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?

Answer:

Yes.

Step-by-step explanation:

(2, 3) means we'll let x be 2 and y be 3. Let's solve both equations first:

y = -2x + 7

3 = -2(2) + 7

3 = -4 + 7

:. 3 = 3

Okay, so one half is proven. Let's do the other half now.

y = x + 1

3 = 2 + 1

3 = 3

:. (2,3) is a solution to the system of equations.

1. Axis of symmetry : x= -5            2. Axis of symmetry : x =2

Vertex: (-5, 1)                                                  Vertex: (2, 8)
Domain: (-∞, ∞)                                                Domain  (-∞, ∞)
Ranges:  [1, ∞)                                                   Ranges (-∞, 8]

3. Axis of symmetry : x = 1                4. Axis of symmetry x = -4

Vertex (1, -1)                                                       Vertex = (-4 0)
Domain (-∞, ∞)                                                    Domain (-∞, ∞)
Ranges  [-1, +∞)                                               Ranges (-∞, 0]

For 4. y = -x² - 8x -16

Axis of symmetry

x = -b / (2a)

x = -(-8) / (2 × -1) = 8 / (-2) = -4

Vertex

y = -(-4)² - 8(-4) - 16

= -16 + 32 - 16

= 0  therefore Vertex is (-4, 0)

Therefore range function  (-∞, ∞)

The above answers are for the questions below as seen in the picture

1) y = x² + 10x + 26                    2. y = -2x² + 8x        3. y = x² - 2x

Axis of symmetry :

Vertex
Domain
Ranges

4. y = -x² - 8x -16

Find more exercises on finding Axis of symmetry;

https://brainly.com/question/29107199

#SPJ1

Answer: The height of the cone is [tex]12 \text{ units}.[/tex]

Step-by-step explanation:

We are given that [tex]L = \pi r \sqrt{r^2+h^2}.[/tex] Plugging in the given values of [tex]L[/tex] and [tex]r[/tex] yields:

[tex]65 \pi = 5 \pi \sqrt{25+h^2} \implies 13 = \sqrt{25+h^2}.[/tex]

Now, squaring each side of the equation, and then isolating [tex]h^2[/tex] gives us [tex]h^2=144[/tex], so [tex]\boxed{h=12}.[/tex] Note that [tex]h[/tex] cannot take any negative values because it is a side length.

The equation in the triangle to find x is x + 84 = 180.

Option B is the correct answer.

We have,

The sum of the angles in a triangle is 180.

And,

42 + 42 + x = 180

84 + x = 180

x = 180 - 84

x = 96

Thus,

The equation in the triangle to find x is x + 84 = 180.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

The volume of the container is 100 cubic inches.

The volume of a rectangular container is calculated by multiplying its base area by its height. Since the base of the container is square with an area of 25 square inches, the length of each side of the square base is the square root of 25, which is 5 inches.

Therefore, the volume of the container can be calculated as follows:

Volume = Base Area × Height

Volume = 25 square inches × 4 inches

Volume = 100 cubic inches

So, the volume of the container is 100 cubic inches.

To know more about volume visit,

https://brainly.com/question/1578538

#SPJ1

The solution set of f(x) > 0 is x ∈ (-2, 8).

To find the solution set of f(x) > 0, we need to first determine the critical values of x where f(x) changes sign.

Let's start by finding the domain of the function:

x² - 6x - 16 ≠ 0

We can solve for x by using the quadratic formula:

x = [6 ± √(6² + 4(16))]/2 = [6 ± √52]/2 = 3 ± √13

So the domain of f(x) is (-∞, 3 - √13) U (3 + √13, ∞).

Now let's factor the numerator and denominator of f(x):

f(x) = (x + 10)/[(x - 8)(x + 2)]

The critical points occur where the numerator or denominator of f(x) changes sign.

The numerator changes sign at x = -10, and the denominator changes sign at x = -2 and x = 8.

Learn more about domain of functions here: https://brainly.com/question/28934802

#SPJ1

The surface area of the triangular prism is 235 cm²

An equation is an expression that uses mathematical operations to show how numbers and variables are related to each other.

The surface area of a triangular prism is gotten by adding the individual area of each surface.

For the triangular prism shown:

Surface area = 2(1/2 * 10 cm * 12 cm) + (10 cm * 5 cm) + 2(13 cm * 5 cm) = 235 cm²

The surface area is 235 cm²

Find more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

D. 263 degrees

Step-by-step explanation:

We know that central angles are congruent to the arcs they encompass or intercept. So, if the minor arc is 97 degrees, and the total measure of a circle's arcs are 360 degrees, then the major arc is 263 degrees.

Therefore, the answer is D.

The sketch of the graph of y = 1/f(x) is added as an attachment

To find the function equation, we need to determine the factors of the equation based on the zeros of the function.

Since the zeros of the function are at x = -5, -1, and 4, the factors of the equation will be:

(x + 5), (x + 1), and (x - 4)

Multiplying these factors together gives us:

f(x) = a(x + 5)(x + 1)(x - 4)

To find the value of the constant term a, we can use the fact that the graph passes through the point (0, -4):

-4 = a(0 + 5)(0 + 1)(0 - 4)

-4 = -20a

So, we have

a = 1/5

Therefore, the function equation is:

f(x) = 1/5(x + 5)(x + 1)(x - 4)

For the graph of y = 1/f(x), we have

y = 5/[(x + 5)(x + 1)(x - 4)]

See attachment for the graph

Read more about functions at

https://brainly.com/question/28532394

#SPJ1

Answer:

24 + c = 40

C= Chau’s height

There is a 0.9830, or 98.30%, probability that the mean clock life will exceed 12.5 years.

Probability is a metric used to express the possibility or chance that a particular event will occur.

Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.

Probability is simply the possibility that something will happen. When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.

The study of events that fit into a probability distribution is known as statistics.

So, the likelihood that the average clock life would exceed 12.5 years:

This is the p-value of Z when X = 12.5 subtracted by 1.

So,

Z = X - μ/σ

Z = 12.5 - 14/.07071

Z = -2.12

Z = The pvalue for -2.12 is 0.0170.

1 - 0.0170 = 0.9830

The likelihood that the mean clock life will be longer than 12.5 years is 0.9830, or 98.30%.

Therefore, there is a 0.9830, or 98.30%, probability that the mean clock life will exceed 12.5 years.

Know more about probability here:

https://brainly.com/question/24756209

#SPJ1

Complete question:

A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 14 years with a variance of 25. If the claim is true, in a sample of 50 wall clocks, what is the probability that the mean clock life would be greater than 12.5 years? Round your answer to four decimal places.

25% percent of the females in Math town have brown eyes. To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes

what is percent  ?

A percent is a way of expressing a number as a fraction of 100. The symbol for percent is %, which means "per hundred".

In the given question,

Let's assume that there are 100 people in Math town.

60% of them are males, so there are 60 males and 40 females.

Out of the 60 males, 30% have brown eyes, so there are 18 males with brown eyes.

28% of the entire population have brown eyes, so there are 28 people with brown eyes.

To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes:

28 - 18 = 10

So, there are 10 females with brown eyes.

Out of the 40 females in Math town, what percentage have brown eyes?

10 brown-eyed females out of 40 females is:

10/40 = 0.25 or 25%

Therefore, 25% of the females in Math town have brown eyes.

To know more about percent , visit:

https://brainly.com/question/28670903

#SPJ1

The measure of the value of x in the circle given is calculated as equal to: x = 12.

A semicircle is a two-dimensional shape that is half of a circle, consisting of a curved boundary or arc and a diameter or straight line segment that connects the two endpoints of the arc. This is always equal to 180 degrees.

Therefore, we have the equation:

12x + 6 + 3x - 6 = 180

Combine like terms:

15x = 180

Divide both sides by 15

x = 180/15

x = 12

Learn more about a circle on:

https://brainly.com/question/28108430

#SPJ1

Answer:

answer int he photos

Step-by-step explanation:

Answer:

This is a product rule and probablity question.  b) 49/400

c) 169/400

Step-by-step explanation:

Given the function h(x) = -2√(x + 3) - 1, the statement that is true about h(x) include the following: B. the function is decreasing on the interval (-3, ∞).

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

For any given function, y = f(x), if the output value (range) is increasing when the input value (domain) is increased, then, the function is generally referred to as an increasing function.

By critically observing the graph of the given function, we can reasonably infer and logically deduce that it is decreasing over the interval (-3, ∞).

Read more on function here: brainly.com/question/9795474

#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 must be 46 chairs in each row and total number of chairs are 1058

To meet the given conditions, we need to find a number that has the following properties:

It should be divisible by 2, as there are an even number of chairs in each row.

It should be divisible by 23, as there are 23 rows of chairs.

It should be the same number in each row.

The smallest number that satisfies these conditions is 46, which is the least common multiple of 2 and 23.

So, we need to set up 46 chairs in each row.

The total number of chairs required will be:

Total number of chairs = 23 rows x 46 chairs per row = 1058 chairs

Hence, the total number of chairs are 1058

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

1. 9(18)^2=324 the first problem is that you multiply 9 by 18 twice then you add and you will get your answer

Therefore, a sharpening costs Dollar 1.85.

The US, Canada, Australia, and some nations in the Pacific, Caribbean, Southeast Asia, Africa, and South America all use the dollar as their primary unit of exchange. The word "$" is used to denote it.

Let's use $a for the sharpener's price. We can state that the price of a book is $a + 1.95 because it costs $1.95 more than a sharpening.

We are aware of the $26.10 total cost of 10 sharpeners and 2 books. This can be expressed as an equation:

10a + 2(a + 1.95) = 26.10

If we simplify this equation, we get:

12a + 3.90 = 26.10

3.90 less from each side results in:

12a = 22.20

By multiplying both sides by 12, you get:

a = 1.85

Therefore, a sharpening costs $1.85.

To know more about dollar visit:

brainly.com/question/28547396

#SPJ1

Answer:

D. 177 ft²

Step-by-step explanation:

the area of a circle is

pi×r²

r is the radius which is half of the diameter, of course.

so, in our case

area = pi×(15/2)² = pi×7.5² = pi×56.25 =

= 176.7145868... ft² ≈ 177 ft²

The expression for the velocity is v(t) = 30m/s

(a) x(t) = 30t

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = 30t, we have:

v(t) = d/dt (30t)

= 30

So the expression for velocity is v(t) = 30 m/s.

(b) x(t) = 7sin(30)

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = 7sin(30), we have:

v(t) = d/dt (7sin(30))

= 7cos(30) * d/dt (30t)

= 3.5cos(30)

So the expression for velocity is v(t) = 3.5cos(30) m/s.

(c) x(t) = ecos(701)

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = ecos(701), we have:

v(t) = d/dt (ecos(701))

= -e sin(701) * d/dt (701t)

= -701e sin(701t)

So the expression for velocity is v(t) = -701e sin(701t) m/s.

Learn more about differentiation here:

https://brainly.com/question/954654

#SPJ1

The equation simplifies to 14 = 14, which is a true statement.

In mathematics, an equation  is defined as a set of numbers that contains operations and may contain a variable. Equations are used to solve for these unknown variables  using various operations such as addition, subtraction, multiplication and division.

Replacing m by 4, we get:

m + 2 (m + 1) = 14

4 + 2 (4 + 1) = 14

4 + 2(5) = 14

4 + 10 = 14

14 = 14

The equation simplifies to 14 = 14, which is a true statement. Therefore, the given value 4 is a solution to Eq.

Learn more about Equations here

https://brainly.com/question/29657992

#SPJ1

The surface area of the composite solid is given as follows:

194 units squared.

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The prism in this problem is composed as follows:

Hence the surface area of the prism is given as follows:

S = 2(4 x 7 + 4 x 3 + 3 x 7) + 4 x 3 + 5² + 5 x 7

S = 194 units squared.

More can be learned about the surface area of a rectangular prism at https://brainly.com/question/1310421

#SPJ1

If the base diameter of the sawdust pile is 35 feet when the height is 30 feet, then when it is 40 feet high, the diameter will be 46.7 feet, while the volume will be 68,545.37 feet³.

The volume refers to the capacity of a three-dimensional object.

The formula for volume with diameter and height is V = πd²h/4.

Base diameter of the sawdust pile = 35 feet

Height = 30 feet

Base diameter of the sawdust pile when the height is 40 feet = 46.7 feet

(35/30 x 40)

Given height = 40 feet

Computed base diameter = 46.7 feet

Volume = πd²h/4

= 22/7 x 46.7² x 40/4

= 3.143 x 2,180.89 x 10

= 68,545.37 feet³

Learn more about the volume at https://brainly.com/question/27710307.

#SPJ1

In the first triangle, the angle x = 45°

In the second triangle, the angle y = 75°

In the second triangle, the angle x = 45°

To find the angles in the triangles, we proceed as folows.

a. In the first triangle, let the base angle to the left be p. We know that we have a parallelogram there.

Now, in the parallelogram,

102° + p = 180°sum of (interior angles of a parallelogram)

So, p = 180° - 102°

= 78°

Now, in the larger triangle,

x + p + 57° = 180° (sum of angles in a triangle)

Since p = 78°, we have that

x + 78° + 57° = 180°

x + 135° = 180°

x = 180° - 135°

= 45°

So, x = 45°

b. In figure 2, we have two isoceles triangles.

i. In the first triangle, both base angles are y.

So, y + y + 30° = 180° (sum of angles in atriangle)

2y + 30° = 180°

2y = 180° - 30°

2y = 150°

y = 150°/2

y = 75°

So, y = 75°

ii. In the second triangle also, both base angles are x and the other angle is a right angle which is 90°.

So, x + x + 90° = 180° (sum of angles in a triangle)

2x + 90° = 180°

2x = 180° - 90°

2x = 90°

x = 90°/2

x = 45°

So, x = 45°

Learn more about angles in a triangle here:

https://brainly.com/question/29403272

#SPJ1

Answer:

1/2 page per second

Step-by-step explanation:

5/10 ÷ 10/10 = .5/1 = .5 or 1/2 page per second.

Helping in the name of Jesus.

Using the given data we know that the sales revenue that Wright recognize on January 1, 2020, is $456108.

Net sales, as used in bookkeeping, accounting, and financial accounting, refer to operating revenues received by a business from the sale of its goods or provision of its services.

They are directly recorded as Sales or Net sales on the income statement and are also referred to as revenue.

The net sales formula is rather simple in profit and sales transactions: net sales = gross sales - (return values + discount losses + sales taxes + allowances).

So, the sales revenue in the given situation would be:

According to the provided data, the sales revenue will be determined as follows:

= Value of note × PVF of receivable

= $528000 × 0.8638

= $456108

Therefore, using the given data we know that the sales revenue that Wright recognize on January 1, 2020, is $456108.

Know more about sales revenue here:

https://brainly.com/question/29436143

#SPJ1

Correct question:

On January 1, 2021, Wright Transport sold four school buses to the Elmira School District. In exchange for the buses, Wright received a note requiring payment of $534,000 from Elmira on December 31, 2023. The effective interest rate is 6%. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.). How many sales revenue would Wright recognize on January 1, 2020, for this transaction?

The probability that the randomly selected person is taking a sunbath is 7/22.

Science uses a figure called the probability of occurrence to quantify how likely an event is to occur.

It is written as a number between 0 and 1, or between 0% and 100% when represented as a percentage.

The possibility of an event occurring increases as it gets higher.

So, the probability formula is:

P(E) = Favourable events/Total events

Now, insert values in the formula as follows:

P(E) = Favourable events/Total events

P(E) = 28/88

P(E) = 14/44

P(E) = 7/22

Therefore, the probability that the randomly selected person is taking a sunbath is 7/22.

Know more about probability here:

https://brainly.com/question/24756209

#SPJ1

Answer:

Yes

Step-by-step explanation:

(-2, 10)

x = -2

y = 10

y = -4x + 2

Substitute or plug in the x and y values

10 = -4(-2) + 2

Multiply(remember a negative times a negative is a positive)

10 = 8 + 2

Add

10 = 10

Because ten is equal to ten (-2, 10) is a solution for this part

Now take your next equation and repeat the same steps

y = -6x - 2

10 = -6(-2) - 2

10 = 12 -2

10 = 10

(-2, 10) is  a solution to this system of equations