The sum of the roots of a quadratic is 1 and the product of the roots is -35/4.

a. find the quadratic.

b. find the roots

The true statements are Numbers with same absolute value are opposites because they are same distance from each other and from 0 on the number line. The |7.1| = 7.1. So, correct options are B, C and E.

b) Numbers with the same absolute value are opposites because they are the same distance from each other. This is true because absolute value is the distance from a number to zero on the number line, and if two numbers have the same distance from zero, then they must be equidistant from zero and therefore, they are opposite in sign.

c) The |7.1| = 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units. This is true because the absolute value of a number is always positive, and it represents the distance of that number from zero on the number line.

d) The |-8.4| = 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units. This is false, as the distance between -8.4 and 8.4 on the number line is 16.8 units. The correct value of the absolute value of -8.4 is 8.4.

e) Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line. This is true because 0 is the midpoint of the number line, and if two numbers have the same distance from 0, then they must be equidistant from zero and therefore, they are opposite in sign.

Therefore, the correct statements are b, c, and e.

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The equivalent expressions are p−3q=11 and 3p+q=3. Option A

It is important to note that equivalent equations are defined as equations that have the same solution but are different in the way with which the values are arranged.

From the information given, we have that;

3 times (p minus q) = 2 times p + 11

This equation is represented as;

3(p - q) = 2(p) + 11)

expand the bracket, we get;

3p - 3q = 2p + 11

collect the like terms

3p - 2p - 3q =11

Subtract the values

p - 3q = 11

Then,

4 times p + q = p + 3

4p + q = p + 3

collect like terms

4p - p + q = 3

3p = q = 3

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To make a number line for the values of x that are less than -1 and greater than 1, we can start by drawing a horizontal line and marking a point at 0. Then, we can label the left side of the line with negative numbers and the right side with positive numbers.

Next, we need to mark all the points that represent the values of x that satisfy the condition X < -1 and x > 1. This means we are looking for all the numbers that are less than -1 and greater than 1 at the same time. However, there are no numbers that satisfy this condition since a number cannot be both less than -1 and greater than 1 simultaneously.

Therefore, there are no points to mark on the number line for this condition.

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Percentage of gumballs that are within standard deviations of the mean is 68% and have a diameter between 2.20 cm and 2.22 cm.

To find the percentage of gumballs that are within one standard deviation of the mean, we need to use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, for a normal distribution:

Here we want to find the percentage of gumballs that are within one standard deviation of the mean. So we can use the first part of the empirical rule and say that approximately 68% of the gumballs have a diameter between:

Mean - Standard deviation = 2.21 - 0.01 = 2.20 cm and Mean + Standard deviation = 2.21 + 0.01 = 2.22 cm

Therefore, approximately 68% of the gumballs have a diameter between 2.20 cm and 2.22 cm.

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Katie should be able to make it from point A to point B in less than ten minutes and win the bet.

A minute is a unit of time equal to 60 seconds or one sixtieth of an hour. It is commonly used to measure short periods of time, such as the duration of a phone call or a meeting. The symbol for minute is "min".

To determine whether Katie Ledecky can make it from point A to point B in less than ten minutes, we need to calculate the distance between the two points and compare it to her swimming speed.

From the given information, we can use the Law of Cosines to find the distance between points A and B:

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

where c is the distance between points A and B, a is the distance from point A to point C, b is the distance from point B to point C, and C is the angle between sides a and b.

Plugging in the given values, we get:

[tex]c^2 = 620^2 + 455^2 - 2(620)(455) cos(150°)\\\\c^2 = 383,825[/tex]

c ≈ 619.5 yards

So the distance between points A and B is approximately 619.5 yards.

Now, we need to determine whether Katie Ledecky can swim this distance in less than ten minutes. We are given that she swam 1,000 yards in 8 minutes and 59.65 seconds, which is approximately 8.99 minutes. So her average speed for the 1,000 yard freestyle was:

speed = distance / time

speed = 1,000 yards / 8.99 minutes

speed ≈ 111.23 yards/minute

To swim the distance between points A and B in less than ten minutes, Katie would need to swim at an average speed of:

speed = distance / time

speed = 619.5 yards / 10 minutes

speed = 61.95 yards/minute

Katie's Olympic level swimming speed of 111.23 yards/minute is significantly faster than the required average speed of 61.95 yards/minute to swim from point A to point B in under ten minutes. Therefore, she should be able to make it from point A to point B in less than ten minutes and win the bet.

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Maximum and Minimum values of f(x, y) = xy on the ellipse 3x² + y² = 9.

The maximum value is 3

The minimum value is -3

To find the maximum and minimum values of f(x, y) = xy on the ellipse 3x² + y² = 9, follow these steps:

1. Use the constraint equation (ellipse equation) to solve for one of the variables, either x or y.

Here, let's solve for y:
y² = 9 - 3x²
y = ±√(9 - 3x²)

2. Substitute y in the function f(x, y) with the expressions found in step 1:
f(x, y) = x(±√(9 - 3x²))

3. Differentiate f(x, y) with respect to x to find critical points (maximum or minimum):
f'(x, y) = ±(√(9 - 3x²) - (3x² / √(9 - 3x²)))

4. Set f'(x, y) = 0 and solve for x:
√(9 - 3x²) - (3x² / √(9 - 3x²)) = 0

5. Find the corresponding y values for the x values found in step 4 by substituting x back into the expressions found in step 1.

6. Evaluate f(x, y) at each critical point (x, y) found in steps 4 and 5 to determine the maximum and minimum values.

The maximum value of f(x, y) = xy on the ellipse 3x² + y² = 9 is 3, and the minimum value is -3.

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Answer:

Step-by-step explanation:

Given:- ABCD is a parallelogram, and AE and CF bisect ∠A and ∠C respectively. To prove:- AE∥CF Proof:- Since in a parallelogram, opposite angles are equal.

The function that best models the number of game consoles sold in millions x years since 2010 is option B, g(x) = 0.15(20).

To answer this question, we need to identify the function that best models the number of game consoles sold in millions x years since 2010.

Option A can be simplified to g(x) = 30, which is a constant function. This means that it does not depend on the value of x and is not a good model for the number of game consoles sold over time.

Option B can be simplified to g(x) = 3x, which is a linear function. This means that the number of game consoles sold increases at a constant rate over time. This could be a good model for the number of game consoles sold, but we need to compare it to the other options.

Option C can be simplified to g(x) = 0.03x, which is also a linear function. However, the rate of increase is much slower than in option B. This is not a good model for the number of game consoles sold.

Option D can be simplified to g(x) = 300, which is a constant function like option A. Again, this is not a good model for the number of game consoles sold over time.

Therefore, the function that best models the number of game consoles sold in millions x years since 2010 is option B, g(x) = 0.15(20). This is a linear function that represents a constant rate of increase in the number of game consoles sold over time.

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complete question:

Based on this information, which function best models the number of game consoles

sold in millions x years since 2010?

A- g(x) = 0.15(20)^x

B- g(x) = 20(0.15)^x

C- g(x) = 20(1.5)^x

D- g(x) = 0.15(.2)^x

The best group of people for Tom to survey would be homeowners in his town, as they are more likely to have a pool in their backyard.

To determine the percentage of people in his town that own a pool, Tom should survey a random sample of residents within the town. This will help him gather accurate and representative data about pool ownership in the area for his potential pool cleaning business.

Tom can also narrow down his survey to neighborhoods that are known to have a higher concentration of pool owners. This will give him a more accurate percentage of pool owners in his town and help him make an informed decision about opening a pool cleaning business.

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The equation 10S + 8W = 192 represents the calories Bridget ate on Monday and the equation 20S + 1W = 99 represents the calories she ate the next day.

The number of calories in each strawberry is 4, and the number of calories in each vanilla wafer cookie is 19.

a. We have two equations for the two days, using S for the number of calories in a strawberry and W for the number of calories in a vanilla wafer cookie:

On Monday:
10S + 8W = 192

On Tuesday:
20S + 1W = 99

b. To solve the system of equations using the substitution method, first solve one of the equations for one of the variables. We'll choose the second equation and solve for W:

W = 99 - 20S

Now substitute this expression for W in the first equation:

10S + 8(99 - 20S) = 192

Expand and simplify:

10S + 792 - 160S = 192

Combine like terms:

-150S = -600

Now divide by -150:

S = 4

Now that we have the value for S, substitute it back into the expression for W:

W = 99 - 20(4)

W = 99 - 80

W = 19

So the number of calories in each strawberry is 4, and the number of calories in each vanilla wafer cookie is 19. The solution is (S, W) = (4, 19).

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The area of a rectangle with base of 3x+1 in and a height of 2x-3 in is given as follows:

D. A = 6x² - 7x - 3 in².

The area of a rectangle of length l and width w is given by the multiplication of dimensions, as follows:

A = lw.

The dimensions for this problem are given as follows:

Hence the expression for the area of the rectangle is given as follows:

A = (3x + 1)(2x - 3)

A = 6x² - 9x + 2x - 3

A = 6x² - 7x - 3 in².

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So the angles that must be right angles are KER and ERI.

An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The rays are usually denoted by the letters A and B, and the vertex is denoted by the letter V. The angle is denoted by the symbol ∠, followed by the letters of the rays with the vertex in between, such as ∠AVB. The measure of an angle is the amount of rotation needed to move one ray to coincide with the other ray, and is usually given in degrees or radians. Angles are used in many areas of mathematics and science, such as trigonometry, geometry, physics, and engineering. They are also used in everyday life, such as in navigation, construction, and design.

Here,

Since RE and RI are secants of the circle, we can use the Intersecting Secants Theorem to find the relationships between the angles in the diagram.

Angle ERK is half of the intercepted arc EIK, so we have m∠ERK = 1/2m(arc EIK).

Similarly, angle KRI is half of the intercepted arc KE, so we have m∠KRI = 1/2m(arc KE).

Angle REI is an exterior angle of triangle KIR, so we have m∠REI = m∠ERK + m∠KRI.

To determine which angles must be right angles, we need to look for cases where the intercepted arcs are semicircles, which have a measure of 180 degrees.

If arc EIK is a semicircle, then m(arc EIK) = 180 and m∠ERK = 1/2(180) = 90. Therefore, angle ERK is a right angle.

If arc KE is a semicircle, then m(arc KE) = 180 and m∠KRI = 1/2(180) = 90. Therefore, angle KRI is a right angle.

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Natalie will have earned a total of $488.97 in interest by March 2025.

To solve this problem, we can use the formula for compound interest:

A = [tex]P(1 + r/n)^(nt)[/tex]

where A is the total amount, P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.

First, let's find out how much money Natalie will have in her first account after 5 years:

P = $800

r = 4.8% per year = 0.048

n = 12 (compounded monthly)

t = 5 years

A = [tex]800(1 + 0.048/12)^(12*5)[/tex]

A = $995.08

So after 5 years, Natalie will have $995.08 in her first account.

Next, let's find out how much money Natalie will have in her second account:

P = $995.08

r = 6% per year = 0.06

n = 2 (compounded semiannually)

t = 5 years

A = [tex]995.08(1 + 0.06/2)^(2*5)[/tex]

A = $1,288.97

So after reinvesting her money in the second account, Natalie will have $1,288.97 after 5 years.

Finally, let's calculate the total interest earned:

Total interest = A - P

Total interest = $1,288.97 - $800

Total interest = $488.97

Therefore, Natalie will have earned a total of $488.97 in interest by March 2025.

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Answer:

16.6666 hours.

Step-by-step explanation:

This conversion of 1,000 minutes to hours has been calculated by multiplying 1,000 minutes by 0.0166 and the result is 16.6666 hours.

Answer:

16,666.67 hours

Step-by-step explanation:

A minute is a unit of time equal to 60 seconds.

The function has a global maximum at the vertex (2/5, 41/25), and there are no local maxima or minima.

To find the critical numbers of the function f(x) = 4 - 5x/4 + x, we first need to find its derivative:

f'(x) = -5/4 + 1

f'(x) = -1/4

To find the critical numbers, we set f'(x) equal to zero and solve for x:

-1/4 = 0

This is never true, so there are no critical numbers for f(x).

Since there are no critical numbers, there are no local maxima or minima for the function. Instead, we can analyze the behavior of the function to determine if it has any extrema.

One way to do this is to examine the end behavior of the function. As x approaches positive or negative infinity, the leading term of the function is -5x/4, which dominates the constant term. Therefore, as x becomes large in either direction, the function approaches negative infinity. This suggests that the function has a global maximum at its vertex.

To find the vertex, we can complete the square:

f(x) = 4 - 5x/4 + x

[tex]f(x) = -(5/4)x^2 + x + 4[/tex]

[tex]f(x) = -(5/4)(x^2 - (4/5)x) + 4[/tex]

[tex]f(x) = -(5/4)(x - 2/5)^2 + 4 + (5/4)(2/5)^2\\f(x) = -(5/4)(x - 2/5)^2 + 41/25[/tex]

Therefore, the function has a global maximum at the vertex (2/5, 41/25), and there are no local maxima or minima.

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The value of h in the triangle shown above is calculated using proportion as: h = 4.

The two triangles shown are similar to each other based on the Angle-angle (AA) Similarity theorem. This implies that the length of their corresponding pair of sides would be proportional to each other.

Therefore, we have:

8/18 = h/9 [proportional sides of similar triangles]

Cross multiply:

h * 18 = 8 * 9

18h = 72

Divide both sides by 18:

18h/18 = 72/18 [Division property of equality]

h = 4

Therefore, the length of h in the given image is determined as: 4 units.

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Pedro and Hal will walk 1800 steps staircase and meet after 25 minutes.

Pedro is walking down the longest staircase ever, which contains 4000 steps. She starts from the top and is walking down the staircase at 150 steps a minute. Hal is walking up the staircase, starting at the bottom, at 80 steps a minute. After how many minutes will they meet?

Let's assume that they will meet at point X, which is y steps away from the top and z steps away from the bottom. As Pedro is walking down the staircase, she will cover a distance of y steps, while Hal is walking up the staircase, he will cover a distance of (4000-z) steps.

The time taken by Pedro to cover a distance of y steps is y/150 minutes, while the time taken by Hal to cover a distance of (4000-z) steps is (4000-z)/80 minutes. Since they will meet at the same point X, we can set these two times equal to each other and solve for y and z.

y/150 = (4000-z)/80

Solving this equation, we get y = 1800 and z = 2200. This means that Pedro will have covered 1800 steps in y/150 = 12 minutes and Hal will have covered (4000-2200) = 1800 steps in (4000-2200)/80 = 25 minutes.

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To find the effective interest rate that Hannah is being offered, we need to take into account the compounding period, which is daily in this case. The effective annual interest rate (EAR) can be calculated using the formula:

EAR = (1 + APR/n)^n - 1

where APR is the annual percentage rate, and n is the number of compounding periods per year.

For the first 30 days, Hannah is offered a 0% APR, so the EAR for this period is simply 0.

After 30 days, Hannah is offered a 12.22% APR compounded daily, which means that there are 365 compounding periods per year. Therefore, the EAR for this period can be calculated as follows:

EAR = (1 + 0.1222/365)^365 - 1

   ≈ 0.1267

So the effective interest rate that Hannah is being offered is approximately 12.67%.

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Answer:

1/11880 or 0.00008417508

Step-by-step explanation:

The probability of this can be determined by 1/12 x 1/11 x 1/10 x 1/9

We subtract one from the denominator each time because that ride has already been used, and cannot appear again in the list.

There are 1350 4-digit numbers that have the second digit even and the fourth digit at least twice the second digit.

To form a 4-digit number, we have 10 choices for each digit, except the first digit, which can't be 0. Hence, there are 9 choices for the first digit.

For the second digit, there are 5 even digits (0, 2, 4, 6, 8) to choose from.

For the third digit, there are 10 choices.

For the fourth digit, we can choose any of the even digits we picked for the second digit, or any of the larger odd digits 4, 6, 8.

Hence, the number of 4-digit numbers that meet the given criteria is

9 × 5 × 10 × 3 = 1350.

Therefore, there are 1,350 4-digit numbers that have the second digit even and the fourth digit at least twice the second digit.

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(a) A vector v parallel to the line of intersection L is v = <1, 1, -2>. (b) The cartesian equation of the plane is -7x + 10y - 3z = -1

(a) To find a vector v parallel to the line of intersection L, we need to take the cross product of the normal vectors to the two given planes. The normal vectors are the coefficients of x, y, and z in the equations of the planes.

In this case, the equations of the planes are:

x + y - 2z = 1

4x + y + 3z = 4

The normal vectors to these planes are <1, 1, -2> and <4, 1, 3>, respectively. Since the line of intersection is parallel to both planes, a vector parallel to the line must be perpendicular to both normal vectors.

We can find such a vector by taking the cross product of the two normal vectors, which gives us: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>

Therefore, a vector v = <1, 1, -2>.

(b) To find the equation of the plane through the point (2, -1, 3) and perpendicular to L, we need to find a normal vector to the plane that is also parallel to L.

We can find such a vector by taking the cross product of the normal vectors to the two given planes. The normal vectors are <1, 1, -2> and <4, 1, 3>, so the cross product is: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>

This vector is parallel to L, so it can serve as the normal vector to the desired plane. The equation of the plane can be written in point-normal form as: -7(x - 2) + 10(y + 1) - 3(z - 3) = 0

Simplifying, we get:

-7x + 10y - 3z = -1

Therefore, the cartesian equation of the plane is -7x + 10y - 3z = -1, and it passes through the point (2, -1, 3) and is perpendicular to the line of intersection between the given planes.

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James says the fraction 3/4 has the same value as the expression 4 ÷ 3. I disagree with James' statement.

The fraction 3/4 is not the same as the expression 4 ÷ 3. A fraction can be interpreted as division of the numerator (top number) by the denominator (bottom number). In this case, 3/4 represents the division of 3 by 4, whereas 4 ÷ 3 represents the division of 4 by 3. These two expressions have different values and are not equal.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

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The volume of prism is 75.6 [tex]in^3[/tex]. The correct answer is option d,

We are given that the rectangle represents the base of a right rectangular prism and the height of the prism is 6 inches. To find the volume of the prism, we need to multiply the area of the rectangle by the height.

The area of the rectangle can be found by multiplying its length and width. However, we are not given any specific values for the length and width of the rectangle. Therefore, we cannot directly calculate its area.

Since we are given answer choices, we can use them to check which option gives the correct volume of the prism. We can start by assuming that the length, width, and height of the prism are integers, and then calculate the volume for each option until we find the one that matches.

Option a: 87.9 in^3 - This is not an integer, so we can eliminate this option.

Option b: 105.8 in^3 - This is not an integer, so we can eliminate this option.

Option c: 12.6 in^3 - This is too small, so we can eliminate this option.

Option d: 75.6 in^3 - To check if this is the correct answer, we can calculate the area of the rectangle by dividing the volume by the height.

Volume of the prism = area of rectangle x height

75.6 in^3 = (length x width) x 6 in

Length x width = 12.6 in^2

Now, we need to find two integers whose product is 12.6 in^2 and whose sum is 16 in (since the rectangle represents the base of a right rectangular prism). After some trial and error, we find that 3.15 in and 4 in satisfy these conditions.

Therefore, the length of the rectangle is 4 inches and the width is 3.15 inches.

Now, we can calculate the area of the rectangle by multiplying its length and width:

Area of rectangle = length x width = 4 in x 3.15 in = 12.6 in^2

Finally, we can calculate the volume of the prism:

Volume of prism = area of rectangle x height = 12.6 in^2 x 6 in = 75.6 in^3

Therefore, the correct answer is option d, 75.6 [tex]in^3[/tex].

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The volume of the given cone is 402.1 cubic feet if the slant height is 10ft and the length is 6ft.

To calculate the volume of a cone, the formula used is :

V = (1/3) * π * [tex]r^2[/tex] * h

Here, the radius is the unknown term. we need to calculate the radius of the cone. We can use the Pythagorean theorem to find the radius of the cone.

[tex]l^2 = r^2 + h^2[/tex]

[tex]10^2 = r^2 + 6^2[/tex]

[tex]r = \sqrt{(10^2 - 6^2)}[/tex]

radius = 8 ft

V = (1/3) *  π * [tex]r^2[/tex] * h

V = (1/3) * π *[tex]8^2[/tex] * 6

V = (1/3) * π * 384

V =  402.1 cubic feet

Therefore we can infer that the volume of the given cone is  402.1 cubic feet.

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The complete question is:

'Find the volume of this cone. Round to the nearest tenth.

slant height = 10ft

length = 6ft

The solution of the system of equations is given by the ordered pairs [10, 0] and [8, -6].

In order to graphically solve the given system of equations on a coordinate plane, we would use an online graphing calculator to create a plot of the system of equations and then determine their point of intersection;

x² + y² = 100   ......equation 1.

3x - y = 30 ......equation 2.

Based on the graph shown in the image attached above, we can reasonably infer and logically deduce that the solution to this system of equations lies in both Quadrant I and Quadrant IV, and it is represented by this ordered pairs (10, 0) and (8, -6).

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Answer:

I believe the answer is D.

Step-by-step explanation:

Her car tires need to be ATLEAST 28. So, the number will be 28 or above.

By law of cosine, the triangle has a side of 1.348 units and two angles of 129.852° and 35.148°, respectively.

In this problem we find the representation of a triangle, in which we must determine the value of a missing side and two missing angles. This can be done by law of cosine. First, find the missing side:

x = √(3² + 4² - 2 · 3 · 4 · cos 15°)

x = 1.348

Second, find the missing angles:

4² = 3² + 1.348² - 2 · 3 · 1.348 · cos α

cos α = - 0.641

α = 129.852°

β = 180° - 15° - 129.852°

β = 35.148°

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A DTH TV connection provides channels in English and other languages in the ratio 7:13. To find out what percentage of the channels are in English, you need to divide the number of English channels by the total number of channels and then multiply the result by 100.

Let's assume that there are a total of 100 channels available on this DTH TV connection. According to the given ratio, 7 out of every 20 channels will be in English. So, the percentage of channels in English will be:

(7/20) x 100 = 35%

Therefore, 35% of the channels on this DTH TV connection are in English.

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The value of the calculated percent markup of the cookie is 100%

From the question, we have the following parameters that can be used in our computation:

The percent markup of the cookie is then calculated as

Percentage = (Selling price - cost price)/cost price

substitute the known values in the above equation, so, we have the following representation

Percentage = (3 - 1.5)/1.5

Evaluate

Percentage = 100%

Hence, the percent markup of the cookie is 100%

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