State what additional information is required in order that the triangles are congruent for the reason given.

The Euler, explicit Trapezoid, and fourth-order Runge-Kutta methods were applied to a given initial value problem on a grid/mesh of step-size h=0.1 in [0,1]. The results were printed in a table, showing the t values, approximations, and global error at each step.

Euler Method

t Approximation Global Error

0 1 0

0.1 1.011 -0.011

0.2 1.0454 -0.0454

0.3 1.1044 -0.1044

0.4 1.1921 -0.1921

0.5 1.3125 -0.3125

0.6 1.4713 -0.4713

0.7 1.6749 -0.6749

0.8 1.9301 -0.9301

0.9 2.2447 -1.2447

1 2.63 -1.63

Explicit Trapezoid Method

t Approximation Global Error

0 1 0

0.1 1.0055 -0.0055

0.2 1.0246 -0.0246

0.3 1.0592 -0.0592

0.4 1.1021 -0.1021

0.5 1.1564

The Euler method is a numerical technique for solving initial-value problems, which involves approximating the solution of a differential equation by the combination of a series of tangent lines. The explicit trapezoid method is an improved version of the Euler method, which uses the average of two slopes instead of the slope at the previous point whencalculating the next approximation. The fourth-order Runge-Kutta method is a technique that uses a weighted average of four different slopes at different points to approximate the solution of a differential equation.

For the given initial value problem, we applied the Euler method, the explicit Trapezoid method, and the fourth-order Runge-Kutta method on a grid/mesh of step-size h=0.1 in [0,1]. We printed a table of the t values, approximations, and global error at each step.

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Bruce can be advised to correct his reasoning as the number divisible by six will also remain divisible to 3.

The factor of a number is any number that divides it completely.

In order to find the factors of a number keep dividing it with the known factors.

Given that,

A number is product of 6.

Then, 6 is the factor of that number.

But the factors of 6 are 2 and 3 which implies that 3 is also a factor of that number.

It implies that Bruce has not applied the correct reasoning to reach the conclusion.

Hence, a number which is a product of 6 can also be a product of 3.

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When the mat's perimeter is 96 inches, the strip that shows around the picture is 4 inches broad.

The perimeter of a shape is the distance around its edge. The perimeter of a form is the length of its contour. To calculate the perimeter of a rectangle or square, sum the lengths of all four sides. The perimeter of a shape is the distance around its exterior. Perimeter is calculated by summing the lengths of all the sides of a form.

Here,

length of paper, l=25 inch

width of paper, w=15 inch

perimeter=96 inch

Let x be the strip of mat,

l=25+2x

w=15+2x

perimeter=2(l+w)

96=2*(25+2x+15+2x)

48=40+2x

2x=8

x=4 inch

The strip of the mat showing around the picture is 4 inch wide when the perimeter of the mat is 96 inch.

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The average rate of change of the temperature from 6 to 10 pm is given as -1.5. Option C is correct

From 6 pm to 10 pm we have a total of 4 hours that is in between this period of time.

From the table the temperature at 6 pm is 34, the temperature at 10 pm is 28 degrees

Such that we would have:

[tex]\frac{28-34}{4}[/tex]

= -6 / 4

= - 1.5

Hence we would have that Negative 1.5 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour from 6 PM to 10 PM.

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Answer:

-3

Step-by-step explanation:

6x + 4 = x - 11

6x - x = -11 - 4

5x = -15

5/5 x = -15/5

x = -3

Six (6) confidence intervals or hypothesis tests would need to be done to make significant statements for each pair-wise comparison.

In an ANOVA F test, the null hypothesis is that the means of all the treatments are equal, and the alternative hypothesis is that at least two of the means are different. If the null hypothesis is rejected at the 5% significance level, this means that the differences between the means are statistically significant and the treatments can be considered different.

Since there are four treatments, there are 6 possible pairs of treatments. These tests would determine whether the means of each pair of treatments are significantly different from each other.

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The possible domain of the convergence are b. (-1,3) and c. (-1,3]

Domain of convergence.

In statistics, domain of the convergence also known as interval of convergence means an interval associated with a given power series such that the series converges for all values of the variable inside the interval and diverges for all values outside it.

Given,

Here we need to identify in which of the options are domain of convergence.

As per the definition of domain of convergence, the interval of the convergence is (-∞ , ∞).

So, the possible convergence in the given options are (b) and (c).

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(a) The component form of the velocity of the airplane is (-453.01 i + 79.88 j) mph.

(b) The actual ground speed and direction of the airplane is 392.76 mph and 30 degrees respectively.

The component form of the velocity of the airplane is calculated as follows;

Vy = V sinθ

Vx = V cosθ

where;

Vy = 460 mph x sin (170 - 90) = 79.88 mph

Vx = 460 mph x cos (170) = -453.01 mph

The bearing of the two speeds forms a triangle and the angle of the triangle is calculated as follows;

θ = θ₁ + θ₂

θ = (180⁰ - 170⁰) + (200⁰ - 180⁰)

θ = 30⁰

The resultant speed of the airplane is calculated as follows;

Vr² = V₁² + V₂² - 2(V₁)(V₂) cos(θ)

Vr² = (460²) + (80²) -  2(460 x 80) x cos(30)

Vr² = 154,260.53

Vr = √(154,260.53)

Vr = 392.76 mph

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Answer:

f(8)= - 3 × 8 + 3

f(8) = - 21......

Amy’s monthly budget for textbooks in course supplies is $900.00

Amy's monthly budget for rent, utilities and food is $12,798.

Her monthly budget for a personal and miscellaneous cost is $2,259.

Her total monthly budget equals $15,957.

A budget is best defined as estimation of the revenue and expenses over a specified future period of time and is usually compiled and re-evaluated on a periodic basis.

Budget for textbooks:

= $900.00

Budget for rent, utilities and food:

= $12,798.

Budget for personal and miscellaneous cost:

= $2,259.

Total monthly budget:

= $900 + $12,798 + $2,259

= $15,957.

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The statement If B ⊂ A, then A U B = A is true.

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

If BCA, then AUB=A.

When the above statement is represented properly, we have the following representation

If B ⊂ A, then A U B = A

The statement If B ⊂ A means that

The set B is a subset of the set A

In other words, the whole of set B is in set A

If this is true, then the union of both sets represented by A U B is set A

Hence, it is true that If B ⊂ A, then A U B = A

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Answer:

D) 1

Step-by-step explanation:

(1/8) x 8= 1

Hope this helps!

Hypothesis testing is the process used to evaluate the strength of evidence from sample and provides a framework for making determinations related to the population i.e. it provides a method for understanding how reliably over can extrapolate observed findings in a sample under study to the larger population from which the sample was drawn.

After a performing a test, scientist can: Reject the null hypothesis or Fail to reject the null hypothesis.

Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter.Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Such data may come from a larger population, or from a data-generating process.

The null hypothesis is usually a hypothesis of equality between population parameters. Hypothesis testing is a procedure, based on sample evidence and probability, used to test claims regarding a characteristic of a population.

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The degree of freedom value for the A× B intersection is  = 6.72

The F value is the value of the F distribution. Various statistical tests generate F values. You can orrect answer is use this value to determine whether your test is statistically significant.

The F value is used in the analysis of variance (ANOVA). It is calculated by dividing the two mean squares. This calculation determines the ratio of explained to unexplained variance.

The F distribution is a theoretical distribution. There are many types of these distributions, each with different degrees of freedom.

Determines the probability of the F value using the degrees of freedom of the F value and the variance source. The probability is the significance value of the test.

AxB intersection:

Interpreting the output of the general linear model command focuses on two parts: the means table and the ANOVA summary table. The average table is the focus of the analysis, while the summary table draws attention to the interesting or statistically significant parts of the average table.

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A) Acceleration Direction

The net force is acting down the surface, as seen in the figure. As a result, the acceleration vector should likewise be directed down the surface.

Labeling the vector of acceleration

The acceleration vector is depicted below:

B)  Determine the velocity vector

According to the free-body diagram, an item should be on an inclined surface with a tension force pulling it down. When a kinetic frictional force is directed up to the surface, the item is said to be sliding down the slope. As a result, the velocity vector should be oriented upside down.

Determine the direction of the velocity vector

The velocity vector is indicated in the picture below:

C) Describe a real-world thing

The diagram shows an item on an inclined surface, with the kinetic force directed up to the surface. As a result, the item may be thought of as a box being pulled down by a rope down an inclined slope.

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Full Question

Problems 35 through 40 show a free-body diagram. For each:

a. Redraw the diagram

b Identify the direction of the acceleration vector  and show it as a vector next to your diagram. Or, if appropriate, write

c. If possible, identify the direction of the velocity vector and show it as a labeled vector.

d Write a short description of a real object for which this is the correct free-body diagram. Use Examples 5.4, 5.5, and 5.6 as models of what a description should be like.

a) The 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month is given as follows:

(747, 853).

b) The sampling error at the 95% confidence level is of: 35.8.

We have the standard deviation for the population is known, hence the z-distribution is used to calculate the confidence interval.

The equation that gives the bounds of the confidence interval is presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The remaining parameters are given as follows:

[tex]\overline{x} = 800, \sigma = 200, n = 55[/tex]

Then the lower bound of the interval is calculated as follows:

800 - 1.96 x 200/square root of 55 = 747.

The upper bound of the interval is calculated as follows:

800 + 1.96 x 200/square root of 55 = 853.

For a sample size of n = 120, the sampling error is obtained as follows:

Sampling error = 1.96 x 200/square root of 120 = 35.8.

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The quotient of 258 divided by 4 is calculated to be 64.5

Division is considered to be one of the four basic operations of arithmetic. The other three are multiplication, addition, and subtraction, and they can be defined as how numbers are combined to make new numbers.

Out of the four basic operations, division is the process of splitting an amount or a number into equal parts.

In division, the numerator is the top number of a fraction, and on the other hand, the denominator is the bottom number of a fraction and the result of division is called the quotient

In this case, 258 is the numerator and 4 is the denominator;

258 / 4 = 64.5

Therefore the quotient of this division is calculated to be 64.5

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The value of n in the equation, 3n - 8 = 32 - n will be 10. The value is obtained by rearranging the equation and adding the like term.

the equation is :-

3n-8=32-n

take all the values of n one side-

3n+n = 32+8

4n = 40

n = 40/4

n = 10

so the value of the n in the equation is 10.

What is the equation?

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

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Answer:

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

Simplify the equation by distribution, then substitute the value of d and solve for c:

After solving the given expression using exponents properties, the resultant answer is h²⁴.

Exponentiation is a mathematical process that involves the base b and the exponent or power n.

It is represented as bⁿ and is pronounced as "b to the n."

Positive, negative, zero, and rational exponents are the four different categories. Positive exponents indicate the number of times a base should be multiplied by itself.

So, we have:

(h¹²/h⁴)³

Now, solve as follows using properties:

(h¹²/h⁴)³

(h¹²)³/(h⁴)³

h³⁶/h¹²

h³⁶⁻¹²

h²⁴

Therefore, after solving the given expression using exponents properties, the resultant answer is h²⁴.

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Answer: -6

Step-by-step explanation:

(0,y)

at y intercept, x is 0. therefore sub x with 0 and solve

y= 3(0)-12/0+2

= -12/2

=-6

All of the above can be a representation of a function:

A function can be represented in a variety of ways, such as:

All of these methods are valid representations of a function and can be used to explore and better understand the function.

Which of the following can be a representation of a function?

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The total amount Emily spent each month for 20 days will be $142.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this situation, Emily spends $4.85 on a latte and $2.25 on a scone. The total amount spent for 20 days will be:

= (4.85 + 2.25) × 20

= 7.1 × 20.

= 142

The amount is $142.

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The formula for calculating it is perimeter of the rectangle = 2(length + width), meaning that it is equal to twice the sum of its length and width.

Given that,

We have to find which equation perfectly describes the ABCD rectangle's perimeter? How do you determine a rectangle's length and width given its perimeter?

We know that,

The total length of a rectangle's outer boundary is known as its perimeter. The formula for calculating it is perimeter = 2(length + width), meaning that it is equal to twice the sum of its length and width.

The sum of a rectangle's boundary lengths on all sides is known as its perimeter. A rectangle's perimeter is a linear measurement that can be expressed in metres, feet, inches, or yards. Let's first comprehend the two fundamental characteristics of a rectangle.

A rectangle has four 90° angles.

The diagonals of a rectangle are all of the same length.

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The number of aerobic classes would be 7 to make the cost of both gyms the same in the first month.

What are linear equations?

First-order equations include linear equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are those in which the linear equation contains two variables.

Let x= number of months, and a=no of aerobic classes.

Let Gym A charge a $10 membership fee plus $20.25 per month plus $5.50 per aerobics class.

So we get the equation:

y= 10+20.25x+5.50a

y=30.25+5.50a ------------ as (x=1)

Next, for Gym B, it charges $46 per month plus $3.25 per aerobics class.

So the equation is:

y=46x+3.25a

y=46+3.25a ------------------as (x=1)

Now since we need to find the number of aerobic classes, we equate both equations:

30.25+5.50a = 46+3.25a

2.25a = 15.75

a = 7

Therefore, there must be 7 aerobic classes that would make the cost of both gyms to be the same.

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Answer:

x=4.75

Step-by-step explanation:

4x+19=8x

-4x -4x

19 = 4x

Divide 4 on each side

4.75=x or x=4.75

Answer: Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

Step-by-step explanation:

Barry's Swimwear sold 15 out of an unknown number of bathing suits in stock, so we can express this fraction as 15/x, where x is the total number of bathing suits in stock at Barry's Swimwear. Similarly, Philip's Sun Wear sold 5 out of 72 bathing suits in stock, so we can express this fraction as 5/72.

To compare these two fractions, we need to express them with a common denominator. One way to do this is to find the least common multiple of the two denominators, which in this case is 72. To express 15/x with a denominator of 72, we can multiply both the numerator and the denominator by a factor of 72/x. This results in the fraction 15*(72/x)/72 = 15/x. Similarly, we can express 5/72 with a denominator of 72 by multiplying both the numerator and the denominator by a factor of 72/72, which results in the fraction 5*(72/72)/72 = 5/72.

Now that we have both fractions expressed with a common denominator of 72, we can compare them directly. 15/x is greater than 5/72 as long as x is less than 72. This means that Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

the interval, the function returns zero (-6,-2)  –6 < x < –2

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

The given f(x) = (x + 2)(x + 6)

In this function, a quadratic equation is represented (vertical parabola open upward)

The vertex stands for a minimum.

the use of a graphing tool

view the attached image

x=-6 and x=-2 are the x-intercepts.

Point: the y-intercept

The point is called the vertex.

The range ——-> is the domain. (-∞,∞) (All real numbers) (All real numbers)

The range is in the range [-4,].

x -6 or x > -2 make the function positive.

For the interval, the function returns zero (-6,-2)  –6 < x < –2

Hence, the interval, the function returns zero (-6,-2)  –6 < x < –2

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The area of the rhombus inside a square formed by two equilateral triangles is 1.856 cm².

Here we have to find the area of the rhombus.

Data given:

sides of a square = 2√3 cm

Let ABCD be a square whose sides are 2√3 cm.

As two triangles are inscribed in a square so ABE and CDG be equilateral triangles in square ABCD.

The altitude of the equilateral triangle ABE and CDE = 2√3 sin 60°

= 2√3 × √3/2

= 3cm

The diagonal EG of the rhombus EFGH = 2√3 - 2(2√3 - 3)

= 2.535 cm

The diagonal FH of the rhombus, EFGH = 2√3 - 2(√3tan 30°)

= 1.464 cm

The formula for the area of the rhombus = d1 × d2 / 2

where d1 and d2= diagonal of a rhombus

Now the area of the rhombus EFGH = EG × FH / 2

= 2.535 × 1.464 / 2

= 1.856 cm².

Therefore the area of the rhombus is 1.856 cm².

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