Apply the Euler method, the explicit Trapezoid method, the fourth-order Runge-Kutta method on a grid/mesh of step-size
h=0.1
in
[0,1]
for the initial value problem
x ′ = x2/t3​x(0)=1
. Print a table of the
t
values, approximations, and global error at each step.

If BCDE is congruent to OPQR, then DE is congruent to QR .

Congruence means the same point on two different shapes , like parallels

so BC is congruent to OP

and

DE is congruent to QR

In plain English, two objects are said to be congruent if they overlap, i.e., have the same size and shape. If two angles have the same measure, they are said to be congruent. They are congruent if the sides' lengths line up.

Two triangles are said to be congruent if their sides and angles are an exact match.

Conditions for Congruence of Triangles:

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Answer:

Below

Step-by-step explanation:

Multiply  L number and Bottom number ...then add the R number to get the top number

? = 100 - (3*24) = 28

The domain and range of the given function is -

Domain :   (- ∞, + ∞)  or  -∞ < x < +∞

Range :   [0 ∞)  or  0 ≤ y < +∞

        |x| = x   |   x ≥ 0

        |x| = -x  |   x < 0

We have the following function -

g(x) = |x +3|

Refer to the graph attached. It can be seen that -

Domain :   (- ∞, + ∞)  or  -∞ < x < +∞

Range :   [0 ∞)  or  0 ≤ y < +∞

Therefore, the domain and range of the given function is -

Domain :   (- ∞, + ∞)  or  -∞ < x < +∞

Range :   [0 ∞)  or  0 ≤ y < +∞

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The parameter (the regression coefficient) indicates the degree to which the line slopes upwards or downwards by indicating the amount by which a change in x must be multiplied by the corresponding average change in y, or the amount by which y changes for each unit increase in x.

Understanding Linear Regression Coefficients, A positive coefficient indicates that the mean of the dependent variable tends to rise in tandem with an increase in the independent variable's value. A negative coefficient indicates that the dependent variable tends to decrease as the independent variable rises.

In a regression model, the statistical measure known as R-Squared (also known as R2 or the coefficient of determination) is used to figure out how much of the variance in the dependent variable can be explained by the independent variable. In other words, the goodness of fit, or r-squared, measurement indicates how well the data fit the regression model.

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STEP ONE: Get a common denominator.

STEP TWO: Add or subtract the numerators.

STEP THREE: Simplify the result if needed. Notice that eg: 3/27 can be simplified, since the numerator and denominator are both divisible by 3.

And that's all there is to it! Final Answer

Answer:

Step-by-step explanation:

The pooled proportion is  [tex]\bar{p}[/tex]=0.64.

The value of test statistic is z=1.614.

In statistical tests, which are formal procedures for drawing inferences or taking choices based on data, two different sorts of conjectures are employed: the null hypothesis and the alternative hypothesis. Based on a sample of the population, the hypotheses are suppositions regarding a statistical model of the population. In order to distinguish between statistical noise and scientific claims, tests, which are fundamental components of statistical inference, are frequently utilized in the interpretation of scientific experimental data. The null hypothesis presupposes that any variation between the selected attributes you observe in a set of data is the result of chance. For instance, if the predicted profits from the gambling game genuinely equal zero, then any discrepancy between the data's average profits and zero results from chance.

Given,

The pooled proportion is:

[tex]\bar{p}[/tex]=(X₁+X₂)/(n₁+n₂)

=(70+90)/(100+150)

=160/250

=0.64

Therefore, the pooled proportion [tex]\bar{p}[/tex]=0.64.

The value of test statistic is:

Test statistic=0.1/0.062

=1.614

Therefore, the value of test statistic is z=1.614.

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Answer: I added a bit more answers the one that answers your question is underlined.

a. Reject H0 when z>1.65

b. p=0.64

c. z=1.614

d. We reject the null hypothesis

Step-by-step explanation:

b. p=[tex]\frac{70+90}{100+150} =\frac{160}{250}=0.64[/tex]

c. z=[tex]\frac{0.70-0.60}{\sqrt{0.64(1-0.64)\sqrt{\frac{1}{100}+\frac{1}{150} } } }[/tex]=1.614

The average price of the stock over the first eight years is 50.69 units / year .

Given :

A stock analyst plots the price per share of a certain common stock as a function of time and finds that it can be approximated by the function :

S ( t ) = 37 + 16 e^0.04t.

We find the average value of the stock ,

[tex]f_{ave} =1/b-a \int\limits^8_0 {f(x)} \, dx[/tex]

[tex]f_{ave} =1/8-0 \int\limits^8_0 {S (t)} \, dx[/tex]

[tex]f_{ave} =1/8( \int\limits^8_0 {37} \, dt + \int\limits^8_0 {16e^{(0.04t) \, dt[/tex]

= 37 / 8 ( 8 - 0 ) - 1 / 0.02 ( [tex]e^{-0.04 * 8 }[/tex] - [tex]e^{-0.04 * 0[/tex])

= 50.69 units / year.

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If you want to invest $20,000 in a no-load mutual fund with a 6.5% yield then 1300 we earn each year.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

The amount to invest is $20,000

Twenty thousand is the investment

and 6.5% is the yield.

We need to find how much we earn in each year.

Convert 6.5% to decimal

6.5/100=0.065

Multiply 0.065 with the 20000

0.65×20000

1300

Hence, we earn 1300 each year as an interest.

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1. The two equations that represent this system of equations include

3896 - 238m

5345 - 187m

2. The months that it will it take for both Richard and Elizabeth's cars to have the same number of miles will be 28.4 months.

Given that Richard's used car has 3,896 miles on it already, and he drives 238 miles per month. The equation will be:

3896 - 238m

Elizabeth's car has 5,345 miles on it already, and she drives 187 miles per month. The equation will be:

5345 - 187m

where m = number of months

The months that it take for both Richard and Elizabeth's cars to have the same number of miles will be:

3896 - 238m = 5345 - 187m

Collect like terms

51m = 1449

m = 1449 / 51

m = 28.4 months

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Answer:

[tex]m\angle BDC = 68\textdegree[/tex]

Step-by-step explanation:

Using the given information, we can deduce that angles BDC and ADC are supplementary; their measures add to 180°.

This can be represented by the following equation:

[tex](-7x + 12)\textdegree + (-8x+48)\textdegree = 180\textdegree[/tex]

First, solve for x.

[tex]-15x\textdegree + (12 + 48)\textdegree = 180\textdegree[/tex]

[tex]-15x \textdegree = (180 - 60) \textdegree[/tex]

[tex]-15x\textdegree = 120\textdegree[/tex]

[tex]x\textdegree = -8\textdegree[/tex]

[tex]x = -8[/tex]

Then, substitute x into the expression for BDC.

[tex]m\angle BDC = (-7x+12)\textdegree[/tex]

[tex]m\angle BDC = (-7(-8) + 12)\textdegree[/tex]

[tex]m\angle BDC = (56 + 12)\textdegree[/tex]

[tex]m\angle BDC = 68\textdegree[/tex]

A few establishments have what are known as Corner windows, which are triangle display spaces with one solid wall and two glass sides.

Given fill-in-the-blank;

A few stores have windows with one solid wall and two glass sides forming a triangular display space called ______ windows.

The solution for the above statement is Corner windows.

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Answer:A topic sentence is used to bring

to a paragraph.

Step-by-step explanation:

A topic sentence is used to bring

to a paragraph.

A system of linear inequalities to describe this situation are as follows;

x + y ≤ 100

3x + 5y ≥ 360

x ≥ 20

The system of inequalities has been solved graphically and one possible solution is selling 20 tacos and 80 burritos.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of tacos sold and number of burritos sold respectively, and then translate the word problem into algebraic equation as follows:

Since Henry only has enough supplies to make 100 tacos or burritos, we have;

x + y ≤ 100

Also, Henry sells each taco for $3 and each burrito for $5 and must sell no less than (at least) $360 worth of tacos and burritos each day

3x + 5y ≥ 360

Lastly, Henry must sell no less than (at least) 20 tacos;

x ≥ 20

In conclusion, you should use a graphing calculator to plot the system of linear inequalities as shown in the image attached below.

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The obtained stress which is acting from every direction is at 45 degree.

The transformation equations will be used to calculate the stresses acting on an inclined element.

(σ x+σ y )/2  =75 MPa

(σ x-σ y )/2  =35 MPa

Tor xy = 28 MPa

sin 2θ = sin 90° = 1          

cos 2θ = cos 90° = 0

Substituting these values into Eqs

σ x1 =(σ x+σ y )/2+ (σ x-σ y )/2 cos2θ+ τxy sin2θ      

= 130 MPa

τ x 1 y 1 =  (σ x-σ y )/sin2θ + τxy cos2θ

σ y 1=  (σ x+σ y )/2- (σ x-σ y )/cos2θ+ τxy sin2θ    

= 47Mpa

Elements of stress

We can easily obtain the stresses acting on all sides of an element oriented at = 45° from these results.

The arrows indicate the true directions of the stresses. Take special note of the shear stress directions, which all have the same magnitude. Also, keep in mind that the sum of the normal stresses remains constant at 150 MPa.

​

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​

​

Sample Output: Code to copy: //Import the required package. import java.util.Scanner; //Define the class Main. class Main { //Start the execution of the main() method.

Origin C is a programming language that is ANSI C compatible and also incorporates C++ and C# features. The majority of Origin objects can be accessed programmatically thanks to built-in C++ classes. The NAG C Library's extensive collection of numerical computational routines is also included.

C, a replacement for the programming language B, was initially created by Ritchie at Bell Labs between 1972 and 1973 to create utilities for Unix. It was used to re-implement the Unix operating system's kernel. C increasingly gained popularity in the 1980s.

import java.io.*;

import java.util.Scanner;

public class histogram

{

   public static void main(java.lang.String[] args)

   throws IOException

   {

       Scanner scan = new Scanner (System.in);

       final int min = 1;

       final int max = 10;

       final int limit = 10;

       int[] a = new int[max];

       for (int b = 0; b < a.length; b++)

       {

           a[b] = 0;

       }

       System.out.println("Enter Number between 1 and 100: \n (Or press 0 to stop)");

       int number = scan.nextInt();

       while (number >= min && number <= (limit*max) && number != 0)

       {

           a[(number-1)/limit] = a[(number - 1 ) / limit] + 1;

           System.out.print("Please enter a value:");

           number = scan.nextInt();

       }

       System.out.println("\n__Histogram__");

       for (int y = 0; y < a.length; y++)

       {

           System.out.print("   " + (y * limit + 1) + " - " + (y + 1) * limit + "\t");

           return;

       }

       for (int z = 0; z < a[b]; z++)

       {

           System.out.print("*");

       }

       System.out.println(0);

   }

}

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The estimate of the number of students studying abroad in 2003 is 169 and the estimate of the number of students studying abroad in 2018 is 433

a. Estimate the number of students studying abroad in 2003.

The function is given as:

y = 123(1.065)^x

Where x represents years from 1998 to 2013

2003 is 5 years from 1998.

This means that

x = 5

Substitute the known values in the above equation

y = 123(1.065)^5

Evaluate the exponent

y = 123 * 1.37008666342

Evaluate the product

y = 168.520659601

Approximate

y = 169

Hence, the estimate of the number of students studying abroad in 2003 is 169

b. Assuming this equation continues to be valid in the future, use this equation to predict the number of students studying abroad in 2018.

2018 is 20 years from 1998.

This means that

x = 20

Substitute the known values in the above equation

y = 123(1.065)^20

Evaluate the exponent

y = 123 * 3.52364506352

Evaluate the product

y = 433.408342813

Approximate

y = 433

Hence, the estimate of the number of students studying abroad in 2018 is 433

Answer:

-------------------------------------

Given sequence:

We observe that it has a linear increase and common difference of terms is 5:

So d = 5, a₁ = - 1, find the nth term:

After solving the equation, the system which has infinitely many solutions will be equal to 2x + y = 3.  Hence, option A is correct.

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

As per the given equation in the question,

6x + 3y = 9  (i)

The system for  infinitely many solutions will be,

Divide the equation (i) by three,

(6x + 3y)/3 = 9/3

2x + y = 3

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Answer:

A) y + 2x = 3

Step-by-step explanation:

As angle M has a measure of 47°, then the measure of angle PNL is 43°

To find: the measure of ∠ PNL .

To proof

As given

∠ M = 47°

In  ΔLMN

If the two sides of a triangle are equal and you use the property, the diagonals are also equal.

As given MN = LN

∠ M =∠ L = 47°

and ∠ MPN = 90 °

∠ MPN +  ∠ NPL = 180°  (Linear pair)

∠ NPL = 180° - 90°

∠ NPL = 90°

Now by using the angle sum property of a triangles.

in Δ NPL

∠NPL +∠PNL + ∠NLP = 180°

90 + 47 + ∠PNL = 180

137+ ∠PNL = 180

∠PNL = 180 - 137

∠PNL = 43 °

Therefor the Measure of angle PNL is 43°.

Hence proved

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Other expression can be used to represent the change in temperature after y minutes is -4y + 12.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

The distributive property is a( b + c) = ab + ac.

Given expression that represents the change in temperature after y minutes for a chemical in a lab can be represented by the expression −4(y − 3).

Given expression is

-4(y - 3)

Applying distributive property:

= -4 × y - (-4)×3

= -4y + 12

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Answer: 210

Step-by-step explanation:

The test statistic for the test of whether the slope is of zero is given as follows:

t = -20.

The equation that gives the test statistic is given as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which the parameters are defined as follows:

The value tested of the slope is of:

[tex]\mu = 0[/tex]

The regression line in this problem is of y = 29.29 - 0.88x, hence the mean slope is of:

[tex]\overline{x} = -0.88[/tex]

The standard error and the sample size are given as follows:

s = 0.22, n = 25.

Then the test statistic is calculated as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{-0.88 - 0}{\frac{0.22}{\sqrt{25}}}[/tex]

t = -20.

The problem asks for the test statistic regarding whether the slope assumes a value of zero or different of zero.

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The inequality of each model cutting, sewing finishing packaging and shipping profit

The maximum value = 5x + 8y

1R + 3/2 C ≤ 900

1/2 R + 1/3 C ≤ 300

1/8 R + 1/4 C ≤ 100

R, C ≥ 0

Consider x be the number of regular model of gloves to be produced

y be the catcher’s model of gloves to be produced

The maximum value = 5x + 8y

Then the inequality will be

The inequality of Cutting and Sewing

1R + 3/2 C ≤ 900

The inequality of Finishing

1/2 R + 1/3 C ≤ 300

The inequality of Packaging and Shipping

1/8 R + 1/4 C ≤ 100

R, C ≥ 0

Therefore, the inequality of each model cutting, sewing finishing packaging and shipping profit has been found

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The value of m+n is 37.

Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen. The range for probability varies from 0 to 1.

Let A signify the flipping of the head, and let B signify the flipping of the tail. The event ends when we get 5 heads or 2 tails while flipping.

Then, the outcomes are given by AAAAA, BAAAAA, BB, ABB, AABB, AAABB, AAAABB. The probability of getting a head is 1/2 and a tail is 1/2. The probability of the possible outcomes is 1/32, 1/64, 1/4, 1/8, 1/16, 1/32, and 1/64.

The outcomes with five heads are AAAAA and BAAAAA. The sum of the probabilities of getting 5 heads is,

[tex]\begin{aligned}\frac{1}{32}+\frac{1}{64}&=\frac{2+1}{64}\\&=\frac{3}{64}\end{aligned}[/tex]

And, the sum of all the outcomes is, [tex]\begin{aligned}\frac{1}{32 }+ \frac{1}{64}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}&=\frac{2+1+16+8+4+2+1}{64}\\&=\frac{34}{64}\end{aligned}[/tex]

Let p is the probability that a run of 5 heads will occur before a run of 2 tails. The desired probability p is,  

[tex]\begin{aligned}p&=\frac{\text{number of event}}{\text{total outcome}}\\&=\frac{\frac{3}{64}}{\frac{34}{64}}\\&=\frac{3}{34}\end{aligned}[/tex]

Given, p is of the form m/n. So, m is 3 and n is 34. Then, m+n=3+34=37.

The answer is 37.

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Answer:

y=x^2 + 1

Step-by-step explanation: the second parabola is only raised by 1 unit up, therefore the entire function shifts upwards by 1.

1) To determine the surface area of a right cone, we must know the radius of the circular base and height of the cone.

2) To determine the surface area and volume of a sphere, we must know the radius of the sphere.

3) The volume of the sphere with a great circle of radius 7 cm is 1436.75 cubic centimeters

4) The area of a regular pentagon with radius 5, and each side of length 6 is 45 square units

To determine the surface area of a right cone:

The formula for the surface area of a right cone is,

A = πr[r + √(h² + r²)]

this means, to determine the surface area of a right cone, we must know the radius of the circular base and height of the cone.

To find the surface area and volume of a sphere:

The formula for the surface area of sphere is,

A = 4πr²

and the formula for the volume of sphere is,

V = 4/3 πr³

This means, to determine the surface area and volume of a sphere, we must know the radius of the sphere.

For a sphere with radius r = 7 cm the volume would be,

V = 4/3 * π * 7³

V = 1436.75 cubic centimeters

Now we need to find the area of a regular pentagon with radius 5, and each side of length 6.

The formula for the area of a regular pentagon is:

A = 1/2 × P × a

where 'p' is the perimeter of the pentagon and 'a' is the apothem of a pentagon.

The perimeter of the pentagon is:

P = 5 * side lengths

P = 5 * 6

P = 30 units

We know that an apothem of a regular polygon is a radius of the inscribed circle.

From given dimensions, a = 5 units

so, the area of a regular pentagon would be,

A = 1/2 × 30 × 5

A = 45 square units

Therefore, the area of a regular pentagon is 45 square units

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The probability that at least one client will have a food allergy is 0.6323 and the percentage of customers who will have a food allergy is 0.08.

What is probability?

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.

As given in the question,

The percentage of customers who will have a food allergy is 0.08

At Ying Ying's bakery,

121 people place orders on a single day.

We can utilize the binomial distribution if we believe that each of the 12 clients has an equal probability of reporting a food allergy.

Formula for Binomial probability distribution:

P(X=x)=ⁿCₓ pˣ (1-p)ⁿ⁻ˣ

Here, P(x) = probability of getting success in x trials, n= sample size ,p = represents the probability that each event will succeed.

As given, we have

n = 12

p=0.08

Let x is the client will have a food allergy.

Following that, the probability that at least one client will have a food allergy will be:

P(x≥1) = 1 - P(x<1)

= 1 - P(x=0)

= 1 - ¹²C₀(0.08)⁰(1 - 0.08)¹²⁻⁰

= 1 - (1)(0.12)¹²

= 1 - 0.3677

= 0.6323

Hence , the probability that at least one client will have a food allergy will be 0.6323 when the percentage of customers who will have a food allergy is 0.08.

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Complete Question

When a customer places an order at Ying Ying's bakery, there is an 8\%8%8, percent probability that the customer will report a food allergy. One day, 121212 customers place orders at Ying Ying's bakery.

Assuming that each of the 121212 customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?

The graph of the point of intersection is given below.

The point of intersection.

(5/√17, 20/√17) and (-5/√17, 20/√17)

A circle is a two-dimensional figure with a radius and circumference of

2πr.

The equation of a circle is x² + y² = r²

We have,

The equation of a circle

x² + y² = r²

r = 5

x² + y² = 25 ______(1)

The line.

y = 4x _____(2)

Now,

The line intersects the circle.

The point of intersection.

x² + (4x)² = 25

x² + 16x² = 25

17x² = 25

x = √(25/17)

x = ± 5/√17

x = 5/√17 and x = -5/√17

Now,

At x = 5/√17,

y = 4 x 5/√17

y = 20/√17

At x = -5/√17,

y = 4 x 5/√17

y = 20/√17

Thus,

The point of intersection.

(5/√17, 20/√17) and (-5/√17, 20/√17)

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This is one way of writing a quadratic function:

[tex]f(x)= a(x-h)^2+k[/tex]

We're given:

[tex]f(x) = -6x^2 - 60x - 151[/tex]

To write a quadratic function in vertex form, we must complete the square.

⇒ Put parentheses around the first two terms containing x and x²:

[tex]f(x) = (-6x^2 - 60x) - 151[/tex]

⇒ Factor out -6 (keeping the x's in the parentheses):

[tex]f(x) = -6(x^2+10x) - 151[/tex]

⇒ To complete the square, add, inside the parentheses, the square of half the coefficient of x.

[tex]f(x) = -6(x^2+10x+25) - 151[/tex]

⇒ Now, we cannot randomly introduce a new value into a function. To balance the +25, subtract -6(25) outside the parentheses:

[tex]f(x) = -6(x^2+10x+25) - 151-(-6*25)\\f(x) = -6(x^2+10x+25) - 151-(-150)\\f(x) = -6(x^2+10x+25) - 151+150\\f(x) = -6(x^2+10x+25) - 1[/tex]

⇒ Finally, complete the square.

[tex]f(x) = -6(x+5)^2 - 1[/tex]

[tex]f(x) = -6(x+5)^2 - 1[/tex]