Solve x^2=6x-9 by graphing. Select all solutions that apply.

The distribution of the data are symmetrical and left skewed, respectively

Stem and leaf plot 2

Here, we can see that the data increases uniformly till it gets to a peak, and then start decreasing till it gets to the initial level

This means that the plot is symmetrical

Hence, the distribution of the data is symmetrical

Stem and leaf plot 3

Here, we can see that the data has more points at the bottom that the upper part

This means that the plot is left skewed

Hence, the distribution of the data is left skewed

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Answer:

−

x

2

−

4

x

−

4

=

0

Graph each side of the equation. The solution is the x-value of the point of intersection.

x

=

−

2

image of graph

Step-by-step explanation:

−

x

2

−

4

x

−

4

=

0

Graph each side of the equation. The solution is the x-value of the point of intersection.

x

=

−

2

image of graph

Answer:

15) Let n = 1 be the first term of each sequence.

[tex] - 65536 \times - 4 = 262144[/tex]

[tex]a(n) = 262144( - { \frac{1}{4}) }^{n} [/tex]

[tex]a(9) = ( {4}^{9} ) {( - \frac{1}{4} )}^{9} = {( - 1)}^{9} = - 1[/tex]

16)

[tex] 6 \div (- 3 )= - 2[/tex]

[tex]a(n )= ( - 2) ({( - 3)}^{n} )[/tex]

[tex]a(9) = - 2(( { - 3)}^{9} ) [/tex]

[tex]a(9) = - 2 \times - 19683 = 39366[/tex]

The total land area of Edgardo's property is 36,400 square meters.

The area is a measure of the amount of two-dimensional space that a flat surface or shape occupies. It is a fundamental concept in geometry and is expressed in square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²).

Edgardo's original rectangular lot has an area of:

140 m x 120 m = 16,800 m²

The square lot he purchased has an area of:

140 m x 140 m = 19,600 m²

To find the total land area of Edgardo's property, we add the areas of the two lots:

16,800 m² + 19,600 m² = 36,400 m²

Therefore, the property owned by Edgardo has a total land size of 36,400 square meters.

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In the original derivation of logistic regression from Naive Bayes assumptions, we assumed that the variance σ^2 of a class-conditional probability distribution is independent of class index k and feature index j. Now, by generalizing and allowing σ^2_jk to depend on both indices, the class-conditional probability distribution p(x|y=k) is now affected by this change.

This new assumption affects the logistic regression formula p(y|X) because it no longer relies on the original independence assumption. Consequently, the logistic regression model will need to account for the new variances σ^2_jk, which depend on both class index k and feature index j.

The new form of logistic regression will likely be different from the original formula, as it must now accommodate the modified variances in class-conditional probability distributions. Unfortunately, without more information, it is not possible to provide the exact new form of logistic regression here. However, it's important to note that this new form should consider the dependency of σ^2_jk on both indices j and k.

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The solution is:

No, this statement is not true, we know that these dimensions are not possible given the amount of fencing.

We have,

Perimeter measures the distance around a shape.

Perimeter Formula

The perimeter is 2w + 2l = P, where w is the width and l is the length. This formula is used because together, it adds together the distance of every side.

If wanted, it can be rewritten as w + w + l + l = P. This form of the formula shows all 4 sides being added together.

Inequality

We can set up an inequality to represent the situation. We know that the perimeter must be less than or equal to 150 because that is the amount of fence John has. So, we can plug the information that we know into the formula.

2(50) + 2(40) ≤ 150

Then, solve.

180 ≤ 150

Since this statement is not true, we know that these dimensions are not possible given the amount of fencing.

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complete question:

John is building a fence around his garden and has 150 feet of

fencing. The length of his garden is 40 feet and the width of

his garden is 50 feet. Does John have enough fencing to go

around the perimeter of his garden? Explain why or why not.

(a) We need to find P(X ≤ 50), where X is the maximum speed of a moped. We have:

μ = 46.8 km/h

σ = 1.75 km/h

Using standardization, we get:

Z = (X - μ) / σ

Z follows a standard normal distribution. Therefore,

P(X ≤ 50) = P(Z ≤ (50 - μ) / σ)

= P(Z ≤ (50 - 46.8) / 1.75)

= P(Z ≤ 1.8286)

= 0.9641 (rounded to four decimal places)

Therefore, the probability that the maximum speed is at most 50 km/h is 0.9641.

(b) We need to find P(X ≥ 49). Using standardization, we get:

P(X ≥ 49) = P(Z ≥ (49 - μ) / σ)

= P(Z ≥ (49 - 46.8) / 1.75)

= P(Z ≥ 1.2571)

= 0.1038 (rounded to four decimal places)

Therefore, the probability that the maximum speed is at least 49 km/h is 0.1038.

(c) We need to find P(|X - μ| ≤ 1.5σ). Using standardization, we get:

P(|X - μ| ≤ 1.5σ) = P(-1.5 ≤ (X - μ) / σ ≤ 1.5)

= P(-1.5 ≤ Z ≤ 1.5)

= P(Z ≤ 1.5) - P(Z ≤ -1.5)

= 0.8664 - 0.0668

= 0.7996 (rounded to four decimal places)

Therefore, the probability that the maximum speed differs from the mean value by at most 1.5 standard deviations is 0.7996.

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The correct matching of the above items with their descriptions is as follows:

Prescription medical abbreviations are those abbreviations that are used by medical practitioners to direct both the patient and pharmacist the dosage, route of administration and duration for the drug treatment regimen.

The typical examples of medical prescription used by doctors include the following:

BID = twice daily (think bi/bilateral or two, or Bicycle which has 2 wheels)

QID = four times daily (think quad/four or 4 quarters)

TID = three times daily (think tri/three, or tricycle which has 3 wheels)

Q or q = means 'every'

extremity= arm or leg

QOD =every other day

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The solution of the formula for the variable, m as required to be determined is; m = Fr² / GM.

It follows from the task content that the complete question indicates a formula;

F = GMm / r²

Hence, to solve for the variable m; multiply both sides by r² so that we have;

Fr² = GMm

Finally divide both sides by GM so that we have;

m = Fr² / GM

Ultimately, the formula with m as the subject is; m = Fr² / GM.

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Step-by-step explanation & Answer:

To find how long it takes for the diver to reach a point 1 meter above the water, we need to set the height equation equal to 1 and solve for t:

-4.9t^2 + 3.5t + 10 = 1

-4.9t^2 + 3.5t + 9 = 0

We can solve for t using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / 2a

t = (-3.5 ± √(3.5^2 - 4(-4.9)(9))) / 2(-4.9)

t ≈ 1.65 seconds or t ≈ 1.06 seconds

Therefore, it takes the diver approximately 1.65 seconds or 1.06 seconds to reach a point 1 meter above the water.

The equation from part A has two solutions.

Not all of the solutions make sense in the situation. One of the solutions is negative, which does not make sense in the context of the problem. The other solution is the time it takes for the diver to reach a point 1 meter above the water.

The probability of getting 2 twice in a row is 1/25 or 0.04.

Since the spinner has five equal parts labeled from 1 to 5, the probability of getting a 2 on any single spin is 1/5.

Since the spinner is spun twice, and we want to know the probability of getting 2 twice in a row, we need to multiply the probability of getting a 2 on the first spin by the probability of getting a 2 on the second spin, assuming that a 2 was already spun on the first spin.

Therefore, the probability of getting 2 twice in a row is (1/5) x (1/5) = 1/25, or 0.04, or 4%.

So, the probability of getting 2 twice in a row is 1/25 or 0.04.

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If the probability that a tire has an expected life of at least 30000 miles is 0.85, then the probability that a tire will have a life of less than 30000 miles is 0.15.

Using this information, we can find the probability that among 20 tires, a certain number will have a life of less than 30000 miles. This can be done using a binomial distribution, where the probability of success (a tire having a life of at least 30000 miles) is p = 0.85 and the number of trials is n = 20.

The probability of having k tires with a life of less than 30000 miles is given by the formula:

[tex]P(k) = (n choose k) * p^k * (1-p)^(n-k)[/tex]

where (n choose k) represents the number of ways to choose k items out of n, and is calculated by the formula:

(n choose k) = n! / (k! * (n-k)!)

Using this formula, we can find the probabilities of having 0, 1, 2, ..., 20 tires with a life of less than 30000 miles.

For example, the probability of having exactly 3 tires with a life of less than 30000 miles is:

P(3) = (20 choose 3) * 0.85^17 * 0.15^3

= 1140 * 0.085 * 0.003375

= 0.02736

Similarly, we can find the probabilities of having any other number of tires with a life of less than 30000 miles.

Note that the sum of all these probabilities is equal to 1, since one of these outcomes must occur.

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Answer: The slope of parallel lines are the same

Step-by-step explanation:

There are not triangles in the image, but instead two lines creating a corner, they want you to connect the opposite corners of each of these sets of lines to create a triangle.

The bigger set of lines is up 2 right 8. slope is rise/run so the slope is 2/8 or if we simplify 1/4

The smaller set of lines is 1 up 4 right. slope is rise over run so the slope is 1/4.

The problem tries to confuse you by not connecting those lines and by having the bigger one go up first then right, and then the smaller one go right first and then up.

But as you can see the parallel lines both have a slope of 1/4

the only difference between parallel lines is the 'b' in the equation y=mx+b

The side x of the given right angle triangle is: 24.388

The six trigonometric ratios that we have are:

sine (sin)

cosine (cos)

tangent (tan)

cotangent (cot)

cosecant (cosec)

secant (sec).

In geometry, trigonometry is defined as a branch of mathematics that caters for the sides and also the angles of right-angled triangles. Thus, trigonometric ratios are evaluated considering the sides and angles

The three main trigonometric ratios are expressed as:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We want to find the side x of the given right angle triangle.

Thus:

16/x = cos 49

x = 16/cos 49

x = 24.388

Thus, we can say that is the value of x

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Answer: (4x+7)-(x+1) = 4x + 7 - x - 1 = 3x + 6.

Therefore, (4x+7)-(x+1) = 3x + 6.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Distribute the Negative sign

(4x +7 ) + (-x - 1)

2. Remove Paranthesis

4x + 7- x - 1

3. Solve

4x - x + 7 - 1

3x + 6

4. (optional) Factor out the 3

3(x+2)

The answer is 3x + 6 or 3(x+2)

Circular permutation refers to the ordering of elements in a circle, factorial refers to the product of all the natural numbers from an integer down to one, series refers to the indicated sum of the terms of an associated sequence, and permutation refers to the order of elements of a set. It is important to understand these terms in order to have a solid foundation in mathematics.

Circular permutation refers to an ordering of elements in a circle. Factorial, on the other hand, is the product of all the natural numbers from an integer down to one. It is denoted by the exclamation mark (!). Series, on the other hand, refers to the indicated sum of the terms of an associated sequence. Finally, permutation is an order of elements of a set.

To summarize, circular permutation refers to the ordering of elements in a circle, factorial refers to the product of all the natural numbers from an integer down to one, series refers to the indicated sum of the terms of an associated sequence, and permutation refers to the order of elements of a set. It is important to understand these terms in order to have a solid foundation in mathematics.

1. Circular permutation - an ordering of elements in a circle.
In a circular permutation, the arrangement of items is considered in a circular fashion rather than in a linear order. The number of circular permutations for 'n' elements can be calculated using the formula (n-1)!.

2. Factorial - the product of all the natural numbers from an integer down to one.
Factorial, denoted by the symbol '!', represents the product of all the positive integers from a given integer down to one. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

3. Series - the indicated sum of the terms of an associated sequence.
A series is the sum of the terms in a given sequence, often represented by the summation symbol Σ. For example, the sum of the first 'n' natural numbers is represented as Σ(i=1 to n) i = n(n+1)/2.

4. Permutation - an order of elements of a set.
A permutation refers to the arrangement of elements in a specific order within a set. The number of possible permutations for a set of 'n' elements, taken 'r' at a time, can be calculated using the formula n!/(n-r)!.

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The triangular prism has a surface area of 1340 square meters. The answer is 1340 m².

To calculate the surface area of a triangular prism, find the area of all its faces and add them together.

The triangular base has a base of 10 m and a height of 14 m, so its area is:

(1/2) × base × height = (1/2) × 10 m × 14 m = 70 m²

There are two identical triangular faces, so the total area of both is:

2 × 70 m² = 140 m²

The rectangular faces have dimensions of 10 m by 25 m and 14 m by 25 m, so their areas are:

10 m × 25 m = 250 m²

14 m × 25 m = 350 m²

Again, there are two rectangular faces, so the total area of both is:

2 × (250 m² + 350 m²) = 1200 m²

Finally, add the areas of all the faces:

140 m² + 1200 m² = 1340 m²

Therefore, the surface area of the triangular prism is 1340 square meters.

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About 3.25 seconds have gone by when the rocket is at its highest point.

The height of the rocket at any time t can be calculated using the equation h = -16t² + 104t.

The vertex of the parabolic function will give the value of the highest point of the rocket. The x-coordinate of the vertex gives us the time at which the rocket reaches its maximum height.

The x-coordinate of the vertex can be found using the formula: x = -b / 2a, the coefficient of the t² term is a and coefficient of the t term is b.

In this case, a = -16 and b = 104, so the x-coordinate of the vertex is,

x = -b / 2a

= -104 / (2*(-16))

= 3.25

Therefore, the rocket is at its highest point 3.25 seconds after launch.

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To find the intersection point of the two constraints of x1 and x2, we need to solve the system of inequalities simultaneously.

First, we can rewrite each inequality in slope-intercept form:

1. 9x1 + 7x2 ≥ 57   ->   x2 ≥ (-9/7)x1 + 57/7
2. 4x1 + 6x2 ≥ 3   ->   x2 ≥ (-2/3)x1 + 1/2

The intersection point will occur where the two lines intersect, so we can set the two equations equal to each other:

(-9/7)x1 + 57/7 = (-2/3)x1 + 1/2

Simplifying:

(-9/7 + 2/3)x1 = 1/2 - 57/7

(-15/21)x1 = -163/42

x1 = (163/42)/(15/21)

x1 = 1.634

To find x2, we can substitute this value back into either of the original equations:

9(1.634) + 7x2 = 57

7x2 = 57 - 14.706

x2 = 6.32

Therefore, the values of x1 and x2 where the two constraints intersect are x1 = 1.634 and x2 = 6.32.

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Answer:

{1/2}{1/2}=1/4

Step-by-step explanation:

The probability of rolling a 1 then a prime number when rolling a fair number cube twice is 1/12.

To find the probability of rolling a 1 then a prime number when rolling a fair number cube twice, we need to determine the possible outcomes. When rolling a number cube, there are six possible outcomes: 1, 2, 3, 4, 5, and 6. The probability of rolling a 1 is 1/6. Now, when rolling the cube a second time, the possible outcomes remain the same. However, only the numbers 2, 3, 5, have prime values. So the probability of rolling a prime number is 3/6.

To find the probability of both events happening together, we multiply the probabilities. Therefore, the probability of rolling a 1 then a prime number is (1/6) * (3/6) = 1/12. This means that there is a 1 in 12 chance of rolling a 1 and then rolling a prime number when rolling a fair number cube twice.

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If we let a = 0, b = 1, and c = 1, then the polynomial

[tex]x(x-1)(x^2 +[/tex]

Since the polynomial has integer coefficients, if one of the roots is a complex number, then its conjugate must also be a root. Therefore, options A and E cannot be roots of the polynomial, since they have non-real conjugates.

We know that the polynomial has degree 4, so it has four roots in total (counting multiplicities). We also know that two of the roots are integers, so let's call them a and b. Then the polynomial can be written as:

[tex](x - a)(x - b)(cx^2 + dx + e)[/tex]

where c, d, and e are integers (because they are the coefficients of the quadratic factor). We know that the leading coefficient is 1, so c must be nonzero.

Since the polynomial has two real roots, its discriminant must be nonnegative:

[tex]d^2 - 4ce > = 0[/tex]

We can use this inequality to rule out some of the answer choices. For example, option C cannot be a root, because if we substitute x = 1/2 + i into the polynomial, we get:

([tex](1/2 + i) - a)((1/2 + i) - b)(c((1/2 + i)^2) + d(1/2 + i) + e)[/tex]

The real part of this expression is:

(1/4 - a + 1/4 - b)(c(1/4 - 1) + d/2 + e) = -(a + b - 1/2)(3c/4 + d/2 + e)

If we assume that a and b are integers, then this expression is an integer multiple of 3c/4 + d/2 + e. However, we can choose values of c, d, and e such that 3c/4 + d/2 + e is not an integer (for example, if c = 4, d = 1, and e = 0, then 3c/4 + d/2 + e = 4.5). Therefore, the real part of the expression cannot be zero, and option C cannot be a root.

We can also rule out option D using the same argument. If we substitute x = 1 + i/2, then the real part of the expression is:

((1 + i/2) - a)((1 + i/2) - b)(c((1 + i/2)^2) + d(1 + i/2) + e)

(1 - a + i/2)(1 - b + i/2)(c(5/4 + i) + d(3/2 + i/2) + e)

The real part of this expression is an integer multiple of c(5/4) + d(3/2) + e, which can be non-integer for some choices of c, d, and e.

Therefore, the only possible answer choices are A and B. To determine whether they are roots of the polynomial, we can use the fact that the sum and product of the roots are given by:

a + b + (complex roots) = -d/c

ab(complex roots) = e/c

We know that a and b are integers, so if we can find a polynomial with integer coefficients that has roots a, b, and either A or B, then that root is also a root of the original polynomial.

For option A, we have:

1 + i√11/2 = 2(cos(75°) + i sin(75°))

Therefore, if we let a = 0, b = 1, and c = 1, then the polynomial

[tex]x(x-1)(x^2 +[/tex]

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The general solution will depend on the values of k, m, and the damping coefficient 8/m. To find the equation of motion for this system.

We can use Newton's second law:

F = ma

where F is the net force acting on the system, m is the mass of the object, and a is the acceleration.

The net force in this case is the sum of the external force and the force due to the spring:

F = f(t) - kx

where k is the spring constant and x is the displacement from equilibrium.

The damping force is given as 8 times the instantaneous velocity, which we can write as:

F_damp = -8v

where v is the velocity of the object.

Putting everything together, we get:

m(d^2x/dt^2) = f(t) - kx - 8v

Substituting in the given values, we have:

1(d^2x/dt^2) = 2 sin 4t - kx - 8(dx/dt)

To simplify this equation, we can use the fact that x is a displacement and therefore the second derivative of x with respect to time is the acceleration. So we can rewrite the equation as:

a = (2/g)sin(4t) - (k/m)x - 8v/m

where g = 32 ft/s^2 is the acceleration due to gravity.

To solve for x, we can use the fact that the velocity is the derivative of displacement with respect to time:

v = dx/dt

Taking the derivative of the equation for velocity, we get:

a = d^2x/dt^2 = dv/dt = d/dt(dx/dt) = d/dt(v) = d/dt(-8v/m - (k/m)x + 2/g sin(4t))

Simplifying this expression, we get:

a = -8/m(dv/dt) - k/m(dx/dt) + (8/g)cos(4t)

Substituting in the value of a from the previous equation, we have:

(2/g)sin(4t) - (k/m)x - 8v/m = -8/m(dv/dt) - k/m(dx/dt) + (8/g)cos(4t)

Rearranging and simplifying, we get:

d^2x/dt^2 + (k/m + 8/m)dx/dt + k/mx = (16/g)cos(4t) - (2/g)sin(4t)

This is a second-order differential equation that we can solve using standard techniques, such as the method of undetermined coefficients or Laplace transforms. The general solution will depend on the values of k, m, and the damping coefficient 8/m.

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For scenario 1, the appropriate statistical test to run is an independent samples t-test. The null hypothesis would be that there is no significant difference in weight gain between cows raised in a pen and those raised in an open pasture.

For scenario 2, the appropriate statistical test to run is a chi-squared test for independence. The null hypothesis would be that there is no significant association between the type of environment the cows were raised in and their weight status (healthy vs. undernourished).

For scenario 3, the appropriate statistical test to run is a one-sample t-test. The null hypothesis would be that the mean weight of the cows raised in the small pen is equal to 1,300 pounds.
1. In the first scenario, the farmer should use an independent samples t-test. The null hypothesis would be: There is no significant difference in the weight of Holstein cows (Bos Taurus) raised in a small pen compared to those raised in an open pasture.

2. In the second scenario, the farmer should use a chi-square test of independence. The null hypothesis would be: There is no significant association between the rearing environment (small pen or open pasture) and the health status (healthy or undernourished) of Holstein cows (Bos Taurus).

3. In the third scenario, the farmer should use a one-sample t-test on the log-transformed weights. The null hypothesis would be: The mean log-transformed weight of Holstein cows (Bos Taurus) raised in a small pen is equal to the log-transformed weight of 1,300 pounds, indicating no significant difference from the expected average adult cow weight.

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The speed of the boat is approximately 9.21 km/h.

In order to ascertain the speed of the boat, we must find out the number of kilometers traversed by it and the amount of time taken for traveling that distance.

The traveled distance by the boat is equal to the space between two points,

or the magnitude of (final position vector - initial position vector),

which in this case is (-7i - 3j). Hence, the total distance of sqrt((-7)^2 + (-3)^2) kilometers is obtained.

Regarding the amount of time taken to travel that predetermined distance, it computes to be 2 hours 45 minutes, or 2.75 hours.

Therefore, through simple division, the speed of the boat can be determined at roughly 9.21 km/h, which results when you divide the traveled distance of sqrt(58) by the time taken in hours, that is, 2.75.

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Applying the Pythagorean Theorem, the diagonal distance is calculated as: 65 cm.

In order to find the diagonal distance between A and C in the image given, recall the Pythagorean Theorem which states that the sum of the square of each leg's length of a right triangle is equal to the square of its hypotenuse.

In this case, the diagonal is the hypotenuse, therefore:

Diagonal distance = √(60² + 25²)

Diagonal distance = 65 cm

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The ratio of freshmen to sophomores at 1 p.m. is approximately 0.98:1, or 98 freshmen to every 100 sophomores.

At noon, there are a total of 3,390 students at the prep rally (1,560 + 1,830). From 12 p.m. to 1 p.m., which is a total of 12 five-minute intervals, 20 freshmen arrive per interval, so 20 x 12 = 240 freshmen arrive. Additionally, 15 sophomores leave per interval, so 15 x 12 = 180 sophomores leave.

Therefore, at 1 p.m., there are a total of (1,560 + 240) - 180 = 1,620 freshmen and (1,830 - 180) = 1,650 sophomores at the prep rally.

To find the ratio of freshmen to sophomores at 1 p.m., we can divide the number of freshmen by the number of sophomores:

1,620/1,650 = 0.98

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The APR charged by Advance America is approximately 443.2%.

Convert the loan term of 14 days to a fraction of a year.

There are 365 days in a year, so the fraction of a year for a 14-day loan is 14/365.

Simple interest is calculated with the following formula:

S.I. = (P × APR × T)/100,

Here P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.

As per the question, we have:

P = $100, S.I. = $17 and T = 14/365.

Substitute the values in the formula,

17 = (100 × APR × 14/365)/100

APR = (365 × 17)/14

APR = 443.2 %

Therefore, the APR is about 443.2%.

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The larger of the two expressions is maxvalue(r, n - k - r, k).

The expression with -1 as the second parameter to maxvalue is maxvalue(n-k-r, -1, k).

To see why this is the case, let's consider the definition of maxvalue(r, a, b). This function returns the maximum value among r, a, and b.

Now, suppose that k < n - r. Then, we have:

n - k - r > n - (n - r) - r = r

This means that n - k - r is greater than r, so maxvalue(r, n - k - r, k) will return either n - k - r or k, whichever is greater.

On the other hand, since -1 is less than any non-negative integer, we have:

-1 < 0 <= r

Therefore, maxvalue(r, -1, k) will return either r or k, whichever is greater.

Since r is non-negative, we have:

maxvalue(r, -1, k) = max(r, -1, k) = max(r, k)

So, the larger of the two expressions is maxvalue(r, n - k - r, k).

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