if p1, p2 and p3 are probabilities of surviving for years 1, 2 and 3 respectively, what is the cumulative probability of surviving for 3 years?

Answer:

his gives us that Chris is walking 69 feet per minute faster than Heidi.

Step-by-step explanation:

1 mile is equal to 5,280 feet, we can multiply 3 by 5,280 to find that Heidi is walking 15,840 feet per hour.

Next, we need to convert both speeds to feet per minute. Since there are 60 minutes in an hour, we can divide both speeds by 60 to convert them to feet per minute. This gives us that Heidi is walking 264 feet per minute and Chris is walking 333 feet per minute.

Finally, to find out how much faster Chris is walking than Heidi, we can subtract Heidi's speed in feet per minute from Chris's speed in feet per minute.

Jasmine sold the fidget spinner to Bryan for the cost of $5.55.

To find the cost that Jasmine sold the fidget spinner to Bryan for, we need to first find the amount of the markup by multiplying the original price by the markup percentage.

As per the question, the original price of the fidget spinner is $3, and the markup percentage is 850%, so the markup amount is :

$3 × 850% = $2.55.

Next, we need to add the markup amount to the original price to find the selling price. So, the selling price is :

$3 + $2.55 = $5.55.

Therefore, Bryan paid $5.55 for the fidget spinner that Jasmine had just sold him.

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The other two roots of the polynomial are x = (7 + √33)/4 and x = (7 - √33)/4.

A polynomial is an expression of one or more algebraic terms, each of which is composed of constants and/or variables raised to non-negative integer powers. A polynomial can be written in the form of an equation, where the coefficients of the terms form a sequence of numbers. Polynomials can also be expressed using a factored form, in which each of the terms is the product of a coefficient and a single variable or factor. Polynomials are commonly used to model real-world phenomena, such as the behavior of a system or process. The degree of a polynomial, which is the highest degree of the terms, determines the number of solutions it has. For example, a polynomial of degree two has two solutions while a polynomial of degree three has three solutions. The solutions of a polynomial are determined by solving the equation formed by the polynomial's terms.

Let us first rewrite the polynomial in a standard form:

2x^3 + 7x^2 + ax + 2 = 0
We can factor this polynomial using the Factor Theorem. The Factor Theorem states that if a is a root of a polynomial, then x-a is a factor of the polynomial.
Since x=-2 is a root of the polynomial, the factor (x+2) must be a factor of the polynomial.
Therefore, we can rewrite the polynomial as:
2x^3 + 7x^2 + ax + 2 = 2(x+2)(x^2 + bx + c)
Now, we can use the coefficients of the polynomial to solve for a, b and c.
Comparing the coefficients of the polynomial on both sides:
2 = 2c
7 = b
a = -2b-4c
Substituting the values of c and b in the equation for a, we get:
a = -2(b) - 4(2)
 = -2(7) - 8
 = -16
Therefore, the value of a is -16.
To find the other roots of the polynomial, we just need to solve the remaining factor (x^2 + bx + c) = 0.
Substituting the values of b and c, we get:
x^2 + 7x + 2 = 0
We can solve this equation using the Quadratic Formula:
x = [-b ± √(b^2 - 4ac)]/2a

Substituting the values of a, b and c, we get:
x = [-7 ± √(7^2 - 4(2)(2))]/2(-2)
 = [-7 ± √(49 - 16)]/-4
 = [-7 ± √33]/-4
Therefore, the other two roots of the polynomial are x = (7 + √33)/4 and x = (7 - √33)/4.

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Twice a number is equal to negative four :

                       2n = -4

Equation:

An equation is a formula that expresses equality by connecting two expressions with an equal sign '='. Equations and their cousins ​​in other languages ​​may have subtly different meanings. For example, in French an equation is defined as containing one or more variables, but in English any formula in its proper form consisting of two equations joined by an equal sign is an equation.

The equation resembles a weighted scale. When two bowls have the same weight (such as grain), the two weights balance the scale and are said to be equal. If you remove a certain amount of grain from one pan of the scale, you must remove the same amount of grain from the other pan to keep the scale balanced. More generally, the equation remains in equilibrium if the same operation is performed on both sides.

According to the question:

If you wanted to solve your equation:

   2x = -4

⇒ 2x/2 = -4/2

Divide both sides by 2

For getting the value of x only:

x = -2

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The inequality expression given by 4x + 6 + 2x < -2(3 + 3y) can be simplified and written as : x + y < - 2.

We have the following inequality -

4x + 6 + 2x < -2(3 + 3y)

We have -

4x + 6 + 2x < -2(3 + 3y)

4x + 6 + 2x < - 6 - 6y

6x + 6 + 6y + 6 < 0

x + y < - 2

Therefore, the inequality 4x + 6 + 2x < -2(3 + 3y) is equivalent to -

x + y < - 2.

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A polynomial function f is equal to x^3- 11x^2+41x- 51 of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

The degree of this polynomial is 3 and the leading coefficient is 1. Three zeros are 3, 4+i, 4-i bc, and a-bi if a+bi is zero, also known as the conjugate postulate. With this information, we can say that the factors are (x-3)(x-(4+i) )(x-(4-i)).

When we start multiplying, we group like this

(x-3)( (x-4) + i )( (x-4) -i )

Multiply the second two factors first.

(x-4)^2 - (i)^2 [This is the difference of squares (a+b)(a-b)].

We know that

i^2 = -1

= x^2 -4x -4x +16 - (-1)

= x^2-8x+16+1

= x^2 -8x +17

Don't forget (x-3).

Solving complete factors

(x-3)(x2-8x+17)

= x^3 -8x^2 +17x -3x^2 +24x -51

= x^3-11x^2+41x-51

This is the final equation of the polynomial.

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Answer:

Step-by-step explanation:

114048

Answer:

114048

Step-by-step explanation:

After solving we can conclude that (c) f(x) = -x is an odd function.

If -f(x) = f(-x), then a function f is said to be odd for all values of x.

When taking into account additive inverses, the functions even and odd are those that satisfy particular symmetry relations.

They are crucial to understanding power, the Fourier series, and mathematical analysis.

So, (a) f(x) = x³ + 5x² + x:

f(-x) = (-x)³ + 5(-x)² + (-x)

      = -x³ + 5x² - x

      = -(x³ - 5x² + x)

Neither even nor odd describe the function.

(b) f(x) = x² + x

f(-x) = (-x)² + (-x)

       = -(-x² + x)

Neither even nor odd describe the function.

(c) f(x) = -x

f(-x) = -(-x)

      = x

      = -f(x)

f(-x) = -f(x) makes the function odd.

Therefore, after solving we can conclude that (c) f(x) = -x is an odd function.

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Complete question:
Which of the following is an odd function?

(a) f(x) = x³ + 5x² + x

(b) f(x) = x² + x

(c) f(x) = -x

The student react that to ask for a cost-of-living increase to her stipend when a graduate student studying economics receives an annual stipend of $18,000. U.S. inflation is quite high.

Given that,

In the United States, a graduate student studying economics receives an annual stipend of $18,000. U.S. inflation is quite high.

We have to find how may the pupil respond.

We know that,

The term "inflation" describes an increase in the cost of any goods or services.

A history graduate who was living in the United States at the time was given an allowance of $18,000. However, the United States economy is negatively impacted by significant inflation. As a result, the price of goods and services that are available to the public rises quickly. Nowadays, everyone has to spend more on everything. As a result, the graduate student must request that the cost of living be added to the stipend because they must now spend more on living expenses.

Therefore, The student react that to ask for a cost-of-living increase to her stipend when a graduate student studying economics receives an annual stipend of $18,000. U.S. inflation is quite high.

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We can use polynomial division concept for the given question. The quotient for the polynomial division is (2x^2+11x+32).

Divide the first term of the dividend by the first term of the divisor to divide polynomials using long division. The quotient's initial term is this. Dividend is calculated by multiplying the new term by the divisor. The new dividend is this difference. A polynomial is divided by another polynomial in an arithmetic operation called division, usually with a lower degree than the dividend. A polynomial may or may not be produced when two polynomials are divided.

Take Dividend as (2x^3 + 5x^2 - x + 6)

Take Divisor denominator as (x-3)

By using long hand division technique,

    (2x^3+5x^2-x+6)/(x-3)

  ⇒(x-3)(2x^2+11x+32)/(x-3)

 ∴ The quotient for the given polynomial division is 2x^2+11x+32 and the    

   Remainder for the polynomial division is 90.

We can use polynomial division concept for the given question. The quotient for the polynomial division is (2x^2+11x+32).

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Answer:

x = 28

Step-by-step explanation:

We can write a proportion to solve

50 dollars       175 dollars

--------------- = --------------------

8 hours                  x hours

Using cross products

50x = 8 * 175

Divide each side by 50

x = 8 * 175 / 50

x = 28

Answer:

[tex]\huge\boxed{\sf 28 \ hours}[/tex]

Step-by-step explanation:

Given that,

$50 = 8 hours

Divide both sides by 50

$1 = 8/50 hours

$1 = 0.16 hours

Multiply 175 to both sides

$175 = 0.16*175 hours

[tex]\rule[225]{225}{2}[/tex]

In the right angle triangle UVW and with help of Pythagoras Theorem, the value of tan W, rounded to the closest hundredth, is 4.55.

According to Pythagoras's Theorem, the square of a right angle triangle's hypotenuse side is equal to the sum of the squares of its other two legs.

The opposite side is the 40 units, while the hypotenuse side is 41 units long in the right angle triangle. Thus, the value of base side W is,

[tex]VW^{2} + 40^{2}=41^2\\VW=\sqrt{41^2-40^2}\\VW= 9 units[/tex]

Now tan W=[tex]\frac{UV}{VW}[/tex]=[tex]\frac{41}{9}[/tex]=4.55;

In the right angle triangle UVW and with help of Pythagoras Theorem, the value of tan W, rounded to the closest hundredth, is 4.55.

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Answer:

Area is calculated by multiplying the length of a shape by its width.

Step-by-step explanation:

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area.

The amount of money each person get at the end of the summer is below;

You = $80

Kyra = $102

Paolo = $98

Total contribution = $22 + $18 + $0

= $40

Amount each person get = (Total earnings after investment - Total contribution) / 3

= ($280 - $40) / 3

= $240/3

= $80

Amount you get = Your contribution + Amount each person get

= 0 + 80

= $80

Amount Kyra get = Kyra contribution + Amount each person get

= $22 + $80

= $102

Amount Paolo get = Paolo contribution + Amount each person get

= $18 + $80

= $98

In conclusion, each person gets an equal amount including their invested money.

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The type of function that describes function f(x) is given as follows:

Rational function.

The four types of functions are given as follows:

These functions are identified as follows from their graphs:

From the graph given by the image at the end of the answer, the features are given as follows:

Hence the function is a rational function.

The graph of the function is given by the image shown at the end of the answer.

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Plot the Graph with time on X-axis and Cost on Y-axis.

It costs 12$ for 8,10,12 hours.

A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables (as a series of one or more points, lines, line segments, curves, or regions). In other words, depending on what you are attempting to prove or establish, values may be represented on a Cartesian coordinate system in a variety of ways. Discrete data would be shown on the graph as single points, such as the average price of vehicles from year to year. Since the calculation is only performed once each year, the data is discrete. The y axis would show the average price of cars for each year, while the x axis would indicate each year.

Given;

5$ for first hour;

10$ for up to 2 hours;

12$ for entire day.

G(t) = 5$ up to first hour, 10$ for up to 2 hours and 12$ for more than 2 hours.(So G is a function of t)

So for 0 hours,[tex]\frac{1}{2}[/tex] hours,1 hours it takes 5$;

and 10$ for 1[tex]\frac{3}{4}[/tex]hours, 2 hours

and 12$ for 5h,8h,12h.

Plot the Graph with time on X-axis and Cost on Y-axis.

It costs 12$ for 8,10,12 hours.

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Answer:

3w + 2

Step-by-step explanation:

3(w + 1) - 1

(3 · w) + (3 · 1) - 1

3w + 3 - 1

3w + 2

Answer:

A. One Solution

Step-by-step explanation:

To determine if a system of equations has no solutions, infinitely many solutions, or exactly one solution, we can solve the system by any method, such as elimination or substitution.

In this case, we can solve the system by elimination. Multiplying the first equation by -2 and adding it to the second equation, we get:

0x + 4y = -3

This equation tells us that y must be equal to -3/4, but we still need to check if this value of y satisfies the original equations. Substituting -3/4 for y in the first equation, we get:

2x + (-3/4) = 7

Solving this equation for x, we get x = 5/4. Substituting this value of x and -3/4 for y in the second equation, we get:

-2(5/4) + 2(-3/4) = -5

which simplifies to:

-5/2 + (-3/2) = -5

This equation is true, so the solution of the system is x = 5/4 and y = -3/4. Since the system has a unique solution, the answer is (A) One Solution.

The balance sheet that correctly represents the engineer's income, expenses and balance is illustrated below.

We should know that a balance sheet is a summary of assets and liabilities and income and expenses of a  legal person. We are told that the balance sheet shows a bi-weekly net pay.

This implies that a month has two bi-weeks, therefore every income and expense is multiplied by 2 to get the following figures.

Income                                             Amount

Bi-weekly income                          $2,175.25

Total Monthly Income                   $4,350.50

Expenses                 Percent                              Amount

Housing                        35%                                $1,522.68

Food/Household          10%                               $435.05

Savings                         10%                                $435.05

Transportation              15%                                $652.58

Debt                              5%                                   $217.53

Entertainment               6%                                   $261.03

Medical/Personal Care 5%                                  $217.53

Giving                             5%                                 $217.53

Clothing                         4%                                  $174.02

Miscellaneous               5%                                 $217.53

                                                                          $4,350.50

Balance

Income $4,350.50

Expenses $4,350.50

Balance $0

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Answer:

To find the asymptotes and the end behavior of the function f(x) = 4x / (x-16), we can first divide both the numerator and denominator by the highest common factor of 4x and (x-16). This gives us:

f(x) = (4x / 4x) / ((x-16) / 4x)

= 1 / ((x-16) / 4x)

Next, we can find the horizontal asymptotes by looking at the values of the function as x approaches positive and negative infinity. When x approaches positive infinity, the denominator of the function approaches 0, so the function approaches 1 / 0, which is undefined. Therefore, the function does not have a horizontal asymptote as x approaches positive infinity.

When x approaches negative infinity, the denominator of the function approaches -16 / -infinity, which is 0. Therefore, the function approaches 1 / 0, which is undefined. Therefore, the function does not have a horizontal asymptote as x approaches negative infinity.

Next, we can find the vertical asymptotes by setting the denominator of the function equal to 0 and solving for x. In this case, the denominator is (x-16) / 4x, so we can set each factor equal to 0 and solve for x:

x-16 = 0

x = 16

4x = 0

x = 0

Therefore, the function has two vertical asymptotes at x = 0 and x = 16.

Step-by-step explanation:

The statement which is true about Data Visualization is:

a) Data presented in charts, graphs, and maps provides an accessible way to see and understand trends, patterns, and outliers.

Data Visualization:

Data visualization is the representation of data using common graphics such as charts, diagrams, infographics, and even animations. The visual representation of this information can communicate complex data relationships and data-driven insights in an easy-to-understand manner.

Data visualization can be used for many purposes, but it's important to note that it's not just for data teams. Executives also use it to teach organizational structure and hierarchy, and data analysts and data scientists use it to discover and explain patterns and trends. Harvard Business Review (link is outside IBM) categorizes data visualization into his four main objectives: idea generation, idea expression, visual discovery, and everyday data visibility.

Importance:

Data visualization provides a quick and effective way to communicate information in a universal way using visual information. Practice also helps businesses understand the factors that influence customer behavior. Identify areas that need improvement or need more attention. Make data more memorable for stakeholders. Understand when and where to place specific products. Then, Predict sales volume.

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Average area of the cross section plane of the solid which lies between the two parallel planes is equal to 197.4square feet.

As given in the question,

Number of parallel planes = 2

Distance between two parallel planes = 22 feet

Volume of the solid is equal to 4343 cubic feet

Let 'x' be the average area of cross section of the solid lies between two parallel planes.

Average area of cross section of the solid lies between two parallel planes  = Volume of the solids / Distance between two parallel planes

⇒ x = 4343/22 square feet

⇒ x = 197.4 square feet

Therefore, the average area of the cross section of the solid lies between two parallel plane is equal to 197.4 square feet.

The complete question is:

A solid lies between two parallel planes 22 feet apart and has a volume of 4343 cubic feet. What is the average area of cross-sections of the solid by planes that lie between the given ones?

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To horizontally translate a function,

1)substitute 'x-h' for 'x' in the function.

2)The value for 'h' controls how much the graph shifts to the left or right

3)In our example, since h = -4, the graph shifts 4 units to the left

4)To vertically translate a function, add 'k' onto the end

5)The value for 'k' controls how much the graph shifts up or down

You can also perform both horizontal and vertical translations on a function at the same time!

Translation

The graph of a function can be moved up, down, left, or right by adding to or subtracting from the output or the input.

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The probability that the mean number of lightning strikes per square kilometer is less than 5 is 0.0016, when  open ground in a year has mean 6 and standard deviation 2.4.

It imply a quantity that falls somewhere between the values of the extreme members of a set in mathematics. There are different types of means, and how they are calculated relies on the relationship that is known about or is regarded as governing the other members.

Given,

Mean = 6

Standard deviation = 2.4

The value that has been reduced by the population mean and divided by the standard deviation is called the z-value.

z = x - mean/ standard deviation/√n

z = 5 - 6/2.4/√50

z = - 2.95

Using table A, calculate the corresponding probability;

= P(x <5)

= P( z < -2.95)

= 0.0016

The probability that the mean number of lightning strikes per square kilometer is less than 5 is 0.0016.

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The amount of money the carnival committee should expect to pay for prizes for the booth is 218.7 dollars.

Therefore, the answer is option C.

At a booth at the school carnival in past years, they've found that 22% of students win a stuffed toy ($3.60), 16% of students win a jump rope ($1.20), and 6% of students win a t-shirt ($7.90). The remaining students do not win a prize.

If 150 students play the game at the booth, the amount of money the carnival committee expect to pay for the prizes of the booth is as follows:

total student that partake = 150

number that win stuffed toy  = 22% of 150

number that win stuffed toy = 33

number that win  jump rope = 16% of 150

number that win  jump rope = 24

number that win  t-shirt = 6% of 150

number that win  t-shirt = 9

Therefore,

prizes for those that win stuffed toy = 33 × 3.60 = 118.8 dollars

prizes for those that win jump rope = 24 × 1.20 = 28.8 dollars

prizes for those that win t-shirt = 9 × 7.90 = 71.1 dollars

Hence,

total amount the committee is expected to pay for prizes = 118.8 + 28.8 + 71.1 = 218.7 dollars

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The sequence's average difference is 12.5.

According to the given information

The sum of an arithmetic sequence's second and third terms is 27.

The combination of the fourth and fifth terms is 77.

We must ascertain,

Let d represent the sequence's common difference.

The arithmetic series' second term is,

Second term = a + d

The arithmetic series' third term is as follows:

Third term = a + 2d

The second and third terms in the sequence add up to 27, thus.

Second term + third term = 27

a + d  + a + 2d  = 27

2a + 3d = 27

The arithmetic series' fourth term is,

Fourth term = a + 3d

The fifth term in the mathematical series is as follows:

Fifth term = a + 4d

The sequence's fourth and fifth terms add up to 77

Fourth term + fifth term = 77

a + 3d + a + 4d = 77

2a + 7d = 77

After resolving the two equations,

2a + 3d = 27

2a + 7d = 77

Subtracting both the equations

2a + 3d - ( 2a + 7d ) = 27 - 77

2a + 3d - 2a - 7d = -50

-4d = -50

d = 12.5

The sequence's average difference is 12.5

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Answer:

All sum of Traingle Angle is 180°

180= 87+31+ Angle C

Angle C = 180 - (31+87)

Angle C = 62

Answer:

I guess this is the answer

Answer:

Step-by-step explanation:

(x+8)(x-4) = 0

x = -8

x = 4

Answer: 15,600 different choices for initials

Step-by-step explanation:

26 choices for the first, 25 for the second, and 24 for the third. When multipled, this is 15600.