how factors and multiples realted

The cumulative distribution function (CDF) of U is also well known and is given by:

F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)

where γ is the lower incomplete gamma function.

What is the chi-squared distribution?

The chi-squared distribution is a continuous probability distribution that is widely used in statistics and other fields.

The random variable U = Y1^2 + Y2^2 has a well-known distribution called the chi-squared distribution with two degrees of freedom. The density function of U is given by:

[tex]f(u) = (1 / (2 \times \pi)) \times e^{(-u/2)} \times (u/2)^{(1/2 - 1)}[/tex]

where e is the base of the natural logarithm and π is the mathematical constant pi. This distribution has a positive support on the interval [0, +∞).

The cumulative distribution function (CDF) of U is also well known and is given by:

F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)

where γ is the lower incomplete gamma function.

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The values of a = 17 and b = - 56

that make the following piece wise defined function both continuous and differentiable everywhere.

A continuous function in mathematics is one that doesn't change value unexpectedly due to discontinuities, or breaks in the function's continuity. A continuous function in mathematics is a function that causes the value of the function to continuously vary as a result of a continuous variation of the argument, or a change without a leap. Thus, there aren't any discontinuities—rapid changes in value.

conditions are:

1.

f(x) is continuous if,

[tex]\lim_{x \to \ 5^{-}}f(x)[/tex] = [tex]\lim_{x \to \ 5^{+}}f(x)[/tex] = f(5)

2.

differentiable if,

[tex]\lim_{x \to \ 5^{-}}f^'(x)[/tex] = [tex]\lim_{x \to \ 5^{+}}f^'(x)[/tex]

for 1st condition:

⇒ [tex]\lim_{x \to \ 5^{-}}f(x) = \lim_{x \to \ 5^{+}}f(x)[/tex]

⇒ [tex]\lim_{x \to \ 5^{-}}(-3x -6) = \lim_{x \to \ 5^{+}}(-2x^2+ax+b)[/tex]

⇒ (-3 × (-5) - 6) = - 2(5)² + a(5) + b

⇒ - 21 = - 50 + 5a + b

⇒ 5a + b = 29 ................... (1)

For 2nd condition:

⇒ [tex]\lim_{x \to \ 5^{-}}f^'(x) = \lim_{x \to \ 5^{+}}f^'(x)[/tex]

⇒ [tex]\lim_{x \to \ 5^{-}} \frac{d}{dx} (-3x - 6) = \lim_{x \to \ 5^{+}} \frac{d}{dx}(-2x^2 + ax + b)[/tex]

⇒ - 3 = - 4x + a

⇒ - 3 = - 4 (5) + a

⇒ a = 17

Substitute a = 17 in equation (1) we get:

5(17) + b = 29

or, b = - 56

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The complete question is as follows:

[tex]V= [0,16] \int\limits {4y^2 \sqrt{(256 - y^2)} } \, dy[/tex] would be the integral that gives the volume of the solid.

What is Disk method of integration?

Disc integration is a method for estimating the volume of a solid of revolution of a solid-state material when integrating along an axis "parallel" to the axis of revolution in integral calculus.

The volume of the solid can be found using the disk method of integration. In this method, we consider thin slices of the solid perpendicular to the x-axis, each of which is a disk with a square cross-section.

The volume of each slice is equal to the product of the area of its cross-section and its thickness, which is equal to the difference in x-coordinates between the top and bottom of the slice.

Let's call the top-right corner of the square cross-section (x, y, z). We k[tex]x^2 + y^2 = 256[/tex]

And we also know that the side length of the square is equal to 2y. So, the area of the cross-section is equal to [tex](2y)^2 = 4y^2.[/tex] The volume of the slice is equal to [tex]4y^2 dx.[/tex]

Since the semicircle is centered at the origin, the value of y ranges from 0 to 16.

The value of x ranges from 0 to the square root of [tex]256 - y^2.[/tex]Using these ranges, the volume of the solid can be calculated as follows:

[tex]V=\int\limits {[0,16] 4y^2 \sqrt{(256 - y^2)} } \, dy\\V= [0,16] \int\limits {4y^2 \sqrt{(256 - y^2)} } \, dy[/tex]

This is the integral that gives the volume of the solid.

Therefore, [tex]V= [0,16] \int\limits {4y^2 \sqrt{(256 - y^2)} } \, dy[/tex] would be the integral that gives the volume of the solid.

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Answer:

55%

Step-by-step explanation:

To find the percentage of juveniles in the local deer population, we need to calculate the proportion of juveniles in the total population and convert it to a percentage.

First, find the total number of deer in the population by adding the number of juveniles and adults:

110 juveniles + 90 adults = 200 deer

Next, divide the number of juveniles by the total number of deer and multiply by 100 to convert to a percentage:

110 juveniles / 200 deer * 100 = 55%

Therefore, 55% of the local deer population were juveniles.

In response to the query, x is equal to 60°, 120°, 240°, and 300°. These four options are the answer to the equation.

A mathematical equation is a statement that two amount or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. An equation is applied when several or more factors must be considered jointly in order to understand or explain the whole situation.

This equation can be solved using the trigonometric identity:

[tex]sinx = \sqrt{ (1 - cos^2x)}[/tex]

This identity can be used as a substitution in the equation:

5 sinx - 5 cosx = 2

5 [tex]\sqrt{(1 - cos^2x) }[/tex] - 5 cosx = 2

5 sqrt[tex](1 - cos^2x)[/tex]) = 7 + 5 cosx

Squaring both sides:

25([tex]1 - cos^2x[/tex]) = 49 + 70 cosx + 25 [tex]cos^2x[/tex]

25 - 25 [tex]cos^2x[/tex] = 49 + 70 cosx + 25 [tex]cos^2x[/tex]

0 = 74 + 45 cosx

45 cosx = -74

cosx = -74/45 = -2/3

The inverted cosine function can be used to determine that x = cos-1(-2/3). x must be within the range of 0° to 360°, hence x must be 300°.

5 sin - 5 cos - 5(-1/2) = 5 sqrt(3)/2 + 5/2 = 2 + 2.5 = 2.5

Since the left side of the equation is not equal to 2, x = 300° is not a solution to the equation.

We can repeat this process for the other solutions to the equation:

x = 60°, x = 120°, x = 240°, and x = 300°

These are the four solutions to the equation for 0° <= x < 360°.

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Step-by-step explanation:

mortgages, lines of credit, checking and savings accounts, auto loans and the convenience of electronic banking and Automated Teller Machines (ATMs)

Step-by-step explanation:

Banks and credit unions offer a variety of financial services, including:

Checking and savings accounts

Personal loans

Mortgages

Credit cards

Investment products (e.g. mutual funds, individual retirement accounts (IRAs))

Foreign currency exchange

Online and mobile banking

Wire transfers

Automated teller machines (ATMs)

Insurance products (e.g. life, auto, homeowners)

Wealth management services

Small business banking services.

Note that the exact services offered may vary depending on the institution.

Answer:

I inch = 7.2 miles

Step-by-step explanation:

Proportion method is applied:

                     1.5 inches on a map = 10.8 miles of actual distance

                  ∴ 1 inches on the map = x miles of the actual distance

Cross-multiplication is applied:

(1.5 inches)(x miles) = (1 inch)(10.8 miles)

x needs to be isolated and made the subject of the equation:

x miles = [tex]\frac{(1 inch)(10.8 miles)}{1,5 inches}[/tex]

Inches in the numerator and denominator will cancel eachother out:

x miles = [tex]\frac{10.8 miles}{1.5}[/tex]

         x miles = 7.2 miles

∴ Scale on the map:

                  1 inch = 7.2 miles

The probability that the discrete random variable x takes a value less than or equal to 50 is 0.50, since F(50) = 50/100 = 0.50.

F(x) = x/100

Then, the probability that x takes a value less than or equal to 50 is 0.50, since

F(50) = 50/100 = 0.50

The cumulative distribution function (CDF) of a random variable is a function that gives the probability that the random variable is less than or equal to a certain value. In this case, the CDF of the random variable x is given by F(x) = x/100.

Therefore, to find the probability that x takes a value less than or equal to 50, we simply need to evaluate the CDF at x = 50. This is done by substituting 50 into the CDF, which gives us F(50) = 50/100 = 0.50. This means that the probability that x takes a value less than or equal to 50 is 0.50.

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Note that a system of two linear inequalities in two variables is made up of at least two inequalities in the same variables.

Consider the following scenarios: highway speed restrictions, minimum credit card payments, the quantity of text messages you may send each month from your cell phone, and the time it will take to commute from home to school.

All of these may be expressed mathematically as inequalities. A linear inequality's solution is the ordered pair that is a resolution to all inequalities in the system, and the graph of the linear inequality is the graph of all system solutions.

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Answer:

not sure but slope doesn't belong

Step-by-step explanation:

The choices if multiplied by √36 would result in an irrational number are

3.454545... and 2.828427... the correct options are A and D.

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Rational numbers are numbers which can be written in the form of \dfrac{a}{b} where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.

Irrational numbers are those real numbers which are not rational numbers.

Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

Given;

The number is multiplied by √36

√36=6

3.454545*6=20.72727

-5*6=-30

3/4*6=9/2

2.828427*6=16.970562

√18*6=  6√18

Therefore, the irrational numbers will be 3.454545... and  2.828427...

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Before any taxes, deductions, and other adjustments, she earns $98.40 per week.

Gross pay refers to the total amount of money an employee earns before any deductions or taxes are taken out. It is the total amount of money earned by an employee for the hours worked, including any overtime or bonuses.

here, we have,

To calculate Talia's gross pay for a week, we need to know how many hours she works per day and her pay rate.

You've provided that information:

Talia works 6 hours per day on Fridays and Saturdays each week.

Her pay rate is $8.20 per hour.

First, we need to find out how many hours she works a week. As she works 6 hours on Friday and 6 hours on Saturday, the total hours she works in a week is 6 hours/day x 2 days/week = 12 hours/week.

Next, we need to multiply her hourly rate by the number of hours she works per week to find her gross pay. Her pay rate is $8.20/hour and she works 12 hours/week, so her gross pay is:

$8.20/hour x 12 hours/week = $98.40/week

So, Talia's gross pay for a week is $98.40.

Therefore, before any taxes, deductions, and other adjustments, she earns $98.40 per week.

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Answer:

y = 14x - 1

Step-by-step explanation:

By equation of the line, we mean the slope intercept form equation [tex]y=mx+b[/tex] where m is the slope and b is the y intercept. As a result, we are given the slope and the y intercept in the problem. So we can use this to write our equation

[tex]y=14x-1[/tex]

Hope this helps!

Answer:

A=F/M

Step-by-step explanation:

m=f/a ......,,, cross product

f= ma......,..., both sides divided by m

then the answer is a=f/m

Answer:

x=2

Step-by-step explanation:

4x+4=12

   -4   -4

_______

4x=8

_____

4     4

x=2

Step-by-step explanation:

Classmate Conjecture

John | All circles are similar if they have the same center and can be dilated or contracted to the same size.

Teresa | All circles are similar if their corresponding radii have a constant ratio.

Evaluate the Conjectures:

2. Yes, it makes intuitive sense that all circles are similar because they all have the same shape and form.

Construct the Circles:

3. [Diagram not provided]

[Diagram not provided]

The hypotenuse of △ABC is the diameter of the smaller circle.

[Diagram not provided]

The hypotenuse of △XYZ is the diameter of the larger circle.

The two triangles, △ABC and △XYZ, are similar because they are both isosceles right triangles with the same angle measures.

The ratio of the lengths of their sides are equal, therefore the ratio of their radii is a constant.

Making a Decision:

10. Both John and Teresa were right as all circles are similar if they have the same center and can be dilated or contracted to the same size (John's method) and also if their corresponding radii have a constant ratio (Teresa's method).

Further Exploration:

11. The circumference of the circle that circumscribes a triangle with side lengths 3, 4, and 5 can be found using the Pythagorean theorem to find the diameter of the circle, which is equal to the sum of the lengths of the three sides. The diameter is equal to 5, so the circumference is equal to 2 * pi * (5 / 2) = 5 * pi

Please provide all information when asking a question

Solving the provided question, we can say by Pythagorean theorem b = [tex]\sqrt{a^2 + b^2}[/tex] = [tex]\sqrt{32.49 + 92.16}[/tex] = 11.231meters

The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.

By Pythagorean theorem

a = 5.7 meters and c = 9.6

b = [tex]\sqrt{a^2 + b^2}[/tex]

b = [tex]\sqrt{32.49 + 92.16}[/tex]

b = [tex]\sqrt{124.65}[/tex]

b = 11.231meters

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The addition of the polynomial P(x) and Q(x) is  5x³ - 13 x² + 3x - 19.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.

Given:

P(x) = 3x³ - 7x² + 3x-4 and Q(x) = 2x³ - 6x² - 15.

Now, adding the both Polynomials

P(x) + Q(x)

= 3x³ - 7x² + 3x-4 + 2x³ - 6x² - 15.

Now, solving the like terms

= 3x³ + 2x³ - 7x² - 6x² +3x -4 -15

= (3+ 2) x³ + (-7-6) x² +3x -4 - 15

= 5x³ - 13 x² + 3x - 19

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Answer: The public debt in 2007 would be 6,783,231,062,743.62 + 595,821,633,586.70 = 7,379,052,696,330.32

Step-by-step explanation:

Answer:

Top one is 3/8

Middle is 4/7

Bottom is 1/3

Step-by-step explanation:

Answer: The sample space of possible outcomes is:

{SM, SJ, MJ, MS, JS, JM}.

There are 6 possible outcomes in the sample space, and 1 of these outcomes results in the first student being a boy (Franklin, represented by "F").

Therefore, the probability of the first student being a boy is P(A) = 1/6.

Step-by-step explanation:

Therefore , the solution of the given problem of function comes out to be Since 4 > 2, function A has a greater rate of change than function B.

The mathematics curriculum covers the study of numbers or rather their variations as well as in our environment, buildings, and both actual and imagined locations. A function presents a graph representation of the relationship between input and output quantities. A function, expression simply, is a collection of sources that, when combined, result in particular outputs by each input. There is a locale, territory, or range assigned to each job.

Here,

The rate of change of a linear function is the slope of the line.

Function A is y = 4x - 3, so the rate of change (slope) is 4.

To find the rate of change of function B, we can calculate the slope of the line passing through the points given in the table. Using the two points (1,4) and (5,12), we get:

slope = (change in y) / (change in x) = (12-4) / (5-1) = 2

So the rate of change of function B is 2.

Since 4 > 2, function A has a greater rate of change than function B.

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Michael writes, "Triangle ABC is congruent to triangle CDA'',

if the segment AC ≅ AC.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given the parallelogram below,

Michael writes, "Triangle ABC is congruent to triangle CDA''.

By the parallelogram property:

AB ≅ CD

BC ≅ AD.

If triangle ABC is congruent to triangle CDA,

then the segment AC ≅ AC.

Therefore, the segment AC ≅ AC.

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Answer:

  x = 5

Step-by-step explanation:

You want the length of x in the figure showing similar triangles.

The bottom edge of the triangle is 2/3 of the left edge.

The similar triangles have the same ratio of side lengths. That means x is 2/3 of (3+4.5):

  (2/3)(7.5) = 5

The length x is 5 units.

Answer:

Addition with the number 3.

Next numbers will be 15, 18, 21,...

The total number of children that ordered Sandwiches  is 1 5/6

From the question, we have the following parameters that can be used in our computation:

Class 1 = 5/6 Hamburger

Class 2 = 2/4 Hot days

Class 3 = 1/2 Chicken wings

So, the total number of children that ordered Sandwiches is

Total =  5/6 + 2/4 + 1/2

Evaluate

Total = 1 5/6

Hence, 1 5/6 of the three classes ordered sandwiches

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The amount of money put by Shannon in her account is $300.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific amount of time.

Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to calculate interest, the principal amount in simple interest remains constant.

Given that Shannon put some money in her savings account. After 6 months, she earned $10.50 in interest. If the interest rate was 7%,

The amount will be calculated as:-

SI = ( P x R x T ) / 100

10.50 = ( P x 7 x 1 ) ( 2 x 100 )

P = ( 10.50 x 2 x 100 ) / ( 7 )

P = $300

Therefore, $300 has been deposited into Shannon's account.

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i) The profit/loss when no cars are produced is a loss of 6600 Rupees.

II) The break even point is at 20 cars

III) The profit/loss if 400 cars are produced is;  a loss of 13400Rupees.

(i) When no cars are produced, x = 0.

Thus, plugging this value into the function p(x) = -x² + 350x - 6600, we have;

p(0) = -0² + 350(0) - 6600 = -6600.

Therefore, the profit/loss when no cars are produced is a loss of 6600 thousand Rupees.

(ii) The break-even point is the point at which the profit is zero, i.e., p(x) = 0. Setting p(x) = 0 and solving for x, we find that;

-x² + 350x - 6600 = 0

x = 20

Therefore, the break-even point is x = 20 cars. T

(iii) If 400 cars are produced, the profit can be found by plugging this value into the function p(x) = -x² + 350x - 6600.

We find that p(400) = -400² + 350(400) - 6600

= -160000 + 140000 + 6600 = -13400. Therefore, the profit/loss if 400 cars are produced is a loss of 13400 Rupees.

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Answer: 2 pounds of flour

Step-by-step explanation:

1/2 of four is two,

4 * 1/2 = 2

Answer:

Jessie used 1/2 of the 4-pound bag of flour, so she used 1/2 * 4 pounds = 2 pounds of flour to bake her cake.