Write the formula of the sinusoidal function (CORRECT ANSWER WILL BE MARKED BRAINLIEST)

The approximate values of y at x = 0.1, 0.2, 0.3, 0.4, and 0.5 using Euler's method with a step size of h = 0.1 are: y(0.1) ≈ 5.41 and y(0.2) ≈ 4.889

To approximate the solution to the initial value problem using Euler's method with a step size of h = 0.1, we can follow these steps:

1. Define the differential equation: dy/dx = x - y.

2. Set the initial condition: y(0) = 6.

3. Choose the step size: h = 0.1.

4. Iterate using Euler's method to approximate the values of y at x = 0.1, 0.2, 0.3, 0.4, and 0.5.

Let's calculate the approximate values:

For x = 0.1:

dy/dx = x - y

dy/dx = 0.1 - 6

dy/dx = -5.9

y(0.1) = y(0) + h * (-5.9)

y(0.1) = 6 + 0.1 * (-5.9)

y(0.1) = 6 - 0.59

y(0.1) = 5.41

For x = 0.2:

dy/dx = x - y

dy/dx = 0.2 - 5.41

dy/dx = -5.21

y(0.2) = y(0.1) + h * (-5.21)

y(0.2) = 5.41 + 0.1 * (-5.21)

y(0.2) = 5.41 - 0.521

y(0.2) = 4.889

For x = 0.3:

dy/dx = x - y

dy/dx = 0.3 - 4.889

dy/dx = -4.589

y(0.3) = y(0.2) + h * (-4.589)

y(0.3) = 4.889 + 0.1 * (-4.589)

y(0.3) = 4.889 - 0.4589

y(0.3) = 4.4301

For x = 0.4:

dy/dx = x - y

dy/dx = 0.4 - 4.4301

dy/dx = -4.0301

y(0.4) = y(0.3) + h * (-4.0301)

y(0.4) = 4.4301 + 0.1 * (-4.0301)

y(0.4) = 4.4301 - 0.40301

y(0.4) = 4.02709

For x = 0.5:

dy/dx = x - y

dy/dx = 0.5 - 4.02709

dy/dx = -3.52709

y(0.5) = y(0.4) + h * (-3.52709)

y(0.5) = 4.02709 + 0.1 * (-3.52709)

y(0.5) = 4.02709 - 0.352709

y(0.5) = 3.674381

Therefore, the approximate values of y at x = 0.1, 0.2, 0.3, 0.4, and 0.5 using Euler's method with a step size of h = 0.1 are:

y(0.1) ≈ 5.41

y(0.2) ≈ 4.889

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Answer:

63/2

Step-by-step explanation:

Multiply the fraction.

\(\frac{9}{4}\cdot \:14\\=\frac{9}{4}\cdot \frac{14}{1}\\=\frac{9\cdot \:14}{4\cdot \:1}\\=\frac{9\cdot \:14}{4}\\=\frac{9\cdot \:2\cdot \:7}{4}\\=\frac{9\cdot \:2\cdot \:7}{2\cdot \:2}\\=\frac{9\cdot \:7}{2}\\=\frac{63}{2}\)

Answer:

63/2

Step-by-step explanation:

\(\frac{9}{4}\) \((\frac{14}{1})\)  You can write 14 as a fraction by putting it over 1.

Now, multiple across

\(\frac{126}{4}\)

Now divide the top and the bottom by 2

\(\frac{63}{2}\)

The median for the given sample of data is A. 20.

To find the median for the given sample of data, we need to arrange the numbers in ascending order and then find the middle value.

Arranging the numbers in ascending order: 16, 17, 18, 18, 19, 19, 21, 22, 22, 23, 25

There are 11 numbers in the sample, so the middle value is the (11 + 1) / 2 = 6th value.

The 6th value in the ordered list is 19.

Therefore, the median for this sample of data is A. 20.

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The probability that student chosen at random is 16 years is 0.28.

The table shows the distribution of student by age in a high school with 1500 students. Therefore, the probability that randomly chosen student is  16 years can be found as follows:

Therefore,

probability = number of favourable outcome to age / total number of possible outcome

Hence,

probability that student chosen at random is 16 years =  420 / 150

probability that student chosen at random is 16 years = 0.28

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Answer:

255 miles

Step-by-step explanation:

if 1 inch is 60 miles then you need to times 60 miles by 4.25 which is the same thing as 4 1/4. you then get 255 miles.

42ab3. = 126ab

70a2b2. =280ab²

that's my answer hope it's help

The equation of line passes through the points (0, 0) and (3a, 5g) will be;

⇒ y = (5g/3a) x

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, 0) and (3a, 5g).

Now,

Since, The equation of line passes through the points (0, 0) and (3a, 5g).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (5g - 0) / (3a - 0)

m = 5g / 3a

Thus, The equation of line with slope 5g/3a is,

⇒ y - 0 = 5g/3a (x - 0)

⇒ y = (5g/3a) x

Therefore, The equation of line passes through the points (0, 0) and

(3a, 5g) will be;

⇒ y = (5g/3a) x

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To answer this question, we will use algebraic expressions. The given condition is that three consecutive even integers have been thought of by Ramses and that 3 times the sum of the first two is 58 less than 14 times the opposite of the third.

To obtain the solution, let's take the smallest integer to be x. Therefore, the next two consecutive even integers are x + 2 and x + 4 respectively. Hence, the algebraic expression for the given statement is,3(x + x + 2) = 14(-x - 4) - 583(2x + 2) = -14x - 56 - 58 Multiplying3 times the sum of the first two consecutive even integers gives us 6x + 6.14 times the opposite of the third is -14x - 56, and 58 less than this is -14x - 56 - 58 = -14x - 114.

Now we have:6x + 6 = -14x - 1146x + 14x = -114 - 6 20x = -120 x = -6The three consecutive even integers are -6, -4, and -2.The sum of the first two consecutive even integers is -6 + (-4) = -10.3 times the sum of the first two consecutive even integers is 3(-10) = -30.14 times the opposite of the third integer is 14(2) = 28.58 less than 28 is -30. Thus, the solution is correct.

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The probability that no students in a survey of five students will be in favor of opening a pub is approximately 0.32768 or 32.768%.

To calculate the probability that no students in a survey of five students will be in favor of opening a pub, we can use the binomial probability formula.

The probability of a single student being in favor of opening a pub is 0.20, and the probability of a single student not being in favor is 1 - 0.20 = 0.80.

Using the binomial probability formula, the probability of having no students in favor can be calculated as:

P(X = 0) = (0.80)^5

P(X = 0) = 0.32768

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The algebraic expression for the scenario is 15 + x = 60

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

Amount saved up = $15

Cost of item = $60

Amount gifted by your grandma = x

The above parameters means that the mathematical statement is an equation statement

So, we have the following representation

Amount saved up + Amount gifted by your grandma = Cost of item

Substitute the known values in the above equation, so, we have the following representation

15 + x = 60

Hence, the algebraic expression is 15 + x = 60

The question does not require that the equation be solved

However, when it is solved, we have:

15 + x = 60

Subtract 15 from both sides

x = 45

So, the amount is 45

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In quantitative research, data collection from the same respondents at 2 or more points (waves) in time is referring to "longitudinal."

A method for gathering and interpreting numerical data is known as quantitative research. It can be used to discover patterns and averages, to make predictions, to verify causal linkages, and to generalize results to larger groups.

Some features regarding quantitative research are-

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Answer:

It's 60 in

Step-by-step explanation:

P = 4s

P = 4 x 15

P = 60 in

Answer:

1) 3 more people

2) 9 teams

Step-by-step explanation:

The divisibility rule for 5 is that it must end in 5 and 0

so the next one is 45, so 3 more people

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

45/5=9 teams

Answer:

Let's actually find the line of best fit...

m=(nΣyx-ΣyΣx)/(nΣx^2-ΣxΣx)

m=(11*836-130*55)/(11*385-3025)

m=2046/1210  

m=93/55

b=(Σy-93Σx/55)/n

b=(55Σy-93Σx)/(55n)

b=(7150-5115)/(55*11)

b=185/55, so the line of best fit is:

y=(93x+185)/55

A)  The approximate y-intercept (the value of y when x=0) is 185/55≈3.36.

Which means that those who do not practice at all will win about 3.36 times

B) y(13)=(93x+185)/55

y(13)≈25.34

So after 13 months of practice one would expect to win about 25.34 times.

The correct option is; 4: this contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) (7 − 1) , but f is not continuous at x = 3.

The function being used is;

f(x) = (x - 3)⁻²

If we separate this function according to x, we obtain;

f'(x) = -2/(x - 3)³

Finding all c values f(7) − f(1) = f '(c)(7 − 1).is our goal.

This suggests that;

0.06 - 0.25 = -2/(c - 3)³ x 6

-0.19 =  -12/(c - 3)³

(c - 3)³ = 63.157

c = 6.98

If the Mean Value Theorem holds for this function, then f must be continuous on [1,7] and differentiable on (1,7).

But when x = 3, f is not continuous, hence the Mean Value Theorem's prediction is false.

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The complete question is-

Let f(x) = (x − 3)−2. Find all values of c in (1, 7) such that f(7) − f(1) = f '(c)(7 − 1). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about the Mean Value Theorem?

Answer:

#14 - t = for each t-shirt(s) sold / h = hour(s) worked

8h + 0.50t

#15 - d = for hot dog(s) sold / h = hour(s) worked

8.50h + 0.35d

Is this what you needed?

Answer:

Question 14

let n = number of t-shirts sold

let h = number of hours worked

let y = total money earned

Given Adila earns $8.00 per hour plus $0.50 for each T-shirts she sells:

\(y = 8h + 0.5n\)

Question 15

let n = number of hot-dogs sold

let h = number of hours worked

let y = total money earned

Given Ramesh earns $8.50 per hour plus $0.35 for each hot-dog he sells:

\(y = 8.5h + 0.35n\)

Answer:

\(\huge\boxed{V=64cm^3}\)

Step-by-step explanation:

The formula of a surface area of a cube:

\(SA=6a^2\)

The formula of a volume of a cube:

\(V=a^3\)

We have

\(SA=96cm^2\)

Calculate the edge length (a).

\(6a^2=96\)           divide both sides by 6

\(a^2=16\to a=\sqrt{16}\\\\a=4(cm)\)

Calculate the volume of a cube:

\(V=4^3=64(cm^3)\)

In ANOVA, the factor refers to the different levels of the variable being studied.

So, the correct answer is C.

Specifically, it refers to the independent variable that is being manipulated and its effect on the dependent variable.

The experimenter is the person conducting the study and manipulating the independent variable, but the factor specifically refers to the levels of the variable being studied.

The content loaded in 120 words would explain the concept of factors in ANOVA and how they relate to the independent and dependent variables in the study. It would also clarify that the experimenter is not the same as the factor being studied.

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Answer:

A polygon is a very big catagory. For example, a triangle has three sides, while a quadrilateral has four sides.

A triangle would be, A=h*w/2 (h being hight, and w being width)

A quadrilateral would be, A=h*w

Answer:

10.5 degrees Celsius

Step-by-step explanation:

Answer: 13.5

Step-by-step explanation:

This is because 3x4.5=13.5

here to help!!

Step-by-step explanation:

by J Orloff · Cited by 3 — We have shown that a line or circle in x, y is transformed to a line or circle in u, v. This shows that inversion maps lines and circles to lines and circles

Answer:

it would be -3i and 3i  of and not half (half circle as factoring -9 would be -6 /2  =-3   = 3 sq rt f(x) -3 = x/2 where x stays 1     sqrt  of 1  * 3 -3 = 0 and here is a low line ascending curve see photo

Step-by-step explanation:

Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are -3 and +3, since (-3) 2 = (+3) 2 = 9. Any nonnegative real number x has a unique nonnegative square root r; this is called the principal square root  The 2nd root of 9, or 9 radical 2, or the square root of 9 is written as -3

The value of f(-3) + g(-3) Or (f + g)(-3) is 11.

When the output of one function is given to the input of another function they are called composite functions. In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Given, f(-3) is 9 and g(-3) is 2.

We know f(x) + g(x) = (f + g)(x).

∴ (f + g)(-3) = 9 + 2.

(f + g)(-3) = 11.

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Answer:

y2-y1/x2-x1

Step-by-step explanation:

No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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If you have a binomial experiment with p = 0.1 and a sample size of 900, then the variance of the distribution is option (b) 81

The variance of a binomial distribution measures the spread or variability of the distribution. It tells us how far the observations are from the mean. In this case, the binomial experiment has a probability of success of 0.1 and a sample size of 900.

The formula for the variance of a binomial distribution is Var(X) = np(1-p), where n is the sample size and p is the probability of success in each trial. Substituting the given values, we get:

Var(X) = 900 × 0.1 × (1 - 0.1) = 81

So the variance of the distribution is option (b) 81.

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The standard form of the given numbers is 207360 × 10¹⁷.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given the numbers is  (5 x 1,000,000) (6 x 100,000) (4 x 10,000) (8 x 1,000) (3 x 100) (2 x 10) (4 x 0.1) (9 x 0.001)

Now standard form means we need to write the exponents form.

So,

5 x 6 x 4 x 8 x 3 x 2 x 4 x 9 = 207360

And

1,000,000 x  100000 x 10000 x 1000 x 100 x 10 x 0.1 x 0.001 = 10¹⁷

So, combine 207360 x  10¹⁷

Hence "The standard form of the given numbers is 207360 × 10¹⁷".

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A variable without a clear operational definition can greatly impact the accuracy and reliability of statistics performed on it. To ensure accurate and meaningful results, it is important to have clear, well-defined variables in any research study.

The lack of a clear definition can lead to inconsistencies in data collection, making it difficult to accurately interpret and analyze the results.

Step 1: When a variable has no clear operational definition, researchers may measure or interpret it in different ways, leading to inconsistencies in data collection.

Step 2: These inconsistencies can affect the reliability and validity of the collected data, which in turn impacts the accuracy of the statistical analysis performed.

Step 3: As a result, the findings from such analyses may not accurately represent the true relationships or patterns within the sample or the population, leading to incorrect conclusions.

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