The simple interest on a sum of money invested at 3% per annum for 2 years was $39.75.
Calculate the sum of money invested

It represents the average amount of change in the function per unit throughout that time period.

Divide the change in y-values by the change in x-values to calculate the average rate of change. When analyzing changes in measurable parameters like average speed or average velocity, finding the average rate of change is quite helpful.

The formula R = D/T, or rate of change equals the distance traveled divided by the time required to do so, can be used to approach rate-of-change problems in general.

It represents the average amount of change in the function per unit throughout that time period. It is generated from the slope of the straight line joining the interval's ends on the graph of the function.

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The requried dimension of the original rectangle is given as length = 25 cm, width = 10 cm.

The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.

Let the length and width of the original rectangle be x and y,
According to the quesiton,

The perimeter of a rectangle is 70 cm.
2 [x + y] = 70
x  + y = 35 - - - -(1)

Now,
its length is decreased by 5 cm and its width is increased by 5 cm, its area will increase by 50 cm².
Area of the new rectangle = area of the original rectangle + 50
(x  - 5)(y + 5) = xy + 50

from equation 1,

(x - 5)(35 - x + 5) = x(35 - x) + 50
-x² - 200 + 40x + 5x = 35x - x² + 50
45x - 35x = 50 + 200
10x = 250
x = 25

Now,
y = 35 - 25
y = 10

Thus, the requried dimension of the original rectangle is given as length = 25 cm, width = 10 cm.

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The solution to the trigonometric equation is x = ( 3π/4 ) , x = ( 7π/4 )

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin (-θ) = -sin (θ)

csc (-θ) = -csc (θ)

cos (-θ) = cos (θ)

sec (-θ) = sec (θ)

tan (-θ) = -tan (θ)

cot (-θ) = -cot (θ)

In the first quadrant, sin, cos and tan are all positive.

In the second quadrant going anti-clockwise, only sin is positive.

In the third quadrant going anti-clockwise, only tan is positive.

In the fourth quadrant going anti-clockwise, only cos is positive

Given data ,

Let the trigonometric equation be represented as A

Now , the value of A is

cot ( x - π/2 ) = 1   be equation (1)

On simplifying the equation , we get

cot ( - ( π/2 - x ) ) = 1

Now , cot (-θ) = -cot (θ)

So , - cot ( π/2 - x ) = 1

And , the value of cot ( π/2 - θ ) = tan θ

Substituting the values in the equation , we get

-tan x = 1 over the interval [ 0 , 2π ]

The value of x for -tan x = 1 is given by x = ( 3π/4 ) + nπ

when n = 1

x = ( 7π/4 )

So , the values of x are ( 3π/4 ) and ( 7π/4 )

Hence , the solutions are ( 3π/4 ) and ( 7π/4 )

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Answer:it is 900 because that’s a number that is irrational

Step-by-step explanation:

Answer:

7.07 units

Step-by-step explanation:

The equation showing the relation between shorter and longer skirt is 3s+4t = 140.

Given that the Scottish dance team used 140 yards of tartan to make dancing skirts.

The skirt pattern for the shorter members is 3- yards of fabric, and the skirt pattern for the taller members is 4 yards of fabric.

So, we need to find the equation represents the relationship between the number of short skirts and the number of long skirts that were made,

So, if there are s short skirts and t long skirts,

So,

The relation will be =

3s + 4t = 140

Hence the equation showing the relation between shorter and longer skirt is 3s+4t = 140.

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Answer: 20

Step-by-step explanation: i did this before on a quiz

Answer:

20

Step-by-step explanation:

online calcs can help with this

Answer:

B. -$0.75

Step-by-step explanation:

that is really very simple.

the value on day 1 (the begin) is $2.50.

the value on day 5 (the end of the week I assume) is $1.75.

so, the value changed by -$0.75 from $2.50 to $1.75.

yes, this is the sum of all little individual changes day by day. but there is no need to do these detailed calculations. at the end it is just

value end - value begin

Answer:

the third one

Step-by-step explanation:

it only passes once

Answer:

The x value of a point where a vertical line intersects a function represents the input for that output y value. If we can draw any horizontal line that intersects a graph more than once, then the graph does not represent a function because that y value has more than one input.

Step-by-step explanation:

In the equation 3x², the variable x²'s coefficient is 3.

The formula is 3x2.

To determine: The expression's variable x2's coefficient

The number next to the variable in the equation is the coefficient.

Three is the coefficient of x in 3x².

The coefficient of a number is the product of the number and the variable. For example, 6 is the value of the x² coefficient in the formula 6x2+99.

The word that is multiplied by x² is 3, as can be seen.

Consequently, the value of x² in the equation 3x² is 3.

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Complete question - What is the coefficient of x² in 3x²?

Answer: A C A B

Step-by-step explanation:

Factor theorem is most commonly used for factoring a polynomial or integer and searching the roots of the polynomial. It is a particular case of a polynomial remainder theorem.

As defined in the introduction, a polynomial f(x) has a factor (x-a), if and only if, f(a) = 0. It is one of the processes to do the factorization of a polynomial.

Here we can prove the factor theorem, according to which we can.

factories the polynomial.

Consider a polynomial f(x) which is divided by (x-b), then f(c)=0.

Using remainder theorem,

f(x)= (x-b) q(x)+f(b)

Where f(x) is the target polynomial and q(x) are the quotient polynomial.

because f(b) = 0, So,

f(x)= (x-b) q(x)+f(b)

f(x) = (x-b) q(x)+0

f(x) = (x-b) q(x)

So, (x-b) is a factor of the polynomial f(x).

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The total cost of the meal, plus tax and tip will be $11.19.

Steps to do are as follows:

Here given,

Meal = $9.45

Tax equals 3% of 9.45, or.

.03 x 9.45 = $0.2835

Meal plus tax equals $9.45 + $0.2835 = $9.7335

Tip equals 15% of $9.7335

or .15 x 9.7335 = $1.460

TOTAL = Meal + Tax + Gratuity = $9.45+ $0.2835 + $1.460

= $11.19

Therefore the total cost is $11.19.

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False. The percentage of children enrolled in public schools that are of non-Caucasian ancestry varies by location and can change over time. According to the National Center for Education Statistics (NCES), as of the 2018-2019 school year, the percentage of public school students who were non-Caucasian was around 50%.

According to the National Center for Education Statistics (NCES), as of the 2018-2019 school year, the percentage of public school students who were non-Caucasian was around 50%. So it is not true that over 62% of children enrolled in public schools are of non-Caucasian ancestry.

It's hard to say why the percentage of non-Caucasian students in public schools is less than 62%. It could be because of a variety of factors, such as demographic changes in the population, socioeconomic factors, or even educational policies. However, it's important to note that the percentage of non-Caucasian students in public schools can vary depending on location and can change over time.

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He will read 700 pages each day.He must be committed to reading this amount of pages each day in order to finish the book in two days.

1. There are 1400 pages in the book.

2. The book must be read in even days.

3. To find the number of pages read each day, divide 1400 by 2 (since it must be read in two days).

4. The answer is 700 pages read each day.

The book contains 1400 pages and must be read in two days. To find the answer, the number of pages must be divided by two. This means that each day, he must read 700 pages. This is the same amount each day, so he will read the same amount of pages for each day he reads it. He will have to read for two days in order to finish the book and will read 700 pages for each day. He must be committed to reading this amount of pages each day in order to finish the book in two days.

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Answer:

SSS

Step-by-step explanation:

They share one common side, and the two other sides are marked with single and double line identifiers, meaning they are the same. Therefore, SSS.

At 2.5 seconds the ball reach its maximum height.

And, Its maximum height will be 25 feet.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation that describes the height (h) of a ball that is thrown straight up as a function of the (t) that the ball has been in the air is,

⇒ h = 40t - 16t²

So, For the time does the ball reach its maximum height, we can put h = 0, so we get;

⇒ h = 40t - 16t²

⇒ 40t - 16t² = 0

⇒ 16t² - 40t = 0

⇒ t (16t - 40) = 0

⇒ 16t - 40 = 0

⇒ 16t = 40

⇒ t = 40/16

⇒ t = 2.5 seconds

Now, The height function is a quadratic function which has the zeroes at  t = 0 and t = 2.5.

So, It has the maximum at x = midpoint between the roots 0 and 2.5, i.e. 1.25 seconds.

Hence, Substitute this value t = 1.25 seconds into the given height function, we get;

⇒ h = 40t - 16t²

⇒ h = 40 × 1.25 - 16 (1.25)²

⇒ h = 50 - 25

⇒ h = 25 feet

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Answer:

625, 125, 25, 5

Step-by-step explanation:

390625, 78125, 15625, 3125

We need to find out the relationship between a number and the previous number.

We can tell that there is no common difference since 78125 - 390625 cannot possibly equal 3125 - 15625.

We can try to check if this is a geometric sequence.

78125/390625 = 0.2

15626/78125 = 0.2

3125/15625 = 0.2

Each number is 1/5 of the previous number.

3125/5 = 625

625/5 = 125

125/5 = 25

25/5 = 5

Answer: 625, 125, 25, 5

The time it takes Timothy to drive to his friend's house does not proportional to the distance. Because all ordered pairs do not pass through a straight line.

What is the ordered pair?

An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), with two values, expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair's numeric values can be integers or fractions.

Given ordered pairs are (5,10), (11,15), and (18,20).

The ordered pairs are plotted on the graph.

A line can not draw through the ordered pairs.

Thus, time is not proportional to distance.

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After solving tan² (0) = 1 on the interval [0, π), The answers are A and B where 0 < A, A = 22 and B = 4.

A set of intervals on the real line are used to create an interval graph, which is an undirected graph in graph theory. Each interval has its own vertex, and there is an edge between vertices where its intervals intersect. It is the graph created by intersecting the intervals.

Chordal and perfect graphs both exist as interval graphs. In these graphs, an optimal graph colouring or maximum clique can be found in linear time, and they are recognisable. The interval graphs comprise all proper interval graphs, which are defined from a set of unit intervals in the same manner.

[tex]$\tan x-1=0 \rightarrow \tan x=\pm 1$[/tex]

Trig table give [tex]$\tan x=1=\tan \left(\frac{\pi}{4}\right)$[/tex]

Trig unit circle gives another arc that has same tan value:

[tex]$x=\left(\frac{\pi}{4}+\pi\right)=\left(\frac{5 \pi}{4}\right)$[/tex]

and

[tex]$ tan \ x=-1=\tan \left(\frac{3 \pi}{4}\right)$[/tex]

Trig circle gives another angle: [tex]$x=\frac{3 p}{4}+\pi=\frac{7 \pi}{4}$[/tex]

In the interval [tex]$(0, \pi)[/tex]   there are 4 answers: [tex]$\frac{\pi}{4} ; \frac{3 \pi}{4} ; \frac{5 \pi}{4} ; \text{and} \frac{7 \pi}{4}$[/tex]

7(22/7)/4

= 22/4

A = 22

B = 4

Thus, After solving tan² (0) = 1 on the interval [0, π), The answers are A and B where 0 < A, A = 22 and B = 4.

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No, these measurements do not form a triangle. The sum of any two sides of a triangle must be greater than the third side. In this case, 7 cm + 8 cm = 15 cm, which is not greater than the third side, 9 cm.

A triangle is a three-sided polygon, and all three sides must meet certain criteria in order to form a triangle. Specifically, the sum of any two sides must be greater than the third side. In this case, the given measurements are 7 cm, 8 cm, and 9 cm. When adding the 7 cm and 8 cm together, the sum is 15 cm, which is not greater than the third side, 9 cm. Therefore, these measurements do not form a triangle. To determine if a triangle can be formed with any given measurements, one must sum any two sides and ensure that the sum is greater than the third side. If the sum is not greater than the third side, then the measurements do not form a triangle.

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Answer:

x<4

Step-by-step explanation:

To solve and make the problem less intimidating, it is easier to just imagine that the < is a = sign. The only difference when solving a inequality versus an equation is that you flip the inequality sign when multiplying or dividing by a negative, which we won't need to worry about in this problem. Now, hopefully, this will make more sense when we are solving.

The first step is to add 20 to both sides:

15x - 20 < 40 (Add 20 to both sides)

15x < 60

Now, divide both sides by 15, so we are juts left with x:

15x < 60 (Divide both sides by 15)

x < 4

So, the inequality is true for any x value that is less than 4, or x<4.

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Answer:

there some rules

Step-by-step explanation:

Answer:

B

I am sorry if this is wrong

(a) We know that 30% of the members of the club are female and 20% of these females own cars, and 30 female members own cars.

We can use this information to calculate the total number of female members in the club.

If 30% of the members are female and 20% of these females own cars,

then 20/100*30 female members = 6% of the total members own cars.

This means that 6% of the total members are female members who own cars.

Therefore, 30 female members / 6% = 500 female members.

So there are 500 female members in the club.

(b) If 30% of the members are female, then the total number of members is (100/30)*500 female members = 1666.67 members

(c) To increase the percentage of female members to 37.5%, we need to calculate the number of additional female members required to reach this goal. The current percentage of female members is 30% and we want to increase it to 37.5%. Therefore, we need an additional 37.5-30 = 7.5%. If the current number of female members is 500, to increase the percentage by 7.5%, we need an additional of 7.5/100*1666.67 = 125 additional female members.

So on solving the provided question we can say that -  the length is 4.5 times the area Area of rectangle = A = x X 4.5x; x = 5

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

here,

the length is 4.5 times the area

let length = x

breadth = 4.5 x

Aare of rectangle = A = x X 4.5x

100 = 4x^2

x = 5

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The statements that are true about the data in the graph include the following:

B. If 200 students were surveyed, 28 would choose art as their favorite subject.

C. If 400 students were surveyed, 64 would chose social studies as their favorite subject.

In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.

Assuming 200 students were surveyed at 14%, the number of students who would choose art as their favorite subject can be calculated as follows;

Number of students for arts = 14/100 × 200

Number of students for arts = 0.14 × 200

Number of students for arts = 28 students.

Assuming 400 students were surveyed at 16%, the number of students who would choose social studies as their favorite subject can be calculated as follows;

Number of students for social studies = 16/100 × 400

Number of students for social studies = 0.16 × 400

Number of students for social studies = 64 students.

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the 1srt one

Step-by-step explanation: