The amount of money in a savings account is given by � = 580(1.03)" where t is the
time in years. After how many years will the account have reached $1000? Clearly
demonstrate your strategy for figuring it out.

We found that translations have the following three properties: line segments are taken to line segments of the same length;

angles are taken to angles of the same measure; and. lines are taken to lines and parallel lines are taken to parallel lines.

Properties of Translations

- Distance Where the lengths of the segments stay the same.

-Angle Measures These remain the same.

-Parallelism Where the parallel lines will stay parallel.

-Collinearity The points will stay on the same line.

-Orientation The order of the letters will stay the same.

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The measure of angles a and b is 144° and 67° respectively.

There are four sides, four vertices, and four angles in a closed quadrilateral. It has a polygonal shape. It is produced by joining four non-collinear points. The total internal angle of a quadrilateral is always 360 degrees.

The English word quadrilateral is derived from the Latin words quadra, which means four, and latus, which means sides. Each of a quadrilateral's four sides does not always have to be the same length.

Given a quadrilateral,

in which opposite sides are parallel,

so, When a transversal cuts between two parallel lines, the interior angles on the same side of the transversal are additional to 180°.

36° + a° = 180°

and 113° + b° = 180°

a° = 180° - 36° = 144°

and b° = 180° - 113°

b° = 67°

Hence the values of a° is 144° and b° is 67°.

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The value of the length will be 17920cm.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Since the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³.

The value of the length will be:

= 7 / (7 +5+2) × 35840

= 7/14 × 35840

= 17920cm

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the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³. Find the value of the length

Answer for the given problem,

a.  Percentage of 160 in number 40 is, 400%

b. The number for which 40 is 160% of that number is,  25

c.  The number which is 40% of 160 is, 64

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

a.   present quantity = 160

     whole quantity  = 40

    Percentage = 400 %

b.  present quantity = 40

    Percentage = 160

    Whole quantity  = 25

c.   whole quantity  = 160

     Percentage = 40%

     Present quantity = 64

Hence, Answers are respectively,  400%,  25,  64

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The domain and range of f(x) = |x| is

Domain: all real numbers

range: positive real numbers

The distance of a number from a number line's origin is referred to as the absolute value of that number. Its representation is |x|, which establishes the size of any integer 'x'.

Any integer's absolute value, regardless of its sign, will be one of the real numbers, whether it is positive or negative. The modulus of x, which is represented by two vertical lines |x|, is a mathematical concept.

Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line. A number can never have a negative absolute value.

Since absolute value can be zero the range is all positive numbers

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Answer:

Parallelogram formula- 1/2 x base xheight

Step-by-step explanation:

The graph of the inverse variation equation is called a rectangular hyperbola.

A form of proportionality called inverse variation occurs when one number falls as the other rises or the other way around. This suggests that if one number rises while the other decreases, the magnitude or absolute value of the first quantity will decrease, resulting in a constant product. The constant of proportionality is another name for this item.

An inverse variation is a relationship between two variables in which the product is constant; as a result, while one of the variables changes, the other changes correspondingly to maintain the same value of the product. This connection has the form of a hyperbola.

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The translation of the coordinate points on the graph by linear displacement in comparison of original points ( x , y ) get translated to     ( x + h,  y + k ) where h ∈R , k ∈R.

As given in the question,

Let us consider original coordinate point on a given graph be ( x ,y ).

Translation represents the change in the linear displacement or the location without changing the shape and size.

Shift of the point may be horizontally or vertically.

Let 'h' and 'k' be the horizontal and vertical shift.

If the horizontal shift is right then it is represented by x + h

If the horizontal shift is left then it is represented by x - h

If the vertical shift is up then it is represented by y +k

If the vertical shift is down then it is represented by y - k.

Therefore, the translation of the coordinate points on a given graph represented by original points ( x , y ) get translated to ( x + h,  y + k ) where h ∈R , k ∈R.

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Elena made 2 batches of bird food, each with 1/8 cup cracked corn, 3/4 cups sunflower seeds, and 1/4 cup dried cranberries, for a total of 1.75 cups of bird food.

Elena made two batches of bird food using a combination of cracked corn, sunflower seeds, and dried cranberries. Each batch uses 1/8 cup of cracked corn, 3/4 cup of sunflower seeds, and 1/4 cup of dried cranberries.

To find the total amount of bird food she made, we need to add the ingredients of the two batches together.

Since she made two batches and each batch contains 1/8 cup of cracked corn + 3/4 cup of sunflower seeds + 1/4 of dried cranberries, the total amount of bird food is 2 × (1/8+3/4+1/4) = 2 × (7/8) = 7/4 = 1.75 cups.

This is the best estimate of the total amount of bird food made by Elena. It's important to note that this estimate is based on the assumption that the proportion of ingredients in each batch is the same, and that the ingredients are measured accurately.

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The measure of ∠S is 59.4° for trignometric identities

What are trigonometric identities?

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

ΔSTU:

s = 50 inches

t = 58 inches

u = 630 inches

Applying the cosines rule on ΔSTU.

s² = t² + u² - 2 x t x u x cos S

cos S = (t² + u² - s²) / 2tu

cos S = (58² + 27² - 50²) / (2 x 58  x 27)

cos S = (3364 + 729 - 2500) / 3132

cos S = 0.5086.

∠S = (0.5086)

∠S = 59.4°

Thus,

∠s angle value is  59.4°.

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The description for the problem involving the linear function is given as follows:

The time it will take to make a total of 20 parts is of 6 minutes.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

In this problem, the function is defined as follows:

y = 2x + 8.

In which the variables are given as follows:

Hence the time needed to make 20 pieces is given as follows:

20 = 2x + 8

2x = 12

x = 12/2

x = 6 minutes.

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Logarithms are used for a variety of purposes in mathematics, science, engineering, and other fields. Some common uses of logarithms are mentioned below:

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, however it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

They are used for:

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Therefore , the solution of the given problem of equation comes out to be 1.39500 profit and 2.-400 loss.

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

For C no of cars

=> Profit = total earning in a month - Expense in a month

=> (25-6)C - (23500-6000)

=> P = 19C-17500

If 3000 cars serviced then,

=> Profit = 19(3000)-17500

=> Profit = 39500

If no of cars received in particular month is 900 then profit or loss

=>Profit = 19(900)-17500

=> Profit = -400

That is loss.

Therefore , the solution of the given problem of equation comes out to be 1.39500 profit and 2.-400 loss.

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The triangle with side lengths given in the question can be classified as a scalene triangle.

A scalene triangle is a type of triangle in which none of its three given length of sides are equal. It can be differentiated from other types with respect to  this property.

A triangle is a plane shape which can be described by three sides and three measure of internal angles. Some other types of triangle are: equilateral, obtuse, isosceles etc. The sum of all internal angles of a triangle is 180^o

Considering the given length of sides in the question, it can be proven the the only type of triangle that can be formed is a scalene triangle. Therefore, the triangle can be classified as a scalene triangle.

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Answer:

Intial money=Rs 3300

final money=3300-(70×5)-(2×125)-2500

=3300-350-250-2500

=3300-3100=RS 200

Now,

share of each of them= 200/2=Rs100

*mark me brainliest

It is not possible to find the height of an isosceles triangle when only the base is given. To find the height, you would need to know at least one other side length, in addition to the base.

The height of an isosceles triangle can be found using the Pythagorean Theorem, which states that the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the two shorter sides. To use the Pythagorean Theorem, you must first know the length of at least two sides of the triangle. Since only the base is given, it is not possible to calculate the height of the isosceles triangle. In order to find the height, you would need to know either the length of the other two sides, or the angle of one of the two equal sides. Once you have this information, you can use the Pythagorean Theorem to calculate the height of the triangle.

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Answer:I know why your father never came back

Step-by-step explanation: So when he got the milk he got stuck in traffic for a long time which caused the milk to expire and so he went back to grab new milk and on his way home he was stuck in traffic again and the milk got expired so he repeats the process and the same thing happens over and over and over, so hes stuck in an infinite loop until he passes away.

Answer: Probably negative 69

The difference between the population means - 3.4 and -1.84 when calculated is found to be -2.62 years.

The 95% confidence interval for the difference in true mean ages of cars owned by students and faculty is between -3.4 and -1.84 years.

We know that the sample of 138 cars which belongs to the students have an average age of 5.13 years. The standard deviation = 3.45 years.

Then again,

A sample of 111 cars which belongs to the faculty have an average age of 7.75 years.  The standard deviation= 2.08 years.

So the difference between them will be , s - f

= 3.45 - 2.08 = 1. 37

and the mean will be , mean of students - mean of faculty =

-2.62.

This is the point of difference between their means.

The SD is found to be as 0.3961.

and MOE is 0.78

with these details now we will calculate the required intervals,

The lower end is found to be as  -2.62 - 0.78 = -3.4

The upper end is found to be as  -2.62 + 0.78 = -1.84

Therefore, the mean difference between the cars is - 3.4 and -1.84.

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The answer choice which represents a number line for the intersection of the given intervals is; (4, ∞).

The answer choice which represents a number line for the union of the given intervals is; (-3, ∞).

It follows from the task content that the number line which represents the intersection and union of both intervals given is to be determined.

Since the given intervals are; (-3, ∞) and (4, ∞)

It follows that the intersection of both intervals is the interval; (4, ∞).

Also, the interval which represents the union of both intervals is; (-3, ∞).

Hence, the image which represents both scenarios is attached.

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An indirect proof is an argument that begins with the assumption that a conclusion is false, then uses logical reasoning to show that the assumption leads to a contradiction.

a fact or assertion that contradicts what someone else said or that differs from another fact or assertion to the point where one of them must be incorrect.

A situation or set of ideas that contradict one another is called a contradiction. A contradiction would be saying out loud that you support the environment while never remembering to empty the recycling. A statement that contains opposing ideas is frequently referred to as a "contradiction in terms."

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Answer: −2<x<0

Step-by-step explanation: 2<x+4<4 2+−4<x+4+−4<4+−4 −2<x<0

Answer:

=4.5

Step-by-step explanation:

the rule is

positive - negative  changes to positive + positive so

3- (-1.5) changes to 3 + 1.5 which equals 4.5

The statement that is true on the system of equations is that A. The system has no solution.

There is no solution in the given system of equations because the lines formed by the equations are parallel to each other. This means that they will never intersect with each other.

A solution is only derived at the points where the systems of equations intersect with each other. As there is no point where these equations intersect, it means there is no solution for these system of equations.

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Answer:

N > -2/21

Step-by-step explanation:

Move -4/7 to the other side

n - 4/7 > - 2/3

n > - 2/3 + 4/7

Find a common denominator

n > - 14/21 + 12/21

Add

n > - 2/21

The answers to all the subparts are shown:

(1) The numerator is simply added. The denominator is copied.

(2) Yes, it has; yet, we include them since that is what needs to be done.

In a fraction, the number above the line is the numerator.

For instance, the numerator of the fraction 3/5 is 3.

A fraction's numerator displays the number of pieces that make up the whole while the denominator, or a number of equal parts, is displayed below the line.

So, we have the equation:

2x² + x/2x - 2 + x - 4/ 2x - 2

Now, answering questions taking the above-given equation into consideration:

(1) The numerator is simply added. The denominator is copied.

(2) Yes, it has; yet, we include them since that is what needs to be done.

(3) We complete the square, but we can also use the straightforward factoring approach.

(4)  We eliminate or simply cancel the factors in the numerator that are also present in the denominator to simplify the sum.

Therefore, the answer to all the subparts are shown:

(1) The numerator is simply added. The denominator is copied.

(2) Yes, it has; yet, we include them since that is what needs to be done.

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Distance between them and their destination after 3.7 hours since entering the freeway is 608 miles and the distance between them and their destination after 2.3 hours since entering the freeway is 692 miles.

We know that the relationship between speed, distance, and time is given as,

Speed = distance/time

Speed = 60 miles an hour

Time = 3 hours

We know that Don and Ana are travelling at a constant speed and they are travelling for 3 hours.

Distance = speed × time

Distance = 60 × 3

Distance = 180 miles

Thus, the distance travelled by them in 3 hours is 180 miles.

We know that Don and Ana are travelling on the freeway for the past 3 hours and they are still 650 miles away, therefore,

Total Distance from their destination

= Distance travelled by them in 3 hours + 650 miles

= 180 miles + 650 miles

= 830 miles

Thus, the distance travelled by then is 830 miles.

Now, the distance between them and their destination after 3.7 hours since entering the freeway,

Distance travelled by them = speed x 3.7 = 60 x 3.7 = 222 miles

Distance between them and the destination

= Total Distance from their destination - Distance travelled by them

= 830 miles - 222 miles

= 608 miles

Therefore, they are 608 miles far from their destination.

And, Distance between them and their destination after 2.3 hours since entering the freeway,

Distance travelled by them = speed x 2.3 = 60 x 2.3 = 138 miles

Distance between them and the destination

= Total Distance from their destination - Distance travelled by them

= 830 miles - 138 miles

= 692 miles

Therefore, they are 692 miles far from their destination.

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AC = 25 units is the length of AD.

The Geometric Mean (Altitude) Theorem (9.7) The hypotenuse of a right triangle is split into two pieces by the height from the right angle. The geometric mean of the lengths of the two hypotenuse segments determines how long the altitude is.

Length of BC = 10 units

Length of DC = 4 units

We will use geometric mean theorem in the given right triangle to get the length of side AC.

[tex]hypotenuse/leg=leg/projection\\AC/BC=BC/DC\\x/10=10/4\\x=25[/tex]

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Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to a humorous effect.

Oscar Wilde wrote a play titled The Importance of Being Earnest, A Trivial Comedy for Serious People.

It is a farcical farce that was first presented on February 14, 1895, at the St James's Theatre in London.

The characters maintain false personae to avoid onerous social duties.

The play's main themes, which are based on late Victorian London social customs, are the triviality with which it treats institutions as important as marriage and the satire that results.

In "The Importance of Being Earnest," Oscar Wilde employs the literary devices of irony and hyperbole to hilarious effect as he criticizes upper-class Victorian society.

Therefore, Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to humorous effect.

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The measure of convex arc upper Z is 243⁰ Option D

We should be aware that a convex angle is the angles that are irregular in nature

Assume that  the radius of the given circle is r.

The central angle of the lower arc ZWX = 41+180 = 221⁰

Note that then central angle of the upper arc ZWX = 360- 221⁰

This implies that the central angle of the upper arc ZWX = 360-221 = 139⁰

Recall that Lenght of arc = A/360 *2*π*r

Where A is the angle made by the radii, r= radius of the circle

Arc length of upper ZWX:

Arc length of upper ZWX = 139π/180*r

Arc length of upper ZWX = 139πr/180

The lenght is (139*22)/ 180*7

= 3058/2360

= 245⁰

In conclusion the measure of the convex upper is 245⁰

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