as in the previous problems, consider the model problem (4.3) with a real constant a < 0. show that the solution of the trapezoidal method i

Answer:

Step-by-step explanation:

Answer:

48,232.8

Step-by-step explanation:

4,823.28 x 0.01

Answer:

$6.48

Step-by-step explanation:

First, let's find the discount.

1.60 * 0.1 = $0.16 (the discount)

Second, subtract the discount to the original price.

1.60 - 0.16 = $1.44 (price after discount was applied)

Third, multiply to 4 1/2 to find how much it will cost.

1.44 * 4.5 = $6.48 (price of 4 1/2 pounds of apples with discount applied)

The tοtal cοst frοm the first stοre is: $2,499 + $291 = $2,790

In the field οf mathematics knοwn as algebra, abstract symbοls rather than cοncrete numbers are subjected tο arithmetic οperatiοns and οther fοrmal manipulatiοns.

The area οf mathematics knοwn as geοmetry studies hοw οbjects are shaped as well as hοw they relate tο οne anοther and the physical characteristics οf the space they οccupy.

The tοtal cοst frοm the secοnd stοre is:

$2,628 + $138 = $2,766

Therefοre, the stοve is cheaper at the secοnd stοre. The tοtal cοst, including splitting the cοst equally between the three οwners, is:

($2,766 / 3) = $922

Each οwner's pοrtiοn οf the cοst is:

$922 / 3 = $307.33

Therefore, your portion of the cost is $307.33.

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Therefore , the solution of the given problem of function comes out to be $25,548.87 is the expected consumption when the available income is $33,000.

The mathematics lesson covers a wide range of topics, including math, numbers, and one's subsets, as well as building, construction, and both real and fictitious geographic places. The relationships between various components that all cooperate to create the same outcome are covered by a work. A utility is composed of an assortment of unique parts that work together to produce unique outcomes for each input.

Here,

Utilizing Excel or statistical software, we can discover a sample linear regression equation. Using the regression analysis function in Excel, we obtain:

=> Consumption = -5117.41 + 0.9694 * Discretionary Income Marginal Propensity to Consume

=> (MPC): 0.9694 Regression equation

MPC interpretation: The MPC shows the percentage of extra disposable income that is spent on consumption.

The MPC in this instance is 0.9694, indicating that on average 0.9694 cents are spent on consumption for every extra dollar of disposable income.

When the available income is $33,000, we can enter the number as follows into the regression equation to determine the predicted consumption:

=> Usage = -5117.41 plus 0.9694 times 33,000.

=>Usage =  $25,548,87

Therefore, $25,548.87 is the expected consumption when the available income is $33,000.

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the answer will be -137

Answer:

To write an expression for the total cost of both memberships after m months, we can use the following vocabulary words:

- Startup fee: a one-time fee charged at the beginning of a service or membership

- Monthly fee: a recurring fee charged every month for a service or membership

Using this information, we can write the expression as:

Total cost = (Startup fee for digital library) + (Monthly fee for digital library x number of months) + (Monthly fee for video streaming service x number of months)

Substituting the given values, we get:

Total cost = (5) + (9.95 x m) + (7.99 x m)

Simplifying the expression, we get:

Total cost = 5 + 17.94m

Therefore, the total cost of both memberships after m months can be expressed as 5 + 17.94m.

If a student looks out of a third story window and sees the top of the school flagpole at an angle of elevation of 22°. the height of the flagpole to the nearest foot is approximately 52 ft.

Let's call the height of the flagpole "h". We can use the tangent function to set up an equation based on the angle of elevation:

tan(22°) = h / 60

Solving for h, we get:

h = 60 tan(22°)

h ≈ 23.7 ft

However, this value is the distance from the base of the flagpole to the top of the flagpole, and we need to find the actual height of the flagpole.

h_actual = h + 28

h_actual  =23.7 + 28

h_actual  = 51.7 ft

h_actual  =  52 ft (Approximately)

Therefore, the height of the flagpole to the nearest foot is approximately 52 ft.

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The solution to the inequality 13x|20 is all real numbers, as any value of x, no matter how small or large, will make the statement true.

The way to address inequity Using only real values, 13x|20. This means that there is no single solution to this inequality. The inequality is essentially asking what values of x will make the statement true. In this case, any value of x, no matter how small or large, will make the statement true. This is because the absolute value of x is being taken, which means that the value of x is being evaluated regardless of the sign--whether it is positive or negative. For example, if x is -1, then 13x|20 would be 13(-1)|20, which simplifies to -13|20, or 20. This means that no matter what the value of x is, it will always make the statement true. Therefore, the solution to the inequality is all real numbers.

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The total cost for watching 4 movies in a month would be:

4 x $10 = $40.

Analysis is, broadly speaking, the process of approximating certain mathematical objects—like integers or functions—by other, simpler objects. For example, if you want to write pi as the limit of a series of numbers that you already know how to calculate, you should do so. This will allow you to discover the first few decimals of pi. Or here's a case that works the other way around: Although the sequence of factorials n! has a pleasing aesthetic quality, calculations frequently require an estimate of n! that more clearly illustrates its growth order; this approximation is provided by the classical Stirling formula.

We need to analyze the overall cost of each choice to decide if Ms. Espiritu should purchase a monthly pass or pay each time she visits the theatre.

Assume that each movie ticket is $10 and that a monthly pass is $30. It would be less expensive for Ms. Espiritu to get a monthly pass if she intends to watch more than three films in a month. This is why:

If she purchases each movie ticket individually, the total price for four movie viewings in a month would be:

4 x $10 = $40

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The amount of felt in the compound shape for the art project is: 313cm².

A compound shape is a 2D shape made up of two or more simpler shapes, often with different sizes and orientations, combined together. When computing the dimensions of a compound shape, the first thing to do is to fragment the shape into regular shapes.

Having fragmented the above given shape (art project) there are:

The required amount of felt for the art project will the sum of the areas of these shapes. The dimensions are given:

We derived 6cm by removing 11cm, 5cm and 3cm from 25cm. That is:

25 - 11 - 5 - 3 = 6cm

We derived 8cm - the height of the right angled tringle by removing 9cm from 17cm. That is:

17cm - 9cm = 8cm.

Areas of the following shapes are given as follows:

1) Area of the rectangle with dimensions 17cm x 5cm:                                  Area = length x width = 17cm x 5cm = 85 square cm

2)  Area of the rectangle with dimensions 17cm x 9cm:

    Area = length x width = 17cm x 9cm = 153 square cm

3) Area of the rectangle with dimensions 17cm x 3cm:

Area = length x width = 17cm x 3cm = 51 square cm

4) Area of the right-angle triangle with base 6cm and height 8cm:

Area = 1/2 x base x height = 1/2 x 6cm x 8cm = 24 square cm

Sum of the areas of all four shapes:

85 + 153 + 51 + 24 = 313 square cm

So the amount of felt required in the shape for the art project is: 313cm².


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Full Question:

Although part of your question is missing, you might be referring to this full question: See the attached images.

For the latte, the values are obtained as -

Absolute change - $0.48

Relative change - 13.7%

What is absolute change?

Absolute change tells us the magnitude of the difference or change between two values, regardless of whether the change was an increase or a decrease. It is often used in economics, finance, and other fields to measure changes in variables such as prices, income, sales, or quantities.

The absolute change in the price of a latte is the difference between the original price and the new price, without regard to the direction of the change.

Absolute change = | New price - Original price |

Absolute change = | $3.02 - $3.50 |

Absolute change = $0.48

The relative change in the price of a latte is the absolute change expressed as a percentage of the original price.

Relative change = (Absolute change / Original price) x 100%

Relative change = ($0.48 / $3.50) x 100%

Relative change = 13.7%

Therefore, the absolute change in the price of a latte is $0.48, and the relative change is 13.7%.

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Answer: volume (cubic units) diameter of base (units) area of base (square units) height (units)

4 1.60 0.785 10

6 2.17 3.54 6

63π 10.03 79 1

Step-by-step explanation:

The value of the x is 8.94.

What is the median?

The median is the middle number. Since there is no number “in the middle” you find the mean of the two numbers in the middle.

In a right triangle, the length of the median drawn from the vertex of the right angle equals half the length of the triangle’s hypotenuse.

here we have given a triangle let's say ABC in this A is a right angle which is divided by the median AD

So, AD = 1/2 * BC

= 1/2 * 8 = 4

Now, we need to find the value of the x, which hypotenuse of the new triangle that is the ADC

SO, AC² = AD² + DC²

x² = (4)² + (6)²

x = √(16+64)

= √(80)

x =8.94

Hence, the value of the x is 8.94.

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Combining events A and B results in the entire event, with a probability of 1 for the entire event. The probability P(EC)= 1-P(E) OR P(EC)= 1-0.42= 0.58 is the result.

When conducting an experiment, the probability of an event serves as a gauge for the likelihood that the event will actually occur. When there are only two possible outcomes, such as passing an exam or failing it, complementary events take place. The opposite of an event is represented by the complement.
When one event only happens if and when the other one doesn't, two events are said to be complementary. For instance, it rains or it doesn't.
The probability of an event occurring when added to the probability of the complement of that event occurring is always 1. Considering A to be an event, P(A) + P(A') = 1.
Associated events are exhausting.
Events that complement one another can never coexist.

P(EC)+P(E)=1

P(EC)= 1-P(E)

P(EC)= 1-0.42

P(EC)= 0.58.

Hence, the probability P(EC)= 0.58.

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The values of 'x' that solve for given conditions are (a) 11.349  (b) 13.29  (c) 7.44 and 12.56  (d) 6.08 and 13.92  (e) 5.84 and 14.16.

The z-score, also known as the standard score, is a measure of how many standard deviations a data point is away from the mean of its distribution.

The formula for calculating the z-score of a data point x, with mean μ and standard deviation σ, is:

where z is the z-score.

Here we have

X is normally distributed with a mean of 10 and a standard deviation of 2

As we know z score, z = (x - μ) / σ.

=> x =  μ + zσ  

Hence, to find the 'x' value we need to know the value of the z score in each situation

(a) P(X > x) = 0.5

The z-score corresponding to a right-tail probability of 0.5 is 0.6745.

=> x = 10 + 0.6745 * 2

=> x = 11.349  

(b) P(X > x) = 0.95

The z-score corresponding to a right-tail probability of 0.05 is 1.645.

Substituting the given values into the formula, we get:

x = 10 + 1.645 * 2

x = 13.29

(c) P(x < X < 10) = 0.2

The z-score corresponding to a left-tail probability of 0.1 is -1.28 and the z-score corresponding to a right-tail probability of 0.1 is 1.28.

From formula, z = (x - μ) / σ

=> -1.28 = (x - 10) / 2

=> x = 7.44

and

=> 1.28 = (x - 10) / 2

=> x = 12.56

Therefore,

The values of x that solve P(x < X < 10) = 0.2 are 7.44 and 12.56.

(d) P(-x < X - 10 < x) = 0.95

The z-score corresponding to a right-tail probability of 0.025 is 1.96.

=> -1.96 = (-x - 10) / 2

=> x = 6.08

and

=> 1.96 = (x - 10) / 2

=> x = 13.92

Therefore,

The values of x that solve P(-x < X - 10 < x) = 0.95 are 6.08 and 13.92.

(e) P(-x < X - 10 < x) = 0.99

The z-score corresponding to a right-tail probability of 0.005 is 2.58.

=> -2.58 = (-x - 10) / 2

=> x = 5.84

and

=> 2.58 = (x - 10) / 2

=> x = 14.16

Therefore,

The values of x that solve P(-x < X - 10 < x) = 0.99 are 5.84 and 14.16.

Therefore,

The values of 'x' that solve for given conditions are (a) 11.349  (b) 13.29  (c) 7.44 and 12.56  (d) 6.08 and 13.92  (e) 5.84 and 14.16.

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The vertex represents the minimum value of the function. The vertex, in this case, is (-4, 7), which is the point where the function reaches its minimum value of 7.

The vertex represents the minimum value of the function because the coefficient of the squared term is positive, which means that the parabola opens upwards, and the vertex is the lowest point on the curve.

To find the vertex of the parabola, we can use the formula x = -b/2a, where a is the coefficient of the squared term, b is the coefficient of the linear term, and c is the constant term. In this case, a = 1, b = 8, and c = 23, so x = -8/2 = -4.

Substituting x = -4 into the function g(x) gives us g(-4) = (0)^2 + 7 = 7. Therefore, the vertex of the parabola is (-4, 7), which is the point where the function reaches its minimum value of 7.

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(a)   3/4

(b)   F(x) = ∫f(x)dx = ∫0^x f(t)dt, where x ≥ 0

(c)   1

(a) Using the definition, we can calculate P r(1 < x < 3) as follows:
P r(1 < x < 3) = ∫1^3f(x)dx = ∫1^2 (x/4)dx + ∫2^3 (4-x)/4dx
= [x^2/8]1^2 + [(4x - x^2/2]2^3
= 1/4 + 5/4 = 3/4

(b) The distribution function of X is F(x) = ∫f(x)dx = ∫0^x f(t)dt, where x ≥ 0.

(c) To find µ = E(X), σ2 , σ for X, we need to use the definition of expected value and variance, respectively:
µ = E(X) = ∫-∞^∞xf(x)dx = ∫0^2 x^2/8 dx + ∫2^4 (4x - x^2/2)dx
= [x^3/24]0^2 + [(4x^2 - x^3/3]2^4
= 0 + 7 = 7

σ2 = Var(X) = ∫-∞^∞(x - µ)^2f(x)dx
= ∫0^2(x - 7)^2(x/4)dx + ∫2^4 (x - 7)^2(4-x)/4dx
= [x^3/24 -14x^2/3 +98x/3]0^2 + [(4x^3 -14x^2 +98x]2^4
= 7 + 36 = 43

σ = √σ2 = √43 ≈ 6.55
a) We have to calculate P r(1 < x < 3) using the definition of the probability density function. f(x) = ( x/4 for 0 < x ≤ 2 (4−x)/4 for 2 < x < 4) ∫f(x)dx = ∫(x/4)dx for 0 < x ≤ 2 ∫f(x)dx = ∫((4−x)/4)dx for 2 < x < 4 = ∫(x/4)dx | from 1 to 2 + ∫((4−x)/4)dx | from 2 to 3= (x^2/8) | from 1 to 2 + [(4x-x^2)/8] | from 2 to 3 = (2-1)/8 + (12-8-2+4)/8= 1/8= 0.125 The probability of 1 < x < 3 is 0.125. b) The distribution function for X is: F(x)=0 for x ≤ 0∫f(x)dx for 0 < x ≤ 2= (x^2/8) + C1 for 0 < x ≤ 2∫f(x)dx for 2 < x < 4= (x/4-2) + C2 for 2 < x < 4= 1 for x ≥ 4c) We have to find µ = E(X), σ2, and σ for X using the definition of the probability density function. µ = E(X) = ∫xf(x)dx from 0 to 4 ∫f(x)dx for 0 < x ≤ 2= ∫((x^2)/16)dx for 0 < x ≤ 2 = (x^3/48) | from 0 to 2= 2/3 ∫f(x)dx for 2 < x < 4= ∫((4x−x^2)/16)dx for 2 < x < 4 = [(2x^2−(x^3)/12)/16] | from 2 to 4= (16−16−(16−8))/48= 1/3 ∴µ= (2/3) + (1/3)= 1 E(X) = 1 σ^2 = V(X) = E(X^2)- (E(X))^2=E(X^2)- µ^2 ∫x^2f(x)dx from 0 to 4 ∫f(x)dx for 0 < x ≤ 2= ∫((x^3)/16)dx for 0 < x ≤ 2 = (x^4/64) | from 0 to 2= 2 ∫x^2f(x)dx from 0 to 4 ∫f(x)dx for 2 < x < 4= ∫((4x^2-2x^3+x^4)/16)dx for 2 < x < 4 = [(2x^3-3x^4+(x^5)/5)/80] | from 2 to 4= (128−240+32−8−64/5+24/5)/80= 8/15 σ^2 = E(X^2)- (E(X))^2=2−1=1 σ = sqrt(σ^2)= 1

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The probability of y that when a point is randomly selected on the surface of a lake that has a maximum depth of 100 feet are all real numbers from 0 to 100.

A lake is a body of freshwater that is surrounded by land. The water in a lake is still, unlike a river or a stream, which flows from one place to another. Lakes are a vital component of the water cycle and play an important role in the ecosystem.

Since the maximum depth of the lake is 100 feet, the depth of the lake at the randomly chosen point cannot be greater than 100 feet. Therefore, y can have any value between 0 and 100. As a result, all real numbers from 0 to 100 are possible values of y.

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Answer:

its c

Step-by-step explanation:

Answer:

We can see that each term in the sequence is 3 more than the previous term. So we can find the 5th term by adding 3 to the fourth term, the 6th term by adding 3 to the 5th term, and so on.

5th term = 11 + 3 = 14

6th term = 14 + 3 = 17

7th term = 17 + 3 = 20

...

We can see that each term can be written as:

term = 2 + 3n

where n is the position of the term in the sequence starting from 0 (i.e. the first term is at position 0, the second term is at position 1, etc.)

To find the 19th term, we can substitute n = 17 into the formula:

19th term = 2 + 3(17) = 53

However, the problem states that the 19th term is actually 56. This means that we need to adjust our formula to account for any initial shift in the sequence. We can do this by subtracting a certain value from n, so that the first term in the sequence corresponds to n = 0.

Let's call this adjustment value "a". We know that when n = 0, the first term in the sequence is 2. So we can set up an equation:

2 + 3a = 2

Solving for a, we get a = 0.

Therefore, the adjusted formula for the nth term is:

term = 2 + 3(n-1)

where n is the position of the term in the sequence starting from 1.

Substituting n = 19, we get:

19th term = 2 + 3(18) = 56

So our adjusted formula is correct, and the answer is 56.

(Please could you kindly mark my answer as brainliest)

Answer:

28

Step-by-step explanation:

Because you're decreased the number, you'll subtract the percentage from 100%. Then , use ratio.

100% : 56

100% - 50% ( 50%) : ?

= 50/100 ×56

= 1/2 × 56

= 56/2

= 28

Choosing a sampling method that changes each time you take a sample is not the meaning of sampling variation.

The correct meaning of sampling variation is the fact that different samples taken from the same population will mostly produce different sample statistics due to random sampling error.

This means that there is a difference in the estimations gotten from different samples, even if the samples are drawn from the same population using the same sampling method.

The other options given are also not correct definitions of sampling variation. selecting a large sample size can help to reduce the amount of sampling variation by increasing the estimates obtained from the sample.

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The probability that the third card will be an ace is 0.0045, probability of all cards to be of same suit is 0.000495, and the probability of two or more aces is 0.004.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

(a) The probability that the third card is an ace:

We can approach this problem by using the conditional probability formula, which states that the probability of an event A given that event B has occurred is:

P(A|B) = P(A and B) / P(B)

Let A be the event that the third card is an ace, and let B be the event that the first two cards are not aces. The probability of the first card being an ace is 4/52 (since there are four aces in a standard deck of 52 cards). The probability of the second card being an ace given that the first card was not an ace is 3/51 (since there are three aces left in the deck of 51 cards). The probability of the third card being an ace given that the first two cards were not aces is 2/50 (since there are two aces left in the deck of 50 cards).

Therefore, using the conditional probability formula, we have:

P(A|B) = P(A and B) / P(B)

P(A|B) = (4/52) * (3/51) * (2/50) / (1 - (4/52) * (3/51))

P(A|B) ≈ 0.0045

So the probability that the third card is an ace is approximately 0.0045.

(b) The probability that all cards are of the same suit:

There are four suits in a standard deck of cards: clubs, diamonds, hearts, and spades. We can compute the probability that all five cards are of the same suit as follows:

P(all cards are of the same suit) = P(first card is a particular suit) * P(second card is the same suit) * P(third card is the same suit) * P(fourth card is the same suit) * P(fifth card is the same suit)

P(all cards are of the same suit) = (13/52) * (12/51) * (11/50) * (10/49) * (9/48)

P(all cards are of the same suit) ≈ 0.000495

So the probability that all cards are of the same suit is approximately 0.000495.

(c) The probability of two or more aces:

We can compute the probability of two or more aces by considering the complementary event: the probability that there are zero or one aces in the five cards dealt. The probability of getting zero aces is:

P(zero aces) = (48/52) * (47/51) * (46/50) * (45/49) * (44/48)

P(zero aces) ≈ 0.617

The probability of getting one ace is:

P(one ace) = (4/52) * (48/51) * (47/50) * (46/49) * (45/48) * 5

P(one ace) ≈ 0.379

Therefore, the probability of two or more aces is:

P(two or more aces) = 1 - P(zero aces) - P(one ace)

P(two or more aces) ≈ 0.004

So the probability of two or more aces is approximately 0.004.

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A circle with an area of [tex]289 cm^2[/tex], 4.25π cm is the length of an arc with a central angle of 45 degrees.

With the radius now known, we can apply the following formula to determine the length of an arc with a central angle of 45 degrees:

L = (45° / 360°) * 2π(17)

L = (1/8) * 34π

L = 4.25π cm

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference.

A circle's arc is referred to as a portion or section of its circumference. A chord of a circle is a straight line that might be created by joining the arc's two ends. A semicircular arc is one whose length is exactly half that of a circle.

from the question:

The following is the formula for an arc's length:

L is the length of the arc, r is the diameter of the circle, and the central angle is expressed in degrees. L = (central angle / 360°) * 2πr

We must first determine the circle's radius in order to solve this problem. The formula for calculating a circle's area is:

A = πr^2

Given that the circle's area is 289 cm2, we can use the following formula to find the radius:

289π = π[tex]r^2[/tex]

[tex]r^2[/tex] = 289

r = 17 cm

With the radius now known, we can apply the following formula to determine the length of an arc with a central angle of 45 degrees:

L = (45° / 360°) * 2π(17)

L = (1/8) * 34π

L = 4.25π cm

A circle with an area of [tex]289 cm^2[/tex], 4.25π cm is the length of an arc with a central angle of 45 degrees.

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Answer:

450

Step-by-step explanation:

larger book= 400+50

=450

The expression (6.25x + 12) - (4.25x - 7) / (6.25 + 12) - (4.25 - 7) to its simplest form, which is (2x + 19) / 21.

To simplify the given expression, we need to apply the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, we will simplify the expression inside the parentheses using the distributive property.

(6.25x + 12) - (4.25x - 7) = 6.25x + 12 - 4.25x + 7

Next, we will combine like terms, which are the terms with the same variable and exponent.

6.25x - 4.25x = 2x

12 + 7 = 19

Therefore, the simplified expression becomes:

2x + 19

Now, we will simplify the expression in the denominator.

(6.25 + 12) - (4.25 - 7) = 18.25 - (-2.75)

Remember that subtracting a negative number is the same as adding a positive number.

18.25 + 2.75 = 21

Finally, we can write the simplified expression as:

(2x + 19) / 21

This is the simplest form of the given expression, and it cannot be further simplified.

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Complete Question:

Simplify the expression: ( 6. 25 x + 12 ) − ( 4. 25 x − 7 ) ( 6. 2 5 + 1 2 ) − ( 4. 2 5 − 7 )

As x approaches to infinity y  also approaches to infinity.

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. Formally, a function f from a set A to a set B is defined as a subset of the Cartesian product A × B such that for every element a in A, there is a unique element b in B such that (a, b) belongs to the subset.

A function can be represented using the function notation f(x) = y, where x is the input (or independent variable), y is the output (or dependent variable), and f is the name of the function. The value of f(x) depends on the value of x and the rules of the function.

From the graph

x approaches to infinity

y  also approaches to infinity.

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Scale ratio is 9 cm which can be calculated by comparing lengths and using division.

The scale ratio between two rectangles is a way to compare the size of their corresponding sides. It is calculated by dividing the length of one side of the first rectangle by the length of the corresponding side of the second rectangle.

In this case, let's compare the length of the longer side of the first rectangle (72 cm) with the length of the longer side of the second rectangle (8 cm):

scale ratio = 72 cm ÷ 8 cm = 9

This means that the longer side of the first rectangle is 9 times as long as the longer side of the second rectangle. We could also calculate the scale ratio using the shorter sides:

scale ratio = 36 cm ÷ 4 cm = 9

In either case, the scale ratio is 9, which tells us that the first rectangle is 9 times as large as the second rectangle. This can be useful for creating accurate scale drawings or models of objects.

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After calculating the future value of the current balance, You will still owe $72.97 after one year.

Calculate the future value of the current balance: FV = PV x (1 + r)
Where, FV = Future Value, PV = Present Value (the current balance of $1,000), and r = interest rate of 2% per month.
Thus, FV = 1,000 x (1 + 0.02) = 1,020

Calculate the future value of the annuity payments of $100 per month:
FV = c x ı((1 + y)+ - 1)
Where, c = $100, y = interest rate of 2% per month.
Thus, FV = 100 x ı((1 + 0.02)12 - 1) = 1,246.24

Calculate the future value of the account balance: FV = 1,020 + 1,246.24 = 2,266.24
Finally, calculate the balance at the end of one year:
Balance at the end of one year = Future Value - Annuity Payments

Thus, Balance at the end of one year = 2,266.24 - (12 x 100) = 72.97.

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