At the start of the month, the counter on the copy machine reads 6,583. At the end of the moth, it reads 82,110. The copies cost 1 1/3 cents a piece. What was the approximate total cost of the copies for this month?

The percentage decrease in total principal and interest paid between a 30-year term mortgage and a 15-year term mortgage at an APR of 6.5% and principal of $242,300.00 is about 31.1%

A mortgage is a loan used to purchase property.

The principal balance = $242,300.00

The Annual Percentage Rate, APR = 6.5%

The term of the loan = 30-year and 15-year

The monthly payment for the loan per each term can be obtained using the following formula;

M = P·[r·(1 + r)^n]/[(1 + r)^n - 1]

Where;

M = The monthly payment

P = The principal amount of the loan = $242,300.00

r = The monthly interest rate = APR/12 = 0.065/12

n = The the number of periods of payment = 12 × 30 = 360

The monthly payment for the 30-year loan term is therefore;

M₃₀ = 242,300 × [(0.065/12)·(1 + (0.065/12))^360]/[(1 + (0.065/12))^360 - 1] ≈ 1531.5

The total payment for the 30-year term ≈ 360 × 1531.5 = 551,340.3

The monthly payment for the 15-year loan term is found as follows;

n = 12 × 15 = 180

M₁₅ = 242,300 × [(0.065/12)·(1 + (0.065/12))^180]/[(1 + (0.065/12))^180 - 1] ≈ 2110.7

The total payment in 15 years ≈ 15 × 12 × 2110.7 = 379962

The percentage decrease, is therefore;

((551,340.3 - 379,962)/551,340.3) × 100 ≈ 31.1%

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Answer:31/36

Step-by-step explanation:

we should find greatest common divisor(GCD) ,

GCD(12,18)=36

7/12=7*3/36=21/36

5/18=5*2/36=10/36

21/36+10/36=31/36

Answer:

31/36

Step-by-step explanation:

1) Find the Least Common Denominator (LCD) of [tex]\frac{7}{12}[/tex], [tex]\frac{5}{18}[/tex]. In other words, find the Least Common Multiple (LCM) of 12, 18.

1) List the multiples of each number

Multiples of 12: 12, 24, 36, ...

Multiples of 18: 18, 36, ...

2) Find the smallest number that is shared by all rows above. This is the LCM.

LCM = 36

1) List the prime factors of each number.

Prime Factors of 12: 2, 2, 3

Prime Factors of 18: 2, 3, 3

2) Find the union of these primes.

2, 2, 3, 3

3) Multiply these number: 2 x 2 x 3 x 3 = 36. This is the LCM.

LCM = 36

STEP 2: Make the denominators the same as the LCD.

[tex]\frac{7\times3}{12\times3} +\frac{5\times2}{18\times2}[/tex]

3) Simplify. Denominators are now the same.

[tex]\frac{21}{36} +\frac{10}{36}[/tex]

4) Join the denominators.

[tex]\frac{21+10}{36}[/tex]

5) Simplify.

[tex]\frac{31}{36}[/tex]

Thank you,

Eddie.

The fοrmula fοr t in terms οf 2kπ is: t = kπ + π/2, where k is an integer.

Tο draw a unit circle fοr the given cοοrdinates, we first draw the hοrizοntal and vertical axes intersecting at the οrigin (0,0):

Next, we draw a circle with radius 1 centered at the οrigin:

Tο find pοints οn the circle with y-cοοrdinate 1, we lοοk at the pοint where the circle intersects the vertical axis. This οccurs when x = 0, sο the pοint οn the circle with y-cοοrdinate 1 is (0,1):

(0,1)

Tο find οther pοints οn the circle, we can use the Pythagοrean identity:

sin²(t) + cοs²(t) = 1

Since we want y = sin(t) tο be 1, we can sοlve fοr x = cοs(t)

cοs(t) = sqrt(1 - sin²(t))

Using this fοrmula, we can find several pοsitive and negative real numbers t that determine pοints Q οn the circle with y-cοοrdinate 1:

t = 0 radians (0 degrees): Q = (1,0)

t = π/6 radians (30 degrees): Q = (√3/2, 1/2)

t = π/4 radians (45 degrees): Q = (√2/2, √2/2)

t = π/3 radians (60 degrees): Q = (1/2, √3/2)

t = π/2 radians (90 degrees): Q = (0,1)

t = 7π/6 radians (-150 degrees): Q = (-√3/2, 1/2)

t = 3π/4 radians (-135 degrees): Q = (-√2/2, √2/2)

t = 5π/6 radians (-120 degrees): Q = (-1/2, √3/2)

t = π radians (-180 degrees): Q = (-1,0)

Tο write a fοrmula fοr t in terms οf 2kπ, we can use the inverse sine functiοn:

sin(t) = 1

t = sin⁻¹(1) + 2kπ

Since sin(π/2) = 1, we have:

t = π/2 + 2kπ

Sο the fοrmula fοr t in terms οf 2kπ is:

t = kπ + π/2, where k is an integer.

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Answer:    -2(x-1)(4x-3)

Step-by-step explanation:   because im just that guy

Answer:

224 more adults than children

Step-by-step explanation:

150+192=342 adults together

460-342=118 children

342-118= 224

sooo there were 224 more adults than children

The probability that O and E are together in a randomly arranged word "COMPUTER" is 0.25, or 25%.

Statistics and probability theory both make substantial use of probability, which is a measure of the possibility or chance of an event occurring. A number between 0 and 1, where 0 denotes an event that is impossible and 1 denotes an event that is certain, is used to indicate the likelihood of an occurrence.

We must count the number of favourable possibilities—those that match the event of interest—and divide that number by the total number of potential outcomes in order to calculate the probability of an occurrence.

There are 8 letters in the word, so the total number of arrangements is 8! = 40,320.

For O and E to be together we consider it as a sing letter, thus:

There are 7! ways to arrange the letters of new word.

Now, OE can be written as OE or EO thus:

2 x 7! = 10,080

Now, the probability of O and E together is:

Probability = 10,080 / 40,320

Probability = 0.25

Hence, the probability that O and E are together in a randomly arranged word "COMPUTER" is 0.25, or 25%.

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The value equivalent tο the expressiοn "4 times 3 cubed" is 108.

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants. An algebraic expressiοn is a mathematical phrase that can cοntain numbers, variables, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

It is a cοmbinatiοn οf numbers, variables, and symbοls arranged in a meaningful way tο represent a mathematical statement οr relatiοnship.

The expressiοn "Fοur times Three cubed" means that we shοuld first cube the number 3, and then multiply the result by 4.

Tο cube 3, we multiply it by itself three times :

[tex]3^3 = 3 * 3 * 3 = 27[/tex]

Next, we multiply this result by 4:

4 * 27 = 108

Therefοre, the value equivalent tο the expressiοn "4 times 3 cubed" is 108.

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The value of 2(s + t)^{3} - 6 is 244.

What is an equation?

In mathematics, an equation is a statement that asserts the equality of two expressions, usually separated by an equals sign (=).

For example, the equation 3x + 5 = 11 asserts that the expression 3x + 5 is equal to the expression 11. An equation can have one or more variables, which are typically represented by letters. In the example above, x is the variable.

To evaluate 2(s + t)^{3} - 6 when s = 3 and t = 2, we can substitute 3 for s and 2 for t in the expression and simplify.

So we have:

2(s + t)^{3} - 6 = 2(3 + 2)^{3} - 6 (substituting s = 3 and t = 2)

= 2(5)^{3} - 6 (evaluating the expression inside the parentheses)

= 250 - 6 (cubing 5 and multiplying by 2, and then subtracting 6)

= 244 (subtracting 6 from 250)

Therefore, when s = 3 and t = 2, the value of 2(s + t)^{3} - 6 is 244.

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The names of the column headers in the table indicates that the function c(x) = q(x) ÷ m(x), where q(x) and m(x) are whole numbers, indicates that the function c(x) is a rational function.

Rational functions are functions that consists of a ratio of polynomial functions. A rational function, f(x), consists of the functions g(x) and h(x), such that f(x) = g(x)/h(x), where h(x) ≠ 0.

The input variable of the functions is; x

The functions in the question are; q(x) and m(x)

The function c(x) is; c(x) = q(x) ÷ m(x)

The function c(x) is composed of two functions q(x) and m(x), that are together presented as a fraction, which indicates that c(x) is a rational function.

The type of function represented by the function c(x) is therefore;

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The GCF (Greatest Common Factor) of 2.4x and 12 is 2.4. Therefore, we can write: 2.4x - 12 = 2.4(x - 5)

What is expression ?

In mathematics, an expression is a combination of symbols and/or numbers that represents a mathematical quantity or relationship. It can be a simple numerical value or a more complex arrangement of terms and operations.

To generate an expression equivalent to 2.4x - 12 using the GCF, we need to find the largest common factor between the terms 2.4x and 12.

First, we can simplify 2.4x by dividing both the numerator and denominator by 0.4, which gives us:

2.4x = 6x

Now, we can find the GCF between 6x and 12, which is 6. We can factor out this GCF from both terms to get:

2.4x - 12 = 6(x - 2)

So, the expression equivalent to 2.4x - 12 using the GCF is 6(x - 2). This expression represents the same quantity as 2.4x - 12, but is simplified and factored.

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Answer:

4

Step-by-step explanation:

The cardinality of a set is the number of elements in the set.

Therefore, the cardinal number for the set A={Pacific, Indian, Atlantic, Gulf of Mexico} is 4, since it has four elements.

The dot represents the data point of 5, and there are no other data points to include on the dot plot.

You can still make a dot plot even if you just have one number in the tens by placing a dot on a number line above the number. If your data point is 5, for instance, you can represent it by placing a dot above the tick mark for 5 on a number line that has tick marks for each integer from 0 to 9. Here is an illustration of how the dot plot might appear:

  |      

5  •      

  |      

  |      

  |      

  |      

  |      

  |      

  |      

  |      

  +   -   -    -   -   -   -   -

  0  1   2   3  4  5  6  7

There are no additional data points to place on the dot plot because the dot in this illustration represents the data point of 5.

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The factored representation of the quadratic function 2x² - 10x - 48 is given as follows:

2(x - 8)(x + 3).

The quadratic function for this problem is defined as follows:

2x² - 10x - 48

The leading coefficient of 2 is common to all the terms of the expression, hence the expression can be simplified as follows:

2x² - 10x - 48 = 2(x² - 5x - 24).

The term with the square of x can be simplified as follows:

x² - 5x - 24 = (x - 8)(x + 3).

Meaning that x = 8 and x = -3 are the roots of the quadratic function, hence, considering the leading coefficients and the linear factors, the simplified expression is given as follows:

2x² - 10x - 48 = 2(x - 8)(x + 3).

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The factorization of the quadratic equation is:

y = 2*(x + 3)*(x - 8)

Here we have the quadratic equation:

2x^2 - 10x - 48

To factorize it, we need to find the roots of the quadratic, to do so we need to solve the equation:

y = 2*x^2 - 10*x - 48 = 0

2x^2 -10x - 48 = 0

Dividing by 2 in both sides we will get:

(2x^2 - 10x - 48)/2 = 0/2

x^2 - 5x - 24 = 0

Now we can use the quadratic formula to get the roots:

[tex]x = \frac{5 \pm \sqrt{(-5)^2 - 4*1*-24} }{2} \\\\x = \frac{5 \pm 11}{2}[/tex]

The roots are:

x = (5 + 11)/2 =8

x = (5 - 11)/2 = -3

Then the factorization will be:

y = 2*(x - (-3))*(x - 8)

y = 2*(x + 3)*(x - 8)

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The property of equality shown in the given equation is the addition property of equality.

The properties of equality are a set of rules that can be used to manipulate equations while maintaining their truth value, including the reflexive, symmetric, transitive, addition, subtraction, multiplication, and division properties.

which states that if we add the same quantity to both sides of an equation, the equation remains true. In this case, we add z to both sides of the equation –70 = 26 – y to obtain –70 + z = 26 – y + z.

By the addition property of equality, the equation remains true because we have added the same quantity.

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Answer:

Step-by-step explanation:

6

Answer: We can use the formula for the future value of an annuity with monthly compounding to determine how much money should be deposited:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

where:

FV = future value (the amount we want to accumulate, which is $13,000 in this case)

P = periodic payment (the amount we need to deposit each month)

r = annual interest rate (2.5% in this case)

n = number of compounding periods per year (12 for monthly compounding)

t = number of years (4 in this case)

We want to solve for P, so we can rearrange the formula as follows:

P = FV * (r/n) / ((1 + r/n)^(n*t) - 1)

Substituting the given values, we get:

P = 13000 * (0.025/12) / ((1 + 0.025/12)^(12*4) - 1)

Calculating this expression gives us:

P = $279.27 (rounded to the nearest cent)

Therefore, we need to deposit $279.27 each month for 4 years in an account that earns 2.5% compounded monthly in order to accumulate $13,000. Alternatively, if we want to make a single deposit today, we can multiply this monthly amount by 12 and then by 4, which gives us:

P = $13,414.08 (rounded to the nearest cent)

Therefore, we need to deposit $13,414.08 today in an account that earns 2.5% compounded monthly in order to accumulate $13,000 after 4 years.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Awnser=48

Answer:

x=43.85

Step-by-step explanation:

solution Given.

let the given angle be θ: 20 degree.

It's opposite side is 12.

It's hypotenuse is x.

Since

We have

Sin θ= opposite/hypotenuse

Sin20 degree=12/x

0.34202014332=12/x

doing criss cross multiplication

x=12/0.34202014332

therefore x=43.8570660032

in two decimal form x=43.85

Since 6 = 6, these side lengths do form a right triangle.

Therefore, the answer is C: √2, 2, √6.

How are lengths of sides of a triangle calculated?

The Pythagorean theorem, which asserts 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 lengths of the other two sides, can be used to identify which side lengths make up a right triangle.

A) The Pythagorean theorem enables us to deduce that: 52 + 62 = 25 + 36 = 61

[tex]\sqrt{30^{2}[/tex] = 30

These side lengths do not create a right triangle because 61 > 30.

B) The Pythagorean theorem enables us to observe that:

[tex]2.5^2 + \sqrt{18^{2} }[/tex] = 6.25 + 18 = 24.25

Also,

[tex]5^{2}[/tex] = 25

Since 24.25 < 25, a right triangle cannot be formed by these side lengths.

C) The Pythagorean theorem enables us to observe that:

[tex]\sqrt{2^{2} } + 2^2[/tex] = 2 + 4 = 6

[tex]\sqrt{6^{2} }[/tex] = 6

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Answer:

To calculate the percent error, we need to find the absolute difference between the correct value and the measured value, divide that by the correct value, and then multiply by 100 to get a percentage.

The absolute difference between the correct value and the measured value is:

$38.07 - $38.06 = $0.01

Dividing this by the correct value ($38.07) gives:

$0.01 / $38.07 ≈ 0.0002626

Multiplying by 100 gives the percent error:

0.0002626 x 100% ≈ 0.02626%

Therefore, the percent error in the student's calculation is approximately 0.02626%.

The percent error in the student's calculation is 2.63%.

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The length of the AG in the cuboid is 7.56 cm.

To find the Length of the diagonal AG, we need to find the length of AC. Use the Pythagorean formula to find the length of AC. Now use the trigonometric ratios formulas to find the length of AG.  

Here we have a cuboid

Where AD = 23 cm, DC = 18 cm and ∠GAC = 75°  

From the right angle triangle, ADC

=> AC² = AD² + DC²    [ Using the Pythagorean formula ]

=> AC² = (23)² + (18)²

=> AC² = 529 + 324

=> AC = √853 = 29.20    

Hence, the length of AC = 29.20

From the right angle triangle, AGC

=> Cos B = AC/AG

=> Cos 75° = 29.20/AG

=> AG = Cos 75° (29.20)

=> AG = (0.26)(29.20)

=> AG = 7.56

Therefore

The length of the AG in the cuboid is 7.56 cm.

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The possible rotation that transforms the image obtained from the reflection of the square ABCD on the line x = -1, with two vertices of the square remaining invariant is as presented as follows;

A rotation transformation is a transformation in which the preimage coordinate points are turned (in a circular manner) about a point.

The vertices of the square ABCD are; A(1, 4), B(3, 4), C(3, 2), D(1, 2)

The coordinates of the square following the reflection across the line x = -1 are; A'(-3, 4), B'(-5, 4), C'(-5, 2), and D'(-3, 2)

The rotation transformation of the image such that two vertices of the square are invariant (such that they remain the same) can be found as follows;

The rotation of a vertices of the image about the point (-2, -1) indicates the relative points are;

A'(-1, 5), B'(-3, 5), C'(-3, 3), and D'(-1, 3)

The image following a rotation of 270° are;

A''(5, 1), B'(5, 3), C'(3, 3), and D'(3, 1)

The above points relative to the origin are;

A''(5 + (-2), 1 - 1) = (3, 0), B''(5 - 2, -1 + 3) = (3, 2), C';(3 - 2, 3 - 1) = (1, 2), and D''(3 - 2, 1 - 1) = (1, 0)

A''(3, 0), B''(3, 2), C''(3, 4), and D''(1, 4)

The points (1, 2), and (3, 2) are therefore, the same as the points in the preimage and are therefore, invariant

The rotation is therefore;

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The function in vertex form is f(x) = 10(x + 2)² - 8.

In this exercise, you are required to determine the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:

y = a(x - h)² + k

Where:

Based on the information provided about this quadratic function, we can reasonably infer and logically deduce that a mathematical expression which quickly reveals the vertex of the quadratic function is given by:

y = a(x - h)² + k

y = 10(x - (-2))² + (-8)

y = f(x) = 10(x + 2)² - 8

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The correct answer is Option B, The amount Jonathan is paid for each hour over 10.

The expression { 7 . 5 x ; 0 ≤ x ≤ 10 75 + 9 ( x − 10 ); x > 10 } gives the amount of money Jonathan is paid each week based on the number of hours he works, x. The first part of the expression, 7.5x, applies when x is between 0 and 10, inclusive. The second part of the expression, 75 + 9(x - 10), applies when x is greater than 10.

So, the term 9(x - 10) represents the amount he is paid for each hour over 10. When Jonathan works more than 10 hours, he is paid a flat rate of $75 for the first 10 hours, and then an additional $9 for each hour over 10. Therefore, if Jonathan works x hours and x is greater than 10, then he is paid 9(x - 10) dollars for each hour over 10.

Therefore, the correct answer is B. the amount he is paid for each hour over 10.

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Answer:

8+the sign over 2

Step-by-step explanation:

The answer of the given question based on the scatterplot for determining  when she will reach 10,000 songs the answer is Maria will reach 10,000 songs in approximately 13.33 months, or about 14 months.

Slope is  measure of  steepness or incline of  line. In geometry and mathematics, slope is defined as  ratio of the change in  y-coordinates to  change in  x-coordinates between two distinct points on  line. This is often represented by  letter "m".

To determine when Maria will reach 10,000 songs, we need to find the point on the line of best fit where the y-value is 10,000.

From the scatterplot, we can estimate that the line of best fit intersects the y-axis at approximately 2000. This means that the initial number of songs downloaded was 2000.

Next, we need to find the slope of the line of best fit. Let's choose the points (5, 6500) and (10, 9500).

The slope of the line passing through these two points is:

slope = (y2 - y1)/(x2 - x1) = (9500 - 6500)/(10 - 5) = 600 songs per month

This means that Maria is downloading 600 songs per month on average.

Finally, we can use the slope-intercept form of a line to find the x-value when the y-value is 10,000:

y = mx + b

10,000 = 600x + 2000

8000 = 600x

x = 13.33

Therefore, Maria will reach 10,000 songs in approximately 13.33 months, or about 14 months.

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Hope this helps.