Find the inverse function.
f(x) =
f-¹(x) =
=
=
2x+5
4
4x + [?]
[

Step-by-step explanation:

When f(x) = g(x), x^4 - 8x^2 = 8x^2.

x^4 - 16x^2 = 0

x^2(x^2 - 16) = 0.

Either x^2 = 0 or x^2 = 16.

The possible values of x are {-4, 0, 4}.

The values of x for which f(x) = g(x) will be {-4, 0, 4}.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division

Given expression is f(x) = x⁴ – 8x², g(x) = 8x²

The value of x will be calculated as:-

When f(x) = g(x), x⁴ - 8x² = 8x².

x⁴ - 16x² = 0

x²(x² - 16) = 0.

Either x² = 0 or x² = 16.

The possible values of x are {-4, 0, 4}.

Therefore, the values of x for which f(x) = g(x) will be {-4, 0, 4}.

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Answer:

Drag and drop 6(2x-1) to 12x-6.

Drag and drop 6(4x-2) to Neither.

Drag and drop 3(8x+4) to 24x+12.

Drag and drop 6(4x+2) to 24x+12.

Drag and drop 2(6x-3) to 12x-6.

Step-by-step explanation:

To check these, use distributive property to solve each one.

6(2x-1) = 12x-6

6(4x-2) = 24x-12

3(8x+4) = 24x+12

6(4x+2) = 24x+12

2(6x-3) = 12x-6

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Answer:

The distance around the circle.

Step-by-step explanation:

Circumference means the outer area of a particular object or the outer border of the object. When we talk about the circle, the total outer round area is the circumference of the circle.
The formula for circle circumference is 2pir

where pi = 3.14 approx  and the r = radius of the circle

Hence, the answer is the distance around the circle.

Answer:

3\(\sqrt{5}\)

Step-by-step explanation:

Calculate the distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (- 1, 1)

d = \(\sqrt{(-1-5)^2+(1-4)^2}\)

   = \(\sqrt{(-6)^2+(-3)^2}\)

   = \(\sqrt{36+9}\)

   = \(\sqrt{45}\)

   = 3\(\sqrt{5}\) ← exact value

   ≈ 6.71 ( to 2 dec. places )

Answer:

x would be 41°

Step-by-step explanation:

Answer:

c) trinomial

Step-by-step explanation:

terms are separated by '+' or '-' signs

Answer:

Step-by-step explanation:

The shape of the distribution of the number of siblings can vary depending on the specific data set.

However, if we are considering the general case, the most common shape of the distribution is likely to be unimodal and skewed to the right.

This means that the majority of individuals are likely to have fewer siblings,

and as the number of siblings increases,

the frequency of individuals with that number decreases.

The distribution may also have a long tail on the right side,

indicating a few individuals with a significantly larger number of siblings.

However, it is important to note that this is just a general observation, and in specific cases,

the distribution may be different.

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Using the master theorem, the Θ-class are: a) T(n) = Θ(n)b) T(n) = Θ(n) and c) T(n) = Θ(√n log n).

a) T(n)=2T(n/2)+n³

To find the Θ class of T(n), we need to apply the Master Theorem. In the Master Theorem, if T(n) = aT(n/b) + f(n) where a >= 1, b > 1, and f(n) is an asymptotically positive function, then:

T(n) = Θ(nᵈ)

where d = logₐ(b).

Here a = 2, b = 2 and f(n) = n³.

So, d = log₂(2)

= 1T(n)

= Θ(nᵈ)

= Θ(n¹)

= Θ(n)

Therefore, the Θ class of T(n) is Θ(n).

b) T(n)=2T(n/2)+3n−2

Similarly to part (a), we can find the Θ class of T(n) by using the Master Theorem.

In this case, a = 2, b = 2 and f(n) = 3n - 2.

Here, d = log₂(2)

= 1T(n)

= Θ(nᵈ)

= Θ(n¹)

= Θ(n)

Therefore, the Θ class of T(n) is Θ(n).

c) T(n)=4T(n/2)+nlogn

For this recurrence relation, a = 4, b = 2 and f(n) = nlogn.

In this case, d = log₄(2) = 0.5.

So,

T(n) is

= Θ(nᵈ)

= Θ(n⁰.⁵)

= Θ(√n log n)

Therefore, the Θ class of T(n) is Θ(√n log n).

Hence, the correct options are:a) T(n) = Θ(n)b) T(n) = Θ(n)c) T(n) = Θ(√n log n).

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. A bigger random sample should be used in order to ensure that the findings are more accurate representations of all players in the league.

Given the weights in pounds of 11 players randomly selected from the roster of a championship sports team are as follows:

238 204 229 193 298 248 205 280 204 266 266,

The results are not likely to be representative of all players in that sport's league.

This is because the sample size is too small to represent the entire population.

In general, a larger sample size provides a more accurate representation of the population.

In order for the results to be more representative of all players in the league, a larger random sample should be taken.

A bigger sample size typically yields a more accurate depiction of the population

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Al-Khwarizmi made significant contributions to the world of mathematics, particularly in the field of algebra. His major accomplishment was the development of algebra as an independent mathematical discipline.

Al-Khwarizmi, a Persian mathematician and scholar, wrote the book titled "Kitab al-Jabr wal-Muqabala," which laid the foundation for modern algebra. In this influential work, he introduced systematic methods for solving linear and quadratic equations. Al-Khwarizmi's algebraic techniques, including the use of variables and equations, greatly advanced mathematical understanding and problem-solving. His work also contributed to the development of algorithms and mathematical notation, such as the concept of the "zero" and the decimal system. Overall, al-Khwarizmi's contributions revolutionized mathematics and had a profound impact on subsequent generations of mathematicians and scientists.

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Answer:

the value of 2 in 0.812 is 2 thousandths/0.002

0.002 = 2/1000

0.812 = 812/1000

The circumference of the wheel of cheese is approximately 56.52 inches.

To calculate the circumference of a wheel of cheese, you need to know its radius.

The radius is the distance from the center of the wheel to its outer edge. In this case, the radius of the wheel is given as 9 inches.

The formula for the circumference of a circle is:

Circumference = 2π x radius

In the formula, "π" represents the mathematical constant pi, which is approximately equal to 3.14.

Let's substitute the given values into the formula:

Circumference = 2 x 3.14 x 9

Calculating this expression, we get:

Circumference = 56.52 inches

Therefore, the circumference of the wheel of cheese is approximately 56.52 inches.

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Answer:

Step-by-step explanation:

\(a_1=9\\ \\ a_n=-2a_{n-1}\\ \\ a_n=9(-2^{(n-1)})\\ \\ a_4=9(-2^{(4-1)})\\ \\ a_4=9(-2)^3\\ \\ a_4=9(-8)\\ \\ a_4=-72\)

Answer:

A

Step-by-step explanation:

You Welcome

A)  The conditional relative frequency of a student who plans to live at home, given that they plan to attend college is; 53.85%

B) Yes,  there is an association between attending college and living at home.

A conditional relative frequency is calculated by dividing a frequency that is not in the Total row or the Total column by the frequency's row total or column total.

A) From the definition above, the conditional relative frequency of a student who plans to live at home, given that they plan to attend college is; 35%/65% = 7/13 = 53.85%

B) Yes there is an association between attending college and living at home because the percentage of students who plans to live at home, given that they plan to attend college over half of those is more than 50%.

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Hi, I believe this should be correct. The way the boxes are phrased is very misleading.

Answer:

x = 38

Step-by-step explanation:

Now,

Answer:

-1/3

Step-by-step explanation:

multiply across

1/2 * -2/3

-2/6

-1/3

Answer: boat

Step-by-step explanation: the farthest it can go is weeks

Step-by-step explanation:

Here,

| −34 |

= 34

As,

| | are absolute symbols so it's denote only the neutral number such as, | - 1 | = 1

Answer:

34

Step-by-step explanation:

|-34|

The absolute value bars means taking the non-negative value

|-34| = 34

Answer:

x ≈ - 5.83 , x ≈ - 0.17

Step-by-step explanation:

x² + 6x + 1 = 0 ( subtract 1 from both sides )

x² + 6x = - 1

Using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(3)x + 9 = - 1 + 9

(x + 3)² = 8 ( take square root of both sides )

x + 3 = ± \(\sqrt{8}\) ( subtract 3 from both sides )

x = - 3 ± \(\sqrt{8}\)

Then

x = - 3 - \(\sqrt{8}\) ≈ - 5.83 ( to 2 dec. places )

x = - 3 + \(\sqrt{8}\) ≈ - 0.17 ( to 2 dec. places )

Given the expression

Use the facts that

So, the expression can be simplified as:

Answer:

32º

Step-by-step explanation:

Solve for sin(x). Then use inverse sine to get your angle measurement. From there, convert radians to degrees by multiplying by 180/π.

sin (x) = opp/hyp = 8/15

sin-1(8/15) = x = 0.56253 radians

0.56253 radians * 180/π = 32.23º

Round this to 32º

The ratio of the number of children to the number of adults in this group is 19:2 or 19/2.

Let the number of children in the group be x, and the number of adults be y.

Since the admission fee is $4 for children and $6 for adults, we can write two equations as follows:

x + y = 21 - - - - - - - - (1)4x + 6y = 900 - - - - - - - - (2)

Solving these equations, we get:x = 9y

Substituting this value in the equation (1), we get:

9y + y = 2110y = 21y = 2.1So, the number of adults in the group is y = 2.1, and the number of children is x = 9y = 9(2.1) = 18.9 (rounded off to 19).

Therefore, the ratio of the number of children to the number of adults in this group is 19:2 or 19/2.

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The profit function of the company is given by P(x)=-4x^3 + 32x^2 - 64, where x is the number of toys sold in hundreds, and P(x) is the profit in thousands of dollars.

The key features of the graph of the profit function are the following:

The degree of the polynomial function is 3, which means that the graph is a cubic curve.

The coefficient of the leading term is negative (-4), which means that the graph opens downwards.

The coefficient of the quadratic term is positive (32), which means that the graph is concave up.

The y-intercept of the graph is -64, which means that the company will incur a loss of $64,000 if it does not sell any toys.

It should be noted that to find the maximum profit, we need to evaluate the profit function at x = 5.33:

P(5.33) = -4(5.33)^3 + 32(5.33)^2 - 64 = 23.78

Therefore, the maximum profit that the company can make is $23,780.

In summary, the graph of the profit function reveals that the company will incur a loss if it does not sell any toys, but it can make a profit if it sells at least some toys. The profit function has a cubic shape that opens downwards, indicating that the profit decreases as the number of toys sold increases beyond a certain point. The maximum profit occurs at x = 5.33, where the profit is $23,780.

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Mixed methods research tends to be more complex when compared to quantitative and qualitative research respectively. This is because mixed methods research combines both quantitative and qualitative research methods in a single study.

Quantitative research involves the collection and analysis of numerical data, while qualitative research involves the collection and analysis of non-numerical data, such as words, images, and sounds.

Mixed methods research, on the other hand, involves the collection and analysis of both types of data. This requires the researcher to have a deeper understanding of both quantitative and qualitative research methods, as well as the ability to integrate the two types of data in a meaningful way.

Furthermore, mixed methods research often involves the use of multiple data sources, multiple research methods, and multiple levels of analysis. This adds an additional layer of complexity to the research process.

As a result, mixed methods research tends to be more complex than either quantitative or qualitative research alone.

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There are 12 players of right handed, according to the question.

What do you mean by percentage?

A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.

According to data in the given question,

We have given data:

A local little league has a total of 60 players of whom 20% are right-handed.

Let x be the total number of players that are right-handed.

The value of x can be found as follow:

x = 20% of 60

x = (20/100)60

x = 0.2(60)

x = 12

Therefore, the total number of players that are right-handed is 12, if the local little league has a total of 60 players of whom 20% are right-handed.

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Answer:

30

Step-by-step explanation:

hope i gave you the right awnser!!! god bless!!!

Answer:

Check pdf

Step-by-step explanation: