domain of the function is all real numbers because the graph stretches left and right infinitely. Therefore, the domain of the function is:
[tex]\{x|x\in\textbb{R}\}[/tex]
(You are correct!)
For the range, notice how the function stops at y=7. The highest point of the function is (-2,7). There graph doesn't and won't ever reach above y=7. Therefore, the range of the graph is all values less than or equal to 7. In set notation, this is:
[tex]\{y|y\leq 7\}[/tex]
2)
We have here an ellipse.
First, for the domain. We can see the the span of x-values covered by the ellipse is from x=-4 to x=6. In other words, the domain is all values in between these two numbers and including them. Therefore, we can write it as such:
[tex]-4\leq x\leq 6[/tex]
So x is all numbers greater than or equal to -4 but less than or equal to 6. This describes the span of x-values. In set notation, this is:
[tex]\{x|-4\leq x\leq 6\}[/tex]
For the range, we can see that the span of x values covered by the ellipse is from y=-5 to y=1. Just like the domain, we can write it like this:
[tex]-5\leq y\leq 1[/tex]
This represents all the y-values between -5 and 1, including -5 and 1.
In set notation, thi is:
[tex]\{y|-5\leq y\leq 1\}[/tex]
14. Twice the sum of a number and eight
Answer: 2(x + 8) is the expression.
Use distributive property to simplify,
2x+16
I didn't know which answer you wanted so....
Answer:
2(x + 8)
Step-by-step explanation:
Hello!
Twice the sum means we multiply by 2
2
the sum of a number and eight is x + 8
2 * x + 8
Since we have to twice the sum we put x + 8 in parenthesis to show to do that first
2(x + 8)
Hope this Helps!
A survey showed that among 785 randomly selected subjects who completed four years of college, 144 of them are smokers and 84 do not smoke (based on data from the American Medical Association). Suppose you want to test at the 0.01 significance level the claim that the rate of smoking among those with four years of college is less than the 27% rate for the general population.
A. State the null and alternative hypotheses.
B. Find the sample statistic and the p-value.
C. What is your conclusion?
Answer:
We conclude that the rate of smoking among those with four years of college is less than the 27% rate for the general population.
Step-by-step explanation:
We are given that a survey showed that among 785 randomly selected subjects who completed four years of college, 144 of them are smokers.
Let p = population proportion of smokers among those with four years of college
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 27% {means that the rate of smoking among those with four years of college is more than or equal to the 27% rate for the general population}
Alternate Hypothesis, [tex]H_A[/tex] : p < 27% {means that the rate of smoking among those with four years of college is less than the 27% rate for the general population}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of smokers = [tex]\frac{144}{785}[/tex] = 0.18
n = sample of subjects = 785
So, the test statistics = [tex]\frac{0.18-0.27}{\sqrt{\frac{0.27(1-0.27)}{785} } }[/tex]
= -5.68
The value of z-test statistics is -5.68.
Also, the P-value of the test statistics is given by;P-value = P(Z < -5.68) = Less than 0.0001
Now, at a 0.01 level of significance, the z table gives a critical value of -2.3262 for the left-tailed test.
Since the value of our test statistics is less than the critical value of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the rate of smoking among those with four years of college is less than the 27% rate for the general population.
On a coordinate plane, 2 lines are shown. Line A B has points (negative 4, negative 2) and (4, 4). Line C D has points (0, negative 3) and (4, 0). Which statement best explains the relationship between lines AB and CD? They are parallel because their slopes are equal. They are parallel because their slopes are negative reciprocals. They are not parallel because their slopes are not equal. They are not parallel because their slopes are negative reciprocals.
Answer:
A. they are parallel because their slopes are equal.
Step-by-step explanation:
edge 2020
Answer:
its A in egde
Step-by-step explanation:
Consider the following ordered data. 6 9 9 10 11 11 12 13 14 (a) Find the low, Q1, median, Q3, and high. low Q1 median Q3 high (b) Find the interquartile range.
Answer:
Low Q1 Median Q3 High
6 9 11 12.5 14
The interquartile range = 3.5
Step-by-step explanation:
Given that:
Consider the following ordered data. 6 9 9 10 11 11 12 13 14
From the above dataset, the highest value = 14 and the lowest value = 6
The median is the middle number = 11
For Q1, i.e the median of the lower half
we have the ordered data = 6, 9, 9, 10
here , we have to values as the middle number , n order to determine the median, the mean will be the mean average of the two middle numbers.
i.e
median = [tex]\dfrac{9+9}{2}[/tex]
median = [tex]\dfrac{18}{2}[/tex]
median = 9
Q3, i.e median of the upper half
we have the ordered data = 11 12 13 14
The same use case is applicable here.
Median = [tex]\dfrac{12+13}{2}[/tex]
Median = [tex]\dfrac{25}{2}[/tex]
Median = 12.5
Low Q1 Median Q3 High
6 9 11 12.5 14
The interquartile range = Q3 - Q1
The interquartile range = 12.5 - 9
The interquartile range = 3.5
Find the sum of (5x3 + 3x2 - 5x + 4) and (8x3 -5x2 + 8x + 9)
Answer:
(5x³+3x²-5x+4) + (8x³-5x²+8x+9)
= 5x³+3x²-5x+4 +8x³-5x²+8x+9
= 5x³+8x³+3x²-5x²-5x+8x+4+9
= 13x³-2x²+3x+13
Hope this helps
if u have question let me know in comments ^_^
A cabinet door has a perimeter of 76 inches. Its area is 357 square inches. What are the dimensions of the door?
Answer:
17 by 21 inches
Step-by-step explanation:
The perimeter is twice the sum of the dimensions, and the area is their product, so you have ...
L + W = 38
LW = 357
__
Solution:
W(38 -W) = 357 . . . . . substitute for L
-(W^2 -76W) = 357 . . expand on the left
-(W^2 -38 +19^2) = 357 -19^2 . . . . complete the square
(W -19)^2 = 4 . . . . . . . write as a square
W -19 = ±√4 = ±2 . . . take the square root; next, add 19
W = 19 ±2 = {17, 21} . . . . if width is one of these, length is the other
The dimensions are 17 by 21 inches.
Find the number of pieces of floor tiles each measuring 26cm long and 10cm wide needed to lay a floor measuring 260m long and 15m wide
Answer:
150,000
Step-by-step explanation:
1 m = 100 cm
260 m = 260 * 100 cm = 26000 cm
15 m = 15 * 100 cm = 1500 cm
area of floor = LW = 26000 cm * 1500 cm = 39,000,000 cm^2
area of 1 tile = 26 cm + 10 cm = 260 cm^2
number of tiles needed = 39,000,000/260 = 150,000
Answer: 150,000 tiles
What is the slope of a line perpendicular to y=-7/4x
O A.
IN
O B.
7
O c.
4
-
O D.
7
4
Answer:
y=4/7x
Step-by-step explanation:
perpendicular lines have opposite slopes. that means reciprocal and opposite sign.
Solve for 2 in the diagram below.
120°
32°
T=
Step-by-step explanation:
Hello, there!!!
It's so simple here,
Here,
we have is 1 angle is 120°and other is 3x°.
now,
3x°=120° {because when two st.line intersects eachother then the opposite angle formed are equal}
so, 3x°=120
or, x=120°/3
=40°
Therefore, the value of x is 40°.
Hope it helps....
Transform the polar equation to a Cartesian (rectangular) equation: r= 4sinθ
options include:
x^2+y^2 = 4y
x^2+y^2 = -4
x^2+y^2 = 4
x^2+y^2 = -4y
Answer:
x^2 +y^2 = 4y
Step-by-step explanation:
Using the usual translation relations, we have ...
r^2 = x^2+y^2
x = r·cos(θ)
y = r·sin(θ)
Substituting for sin(θ) the equation becomes ...
r = 4sin(θ)
r = 4(y/r)
r^2 = 4y
Then, substituting for r^2 we get ...
x^2 +y^2 = 4y . . . . . matches the first choice
A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with mean 100 lb and 5 lb and standard deviation 1 lb and 0.5 lb, respectively. What percent of filled boxes weighing between 104 lb and 106 lb are to be expected?
a. 67%
b. None
c. 37%
d. 57%
Answer:
Option b. None is the correct option.
The Answer is 63%
Step-by-step explanation:
To solve for this question, we would be using the z score formula
The formula for calculating a z-score is given as:
z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
We have boxes X and Y. So we will be combining both boxes
Mean of X = 100 lb
Mean of Y = 5 lb
Total mean = 100 + 5 = 105lb
Standard deviation for X = 1 lb
Standard deviation for Y = 0.5 lb
Remember Variance = Standard deviation ²
Variance for X = 1lb² = 1
Variance for Y = 0.5² = 0.25
Total variance = 1 + 0.25 = 1.25
Total standard deviation = √Total variance
= √1.25
Solving our question, we were asked to find the percent of filled boxes weighing between 104 lb and 106 lb are to be expected. Hence,
For 104lb
z = (x-μ)/σ,
z = 104 - 105 / √25
z = -0.89443
Using z score table ,
P( x = z)
P ( x = 104) = P( z = -0.89443) = 0.18555
For 1061b
z = (x-μ)/σ,
z = 106 - 105 / √25
z = 0.89443
Using z score table ,
P( x = z)
P ( x = 106) = P( z = 0.89443) = 0.81445
P(104 ≤ Z ≤ 106) = 0.81445 - 0.18555
= 0.6289
Converting to percentage, we have :
0.6289 × 100 = 62.89%
Approximately = 63 %
Therefore, the percent of filled boxes weighing between 104 lb and 106 lb that are to be expected is 63%
Since there is no 63% in the option, the correct answer is Option b. None.
The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be 63%.
What is a normal distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with a mean of 100 lb and 5 lb and standard deviation of 1 lb and 0.5 lb, respectively.
The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be
Then the Variance will be
[tex]Var = \sigma ^2[/tex]
Then for X, we have
[tex]Var (X) = 1^2 = 1[/tex]
Then for Y, we have
[tex]Var (Y) = 0.5^2 = 0.25[/tex]
Then the total variance will be
[tex]Total \ Var (X+Y) = 1 + 0.25 = 1.25[/tex]
The total standard deviation will be
[tex]\sigma _T = \sqrt{Var(X+Y)}\\\\\sigma _T = \sqrt{1.25}[/tex]
For 104 lb, then
[tex]z = \dfrac{104-105}{\sqrt{25}} = -0.89443\\\\P(x = 104) = 0.18555[/tex]
For 106 lb, then
[tex]z = \dfrac{106-105}{\sqrt{25}} = 0.89443\\\\P(x = 106) = 0.81445[/tex]
Then
[tex]P(104 \leq Z \leq 106) = 0.81445 - 0.18555 = 0.6289 \ or \ 62.89\%[/tex]
Approximately, 63%.
More about the normal distribution link is given below.
https://brainly.com/question/12421652
3.24 (4 being repeated) to a fraction
Answer:
146/45
Step-by-step explanation:
Let x represent the value of the number of interest. Then we can do the following math to find its representation as a fraction.
[tex]x=3.2\overline{4}\\10x=32.4\overline{4}\\10x-x=9x=32.4\overline{4}-3.2\overline{4}=29.2\\\\x=\dfrac{29.2}{9}=\boxed{\dfrac{146}{45}}[/tex]
__
Comment on procedure
The power of 10 that we multiply by (10x) is the number of repeated digits. Here, there is a 1-digit repeat, so we multiply by 10^1. If there were a 2-digit repeat, we would compute 10^2x -x = 99x to rationalize the number.
write a thirdthird-degree polynomial expression that has only two terms with a leading term that has a coefficient of five and a constant of negative two
Answer:
5x^3-2
[tex]ax^{3} +bx^{2} +cx+d\\5x^{3}-given\\ d=-2-given\\5x^{3} -2[/tex]
Explanation:
The two terms are [tex]5x^3[/tex] and [tex]2[/tex]. Terms are separated by either a plus or minus.
We can write it as [tex]5x^3+(-2)[/tex] which is an equivalent form. Here the two terms are [tex]5x^3[/tex] and [tex]-2[/tex]. This is because adding a negative is the same as subtracting.
The coefficient is the number to the left of the variable.
The degree is the largest exponent, which helps form the leading term.
The third degree polynomial written above is considered a cubic binomial. "Cubic" refers to the third degree, while "binomial" means there are 2 terms.
We can write something like [tex]5x^3[/tex] as 5x^3 when it comes to computer settings.
Which expression is equivalent to (jk)l? A. (j + k) + l B. j(kl) C. (2jk)l D. (j + k)l
Answer:
B. j(kl)
Step-by-step explanation:
(jk)l
We can change the order we multiply and still get the same result
j(kl)
Answer:
Step-by-step explanation:
its B i did it
what is the distance between the first and third quartiles of a data set called?
Answer:
Interquartile range is the distance between the first and third of a data.
Step-by-step explanation:
Hope it will help you :)
if f(x)=3x-3 and g(x)=-x2+4,then f(2)-g(-2)=
Answer:
3
Step-by-step explanation:
f(x)=3x-3
g(x)=-x^2+4,
f(2) = 3(2) -3 = 6-3 =3
g(-2) = -(-2)^2+4 = -4+4 = 0
f(2)-g(-2)= = 3-0 = 3
Please answer this correctly without making mistakes
Answer:
so to get a third you divide it by 3
first convert it to fraction
so it is 26/3
so do 26/3 divided by 3
so we do keep switch flip
26/3*1/3
so answer is 26/9 or 2 8/9
Step-by-step explanation:
Answer:
[tex]\large \boxed{\mathrm{2 \ 8/9 \ tablespoons \ of \ red \ chilies }}[/tex]
Step-by-step explanation:
8 2/3 tablespoons of red chilies is required for a recipe.
One-third of the original recipe would mean that the quantity of red chilies will be also one-third.
8 2/3 × 1/3
Convert to an improper fraction.
26/3 × 1/3
Multiply the fractions.
26/(3 × 3) = 26/9
Convert to a mixed fraction.
26/9 = 2 8/9
Brian needs to paint a logo using two right triangles. The dimensions of the logo are shown below. What is the difference between the area of the large triangle and the area of the small triangle?
Answer:
7.5 cm²
Step-by-step explanation:
Dimensions of the large ∆:
[tex] base (b) = 3cm, height (h) = 9cm [/tex]
[tex] Area = 0.5*b*h = 0.5*3*9 = 13.5 cm^2 [/tex]
Dimensions of the small ∆:
[tex] base (b) = 2cm, height (h) = 6cm [/tex]
[tex] Area = 0.5*b*h = 0.5*2*6 = 6 cm^2 [/tex]
Difference between the area of the large and the small ∆ = 13.5 - 6 = 7.5 cm²
The value (in dollars) of an airplane depends on the flight hours as given by the formula V= 1,800,000 - 250x . After one year, the value of the plane is between $1,200,000 and $1,300,000. Which range for the flight hours does this correspond to?
a. 1800 <= x <= 2100
b. 2200<= x <= 2500
c. 1500<= x <= 1800
d. 2000<= x <= 2400
Answer:
D
Step-by-step explanation:
To determine the range we must solve this inequality;
● 1200000<1800000-250x<1300000
Substract 1800000 from both sides.
● 1200000-1800000<1800000-250x<1300000-1800000
● -600000< -250x < -500000
Divide both sides by 250
● -600000/250 < -250x/250 < -500000/250
● -2400 < -x < -2000
Multiply both sides by -1 and switch the signs
● 2000 < x < 2400
The correct option is D. 2000<= x <= 2400
Given, the value of an airplane depends on the flight hours,
[tex]V= 1800000-250x[/tex], here x is the flight hours.
We have to calculate the range of x After one year.
Since, [tex]V= 1800000-250x[/tex]
[tex]250x=1800000-V\\\\x=\dfrac{1800000-V}{250}[/tex]
Since the value of the plane is between $1,200,000 and $1,300,000. So,
[tex]x=\dfrac{1800000-1200000}{250}[/tex]
[tex]x=\dfrac{600000}{250}[/tex]
[tex]x=2400\\[/tex]
When V is 1300000 then x will be,
[tex]x=\dfrac{1800000-1300000}{250} \\[/tex]
[tex]x=\dfrac{500000}{250}[/tex]
[tex]x=2000[/tex]
Hence the range of x will be from 2000 to 2400.
The correct option is D. 2000<= x <= 2400.
For more details on range follow the link:
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The area of the circle x² + y2 - 6x-4y +9 = 0 is
Answer:
Your answer is here.Enjoy dude
Answer:
12.56 unit²
Step-by-step explanation:
Given:x² + y² - 6x - 4y + 9 = 0To find:The area of circleSolution:The form of the circle is:
(x- h)² + (y-k)² = r²Let's bring the given to the form of a circle as above:
x² + y² - 6x - 4y + 9 = 0x² - 6x + y²- 4y + 9 = 0 ⇒ combining like terms and completing squarex² - 6x + 9 + y²- 4y + 4 = 4 ⇒ adding 4 to both sides(x-3)² + (y - 2)² = 2² ⇒ got the form of this circleAs per the form, we got r² = 2², so the radius of circle is 2 units.
The area of circle:
A= πr² = 3.14×2² = 12.56 unit²
What is the volume of a cube with a side length of
of a unit?
. A discount brokerage selected a random sample of 64 customers and reviewed the value of their accounts. The mean was $32,000 with a population standard deviation of $8,200. What is a 90% confidence interval for the mean account value of the population of customers
Answer:
The 90% confidence interval is [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 64
The sample mean is [tex]\= x = \$ 32, 000[/tex]
The standard deviation is [tex]\sigma= \$ 8, 200[/tex]
Given that the confidence interval is 90% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10 \%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table , the value is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{ \sqrt{n} }[/tex]
=> [tex]E = 1.645 * \frac{ 8200 }{ \sqrt{64} }[/tex]
=> [tex]E = 1686.13[/tex]
The 90% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]32000 - 1689.13 < \mu < 32000 + 1689.13[/tex]
=> [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]
How should a musician effectively convey emotions or ideas in a performance?
Answer:
Within the factors hindering expression in music, tempo is the most important number of factors such as your mood.
Step-by-step explanation:
If one wants to convey a message, they should try these:
a) Use real life
b) introduce symbolism
c) convey sensory disruption, e.t.c.
Hope these helps.
The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. A 2-row table with 10 columns. The first row is labeled time (seconds), x with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.6. The second row is labeled height (meters), h with entries 100, 98.8, 95.1, 89.0, 80.4, 69.4, 55.9, 40.0, 21.6, 0. A line of best fit for the data is represented by h = –21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table? According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground. According to the line of best fit, the object was dropped from a lower height. The line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds. The line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.
Answer: A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
The statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
We have a line of best fit:
h = –21.962x + 114.655
As per the data given and line of best fit, we can say the object would have impacted the ground 0.6 seconds later than it did according to the line of best fit.
Thus, the statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
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The formula for the area of a square is s2, where s is the side length of the square. What is the area of a square with a side length of 6 centimeters? Do not include units in your answer.
Answer:
36
Step-by-step explanation:
formula of area for square:
A=s^2
s=6
A=6^2
A=36
Answer:
36
Step-by-step explanation:
I got it right
(a^8)3/2 in simplest form
Answer:
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Step-by-step explanation:
([tex]a^{8}[/tex]) * [tex]\frac{3}{2}[/tex]
Remove the parenthesis by multiplying
[tex]\frac{3}{2}[/tex][tex]a^{8}[/tex]
This expression cannot be simplified further
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Hope this helps :)
What is 5 feet and 11 inches in inches
Answer:
60
Step-by-step explanation:
5 is 60 inch
If f(x)=ax+b/x and f(1)=1 and f(2)=5, what is the value of A and B?
Answer:
[tex]\huge\boxed{a=9 ; b = -8}[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{ax+b}{x}[/tex]
Putting x = 1
=> [tex]f(1) = \frac{a(1)+b}{1}[/tex]
Given that f(1) = 1
=> [tex]1 = a + b[/tex]
=> [tex]a+b = 1[/tex] -------------------(1)
Now,
Putting x = 2
=> [tex]f(2) = \frac{a(2)+b}{2}[/tex]
Given that f(2) = 5
=> [tex]5 = \frac{2a+b}{2}[/tex]
=> [tex]2a+b = 5*2[/tex]
=> [tex]2a+b = 10[/tex] ----------------(2)
Subtracting (2) from (1)
[tex]a+b-(2a+b) = 1-10\\a+b-2a-b = -9\\a-2a = -9\\-a = -9\\a = 9[/tex]
For b , Put a = 9 in equation (1)
[tex]9+b = 1\\Subtracting \ both \ sides \ by \ 9\\b = 1-9\\b = -8[/tex]
An experimental probability is ______ likely to approach the theoretical probability if the number of trials simulated is larger. A. as B. more C. less D. not
Answer:
B. More
Step-by-step explanation:
This is according to the law of large numbers
An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger.
What is an experimental probability and theoretical probability?Experimental probability is an experimental outcome whereas theoretical probability is a possible or expected outcome.
An experimental probability is more likely to approach the theoretical probability if the number of trials increased because of the law of large numbers which states that the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed
Thus using the concept of the law of large numbers we can say that an experimental probability is more likely to approach the theoretical probability.
Learn more about probability here:
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