the equation Pr[A] = Σ[Pr[A | Bi] Pr[Bk] / Pr[Bi]] provides a general formula for calculating the probability of event A based on the given partition B1, B2, ..., Bt of the sample space.
(a) To prove the equation Pr[A] = Σ[Pr[A | Bx] Pr[Bx]], we start by using the law of total probability. The law of total probability states that for any event A and a partition B1, B2, ..., Bt of the sample space, we have Pr[A] = Σ[Pr[A | Bi] Pr[Bi]], where Pr[A | Bi] is the conditional probability of A given Bi.
By rearranging the terms, we get Pr[A] = Σ[Pr[A | Bi] Pr[Bi]] = Σ[Pr[A | Bi] Pr[Bi] / Pr[Bk] Pr[Bk]], where Pr[Bk] is the probability of the event Bk.
Next, we multiply and divide Pr[A | Bi] by Pr[Bk], giving us Pr[A] = Σ[(Pr[A | Bi] Pr[Bk]) / Pr[Bk] Pr[Bi]].
Since the summands have the same denominator Pr[Bk] Pr[Bi], we can write Pr[A] = Σ[(Pr[A | Bi] Pr[Bk]) / Pr[Bk] Pr[Bi]] = Σ[Pr[A | Bi] Pr[Bk] / Pr[Bk] Pr[Bi]].
Finally, by canceling out the common factor Pr[Bk], we obtain Pr[A] = Σ[Pr[A | Bi] Pr[Bk] / Pr[Bi]], which proves the equation.
(b) From the equation Pr[A] = Σ[Pr[A | Bi] Pr[Bk] / Pr[Bi]], we can see that Pr[A] can be expressed as a sum of terms involving the conditional probabilities Pr[A | Bi] and the probabilities of the partition sets Pr[Bi]. This equation allows us to compute the probability of A by considering the conditional probabilities and the probabilities of the partition sets.
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The perimeter of the figure to the right, made up of identical squares, is equal to 56 cm. What is the area of the figure?
The area of the square will be 196cm².
How to calculate the area?It should be noted that the perimeter of a square is the addition of all its sides. Therefore, the length of the side will be:
= 56/4
= 14
Therefore, the area of the figure will be:
= 14²
= 14 × 14
= 196cm²
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Which options reflect the requirements for factoring using quadratic form? (Select all that apply.)
Answer:
The exponent of the first term must have twice the value of the exponent of the second term.
Step-by-step explanation:
HELP NOW GIVING BRAINLIEST AND 15 POINTS THANK U :) <3
Answer:
its not 15 points ):
Step-by-step explanation:
If BE−→− bisects ∠ABD and m∠ABD = 66°, find m∠ABE.
Answer:
∠ABE = 33°
Step-by-step explanation:
Angle bisector:Angle bisector is a straight line that divides the angle into two congruent (equal) angles.
So, BE bisects the ∠ABD into two equal angles.
⇒∠ABE will be half of ∠ABD
∠ABD = ∠ABE + ∠BED
66° = ∠ABE + ∠ABE
66 = 2∠ABE
∠ABE = 66/2
∠ABE = 33°
Evaluate 5a + 5b, where a
=
-6 and b = -5.
Substitute -6 in a and -5 in b
5(-6) + 5(-5)
-30+(-25)
=-55
Hope it helps!
Answer:
-55
5x-6 = -30
5 x -5 = -25
-25 + -30 = -55
Step-by-step explanation:
hope this helps
All the students in a science class complete a 15-point extra-credit assignment to raise their test scores the new test score is 15 points more than the original score let x = original score let y = new score ehich equation represents this situation?
The equation that represents the situation is,
y = x + 15
Given Information
It is given that the students complete a 15-point extra-credit assignment in order to raise their test scores.
The new test score is 15 more than the old test score.
We have to find an equation for this situation. A mathematical equation is a formula that uses the equals sign to connect two expressions in order to express their equality.
Forming Equation
Original Score = x
New Score = y ................... (1)
Thus, after the test, the score is raised by 15 points.
⇒ New score = x + 15 .................... (2)
The following equation can be deduced from (1) and (2)
y = x + 15
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A rectangle with a length of x - 4 and a width of 8 has a perimeter of 34. what is the value of x?
Answer:
13
Step-by-step explanation:
2(x-4+8)=34
x-4+8=17
x+4=17
x=13
3. Jorge earns a 9% commission on all of his sales. He had sales of
$89,400 for the month. Harris works for a different company, and also
sold $89,400 for the month but made $447 more than Jorge. What is
Harris' commission rate?
The commission rate exists at $8,493 with a rate of 9.5%.
How to estimate the commission rate?
Jorge earns 9% from all his sales, so his commission exists
89400 × 0.09 = $8046
Harris made $447 more than that, so his commission exists
8046 + 447 = $8493
To estimate his commission rate, we can utilize the subsequent equation
89400 × rate percentage = 8493
Rate percentage = 8493 / 89400
Rate percentage = 0.095
Rate percentage = 9.5%
So Harris' commission exists at $8,493 with a rate of 9.5%.
Therefore, the commission rate exists at $8,493 with a rate of 9.5%.
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Green’s Sport Shop offers its salespeople an annual salary of $10,000 plus a 6% commission on all sales above $20,000. Every employee receives a Christmas bonus of $500. What are Mr. Cahn’s total earnings in a year in which his sales amounted to $160,000?
(A) $18,900
(B) $18,400
(C) $19,600
(D) $20,100
The total earnings for the year is $18,900.
What is the total earnings?The total earnings is a sum of the annual salary, commission and Christmas bonus.
Commission = 6% x (160,000 - 20,000) =
6% x $140,000
0.06 x 140,000 = $8,400
Total earnings = $8,400 + 10,000 + $500 = $18,900
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Alice and Bob both go to a party which starts at $5:00$. Each of them arrives at a random time between $5:00$ and $6:00$. What is the probability that the number of minutes Alice is late for the party plus the number of minutes Bob is late for the party is less than $45$
The probability comes out to be 9/32.
Deducing Arrival Time Possibility
All the possible arrival times by Alice and Bob, in minutes after 5 PM, is constrained by the values of given values of x and y,
x = 0, y = 0, x = 60, y = 60.
Here, let the values of x represent how many minutes after 5 PM Alice arrives at the party.
Let the y values represent the time in minutes that Bob arrives at the party after 5 PM.
Calculating the Required Probability
The times that concern us, however, are obtained by the following probability function,
x + y ≤ 45.
And x = 0, y = 0, and x + y ≤ 45 define the constraints of this probability function. Thus the perimeter of such a graph will be given as,
(45² / 2) = 1012.5 square units
Since the total area of the various arrival times is 60 x 60, or 3600 square units, the probability that Alice and Bob will arrive together after 5 o'clock in the evening in less than 45 minutes is therefore = 1012.5 / 3600 = 9/32
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Please help!
I don't understand part B.
The median value of x is 2.
According to the statement
we have given the values of x at some points then
and we have to find the median for the x.
We know that the median formula is {(n + 1) ÷ 2}th, where “n” is the number of items in the set and “th” just means the (n)th number.
and after put the values in this formula we get our median value for x.
So,
we have given that the f(x) is 0.2 when x is from -1 to 0
and f(x) is 0.2 +1.2x when x is grater than 0 but less than 1
and f(x) is 0 when x is less than -1 or grater than 1
From these statements it is clear that the the f(x) is only exist when the x lies in between from the -1 to 1.
So, the total value of x becomes is -1,0,1
Then according to the median formula
median = (n + 1) ÷ 2
median = (3+1) / 2
median = 2.
So, The median value of x is 2.
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An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle
Answer: [tex]\theta=\frac{8}{3} \text{ radians}[/tex]
Step-by-step explanation:
[tex]8=3\theta\\\\\theta=\frac{8}{3} \text{ radians}[/tex]
Instructions: Find the measure of the indicated angle to the nearest degree.
The measure of the indicated angle to the nearest degree is 47°.
What is the measure of the angle?Given the data in the question;
Adjacent = 36Hypotenuse = 53Angle θ = ?From trigonometric ratio, Cosθ = Adjacent / Hypotenuse
Cosθ = 36/53
θ = cos⁻¹( 36/53 )
θ = 47°
Therefore, the measure of the indicated angle to the nearest degree is 47°.
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For the following distribution: x p(x) 0 01.30 1 0.346 2 0.346 3 0.154 4 0.026 what is the mean of the distribution?
The mean of the distribution given is 0.569.
Given some distribution like under:
x p(x)
0 0.650
1 0.216
2 0.087
3 0.026
4 0.014
5 0.009
We have to find the mean of the distribution.
Mean is the sum of numbers divided by the numbers which are taken into consideration. It is also known as average.
Mean=sum/n
To find the mean of distribution we have to find sum of x*p(x)
∑xp(x)=0*0.650+1*0.216+2*0.0087+3*0.026+4*0.014+5*0.009
=0+0.216+0.174+0.078+0.056+0.045
=0.569
Hence the mean of the distribution given in the question is 0.569.
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Distribution in the given question is wrong and the right question is as the right distribution is as under:
x p(x)
0 0.650
1 0.216
2 0.087
3 0.026
4 0.014
5 0.009
Which equation could represent the graph shown below?
F(x) = ^3√x + 2 (sqrt just over the x)
F(x) = ^3√x - 2 (sqrt just over the x)
F(x) = ^3√x + 2 (the sqrt is over the whole equation)
F(x) = ^3√x - 2 ( the sqrt is over the whole equation)
I DONT KNOW HOW TO PUT A PICTURE OF THE GRAPH!!
The equation of the graph is [tex]f(x) = -\sqrt{x -2[/tex]
How to determine the graph equation?The graph is added as an attachment
The form of the graph is
[tex]f(x) = a\sqrt{x + b[/tex]
The graph passes through the points (2, 0) and (6, -2).
So, we have:
[tex]0 = a\sqrt{2 + b[/tex] and [tex]-2 = a\sqrt{6 + b[/tex]
Solve for b in [tex]0 = a\sqrt{2 + b[/tex]
Divide both sides by a
[tex]0 = \sqrt{2 + b[/tex]
Square both sides
0 = 2 + b
Subtract 2 from both sides
b = -2
Substitute b = -2 in [tex]-2 = a\sqrt{6 + b[/tex]
[tex]-2 = a\sqrt{6 -2[/tex]
[tex]-2 = a\sqrt{4[/tex]
Evaluate the square root
-2 = 2a
Divide by 2
a = -1
Substitute b = -2 and a = -1 in [tex]f(x) = a\sqrt{x + b[/tex]
[tex]f(x) = -\sqrt{x -2[/tex]
Hence, the equation of the graph is [tex]f(x) = -\sqrt{x -2[/tex]
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The vehicle preference of police officers and firefighters is given in the table.
Police Officers Firefighters
Cars 12 3
Trucks 9 4
SUVs 15 2
Based on the information in the table, which of the following is an example of independent events.
Based on the information in the table, an example of independent events is the: P(policer officer and chooses car).
What is an independent event?An independent event can be defined as an event that isn't dependent on other events. Thus, it isn't affected by any previous event.
Based on the information provided, we can infer and logically deduce that an example of independent events is the probability of being a policer officer and chooses a car because they aren't overlapping probabilities.
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hwlppppppp!!!!!!!!!
look at pic
The correct option is the third one:
-1 ≤ y - 3 and y - 3 ≤ 1
Which compound inequality represents the absolute value inequality?
Here we have:
|y - 3| - 4 ≤ -3
We can rewrite it to:
|y - 3| ≤ -3 + 4
|y - 3| ≤ 1
This can be decomposed in two inequalities, which are:
(y - 3) ≤ 1
(y - 3) ≥ -1
Then we can see that the correct option is the third one, as both inequalities must be meet.
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The median for the samples from the school math contest are:
The median of Sample 1 from Grades 9 and 10 is 79.
The median of Sample 2 from Grades 11 and 12 is 86.
What conclusions can you derive from the random samples?
The students performed equally between all the grades.
The students in grades 11 and 12 scored higher than the students in grades 9 and 10.
The students in grades 11 and 12 are likely to do well in college.
The students in grades 9 and 10 were not allowed enough time in the school math contest.
The sample size was too small to derive a valid conclusion
A conclusion which can be derived from these random samples is that: B. the students in grades 11 and 12 scored higher than the students in grades 9 and 10.
What is a median?A median can be defined as the middle number (center) of a sorted data set, which is when the data set is arranged in from the greatest to least or the least to greatest.
In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.
Based on the information provided for these samples, we can logically conclude that the students in grades 11 and 12 scored higher than the students in grades 9 and 10 because a median score of 86 is greater than a median score of 79.
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please help me with this
Answer:
x = -9, y = 8
or,
(-9, 8)
Explanation:
Equation 1: 2x + 3y = 6
Equation 2: 4x - y = -44
To solve by substitution, make y subject for equation 2.
4x - y = -44
-y = -44 - 4x
y = 4x + 44
Substitute this y value into equation 1.
2x + 3(4x + 44) = 6
2x + 12x + 132 = 6
14x = 6 - 132
14x = -126
x = -9
Now, find y value:
y = 4x + 44
y = 4(-9) + 44
y = 8
To check for solution, insert x and y value in either equations.
2x + 3y = 6
insert values
2(-9) + 3(8) = 6
6 = 6
Hence, the solution is correct as both sides equal.
Therefore x = -9 and y = 8.
Step-by-step explanation:Substitution method
Equation (1) ——— 2x + 3y = 6
Equation (2) ——— 4x - y = -44
When using substitution method , make x the subject of equation (1).
2x + 3y = 6
2x = 6 - 3y
x = 3 - 3y/2
Substitute the value of x in equation (2) to find y.
4(3 - 3y/2) - y = -44
12 - 6y - y = -44
Subtract 12 from both sides.
12 - 12 - 7y = -44 - 12
-7y = -56
y = 8
Substitute the value of y in equation (1) to find x.
2x + 3y = 6
2x + 3(8) = 6
2x +24 = 6
Subtract 24 from both sides.
2x + 24 - 24= 6 - 24
2x = -18
x = -9
Therefore x = -9 and y = 8.
To check out the solution.
Equation (1) 2x + 3y = 6 , x = -9 , find y.
Substitute the value of x
2(-9) + 3y = 6
-18 + 3y = 6
Add 18 to both sides.
-18 + 18 + 3y = 6 + 18
3y = 24
y = 8
Substitute the value of y in equation (1) .
2x +3(8) = 6
2x + 24 = 6
Subtract 24 from both sides.
2x + 24 - 24 = 6 -24
2x = -18
x = -9
As you can see when you substitute the value of x and y in the equation(1) , you get the same value of x and y ,which is -9 and 8 respectively. So the solution is correct.
Towards neural Earth system modelling by integrating artificial intelligence in Earth system science
Answer:
This has nothing to do with math
Step-by-step explanation:
I don't know what this even means
Please help
!!!!!!!!!!!!!!
Answer: Option (2)
Step-by-step explanation:
[tex]DE=\sqrt{(-a-b-0)^2 + (c-2c)^2}=\sqrt{(a+b)^2 + c^2}[/tex]
f(x) = (two-fifths) Superscript x
g(x) = (two-fifths) Superscript x – 3
Which statement about f(x) and its translation, g(x), is true?
The range of g(x) is , {y | y > 0} and the range of f(x) is {y | y > –3}.
The range of g(x) is , {y | y > 3} and the range of f(x) is {y | y > 0}.
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
The asymptote of g(x) is the asymptote of f(x) shifted three units up.
Answer: The asymptote of g(x) is the asymptote of f(x) shifted three units down.
Step-by-step explanation:
Answer:
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
Step-by-step explanation:
bc I said so
Identify the range of values for y.
The figure shows a triangle. The first side of the triangle goes from the lower left corner to the upper right corner. The second side of the triangle goes from the lower right corner to the upper left corner. An angle between these sides is an obtuse angle. The third side of the triangle goes from the lower left corner to the lower right corner. A line connects a vertex of the obtuse angle with a point on the third side. This line divides the third side into left and right segments. An angle between this line and the second side measures 60 degrees. An angle between this line and the left segment of the third side measures 105 degrees. The second side of the triangle is congruent to the left segment of the third side. The right segment of the third side has a length of 5 times y plus 8 units. The first side of the triangle has a length of 4 times y plus 15 units.
The range of values of y is -1.6 < y < 7
How to determine the range?The complete question is added as an attachment
From the attached image, we have the following sides
4y + 15 and 5y + 8
Both sides must be greater than 0.
So, we have:
4y + 15 > 0 and 5y + 8 > 0
Rewrite as:
4y > -15 and 5y > - 8
Solve for y
y > -3.75 and y > -1.6
If y is less than -1.6, the side 5y + 8 would be negative.
So, we make use of the inequality y > -1.6 as one of the range
Also, 4y + 15 is greater than 5y + 8.
So, we have:
4y + 15 > 5y + 8
Evaluate the like terms
-y > -7
Divide by -1
y < 7
So, we have:
y > -1.6 and y < 7
Combine both inequalities
-1.6 < y < 7
Hence, the range of values of y is -1.6 < y < 7
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What steps may be necessary to predict data not included in a data set using a scatter plot and line of best fit? Select all that apply.
the necessary steps to predict data not included in a data set using a scatter plot and line of best fit are Options 2, 3, 4
Graph the data in a scatter plotExtend the line of best fit beyond the dataFind the average of the dataSteps involved in predicting dataIn using the line of best fit also known as the slope, they following steps are involved;
Draw the line of best fitFind the direction of association between the two variablesIn using scatterplot, they following steps are involved;
Draw line of best fit that passes close to most of the data pointsApproximately half of the data points should be below the line and half of the points above the lineThis explains that the average of the set of data is found from the scatter plot and line of best fit.
Thus, the necessary steps to predict data not included in a data set using a scatter plot and line of best fit are Options 2, 3, 4
Graph the data in a scatter plot
Extend the line of best fit beyond the data
Find the average of the data
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A forest ranger wants to estimate the probability of catching a bass in a lake when using a special type of bait. Describe a process the ranger could use to estimate the probability of catching a bass in the lake.
The probability of catching a bass in the lake is given by:
Probability = probability 1 × probability 2
How to calculate the probability of catching a bass?Since the forest ranger caught a fish from his prior fishing experience, we can infer that he has a probability of catching a bass in a lake:
Probability 1 = Number of fish caught/Number of tries
By using a special type of bait, he should calculate the probability of catching a fish as follows:
Probability 2 = Number of fish caught/Number of tries
Therefore, the probability of catching a bass in the lake is given by:
Probability = probability 1 × probability 2
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Is someone able to help me? You don’t have to explain just give answers
a. The continuous growth rate of the bacteria is 21%
b. The initial population of bacteria is 715
c. The culture will contain 2043 bacteria after 6 × 10⁻⁴ years
a. What is the continuous rate of growth of this bacteria population?Since [tex]n(t) = 715e^{0.21t}[/tex] represents the number of bacteria in the culture.
This function is similar to an exponential function of the form [tex]y(t) = Ae^{\lambda t}[/tex] where λ = growth rate
Comparing n(t) and y(t), we see that λ = 0.21
So, the continuous growth rate of the bacteria is 0.21 = 0.21 × 100 %
= 21%
So, the continuous growth rate of the bacteria is 21%
b. What is the initial population of the culture?Since [tex]n(t) = 715e^{0.21t}[/tex] represents the number of bacteria in the culture, the initial population of bacteria is obtained when t = 0.
So, [tex]n(t) = 715e^{0.21t}[/tex]
[tex]n(0) = 715e^{0.21(0)} \\= 715e^{0} \\= 715 X 1\\= 715[/tex]
So, the initial population of bacteria is 715
c. When will the culture contain 2043 bacteria?To find the time when the number of bacteria will be 2043, this means n(t) = 2043.
Since [tex]n(t) = 715e^{0.21t}[/tex]
Making t subject of the formula, we have
t = ㏑[n(t)/715]/0.21
So, substituting n(t) = 2043 into the equation, we have
t = ㏑[n(t)/715]/0.21
t = ㏑[2043/715]/0.21
t = ㏑[2.8573]/0.21
t = 1.05/0.21
t = 4.99
t ≅ 5 hours
Converting this to years, we have t = 5 h × 1 day/24h × 1 year/365 days
= 5/8760
= 5.7 × 10⁻⁴ years
≅ 6 × 10⁻⁴ years
So, the culture will contain 2043 bacteria after 6 × 10⁻⁴ years
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Question 12 of 20
Subtract.
(2x²+5)-(4x-3)
OA. 2x²-4x+2
OB. -2x² +8
OC. 2x2²-4x+8
OD. -2x²+2
Answer:
C
Step-by-step explanation:
Distribute the negative, (2x^2 + 5) + (-4x+3)
Add like terms, 2x^2 - 4x +(5+3)
2x^2-4x+8
Using algebra, prove that 0.136 (3,6 recurring) is equal in value to 1/33.
Answer:
0.1363636... = 3/22
Step-by-step explanation:
Let x = 0.1363636...
100x = 13.6363636...
(-) x = 0.1363636...
------------------------------------------
99x = 13.5
x = 13.5/99
x = 135/990
x = 27/198
x = 9/66
x = 3/22
0.1363636... = 3/22
0.1363636... is not equal to 1/33.
1/33 = 0.030303...
Here is a list of numbers: 8.2, 0.4, 7.7, 2.8, 4.8, 6.1, 6.1 ,10 ,8.2 ,3 state the median.
Answer: 6.1
Step-by-step explanation:
if roni and allie work together to mow the field, what part of the field would roni mow?
Based on the Roni using a lawn mower and Allie pushing one, Roni would be able to mow 0.71 of the field.
How much of the field would Roni mow?Assume that the part of the field that Roni would mow is x.
The relevant equation would be:
x/30 + x/75 = 1
5x/150 + 2x/150 = 1
7x / 150 = 1
x = 21.43
In 30 minutes, Roni would have mowed:
= 21.43 / 30
= 0.71
Full question is:
Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie is pushing a lawn mower and can mow the field in 75 minutes.
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