The number of acres of wetland infested by an invasive plant species after t Years is given by u(t)=12•2^t/3. Solve the equation u(t)=50. What does your answer tell you about the wetland?

The commutative property in mathematics says that the order in which numbers are multiplied doesn't change the product. For example, using the commutative property, the product of 13 x 7 x 21 will be the same as 7 x 21 x 13, which is 1911.

The commutative property is a fundamental concept in Mathematics which states that for multiplication and addition, numbers can be moved around (or commuted) without changing the result. For example, if you have the multiplication problem 13 * 7 * 21, thanks to the commutative property, you can rearrange this problem to: 7 * 21 * 13 or 21 * 13 * 7 or any other arrangement of these three numbers, and the result will remain the same.

Let’s see this in action:
Original arrangement: 13 * 7 * 21 = 1911
Changed arrangement: 7 * 21 * 13 = 1911
As you can see, regardless of how the terms were rearranged, the answer remained the same, thus demonstrating the commutative property.

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Option: C is the correct answer.

    C     The mean will increase, and the median will stay the same.

We know that the mean of scores is the average value of the scores of  the score obtained by 4 friends.

i.e. it is the ratio of sum of scores of 4 friends to the total number of person i.e. 4.

Hence, if the score of any of the person will increase then the mean will also increase

( Since, the denominator remains the same and the numerator is increasing so , the resultant value will increase )

Also, we know that the median of the score lie between the data set, i.e. the change in the score of the last score won't affect the median :

Since, here we have  4 data points and the median lie between the 2nd and 3rd data point so change in the 4th data point won't affect the median.

Hence, increasing Adam's high score affect the mean and median as:

Mean will increase and Median remains the same.

The mean and median will increase as Adam's high score rises, while the median will remain unchanged. Then the correct option is C.

Mean is simply defined as the average of the given set of numbers. The mean is considered one of the measures of central tendencies in statistics.

The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.

A group of 4 friends likes to bowl together, and each friend keeps track of his all-time highest score in a single game.

Their high scores are all between 180 and 220, except for Adam, whose high score is 250.

Adam then bowls a great game and has a new high score of 290.

If any of the individuals' scores improve, the mean will improve as well.

We also observe that the median of the scoring lies inside the data set, implying that a change in the last score will have no effect on the median.

Because we have four data sets and the median is between the second and third, a change in the fourth data point will have no effect on the median.

More about the mean and the median link is given below.

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To solve the equation 8/x + 1/5 = 3/x, we multiply the entire equation by 5x to get rid of the fractions to get 40 + x = 15. Solving for x we get x = -25.

To solve the given rational equation 8/x + 1/5 = 3/x, we first need to find a common denominator to combine the fractions. Hence, we multiply the entire equation by 5x to get rid of the denominators:

5 * 8 + x = 15

which simplifies to

40 + x = 15.

Then by subtracting 40 from both sides to solve for x, we get:

x = -25.

That is the solution to the rational equation.

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The rational equation 8/x + 1/5 = 3/x is solved by finding a common denominator, simplifying the equation and then factoring the resulting polynomial to find the roots.

To solve the given rational equation 8/x + 1/5 = 3/x, we first find a common denominator for the fractions. Seeing x and 5, we can take the common denominator as 5x.

Next, we rewrite each term with the common denominator: (40/5x) + (x/5x) = (15/5x). This simplifies to 40/5x + x/5x - 15/5x = 0. Simplifying further we have 8/x - 3/x + 1/5 = 0.

After setting the equation to zero, one may notice that this equation can be solved by bringing the terms together and then trying to factorize the resulting polynomial. The solution of the equation are the roots of the factored polynomial.

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The woman's new office has twice the area of her current office. By calculating the side length of the current square office from the perimeter and then finding the area, we determine the new office's area to be 968 square feet.

The question asks about calculating the area of a larger office which is twice the area of the woman's current office. Knowing the current office perimeter allows us to find the side length of the current square office and use it to calculate the area of both the current and the new office.

The area of the new, larger office is 968 ft².

To determine if a formula represents a length, area, or volume, consider the units used in the formula.

When determining if a formula represents a length, area, or volume, you need to consider the units used in the formula. Length is typically measured in units such as meters or feet. Area is measured in square units, such as square meters or square feet. Volume is measured in cubic units, such as cubic meters or cubic feet.

For example, suppose you have a formula that involves only one variable and it includes units such as meters. This formula would most likely represent a length. If the formula involves two variables and includes units like square meters, then it represents an area. And if the formula involves three variables and includes units like cubic meters, then it represents a volume.

It's important to pay attention to the units to determine whether a formula represents a length, area, or volume.

Answer:

vertex (  [tex]\frac{1}{7}[/tex], [tex]\frac{131}{7}[/tex]).

Step-by-step explanation:

Given : The equation of a parabola is given.

       y=−14x²+4x−19

To find  : What are the coordinates of the vertex of the parabola.

Solution : We have given that

y = −14x²+4x−19

we will be "completing the square" .

Factor out -14 to make leading coefficient 1

y = -14 ([tex]x^{2} -\frac{2x}{7} +\frac{19}{14}[/tex])

Add and subtract [tex](\frac{-1}{7}) ^{2}[/tex]

y = -14 ([tex]x^{2} -\frac{2x}{7} +\frac{19}{14}+\frac{-1}{7}) ^{2} - (\frac{-1}{7})^{2})[/tex] .

Complete the square

y = -14 ( [tex](x -\frac{1}{7}) ^{2} +\frac{19}{14}- (\frac{-1}{7})^{2})[/tex].

y = -14 ( [tex](x-\frac{1}{7}) ^{2} -\frac{131}{7}[/tex]

Standard form of parabola vertex form y  = a(x - h)²+ k,

Where, ( h, k)  are vertex

On comparing a = -14 , h= [tex]\frac{1}{7}[/tex], k =  [tex]\frac{131}{7}[/tex]

Therefore, vertex (  [tex]\frac{1}{7}[/tex], [tex]\frac{131}{7}[/tex]).

Volume is a three-dimensional scalar quantity. The volume of the trash can is 62.8318 ft³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the trash can = π×r²h = π×(2ft)²×(5ft) = 62.8318 ft³

Hence, the volume of the trash can is 62.8318 ft³.

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Answer:

Part A : 2 snacks

Part B : Solution to both the inequality and the problem situation ⇒ 1 , 2

             Solution to the inequality only ⇒ -4 , 3/4 , 2.3

             Not a solution ⇒ 2.5

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Step-by-step explanation:

Part A :

Janelle  has $20 to spend

She spends $8 on a ticket, so , the remaining = 20 - 8 = $12

Each snack costs $4.99

So, the number of snacks =

the integer of ( 12 / 4.99 ) = integer of (2.4) = 2 snacks

Part B:

Inequality that represents this situation: 20 ≥ 8 + 4.99x

Solve for x

∴ 20 - 8 ≥ 4.99 x

12 ≥ 4.99 x

divide both sides by 4.99

∴ (12/4.99) ≥ x

∴ x ≤ 2.4048

The given options are : -4 , 3/4 , 2.3 , 2.5 , 1 , 2

So,

Solution to both the inequality and the problem situation ⇒ 1 , 2

solution to the inequality only ⇒ -4 , 3/4 , 2.3

Not a solution ⇒ 2.5

Answer:

Solutions to Both:

1

2

Solutions to the Inequality Only;

3/4

-4

2.3

Not a Solution:

2.5

Step-by-step explanation: