Which statement is true about whether Z and B are independent events?
Z and B are independent events because P(Z∣B) = P(Z).
Z and B are independent events because P(Z∣B) = P(B).
Z and B are not independent events because P(Z∣B) ≠ P(Z).
Z and B are not independent events because P(Z∣B) ≠ P(B).
Answers
Answer:
Z and B are independent events because P(Z∣B) = P(Z).
Step-by-step explanation:
After a small online search, I've found a table to complete this problem, that we can see below.
For two events Z and B, we have:
P(Z|B) = probability of Z given that B
such that:
P(Z|B) = P(Z∩B)/P(B)
So, two events are independent if the outcome of one does not affect the outcome of the other.
So, if the probability of Z given B is different than P(Z) (the probability of event Z) means that the events are not independent.
So Z and B are independent if the probability of Z given B is equal to the probability of Z.
P(Z|B) = P(Z)
In the table we can see:
P(Z|B) will be equal to the quotient between all the cases of Z given B (126) and the total cases are given B (280)
P(Z|B) = 126/280 = 0.45
Similarly, we can find P(Z):
And P(Z) = 297/660 = 0.45
So we can see that:
P(Z|B) = P(Z)
Thus, B and Z are independent.
Related Questions
Now measure the lengths of the sides of polygon ABCD and tbe lengths of the sides of the translated images. Record the measurements in the table.
Answers
Answer:
3.16, 3.16, 3.16
3.16, 3.16, 3.16
1.41, 1.41, 1.41
3.16, 3.16, 3.16
Step-by-step explanation:
Answer:
Length Length Length
3.16 3.16 3.16
3.16 3.16 3.16
1.41 1.41 1.41
3.16 3.16 3.16
Step-by-step explanation:
A biased 3-coloured spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times. If you spin this spinner 1000 times, how many times do you expect it to land on Red?
Answers
Answer:
83 spins
Step-by-step explanation:
Number of red spins = n
Number of orange spins = 8n
Number of yellow spins = 3n
Total number of trials = 240
Total number of spins :
(n + 8n + 3n) = 240
12n = 240
n = 240 / 12
n = 20
Number of red spins = 20
(1000/240) * n
4.1666666 * 20
= 83.333
= 83 spins
art I) 69% 2
Amelia is 1.5 m tall. She is standing in front of a tree. Her friend places a
mirror on the ground and moves it until Amelia can see the top of the tree.
The mirror is 4 m from Amelia and 12 m from the tree. How tall is the tree?
a
Answers
Answer:
Step-by-step explanation:
this is a question about two similar triangles , one is from Amelia , the other is the tree.
1.5/4 = x/12
solve for x
4.5 = x
the tree is 4.5 meters tall
Please help me asap! I don’t understand
Answers
Answer:
18
Step-by-step explanation:
4*3 = 12
1/2 * 3 * 4 = 6
Area = 18
Step-by-step explanation:
Area = length x width
but oops there isn’t a length so we must use Pythagorean theorem
Pythagorean theorem: a^2 + b^2 = c^2 in this case we’re looking for side a
a^2 + 4^2 = 5^2
a^2 + 16 = 25
a^2 = 25 - 16
a^2 = 9
Then square root 9 = 3
so the length is 3
Then we can start solving for area!
Area = length x width
Area = 3 x 4
Area = 12
Now for the triangle
Area = 1/2 bh
Area = 1/2 (4)(3)
Area = 1/2 12
Area = 6
6 + 12 = 18
Explain how you can find the constant of proportionality from a graph representing a proportional relationship when it shows a point with an x - value of 1 and if it doesn't show an x - value of 1 .
Answers
tienees que fijartelos extrreemos
Choose ALL of the ordered pairs that are solutions to the equation.
5y = 2x - 7
a) (6, 0)
b) ( 7, 21)
c) (8, 18)
d) ( -3, 4)
Answers
b) ( 7, 21)
Step-by-step explanation:
5(7)=2(21)-7
35=42-7
35=35
Answer:
None of them
Step-by-step explanation:
a: 5*0=2*6-7 False
b: 5*21=2*7-7 False
c: 5*18=2*8-7 False
d: 5*4=2*-3-7 False
pls help and pls provide workings
Answers
(x-h)²+(y-k)²=r²
(3-h)²+(3-0)²=5²
h²-6h+9+9=25
h²-6h-7=0 —> (h-7)(h+1)=0
h=7 , h=-1
h=7 —> (x-h)²+y²=r² —> (x-7)²+y²=25 —>
x²-14x+49+y²=25 —> x²+y²-14x+24=0
h=–1 —> (x-h)²+y²=r² —> (x+1)²+y²=25 —>
x²+2x+1+y²=25 —> x²+y²+2x–24=0
I hope it helped you ^_^
Solve the system of equations.
6x – Зу = 3
-2x + y = 14
1.What number would you multiply the second equation
by in order to eliminate the x-terms when adding to the
first equation?
2.What number would you multiply the first equation by in
order to eliminate the y-terms when adding to the
second equation?
Answers
Answer:
1. Multiply by 3
2. Multiply by 1/3
Step-by-step explanation:
6x - 3y = 3
-2x + y = -14
1. In order to eliminate the x-terms, they would both have to equal the same number with opposite signs (positive and negative). Since we are only touching the second equation, how can we get from 2 to 6? We can multiply 2 by 3 to get to 6 (negative 6 in the end.) This would result as follows:
6x - 3y = 3
-6x + 3y = 42
2. In order to eliminate the y-terns through multiplying with the first equation, we have to figure out how to make 3y into 1y. We can do this by adding its reciprocal, 1/3. 1/3 × 3 = 1. This would result as follows:
2x - y = 1
help help help pls pls
Answers
Answer:
abcd is a quadrilateral so ,
a is ( 0,-5 )
b is ( 2,-5 )
c is ( 1,-7 )
and d is ( 0,-7 )
Please help me find this angle
Answers
Answer:
x = 78
Step-by-step explanation:
We can find angle y
D + B + y = 180 since the sum of the angles of a triangle are 180
31+47+ y =180
78+y = 180
y = 180 - 78
y = 102
x+y = 180 since they form a straight line
x + 102 = 180
x = 180-102
x = 78
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
we have to find the value of the x°=<GHC
In the triangle BDH,
<D=31°<B=47°we know that,
Sum of three angle of a triangle is 180°
According to the question,
<D+<B+<BHD=180°31°+47°+<BHD=180°78°+<BHD=180°<BHD=180°-78°<BHD=102°But,
<GHC and <BHD forms a straight line
so,
<GHC+<BHD=180°102°+x=180°x=180°-102°x=78°Therefore,
The value of x is 78°
Which are the solutions of x2 = -7x – 8?
Ž
17 7
4
+
17
4
-
글
그를
+
ZIA
+
V 17
4
4
7 - 17 7 + /17
-
-7 - V 17 -7 + v17 .
2
Answers
Answer:
( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
Step-by-step explanation:
x^2 = - 7x - 8
x^2 + 7x + 8 = 0
Here,
a = 1
b = 7
c = 8
D = b^2 - 4ac
= 7^2 - 4 ( 1 ) ( 8 )
= 49 - 32
D = 17
x = - b ± √D / 2a
= - 7 ± √17 / 2 ( 1 )
x = ( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
Find the distance between (-5,5) and (2,-2)
Answers
Answer:
The distance is 7[tex]\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{The formula for \underline{distance between} is: }\mathsf{\sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}}[/tex]
[tex]\large\textsf{Whereas }\mathsf{x_2}\large\textsf{ is }\mathsf{2}\large\textsf{ and }\mathsf{x_1}\large\textsf{ is }\mathsf{ -5}\\\\\large\textsf{And also }\mathsf{y_2}\large\textsf{ is }\mathsf{ -2}\large\textsf{ and }\mathsf{ y_1}\large\textsf{ is }\mathsf{5}[/tex]
[tex]\mathsf{\sqrt{(2 - -5)^2+ (-2 + 5)^2}}\\\mathsf{2 - -5}\\\mathsf{= 2 + 5}\\\mathsf{= \bf 7}\\\\\mathsf{-2 + 5}\\\mathsf{= \bf -7}\\\\\mathsf{= \sqrt{(7)^2+ (-7)^2}}\\\\\mathsf{7^2}\\\mathsf{= 7\times7}\\\mathsf{= \bf 49}\\\\\mathsf{(-7)^2}\\\mathsf{= -7\times-7}\\\mathsf{= \bf 49}\\\\\mathsf{= \sqrt{49 +49}}\\\\\mathsf{49+49}\\\mathsf{=\bf 98}[/tex]
[tex]\mathsf{= \sqrt{98}}\\\mathsf{= 7\sqrt{2}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf 7\sqrt{2}}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
if triangle 3 shows a 100 degree rotation of triangle 1 about point p what is the degree of intersection of lines m and n?
Answers
The given transformations are rigid transformations, such that
the image and the preimage have the same dimensions.
Correct responses:
The degree of the intersection of lines m and n is; 50°This image also shows two A. reflection about lines m and then line n. How can the angle between the lines be determined, and what is a reflection?Given;
The images of triangle 1 are; Triangle 2, and triangle 3
Taking the image of line m as line m, we have;
Required:
The degree of the intersection of lines m and n
Solution:
Triangle 2 is the reflection of triangle 1 across line m, and
triangle 3 is the reflection of triangle 2 across line n
The distance of triangles 1 and 2 from line m are equal
The distance of triangle 2 and 3 from line n are equal.
Whereby the degree of rotation of triangle 1 to triangle 2, θ₁ is
equal to the degree of rotation of triangle 2 to triangle 3, θ₂,
we have;
θ₁ = θ₂
100° = θ₁ + θ₂ = 2·θ₁
θ₁ = θ₂ = 100° ÷ 2 = 50°
The angle of rotation of line m to line n = Rotation of triangle 1 to triangle 2 = θ₁ = 50°
The degree of the intersection of lines m and n = 50°The transformation to give triangle 2 from triangle 1 is a reflection about line m.
Similarly, the transformation that gives triangle 3 from triangle 2 is a reflection about line n.
Therefore;
The image also shows two A. Reflections about line m and then line n.Learn more about rigid transformations here:
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What conclusion can be derived by comparing the central tendencies of the two data sets?
A: (7, 6, 3, 1, 6, 2, 4, 6, 3, 5;
B: {2, 2, 2, 3, 4, 5, 2, 8, 7, 6}
Answers
An automobile manufacturing plant produced vehicles today: were sedans, were trucks, and were motorcycles. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles. What is the probability that two motorcycles will be selected
Answers
Answer:
120 / 561
Step-by-step explanation:
An automobile manufacturing plant produced 34 vehicles today: 16 were motorcycles, 9 were trucks, and 9 were vans. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles.What is the probability that two motorcycles will be selected
16/34 X 15 X 33
Which function of x has the least value for they intercept?
Answers
Which rule is a recursive rule for the sequence 1, -6, 36, -216,...?
( I'll put the answers a screenshot )
PLZZ Help I've been stuck for so long
Answers
Answer:
The last answer
Step-by-step explanation:
We can check
For example,
a5=-6×a4
a5=-6×(-216)
a5=1296
What is the midline equation of the function h(x) = -4 sin (x- pi/4)
Answers
Answer:
[tex]y = \boxed0[/tex]
Step-by-step explanation:
we are given a sin function
[tex] \displaystyle h(x) = - 4 \sin(x -\pi /4) [/tex]
we want to figure out the midline of the function graphically The midline of a sinusoidal function is the horizontal line that passes exactly in the midline of its extreme value however since we a function recall that,
[tex] \displaystyle f(x) = a \sin(bx -c) + d[/tex]
where the midline is
[tex]y = d[/tex]to figure out the midline rewrite the function
[tex] \displaystyle h(x) = - 4 \sin(x -\pi /4) + 0[/tex]
therefore the midline is
[tex]y = \boxed0[/tex]
The iPod costs $200.00. If Alex did his jobs every week, then how long would it take him to earn $200.00??
Plz help I’m confused
Answers
Answer:
It would take him 5.9 weeks (rounded). basically almost 6 weeks
Step-by-step explanation:
he makes 6 dollars a week by walking the dog out. he earns 2$ every time he walks the dog out, and he does it 3 times, so 2 x 3 = 6
he makes another 10 dollars a week by babysitting. he earns 2.50$ per hour of babysitting, and he does it for 4 hours per week, so 2.50 x 4 = 10
he makes another 18$ dollars a week by mowing the lawn. he does this once a week. he gets 15$ dollars if he mows, and another 3$ if he pulls weeds. if he does both, he would get 15+3 = 18$ per week by mowing
so add the numbers 6, 10, and 18, and you get 34.
he makes 34 dollars a week
divide the number he wants to make by what he earns in a week to figure out how many weeks it would take.
he wants to get 200$, so the equation is
200 / 34 = 5.88
Its 5.9 rounded or 5.88 weeks exact.
Answer:
6 weeks
Step-by-step explanation:
Job 1:
2 x 3 = 6
$6 per week
Job 2:
2.50 x 4 = 10
$10 per week
Job 3:
15 + 3 = 18
$18 per week
6 + 10 + 18 = 34
$34 per week
200/34 = 5.88
53. A right triangle has a hypotenuse measuring 15 inches and one leg measuring 9 inches What is the length, in inches, of the other leg of the triangle?
A. 3
B.6
C. 10
D. 12
Answers
Answer:
D
Step-by-step explanation:
Pythagorean
[tex]x^{2} + 9^{2} = 15^{2}[/tex] (x>0)
=> [tex]x=\sqrt{15^{2}-9^{2} }[/tex] [tex]=12[/tex]
Let 0 be an acute angle of a right triangle. Evaluate the other five trigonometric functions of 0.
Answers
Answer:
sin θ = (√119)/12
tan θ = (√119)/5
csc θ = 12/(√119)
cot θ = 5/(√119)
Five trigonometric functions of θ are
sinθ = [tex]\frac{\sqrt{119} }{12}[/tex]cosθ = [tex]\frac{5}{12}[/tex]tanθ = [tex]\frac{\sqrt{119} }{5}[/tex]cosecθ = [tex]\frac{12}{\sqrt{119} }[/tex]secθ = [tex]\frac{12}{5}[/tex]cotθ = [tex]\frac{5}{\sqrt{119} }[/tex]
What is trigonometric functions?"The trigonometric functions of θ are functions of an angle. sine, cosine, and tangent are familiar trigonometric functions. The trigonometric functions relates the angles of a triangle to the length of its side."
Let θ be an acute angle of a right angle triangle
What is acute angle?"An acute angle ("acute" meaning "small") is an angle smaller than a right angle. The range of an acute angle is between 0 and 90 degrees."
What is right angled triangle?"A right angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle).
What is hypotenuse?"The side opposite the right angle is called the 'hypotenuse'. The hypotenuse is always the longest side. The sum of the other two interior angles is equal to 90°."
What is opposite side?"An 'opposite' side is the one across from a given angle."
What is adjacent side?"An 'adjacent' side is next to a given angle. We use special words to describe the sides of right triangles."
we have,
cosθ = [tex]\frac{5}{12}[/tex]
secθ = [tex]\frac{12}{5}[/tex]
Hypotenuse side = 12
Adjacent side = 5
∴ Opposite side = [tex]\sqrt{hyp^{2}-adj^{2} }[/tex]= [tex]\sqrt{12^{2}-5^{2} }[/tex] = [tex]\sqrt{119}[/tex]
sinθ = [tex]\frac{opp}{hyp}[/tex] = [tex]\frac{\sqrt{119} }{12}[/tex]
tanθ = [tex]\frac{opp}{adj}[/tex] = [tex]\frac{\sqrt{119} }{5}[/tex]
cosecθ = [tex]\frac{hyp}{opp}[/tex] = [tex]\frac{12}{\sqrt{119} }[/tex]
cotθ = [tex]\frac{adj}{opp}[/tex] = [tex]\frac{5}{\sqrt{119} }[/tex]
Learn more about trigonometric functions, acute angle and right angle triangle here
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#SPJ2
what is x: |3x-1| = 4
Answers
Step-by-step explanation:
here's the answer to your question
SOMEONE PLEASE HELP ME ASAP !!!
Mrs. Pregnals's biology classes are going on a field trip. She has them break into groups of three or four students in order to do labs. She has a total of 120 students and 32 total groups are formed.
If t represents the number of three person groups and frepresents the number of four person groups, then write a system of equations that models this situation.
How many four person groups are there? Only an algebraic solution will receive full credit.
PLEASE HELP !!!!
Answers
x + y = 32 (1)
3x + 4y = 120 (2)
x = 8; y = 24
Step-by-step explanation:
Total students = 120
Number of groups = 32
If the number of three person groups = x
Number of four person groups = y
write a system of equations that models this situation
x + y = 32 (1)
3x + 4y = 120 (2)
From (1)
x = 32 - y
Substitute x = 32 - y into (2)
3(32 - y) + 4y = 120
96 - 3y + 4y = 120
- 3y + 4y = 120 - 96
y = 24
Substitute y = 24 into (1)
x + y = 32
x + 24 = 32
x = 32 - 24
x = 8
x = 8; y = 24
зх:
90
Х
2х:
What is the value of x?
Answers
Answer:
60
Step-by-step explanation:
To get the value of x;
3x:90
(90/3) = 30
x = 30
To get the value of 2x;
(2×X);
2 × 30
=60
Solve for x. 4/3 = 24/x
Help me please!!
Answers
First cross multiply 4/3=24/x to get 4x= 3*24
Then simplify: 4x=72; x=18
Determine which quadratic equations have
2 real solutions. Select two that apply.
Answers
Answer:
A & D
First and last
Step-by-step explanation:
Kasey has three pieces of wood that measure 9 inches, 12 inches, and 21 inches. Can she make a right triangle
with the three pieces of wood (without cutting or overlapping)?
Answers
Answer: No
Step-by-step explanation:
Add 2 sides together. If the sum of greater than the length of the 3rd side for all 3 options it can form a right triangle if it doesn’t than it can’t:
9 + 12 = 21 which is not greater than the 3rd side length of 21 so this cannot form a right triangle.
PLS HELP!!! The problem is in the photo attached
Answers
Answer:
The answer is C!
Step-by-step explanation:
Answer:
D
NOTE: the answer "C" is NOT correct... see the image the green is "C" the purple is "D"
Step-by-step explanation:
Titus works at a hotel. Part of his job is to keep the complimentary pitcher of water at least half full and always with ice. When he starts his shift, the water level shows 8 gallons, or 128 cups of water. As the shift progresses, he records the level of the water every 10 minutes. After 2 hours, he uses a regression calculator to compute an equation for the decrease in water. His equation is W –0.414t + 129.549, where t is the number of minutes and W is the level of water. According to the equation, after about how many minutes would the water level be less than or equal to 64 cups?
Answers
Answer:
Step-by-step explanation:
If we are looking for how long it will take the level to be less than or equal to 64 cups, we are solving an inequality as opposed to an equation. It would look like this:
-.414t + 129.549 ≤ 64 We subtract 129.549 from both sides to get
-.414t ≤ -65.549 and then divide by -.414. But because we are dividing by a negative number we need to change the way the inequality is pointing:
t ≥ 158.3 minutes which is about 2.6 hours
Answer:
t ≥ 158.33, or rounded, t ≥ 160.
Explanation:
The equation we're given is
W = -0.414t + 129.549, which an be written as
-0.414t + 129.549 = W.
We are asked to find the amount of time it would take for the water level to be less than or equal to 64 cups. Plugging this information in, we have:
-0.414t + 129.549 ≤ 64
To solve this, we first cancel 129.549 by subtracting from both sides:
-0.414t + 129.549 - 129.549 ≤ 64 - 129.549
-0.414t ≤ -65.549
Now divide both sides by -0.414:
-0.414t/-0.414 ≤ -65.549/-0.414
t ≥ 158.33
(When we multiply or divide both sides of an inequality by a negative number, we must flip the inequality symbol)
Can someone help me with this math homework please!
Answers
Answer:
X1 = 2 Y1 = -5
Step-by-step explanation:
math simple slope
