Remember to use information in the
problem to make assumptions that can help
you model and solve the problem.
Monica wants to buy a 1-month supply of dog
food. She can buy a 20-pound bag of dog food
for $18 or a 30-pound bag for $24. Twice a
day, she feeds her dog 6 ounces of food. Which
bag of dog food should she buy? Explain.
1. What assumptions can you make?
2. What model can you use to solve the
problem?

Plssss helppp it’s a grade

Answer:

$391.2 per owner

Step-by-step explanation:

find the total price of the items and divide it by five

If "3 marks" are awarded for each "correct-answer" and "-1 marks" for each "incorrect-answer", then the total score of Varun in quiz is 47.

Out of the 25 questions in the quiz, Varun attempted all of them, which means he has answered 25 questions in total.

Out of the 25 questions, Varun answered only 18 correctly, which means he answered 7 questions incorrectly.

Therefore, the total score for his correct answers would be : 18 × 3;

⇒ 54 marks,

The total score for his incorrect answers would be : 7 × (-1) = -7;

Varun did not leave any question "un-attempted", so he did not gain or lose any marks for those questions.

Varun's total score in the quiz would be : (Score for correct answers) + (Score for incorrect answers)

⇒ Total Score = 54 + (-7) = 47 marks,

Therefore, Varun's total score in quiz is 47 marks.

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The given question is incomplete, the complete question is

In a Mathematics quiz, the total number of questions are 25. According to the marking scheme, 3 marks are given for every correct answer and -1 marks for every incorrect answer, and 0 for questions not attempted.

Varun attempts all questions but only 18 of his answers are correct. What is his total score in the quiz?

Answer:

24 coins

Step-by-step explanation:

We give the dimes a unknown number like y since the nickels are twice as much we give it 2y we multiply the numbers with their value and form an equation like 2y×5+y×10=160 find the value of y then get value of 2y+y to get the number of coins

As x approaches infinity, the limit of function [(2x-1)(3-x)]/[(x-1)(x+3)] is equal to -2.

What is function?

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain) with the property that each input is related to exactly one output.

To find the limit of [(2x-1)(3-x)]/[(x-1)(x+3)] as x approaches infinity, we need to consider the highest power of x in the numerator and the denominator.

In the numerator, the highest power of x is [tex]x^2[/tex], which comes from the product of (2x)(3). In the denominator, the highest power of x is also [tex]x^2[/tex], which comes from the product of (x)(x).

Thus, we can use the rule that when the highest powers of x in the numerator and denominator are equal, the limit is the ratio of the coefficients of these highest powers. Therefore:

lim [(2x-1)(3-x)]/[(x-1)(x+3)]

= lim [([tex]-2x^2[/tex] + 7x - 3)/([tex]x^2[/tex] + 2x - 3)]

= lim [-2 + (7/x) - (3/[tex]x^2[/tex])] / [1 + (2/x) - (3/[tex]x^2[/tex])]

= -2/1

= -2

Therefore, as x approaches infinity, the limit of [(2x-1)(3-x)]/[(x-1)(x+3)] is equal to -2.

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When it comes to printing full-color pictures, it usually involves using the CMYK color model which stands for cyan, magenta, yellow, and black.

These colors are combined in different amounts to create a wide range of colors and shades. Therefore, the answer to your question is three plus black. The colors cyan, magenta, and yellow are combined to produce a wide range of colors, while the black is added to enhance contrast and to create darker tones.

This combination of colors provides a more accurate and vibrant representation of the original picture. It is important to note that there are other color models used for printing such as RGB (red, green, and blue) which is used for digital displays, but for printing purposes, CMYK is the most common.

In conclusion, full-color pictures are printed using three colors (cyan, magenta, and yellow) plus black to enhance contrast and create darker tones. This combination of colors provides a more accurate and vibrant representation of the original picture.

This model consists of four ink colors: cyan (C), magenta (M), yellow (Y), and key (black, K). These four inks are combined in various proportions to produce a wide range of colors in the final print. Therefore, the correct answer would be four colors (CMYK), including black.

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This method of completing the square can be used to solve any quadratic equation, even if the coefficients a, b, and c are not whole numbers.

Completing the square is a method used to solve quadratic equations in the form of ax^2 + bx + c = 0, where a, b, and c are constants. To use this method, follow these steps:

1. Move the constant term (c) to the other side of the equation, so that you have ax^2 + bx = -c.

2. Divide both sides of the equation by the coefficient of the x^2 term (a), so that you have x^2 + (b/a)x = -c/a.

3. Take half of the coefficient of the x term (b/a), square it, and add it to both sides of the equation, so that you have x^2 + (b/a)x + (b/2a)^2 = (b/2a)^2 - c/a.

4. Simplify the left side of the equation by factoring it as (x + b/2a)^2.

5. Take the square root of both sides of the equation, remembering to include both the positive and negative square roots.

6. Solve for x by subtracting b/2a from each side of the equation.

This method of completing the square can be used to solve any quadratic equation, even if the coefficients a, b, and c are not whole numbers. It is a useful tool to have in your mathematical toolbox, as it can simplify complicated equations and help you find the solutions you need.

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The solution to the equation −18 − 6k = 6(1 + 3k) in terms of k is k = -3/4.

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.

Your steps are correct, and here's the solution to the equation:

−18 − 6k = 6(1 + 3k)

To solve for k, we first use the distributive property to remove the parentheses:

−18 − 6k = 6 + 18k

Then, we simplify the equation by combining like terms:

−18 − 6k + 6k = 6 + 18k + 6k

-18 = 24k

Finally, we isolate k by dividing both sides by 24:

-18/24 = 24k/24

-3/4 = k

Therefore, the solution to the equation −18 − 6k = 6(1 + 3k) in terms of k is k = -3/4.

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The complete question is:

Solve for the value of k in the equation:

-18 - 6k = 6(1 + 3k)

where k is an unknown constant.

The hypothesis test is a one-tailed test, since we are testing for a specific direction (greater than 72%).

An assumption is said to as a hypothesis when it is supported by evidence. Any investigation that turns the research questions into predictions must start here. Variables, the population, and the relationships between the variables are among its constituent parts.

The hypotheses for the test are:

H0: p = 0.72 (null hypothesis)

Ha: p > 0.72 (alternative hypothesis)

The claim is that the proportion of college students who recycle is greater than 72%, which corresponds to the alternative hypothesis.

The hypothesis test is a one-tailed test, since we are testing for a specific direction (greater than 72%).

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The solution to the equation (a - b) / (a + b) = 3/5 in terms of b is a = 4b.

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.

Your steps are correct, and here's the solution to the equation:

(a - b) / (a + b) = 3/5

To solve for a in terms of b, we cross multiply:

5(a - b) = 3(a + b)

Expanding the brackets, we get:

5a - 5b = 3a + 3b

Simplifying the equation by combining like terms, we get:

5a - 3a = 8b

2a = 8b

Dividing both sides of the equation by 2, we get:

a = 4b

Therefore, the solution to the equation (a - b) / (a + b) = 3/5 in terms of b is a = 4b.

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The complete question is:

The equation given is A = 4b. Please write an appropriate question related to this equation.

To find the probability of rolling a sum of either 3 or 7, we need to find the number of ways we can get each sum and divide by the total number of possible outcomes. For a sum of 3, the only way to get this is by rolling a 1 and a 2. There are two ways to arrange this: 1-2 and 2-1.


Probability = (Number of desired outcomes) / (Total number of possible outcomes)
Probability = 8 / 36

We can simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 4:

Probability = (8/4) / (36/4)
Probability = 2/9

So, the probability of rolling a sum of 3 or 7 with two dice is 2/9, or approximately 0.222222 as a decimal rounded to the nearest millionth.

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It is true that every invertible square matrix can be written as a product of elementary matrices. because, it depends on whether you are talking about invertible square matrices or all square matrices.

An elementary matrix is a matrix that can be obtained from the identity matrix by performing a single elementary row operation (such as swapping two rows, multiplying a row by a scalar, or adding a multiple of one row to another).

Moreover, any matrix that can be expressed as a product of elementary matrices is invertible.

However, not every square matrix is invertible, and so not every square matrix can be written as a product of elementary matrices. For example, the zero matrix cannot be written as a product of elementary matrices since it is not invertible.

So, it depends on whether you are talking about invertible square matrices or all square matrices.

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After using the formula: z = (x - μ) / σ , the z-score for Allison's weight is 0.5.So, the z-score for Allison's weight is 0.5.

To find the z-score for Allison's weight, we use the formula:
z = (x - μ) / σ

where x is Allison's weight (145 lbs), μ is the mean weight of females (135 lbs), and σ is the standard deviation (20 lbs).

Substituting the values, we get:

z = (145 - 135) / 20
z = 0.5

Therefore, the z-score for Allison's weight is 0.5.

To calculate the z-score for Allison's weight, we can use the following formula:

z-score = (Allison's weight - mean weight) / standard deviation

Plugging in the given values:
z-score = (145 lbs - 135 lbs) / 20 lbs = 10 lbs / 20 lbs = 0.5

So, the z-score for Allison's weight is 0.5.

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The orthocenter will lie in the interior of a(n) acute triangle.  In Euclidean geometry, the orthocenter is a point where the three altitudes of a triangle intersect.

All three angles in an acute triangle are less than 90 degrees.  If we draw the altitudes from each vertex, they will all intersect inside the triangle. Therefore, the orthocenter of an acute triangle will always be located in the interior of the triangle.

On the other hand, in an obtuse triangle, at least one angle is greater than 90 degrees. In this case, one of the altitudes will lie outside of the triangle, so the orthocenter will be located outside of the triangle.

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The curve f(x) is f(x) = -2x + 3.

Given that dy/dx = -2, we can integrate both sides with respect to x to obtain:

dy/dx = -2

dy = -2 dx

Integrating both sides, we get:

y = -2x + C

where C is the constant of integration. To find the value of C, we use the initial condition f(0) = 3:

y = -2x + C

f(0) = 3

-2(0) + C = 3

C = 3

Thus, the equation of the curve is:

y = -2x + 3

Therefore f(x) is -2x + 3

We can sketch the curve by plotting a few points. For example, when x = 0, y = 3 (as required by the initial condition). When x = 1, y = 1. When x = -1, y = 5. We can also note that the slope of the curve is always -2, meaning that the curve is a straight line with a negative slope.

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Since ABCD is an isosceles trapezoid, we know that AB = CD. Additionally, we know that AD = BC. Therefore, we can set up two equations:

AB = CD

AD = BC

Using the fact that B = x + 10 and C = 2x - 30, we can substitute those values into the equations:

AB = CD

x + 10 + AD = 2x - 30 + BC

Since AD = BC, we can simplify the second equation to:

x + 10 + AD = 2x - 30 + AD

x + 10 = 2x - 30

x = 40

Now that we know x, we can find the measures of angles B and C:

B = x + 10 = 50

C = 2x - 30 = 50

Since ABCD is an isosceles trapezoid, we know that angles B and C are congruent. Therefore, each of them measures 50 degrees. Since the sum of the angles in a quadrilateral is 360 degrees, we can set up the equation:

A + B + C + D = 360

Substituting in the values we have:

A + 50 + 50 + D = 360

Simplifying the equation:

A + D = 260

Since ABCD is an isosceles trapezoid, we know that angles A and D are congruent. Therefore, we can set up the equation:

A + D = 2D

Substituting in the value we have:

2D = 260

Simplifying the equation:

D = 130

Therefore, the measure of angle D is 130 degrees.

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If the point (3, -2) were reflected across the y-axis what would be the new y-coordinate is same as before, which is -2.

If a point (x, y) is reflected across the y-axis, its x-coordinate becomes its opposite (-x), while its y-coordinate remains the same.

In this case, the point is (3, -2). If we reflect this point across the y-axis, its x-coordinate will become its opposite, which is -3. The new coordinates of the reflected point will be (-3, -2).

Therefore, the new y-coordinate is still -2, as the point is only being reflected across the y-axis and not moving up or down in the y-direction. The change is only in the x-coordinate, which becomes its opposite.

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The solution of the given simultaneous equations is x = 3 and y = 5.

The given equations are:

3x + 2y = 19

x + 2y = 13

To solve them using the elimination method, we need to eliminate one variable from the equations. In this case, we can eliminate y by subtracting the second equation from the first equation, as follows:

(3x + 2y) - (x + 2y) = 19 - 13

Simplifying the left-hand side, we get:

2x = 6

Dividing both sides by 2, we obtain:

x = 3

Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y. Let's substitute it into the second equation:

x + 2y = 13

3 + 2y = 13

Subtracting 3 from both sides, we get:

2y = 10

Dividing both sides by 2, we obtain:

y = 5

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The degree of the polynomial P(x) is 2.

Let the degree of the polynomials P(x) and Q(x) be 'm' and 'n' respectively.

deg {P(x)} = m

deg {Q(x)} = n

So deg {P(x²)} = 2m

and deg {Q³(x)} = 3n

Given that the degree of polynomial {P(x²).Q³(x)} is 12.

So, 2m*3n = 12

6mn = 12

mn = 12/6

mn = 2

n = 2/m ..................... (i)

Again, deg {P³(x)} = 3m

deg (Q(x)) = n

Now given that, deg[P³(x)/Q(x)] = 7

So, 3m/n = 7

3m = 7n

3m = 7*(2/m) [Using the equation (i)]

3m² = 14

m² = 14/3

m = 2 (approximating to nearest whole number)

Hence, the degree of the polynomial p(x) is 2.

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The confidence interval for proportion of adults who liked video game is (0.575091,0.8915756 ) from sample. It has a parameter 65%.

Number of enrolled students in STAT during year 2020 = 70

The population of adults that is 18 or above in 2020 = 258.3 million

Number of students are classmates= 30

Out of 30, number of students who like video game = 22

level of significance = 0.95

Let p denote the proportion of students in sample who liked video games. it is p = 22/30 = 0.733.

Using the distribution table, value of z for 95% is equals to the 1.96. From the formula of confidence interval, [tex]CI = p ± z\sqrt{ \frac{ p( 1 - p)}{n}}[/tex]

[tex]= 0.733 ± \sqrt{ \frac{0.733( 1 - 0.733)}{30}}[/tex]

= (0.575091, 0.8915756), the lower limit and upper limit of interval. This interval contains 65% which is population parameter. Hence, required value is (0.575091, 0.8915756).

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The amount of the check is $94.08.

To calculate the amount of the check, we need to consider the cost per dozen shirts, the number of dozens purchased, and any applicable discounts.

Given information:

Cost per dozen shirts: $16

Number of dozens purchased: 6

Cost per shirt from the wholesaler: $16.32

Terms of the sale: 2/15, n/30 (meaning a 2% discount if paid within 15 days, and the full amount is due within 30 days)

Invoice paid on: March 29

Let's break down the calculations step by step:

Cost of 6 dozen shirts:

Cost per dozen shirts = $16

Cost of 6 dozen shirts = 6 * $16 = $96

Applying the discount:

Discount percentage = 2% = 0.02

Discount amount = 0.02 * $96 = $1.92

Total amount after discount = $96 - $1.92 = $94.08

Check the payment due date:

The invoice was paid on March 29, which is within the 30-day period. Therefore, there is no additional penalty or interest.

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The volume of the completed rectangular prism that have a height of 7 cubes will be 63 cubic units.

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the prism. In this case, the base of the prism has 3 x 3 cubes, which means the length and width are both 3 cubes.

Therefore, l = 3 and w = 3. The height of the prism is given as 7 cubes. Thus, h = 7.

Substituting the given values in the formula for volume, we get:

V = lwh

= 3 x 3 x 7

= 63

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The horizontal asymptote is y = 0 and the vertical asymptotes are x = -1 and x = -5. The graph of g(x) can be sketched as given in the picture.

Asymptotes are lines that a curve approaches but never touches. There are two types of asymptotes:

Horizontal asymptote: A horizontal asymptote is a horizontal line that a curve approaches as the value of x becomes very large or very small. In other words, if the curve approaches a specific y-value as x approaches infinity or negative infinity, then that y-value is the horizontal asymptote.

Vertical asymptote: A vertical asymptote is a vertical line that a curve approaches but never touches. A vertical asymptote occurs when the denominator of a function becomes zero and the numerator does not.

Here we have

The horizontal and vertical asymptotes of the reciprocal squared function that has been shifted left 3 units and down 4 units.

The reciprocal squared function is given by:

=> f(x) = 1/(x²)

To shift this function left 3 units and down 4 units, we need to modify the equation as follows:

=> g(x) = 1/((x+3)²) - 4

=> g(x) = 1/x² + 6x + 9 - 4

=> g(x) = 1/x²+6x+5

To find the horizontal asymptotes, consider what happens to the function as x approaches infinity and negative infinity.

As x approaches infinity, the x² term dominates the denominator, so we can approximate g(x) as 1/x².

Thus, the horizontal asymptote is y = 0.

As x approaches negative infinity, the x² term still dominates the denominator, and so g(x) also approaches 0.

Thus, the horizontal asymptote is also y = 0.

To find the vertical asymptotes, we need to look for values of x that make the denominator of g(x) equal to zero. We can factor the denominator as (x + 1)(x + 5),

so the vertical asymptotes occur at x = -1 and x = -5.

Therefore,

The horizontal asymptote is y = 0 and the vertical asymptotes are x = -1 and x = -5. The graph of g(x) can be sketched as given in the picture.

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The total cost for all the foam and vinyl needed to build the play structure would be $419.91

Let's say the play structure is a cube with each side measuring 36 inches. The total volume of the foam needed to build this cube would be:

V = (36 in)³ = 46,656 in³

Since the structure is a cube, the surface area would be:

A = 6 × (36 in)² = 7,776 in²

The cost for the foam would be:

46,656 in³ × $0.008/in³ = $373.25

The cost for the vinyl would be:

7,776 in² × $0.006/in² = $46.66

Total cost will be:

$373.25 + $46.66 = $419.91

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the probability of choosing exactly 5 red marbles when 12 marbles are chosen at random is approximately 0.028.

This is a hypergeometric probability problem .

The total number of ways to choose 12 marbles from 27 is:

${{27}\choose{12}} = \frac{27!}{12!15!} = 10,!626,!766$

The number of ways to choose 5 red marbles and 7 blue marbles is:

$ {{15}\choose{5}}\cdot{{12}\choose{7}} = \frac{15!}{5!10!}\cdot\frac{12!}{7!5!} = 300,!450$

So the probability of choosing exactly 5 red marbles is:

$P(\text{5 red}) = \frac{300,!450}{10,!626,!766} \approx 0.028$

what is probability?

Probability is the measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1, where 0 indicates an impossible event and 1 indicates a certain event.

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Answer:

Part A:

The price of product A is determined by the function f(x) = 12500(0.82)^x. To determine whether the price is increasing or decreasing, we can look at the behavior of the function as x increases.

When x increases by 1 year, the value of the function is:

f(x+1) = 12500(0.82)^(x+1) = 10250(0.82)^x

To find the percentage change in price per year, we can calculate:

[(f(x+1) - f(x)) / f(x)] * 100%

= [(10250(0.82)^x - 12500(0.82)^x) / 12500(0.82)^x] * 100%

= -0.16 * 100%

= -16%

Therefore, the price of product A is decreasing by 16% per year.

Part B:

To determine which product recorded a greater percentage change in price over the previous year, we need to calculate the percentage change in price for each product from year to year.

For product B, the percentage change in price from year to year is:

   From year 1 to year 2: [(f(2) - f(1)) / f(1)] * 100% = [(3136 - 5600) / 5600] * 100% = -43.14%

   From year 2 to year 3: [(f(3) - f(2)) / f(2)] * 100% = [(1756.16 - 3136) / 3136] * 100% = -44.06%

   From year 3 to year 4: [(f(4) - f(3)) / f(3)] * 100% = [(983.45 - 1756.16) / 1756.16] * 100% = -43.99%

For product A, we already determined that the percentage change in price per year is -16%.

Therefore, product A recorded a smaller percentage change in price over the previous year compared to product B.

Step-by-step explanation:

Based on the above, the height from which the stone is said to be dropped is approximately 176.4 meters.

Looking at the question given, the formula to calculate the height from which an object that is dropped will be:

h = 4.9t²

where:

h = the height (m)

t  = time (seconds)

So by substituting t = 6 seconds into the formula, we will  have:

h = 4.9 x 6²

h = 4.9 x 36

h = 176.4

Therefore, the height from the point that the stone is dropped is 176.4 meters.

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See transcribed text below

To calculate the height, in meters, from which an object is dropped, knowing the time it takes to reach the ground, the following formula is used: h equals 4.9 t squared, where h is the height and t is the time in seconds. What is the height from which a stone is dropped that takes 6 seconds to hit the ground? The height is meters

Answer:

72 cm²

Step-by-step explanation:

We can split this composite figure into 3 simple shapes:

First, we can solve for the area of the rectangles:

A(rect) = length × width

A(rect1) = 4 × (9 - 3) = 24

A(rect2) = 10 × 3 = 30

Next, we can solve for the area of the triangle:

A(triangle) = (1/2) × base × height

A(triangle) = (1/2) × (10 - 4) × 6

A(triangle) = 3 × 6 = 18

Finally, we can add each the simple shapes' areas together to get the area of the whole figure.

A = A(rect1) + A(rect2) + A(triangle)

A = 24 + 30 + 18

A = 72 cm²

Answer:

30 meters

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

30 meters

Step-by-step explanation:

There is one specific type of transformation that can cause a change in the period of a tangent or cotangent function, and that is a dilation.

A dilation is a transformation that stretches or compresses a function horizontally or vertically. When a tangent or cotangent function is dilated horizontally, the period of the function changes. The period of a tangent function is π, while the period of a cotangent function is also π.

If the function is dilated by a factor of k, then the new period will be π/k. This means that the function will oscillate faster if it is compressed horizontally (k > 1) and slower if it is stretched horizontally (k < 1). Therefore, it is important to consider the effects of dilations when analyzing the period of a tangent or cotangent function.

The type of transformation that could cause a change in the period of a tangent or cotangent function is called a "horizontal stretch" or "horizontal compression." These transformations affect the frequency of the function by scaling it horizontally, which in turn alters the period of the tangent or cotangent function.

In mathematical terms, the general form of a tangent function is y = A * tan(B(x - C)) + D, and for a cotangent function, it's y = A * cot(B(x - C)) + D. In these expressions, A represents the amplitude, B determines the horizontal stretch or compression, C is the phase shift, and D is the vertical shift.

The factor B directly affects the period of the function. For a tangent or cotangent function, the standard period is π. To find the new period after a horizontal transformation, you can use the formula: new period = (standard period) / |B|. Thus, by changing the value of B, the period of the tangent or cotangent function will be affected accordingly.

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