can someone help pls​

The equations are:

M = 21 + 18t

G = 42 + 11t

The page they would be on is 75 pages.

The linear equation that represents the total number of pages read by each person at day t, is :

Total pages read = pages read at the beginning of the month + (number of pages read per day x number of days)

Total pages read by Matthew =   21 + (18 x t)

= 21 + 18t

Total pages read by Guadalupe = 42 + (11 x t)

= 42 + 11t

When they are on the same page, the two above equations would be equal:

21 + 18t = 42 + 11t

18t - 11t = 42 - 21

7t = 21

t = 21 / 7

t = 3 days

Page they would both be on = 21 + 18(3)

21 + 54 75 pages

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Yes, this is a binomial experiment because it meets the criteria of having a fixed number of trials (testing ovens until a defective one is found), independent trials (each oven tested is independent of the others), and two possible outcomes (defective or non-defective).

Yes, this is a binomial experiment.

A binomial experiment is characterized by having a fixed number of trials, independent and identically distributed outcomes, and two possible outcomes (success or failure).

In this case, the quality control inspector randomly tests ovens until a defective one is found, which implies a fixed number of trials.

The probability of finding a defective oven remains the same for each trial, satisfying the condition of identically distributed outcomes.

Additionally, the outcomes of testing an oven can be classified as either defective or non-defective, fulfilling the requirement of two possible outcomes.

Therefore, this situation qualifies as a binomial experiment.

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To estimate the integral ∫[0 to 5] f(x) dx, we can use the midpoint rule, which approximates the integral by dividing the interval [0, 5] into subintervals of equal width and evaluating the function at the midpoint of each subinterval.

Let's divide the interval [0, 5] into n subintervals, each of width Δx = 5/n. The midpoint of each subinterval will be x_i = (i - 0.5)Δx, where i ranges from 1 to n.

Since f(x) is an increasing function, the best estimate of the integral would be the sum of the areas of rectangles with base Δx and height f(x_i).

The approximation of the integral is given by:

∫[0 to 5] f(x) dx ≈ Δx * [f(x_1) + f(x_2) + ... + f(x_n)]

In this case, Δx = 5/n. Let's choose n = 10 for a reasonable approximation:

Δx = 5/10 = 0.5

Now we need to evaluate f(x_i) at the midpoints of each subinterval:

x_1 = (1 - 0.5) * 0.5 = 0.25

x_2 = (2 - 0.5) * 0.5 = 0.75

x_3 = (3 - 0.5) * 0.5 = 1.25

x_4 = (4 - 0.5) * 0.5 = 1.75

x_5 = (5 - 0.5) * 0.5 = 2.25

Now we can calculate the approximation:

∫[0 to 5] f(x) dx ≈ Δx * [f(x_1) + f(x_2) + f(x_3) + f(x_4) + f(x_5)]

≈ 0.5 * [f(0.25) + f(0.75) + f(1.25) + f(1.75) + f(2.25)]

Given that f(0) = 10 and f(5) = 18, we can estimate the integral:

∫[0 to 5] f(x) dx ≈ 0.5 * [10 + f(0.75) + f(1.25) + f(1.75) + f(2.25) + 18]

≈ 0.5 * [10 + f(0.75) + f(1.25) + f(1.75) + f(2.25) + 18]

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The story that can be represented by the equation 9x = 99 is A. Chris finished reading his book in 9 days. Each day, he read x pages. His book has 99 pages.

An equation is a statement that uses an equal sign to show that two expressions are the same.

Equations can have letters that stand for unknown numbers (eg x, y, a), and solving an equation means finding the values that make the equation true.

Therefore, the equation: 9x = 99, shows how the number of pages Chris reads each day (x) is connected to the total number of pages in the book (99).

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To multiply the algebraic expression x(9x - 9), we can use the special product formula (a-b)(a+b) = a^2 - b^2.

Using the formula, we can see that 9x - 9 can be written as (3x - 3)(3x + 3), where a = 3x and b = 3. Therefore, x(9x - 9) can be written as x(3x - 3)(3x + 3). Multiplying the expression, we get 3x^2(x - 1)(3x + 3). We can simplify this further by factoring out 3x^2 from the last two terms, which gives us the final answer of 3x^2(x - 1)(3x + 3) = 9x^4 - 27x^2.

To multiply the algebraic expression x(9x - 9), we used the special product formula (a-b)(a+b) = a^2 - b^2. By applying the formula, we simplified the expression to 3x^2(x - 1)(3x + 3), which we further simplified to the final answer of 9x^4 - 27x^2.

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I'm sorry, but I don't have enough context to answer these questions. It seems like they are related to a specific problem or scenario, but I don't have any information about what that might be. Could you please provide more information or context so I can better understand the questions and provide a helpful response?

A radius of 3cm guarantees uniform-sized meatballs for cooking. Compare the total meatball volume with the pot's remaining capacity. Utilize equation, 6 meatballs cause pot to flood.

The cook employments a radius of 3 centimeters for the meatballs since it permits uniform-sized meatballs, making them less demanding to cook equitably.

To discover the number of meatballs that would make the sauce start to spill over, the cook has to calculate the entire volume of the meatballs and compare it to the pot's remaining capacity after filling it with sauce. The equation for the volume of a circle is V = (4/3) * π * r^3, where "r" is the span of the circle (meatball). The pot's remaining capacity can be calculated as the entire capacity short of the introductory sauce volume.

Given that the pot's capacity is 5 liters, which rises to to 5000 cubic centimeters (1 liter = 1000 cubic centimeters), and the starting sauce volume is since the meatballs are included together with the sauce, the remaining capacity is 5000 cubic centimeters.

Let's accept the number of meatballs is "n," and their add up to volume is V_total = n * (4/3) * π * 3^3 cubic centimeters.

For the pot to flood, the full volume of meatballs and sauce combined ought to surpass the pot's remaining capacity:

V_total > 5000 cubic centimeters.

Presently, able to plug within the esteem of V_total:

n * (4/3) * π * 3^3 > 5000.

Disentangle and illuminate for "n":

n > 5000 / [(4/3) * π * 3^3].

n > 5000 / [4 * 3.14 * 27].

n > 5.95.

Since you cannot have a division of a meatball, the genuine number of meatballs that would make the pot flood is 6.

Hence, the cook would require at slightest 6 meatballs to cause the pot to flood when they are cooked alongside the sauce.

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The complete question:

A cook is planning a clump of meatballs to be cooked in a sauce pot. The sauce pot incorporates a capacity of 5 liters. The meatballs are superbly spherical and are put within the sauce pot in conjunction with the sauce. Each meatball features a span of 3 centimeters.

What is the reason for employing a sweep of 3 centimeters for the meatballs?

How can the cook discover the number of meatballs that would make the sauce start to spill over?

Calculate the real number of meatballs that would make the pot flood, and appear how you arrived at the arrangement employing a equation.

The length of segment RS is,

⇒ RS = 13.8 units

Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Here, We have to given that;

A line segment RS is shown in figure.

Since, The coordinate of R is,

R = (- 3, - 4)

And, The coordinate of S is,

S = (1, 9)

Hence, The length of segment RS is,

RS = √ (x₂ - x₁)² + (y₂ - y₁)²

RS = √(1 - (- 3))² + (9 - (- 4))²

RS = √16 + 169

RS = √185

RS = 13.8 units

Thus, The length of segment RS is,

⇒ RS = 13.8 units

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If the distribution for a random variable X is P .27 .31 .18 .09 .15, then the mean is 2.54 and the standard deviation is 0.81. The distribution in #1 is a legitimate probability distribution.

To find the mean and standard deviation, follow these steps:

To verify that the distribution in #1 is a legitimate probability distribution, follow these steps:

Hence, the mean is 2.54 and the standard deviation is 0.81 and the distribution in #1 is a legitimate probability distribution.

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Answer:

A. 2

Step-by-step explanation:

Here are the steps to solve the equation (x + 5)^2 = 49 using the square root property:

Take the square root of both sides of the equation: √[(x + 5)^2] = √49.

Simplify the square root on the left side: |x + 5| = 7.

Split the equation into two cases based on the positive and negative values of the absolute value:

Case 1: x + 5 = 7.

Solve for x by subtracting 5 from both sides: x = 7 - 5 = 2.

Case 2: -(x + 5) = 7.

Solve for x by multiplying both sides by -1 and simplifying: -x - 5 = 7.

Add 5 to both sides: -x = 7 + 5 = 12.

Multiply both sides by -1 to isolate x: x = -12.

Therefore, the solutions to the equation (x + 5)^2 = 49 are x = 2 and x = -12. Among the given options, the correct answer is: A. 2

Using the square root property, the answer for the situation (x + 5)^2 = 49 is x = - 5 ± 7. In this manner, the right response is Answer 2.

To solve the equation (x + 5)^2 = 49 utilizing the square root property, we take the square foundation of the two sides of the situation. This gives us the equation x + 5 = ±√49, which rearranges to x + 5 = ±7.

Then, we confine x by taking away 5 from the two sides of the situation. This gives us two potential arrangements: x = - 5 + 7 and x = - 5 - 7. Simplifying further, we have x = 2 and x = - 12.

Notwithstanding, since the first condition just includes squares, we dispose of the adverse arrangement (- 12) since figuring out a negative number yields a positive outcome. Accordingly, the right arrangement is x = 2.

All in all, by applying the square root property, we track down that the answer for the situation (x + 5)^2 = 49 is x = 2. This implies that choice A is the right response.

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The correct function to calculate the average of the variables Var1, Var2, Var3, and Var4 is mean(Var1, Var4).

So, the correct answer is A.

This function takes the first and last variables in the range, and calculates the average of all variables within that range, including Var1 and Var4. The mean function computes the sum of the values and divides it by the total number of values, providing you with the average.

Option b), c), and d) are not the correct functions for this purpose, as they either use incorrect syntax or do not properly specify the range of variables needed to calculate the average.

Hence, the answer of the question is A.

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The point (3, 2) is feasible for the constraint 2x1 + 6x2 ≤ 30. (False)

To determine if a point is feasible for a constraint, we need to substitute the values of the point into the constraint equation and check if the resulting inequality holds true.

In this case, the constraint is 2x1 + 6x2 ≤ 30. Substituting x1 = 3 and x2 = 2 into the equation, we get 2(3) + 6(2) = 6 + 12 = 18. Since 18 is not less than or equal to 30, the inequality is not satisfied.

Therefore, the point (3, 2) is not feasible for the given constraint. Feasible points satisfy the constraint, while infeasible points do not. In this case, any point that lies below the line represented by the constraint equation would be feasible, while points above the line would be infeasible.

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Answer:

--------------

Use area formula: for a square:

Substitute s = 10 for side length and calculate:

The missing side is √130.

The value of sin θ is 0.61.

We have,

The Pythagorean theorem is a mathematical principle that relates the sides of a right triangle.

It states that 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 equation form, it can be written as:

a² + b² = c²

where "a" and "b" represent the lengths of the two shorter sides (also known as the legs), and "c" represents the length of the hypotenuse.

Applying the Pythagorean theorem.

Missing side = x

So,

x² = 7² + 9²

x² = 49 + 81

x² = 130

x = √130

Now,

Sin Θ = BC/AB = 7/√130 = 7/11.40 = 0.61

Thus,

The missing side is √130.

The value of sin θ is 0.61.

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The slant height of the solid cone with a base radius of 8 m and a surface area of 850 m² is approximately 13.62 m.

We have,

To find the slant height of a solid cone, we need to use the formula for the surface area of a cone.

The formula for the surface area of a cone is given by:

Surface Area = πr(r + l)

Where:

r is the base radius of the cone

l is the slant height of the cone

We are given that the base radius (r) is 8 m, and the surface area is 850 m².

Let's substitute these values into the formula and solve for the slant height (l):

850 = π x 8(8 + l)

850 = 64π + πl

To isolate the term with l, we subtract 64π from both sides:

850 - 64π = πl

Now, we divide both sides by π to solve for l:

l = (850 - 64π) / π

Using a calculator, we can find the numerical value of l:

l ≈ 13.62 m

Therefore,

The slant height of the solid cone with a base radius of 8 m and a surface area of 850 m² is approximately 13.62 m.

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The statement that correctly rounds the GPA to the hundredth position is b. newgpa = round(gpa, 2).

Rounding to the hundredth position means keeping only two decimal places. To do this in Python, we use the round() function with a second argument of 2, which specifies the number of decimal places to keep. Therefore, the correct statement is b. newgpa = round(gpa, 2).

It's important to understand what each of the answer choices means to see why b is the correct option. Option a. newgpa = round(gpa, 100) would round the GPA to the nearest multiple of 100, which is not what we want. Option c. newgpa = round(gpa, .01) and d. newgpa = round(gpa, '$.01') are invalid statements because the second argument of the round() function must be an integer, not a string or float. Therefore, the only valid option is b. newgpa = round(gpa, 2), which rounds the GPA to two decimal places.

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The Laplace transform of10. To inverse Laplace transform is given by:

L^-1{(s - 1)/(2s^2 + s + 6)} = e^(-t)*(cos(2t) - (1/2)*sin(2t))

What is Inverse Laplace Transform?

To determine the inverse Laplace transform of 6/(s-1)^4:

The inverse Laplace transform is given by:

L^-1{6/(s-1)^4} = t^3*e^t

To determine the inverse Laplace transform of 2/s^2 + 4:

The inverse Laplace transform is given by:

L^-1{2/s^2 + 4} = 2*sin(2t)

To determine the inverse Laplace transform of (ss^2+1)/( + 2s + 10):

The inverse Laplace transform is given by:

L^-1{(s+1)/(s^2 + 2s + 10)} = e^(-t)*cos(3t)

To determine the inverse Laplace transform of 4/(s^2 + 9):

The inverse Laplace transform is given by:

L^-1{4/(s^2 + 9)} = 2*sin(3t)

To determine the inverse Laplace transform of 1/(s^2 + 4s + 8):

The inverse Laplace transform is given by:

L^-1{1/(s^2 + 4s + 8)} = (1/2)*e^(-2t)*sin(2t)

To determine the inverse Laplace transform of 3/(s(x + 5))^3:

The inverse transform is given Laplace by:

L^-1{3/(s(x + 5))^3} = (1/2)(x +2t*e^(- 5)^t(x + 5))

To determine the inverse Laplace transform of (2s + 16)/(s^2 + 4x + 13):

The inverse Laplace transform is given by:

L^-1{(2s + 16)/(s^2 + 4x + 13)} = e^(-2x)cos(3x) + 4sin(3x)

To determine the inverse Laplace transform of 1/s^2:

The inverse Laplace transform is given by:

L^-1{1/s^2} = t

To determine the inverse Laplace transform of (3x - 15)/(2s^2 - 4s + 10):

The inverse Laplace transform is given by:

L^-1{(3x - 15)/(2s^2 - 4s + 10)} = (3/2)*e^(2t)*cos(t) - (15/2)*e^(2t)*sin(t)

(s -2s^2 + s 1)/( + determine the inverse6):

The Laplace transform of10. To inverse Laplace transform is given by:

L^-1{(s - 1)/(2s^2 + s + 6)} = e^(-t)*(cos(2t) - (1/2)*sin(2t))

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The height that the tennis ball attains from the ground while executing the present stroke is up to 34 feet.

Assuming the tennis ball reached a peak height of 25 feet in the previous shot, it is now expected to reach a peak height of 28 feet in the current shot as it has climbed an additional 3 feet from the previous peak.

Given that the tennis ball was launched from a height of six feet, its maximum elevation above the ground can be calculated by adding the height of its ascent, which is 28 feet, resulting in a total of 34 feet.

Thus, the height that the tennis ball attains from the ground while executing the present stroke is up to 34 feet.

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The Complete Question

A tennis ball is shot straight up into the air from a height of 6 feet. If the maximum height it reaches during this shot is 3 feet higher than the previous shot, and the maximum height during the previous shot was 25 feet, what is the final maximum height of the tennis ball during the current shot?

A relationship might exist in a sample even though it does not exist in the population, because of b) Sampling error

In statistical analysis, a relationship might appear in a sample even though it does not exist in the population due to sampling error. This occurs when the sample is not fully representative of the population, leading to discrepancies between the sample statistics and the true population parameters.

Sampling error can cause random fluctuations that mistakenly suggest a relationship, which may not be present in the larger population. It is important to consider the limitations and potential sources of error when generalizing findings from a sample to the broader population. So b option is correct.

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The given information 7,234 people paid $10 for Reserved seats,10,172 people paid $6 for general admission.

The number of people who paid $10 for reserved seats instead of $6 for general admission without counting the ticket stubs, we can set up a system of equations based on the given information.

x represents the number of people who paid $10 for reserved seats, and y represents the number of people who paid $6 for general admission.

From the information given, we can establish the following equations:

1. The total number of people who paid admission: x + y = 17,406

2. The total cash received from ticket sales: 10x + 6y = $133,372

We now have a system of two equations with two variables. To solve for x and y, we can use a method such as substitution or elimination.

Let's use the substitution method to solve the system:

From equation (1), we can express y in terms of x: y = 17,406 - x

Substituting this value of y in equation (2):

10x + 6(17,406 - x) = $133,372

10x + 104,436 - 6x = $133,372

4x = $133,372 - $104,436

4x = $28,936

x = $28,936 / 4

x ≈ 7,234

Therefore, approximately 7,234 people paid $10 for reserved seats.

To find the number of people who paid $6 for general admission, we can substitute the value of x back into equation (1):

7,234 + y = 17,406

y = 17,406 - 7,234

y ≈ 10,172

Therefore, approximately 10,172 people paid $6 for general admission.

In conclusion, based on the given information, approximately 7,234 people paid $10 for reserved seats, while approximately 10,172 people paid $6 for general admission.

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The width of the rectangle with the given area and length is 2n² - 5n + 28.

To find the width of the rectangle, we need to divide the area by the length. So, we have:

Width = Area/Length
Width = (12n² - 30n + 168n)/(6n)
Width = 2n² - 5n + 28

Therefore, the width of the rectangle is option A, 2n² - 5n + 28.

To find the width of the rectangle, we use the formula Width = Area/Length.

Substituting the given values, we get Width = (12n² - 30n + 168n)/(6n). Simplifying this expression, we get Width = 2n²- 5n + 28. Therefore, the width of the rectangle is option A, 2n² - 5n + 28.

The width of the rectangle with the given area and length is 2n² - 5n + 28.

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The radius of the cylindrical vessel is , 29.4 cm.

Now, For the volume of water displaced by the steel ball. We can use the formula:

V = Ah

Where V is the volume of water displaced, A is the cross-sectional area of the submerged portion of the steel ball, and h is the rise in water level.

And, The cross-sectional area of the steel ball can be found using the formula for the area of a circle:

A = πr²

where r is the radius of the steel ball.

Here, The rise in water level is, 5 cm.

So we have:

V = πr²h

We can also find the volume of the steel ball using the formula:

V = (4/3)πr³

We know that the diameter of the steel ball is 60 cm, so the radius is 30 cm.

The volume of the steel ball is:

V = (4/3)π(30)³

V = 113,097.34 cubic centimeters

Now we can find the volume of water displaced by the steel ball:

V = πr²h

V = 113,097.34 cubic centimeters

We know that the rise in water level is 5 cm and the initial depth of the water is 125 cm,

Hence, the final depth of the water after the steel ball is dropped in is,

125 + 5 = 130 cm.

Now, Let us assume that, the radius of the cylindrical vessel r.

The volume of water in the vessel can be found using the formula:

V = πr²h

where h is the height of the water in the vessel.

We know that the initial height of the water is 125 cm, and the final height is 130 cm, so the height of the water displaced by the steel ball is 5 cm.

We can now set up an equation to solve for r:

πr²(125) + πr²(5) = 113,097.34

Simplifying:

πr²(130) = 113,097.34

r² = 864.96

r = 29.4 cm

Therefore, the radius of the cylindrical vessel is 29.4 cm.

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The sample that can best help the owner see the preferences of all the audience members is given as follows:

B) 5 people in VIP seats, 35 on the main floor, and 20 in the balcony.

The best sample is obtained considering the proportions in the sample, as follows:

Hence, considering 5 VIP seats, the amounts are given as follows:

Hence option B is the correct option for this problem.

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The graph of g is translated left 3 units than that of f(x).

We have,

Translation is a type of transformation of geometrical figures. After translation, the original figure is shifted from a place to another place without affecting it's size.

Given that,

Equation of graph of f is f(x) = 4x + 1

Equation of graph of g is g(x) = 4(x + 3) + 1

From the equation is is clear that, graph of f(x) and g(x) are lines.

Now, g(x) = 4(x + 3) + 1

g(x) = f(x + 3)

We know that, if two functions exists such that h(x) = f(x - k), then the graph of h(x) will be a graph translated right k units compared to the graph of f(x).

Here g(x) = f(x + 3) = f(x - -3)

Since is is -3, the graph of g(x) is a graph translated left to 3 units of f(x).

Hence the g(x) is translated 3 units to the left of f(x).

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May be the correct question is as follows.

attached

Parent function is f(x) = x^2

We shift the parent function 8 units down to arrive at g(x) = x^2-8

This can be confirmed with a graphing tool like Desmos or GeoGebra.

The -8 at the end basically means "subtract 8 from the y coordinate", which will move each point down 8 units.

The Frequency of the system is 0.5 hertz.

The frequency of the system, we can use the formula:

f = 1 / T

where f represents the frequency and T is the period of the system.

Given that the period of the system is 2 seconds (sec), we can substitute this value into the formula to find the frequency:

f = 1 / 2 sec

Calculating this expression, we get:

f = 0.5 Hz

Therefore, the frequency of the system is 0.5 hertz.

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The equation of the ellipse in the following cases are:

(i) (x^2/4) + (y^2/(b^2 + 4)) = 1.

(ii) (x^2/(a^2 - c^2)) + (y^2/b^2) = 1,

(iii) (x^2/16) + (y^2/b^2) = 1, and all the others are below.

(i) For an ellipse with eccentricity e = 1/2 and foci (±2,0):

We can find the equation using the formula c = ae, where c is the distance from the centre to each focus and a is the semi-major axis.

Since the foci are located at (±2,0), we have c = 2.

We can also determine a using the relationship.

a² = b² + c², where b is the semi-minor axis.

Since the distance from the center to each focus is 2, and the distance from the center to each vertex is a,

We have

a² = b² + 2² = b² + 4

Thus, the equation of the ellipse is (x²/4) + (y²/(b² + 4)) = 1.

(ii) For an ellipse with eccentricity e = 2/3 and length of the latus rectum = 5,

We can find the equation using the relationship,

4a² = (2b)² + l²,

Where a is the semi-major axis, b is the semi-minor axis, and l is the length of the latus rectum. Since the latus rectum = 5,

We have

4a² = (2b)² + 5

We can also determine b using the relationship.

b² = a² - c²

where c is the distance from the center to each focus. Since e = 2/3, we have c = (2/3) a.

Thus, the equation of the ellipse is (x²/(a² - c²)) + (y²/b²) = 1.

(iii) For an ellipse with eccentricity e = 1/2 and semi-major axis a = 4,

We can determine b using the relationship.

b² = a² - c²,

Where c is the distance from the center to each focus. Since e = 1/2, we have c = (1/2)a = 2.

Thus, the equation of the ellipse is (x²/16) + (y²/b²) = 1.

(iv) For an ellipse with eccentricity e = 1/2 and major axis = 12,

We can determine b using the relationship.

b² = a² - c²,

Where c is the distance from the center to each focus.

Since e = 1/2, we have c = (1/2) a = 6.

Thus, the equation of the ellipse is (x²/36) + (y²/b²) = 1.

(v) For an ellipse passing through (1,4) and (-6,1),

We can use the general equation of an ellipse:

(x²/a²) + (y²/b²) = 1.

Substituting the coordinates (1,4) and (-6,1), we get two equations:

(1/a²) + (16/b²) = 1 and (36/a²) + (1/b²) = 1.

Solving these two equations simultaneously will give us the values of a and b, which can then be used to determine the equation of the ellipse.

Therefore, the remaining cases can be solved in a similar manner by applying the relevant formulas and using the given information to determine the values of a, b, and c, and subsequently finding the equation of the ellipse.

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The researcher wants to determine if the number of calories burned during an hour is the same for running and walking. To conduct this investigation, the researcher would measure continuous scale data.

Continuous scale data is quantitative data that can take any numerical value within a certain range.

In this case, the researcher would measure the number of calories burned, which is a continuous variable that can have various values within a specific range (e.g., 0, 100, 200, etc.).

By measuring the calories burned for both running and walking, the researcher can compare and analyze the numerical data to determine if there is a significant difference between the two activities.

It is important to note that the type of statistical analysis required to evaluate the data would depend on the specific research design and the number of groups involved.

If the researcher is comparing only two groups (running and walking), an independent t-test may be appropriate.

On the other hand, if there are more than two groups or additional factors being considered, an analysis of variance (ANOVA) might be more suitable.

The choice of statistical analysis method would depend on the specific research question and study design.

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Answer:

C. tan B

Step-by-step explanation:

In ∆ABC, if angle A is 45 degrees and angle C is also 45 degrees, then the triangle is an isosceles right triangle. In such a triangle, the legs (the sides opposite and adjacent to the 45-degree angles) are congruent.

Since the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle, and since these two sides are congruent in an isosceles right triangle, we have tan A = 1.

Therefore, the correct answer is C. tan B.

To determine whether a geometric series is convergent or divergent, we need to examine the common ratio (r) of the series. A geometric series has the form:

S = a + ar + ar^2 + ar^3 + ...

where 'a' is the first term and 'r' is the common ratio.

If the absolute value of the common ratio (|r|) is less than 1, then the series converges. If |r| is equal to or greater than 1, then the series diverges.

In the given problem, we don't have specific values for 'a' and 'r', so we cannot directly determine convergence or divergence. We need additional information about the series.

Please provide the values of 'a' and 'r' in order to determine the convergence or divergence of the geometric series and calculate the sum if it is convergent.

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