Coin A is tossed three times and coin B is tossed two times. What is the probability that more heads are tossed using coin A than coin B?

x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)

x,y,z=(larger z-value)=(56/3, 32/3, -16/3)

These are the points on the cone that are closest to the point (14, 8, 0).

In a two-dimensional space, a point is defined by two coordinates, typically denoted by (x, y), where x represents the horizontal position, and y represents the vertical position. In a three-dimensional space, a point is defined by three coordinates, typically denoted by (x, y, z), where x, y, and z represent the horizontal, vertical, and depth positions, respectively.

We want to minimize the distance between the point (14, 8, 0) and the surface of the cone defined by the equation z² = x² + y², subject to the constraint that we stay on the surface of the cone.

Let f(x,y,z) = (x-14)² + (y-8)² + z² be the function we want to minimize subject to the constraint g(x,y,z) = z² - x² - y² = 0.

The Lagrange multiplier method involves finding the critical points of the function L(x,y,z,λ) = f(x,y,z) - λg(x,y,z), where λ is the Lagrange multiplier.

So we have:

L(x,y,z,λ) = (x-14)² + (y-8)² + z² - λ(z² - x² - y²)

Taking the partial derivatives with respect to x, y, z, and λ, and setting them equal to zero, we get the following system of equations:

2(x-14) + 2λx = 0

2(y-8) + 2λy = 0

2z - 2λz = 0

z² - x² - y² = 0

The third equation simplifies to z(1-λ) = 0, which gives us two possibilities:

Case 1: z = 0

In this case, the fourth equation becomes -x² - y² = 0, which implies that x = y = 0. But this point does not lie on the surface of the cone, so it is not a valid critical point.

Case 2: λ = 1

In this case, the first two equations become x-14 = -xλ and y-8 = -yλ, which imply that x = -7λ and y = -4λ. Substituting into the fourth equation gives:

z² = x² + y² = 65λ²

To minimize the distance between the point (14, 8, 0) and the surface of the cone, we want to find the value of λ that minimizes the function f(x,y,z) subject to the constraint g(x,y,z) = 0. Substituting x = -7λ, y = -4λ, and z = √(65λ²) into f(x,y,z), we get:

f(λ) = (7λ-14)² + (4λ-8)² + 65λ²

To minimize this function, we take its derivative with respect to λ and set it equal to zero:

f'(λ) = 30λ - 80 = 0

Solving for λ, we get λ = 8/3. Substituting this back into x = -7λ, y = -4λ, and z = √(65λ²), we get:

x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)

x,y,z=(larger z-value)=(56/3, 32/3, -16/3)

These are the points on the cone that are closest to the point (14, 8, 0).

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Since Sour Drops, Chocolate Chews and Tangy Twists are in the ratio 2:3:4, respectively, it follows that Sour Drops account for 2/9 and Tangy Twists account for 4/9 of the candy mixture. So, Sour Drops make up (2/9)(45) = 2 × 5 = 10 pounds, while Tangy Twists make up (4/9)(45) = 4 × 5 = 20 pounds of the 45-pound candy mixture. Therefore, there are 20 – 10 = 10 pounds more Tangy Twists than Sour Drops. Alternatively, the given ratio means that Tangy Twists account for 4/9 – 2/9 = 2/9 more of the candy mixture than Sour Drops do. So, in a 45-pound batch of the candy mixture, there would be (2/9)(45) = 2 × 5 = 10 pounds more Tangy Twists than Sour Drops.

Nyelle purchases some Sour Drops, Chocolate Chews and Tangy Twists to combine into her personal batch of the Sugar Shack’s signature candy mixture using the same proportions as the previous problem. If the prices per pound for the candies are $6.00 for Sour Drops, $3.50 for Chocolate Chews and $4.25 for Tangy Twists, what is the total cost (not including tax) to purchase the exact amounts of all three candies required to make 4.5 pounds of this signature candy mixture?

Again, since Sour Drops, Chocolate Chews and Tangy Twists are in the ratio 2:3:4, respectively, it follows that Sour Drops, Chocolate Chews and Tangy Twists account for 2/9, 3/9 = 1/3 and 4/9 of the candy mixture, respectively. So, to make 4.5 pounds of this candy mixture, Nyelle needs (2/9)(4.5) = 2 × 0.5 = 1 pound of Sour Drops, (1/3)(4.5) = 1.5 pounds of Chocolate Chews and (4/9)(4.5) = 4 × 0.5 = 2 pounds of Tangy Twists. At the given prices per pound, we calculate Nyelle’s total cost to be 1(6.00) + 1.5(3.50) + 2(4.25) = 6 + 5.25 + 8.50 = $19.75.

Rae purchases 4.5 pounds of the signature candy mixture when it goes on sale at the Sugar Shack for $4.00 per pound. What is the absolute difference between Nyelle’s and Rae’s total costs (not including tax) to get 4.5 pounds of the signature candy mixture?

At a sale price of $4.00 per pound, 4.5 pounds of the candy mixture would cost Rae 4.5(4.00) = $18.00. From the previous problem, we know that Nyelle’s total cost was $19.75. Therefore, the absolute difference between Nyelle’s and Rae’s total costs is 19.75 – 18.00 = $1.75.

TU is a perpendicular bisector.

A line that divides a line segment into two equal halves and forms a 90-degree angle at the point of intersection is called a perpendicular bisector.

To put it another way, a perpendicular bisector separates a line segment at its midpoint, creating a 90-degree angle.

A line or line segment that divides a given line segment into two equal portions is known as a perpendicular bisector.

The word "bisect" refers to dividing equally.

The line segment that perpendicular bisectors overlap forms four 90° angles on either side.

A line or line segment is said to be perpendicular when it forms a 90° angle with another line or line segment.

Hence, TU is a perpendicular bisector.

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How does cellular respiration help maintain homeostasis in animals?

Answer: Cellular respiration helps animals maintain homeostasis by breaking down glucose to produce ATP, which is the energy currency of the cell. ATP is necessary for many cellular processes that help maintain homeostasis such as active transport and protein synthesis.

Explain why cells separate and expel waste.

Answer: Cells separate and expel waste to prevent the accumulation of toxic substances that can disrupt cellular function and lead to disease. The waste products are transported out of the cell and into the bloodstream where they are filtered and excreted by organs such as the kidneys.

Why do cells in organisms such as animals reproduce?

Answer: Cells in organisms such as animals reproduce to replace damaged or dying cells, and to enable growth and development. Reproduction ensures that the organism maintains the proper balance of cells and that there is enough tissue to perform necessary functions.

Explain how plant cells use photosynthesis to maintain homeostasis?

Answer: Plant cells use photosynthesis to maintain homeostasis by converting light energy into chemical energy in the form of glucose. This glucose is then used to produce ATP, which is necessary for cellular processes such as active transport and protein synthesis. Additionally, plants use photosynthesis to produce oxygen, which is necessary for respiration.

I hope this helps :)

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The greatest time that the fourth runner can run for the team to reach its goal is 63.23 seconds.

To find the greatest time that the fourth runner can run for the team to reach its goal, we need to subtract the total time of the first three runners from the goal time of 4 minutes (240 seconds).

Total time of the first three runners = 57.38 seconds + 60.92 seconds + 58.47 seconds = 176.77 seconds

Greatest time the fourth runner can run = Goal time - Total time of the first three runners = 240 - 176.77 = 63.23 seconds

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The probability that a person treated for an energy drink-related emergency was under 40 given that the person was at least 18 years old is approximately 0.550 or 55.0%.

In general, probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in a sample space. Event probability P(E) = (number of favourable outcomes) (Sample space).

We must use conditional probability to determine the likelihood that a person treated for an energy drink-related emergency was under 40, given that the person was at least 18 years old.

We can use the following formula:

P(A | B) = P(A and B) / P(A and B) (B)

where A is the event "the person is under 40" and B is the event "the person is over 18".

According to the table, 11,146 people under the age of 40 and over the age of 18 were treated for energy drink-related emergencies. The total number of people over the age of 18 who have been treated for energy drink-related emergencies is 20,244.

So,

P(A, B) = 11,146

P(B) = 20,244

Therefore,

P(A and B) / P(B) = 11,146 / 20,244 0.550

So the probability that a person treated for an energy drink-related emergency was under 40 is approximately 0.550 or 55.0% if the person was at least 18 years old.

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Answer:

Step-by-step explanation:

To solve this problem, we need to find out how many seats there are in total, and then multiply that by the price per ticket.

To find the total number of seats, we need to add up the number of seats in each row. We can use the formula for an arithmetic sequence to do this:

S = n/2 * (a + l)

where S is the sum of the sequence, n is the number of terms, a is the first term, and l is the last term.

In this case, we have:

n = 20 (since there are 20 rows)

a = 25 (since there are 25 seats in the first row)

d = 2 (since the difference between each row is 2 seats, the common difference is 2)

We can use d to find the last term as well:

l = a + (n-1)*d

l = 25 + (20-1)*2

l = 25 + 38

l = 63

Now we can plug these values into the formula:

S = 20/2 * (25 + 63)

S = 10 * 88

S = 880

So there are 880 seats in total.

To find the total sales, we just need to multiply by the price per ticket:

total sales = 880 * $32

total sales = $28,160

Therefore, the total sales for a one-night concert with all seats taken would be $28,160.

Answer:

B.6 pages per day

Step-by-step explanation:

let's first transform these terms into real fractions :

2/5 = 2/5

4 1/8 = (4×8 + 1)/8 = 33/8

2 1/4 = (2×4 + 1)/4 = 9/4

first we need to handle the division (remember the priorities of arithmetic operations) :

-33/8 / -9/4 = (-33×4) / (-9×8) = 33 / (9×2) = 33/18

then we have to calculate

2/5 + 33/18

to do that we have to bring both fractions to the same denominator (must be divisible by 18 and by 5, so in this case it is 5×18 = 90) :

2/5 = 2/5 × 18/18 = 36/90

33/18 = 33/18 × 5/5 = 165/90

so,

36/90 + 165/90 = 201/90 = 67/30 = 2 7/30

Step-by-step explanation:

Area of a square = s x s   and this equals  10 x s

 this is :  

     s^2 = 10 s    divide both sides of the equation by 's'

  s = 10   units    ( or zero....but that makes no sense)

Step-by-step explanation:

6x - 2 = 4x + 36

2x - 2 = 36

2x = 38

x = 19

4*19 + 36= 76 + 36= 112

180-112= 68

m<N= 68 degrees

The area of the given shape is 109.25 ft² .

What is Area?

Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is the size of the surface of the shape, and it is measured in square units, such as square meters, square centimeters, or square inches.The area of a shape can be found by multiplying the length and width of a rectangle or the base and height of a triangle, or by using specific formulas for other shapes such as circles, trapezoids, or parallelograms

Given : height of triangle = diameter of semicircle = 10 ft

            radius of semicircle = 5 ft

           base of triangle = 14 ft

we know that, The area of given shape :

= area of given triangle + area of semi circle

=  1/2 × base × height  +   πr²/2

= 1/2 × 14 × 10 + (3.14 × 5²)/2

= 70 + 39.25

= 109.25 ft²                                  

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Jo has read 14% of the book if she has read 35 pages of a 250 pages book.

If Jo has read 35 pages out of a 250-page book, we can calculate what percentage of the book she has read by dividing the number of pages she has read by the total number of pages and multiplying by 100:

Percentage of book read = (35 / 250) x 100%

Percentage of book read = 0.14 x 100%

Percentage of book read = 14%

Therefore, Jo has read 14% of the book. Percentage is a way of expressing a number as a fraction of 100. It is often used to describe the relationship between a part and a whole, where the part represents a portion of the whole. Percentages are commonly used in various fields, including mathematics, finance, and statistics, to measure changes or represent data in a more accessible format.

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Answer:

To solve the system of equations:

n + d = 21 ---(1)

0.05n + 0.10d = 1.70 ---(2)

We can use the substitution method by solving for one variable in terms of the other from equation (1) and substituting it into equation (2).

Solving equation (1) for n:

n = 21 - d

Substituting this expression for n into equation (2):

0.05(21 - d) + 0.10d = 1.70

Distributing the 0.05:

1.05 - 0.05d + 0.10d = 1.70

Combining like terms:

0.05d = 0.65

Dividing both sides by 0.05:

d = 13

Substituting this value of d into equation (1):

n + 13 = 21

Solving for n:

n = 8

Therefore, the solution to the system of equations is n = 8 and d = 13.

Answer:

no lol im too lazy

Step-by-step explanation:

give me brain

Answer:

x = 9/10.

Step-by-step explanation:

0.5(4x + 9) = 3x * 7/3

2x + 9/2 = 3x * 7/3

2x + 9/2 = 7x

5x = 9/2

x = 9/10.

Deion now has 2.30 grammes of pepper remaining.

pre-warnt g The g the l e the l the l a n no. If you entered x=0 into your equation, you would receive this result. Your original amount is the part of your equation that is NOT increased to the x power.

We must take the amount of pepper Deion used from the total amount he had in order to determine how much pepper he still has.

Initial amount of pepper = 4.22 grams

Amount of pepper used = 1.92 grams

Pepper remaining = Initial amount - Amount used

Pepper remaining = 4.22 grams - 1.92 grams

Pepper remaining = 2.30 grams

Therefore, Deion has 2.30 grams of pepper left.

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There were 8-1 = 7 more students who slept for 4-7 hours than for 12-15 hours.

In a survey conducted by Mr. Hamilton, he asked his class about the total number of hours they slept the previous night. The histogram provided in the question shows the distribution of their responses. To find out how many more students slept for 4-7 hours than 12-15 hours, we need to count the number of bars in the 4-7 hours range and subtract it from the number of bars in the 12-15 hours range. By counting the bars in the histogram, we can see that there are 9 bars in the 4-7 hours range and 4 bars in the 12-15 hours range. Therefore, there were 5 more students who slept for 4-7 hours than 12-15 hours.

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Complete question:

Mr. Hamilton surveyed his class to find the total number of hours each of his students slept the previous night. The histogram shows the results of the survey. How many more students slept 4 – 7 hours than 12 – 15 hours? Amount of Sleep Mr: Hamilton surveyed his class to find the total number of hours each of his students slept the previous night The histogram shows the results of the survey: How many more students slept 4 ~ 7 hours than 12 15 hours? L 0 -3 8 _ [1 12 - 15 submit Time (hours)'

There are 1124 ways to choose a committee of 7 members with at least one member from each group and at least 3 artists.

Here, we have to solve this problem, we can use the concept of combinations, which involves counting the ways to choose a specific number of items from a larger set without regard to the order of selection.

Given the conditions that at least one member must be chosen from each group (artists, singers, writers) and there must be at least 3 artists, we can break down the problem into cases.

Case 1: Choosing 1 artist, 1 singer, and 5 members from the remaining groups (writers).

Case 2: Choosing 2 artists, 1 singer, and 4 members from the remaining groups (writers).

Case 3: Choosing 3 artists, 1 singer, and 3 members from the remaining groups (writers).

For each case, we will calculate the number of ways to choose members and then sum up the results from all three cases to get the total number of ways.

Let's calculate the number of ways for each case:

Case 1:

Number of ways to choose 1 artist: 6C1 (6 ways)

Number of ways to choose 1 singer: 4C1 (4 ways)

Number of ways to choose 5 writers: 5C5 (1 way)

Total ways for case 1: 6C1 * 4C1 * 5C5 = 6 * 4 * 1 = 24

Case 2:

Number of ways to choose 2 artists: 6C2 (15 ways)

Number of ways to choose 1 singer: 4C1 (4 ways)

Number of ways to choose 4 writers: 5C4 (5 ways)

Total ways for case 2: 6C2 * 4C1 * 5C4 = 15 * 4 * 5 = 300

Case 3:

Number of ways to choose 3 artists: 6C3 (20 ways)

Number of ways to choose 1 singer: 4C1 (4 ways)

Number of ways to choose 3 writers: 5C3 (10 ways)

Total ways for case 3: 6C3 * 4C1 * 5C3 = 20 * 4 * 10 = 800

Now, add up the total ways from all three cases:

Total ways = 24 + 300 + 800 = 1124

So, there are 1124 ways to choose a committee of 7 members with at least one member from each group and at least 3 artists.

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The sum of the decimal fraction equation is:

seventy-six hundredths

The equation we are given is sixteen hundredths plus six-tenths

Now, when we talk about the decimal hundredths. Hundredths after decimal points shows 1/100th part of a whole. It represents the place value of the digit that occurs two places after the decimal.

Thus:

sixteen hundredths = 16/100

Similarly, six-tenths = 6/10

Thus:

The sum is:

16/100 + 6/10

= (16 + 60)/100

= 76/100 or seventy-six hundredths

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The solution to the system of equations is (15, 30).

A group of two or more equations that must be solved all at once is known as a system of equations. The system's equations each show how two or more variables relate to one another. The variables' values that satisfy every equation in the system can be discovered using algebraic techniques.

Algebraic systems of equations can be solved using a variety of techniques, such as substitution, elimination, and graphing. The substitution approach involves solving one equation for one variable in terms of the other variable, and then substituting the result for that variable's expression into the other equation.

The given system of equations are y=x + 15, y= 2x.

Substitute the value of y from equation 2 in equation 1:

x + 15 = 2x

15 = x

Substitute the value of x to get the value of y:

y = 2x = 2(15) = 30

Hence, the solution to the system of equations is (15, 30).

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there is no polygon that satisfies the given conditions.

Why it is and what is a Polygon?

Let the number of sides of the polygon be n.

We know that the sum of angles of an n-sided polygon is (n-2) × 180 degrees.

In this polygon, two angles are 100 degrees each, and the remaining (n-2) angles are 130 degrees each.

So, we can set up an equation:

2 × 100 + (n-2) × 130 = (n-2) × 180

Simplifying this equation, we get:

200 + 130n - 260 = 180n - 360

Solving for n, we get:

50n = 100

n = 2

However, a polygon with only 2 sides is not possible.

Therefore, there is no polygon that satisfies the given conditions.

A polygon is a 2-dimensional geometric figure that is formed by connecting a finite number of line segments to create a closed shape. These line segments are called sides of the polygon. The sides of a polygon only intersect at their endpoints, and the endpoints of each side are called vertices. A polygon with three sides is called a triangle, a polygon with four sides is called a quadrilateral, and a polygon with more than four sides is generally referred to by its number of sides (e.g. a pentagon has five sides, a hexagon has six sides, etc.).

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Answer:

  (A)  10e^(i7π/4)

Step-by-step explanation:

You want the exponential form of 5√2 -5i√2.

There are numerous ways a complex number can be written in "polar form".

The usual choices are ...

  a +bi . . . . . . . . . . . . . rectangular form

  A(cos(θ) +i·sin(θ)) . . . . a sort of hybrid form

  A·cis(θ) . . . . . . . . . . an abbreviation of the above

  A∠θ . . . . . . . . . . . . polar form

  A·e^(iθ) . . . . . . . . . using Euler's formula

The conversion from rectangular form to any of the others makes use of trig identities and the Pythagorean theorem.

  A = √(a² +b²)

  θ = arctan(b/a) . . . . . with attention to quadrant

For the given number, ...

  A = √((5√2)² +(-5√2)²) = (5√2)√(1 +1) = 5·2

  A = 10

  θ = arctan(-5√2/(5√2)) = -1 . . . in the 4th quadrant

  θ = 7π/4

Then the desired exponential form of the complex number is ...

  10e^(i7π/4)

__

Additional comment

Spreadsheets and some calculators have an ATAN2(x, y) function that performs a quadrant-sensitive angle conversion.

c. The mean of the random variable X is calculated as:

mean(X) = (-5)(1/4) + (0)(1/2) + (5)(1/4) = 0

The variance of X is calculated as:

var(X) = (-5 - 0)^2(1/4) + (0 - 0)^2(1/2) + (5 - 0)^2(1/4) = 25/2

d. The mean of the random variable X is calculated as:

mean(X) = (-5)(.01) + (0)(.98) + (5)(.01) = 0

The variance of X is calculated as:

var(X) = (-5 - 0)^2(.01) + (0 - 0)^2(.98) + (5 - 0)^2(.01) = 50.25

e. The mean of the random variable X is calculated as:

mean(X) = (-50)(.0001) + (0)(.9998) + (50)(.0001) = 0

The variance of X is calculated as:

var(X) = (-50 - 0)^2(.0001) + (0 - 0)^2(.9998) + (50 - 0)^2(.0001) = 500

g. The mean of the random variable X is calculated as:

mean(X) = (0)(1/2) + (2)(1/2) = 1

The variance of X is calculated as:

var(X) = (0 - 1)^2(1/2) + (2 - 1)^2(1/2) = 1

h. The mean of the random variable X is calculated as:

mean(X) = (.01)(.01) + (1.01)(.99) = 1

The variance of X is calculated as:

var(X) = (.01 - 1)^2(.01) + (1.01 - 1)^2(.99) = .098

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Option 1 with the discount and 4% simple interest has a total cost of $972, while Option 2 with no discount and no interest has a total cost of $1000. Option 1 is the better choice as it has a lower total cost.

Simple interest is a type of interest that is calculated on the original principal amount of a loan or investment. It is a fixed percentage of the principal amount that is paid by the borrower or earned by the lender over a specific period of time.

To compare the two options, we need to calculate the total cost of each option and compare them.

Option 1: 10% discount and pay off with 4% simple interest

The discount reduces the price of the television to $1000 x 0.9 = $900. If the customer chooses to pay it off at 4% simple interest, the total cost would be:

Total cost = $900 + ($900 x 0.04 x 3) = $972

Option 2: Full price and pay off in 3 years with no interest

The total cost of this option would be simply the full price of $1000 paid over 3 years, so:

Total cost = $1000 / 3 = $333.33 per year x 3 years = $1000

Comparing the two options, we see that Option 1 with the discount and 4% simple interest has a total cost of $972, while Option 2 with no discount and no interest has a total cost of $1000. Therefore, Option 1 is the better choice as it has a lower total cost.

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The complete question is: The store sells a television for $1000. customers can choose to receive 10% discount and pay it off at a simple interest rate of 4% or they can choose to pay the full price and pay it off in 3 years with no interest. which option is better?

Option 1 with the discount and 4% simple interest.

Option 2 with no discount and no interest.

Answer:

700

Step-by-step explanation:

28 % of n = 28/100 x n = 0.28n

If 28% of n = 196 that means

0.28n = 196

Divide both sides by 0.28

0.28n/0.28 = 196/0.28

n = 700

Answer:

Step-by-step explanation:

i assume the figure he needs to "make" is the turnover and not the marginal profit - no indication of the cost of the toys he sells is given so it is impossible to work out the marginal profit of the each toy sold. (Though how the toymaker worked out the turnover required without knowing the cost of the toy is beyond me - though that didn't stop British Leyland pricing their best selling Mini in the 1970s.)

In this case divide the income required by the price of each toy, but as the income must be at least the required amount, any fractional part of a toy must be rounded *UP* to the next whole number.

17,235 ÷ 45 = 383 (so no rounding is needed).

He needs to sell 383 toys (made at zero marginal cost).

The possible values of n are 1 and 2, as there can be two non-integer positive numbers whose product is equal to 12. Option B is correct.

All the possible ways to express 12 as a product of three positive numbers:

1 x 2 x 6

1 x 3 x 4

To identify which products have two non-integer factors.

From the above list, we see that only the first product, 1 x 2 x 6, has two non-integer factors (2 and 6).

From the  following complete list of the possible values of n if the product of 3 positive numbers is equal to 12 and 3 positive numbers of n are not integers then answer is option (b) 1, 2.

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We can also check this by graphing the function, which would show us the symmetry about the y-axis.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is associated with exactly one output. This means that for every value of the input, there is a unique corresponding value of the output.

by question.

To prove that a function is even, we need to show that it satisfies the property:

g(-x) = g(x) for all x in the domain of g.

So, let's substitute -x for x in g(x) and simplify:

g(-x) = 2[tex](-x)^{6}[/tex] - [tex](-x)^{2}[/tex] + 4

= 2[tex]x^{6}[/tex] -[tex]x^{2}[/tex] + 4

Notice that we obtained the same expression as g(x), which means that g(x) is even. Therefore, we can write:

g(x) = g(-x)

This means that the graph of the function is symmetric with respect to the y-axis, since for any value of x, the value of g(x) is the same as the value of g(-x).

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