How do you translate a horizontal graph?

The distance, which is determined by integrating the velocity function over the specified time interval, is calculated as 2.98 and 2.58.

We will use left Riemann sum and right Riemann sum to obtain an overestimate and an underestimate. The definite integral, which in this case is a distance, can also be approximated using the average of these estimates.

1 ) The distance the bug crawls obtained by integrating the velocity function v(t) = 4/1+t over the inclined time interval is

[tex]\int\limits^1_0 \, \frac{4}{1+t} dt.[/tex]

Splitting the interval [0, 1] into sub intervals of length Δt = 0.2, we get the Riemann sum L and the right Riemann sum R:

L = ∑⁴ v(ti) Δt

L = (0.2) (v(0) + v(0.2) + v(0.4) + v(0.6) + v(0.8))

L ≈ 2.98

R = ∑⁵ v(ti) Δt

R = (0.2) (v(0.2) + v(0.4) + v(0.6) + v(0.8) + v(1.0))

R ≈ 2.58

2 )The average of these two Riemann sums gives us a new estimate for the distance :

AVG = (2.98 + 2.58)/2

=2.78.

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The four ways of simplifying an expression are combining like terms, using the order of operations, applying the distributive property, and factoring.

Combining like terms is the process of adding or subtracting expressions that have the same variables raised to the same powers. The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction), is a set of rules that dictate the order in which mathematical operations should be performed. Applying the distributive property allows you to multiply a single term and a sum or a difference of two or more terms by multiplying each term inside the parentheses by the term outside the parentheses. Factoring is the process of finding common factors in an expression and dividing them out. All these steps are used to simplify an expression and make it easier to understand and work with.

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Answer:

Step-by-step explanation:

The shortest measurement of the length of the insects is 1/8 inch.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

From the line plot,

The longest length of insects is 7/8 inches.

The shortest length of the insect is 1/8 inch.

Thus,

The shortest measurement of the insect is 1/8 inch.

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The required value of k will the system of linear equations has infinite number of solutions is -9.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We know that

2x+3y13=0. ..........(1)

6x−ky−39=0 ..........(2)

Because there are infinity many solutions to linear equations.

[tex]\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}[/tex]

⇒ 2/6 = -3/k = -13/-39

-3/k = 1/3

k = -9

Thus,required value of k is -9.

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The correct statement is "only a and c are correct"  so option g is the answer.

The statement that is true in a normal distribution is "approximately 70% of the values are within one standard deviation from the mean" (a), and "2.1% of the values are between -2 and -3 standard deviations from the mean" (c).

These statements are true because of the properties of a normal distribution, also known as a Gaussian distribution or bell curve. In a normal distribution, the majority of values cluster around the mean, with fewer and fewer values as you move further away from the mean.

The statement "twenty-seven percent of the values are between one and two standard deviations from the mean" (b) is not true, as the correct percentage is approximately 27.7% (68-95-99.7 rule).

The statement "0.1% of the values are 3 or higher standard deviations from the mean" (d) is also not true, as the correct percentage is approximately 0.3%.

Therefore, the correct statement is "only a and c are correct".

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The rate of change of the height of the oil slick with respect to time is:

0 centimeters per minute.

At the instant when the radius of the oil slick is 100 centimeters and the height is 0.5 centimeter, the rate of change of the height of the oil slick with respect to time is 0 centimeters per minute.

This is because, even though the radius of the oil slick is increasing at a rate of 2.5 centimeters per minute, the height of the oil slick remains constant.

The height of the oil slick is at its maximum value of 0.5 centimeters, and since it is not changing, the rate of change of the height of the oil slick with respect to time is 0 centimeters per minute.

It is important to note that the height is not changing at this moment, since it is already at its maximum value of 0.5 centimeters.

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Answer: w = 8 miles

Step-by-step explanation:

The area of the shaded region is 16 mi^2.

The height is already given as 4mi. Using this, we can set up the equation to find w, the base of the shaded region.

1/2*4*w = 16

2*w=16

w=8

Therefore, w=8 miles

Polynomials are mathematical expressions that involve a sum of powers in one or more variables. Example : x^2 + 3x - 4, 2x^3 - x^2 + 5x - 7, 4x^4 - x^3 + x + 2.

They can be defined as follows:

A polynomial in one variable x is an expression of the form a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0, where n is a non-negative integer and the coefficients a_0, a_1, ..., a_n are real or complex numbers.

Three examples of polynomials in one variable x are:

x^2 + 3x - 4

2x^3 - x^2 + 5x - 7

4x^4 - x^3 + x + 2

Note that any constant is also a polynomial, for example, 3, -2 and 0.

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On graphing function A: 3x - 21 and function B: y = 2x - 3, it is known that both are linear as they both form a straight line.

What is a linear function?

A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nevertheless, calculus and linear algebra are also used to represent linear functions.

The function A is given as 3x - 21.

The function B can be written in slope intercept form -

y = mx + b

where m is the slope and b is the y-intercept.

m = (y2-y1)/(x2-x1)

m = [1-(-1)]/(2-1)

m = 2/1

m = 2

To find y-intercept substitute x = 1 and y = -1.

y = mx + b

-1 = 2(1) + b

-1 = 2 + b

b = -1 - 2

b = -3

Hence the equation for function B is y = 2x - 3.

Therefore, on graphing function A and B it can be seen that both are linear.

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When the  value of k is 4 then the roots of the equation be real and equal.

Correct option is C)

The given quadratic equation is :

[tex]$$\mathrm{kx}^2+4 \mathrm{x}+1=0$$[/tex]

Here, a=k, b=4, c=1

Now, [tex]$\mathrm{D}=\mathrm{b}^2-4 \mathrm{ac}=(4)^2-4 \times \mathrm{k} \times 1=16-4 \mathrm{k}$[/tex]

We know that a quadratic equation has real and equal roots

If [tex]$\mathrm{D}=0$[/tex]

[tex]$\Rightarrow 16-4 \mathrm{k}=0$[/tex]

[tex]$\Rightarrow-4 \mathrm{k}=-19$[/tex]

[tex]$\therefore \mathrm{k}=\frac{-16}{-4}=4$[/tex]

The complete question is,

For what value of [tex]$\mathrm{k}$[/tex] will the quadratic equation: [tex]$\mathrm{kx}^2+4 \mathrm{x}+1=0$[/tex] have real and equal roots?

a. 2

b.3

c.4

d.1

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For all x ∈ R - {-√11, √11} f(x) is defined

So, the range of f(x) is f(x) ∈ R.

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The whole set of values that the function's output can produce is referred to as the range. The set of values that might be a function's outputs is known as the co-domain.

The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A - > B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output.

The function is

f(x) = [tex]\frac{x^{2} }{11-x^{2} }[/tex]

now for x² = 11 the function is not defined.

but for all x ∈ R - {-√11, √11} f(x) is defined

So, the range of f(x) is f(x) ∈ R.

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The function's range is y 0 in the current situation.

The difference between values in a collection of data can be measured simply by looking at the range. Simply take the difference between the lowest and highest values and ignore the others to determine the range.

The function's range is the range between all of the y values, from least to maximum.

Graph points (-1,1), (-2,2), (0,0), and (1,1) (2,2)

The group of outputs or y values is referred to as the range.

range = 0,1,2,3 ......

Means have a range that extends from 0 to all positive numbers, infinity.

Thus, range = y 0.

The supplied function's range is therefore y 0.

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The greatest common factor (GCF) of two or more numbers is the largest number that divides evenly into each of the numbers without leaving a remainder. To find the GCF of 24, 30 and 50, we can use the prime factorization method. The prime factorization of 24 is 2^3 * 3^1, the prime factorization of 30 is 2 * 3^1 * 5^1, and the prime factorization of 50 is 2 * 5^2. We can see that the GCF of these numbers is 2 * 3^1 = 6, since 6 is the highest power of 2 and 3 that divides all three numbers evenly. So, the GCF of 24, 30 and 50 is 6.

I hope this helps :)

Answer:

2

Step-by-step explanation:

I did the work.

Answer:

a) To calculate the remaining balance on the loan at the end of the first year, you need to first calculate the interest that has accumulated on the loan. This can be done using the formula:

Interest = Principal x Rate x Time

In this case, the interest for the first year would be:

Interest = 150000 x (10/100) x 1 = 15000

So the total amount owed at the end of the first year, including interest, would be:

Total = Principal + Interest = 150000 + 15000 = 165000

Now, after paying Rs 85000 at the end of the first year, the remaining balance on the loan would be:

Remaining Balance = Total - Payment = 165000 - 85000 = 80000

To calculate the amount that needs to be paid at the end of the second year, you need to calculate the interest that has accumulated on the remaining balance of the loan. This can be done using the same formula as before:

Interest = Remaining Balance x Rate x Time = 80000 x (10/100) x 1 = 8000

So the total amount that needs to be paid at the end of the second year would be:

Total = Remaining Balance + Interest = 80000 + 8000 = 88000

b) If he had paid the loan only at the end of second year, the interest would have been:

Interest = Principal x Rate x Time = 150000 x (10/100) x 2 = 30000

Thus, he would have paid 30,000 more than he paid by paying partly at the end of first year.

Step-by-step explanation:

Based on the information given, the computation shows that the distance between them is 4.330 miles.

Velocity, as opposed to speed, refers to the pace and direction of such an object's travel as it moves down a path. Alternatively, velocity is a vector while speed is a scalar quantity.

The pace at which distance and time change is what is meant by speed. It has the aspect of temporal and spatial remoteness. The combination of the fundamental units of distance and time is what is described as the SI unit of speed. As a result, the SI unit of speed is the meter per second.

Solving the distance.

Since one has bearing 42°30', this will be: = 42° + (30/60) = 42° + 0.5 = 42.5°.

The other has bearing 52°12'. This will be:

= 52° + (12/60) = 52° + 0.2 = 52.2°.

The difference of the angles will be:

= 52.2° - 42.5°

= 9.7°

Let the distance between them be represented by c. Therefore, we'll use cosine law to solve the question. This will be:

c² = a² + b² - 2ab cos 9.77°

c² = 25² + 25² - (2 × 25 × 25 × 0.985)

c² = 18.75

c = 4.330

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The rational expression is

[tex]\frac{8(x+4)}{(x+4)(x-1)} = \frac{8}{(x-1)}[/tex]

for x ∈ R - {1}

The ratio of two polynomials is a rational expression. If an expression is rational, it may be expressed in the form p/q, where p and q are polynomials.

When the numerator and denominator of an equation are both polynomials, the expression is said to be rational. The lowest form of the numerator and denominator is used to simplify rational formulas. An algebraic fraction is another name for a rational expression.

The value of a logical statement is diminished to its simplest form or lowest terms when it is simplified. Similar to how we simplify fractions, we can simplify a rational equation. In fractions, a rational number is said to be in its simplified form if its numerator and denominator share no factors other than 1. The only distinction is that when simplifying rational expressions, the same strategy also applies because the fraction contains polynomials.

The expression is

[tex]\frac{8(x+4)}{(x+4)(x-1)} = \frac{8}{(x-1)}[/tex]

for x ∈ R - {1}

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Answer:

480 acres ig

Step-by-step explanation:

i think i understand the problem.

if so, then the solution is as follows:

let x = the number of days required to finish the job.

let y = number of acres that had to be cleaned.

without the new machine, the formula would be:

80x = y

that means cleaning 80 acres per day * x days will equal y acres that are cleaned.

with the new machine, the formula would be:

90(x-1) + 30 = y

that means cleaning 90 acres per day for one less day and then cleaning 30 acres on the last day will equal y acres that are cleaned.

so you have 2 equations.

80x = y

90(x-1) + 30 = y

replace y in the second equation with the value of y from the first equation gets you:

90(x-1) + 30 = 80x

solve for x to get:

x = 6

what this means is:

80 acres a day for 6 days will equal 480 acres that are cleaned.

90 acres a day for 5 days and then 30 acres on the last day will equal 480 acres that are cleaned.

with the old machine we are looking at:

80 + 80 + 80 + 80 + 80 + 80 = 480.

with the new machine we are looking at:

90 + 90 + 90 + 90 + 90 + 30 = 480.

looks like they had to clean 480 acres.

Answer: this is simplist form but put it as a fractoin 7 1/2

Step-by-step explanation:

Answer: y-axis

Step-by-step explanation:

The y-axis determines the "height" of the graph, so 2 units higher would mean 2 units higher on the y-axis.

The length of the ball from the center green using the cosine rule is;  84.4 yards

In trigonometry, the Cosine Rule is a rule that states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle that is included between them.

This can be expressed as;

c = √(a² + b² - 2ab cos C)

In this question, the length of the length of the ball from the center green is c and as such using the cosine rule, we have;

c = √(110² + 45² - 2(110 * 45)cos 45)

c = √(14125 - 7000.36)

c = 84.4 yards

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The length of the guy wire, to the nearest foot is: 207 ft.

What is Pythagorean theorem ?

Pythagorean theorem can be defined as the square of hypothenuse is equal to sum of squares of base and adjacent

Given ,

The length of the guy wire, to the nearest foot is: 207 ft.

After sketching the information given, we have two similar right triangles, ΔABE and ΔCDE.

CD = 11 ft

DE = 2 ft

BD = 35 ft

Required:

Length of the guy wire (AE)

First, find AB:

Since ΔABE ~ ΔCDE, therefore,

AB/CD = BE/DE (proportional sides)

Plug in the values

AB/11 = (35 + 2)/2

AB/11 = 37/2

Cross multiply

AB = (37 × 11)/2

AB = 203.5 ft

Apply Pythagarean Theorem to find AE:

AE = √(AB² + BE²)

AE = √(203.5² + 37²)

AE = 207 ft (nearest foot)

Therefore, the length of the guy wire, to the nearest foot is: 207 ft.

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Solving the provided question, we can say we have linear equation  y= -0.00211x^2 + 1.06x and here, x = 10 => y = -0.211 + 10.6 => y = 10.389

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here, we have equation

y= -0.00211x^2 + 1.06x

and here, x = 10

y = -0.211 + 10.6

y = 10.389

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Answer:

Perimeter of rectangle is larger by 6 cm

Step-by-step explanation:

area of rectangle = 48 * 27 = 1296

√1296 =  36

length of square = 36 cm

Perimeter of square = 36 + 36 + 36 + 36 = 144

Perimeter of rectangle = 48 + 48 + 27 +27 = 150

Perimeter of rectangle is larger by 6 cm

The PPF represents the maximum combinations of two goods that can be produced with a given set of resources and technology, and each point on the PPF represents a trade-off between the two goods in terms of the opportunity cost. Therefore the PPF is called the opportunity cost.

The production possibility frontier (PPF) is a graph that shows the different combinations of two goods that can be produced with a fixed set of resources and technology. The PPF is often used to illustrate the concept of opportunity cost, which is the cost of one alternative in terms of the benefits forgone of the best alternative.

The PPF represents the trade-offs that society must make between producing different goods. As we move along the PPF, we can see that as we produce more of one good, we must give up some production of the other good. This trade-off is represented by the slope of the PPF, which is the opportunity cost of producing one good in terms of the other good. The opportunity cost of producing one good increases as we move along the PPF.

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After log2n rounds, you may expect one coin to remain

There are n coins, then. According to probability, half of them will display tails, and the other half heads when you flip all of them. We now have n/2 coins after setting aside n/2 coins. We set the n/2/2 coins aside since this time they will all show tails, and the trend continues.

There is only one coin remaining, hence the sum of this GP must equal n-1.

After the first round, n/2 coins are anticipated to be withdrawn.

After the second round, n/4 coins are anticipated to be withdrawn.

Therefore, one coin should be left after log2n rounds.

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Answer:

Quarter, Dime, and Nickel

Step-by-step explanation:

1. How much is the largest coin? Quarter. 25 cents.

2. Try dime next: 25+10=35.

3. Do 40-35 to see how much is left. 5.

4. Nickel=5 cents.

Quotients of polynomials are called rational expressions.

The quotient of two polynomials is the concept of a rational expression. Or to put it another way, it is a fraction using polynomials as the numerator and denominator. We must first identify any common factors, such as constants, variables, or polynomials, or the numerator and denominator, in order to formulate a rational expression in the simplest possible form. As a result, we must factor the denominator and numerator. Cross out any common factors after factoring the numerator and the denominator.

An algebraic expression known as a rational expression is the ratio of two polynomial expressions. A function whose value is determined by a reasonable expression is said to be rational.

A polynomial is an equation made up of exponents, constants, and variables that have been joined using mathematical operations.

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Answer:

Horizontal line on the "2" line of the y axis.

Step-by-step explanation:

y=2 means y is constantly at 2, so it would be a horizontal line there.

Yes, the two triangles as represented in the attached image are similar by virtue of the; SAS Similarity theorem.

As evident in the task content; the angle measure 60° is common to both triangles.

Also, it is important to know that; the angle 60° is formed at the intersection of two side lengths in each of the triangles.

Finally, it is noteworthy to know that the ratio of corresponding sides of both triangles are equal; since

6 / 2 = 9 / 3.

Ultimately, it can be inferred that the two triangles are similar by the; Side-Angle-Side Similarity theorem.

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