Which of the following numbers sets does not include \large -\sqrt{25} ?

a
Integers

b
Whole Numbers

c
Real Numbers

d
Rational Numbers

Answer:

The integral form of the given differential equation is:

yp(x) = x * ∫[x0 to x] G(x, t) * f(t) dt

where G(x,t) is the Green's function for the differential equation, which depends on the specific form of the equation and the boundary conditions.

To find the Green's function, we first solve the homogeneous equation y'' + 2y' + y = 0, which has the characteristic equation r^2 + 2r + 1 = 0. This has a double root of -1, so the general solution to the homogeneous equation is yh(x) = c1e^(-x) + c2x*e^(-x).

Next, we need to find a particular solution to the non-homogeneous equation y'' + 2y' + y = f(x). We can use the method of undetermined coefficients to guess a particular solution of the form yp(x) = A*x, where A is a constant. Taking the first and second derivatives of yp(x), we get yp'(x) = A and yp''(x) = 0. Substituting these into the differential equation, we get:

0 + 2A + Ax = f(x)

Solving for A, we get A = (1/x) * ∫[x0 to x] f(t) dt.

Therefore, the general solution to the non-homogeneous equation is y(x) = yh(x) + yp(x) = c1e^(-x) + c2xe^(-x) + (1/x) * ∫[x0 to x] G(x, t) * f(t) dt, where G(x,t) = e^(-(x-t)) - e^(-(x-t))(x-t).

Using this expression for yp(x), we can now substitute it into the integral form of the differential equation to get:

yp(x) = x * ∫[x0 to x] (e^(-(x-t)) - e^(-(x-t))*(x-t)) * f(t) dt

Therefore, the solution to f(x) = g(x) is x = 1.

Step-by-step explanation:

Answer:

If you have more than one vertex they are called vertices. You can also count the number of vertices in order to identify solid figures. Let's look at an example. When you count the number of vertices in the figure above you see there are 7 vertices.

The probability that a white car will drive by before x=5 is 87.04%

The probability that a white car will drive by before x=5 is equal to the probability that the first white car will appear on the first, second, third, or fourth car.

The probability that the first white car will appear on the first car is 40%.

The probability that it will appear on the second car is (1-40%)40% = 24%. The probability that it will appear on the third car is (1-40%)(1-40%)40% = 14.4%.

The probability that it will appear on the fourth car is (1-40%)(1-40%)*(1-40%)*40% = 8.64%.

The total probability that the first white car will appear on any of the first four cars is 40% + 24% + 14.4% + 8.64% = 87.04%.

Therefore, the probability that a white car will drive by before x=5 is 87.04%.  

To learn more about probability, visit:

brainly.com/question/11234923

#SPJ4

The sampling distribution of is a binomial distribution with parameters n and p, where n is the sample size and p is the population proportion of the specified characteristic.

The mean of the sampling distribution is np and the standard deviation is  \($\sqrt{np(1-p)}$\).

Round the standard deviation to three decimal places, it is \($\sqrt{np(1-p)}$ = $\sqrt{n \cdot p \cdot (1-p)} \approx \sqrt{n \cdot p \cdot 0.99}$\).

The sampling distribution of is a binomial distribution with parameters n and p, where n is the sample size and p is the population proportion of the specified characteristic. The mean of the sampling distribution is np and the standard deviation is \($\sqrt{np(1-p)}$\). This means that for a given sample size n and population proportion p, the standard deviation of the sampling distribution can be calculated by taking the square root of the product of n, p, and (1-p).

Learn more about sampling distribution: https://brainly.com/question/12892403

#SPJ4

Given the equation of the circle in center radius form:

From the equation, we can conclude the following:

1) Center = (h, k)

2) radius = r

3) any point on the circle = (x, y)

So, the answer will be option 4) (x,y)

Answer:

660.4 Millimeters

Step-by-step explanation:

The conversion for inches to millimeters is 25.4, therefore to get the answer. I multiplied 26 by 25.4

25 8 25.4 = 660.4 Millimeters

Answer:

yes

Step-by-step explanation:

it is going by 5s.

Answer:

Yes. This is because if you plot the numbers on a ration table or see the graph points, you can see a pattern: you multiply by 5. The equation to solve this would be y=5x. Another reason why this is proportional is that the graph starts from the origin (0,0) This is the opposite for non-proportional relationships. Hope this helps! :)

Answer:

centre = (5, - 6 ) , radius = 7

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 10x + 12y + 12 = 0 ( subtract 12 from both sides )

x² + y² - 10x + 12y = - 12 ( collect terms in x/ y )

x² - 10x + y² + 12y = - 12

using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 5)x + 25 + y² + 2(6)y + 36 = - 12 + 25 + 36

(x - 5)² + (y + 6)² = 49 = 7² ← in standard form

with centre (5, - 6 ) and radius = 7

Answer:

Center = (5, -6)

Radius = 7

Step-by-step explanation:

To find the center and the radius of the circle represented by the given equation, rewrite the equation in standard form by completing the square.

To complete the square, begin by moving the constant to the right side of the equation and collecting like terms on the left side of the equation:

\(x^2-10x+y^2+12y=-12\)

Add the square of half the coefficient of the term in x and the term in y to both sides of the equation:

\(x^2-10x+\left(\dfrac{-10}{2}\right)^2+y^2+12y+\left(\dfrac{12}{2}\right)^2=-12+\left(\dfrac{-10}{2}\right)^2+\left(\dfrac{12}{2}\right)^2\)

Simplify:

\(x^2-10x+(-5)^2+y^2+12y+(6)^2=-12+(-5)^2+(6)^2\)

       \(x^2-10x+25+y^2+12y+36=-12+25+36\)

       \(x^2-10x+25+y^2+12y+36=49\)

Factor the perfect square trinomials on the left side:

\((x-5)^2+(y+6)^2=49\)

The standard equation of a circle is:

\(\boxed{(x-h)^2+(y-k)^2=r^2}\)

where:

Comparing this with the rewritten given equation, we get

Therefore, the center of the circle is (5, -6) and its radius is r = 7.

Answer: D

Step-by-step explanation:

Trenton earnings are $190/week + $1.50/item sold.

Let x represent the number of items he sold and y represent his total earnings then:

y=190+1.50x

This means that in a bad week, if he sells no items (x=0) he will earn $190, and each time he sells one item (x increases one unit) he earns + $1.50

If his goal is to earn $550, you hace to replace y=550 in the formula and solve it for x:

To earn $550 Trenton needs to sell 240 items

1. Considering the jumping jacks: 50, 100, 150, and 200, the common difference is 50.

2. Using this ordered pair (1, 50), the slope of the line that connects the first two points is 50.

3. The slope of the line that connects the 3rd and 4th points (3, 150) and (4, 200) is 50.

4. The slope of the line that connects the 1st and the 4th point is 50.

5. The common difference (aka slope aka rate of change) is constant.

6. The slope is constant because it increases by 50 from one point to the next.

The slope is the common difference or rate of change from one data point to the next.

We can compute the slope as the change in y divided by the change in x or rise over run.

For instance, between point 1 and point 2:

Rise = y2 - y1

Run = x2 - x1

Where y2 = 100, y1 = 50, x2 = 2, and x1 = 1.

Slope = y2 - y1 ÷ x2 - x1

= 100 - 50 ÷ 2 - 1

= 50

Check:

Slope = y4 - y3 ÷ x4 - x3

= 200 - 150 ÷ 4 - 3

= 50

Learn more about slope, common difference, or rate of change at https://brainly.com/question/18550782

#SPJ1

Answer:

1 1/4

1 1/2

Step-by-step explanation:

Given that :

Length of cloth purchased = 2 1/4

Length used for project = 3/4

Length remaining = (length purchased - length used)

= 2 1/4 - 3/4

= (9/4 - 3/4)

= (9 - 4) / 4

= 5/4

= 1 1/4

Length of cloth purchased = 5 1/4

Length used for project = 3 3/4

Length remaining = (length purchased - length used)

= 5 1/4 - 3 3/4

= 21/4 - 15/4

= (21 - 15) / 4

= 6/4

= 1 2/4

= 1 1/2

Answer:

The product of (k + 1) series starts with 3 (because k = 2) and you need 2 to be multiplied to this in order to get (n + 1)!

Therefore you need to multiply 2 and 1/2 to make it right. 2 completes the factorial and 1/2 remains.

Hope it was clear explanation.

Answer:

3/10ths is bigger

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

\(Volume = 314500cm^3\)

Step-by-step explanation:

Given

\(Length = 125cm\)

\(Width = 37cm\)

\(Height = 68cm\)

Required

Determine the volume

Volume is calculated as:

\(Volume = Length * Width * Height\)

Substitute values for Length, Width and Height

\(Volume = 125cm * 37cm * 68cm\)

\(Volume = 314500cm^3\)

Hence, the volume of the box is \(314500cm^3\)

Answer:

4x^2-22x+30

=2(2x^2 - 11x + 15)

=2(2x^2 -6x -5x +15)

= 2 { 2x(x-3) - 5(x-3) }

= 2 (x-3) (2x - 5)

Step-by-step explanation:

Hey, there!!!

The answer is option B

here, we have;

=4x^2-22x+30

=4x^2-(10+12)x+30

= 4x^2-10x-12x+30

now, taking common,

=2x(2x-5) -6(2x-5)

= 2(x-3)(2x-5).

Hope it helps

The lowest common denominator of the fraction is 6

The lowest common denominator (LCD) is the smallest common multiple of the denominators of a set of fractions. It is used to add or subtract fractions with different denominators.

The LCD of a set of fractions is the smallest number that is divisible by all the denominators in the set. When all the denominators are divided into the LCD, each fraction has an equivalent fraction with the same value and a denominator equal to the LCD.

In the fraction given;

x / 3 + x / 2 = 20

The lowest common denominator is 6

Using 6, we can divide through each of the fraction.

Learn more on lowest common denominator here;

https://brainly.com/question/10749076

#SPJ1

The genotype ratio is:  1   TT : 1   Tt : 0  tt

The phenotype ratio is :  4   Tall :   0   Short

100 percent of the offspring will be tall.

Genotypic ratio is the ratio between the genetic makeup among the offspring population.

On the other hand, the ratio between the offspring population for an observable characteristic is the phenotype ratio.

The given test cross is between a homozygous tall parent and a heterozygous tall parent.

Using a Punnett square,

The result will be as shown below.

                     T                   t

          T        TT                 Tt

           T       TT                 Tt

Genotype :  1   TT : 1   Tt : 0  tt

Phenotype :  4   Tall :   0   Short

100 percent of the offspring will be tall.

Learn more on Genotypic and Phenotypic ratio here: https://brainly.com/question/22108809

#SPJ1

Answer:

4x2+3=

Step-by-step explanation:

a) The value of x is 21

b) The value of the expression is 135.

c) The value of the expression is 135.

Here we know that the lines G and M are parallel, meaning that the two shown angles are alternarte exterior angles, and thus, have the same measure, then we can write:

5*(x + 6) = 9*(x - 6)

We can solve that linear equation for x:

5x + 30 = 9x - 54

30 + 54 = 9x - 5x

84 = 4x

84/4 = x

21 = x

Then the measures of the angles are:

a1 = 5*(21 + 6) = 135°

a2 = 9*(21 - 6) = 135°

Learn more about angles at:

https://brainly.com/question/25716982

#SPJ1

The the length of each side of the triangle are: 5 units, 8.7 units and 10 units respective

A triangle is a polygon with three sides, three angles, three vertices and sum of angles equal to 180 degrees

From the triangle, Using the trigonometric ratio of sine

Sin C = opposite/Hypothenuse

Sin30 = 5/H

Making h the subject of the relation we have

h= 5/sin30

h=5/0.5

Therefore the value of h=10 units

To find the third side use Pythagoras theorem

10² = 5²+p²

100-25 = p²

75 = p²

Taking the square of both sides

p=√75

p=8.7 units

Learn more about triangles on https://brainly.com/question/2773823

#SPJ1

Answer:

2 1/2

Step-by-step explanation:

To Find x It the same things as 1 3/4 + 3/4 = x.

Look in the picture for the work or below:

Add \(\frac{7}{4}\) to both sides of the equation

\(x-\frac{7}{4}+\frac{7}{4}=\frac{3}{4}+\frac{7}{4}\)

Simplify

\(\frac{5}{2}\)

\(\frac{5}{2}=2\frac{1}{2}\)

Answer:

Step-by-step explanation:

\(x - 1\frac{3}{4} =\frac{3}{4}\)

\(x =\frac{3}{4} + 1\frac{3}{4}\)

\(x =\frac{3}{4} + \frac{7}{4}\)

\(x = \frac{3+7}{4}\)

\(x=\frac{10}{4}\)

\(x = \frac{5}{2}\)

\(x = 2\frac{1}{2}\) or \(2.5\)

Answer:1000

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

6[(2×5)-4]

6(10-4)

6(6)

=36

Answer:

36

Step-by-step explanation:

  6(2b-4)        where b=5

= 6(2(5)-4)

= 6(10-4)

= 6(6)

= 36

Answer:

Step-by-step explanation:

\(f(x)=x^3+x^2\\\\g(x)=x^4+x^2+x\)

\(f(x)-g(x)=(x^3+x^2)-(x^4+x^2+x)=x^3+x^2-x^4-x^2-x\\\\=-x^4+x^3-x\\\\x=1\\\\-1^4+1^3-1=-1+1-1=-1\)

\(x=1\\\\f(1)=1^3+1^2=1+1=2\\\\g(1)=1^4+1^2+1=1+1+1=3\\\\f(1)-g(1)=2-3=-1\)

Answer:0.67

Step-by-step explanation: