A teacher purchased a fish tank for her classroom. The dimensions of the tank are 34 inches by 58 inches by 42 inches. What is the maximum amount of water that the tank can hold? a. 82,824 in3 c. 41,412 in3 c. 2,436 in3 d. 1,972 in3

The volume of the ball is 904.78 cubic cm

We know that the formula for the volume of sphere is:

V = (4/3) × π × r³

where r is the radius of the sphere

Here, Michael fills a plastic ball with air until it is a sphere with a radius of 6 cm.

So, the radius of spherical ball r = 6 cm

Using above formula of volume of sphere, the volume of the ball would be,

V = (4/3) × π × r³

V = (4/3) × π × (6)³

V = (4/3) × π × 216

V = 904.78 cubic cm

Therefore, the required volume = 904.78 cubic cm

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The amount of interest that is earned on Sandra's card after 1 year if Sandra makes no payment is: $538.48.

We can obtain the right answer by using using the formula for compound interest as follows: A = P(1 + r/n)^(nt)

where:

P = $2,500

r = 0.1999 (since the APR is 19.99%)

n = 4 (since the interest compounds quarterly)

t = 1 (since we're looking at the interest earned after 1 year)

Substituting these values into the formula, we get:

A = $2,500(1 + 0.1999/4)^(4*1)

A = $2,500(1.049975)^4

A = $2,500(1.207789)

A = $3,019.47

So after 1 year, Sandra will owe $3,019.47 on her credit card. The interest earned is the difference between this amount and the initial amount charged, which is:

Interest = $3,019.47 - $2,500

Interest = $519.47

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The resulting histogram would show the distribution of the grades on the exam, with the bins and frequency of data points clearly displayed. The title, axis labels, and scales would provide context for the graph and make it easy to interpret the data.

In mathematics and computer science, a graph is a collection of points, called vertices or nodes, that are connected by lines, called edges or arcs. Graphs can be used to model and analyze relationships between objects or data, such as social networks, transportation systems, or web pages.

Here,

Part A:

The best graphical representation to display the given data is a histogram. A histogram is a bar graph-like representation of data that divides the data into intervals or bins and shows the frequency of each interval. Histograms are appropriate for displaying continuous data, which the grades on the exam can be considered as, and can also show the distribution of the data.

Part B:

To create a histogram of the given data, follow these steps:

Choose the number of bins or intervals. In this case, we can choose a reasonable number of bins, such as 6-8, to display the distribution of the grades.

Determine the range of the data. The lowest grade is 60 and the highest is 99, so the range is 99-60 = 39.

Calculate the bin size. The bin size is calculated by dividing the range by the number of bins. For example, if we choose 6 bins, the bin size would be 39/6 ≈ 6.5. Since it is difficult to have bins that are fractions of a point, we can round the bin size up to the nearest whole number to get a bin size of 7.

Create the bins. Starting from the lowest grade, create intervals or bins of size 7 that cover the range of the data. For example, the first bin would be 60-66, the second bin would be 67-73, and so on.

Count the frequency of data points that fall into each bin. For example, there are 2 data points in the first bin, 3 data points in the second bin, and so on.

Draw the histogram. On the horizontal axis, label and scale the bins. On the vertical axis, label and scale the frequency of data points in each bin. Draw a rectangle above each bin with a height equal to the frequency of data points in that bin.

Title: Grades on Recent 8th Grade Mathematics Exam

X-axis label: Grades

Y-axis label: Frequency

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The surface area of the figure, given the diameter of the base and the height, would be 353.43 square millimeters.

We can use the formula for the surface area of a cone:

Surface Area = πr² + πr√(r² + h²)

where r is the radius of the base and h is the height of the cone.

Since the diameter of the base is 9mm, the radius is half of that, or 4.5mm. The height of the cone is 20mm. Plugging these values into the formula, we get:

Surface Area = π(4.5)² + π(4.5)√(4.5² + 20²)

Surface Area = π(20.25) + π(4.5)√(436.25)

Surface Area = 353.43 millimeters²

Therefore, the surface area of the cone is approximately 353.43 square millimeters.

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Answer:

Yes

Step-by-step explanation:

The definition of dimension is Length, Width, and Height so if he doubles the dimensions it will be double. The volume is 630.

The IQR of 13 is more appropriate to use than the range of 13, as it provides a more accurate representation of the variability in the data when the data is skewed. Thus, option B is correct.

The range is the difference between the maximum and minimum values in a dataset, and it is affected by extreme values, which can result in a misleading representation of the variability in the data.

if the data is skewed or contains outliers, the range may not accurately represent the variability in the data.

However, it is not appropriate to use the range of 20 to show that they have plenty of money or the IQR of 20 to show.

Therefore, in this case, the IQR of 13 is more appropriate to use than the range of 13, as it provides a more accurate representation of the variability in the data when the data is skewed.

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Answer:

y = (-5/9)x + 30/9

Step-by-step explanation:

To rewrite the equation 5x + 9y = 30 in slope-intercept form, we need to isolate y on one side of the equation.

5x + 9y = 30

Subtract 5x from both sides of the equation to isolate 9y:

5x - 5x + 9y = -5x + 30

9y = -5x + 30

Divide both sides of the equation by 9 to solve for y:

9y/9 = (-5x + 30)/9

y = (-5/9)x + 30/9

Answer:

9m^3

Step-by-step explanation:

since there is a square root remove it and find it square which is 9

Answer:

e = - [tex]\frac{1}{2}[/tex] q + [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

- 12e = 6q - 4 ( divide through by - 12 )

e = [tex]\frac{6}{-12}[/tex] q - [tex]\frac{4}{-12}[/tex] , that is

e = - [tex]\frac{1}{2}[/tex] q + [tex]\frac{1}{3}[/tex]

In the given equation which is 3 + 2n = 7, the value of n = 2.

For, further explanation to find the value of the variable in the given equation, we can solve the given equation by transferring the non-variable digits to one side either to L.H.S or R.H.S.

Given equation = 2n + 3 =7

In the above equation, the variable is 'n' and the non-variable digits are '3' and '7'. To find the value of 'n', we can transfer the non-variable digits to the R.H.S (Right Hand Side) as shown below:

2n + 3 = 7

2n = 7 - 3

2n = 4

n = [tex]\frac{4}{2}[/tex]

n = 2.

So, from the above solution the value of 'n' is 2.

Given question is incomplete/incorrect, I assume the given question was to "obtain the value of n from the linear equation 3 + 2n = 7"

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Plot B shows a negative correlation between the age and the number of items in the backpack, while plot A does not show any clear correlation. Therefore, the correct answer is B. Only plot B.

In plot A, the data points appear scattered and do not show a clear trend or pattern.

In plot B, the data points are mostly clustered around a diagonal line that slopes downward from left to right, indicating a negative correlation between the age and the number of items in the backpack. Since the question asks for a positive correlation, the correct option is B. Only plot B.

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--The given question is incomplete, the complete question is given

"  Question

Select the correct answer.

Kristen gathered data from her classmates about the age and contents of their backpacks. She displayed the data in two scatter plots.

Does either scatter plot indicate a positive correlation between the variables?

A. Only plot A

B. Only plot B

C. Both plot A and plot B

D. Neither plot A nor plot B"--

The quadratic formula x = (-b ± √ ( [tex]b^2[/tex] - 4ac)  / (2a) is used to find the solutions (or roots) of a quadratic equation of the form [tex]ax^2[/tex] + bx + c = 0.

In this formula, "a", "b", and "c" are coefficients of the quadratic equation, and the ± symbol indicates that there are two possible solutions, one with a positive square root and one with a negative square root. By plugging in the values of "a", "b", and "c" from the given quadratic equation, one can use the quadratic formula to calculate the solutions for x that satisfy the equation.

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x = (-b ± √(b² - 4ac)) / (2a) is the formula x=-b±b2-4ac2a, used to find the solutions to a quadratic equation of the form ax2+bx+c=0.

The formula x = (-b ± √(b² - 4ac)) / (2a) is known as the Quadratic Formula, used to find the solutions to a quadratic equation of the form ax² + bx + c = 0.

The formula x=-b± b2 -4ac2a, is called the quadratic formula, which is used to find the solutions (or roots) to a quadratic equation of the form ax2+bx+c=0,

where a, b, and c are coefficients of the equation.

The term under the square root sign (b2-4ac) is called the discriminant and can tell you whether the quadratic equation has two real solutions (if the discriminant is positive), one real solution (if the discriminant is zero), or two complex conjugate solutions (if the discriminant is negative).

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The equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36

To find the equation of a circle in general form, we need to complete the square for both x and y terms.

x^2 + y^2 - 2x - 6y - 26 = 0

First, we will complete the square for x terms:

x^2 - 2x + y^2 - 6y - 26 = 0

(x - 1)^2 - 1 + y^2 - 6y - 26 = 0

(x - 1)^2 + y^2 = 27

Now, we will complete the square for y terms:

(x - 1)^2 + (y - 3)^2 = 36

Therefore, the equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36

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Answer:

x2+y2−2x−6y−26=0

Step-by-step explanation:

Just took the test.

Answer:

0.16%

Step-by-step explanation:

Imagine you are a politician who wants to increase taxes in your city. You decide to conduct a survey among 450 residents to see how many of them are against your proposal. You know that the probability of finding someone who is against increasing taxes is 0.38. You hope that the survey will show that most people support your idea, or at least that the opposition is not too strong. However, when you get the results, you are shocked to see that more than 180 people are against increasing taxes. How unlucky are you? Well, let's do some math. This is a binomial probability problem. The probability of success (being against increasing taxes) is p = 0.38 and the number of trials (residents surveyed) is n = 450. The question asks for the probability of more than 180 successes, which is equivalent to the probability of at least 181 successes. Using a binomial calculator, the answer is approximately 0.0016 or 0.16%. That means that there is only a 0.16% chance of getting at least 181 people against increasing taxes in a sample of 450 residents. That's very rare and unlucky indeed! You might want to reconsider your proposal or find a better way to convince people that paying more taxes is good for them.

If a large cube is made up of 27 equal-sized smaller cubes, and all faces of the large cube are painted, then the cubes on the interior of the large cube will not have any paint on any of their faces.

The large cube consists of 27 smaller cubes arranged in a 3x3x3 pattern. The smaller cubes on the exterior faces of the large cube will have some of their faces painted, while the smaller cubes on the interior will not have any of their faces painted.

To calculate the number of smaller cubes that will not have any paint on any of their faces, we need to subtract the smaller cubes on the exterior faces from the total number of smaller cubes in the large cube.

The number of smaller cubes on the exterior faces of the large cube can be calculated as follows:

There are 9 smaller cubes on each of the six faces of the large cube (3x3=9), for a total of 54 smaller cubes on the exterior faces.

So, the total number of smaller cubes in the large cube is 27, and the number of smaller cubes on the exterior faces is 54. Therefore, the number of smaller cubes that will not have any paint on any of their faces is:

27 - 54 = -27

Since we cannot have a negative number of cubes, the correct answer is 0. There will be 0 smaller cubes that will not have any paint on any of their faces.

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The probability of exactly 17 successes in a binomial distribution with p=0.20 and n=60, using normal approximation to the binomial, is approximately 0.0129.

To use the normal approximation to the binomial, we need to check if the conditions for the approximation are met

np = 60 x 0.20 = 12 ≥ 10

n(1-p) = 60 x 0.80 = 48 ≥ 10

Both conditions are met, so we can use the normal approximation to the binomial.

The mean of the binomial distribution is μ = np = 12, and the standard deviation is σ = √(np(1-p)) = √(60 x 0.20 x 0.80) ≈ 2.19.

To find the probability of exactly 17 successes, we can use the normal distribution with mean μ = 12 and standard deviation σ ≈ 2.19, and approximate the discrete binomial distribution with a continuous normal distribution

P(X = 17) ≈ P(16.5 < X < 17.5)

where X is a continuous random variable that follows a normal distribution with mean μ = 12 and standard deviation σ ≈ 2.19.

Using the standard normal distribution, we can calculate the z-scores for 16.5 and 17.5

z1 = (16.5 - 12) / 2.19 ≈ 1.83

z2 = (17.5 - 12) / 2.19 ≈ 2.28

Using a standard normal distribution table or a calculator, we can find the probabilities associated with these z-scores

P(1.83 < Z < 2.28) ≈ P(Z < 2.28) - P(Z < 1.83) ≈ 0.0129

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Yes, the walls form a right angle.

To determine if the walls form a right angle, we can use the Pythagorean theorem. The question states that a wall 12 feet long makes a corner with a wall that is 14 feet long, and the other ends of the walls are about 18.44 feet apart.

The Pythagorean theorem states that in a right-angled 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. In this case, let's consider the 12-foot and 14-foot walls as the two shorter sides, and the 18.44-foot distance as the potential hypotenuse.

Step 1: Calculate the square of the lengths of the 12-foot and 14-foot walls.

12² = 144

14² = 196

Step 2: Calculate the sum of the squares of these two sides.

144 + 196 = 340

Step 3: Calculate the square of the length of the 18.44-foot distance.

18.44² ≈ 339.95

Since 339.95 is very close to 340, we can conclude that the walls form a right angle.

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we are 95% confident that the true proportion of people with brown hair in the U.S. falls between 0.532 and 0.728.

To construct a 95% confidence interval for the proportion of people with brown hair in the U.S., we can use the following formula:

[tex]Confidence Interval = p± z \sqrt{\frac{p(1-p)}{n} }[/tex]

where p is the proportion of people with brown hair in our sample, z is the critical value for a 95% confidence level (which is 1.96), and n is the sample size.

In this case, our sample proportion is , and our sample size is 100. Plugging these values into the formula, we get:

[tex]Confidence Interval = 0.63  ± 1.96\sqrt{\frac{0.63(1-0.63)}{100} }[/tex]

Simplifying the expression inside the square root, we get:

[tex]Confidence Interval= 0.63 ± 0.098[/tex]

Therefore, the 95% confidence interval for the proportion of people with brown hair in the U.S. is:

[tex]\frac{63}{100}  = 0.63[/tex](0.532, 0.728)

This means that we are 95% confident that the true proportion of people with brown hair in the U.S. falls between 0.532 and 0.728.

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Answer:18

Step-by-step explanation:

The probability of selecting a J or an A on the second draw, given that an E was selected on the first draw is 0.101.

The number of tiles which have an E on them are shown to be 12 which means that if an E was selected on the first draw, there are now 99 tiles left.

The probability that an A or J will be selected in this second draw would be :

= ( Number of A tiles and J tiles ) / 99

Number of A tiles = 9

Number of J tiles = 1

The probability is then :

= ( 9 + 1 ) / 99

= 10 / 99

= 10.1%

= 0.101

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Value of matrix X=[tex]\left[\begin{array}{ccc}-31/135 & 1/45 \\14/135&1/45 \\ \end{array}\right][/tex]

Matrices are a type of mathematical object that consists of a rectangular array of numbers or other mathematical objects, such as variables, functions, or even other matrices. Matrices are widely used in mathematics, science, engineering, computer graphics, and other fields to represent and manipulate data, perform transformations, and solve systems of equations.

A matrix can be represented using a set of ordered pairs, where each pair represents a specific element of the matrix, and the position of the element is determined by its row and column indices. For example, a 3x3 matrix can be represented as:

| a11 a12 a13 |

| a21 a22 a23 |

| a31 a32 a33 |

 Given matrix;

A=[tex]\left[\begin{array}{ccc}-1&-2 \\2&2 \\ \end{array}\right][/tex]

B=[tex]\left[\begin{array}{ccc}-6&5 \\2&-1 \\ \end{array}\right][/tex]

C=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]

Solving the equation

(A-4B)X=C

[tex]\left[\begin{array}{ccc}-1&-2 \\2&2 \\ \end{array}\right][/tex]-  4 [tex]\left[\begin{array}{ccc}-6&5 \\2&-1 \\ \end{array}\right][/tex]X=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}23&-22 \\-6&6 \\ \end{array}\right][/tex] X=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]

Taking the inverse and multiplying it with RHS,  we get

X=[tex]\left[\begin{array}{ccc}-31/135 & 1/45 \\14/135&1/45 \\ \end{array}\right][/tex]

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The candy company's package can be modeled as a right circular cone with a height of 13 inches and a base diameter of 9 inches.

The circular base of the cone holds the chocolates, while the curved surface extends up to a point at the top. To calculate the surface area, we need to find the area of the circular base and the area of the curved surface. The formula for the area of a circle is pi times the radius squared, so the radius of the base is 4.5 inches.

The area of the base is pi times the radius squared, or approximately 63.62 square inches. The formula for the curved surface area of a cone is pi times the radius times the slant height, which is the square root of the height squared plus the base radius squared. Substituting the given values into the formula, the curved surface area is approximately 207.35 square inches. Thus, the approximate surface area of the package is the sum of the area of the base and the curved surface area, or approximately 271.97 square inches.

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Answer:

Quadrant III

Step-by-step explanation:

The point has a negative x AND y value, so it would be in Quadrant III

Taking a look at the quadrant graph will help you.

We can conclude:

a) For an initial population size of 286, the population will trend towards extinction.

b) For an initial population size of 16, the population will exhibit unbounded growth in finite time.

What is differential equations?

Differential equations are mathematical equations that describe the relationship between an unknown function and its derivatives (or differentials).

The modified logistic equation is given by:

dP/dt = aP - bP²

where P is the population size, and a and b are positive constants.

To determine the limiting behavior of the population, we need to analyze the phase portrait of the differential equation. This can be done by finding the equilibria of the system, and then examining the direction of the vector field near each equilibrium.

The equilibria of the system occur when dP/dt = 0. This leads to two possible equilibria:

P = 0, and P = a/b

The direction of the vector field near each equilibrium can be determined by examining the sign of dP/dt for values of P slightly greater and less than the equilibrium value.

Near P = 0, dP/dt = aP > 0 for P > 0, indicating that the population will grow in this region.

Near P = a/b, dP/dt = -bP² < 0 for P slightly greater than a/b, indicating that the population will decrease in this region.

Based on this analysis, we can conclude:

a) For an initial population size of 286, the population will trend towards extinction. This is because 286 is larger than a/b, so the population starts in the region where the vector field is pointing towards extinction.

b) For an initial population size of 16, the population will exhibit unbounded growth in finite time.

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By probability, the likelihood that a candidate chosen at random played an electric guitar and wore sequins is 0.3.

Using probabilities, one can determine how likely something is to occur.. It is represented by a number between 0 and 1, with 1 denoting a certain event and 0 an impossibility.

For instance, you can get either heads or tails when you flip a coin. There is only one way to get heads and two outcomes, hence the probability of receiving heads is 0.52.

The likelihood that a competitor played an electric guitar is 0.8, the likelihood that they were wearing sequins is 0.4, and the combined likelihood that they both played an electric guitar and wore sequins is 0.91.

The following formula can be used to determine the likelihood that a competitor chosen at random played an electric guitar and wore sequins:

P(A and B) equals P(A) times P(B|A)

where there are two events, A and B.

In this instance, A stands for the competitor who played an electric guitar, and B is for the person who wore sequins.

P(A) is known to equal 0.8. and P(B) = 0.4.

We also know that P(A or B) = 0.9.

Using the following equation to determine the likelihood of two events occurring together:

P(A or B) = P(A) + P(B) - P(A and B)

we can find P(A and B):

P(A and B)

           = 0.8 + 0.4 - 0.9

           = 0.3

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If Mariana needs to surround the garden with a stone-path, then she would need 20 feet of stone, Option (d) is correct.

The "Perimeter" of a rectangle is defined as the "total-length" of the outer boundary.

The length of the rectangle can be calculated as the difference between the x-coordinates of the vertices on the same vertical side.

In this case, the "x-coordinates" of vertices on same vertical side are 4 and -2.

So, the length of the rectangle is = 4 -(-2) = 6 feet.

Similarly, the width of rectangle is calculated as difference between "y-coordinates" of vertices on same horizontal side.

In this case, the "y-coordinates" of vertices on same horizontal side are 1 and -3.

So, the width of the rectangle is = 1 -(-3) = 4 feet,

To surround rectangle with a stone path, Marina need to add length of stone needed for the perimeter of rectangle, which is sum of all four sides.

The perimeter (P) is ⇒ P = 2(length + width),

Substituting the values,

We get,

⇒ P = 2(6 + 4) = 2(10) = 20 feet

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

Marina is drawing a plan for a new garden. The rectangle with the vertex (4,1) , (4,-3) , (-2,-3) , (-2,1)in the coordinate plane represents the garden, measured in feet. To surround the garden with a stone path, how many feet of stone does she need?

(a) 4 feet

(b) 6 feet

(c) 10 feet

(d) 20 feet

Answer:

20 feet because ik from experience

Answer: 13. 30

Step-by-step explanation:

13. Area = 18x * 10y = 180xy

Length = 6th

With ?

180xy = 6xy x width

180 x/6xy

Width = 30

14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver

3^5

If you buy a ticket, you can expect to make a profit of approximately $0.96 on average.

To calculate the expected profit, we need to consider the probability of winning each prize and the value of each prize.

The probability of winning each prize can be calculated by dividing the number of winning tickets by the total number of tickets. There is 1 winning ticket for each prize, so the probability of winning each prize is:

$240 prize: 1/250

$130 prize: 1/250

$120 prize: 1/250

$70 prize: 1/250

The value of each prize is already given, so we can multiply the probability of winning each prize by its value and sum the results to find the expected profit:

Expected profit = (1/250 x $240) + (1/250 x $130) + (1/250 x $120) + (1/250 x $70) - ($16)

Expected profit = $0.96

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The solution for the given quadratic equation is √27.

What is a quadratic equation?

A quadratic equation is any algebraic equation that can be written in the standard form as where variable 'x' is an unknown number and where a, b, and c are known values, with a ≠ 0.

We are given a quadratic equation in variable 'w' as 3[tex]w^{2}[/tex] + 9 = 90.

Now, on solving the given equation , we get

⇒ 3[tex]w^{2}[/tex] + 9 = 90

⇒ 3[tex]w^{2}[/tex] = 81

⇒ [tex]w^{2}[/tex] = 27

⇒ w = √27

Hence, the solution for the given quadratic equation is √27.

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The complete question has been attached below.

The simplified form of the given expression is:

(cosx * (tanx + 1) + 1) / cosx

To solve the given expression, we can start by simplifying it using trigonometric identities.

Given expression: tanx / (1 + secx) + (1 + secx) / tanx

Step 1: Simplify denominators

We can rewrite secx as 1/cosx, and tanx as sinx/cosx. Using these identities, we get:

tanx / (1 + 1/cosx) + (1 + 1/cosx) / (sinx/cosx)

Step 2: Find the least common denominator (LCD)

The LCD is cosx, as it is the common denominator for both fractions.

Step 3: Combine the fractions

Using the LCD, we can combine the fractions:

[(tanx * cosx) + (1 + 1/cosx)(cosx)] / cosx

Step 4: Simplify the numerator

Multiplying through by cosx to simplify the numerator, we get:

[tanx * cosx + (cosx + 1)] / cosx

Step 5: Combine like terms

Combining like terms in the numerator, we get:

[tanx * cosx + cosx + 1] / cosx

Step 6: Factor out cosx

We can factor out cosx from the numerator:

cosx * (tanx + 1) + 1 / cosx

So, the simplified form of the given expression is:

(cosx * (tanx + 1) + 1) / cosx

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QUESTION IS - simplify . tanx/1+secx  +  1+secx/tan x