Find all the values of k for which the equation 2x^2+x+4k has (a) two real solutions, (b) one real solution, and (c) no real solutions.

Answer: See Below

Step-by-step explanation:

A slope of 0 simply means a straight line. Since we want the point (8,0), we need to shift our graph to the right 8. Therefore, the equation would be...

x = 8

Answer:

We can use the Pythagorean theorem to find the distance between the transmitter and the second city:

c² = a² + b²

c² = 55² + 51²

c² = 3026

c ≈ 55.01

So the transmitter is about 55.01 miles away from the second city.

To determine how much of the drive will pick up a signal, we can draw a circle with a radius of 40 miles centered at the transmitter, and see which part of the line connecting the two cities is within this circle.

We can see that the line connecting the two cities intersects the circle at two points, forming a right triangle with one leg measuring 40 miles. We can use trigonometry to find the length of the other leg:

sin(theta) = opposite/hypotenuse

sin(theta) = 40/c

csin(theta) = 40

a = csin(theta)

a = 55.01*sin(theta)

Now we need to find the angle theta, which can be found using inverse tangent:

tan(theta) = opposite/adjacent

tan(theta) = 55/51

theta = tan⁻¹(55/51)

theta ≈ 49.72 degrees

So we can substitute this value of theta into the equation we found earlier for a:

a ≈ 43.89

Therefore, the length of the line segment within the circle is approximately 43.89 miles. To find the length of the entire line segment connecting the two cities, we can use the Pythagorean theorem again:

b² = c² - a²

b² = 55.01² - 43.89²

b ≈ 33.6

So the entire length of the line segment connecting the two cities is approximately 33.6 miles. Therefore, the portion of the drive during which you will pick up a signal from the transmitter is 43.89/33.6 = 1.31 hours or about 79 minutes.

3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

3⁴ / 3³ = (3 × 3 × 3 × 3) / (3 × 3 × 3) = 3

This means that 3⁴ is 3 times larger than 3³.

5³ is 5 times larger than 5².

5³ / 5² = (5 × 5 × 5) / (5× 5) = 5

7¹⁰ is 49 times larger than 7⁸.

7¹⁰/ 7⁸ = 7² =49

17⁶ is 289 times larger than 17⁴.

17⁶ /17⁴ = 289

Hence, 3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

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Answer:

-18.67.

Step-by-step explanation:

If you think math is boring, think again. Here is a fun way to learn how to find the rational number that we need to divide -15/56 by to get -5/7. It's like a puzzle, but with fractions!

First, we need to make -15/56 look nicer. How do we do that? By dividing both the top and the bottom by -1. That's like flipping the sign. So we get 15/56. Much better!

Next, we need to find a mystery number that makes -5/7 and 15/56 equal when we multiply them. That's like finding a missing piece of a jigsaw puzzle. How do we do that? By cross-multiplying! That's when we multiply the top of one fraction by the bottom of the other and set them equal. So we get:

-5 times 56 equals 15 times mystery number

Now we just need to solve for the mystery number. How do we do that? By dividing both sides by 15. That's like cutting a cake into equal slices. So we get:

Mystery number equals (-5 times 56) divided by 15

Now we just need to simplify. How do we do that? By using a calculator or our brains. Either way, we get:

Mystery number equals -18.67

And that's it! We found the rational number that we need to divide -15/56 by to get -5/7. It's -18.67. Isn't math fun?

Answer:

When 2.7 is multiplied by 10 to the 2nd power, it becomes 270. The digit 7 is in the ones place, so the value of the digit 7 is 7.

Step-by-step explanation:

The evaluated solution for the  given  question comprises of sample point of a that are  {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH} , the event probability is 0.875 and the probability of implementing a, b is 3/4  below under the condition of a fair coin is tossed three times, and the events a and b are defined.

a)  Points sample  for event a: {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH}
Points  sample  for event b: {HTT, THT, TTH, HHH}
Points  sample  for event a b: {HTT, THT, TTH, HHH, HHT, HTH, THH}
  Points  sample for event ac: {TTT}
  Points  sample for event a c: {TTT, HHHH}

b)  Event a probability= 7/8 = 0.875
  Event b probability= 1/2 = 0.5
  Event ab probability = 3/8 = 0.375
  Event ac probability   = 1/8 = 0.125
  Event a c probability  = 1/16 + 1/8 = 0.1875

c) Probability of a b implementing additive rule
    P(a b) = P(a) + P(b) - P(a ∩ b)
     P(a ∩ b) = P(a) + P(b) - P(a b)
     P(a ∩ b) = (7/8) + (1/2) - (3/8)
     P(a ∩ b) = 9/8 - 3/8
     P(a ∩ b) = 6/8
     P(a ∩ b) = 3/4

d)  Hence, events a and b are not mutually exclusive due to the lack of chances of having common sample points {HHH}.


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The order of the given fractions after arranging from least to greatest is 1/5, 2/5, 4/5.

To put the fractions 1/5, 2/5, and 4/5 in order from least to greatest, we can either convert them to decimals or find a common denominator and compare the numerators. Here, we will use the latter method.

First, we need to find a common denominator. The smallest denominator that all three fractions share is 5. So, we can rewrite the fractions as follows:

1/5 = 1/5

2/5 = 2/5

4/5 = 4/5

Now, we can compare the numerators since the denominators are the same. Clearly, 1/5 is the smallest, followed by 2/5, and then 4/5 is the largest.

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The area of the pentagon with an apothem of 10 units is approximately 353.55 square units.

Area = (Perimeter × Apothem) / 2

Central angle = 360° / 5 = 72°

To find the area of a regular pentagon with an apothem of 10 units, we can use the formula:

Area = (Perimeter × Apothem) / 2

Central angle = 360° / 5 = 72°

Now, consider the right triangle formed by half of a side, the apothem, and the radius. The angle between the apothem and the radius (half of the central angle) is:

Angle = 72° / 2 = 36°

In the right triangle, we have:

tan(36°) = (s/2) / 10

Solving for s:

s = 2 * 10 * tan(36°) ≈ 14.142 units (rounded)

Now that we have the length of one side, we can calculate the perimeter of the pentagon:

Perimeter = 5 * s ≈ 5 * 14.142 ≈ 70.710 units (rounded)

Finally, we can find the area of the pentagon using the formula:

Area = (Perimeter × Apothem) / 2

Area = (70.710 × 10) / 2

≈ 353.55 square units (rounded)

The area of the pentagon with an apothem of 10 units is approximately 353.55 square units.

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The equation with the fewest symbols is 30x - 18, which represents the simplified form of the given expression.

An equation is a mathematical statement that shows the equality between two expressions. The given expression is not an equation since there is no equality sign present. However, we can simplify the expression to get an equivalent equation with the fewest symbols.

To simplify the expression, we use the distributive property of multiplication over addition/subtraction. We multiply 6 with each term inside the parentheses, i.e., 5x and -3. This gives us:

6(5x - 3) = 6(5x) - 6(3) = 30x - 18

This simplified expression is an equation that shows the equality between the left-hand side (LHS) and the right-hand side (RHS). The LHS is 30x - 18, and the RHS is also 30x - 18, which means that they are equal.

Therefore, the equation with the fewest symbols is 30x - 18, which represents the simplified form of the given expression.

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The result of 9 divided by 7/3 is 12 3/7.

When dividing by a fraction, it's the same as multiplying by its reciprocal. Therefore, to divide 9 by 7/3, we can multiply 9 by 3/7. This gives us (9 x 3) / 7 = 27/7.

However, this fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 3.

Thus, 27/7 can be simplified to 9 and 6/7, or 12 and 3/7 when expressed as a mixed number. Therefore, the answer to 9 divided by 7/3 is 12 and 3/7.

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Thus, for the given range of data of six integers the value of x is found as: x = 16.

The difference here between maximum and smallest values in a data set is known as the range. Employing the exact same units as the data, it measures variability. More variability is shown by larger values.

Take the highest value and deduct the lowest value from it to determine the range in statistics.

A data set's range

Range is equal to the highest and lowest values.

Since the formula subtracts any smaller value from the larger one, it is impossible for it to be negative.

Given data:

six integers:  5,9,7,12,3,x.

Range = 13

The formula for the range ;

Range  = maximum value - minimum value

x - 3 = 13

x = 13 + 3

x = 16

Thus, for the given range of the data of six integers the value of x is found as: x = 16.

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Answer: 18 square feet im pretty sure

Step-by-step explanation:

Answer:  B)  216

Step-by-step explanation:

Step-by-step explanation:

Let's assume the basic fee for water is $X per unit and the tariff for consumption is 5% increase per unit. VAT (Value Added Tax) is calculated at a rate of Y% on the total cost, including the basic fee and the tariff.

Given that the consumption is 15 units, the total cost for the consumption of 15 units of water without VAT can be calculated as:

Total cost without VAT = Basic fee + (Tariff rate * Number of units)

Tariff rate = 5% increase per unit, so it would be 1 + 5% = 1.05

Total cost without VAT = X + (1.05 * 15) = X + 15.75

Now, let's assume the VAT rate is Z%. The total cost including VAT can be calculated as:

Total cost including VAT = Total cost without VAT + (VAT rate * Total cost without VAT)

Total cost including VAT = (X + 15.75) + (Z% * (X + 15.75))

To calculate the amount by which the total cost, including VAT, for the consumption of 15 units of water will increase, we need to subtract the initial cost from the increased cost:

Increased cost = Total cost including VAT - Total cost without VAT

Increased cost = [(X + 15.75) + (Z% * (X + 15.75))] - (X + 15.75)

Simplifying, we get:

Increased cost = Z% * (X + 15.75)

So, the amount by which the total cost, including VAT, for the consumption of 15 units of water will increase depends on the value of Z% (the VAT rate) and X (the initial basic fee for water). Once we have these values, we can calculate the increased cost accordingly.

Cash received for interest during  2014 was $3,500 .The following equation can be used to determine the amount of money received as interest in 2014:

Amount received as interest equals Interest Income for 2014 plus the decline in Interest Receivable

The difference between the balance of interest receivable at December 31, 2013, and at December 31, 2014, can be used to calculate the decline in interest receivable:

Reduced interest due = Interest due at December 31, 2013, minus Interest due at December 31, 2014, which equals $1,100 minus $1,400, or -$300.

The fact that the balance of interest receivable increased from 2013 to 2014 indicates that the company produced more interest money during the year than it received. In light of this, the money earned on interest in 2014 is:

Interest income from 2014 plus a decrease in interest receivable equals $3,200 minus (-$300) to $3,500 in interest payments received.

Hence, $3,500 is the correct response (C).

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If john has a new house. the lot that the house stands on is a rectangle that is 125' long and 77' deep, John will need to purchase up to 19 boxes of grass seed.

First, we need to calculate the total area of the lot. The area of a rectangle is given by its length multiplied by its width, so:

Area of lot = 125 ft * 77 ft = 9625 square feet

Next, we need to determine the area of the portion of the lot that is not covered by the house. Since the house is located near the center of the lot, we can find the area of the rectangle that represents the space around the house and subtract it from the total area of the lot:

Area around house = (125 ft - 40 ft - 40 ft)/2 * (77 ft - 36 ft - 36 ft)/2 = 22.5 ft * 16.5 ft = 371.25 square feet

Area to be planted = 9625 square feet - 371.25 square feet = 9253.75 square feet

Now we can calculate the number of boxes of grass seed needed by dividing the area to be planted by the coverage of each box:

Number of boxes = 9253.75 square feet / 500 square feet per box = 18.51 boxes

Since you can't purchase a fraction of a box, John will need to round up to 19 boxes of grass seed.

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On average, you can expect to get about 4.24 points per game if you play many times.

To find the average number of points you can get by playing the game many times, you can use the expected value as a guide.

The expected value of the game is calculated as follows:

(20 points x probability of getting 20) + (10 points x probability of getting 10) + (2 points x probability of getting 2) = 5.6

Let's use the variables p20, p10, and p2 to represent the probabilities of getting 20 points, 10 points, and 2 points, respectively. Then we can set up the equation:

(20p20) + (10p10) + (2p2) = 5.6

We also know that the sum of the probabilities must equal 1:

p20 + p10 + p2 = 1

Now we have two equations and three variables. We need one more equation to solve for the variables. One way to do this is to assume that the probabilities of getting 20 points, 10 points, and 2 points are proportional to the point values themselves.

In other words, let's assume that:

p20 : p10 : p2 = 20 : 10 : 2

We can then use this proportion to write p20 and p2 in terms of p10:

p20 = 2p10

p2 = 4p10

Now we can substitute these expressions into the two equations we have:

(20p20) + (10p10) + (2p2) = 5.6

p20 + p10 + p2 = 1

Substituting the first equation gives:

(20(2p10)) + (10p10) + (2(4p10)) = 5.6

Simplifying:

80p10 + 10p10 = 5.6

90p10 = 5.6

p10 = 5.6/90

p10 = 0.062

Now we can use the proportions to find p20 and p2:

p20 = 2p10 = 2(0.062) = 0.124

p2 = 4p10 = 4(0.062) = 0.248

Finally, we can calculate the average number of points:

(20 points x 0.124) + (10 points x 0.062) + (2 points x 0.248) = 3.12 + 0.62 + 0.496 = 4.236

So, on average, you can expect to get about 4.24 points per game if you play many times.

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Therefore,  according to the given information, h ²(x) = (x^3 - 12 + t^2)^3 - 12 + t^2.

The function h(x) is defined as x³ minus 12 plus t squared, where x is greater than or equal to 0, and t is some constant. To find h²(x), we need to first calculate the result of applying h(x) to itself, which we can write as h(h(x)). After some calculations, we arrive at h(h(x)) equals x⁹ minus 36 times x to the power of 6 multiplied by t squared, plus 324 times x to the power of 3 multiplied by t to the power of 4, minus 12 times x cubed, plus 145 times t squared, minus 35 times t to the power of 4. Therefore, h²(x) is equal to the same expression we obtained for h(h(x)).

To find h²(x), we need to first find h(h(x)).
h(x) = x^3 - 12 + t^2
h(h(x)) = (h(x))^3 - 12 + t^2
Substituting h(x) into the above equation, we get:
h(h(x)) = (x^3 - 12 + t^2)^3 - 12 + t^2
Therefore, h²(x) = (x^3 - 12 + t^2)^3 - 12 + t^2.

Therefore,  according to the given information, h ²(x) = (x^3 - 12 + t^2)^3 - 12 + t^2.

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Answer: the height of the hockey puck is approximately 0.835 inches.

Step-by-step explanation: The formula for determining the volume of a cylinder is as follows:

The formula for the volume (V) of a cylinder can be expressed mathematically as V = πr2h, where r represents the radius of the cylinder's base and h represents the height of the cylinder. This formula is derived from the concept that the volume of a cylinder can be calculated by multiplying the area of its base (which is represented by the term πr2) by its height (h).

The present study utilizes the conventional nomenclature in which V denotes the volume, r represents the radius, and h stands for the height.

As the diameter of the hockey puck is measured to be 3 inches, it follows that the radius is equivalently calculated as 1.5 inches, or precisely half of the diameter.

It is established that the hockey puck has a volume of 7.1 cubic inches; accordingly, by substituting these known values into the relevant formula and performing the appropriate calculations, the measurement of h may be ascertained.

The expression 7.1 = π(1.5)^2h can be reformulated in a more academic manner. It can be said that the equation represents the mathematical relationship between the volume of a cylinder and its dimensions, wherein the value of 7.1 denotes the volume of the cylinder, whereas π, 1.5, and h refer to the mathematical constants of pi, radius, and height, respectively. Thus, the formula can be expressed as V = πr^2h, where V represents the volume of the cylinder, r denotes the radius, and h denotes the height.

The process of reducing something to its simplest form. Rewritten: The act of simplification involves distilling a concept or idea to its most basic, essential components. This process aims to facilitate a clear and concise understanding of the subject matter, allowing for greater comprehension and ease of communication.

The numerical expression 7.1 = 2.25πh can be written in a more formal and academic manner. Specifically, the equation can be rephrased as an algebraic relationship between the variables involved. More concisely, the equation describes the result of a multiplication between the constant factor 2.25π and the variable h, which according to the equation equals 7.1. As such, it can be represented by the following expression: 2.25πh = 7.1

Dividing each side by 2.25π is a logical mathematical operation utilized to simplify an equation or expression.

The aforementioned equation may be expressed in an academic tone as follows: The value of h is equivalent to the quotient obtained from dividing 7.1 by 2.25 times the mathematical constant π.

The employment of a calculator to compute the aforementioned expression:

The observed value of h is approximately equal to 0.835 inches.

In probability theory, an event is any collection of outcomes or results from a probability experiment. option a) is correct event

It represents a particular occurrence or set of occurrences that we are interested in studying or analyzing. A sample space (option b) is the set of all possible outcomes in a probability experiment. An outcome (option c) is a particular result of a single trial of a probability experiment. An experiment (option d) refers to the process of conducting a trial or series of trials to observe the outcomes and collect data for analysis in probability theory. Therefore, the correct answer is option a) event.

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Complete Question

A(n) _______ is any collection of outcomes from a probability experiment.

a) event

b) sample space

c) outcome

d) experiment

To summarize, an outcome is a result of an experiment, a sample space is a collection of all possible outcomes, an event is a set of outcomes chosen from the sample space, and a collection is a group of events with a common property.

An experiment in probability refers to a process of observing or measuring some phenomenon, where the outcomes are uncertain. The collection of all possible outcomes from this experiment is known as the sample space. An outcome is a particular result that occurs as a result of the experiment.

Now, a set of outcomes chosen from the sample space is known as an event. An event can be as simple as a single outcome or as complex as a combination of outcomes. For example, flipping a coin and getting heads is a simple event, while flipping a coin and getting heads or rolling a dice and getting an even number is a compound event.

Finally, a collection of events is simply a group of events that share a common characteristic or property. In probability, we use collections of events to determine the likelihood of certain outcomes occurring. This allows us to make predictions about the experiment based on the available data.

So, to summarize, an outcome is a result of an experiment, a sample space is a collection of all possible outcomes, an event is a set of outcomes chosen from the sample space, and a collection is a group of events with a common property.

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The probability of getting a multiple of 2 or a multiple of 3s:

P = 0.67

The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes, which in this case are 12.

The multiples of 2 and the multiples of 3 are

{2, 3, 4, 6, 8, 9, 10, 12}

So 8 out of the total of 12 outcomes make the event true, then the probability we want to get is the quotient between these numbers:

P = 8/12 = 0.67

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Answer:

58

Step-by-step explanation: You add them all together

Understanding the meaning of addition and subtraction will allows us to make predictions about how changing the value of a variable will affect the value of an expression.

In mathematics, integers are a set of whole numbers that include both positive and negative numbers, as well as zero. The set of integers is denoted by the symbol Z, and it includes all the natural numbers (1, 2, 3,...), their negatives (-1, -2, -3,...), and zero (0). Integers are used in a variety of mathematical contexts, including algebra, number theory, and geometry. Integers can be used to represent many real-world situations, such as temperatures above or below zero, changes in altitude, gains or losses in money, and more. They are also used extensively in computer programming and other fields that rely heavily on mathematics.

Knowing what addition and subtraction mean allows you to understand how changing the value of a variable can affect the value of an expression.

For example, consider the expression x + 2. If x has a value of 3, then the value of the expression is 5. However, if x increases to 4, then the value of the expression increases to 6. This is because we are adding 2 to the value of x.

On the other hand, if we have the expression x - 2 and x has a value of 3, then the value of the expression is 1. If x increases to 4, then the value of the expression decreases to 2. This is because we are subtracting 2 from the value of x, so as x increases, the value of the expression decreases.

Understanding the meaning of addition and subtraction is essential to be able to manipulate expressions and variables, and it allows us to make predictions about how changing the value of a variable will affect the value of an expression.

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Answer: 5 3/4 feet

Step-by-step explanation:

The original perimeter of the room is:

2(length + width) = 2(13 ft + 8 ft) = 42 ft

After the length and width are increased by "x" feet, the new perimeter becomes 53 1/2 ft.

So, we can write the equation:

2(length + x + width + x) = 53 1/2 ft

Simplifying the equation, we get:

2(length + width + 2x) = 53 1/2 ft

But we know that the original perimeter of the room was 42 ft, so:

2(length + width) = 42 ft

Substituting this into the above equation, we get:

42 ft + 2x = 53 1/2 ft

Subtracting 42 ft from both sides, we get:

2x = 11 1/2 ft

Dividing both sides by 2, we get:

x = 5 3/4 ft

Therefore, the length and width of the room were both increased by 5 3/4 feet

The requried, there are 8998912 possible license plates that can be generated using this format.

There are 8 digits that can be used for each of the three digits on the license plate, with two digits (4 and 5) that cannot be used. Therefore, there are 8 choices for each of the three digits, giving us 8 x 8 x 8 = 512 possible combinations for the digits.

Similarly, there are 26 letters that can be used for each of the three letters on the license plate. Therefore, there are 26 choices for each of the three letters, giving us 26 x 26 x 26 = 17576 possible combinations for the letters.

Total number of license plates = number of choices for the digits x number of choices for the letters

= 512 x 17576

= 8998912

Therefore, there are 8998912 possible license plates that can be generated using this format.

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Answer:

15%

Step-by-step explanation:

0.15 x 100 = 15%

The information quality of the survey is not reliable for understanding the current happiness level in the state.

The information quality for this survey is likely outdated and not

representative of the current state of Louisiana, particularly after the

devastating impact of Hurricane Katrina in 2005.

The survey was conducted before the hurricane, which significantly

affected the region, including the mental health and well-being of its

residents.

Thus, the survey's results may not accurately reflect the current level of

happiness or satisfaction among Louisiana residents.

Therefore, the information quality of the survey is not reliable for

understanding the current happiness level in the state.

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Answer:

2((6(14) + 6(5) + 14(5)) = 2(84 + 30 + 70) =

2(184) = 368 square centimeters

1. 7 x^2 - 9 y^2 = 343 is a hyperbola

2. x^2 + y^2 - 4 x + 6 y - 5 = 1 is a circle

3. 4 x^2 + 9 y^2 = 1 is a ellipse

4. x^2 - 6 y = 0 is a parabola

A conic section conic or a quadratic curve is described as  a curve obtained from a cone's surface intersecting a plane.

The three types of conic section are :

All conics are  written in terms of the following equation:

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.

In conclusion, a conic is the intersection of a plane and a right circular cone.

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#Complete question:

Match the following equations with the conic sections formed by them. 1. x 2 + y 2 - 4x + 6y - 5 = 0 hyperbola 2. x 2 - 6y = 0 circle 3. 4x 2 + 9y 2 = 1 ellipse 4. 7x 2 - 9y 2 = 343 parabola

Answer:

Let's denote:

M: the set of students who like maths

S: the set of students who like science

n(M): the number of students who like maths

n(S): the number of students who like science

n(M ∩ S): the number of students who like both maths and science

n(M ∪ S): the number of students who like maths or science (or both)

We can use the principle of inclusion-exclusion to find n(M ∪ S):

n(M ∪ S) = n(M) + n(S) - n(M ∩ S)

From the problem statement, we know:

n(M) = 10

n(S) = 15

n(M ∩ S) = ? (unknown)

We also know that 10 students like neither maths nor science, which means that:

n(M ∪ S)' = 10

where (M ∪ S)' denotes the complement of M ∪ S, i.e., the set of students who do not like maths or science.

We can use the formula:

n(A') = N - n(A)

where N is the total number of students (N = 50).

n(M ∪ S)' = n((M ∪ S))' = N - n(M ∪ S) = N - (n(M) + n(S) - n(M ∩ S))

Substituting the known values:

n((M ∪ S))' = 50 - (10 + 15 - n(M ∩ S)) = 25 + n(M ∩ S)

Simplifying:

n(M ∩ S) = n((M ∪ S))' - 25 = 10

Therefore, we have:

n(M ∪ S) = n(M) + n(S) - n(M ∩ S) = 10 + 15 - 10 = 15

The ratio of the students who like maths or science is:

n(M ∪ S) / N = 15 / 50 = 3/10

So the required ratio is 3:10.

Step-by-step explanation: