Let A and B be two events such that
P(A) = 1/5 While P(A or B) = 1/2
Let P(B) = P. For what values of P
are A and B independent?​

It should be noted that f(x) is increasing on the intervals (-1/2, 0) and (0, ∞), and decreasing on the interval (-∞, -1/2).

The derivative of f(x) is denoted as:

f'(x) = 2x - 1 - 1/x

It should be noted that to determine the critical points, set f'(x) to equal 0 and solve for x:

2x - 1 - 1/x = 0

Multiplying by x gives:

2x^2 - x - 1 = 0

On the intervals (-1/2, 0) and (0, ∞), the function f(x) exhibits increasing behaviour; in (-∞, -1/2). it's decreasing.

Learn more about functions on

https://brainly.com/question/11624077

#SPJ1

The distance Ben travels to get to the park is approximately 2.21 times greater than the distance David travels. This is found by using the distance formula to calculate the distances each person travels and then comparing the results.

To solve this problem, we need to find the distance between each person's house and the park using the distance formula

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

For Ben

distance = √((-2 - 4)² + (-2 - 6)²) = √((-6)² + (-8)²) = √(100) = 10

For David

distance = √((-2 - (-7))² + (-2 - (-6))²) = √((5)² + (4)²) = √(41)

So the ratio of Ben's distance to David's distance is

10 / √(41) ≈ 2.21

Therefore, Ben's distance is about 2.21 times greater than David's distance.

To know more about distance:

https://brainly.com/question/30308375

#SPJ1

The volume of the composite solid is  452. 160 ft³

First, it is important to note that the formula for calculating the volume of a cone is expressed as;

V = πr²h/3

Such that the parameters of the formula are;

From the information given,

substitute the values

Volume = 3.14 × 6² × 12/3

Divide the values

Volume = 31.4 × 36 × 4

Multiply the values

Volume = 452. 160 ft³

Learn more about cones at: https://brainly.com/question/6613758

#SPJ1

The possible values for the perimeter of Rebecca’s garage door are 48 feet or 48 inches

What is meant by perimeter?

Perimeter is the total length of the boundary of a two-dimensional shape. It is the sum of the lengths of all sides of the shape. The perimeter is commonly used to measure the distance around an object or figure and is often used in geometry to calculate the area of a shape.

According to the given information

The perimeter of a rectangle is calculated by adding the four sides of the rectangle. The formula for the perimeter of a rectangle is given as P = 2 (Length + Width) 12.

Therefore, the possible values for the perimeter of Rebecca’s garage door are 48 feet or 48 inches

Complete question is

Rebecca found the length and width of the 6. garage door. She used the measurements to find the perimeter of the garage door. Which of the following could be the perimeter of Rebecca's garage door? F 48 square feet /G 48 square inches/ H 48 feet/ J 48 cubic feet​

To know more about perimeter visit

brainly.com/question/6465134

#SPJ1

The circumference of a circle with a radius of 4 is 8π.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The circumference of a circle is the distance around a circle or the length of a circle. It is expressed mathematically as;

C = 2πr

Where r is radius and π is constant pi.

Given that the radius of the circle is 4 units.

Plug into the above formula.

C = 2πr

C = 2 × π × 4

C = 8π

Therefore, the circumference is 8π.

Option C) 8π is the correct answer.

Learn more about circles here: https://brainly.com/question/20693416

#SPJ1

There are currently about 10,361,248 people requesting financial aid, which is an increase of 6.74% from ten years ago.

By reducing the financial barrier, it supports the advancement of your academic and professional ambitions.

Its current number of applications can be determined by multiplying 9,720,000 with 1.0674 (which equals a 6.74% increase)

If there were 9,720,000 people asking for financial help 10 years ago and there have been 6.74 times as many applicants since then. As a result, there are currently 10,361,248 applicants for financial aid, or 9,720,000 x 1.0674.

To know more about financial aid visit:

https://brainly.com/question/14143487

#SPJ1

Answer:

7

Step-by-step explanation:

Answer:

The equation of function g after horizontal compression by a factor of 3 is:

g(x) = 7(3x) + 1 = 21x + 1

To substitute a numerical value for k into the function equation, we need to know the value of k. It is not given in the question, so we cannot provide a numerical answer.

Step-by-step explanation:

When a function is horizontally compressed by a factor of k, we divide the input (x) by k to obtain the new input for the transformed function.

The equation for the horizontally compressed function is:

g(x) = f(x/k)

Substituting f(x) = 7x + 1, we get:

g(x) = 7(x/k) + 1

Simplifying, we get:

g(x) = (7/k)x + 1

Thus, the equation for the transformed function g is obtained by replacing k with the given compression factor.

For example, if the compression factor is 3, then:

g(x) = (7/3)x + 1

And to substitute a numerical value for k, we need to know the value of k. If k = 2, for example, then:

g(x) = (7/2)x + 1

The ratio of the volume of both spheres is: 1/(24√3)

The formula for the volume of a sphere is expressed as:

V = ⁴/₃πr³

where:

r is radius

V is volume

We are told that the radii of the two spheres have a ratio of 1:2√3. Thus:

Volume of sphere A/Volume of sphere B = (1:2√3)³

= 1/(24√3)

Read more about Volume of sphere at: https://brainly.com/question/10171109

#SPJ1

hi

First, dont keep the equation  this way.  

f(x) = 2 (x+2) +4x

f(x) = 2x+4+4x

f (x) =  6x+4

after :

x= 0        f(x) = 4

x= 2            f(x)= 16

x= 10           f(x) = 64

x = 30          f(x) = 94

Step-by-step explanation:

sin (pi/4)  = sqrt(2) / 2 = .707

  you either just know this after a time or you can use a calculator (in RADIAN mode)

Answer:

sin(π/4) = sin(45°) = 0.707106781186548 ≈ 0.707 (rounded to 3 decimal places)

Step-by-step explanation:

here are the steps:

Convert π/4 to degrees: π/4 * (180/π) = 45°

sin(45°) = opposite/hypotenuse

sin(45°) = opposite/hypotenuse = adjacent/hypotenuse = 1/√2

sin(45°) = 1/√2 * √2/√2 = √2/2

Therefore, sin(π/4) = sin(45°) = √2/2 ≈ 0.707 (rounded to 3 decimal places).

Yes, (3, 5) is a solution to this system of equations.

How do you calculate the equation system?

The system has a single solution if the m-values of the two equations differ. The system has no solution if the two equations have the same m-value but distinct b-values.

Substituting x = 3 and y = 5 into the equations, we get:

y = 5 (which is already given)

y = (-5/3)x + 10

y = (-5/3) * 3 + 10

y = -5 + 10

y = 5

Therefore, both equations are satisfied by the point (3, 5), making it a solution to the system of equations.

Yes, (3, 5) is a solution to this system of equations.

To know more about equations visit:-

brainly.com/question/10413253

#SPJ1

There are four significant digits in the number 9.15 x 10⁴.

The digits that provide the number with useful information are known as the important digits.

As they add to the value of the number in this instance, the numbers 9, 1, and 5 are all important.

The exponent, 4, just instructs us on how many places to relocate the decimal point, therefore it has no bearing on the number of significant digits.

Therefore, the number 9.15 x 10⁴ has four significant digits.

Learn more about Simplification here:

https://brainly.com/question/28996879

#SPJ1

Answer:0.67

Step-by-step explanation:

those attending the party ate 4 1/2 pounds of candy in total.

How to solve the question?

To solve this problem using an array model on graph paper, we can draw a rectangular array with 2 1/4 rows and 3 1/2 columns. Each cell in the array represents a 1/4 pound of candy. The total number of cells in the array will give us the total amount of candy eaten.

To start, we can divide each row into four equal parts to represent 1/4 pound of candy. We can also divide each column into two equal parts to represent 1/2 pound of candy. Then, we can shade in the cells that represent the amount of candy eaten.

Starting with the first row, we shade in two full rows and an additional half row, representing 2 1/2 bags of candy. Then, in the second row, we shade in two full columns and an additional half column, representing 2 1/4 bags of candy.

When we count the total number of shaded cells in the array, we see that there are 18 cells shaded. Each cell represents 1/4 pound of candy, so we can multiply 18 by 1/4 to get the total amount of candy eaten:

18 * 1/4 = 4 1/2 pounds

Therefore, those attending the party ate 4 1/2 pounds of candy in total.

To know more about graph visit :-

https://brainly.com/question/19040584

#SPJ1

The new mixture contains 34% peanuts.

The correct option is A

We have,

Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts.

First, Total weight = 4 kg + 12 kg = 16 kg

Now, Total weight in kilograms is =  (4 kg) (0.16) + (12 kg) (0.40)

= 0.64 kg + 4.80 kg

= 5.44 kg.

Now, the Percent of peanuts

= (Total amount of peanuts / Total weight) x 100%

= (5.44 kg / 16 kg) x 100

= 34%

Thus, the new mixture contains 34% peanuts.

Learn more about weighted averages here : brainly.com/question/18554478

#SPJ1

A function relating these variables is D(x) = 10 + 2x,

D(9) = 28, meaning after 9 hours of snowfall,

An independent variable is a variable that is manipulated or controlled by the researcher in an experiment to observe its effect on the dependent variable. It is the variable that is changed deliberately to see how it affects the outcome of the experiment.

The independent variable, x, represents the number of hours since snow began falling,

and the dependent variable is the total amount of snow on Jace's lawn because the amount of snow depends on the number of hours since it began to snow.

A function relating these variables is D(x) = 10 + 2x, where D(x) is the total amount of snow on Jace's lawn in inches after x hours of snowfall.

So, D(9) = 28, meaning after 9 hours of snowfall, Jace will have a total of 28 inches of snow on his lawn.

To know more about variable, visit:

https://brainly.com/question/28248724

#SPJ1

The characteristics of the above quadratic unction y=-0.8x^2 - 4x are given as follows.

The vertex is (5, -22).

The axis of symmetry is x = 5.

The function is increasing when x < 5 and decreasing when x > 5.

The x-intercepts are (-5, 0) and (0, 0).

The domain is all real numbers and positive when x < 0.

The range is (-∞, -22].

The function is negative when x > -5.

The  y-intercept is (0,0).

The function is negative when x is less than -5/2 and positive when x is greater than -5/2.

Learn more about Quadratic Functions;
https://brainly.com/question/27958964
#SPJ1

If the vector is drawn from (0,0) to (5, -1), the outcome or the required vector is drawn.

A mathematical concept known as a vector has both a magnitude and a direction. Physical quantities like force, velocity, and acceleration are represented by it. In the physical sciences, engineering, and computer graphics, vectors are frequently employed. They can also be used to represent abstract concepts like magnitude, directions, and other things.

Here in the question,

(0, 0) is the beginning position. There should be an arrow above each vector name listed below.

Ink a line beginning at (3, -1). A vector has an origin of (0,0) and a destination of (3, -1).

Put a line through points (2,2). The vector B has a start point of (0, 0) and an end point of (2, 2).

These two vectors add up to: a + b = (3-1) + (2,2) = (5,1) when combined.

Whatever order they are in, b + a = (2,2) + (3, -1) = (5,1) regardless.

Either way, the same conclusion is reached.

The terminal point of A + B is at (5, 1).

If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.

To know more about vector, visit:

brainly.com/question/12949818

#SPJ1

The vertical component of the particle's location, when its horizontal component is 2, is:

y = -1.25

To find the vertical component of the particle's location when its horizontal component is 2, we need to first find the value of t when x = 2.

Given the equation:

x = 3sin(t)

Substitute x with 2:

2 = 3sin(t)

Now, isolate t by dividing both sides by 3:

sin(t) = 2/3

Take the inverse sine (arcsin) of both sides:

t = arcsin(2/3)

Now, plug the value of t back into the y equation:

y = t - 4cos(t) + 1

y = arcsin(2/3) - 4cos(arcsin(2/3)) + 1

Using a calculator to find the approximate value of y, we get:

y ≈ -1.25

Therefore, the vertical component of the particle's location when its horizontal component is 2 is:

y = -1.25

Read more about vertical components here:

https://brainly.com/question/25854506
#SPJ1

Answer: The area of circle is 28.26 cm^2

Step-by-step explanation: As the diameter of the given circle is 6 cm, the radius of the same would be 3 cm.

Area of circle = pi r^2

And the value of pi is to be taken 3.14

The area of the given circle is 28.26cm^2.

second square

add up all the inches and youll see second had bigger number leading to the answer b

Applewood Farmstand sold 102 pieces of apples over the weekend.

Graph is a data structure which consists of nodes (vertices) that are connected with each other. Graphs are used to represent relationships between different objects, such as networks, social connections, and pathways. Graphs are useful for representing data as they can provide a visual representation that is easy to interpret, and can be used to analyse patterns in the data. Graphs can also be used to represent problems such as shortest path problems, and can be used to solve problems such as finding the most efficient route between two points.

The graph shows that apples accounted for 32% of the total fruit sales. To find the exact number of apples sold, we can calculate the following:

Apples = (320 pieces of fruit) x (0.32)

Apples = 102 pieces

Therefore, Applewood Farmstand sold 102 pieces of apples over the weekend.

To know more about graph click-
http://brainly.com/question/19040584
#SPJ1

Answer: i. y = 60÷5

Step-by-step explanation: If he has 60 sheets of paper and 5 notebooks, it would only make sense to divide the number of sheets by the number of notebooks to get the sum. Which is 12 btw! <33

If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.

A mathematical concept known as a vector has both a magnitude and a direction. Physical quantities like force, velocity, and acceleration are represented by it. In the physical sciences, engineering, and computer graphics, vectors are frequently employed. They can also be used to represent abstract concepts like magnitude, directions, and other things.

Here in the question,

(0, 0) is the beginning position. There should be an arrow above each vector name listed below.

Ink a line beginning at (3, -1). A vector has an origin of (0,0) and a destination of (3, -1).

Put a line through points (2,2). The vector B has a start point of (0, 0) and an end point of (2, 2).

These two vectors add up to: a + b = (3-1) + (2,2) = (5,1) when combined.

Whatever order they are in, b + a = (2,2) + (3, -1) = (5,1) regardless.

Either way, the same conclusion is reached.

The terminal point of A + B is at (5, 1).

If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.

To know more about vector, visit:

https://brainly.com/question/12949818

#SPJ1

The direct write-off method and the allowance method are two different ways of accounting for uncollectible accounts receivable.

The direct write-off method is a simple method of accounting for bad debts, where the uncollectible accounts receivable are written off as an expense at the time they are deemed uncollectible.

In contrast, the allowance method is a more complex method of accounting for bad debts, where the company estimates the amount of bad debt expense that it expects to incur over time and creates an allowance account to record this estimate.

The main difference between the two methods is the timing of the recognition of bad debt expense. Under the direct write-off method, bad debt expense is recognized only when an account is written off, whereas under the allowance method, bad debt expense is recognized in advance based on an estimate of the amount of bad debts.

The direct write-off method is not considered to follow generally accepted accounting principles (GAAP) because it violates the matching principle, which requires that expenses be matched with the revenues they generate in the same accounting period.

Find out more on the direct write-off method at https://brainly.com/question/24108628

#SPJ1

Answer:

It is not a function

Step-by-step explanation:

A function is a rule from x to y that applies to all elements of x. Every element of x should have one image only.

Here, element "1" has two images 3 and 7. Therefore it's not a function.