When P(A | B) = P(A) and P(B ∩ A) = P(B). Then, the given events A and B are independent events.
What is defined as the independent events?Independent events are those where the occurrence is unrelated to any other event.
For example, suppose we toss a coin as in air and the result Head, then we throw the coin again and get the result Tail. Both events occur independently of one another in both cases.Now, as for the given question.
There are two events given as A and B.
The probability of occurrence of event A is P(A).
The probability of occurrence of event B is P(B).
The occurrence of the event A when B is already happened is denoted by P(A | B).
The intersection of events A and B are given as; P(B ∩ A).
Now, it is given in the question that;
P(A | B) = P(A) and P(B ∩ A) = P(B)
And, we already know that, the formula of the conditional probability for event A when event B has already occurred is;
P(A | B) = P(B ∩ A)/P(B)
This can also be written as;
P(B ∩ A) = P(A | B).P(B)
Now, P(A | B) = P(A), replace in the obtained equation.
P(B ∩ A) = P(A).P(B)
The obtained result is the condition for independent events.
Therefore, the events A and B are found to be independent events.
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Which two decimal numbers are greater than 5.06 and less than 5.13 ?
5.18
5.0
5.21
5.09
5.1
The two decimal numbers that are greater than 5.06 and less than 5.13 are 5.09 and 5.1.
How to illustrate the information?It should be noted that decimals simply means.the numbers that aren't whole numbers.
It should be noted that this is a straight forward question.
Here, the two decimal numbers that are greater than 5.06 and less than 5.13 are 5.09 and 5.1.
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Find the value of A if the 4-digit number 3A5A is divisible by 15.
The value of A in the 4-digit number is 5.
What is the value of A?Given the information provided in the question, the 4-digit number is a multiple of 15. A multiple of a number is the product of an integer and that number.
The multiple of a number is divisible by that number. For example, a multiple of 2 is 20. This is because 2 multiplied by 10 is equal to 20 and 20 is divisible by 2 to yield a value of 10.
The multiplies of 15 either have a unit value of 5 or 0.
If A is 5, the number becomes 3555.
3555 / 15 = 237
If A is 0, the number becomes 3050
3050 / 15 = 203.333
Thus, the value of A is 5 because 3555 is divisible by 15.
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How is the Additive Identity Property similar to the Multiplicative Identity Property? How is it different?
How is the Additive Identity Property similar to the Multiplicative Identity Property?
A number's original value is returned when additive identity is applied to it. The original number is returned when multiplicative identity is multiplied by any number, too.All real numbers have both of these characteristics.How is it different?
Additive Identity is used in addition operation and multiplicative identity is used in multiplication operation.Additive Identity is denoted by a + 0 = a but multiplicative identity is denoted by a x 1 = a.The additive identity for any real number is 0 and multiplicative identity for any real number is 1.To learn more about additive identity property, refer:
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Order the numbers from least to greatest. Put the lowest number on the left. 6.826 6.628 6.286
The ordering of the number is 6.286 , 6.628 , 6.826
According to the question we have been given three numbers which are
6.826 , 6.628 and 6.286
We need to arrange in ascending order that is from least number to the greatest number.
when we arrange number in ascending order for decimal number we first look at the number before the decimal point then if they are all same then we look at the number after the decimal point. After the decimal point the first number is compared which is closest to the decimal point.
If we look into this question the number before decimal points are all same thus we will look the numbers after the decimal point. Therefore we will arrange according to the first number after the decimal that is 8 , 6 and 2
Hence the ordering the number we get:
6.286 , 6.628 , 6.826
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The difference of a number x and 5 is 6
fewer than twice the number x. (hint:
what type of phrase does "fewer than" or
"less than" mean?)
WILL GIVE BRAINLIEST! NEED HELP!!!
Answer: x=1
Step-by-step explanation:
x-5=2x-6
x-5+6=2x-6+6
x+1=2x
x-x+1=2x-x
2x-x=1
x=1
Answer: x = 1
Step-by-step explanation:
fewer or less than means minus -
difference of x and 5 = x - 5
6 fewer = - 6
twice the number of x = 2x
x - 5 = 2x - 6
x = 2x - 6 + 5
x -2x = - 6 + 5
- x = - 1
x = 1
checking
1 - 5 = 2(1) - 6
4 = 2 - 6
4 = 4
Please help me with this problem! DUE TONIGHT!
Answer:
b=v
Step-by-step explanation:
Answer:
I got b=v so it would be 0
Step-by-step explanation:
I'm sorry if I'm wrong
kx² 12x +9=0 find the value of K given that each equation has equal roots
Answer:
value of k is 3 to make it perfectly
The monthly minutes on your cell phone can add
up to no more than 700 minutes. You have used
648 minutes. Write an inequality that represents
how many more minutes m you can use during the
rest of the month.
The knowledge of how many more minutes m you can use during the rest of the month is given by the linear inequality 648 + m ≤700, where 'm' is the minutes on the cell phone or simply m ≤ 52
It is given that the monthly minutes on your cell phone can add up to no more than 700 minutes so the highest limit is 700
And You have already used 648 minutes so this is our base for the formation of linear inequality
We are provided to use 'm' for rest of the minutes on the cell phone
Hence, we can form a linear inequality using the three points as the sum of already used minutes and the maximum minutes that can be used in this month is at most 700 minutes is given by 648 + m ≤700
This can also be simplified as
m ≤ 700 - 648
m≤52
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A scientist was in a submarine below sea level studying oceam life. Over the next ten minutes, she ascended 61.9 feet. How many feet had she been below sea level, if she was 21.6 feet below sea level after she ascended?
You can add the distance she travelled upwards to her new distance to get her old distance.
Essentially, 21.6 + 61.9 = 83.5.
This means she was 83.5 feet below sea level, before ascending 61.9 feet to 21.6 feet below sea level.
Answer: she was 83.5 feet below sea level, before ascending 61.9 feet to 21.6 feet below sea level.
Step-by-step explanation:
find the perimeter of the new similar triangle to the triangle below with a ratio of 3:5, old to new triangle
Answer:
perimeter: 14.5
Step-by-step explanation:
Write in point-slope form an equation of the line through each pair of points. (-4,10) and (-6,15)
The equation of the line in point-slope form, which passes through the pair of points located at (-4 , 10) and (-6 , 15), is y - 10 = -5/2(x + 4).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (-4 , 10) and (-6 , 15).
m = (y2 - y1)/(x2 - x1)
m = (15 - 10)/(-6 - -4)
m = 5/-2
m = -5/2
Using the point slope form, plug in the values of the slope and one point to set up the equation.
(y - y1) = m(x - x1)
where m = -5/2 and (x1 , y1) = (-4 , 10)
(y - 10) = -5/2(x - -4)
y - 10 = -5/2(x + 4)
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The sum of three consecutive even integers is 18 more than five-halves the smallest integer. What is the product of the smallest and largest integer?
The product of the smallest and largest integer is 672
What is the product of the smallest and largest integer?Represent the smallest even integer with x.
So, the other even integers are x + 2 and x + 4
The sum is represented as
x + x + 2 + x + 4 = 18 + 5/2x
Evaluate the like terms
3x + 6 = 18 + 5/2x
Evaluate the like terms
1/2x = 12
Multiply by 2
x = 24
The largest integer is x + 4
So, we have
x + 4 = 24 + 4
x + 4 = 28
The product of the smallest and largest integer is
Product = 24 * 28
Evaluate
Product = 672
Hence, the product of the smallest and largest integer is 672
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What is the value of x ?
10 /x(x-2) + 4 / x=5 / x-2
Answer:
ue7e7373777 is is and 88877376363778
In a company, 70% of the workers are men. If 990 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
Answer:
Step-by-step explanation:
990 x 70% = 693 people
Δ A B C has vertices A(-3,3), B(2,5) , and C(4,-3) . What are the coordinates of the centroid of ΔA B C ? Explain the process you used to reach your conclusion.
The coordinates of the centroid of Δ ABC is y = -1/3x + 2.
What is meant by the slope of the line?
The slope of the line is the rise-to-run ratio or the rise divided by the run. It expresses the slope of a line in the coordinate plane. Finding the slope of a line is similar to determining the slope between two points.
The midpoint D of AC is (-3+4/2, 3-3/2) or (1/2, 0).
Note that DB is a line that connects the vertex B and D, the midpoint of AC.
The slope of the line DB is ((5-0)/(2-1/2)) or 10/3.
The equation of DB is
y - 5 = 10/3 (x - 2)
simplifying the above equation, we get
y - 5 = 10x/3 - 20/3
y - 5 + 5 = 10x/3 - 20/3 + 5
y = 10x/3 - 5/3
Use the same method to find the equation of the line between point A and the midpoint of BC.
Therefore, the coordinates of the centroid of Δ ABC is y = -1/3x + 2.
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What is the solution of the equation 3⁻ˣ = 1/243 ?
Answer:
well done .....I hope it's helpful
23.7-8.3+4.14=============
ANSWER:
19.54
Step-by-step explanation:
23.7-8.3
=15.4
15.4+4.14
=18.54
Example 1 Position and label each triangle on the coordinate plane.right ΔA B C with legs AC and AB so that AC is 2 a units long and leg AB is 2 b units long
The right-angle triangle on the coordinate plane will be drawn. Then the third length of the right triangle will be 2√(a² - b²) units.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The right triangle ΔABC with legs AC and AB so that AC is 2a units long and leg AB is 2b units long.
We know that the angle ABC is a right angle which means 90°.
Then the third length of the right triangle will be
H² = P² + B²
(2a)² = (2b)² + B²
B² = 4a² - 4b²
B² = 4(a - b²)
B = 2√(a² - b²)
The right-angle triangle on the coordinate plane will be drawn.
The diagram is attached below.
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x^2(3x-1)^4 integrate by parts
Answer:
[tex]81x {}^{6} - 108 { \times }^{5} + 54 { \times }^{4} - 12 { \times }^{3} + { \times }^{2} [/tex]
Write the component form of →PQ .
The vector PQ is given by the addition of the components of the two vectors i.e. →PQ = →Q + →P
Vector is a quantity having magnitude as well as direction and is used to denote the mathematical and geometrical direction of the given quantity.
For example : Velocity, Displacement etc.
Let us first assume that,
P(x,y,z) and Q(u,v,w)
Now, we need to find the vector PQ
→PQ = →Q + →P
= (ui + vj + wk ) + (xi + yj + zk)
= (ui + xi ) +(vj + yj) + (wk +zk)
= (u+x) i + (v + y) j + (w + z)k
= →PQ
For example : Let P(1,2,1) and Q ( -1, -2,4)
Then, →PQ = →Q + →P
= (1i + 2j + 1k ) + (-1i + (-2)j + 4k)
= (1-1) i + (2 -2) j + (1 + 4)k
= oi+0j +5j
= 5j
Hence, the vector PQ is given by the addition of the components of the two vectors.
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You are choosing between two health clubs. Club A offers membership for a fee of $28 plus a monthly fee of $28. Club B offers membership for a fee of $23 plus a monthly fee
of $29. After how many months will the total cost of each health club be the same? What will be the total cost for each club?
Answer:
Step-by-step explanation:
graph the solution to the following inequality: 38 - k < 5 - 2k
Answer:
k <−33
Step-by-step explanation:
In a company, the penalty for being late for work in one month
follows the table below.
Late the first 3 times
$10 total
For every additional time $8 per time
If Jane paid $42 for the penalty last month, how many times
was she late for work?
___times
Help me please please
p=a+b solve for letter b
The value of b is b=p-a.
Given the equation is p=a+b.
A pair of inverse operations is defined as two operations to be performed on a number or. variable, always returns the original number or variable And inverse means opposite.
equation means a mathematical statement with the symbol "equal" between two expressions of equal value. This is represented by '='.
The given equation is p=a+b.
Now, we will apply the inverse operations on both sides.
Subtract a from both sides, we get
p-a=a+b-a
Now, we will simplify the above equation, we get
p-a=b
Hence, the value of b from the given equation p=a+b is b=p-a.
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If you draw four cards at random from a standard deck of 52 cards, what is the probability that all 4 cards have distinct characters (letters or numbers)? report answer to 3 decimal places.
Using it's concept, there is a 0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
A standard deck is given by 4 suits of 13 cards, each with either a number from 1 to 10 or one letter from A, Q or K, hence:
For the first card, all can be selected.For the second card, 48 out of the remaining 51 cards will be available, removing the three cards with the same letter or number as the first.For the third card, 45 out of the remaining 50 cards will be available, removing the six cards whose letters or numbers have already been chosen.For the fourth card, 42 out of the remaining 49 cards will be available, removing the nine cards whose letters or numbers have already been chosen.Hence the probability is given by:
p = 48/51 x 45/50 x 42/49 = 0.726.
0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).
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Solve for d.
19d -16d-d-d-1 = 12
Answer:
d = 13
Step-by-step explanation:
19d - 16d - d - d - 1 = 12
19d + (-16 - 1d - 1d) - 1 = 12
19d + (--18d) - 1 = 12
19d - 18d - 1 = 12
1d = 12 + 1
d = 13
Check:
19*13 - 16*13 - 13 - 13 - 1 = 12
247 - 208 - 26 - 1 = 12
39 - 27 = 12
Please help ASAP and explain the way to get the answer!
Answer:
860.9 m³
Step-by-step explanation:
We can obtain the volume of the composite figure by subtracting the volume of cylinder from the volume of cuboid.
Cuboid or rectangular prism:l = 10 m
w = 10 m
h = 12 m
[tex]\sf \boxed{\text{ \bf Volume of cuboid = l *w * h}}[/tex]
= 10 * 10 * 12
= 1200 m³
Cylinder:r = 3 m
h = height of the cuboid = 12 m
[tex]\sf \boxed{\text{\bf Volume of cylinder = $\pi r^2h$}}[/tex]
= 3.14 * 3 * 3 * 12
= 339.1 m³
Volume of composite figure = 1200 - 339.1
= 860.9 m³
What are the solutions to the equation x² = 169? select each correct answer. −84.5 negative 84.5 −13 negative 13 13 13 84.5
The correct answer is A. 13.
We have been given equation. Now, to find the value of x, we will take square root. So, solving the mathematical expression now -
x = √169
Taking square root to find the value of x
x = 13
Since the number is positive. the square root of the number will also be positive.
Hence, the solution to equation is A. 13.
Further to cross check, we can also square the resultant number.
On squaring the number 13 for validation of our result, we get 169. It is the same number as in mathematical expression provided to us. Thus, our resultant solution to equation is correct.
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The complete question is -
What are the solutions to the equation x² = 169? Choose all answers that are correct. A. 13 B. –13 C. 84.5 D. –84.5
Write a recursive formula for each sequence. 1,3,6,10, . . . . . . .
The recursive formula for the given sequence is a(n) = 2 a(n-1) - a(n-2) + 1
A recursive formula is an equation that express the nth term as a function of preceding term(s), i.e. as function of (n-1)th term, (n-2)th terms, and so on. Mathematically it can be written as:
a(n) = f(a(n-1), a(n-2), ..., a(1))
The given sequence: 1,3,6,10, . . .
Here a(1) = 1. Notice that:
a(2) = 3 = 1 + 2
a(3) = 6 = 3 + 3
a(4) = 10 = 6 + 4
Notice that the differences between terms increase by 1.
Further, we can write:
a(2) = 3 = 1 + (1 - 0) + 1
= a(1) + a(1) + 1
= 2a(1) + 1
a(3) = 6 = 3 + (3 -1) + 1
= a(2) + a(2) - a(1) + 1
= 2a(2) - a(1) + 1
a(4) = 10 = 6 + (6 - 3) + 1
= a(3) + a(3) - a(2) + 1
= 2 a(3) - a(2) + 1
We can continue this recursive pattern to find a(n),
a(n) = 2 a(n-1) - a(n-2) + 1
We can find next term for n = 5:
a(5) = 2a(4) - a(3) + 1
= 2. 10 - 6 + 1 = 15
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