A rectangular piece of paper has side lengths of 30 cm and 25 cm.
Jasmin cuts the paper to make a new rectangle. The side lengths of the
new rectangle are 20% shorter than the side lengths of the original piece
of paper.
What is the area of the new rectangle?
Give your answer in cm².

That is a question about circle area.

To calculate the area of a circle, we multiplicate the constant pi (\(\pi \approx 3.14\)) by the radius (of the circle) squared. The expression represents that is below:

\(\boxed{A_c = \pi \times r^2}\)

In our problem, we don't know what is the circle raius, but we know the diameter. In a circle, the diameter is equal the double radius.

So, to know the radius of our circle, we divided the diameter by 2. Consequently, the raius of our circle is \(63 \div2 = 31.5\).

Now, we should use the expression and we will find the area:

\(A_c = 3.14\times 31.5^2\\A_c = 3.14\times 31.5\times 31.5\\A_c =3.14\times 992.25\\A_c = 3115.665\)

Therefore, the area of a circle with a diameter of 63 is approximately 3115.665.

I hope I've helped. :D

Enjoy your studies! \o/

The original air present after 8 breaths will be equal to 179.81 ml.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

It is given in the question that:-

During normal breathing, about 12% of the air in the lungs is replaced after one breath

If the initial amount of air in the lungs is 500 mL

how much of the original air is present after 8 breaths?

The calculation for the eduction of the air will be done by the following equation:-

\(\rm =Volume \ present\times (0.88)^n\\\\\\= 500\times (0.88)^8\)

=179.88 ml

Hence original air present after 8 breaths will be equal to 179.81 ml.

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Answer:

Step-by-step explanation:

Answer:

You end up with $15,091.44 This means you earned $12,531.44

Step-by-step explanation:

Step-by-step explanation:

It is given that,

Volume of the cylindrical can 1 is 2 litres and that of cylindrical can 2 is 6.75 litres. The diameter of the smaller can is 16 cm. We need to find the diameter of the larger can.

The formula of the volume of a cylinder is given by :

\(V=\pi r^2h\)

So,

\(\dfrac{V_1}{V_2}=\dfrac{r_1^2}{r_2^2}\)

Diameter, d = 2r

\(\dfrac{V_1}{V_2}=\dfrac{(d_1/2)^2}{(d_2/2)^2}\\\\\dfrac{V_1}{V_2}=(\dfrac{d_1^2}{d_2^2})\)

V₁ = 2 L, V₂ = 6.75 L, d₁ = 16 cm, d₂ = ?

\(\dfrac{2}{6.75}=(\dfrac{16^2}{d_2^2})\\\\d_2=29.39\ cm\)

So, the diameter of the larger can is 29.39 cm.

The sum expressed in sigma notation is:

Σ(8n + 5), where n goes from 1 to 5.

1. Identify the pattern in the given sequence:

13, 21, 29, 37, 45.
2. Notice that each term is 8 more than the previous term, so the common difference is 8.
3. Find the general formula for the sequence:

an = a1 + (n-1)d, where an is the nth term, a1 is the first term (13), n is the term's position, and d is the common difference (8).
4. Plug in the values to get the formula:

an = 13 + (n-1)8.
5. Simplify the formula:

an = 8n + 5.
6. Express the sum in sigma notation:

Σ(8n + 5), where n goes from 1 to 5.

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Answer:

C

Step-by-step explanation:

use the formula a²+b²=c²

The system of equations that model the situation is:

4c + 2s+ 3b == $29.51

c + 4s + 2b = $21.83

2c + 5s = $21.93

Simultaneous equations are more than one equation that would have to be solved jointlu in order to determine the required values.

Methods of solving simultaneous equations are:

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The ABC in the Pythagorean Theorem refers to the sides of a right triangle.

The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The formula is written as a^2 + b^2 = c^2, where "a" and "b" are the lengths of the legs of the triangle, and "c" is the length of the hypotenuse.

For example, let's consider a right triangle with side lengths of 3 units and 4 units. We can use the Pythagorean Theorem to find the length of the hypotenuse.

a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2

Taking the square root of both sides, we find that c = 5. So, in this case, the ABC in the Pythagorean Theorem represents a = 3, b = 4, and c = 5.

In summary, the ABC in the Pythagorean Theorem refers to the sides of a right triangle, where a and b are the lengths of the legs, and c is the length of the hypotenuse. The theorem allows us to calculate the length of one side when we know the lengths of the other two sides.

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To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.

First, let's rewrite the expression for the nth term of the sequence:

an = 5n / (4n + 1)

As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:

an ≈ n / (4n + 1)

Now, we can consider the limit of the sequence as n approaches infinity:

lim(n→∞) n / (4n + 1)

To evaluate this limit, we can divide both the numerator and denominator by n:

lim(n→∞) (1 / 4 + 1/n)

As n approaches infinity, the term 1/n approaches zero, leaving us with:

lim(n→∞) 1 / 4 = 1/4

Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.

In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.

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Answer:

This is your graph to the following equation f(x) = 1/4(x) - 7

Answer:

  f(x) = 6·sin(8(x -π/2))

Step-by-step explanation:

A transformed sine function with amplitude A, period P, and horizontal shift S can be written as ...

  f(x) = A·sin(2π/P(x -S))

__

The equation for A=6, P=π/4, and S=π/2 is then ...

  f(x) = 6·sin(8(x -π/2))

_____

Additional comment

The horizontal shift is equal to two full periods, so the shifted function is indistinguishable from the unshifted function.

Answer: Yes

Step-by-step explanation:

It can have angles of 90 degrees, 45 degrees, and 45 degrees.

Yes, a triangle in which at least two sides are equal. Since the two legs of the triangle are equal, which makes the corresponding angles are equal to each other.

The Isosceles Right Triangle has one of the angles exactly 90 degrees and two sides, which are equal to each other.

Since the two sides are equal it makes the corresponding angle congruent.

An Isosceles triangle is a triangle in which at least two sides are equal. Since the two legs of the triangle are equal, which makes the corresponding angles are equal to each other.

Hence, Yes, a triangle in which at least two sides are equal. Since the two legs of the triangle are equal, which makes the corresponding angles are equal to each other.

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Answer:

-5.33333.....

Step-by-step explanation:

Because f(x) is equal to -2/3 so actually multiply, (usually divide that it's multiplying but you divide when fractions or decimals are involved) and you have  -5.3333333333333.....

Pls consider giving me Brailniest! It would help out a lot!

Since the limit of F(x) is infinity, we can conclude that F(x) = logx xlogx 5 grows at the same rate as logx as x approaches infinity. Therefore, F(x) = logx xlogx 5 is not ω(logx).

A function is a relation between sets that assigns to each element of a first set, exactly one element of the second set. Functions are typically written as an equation, with the first set (the domain) on the left side and the second set (the range) on the right side. The most common type of function is a function from real numbers to real numbers, which is often referred to as a real-valued function. Examples of real-valued functions include linear, polynomial, exponential, and trigonometric functions.


False. F(x) = logx xlogx 5 is not ω(logx). ω(logx) is a notation used to denote a function that grows faster than logx as x approaches infinity. However, F(x) = logx xlogx 5 grows at the same rate as logx as x approaches infinity. To prove this, we can calculate the limit of F(x) as x approaches infinity:

lim F(x) = lim (logx xlogx 5)

= lim (logx xlogx) lim 5

= ∞∞ 5

= ∞

Since the limit of F(x) is infinity, we can conclude that F(x) = logx xlogx 5 grows at the same rate as logx as x approaches infinity. Therefore, F(x) = logx xlogx 5 is not ω(logx).

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The least number that, when divided by 12, 20, and 36, leaves a remainder of 11 in each case is 191.

To find the least number that satisfies the given conditions, we can use the concept of the least common multiple (LCM).

Step 1: Find the LCM of 12, 20, and 36.
The prime factors of 12 are 2 and 3.
The prime factors of 20 are 2 and 5.
The prime factors of 36 are 2, 3, and 3.

To find the LCM, we take the highest power of each prime factor that appears in any of the given numbers.

LCM = 2² * 3² * 5 = 180.

Step 2: Add the remainder (11) to the LCM.
180 + 11 = 191.

Therefore, the least number that satisfies the given conditions is 191.

The least number that, when divided by 12, 20, and 36, leaves a remainder of 11 in each case is 191.

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Answer: 8.08

Step-by-step explanation:

The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

In the Social Exchange Theory of interpersonal relationship satisfaction, you would feel happiest in relationships when you feel that the rewards of the relationship equal or exceed its costs.

The Social Exchange Theory states that people evaluate their relationships in economic terms, with rewards being the benefits of the relationship and costs being the negatives. Rewards can include affection, attention, emotional support, sex, and companionship. Costs can include time, effort, money, and negative emotions such as stress, anxiety, and sadness.

According to the theory, individuals will be motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

The opposite is also true; if individuals feel that the costs of the relationship are greater than the rewards, they will be motivated to leave the relationship.

Therefore, people are constantly evaluating their relationships to determine whether they are getting what they need from the relationship and whether it is worth continuing.

The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

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Answer: The walkway should be 8.5 feet wide.

Step-by-step explanation: First, let's find the total area of the pool and the walkway. The pool measures 8 feet by 10 feet, so its area is:

8 ft x 10 ft = 80 ft²

The walkway will go around the pool, so it will add an equal amount to each side of the pool. If we let x represent the width of the walkway, then the length of the pool and walkway together will be:

10 ft + 2x (one width of the pool plus two widths of the walkway)

and the width of the pool and walkway together will be:

8 ft + 2x (one length of the pool plus two widths of the walkway)

So the total area of the pool and walkway will be:

(10 ft + 2x) x (8 ft + 2x) = 360 ft²

Expanding the left side of the equation, we get:

80 ft² + 20x ft² + 16x ft² + 4x² = 360 ft²

Combining like terms and simplifying, we get:

4x² + 36x - 280 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b² - 4ac)) / 2a

In this case, a = 4, b = 36, and c = -280, so:

x = (-36 ± sqrt(36² - 4(4)(-280))) / 8

x = (-36 ± sqrt(16976)) / 8

x = (-36 ± 130) / 8

We take only the positive value of x since it is a width. Thus, x = 8.5.

Therefore, the walkway should be 8.5 feet wide.

Answer:

y=-2/3x-1

Step-by-step explanation:

Answer:

y=-2/3x-1

Step-by-step explanation:

Answer:

\(\LARGE\mathsf{slope\:=\:\frac{9}{5}}\)

y-intercept: (0, 32), b = 32

\(\LARGE\mathsf{y\:=\:\frac{9}{5}x\:+\:32}\)

Step-by-step explanation:

Given (0, 32) as the freezing point of water in Celsius and Farenheit, and (100, 212) as the boiling point of water in Celsius and Farenheit.

Use these points to solve for the slope of their line.

Let (x₁, y₁) = (0, 32)

    (x₂, y₂) = (100, 212)

Substitute these points into the following formula for the slope:

\(\LARGE\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}\)

\(\LARGE\mathsf{m = \frac {(212\: -\: 32)}{(100\: -\: 0)}\:= \frac {180}{100}}\)

\(\LARGE\mathsf{m\:=\:\frac{9}{5}}\)

Therefore, the slope of the line is  \(\LARGE\mathsf{m\:=\:\frac{9}{5}}\).

Next, the given problem asks for the value of the y-intercept.  The y-intercept is the point on the graph where it crosses the y-axis, with its coordinates occurring at point, (0, b ). Thus, the y-intercept provides the value of y when its corresponding x-coordinate is 0.

To solve for the y-intercept, b, we must choose one of the given points, (100, 212), and the slope, \(\LARGE\mathsf{m\:=\:\frac{9}{5}}\), and substitute these values into the slope-intercept form, y = mx + b:

y = mx + b

\(\LARGE\mathsf{212\:=\:\frac{9}{5}(100)\:+\+b}\)

212 = 180 + b

Subtract 180 from both sides to isolate b:

212 - 180 = 180 - 180 + b

32 = b

The y-intercept is (0, 32), where b = 32.

Given the slope, \(\LARGE\mathsf{m\:=\:\frac{9}{5}}\),  and the y-intercept, b = 32:

The linear equation in slope-intercept form is:  \(\LARGE\mathsf{y\:=\:\frac{9}{5}x\:+\:32}\)

Answer:

9x

Step-by-step explanation:

x^3*-1(x^2-3x)(x+3)

      (-x^2+3x)(x+3)

distribute

x^3 - x^3-3x^2+3x^2+9x

x^3-x^3+9x

=9x

Answer:

10p

Step-by-step explanation:

have a good day :)

Answer:

(2+4)÷12

Step-by-step explanation:

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The linear equation y = x - 5 show's Evie's net loss or gain

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.

In solving this problem, we have to write the problem in a form of linear equation.

Let;

y = x + 4 - 9

y = x - 5

The equation to show Evie's net gain or loss is y = x - 5

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Let us begin by finding the equation for the rational function. We have:Vertical asymptotes: `x = 1` and `x = -3`.Hence, the denominator of the rational function is `(x - 1)(x + 3)`.

x-intercepts: `x = -6` and `x = 6`. Hence, the numerator of the rational function is `A(x + 6)(x - 6)`.Y-intercept: `y = 7`. The rational function is as follows: ```f(x) = A(x + 6)(x - 6)/[(x - 1)(x + 3)]```

To find the value of A, let us substitute `x = 0` and `y = 7` in the above equation:`7 = A(6)(-6)/[(0 - 1)(0 + 3)]`Simplifying the above equation, we get: `A = -1`. Thus, the required rational function is: `f(x) = -(x + 6)(x - 6)/[(x - 1)(x + 3)]`The answer in the main part is `- (x + 6)(x - 6)/[(x - 1)(x + 3)]`.

Explanation: We have given the following in the problem.1. Vertical asymptotes at `x = 1` and `x = -3`.2. `x`-intercepts at `x = -6` and `x = 6`.3. `y`-intercept at 7.

To find the required rational function, we must first find the denominator of the rational function. We know that the denominator of the rational function will have factors of the vertical asymptotes. Hence, the denominator is `(x - 1)(x + 3)`.To find the numerator of the rational function, we know that it must have factors of the `x`-intercepts. Hence, the numerator is `A(x + 6)(x - 6)`.The rational function is as follows: `f(x) = A(x + 6)(x - 6)/[(x - 1)(x + 3)]`

To find the value of `A`, we substitute `x = 0` and `y = 7` in the above equation: `7 = A(6)(-6)/[(0 - 1)(0 + 3)]`.

Simplifying the above equation, we get `A = -1`.Thus, the required rational function is: `f(x) = -(x + 6)(x - 6)/[(x - 1)(x + 3)]`Therefore, the answer in the main part is `- (x + 6)(x - 6)/[(x - 1)(x + 3)]`.

Conclusion: The required rational function is `-(x + 6)(x - 6)/[(x - 1)(x + 3)]`.

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The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Answer:

5/3, 4/3, 3/3, 2/3, 1/3

Step-by-step explanation:

since there is a common denominator of 3, you just order them from greatest to least or biggest to smallest