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).
Answer:
Z and B are independent events because P(Z∣B) = P(Z).
Step-by-step explanation:
Z and B are independent events
When Z and B are independent events then
P(Z and B) = P(Z) * P(B)
P(Z∣B)= [tex]\frac{P(Z and B)}{P(B)}[/tex]
P(Z∣B)= [tex]\frac{P(Z)*P(B)}{P(B)}[/tex]
We cancel out P(B) on both sides
P(Z|B) = P(Z)
The table below shows the surface area y in square inches, of a shrinking puddle in x hours
Time (x) (hours) 2 5 8 11
Surface area (y) 25 15 9 2
(Square inches)
Part a- what is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface are puddle. [choose the value of the correlation coefficient from -1,-0.99,-0.5,-0.02]
Part b - what is the value of the slope of the graph of surface area versus time between 5 and 8 hours and what does the slope represent?
Part c- does the data in the table represent correlation or causation?
Answer:
Step-by-step explanation:
Given is a table showing the surface area y in square inches, of a shrinking puddle in x hours
x y
2 25
5 15
8 9
11 2
r -0.993835256
Hence correlation coefficient is option B) -0.99
Part b:
Time Sur area
x y
2 25
5 15
8 9
11 2
r -0.993835256
slope -0.395083406
Intercept 11.53731343
slope =-0.395
Between 5 and 8, slope = [tex]\frac{change in y}{change in x} \\=\frac{9-15}{8-5} \\=-2[/tex]
Slope represents the change of y with respect to 1 unit change in x.
Part c:
Yes correlation strong and negative.
Find the value of each variable. Please help me!!
The sum of a number and -20 is 40.What is the number?
sum means addition
so x +-20 = 40
x = 40 +20 = 60
x=60
if BD is the midsegment and BD is parallel to to AE, then value of AE is
28.
56.
112.
None of the choices are correct.
A wheel makes 5 13/16 revolutions per minute. If it rotates for 76 minutes, how many revolutions does it make?
multiply 5 13/16 by 76
5 13/16 * 76 = 441 3/4 revolutions
y varies inversely with x k = 0.6 What is the value of x when y is 0.6? A. x = 0.36 B. x = 1 C. x = 3.6 D. x = 10
Answer:
.
Step-by-step explanation:
.
A line segment that goes from one side of the circle to the other side of the circle and doesn’t go through the center is
Answer:
A line segment that goes from one side of the circle to the other side of the circle and doesn’t go through the center is called chord of the circle.
Step-by-step explanation:
Consider the provided information.
It is given that the line segment goes from one side of the circle to the other side of the circle and doesn’t go through the center.
Diameter: A line segment goes from one side to another side of a circle passes through the center is called the diameter of the circle.
Chord: A line segment goes from one side to another side of a circle but do not passes through the center is called the chord of the circle.
For better understanding refer the attached figure:
Hence, A line segment that goes from one side of the circle to the other side of the circle and doesn’t go through the center is called chord of the circle.
find the x intercepts of the parabola with vertex (5,-12) and y intercept (0,63)
Final answer:
To find the x-intercepts of the parabola with vertex (5,-12) and y intercept (0,63), substitute the vertex values into the equation of the parabola and find the value of the constant. Then, substitute the value of the constant back into the equation and solve for x to find the x-intercepts. The x-intercepts of the parabola are x = 3 and x = 7.
Explanation:
To find the x-intercepts of the parabola with vertex (5,-12) and y-intercept (0,63), we need to find the values of x when y is equal to zero. Since the vertex of the parabola is (5,-12), the equation of the parabola can be written as[tex]y = a(x-5)^2 - 12.[/tex] To find the value of a, we can use the y-intercept (0,63) by substituting the values of x and y into the equation.
[tex]63 = a(0-5)^2 - 12[/tex]
63 = 25a - 12
25a = 75
a = 3
Now that we have the value of a, we can substitute it back into the equation and solve for the x-intercepts:
[tex]0 = 3(x-5)^2 - 12[/tex]
[tex]3(x-5)^2 = 12[/tex]
[tex](x-5)^2 = 4[/tex]
x-5 = ±2
x = 5 ± 2
Therefore, the x-intercepts of the parabola are x = 3 and x = 7.
Add 2 then add 4! I dont get it at all plz help!
How do you find common factors
To find common factors between numbers, list all factors of each number and identify numbers that are in both lists. When multiplying fractions, multiply numerators and denominators then simplify by common factors. Multiplying both sides by the same factor can help in solving equations with fractions.
Explanation:To find common factors between two or more numbers, you first list out all the factors of each number. Factors are numbers that divide into the original number without leaving a remainder. For instance, if we are looking for common factors of 8 and 12, we list their factors as follows: the factors of 8 are 1, 2, 4, and 8, and the factors of 12 are 1, 2, 3, 4, 6, and 12. After listing out the factors, you look for numbers that appear in both lists. In this example, the common factors of 8 and 12 are 1, 2, and 4.
Another approach mentioned involves multiplying both sides by the same factor to make both sides integers when working with equations. This can be useful when seeking to simplify fractions or solve equations with fractional components.
It is also important to recognize that while multiplying fractions, we multiply the numerators together and the denominators together. Simplifying the result by common factors as needed helps in reducing fractions to their simplest form. For example, if we multiply ½ by ¾, we get a result of ¼ (numerator 1x3=3, denominator 2x4=8) which we can simplify to ¾ by dividing both numerator and denominator by the common factor 3.
A soccer team is having a car wash.the team spent $55 on supplies.they earned $275 including tips.The teams profit is the amount the team made after paying for supplies.Write a sum of integers that repersents the teams profit.
You have $5. If candy bars cost $0.75, what is the greatest number of candy bars you can buy
Adam is going to cook a turkey for 14 people and wants to allow ¾ lb of turkey for each person.
1lb = 450 g
How much would a turkey cost for 14 people?
Six nickel is what Percent of a dollar
The standard error of the estimate, sest, is essentially the
A trinomial that contains the variable k the coefficient of the second degree term is 1, the coefficient of the first degree term is -7 and the constant term is -15 how would you write this?
in a grocery store steak cost $3.85 per pound if you buy a three pound steak and pay for it with a $20 bill how much change will you get
The change to be recieved is equal to $8.45
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: The price per steak is given as $3.85 per pound.
Thus 3 pound of steak will cost 3×3.85=$11.55
Therefore the change to be recieved is =20-11.55
=$8.45
Hence, The change to be recieved is equal to $8.45
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Paula is given a litre of water during her fitness assessment at the gym she drinks 375 milliliters of water how much is left
If 5(3x-7)=20, then what is 6x-8
5(3x-7) = 20
15x-35 = 20
15x = 55
x = 3.666666
so 6(3.666666) -8 = 13.99999 round to 14
Suppose f⃗ (x,y,z)=⟨x,y,4z⟩f→(x,y,z)=⟨x,y,4z⟩. let w be the solid bounded by the paraboloid z=x2+y 2 z=x2+y2 and the plane z=9.z=9. let ss be the closed boundary of ww oriented outward. (a) use the divergence theorem to find the flux of f⃗ f→ through s.
To find the flux of a vector field through a closed boundary using the divergence theorem, calculate the divergence of the vector field and evaluate the triple integral of the divergence over the solid bounded by the boundary. In this case, the flux is 3 times the volume of the solid.
Explanation:The student is asking how to use the divergence theorem to find the flux of a vector field through a closed boundary. In this case, the vector field is defined as f(x, y, z) = ⟨x, y, 4z⟩ and the closed boundary is a solid bounded by the paraboloid z = x^2 + y^2 and the plane z = 9.
To use the divergence theorem, we need to calculate the divergence of the vector field, which is the sum of the partial derivatives of f with respect to each variable. In this case, the divergence is 3.
Then, we can use the divergence theorem to find the flux through the closed boundary by evaluating the triple integral of the divergence over the solid bounded by the paraboloid and the plane. In this case, the flux is 3 times the volume of the solid.
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The flux of [tex]\(\vec{F}\)[/tex] through S is 24π.
To apply the divergence theorem, we first compute the divergence of [tex]\(\vec{F}\)[/tex]:
[tex]\nabla \cdot \vec{F} = \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial y} (y) + \frac{\partial}{\partial z} (4z) = 1 + 1 + 4 = 6.[/tex]
The divergence theorem states that the flux of a vector field through a closed surface is equal to the triple integral of its divergence over the region enclosed by the surface.
Thus, we have:
[tex]\iint_S \vec{F} \cdot d\vec{A} = \iiint_W (\nabla \cdot \vec{F}) \, dV = \iiint_W 6 \, dV[/tex]
The region W is bounded below by the paraboloid [tex]\(z = x^2 + y^2\)[/tex], and above by the plane z = 4.
Converting to cylindrical coordinates, we have:
[tex]\iiint_W 6 \, dV = \int_0^{2\pi} \int_0^2 \int_{r^2}^4 6 \cdot r \, dz \, dr \, d\theta = 24\pi.[/tex]
The revenue in dollars of a company that produces jeans can be modlelded by 2x^2+17x-175 the cost In dollars of producing the jeans can be modeled by 2x^2-3x-125 the number of jeans that have been sold is represented by x the profit is the difference between revenue and cost 20x-50 if 75 pairs of jeans are sold what's the company's profit
replace x with 75
20x-50 becomes
20(75)-50
20*75 = 1500-50 = 1450
the profit was $1450
Answer:
B
Step-by-step explanation:
The value of a car decreases by 20 percent per year. Mr. Sing purchases a $22,000 automobile. What is the value of the car at the end of the second year?
22,000 - 20% = 17,600
17,600 - 20% = 14,080
$14,080 at the end of the second year .
Which of the following represents the linear equation 3x =12 - 2y in standard form?
A: y=-2/3x-2
B: y=-2/3x-6
C: y=-3/2x+6
D: y= 2/3x-17/3
factor out the polynomial: 12x^2+26x+12
if f(x) = x^2 + 1 and g(x) = x - 4, which value is equivalent to ( f ○ g)
a. 37
b 97
c 126
d 606
(Compostition of Functions)
Chin Woo bought a home for $160,000. He put down 20%. The mortgage is a 8 1/2% for 25 years. His yearly payments are?
Chris can be paid in one of two ways. Plan A is a salary of $350 per month, plus a commission of 7% of a sales. pLan B is a salary of $436 per month, plus a commission of 5% of sales. For what amount of sales is Chris better off selecting plan A
If a wheel with a radius of 80 inches spins at a rate of 50 revolutions per minute, find the approximate linear velocity in miles per hour.
Please explain to me 1) the similarities/differences in the two lines, 2) how are the two graphs related to one another, and 3) how do the equations show this relationship for the following: