You have a circular mirror. The mirror has a diameter of 8 inches. There is a circular frame around the mirror. If the mirror and frame together have a radius of 6 inches, what is the area of just the frame?

Answer:

f(g(2)) = 50

Step-by-step explanation:

evaluate g(2) then substitute the result obtained into f(x)

g(2) = 3(2) - 2 = 6 - 2 = 4 , then

f(4) = 2(4 + 1)² = 2(5)² = 2(25) = 50

Answer:

f[g(2)] = 50

Step-by-step explanation:

Given functions:

\(f(x)=2(x+1)^2\)

\(g(x)=3x-2\)

We are asked to determine f[g(2)], which is known as a composite function. When solving composite functions, you always work inside out.

Step 1: Find the value of g(2) by substituting 2 for x in function g(x).

\(\implies g(2)=3(2)-2\)

\(\\\implies g(2)=6-2\Rightarrow g(2)=\boxed{4}\)

Step 2: Substitute the found value into the composite function.

\(\\\implies f[g(2)]= 2(4+1)^2\)

\(\implies f[g(2)] = 2(5)^2 \Rightarrow 2(25) \Rightarrow \boxed{50}\)

Hence, the value of the composite function f[g(2)] is 50.

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Answer:

boron

particle 1

Step-by-step explanation:

boron is number 5 on the periodic table of elements.

mass - protons= neutrons

11(rounded up) - 5 = 6 neutrons

ions are when an atom is positively or negatively charged. for example electrons are higher than protons or vice versa.

Answer:

5, -25, 125, -625

Step-by-step explanation:

A geometric sequence is where a number is divided or multiplied by same number continuously

in the third option the number are multiplied by (-5) continuously

Según el método de diferenciales, el cambio aproximado del volumen del prisma es aproximadamente igual a 60 centímetros cúbicos.

Las diferenciales son una generalización del concepto matemático de cambio para funciones de una o más variables. Las versiones de una sola variable involucran derivadas ordinarias, mientras las versiones multivariables utilizan derivadas parciales.

El volumen del prisma es igual al producto del área de la base (A), en centímetros cuadrados, y la altura (h), en centímetros.

V(h, A) = h · A

El área de la base es igual al área de un cuadrado, es decir:

A(x) = x²

Donde x es la longitud del lado, en centímetros.

Según el enunciado, la altura del prisma es constante, mientras la longitud del lado de la base es una variable. En consecuencia, tenemos un diferencial que emplea derivadas ordinarias, esto es:

ΔV = (dV / dx) · Δx

V(x) = 15 · x²

dV / dx = 30 · x

Si sabemos que x = 10 cm y Δx = 0.02 cm, entonces el cambio en el volumen del prisma es:

ΔV = 30 · (10 cm)² · (0.02 cm)

ΔV = 60 cm³

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The angles that form linear pairs are ∠SRT and ∠TRU, and ∠VRW and ∠WRS. These pairs of angles are adjacent and their measures add up to 180 degrees, making them linear pairs.

To determine which angles are linear pairs, we need to identify pairs of adjacent angles whose measures add up to 180 degrees. Based on the given angles, ∠SRT and ∠TRU form a linear pair because they are adjacent and their measures add up to 180 degrees.

Similarly, ∠VRW and ∠WRS also form a linear pair because they are adjacent and their measures add up to 180 degrees. On the other hand, the remaining angle pairs, ∠SRT and ∠TRV, ∠VRU and ∠URS, and ∠URW and ∠WRS, do not meet the criteria for being linear pairs since their measures do not add up to 180 degrees.

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The coordinates of the reflected polygon F'G'H'I' are as follows:

F'(-2, -1), G'(5, -4), H'(8, -5), and I'(6, -2).

What is the reflection?

In mathematics, reflection is defined as the mirror image of a figure crossing a line (drawn or imagined), known as the line of reflection.

The vertices of the polygon FGHI are as follows:

F(2, -1)

G(5, 2)

H(8, 3)

I(6, 0)

To reflect the polygon FGHI across the line y = -1, we need to flip the points over the line.

Now we can reflect each of the points of the polygon across the line y = -1 to get the image:

F(2, -1) stays in the same place because it lies on the line of reflection.

G(5, 2) is reflected to G'(5, -4) by flipping it vertically across the line y = -1.

H(8, 3) is reflected to H'(8, -5), and

I(6, 0) is reflected to I'(6, -2).

Hence, The coordinates of the reflected polygon F'G'H'I' are as:

F'(-2, -1), G'(5, -4), H'(8, -5), and I'(6, -2).

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Complete question:

The complete question is attached in the image.

f(n) = ϴ(g(n)) is not true in cases B(sqrt(n)log(n), C(\(3^n 5^n\)), and D(sin(n)+3 cos(n)+1).

A) \(log(n^200) log(n^2)\)

Here, f(n) = \(log(n^200)\) and g(n) = \(log(n^2)\). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([log(n^200) / log(n^2)]\) = 100

This means that as n approaches infinity, the ratio f(n) / g(n) is constant, and so we can say that f(n) = ϴ(g(n)). Therefore, f(n) = ϴ(g(n)) is true in this case.

B) sqrt(n) log(n) Here, f(n) = sqrt(n) and g(n) = log(n). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sqrt(n) / log(n)]

As log(n) grows much slower than sqrt(n) as n approaches infinity, this limit approaches infinity. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

C) 3^n 5^n

Here, f(n) = \(3^n\) and g(n) = \(5^n\) . Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([3^n / 5^n]\)

As \(3^n\) grows much slower than \(5^n\) as n approaches infinity, this limit approaches zero. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

D) sin(n) + 3 cos(n) + 1

Here, f(n) = sin(n) + 3 and g(n) = cos(n) + 1. Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sin(n) + 3] / [cos(n) + 1]

As this limit oscillates between positive and negative infinity as n approaches infinity, we cannot say that f(n) = ϴ(g(n)) is true in this case.

Therefore, f(n) = ϴ(g(n)) is not true in cases B, C, and D.

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Answer:

A. 1.20x; individuals signing up the day of the activity get charged 20% more

Step-by-step explanation:

Amount charged before the day of activity = x

Amount charged on any individual who decides to sign up on the day of activity would be the normal price, x dollars, plus an additional price of 0.20x dollars.

0.20x = 20% of x.

That is, the additional fee added to the normal price is 20% of the normal price.

Therefore, amount paid on the day of the activity is x + 0.20x = 1.20x dollars.

What this fee means is that those who decide to sign up on the day of the activity are charged 20% more.

Answer:

28. C

29. D

30. C

Step-by-step explanation:

28.From the graph you can see that the height i.e f(x) was only increasing from 200 to 300 of x and 100 to 150 of f(x) and then continue to decrease. therefore we can then say f(x) is increasing when x is greater than or equal to 200 and when x is less than or equal to 300 i.e option C.

29. at x=500 f(x)=0

therefore at x= 500 f(x) was at it minimum

The Project Triangle is also known as the triple constraints model and consists of three elements: cost, time and scope.

The Project Triangle is also known as the Iron Triangle or Triple Constraints and is a graphical representation of the connection between project costs, schedule, and scope. It is one of the key principles of project management, and it is utilized to help organizations and project managers understand and handle trade-offs between different objectives of a project.

The three elements of the Project Triangle are:

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Answer:
X = 5
X = 1

Step-by-step explanation:

You have to do this:
x^2 - 6x +5 = 0
(x-1)(x-5) =0
X = 5
X = 1

Remember that the middle variable has to be added together, so -1 + (-5) = -6.

I hope this was able to help you out :D

Answer:

x = 5, x = 1

Step-by-step explanation:

We can first figure out what digits add to -6 and multiply to 5.

In this case, -5 and -1 will add to -6, and -5 times -1 will equal to 5.

Therefore, we can create this equation:

y = (x-5)(x-1)

Since the problem asks for the solutions, we need to set the equation equal to 0:

(x-5)(x-1) = 0

This will be set to two other equations:

(x-5) = 0

(x-1) = 0

We can solve these:

x = 5

x = 1

(Typically, we can use the diamond method and/or box method to solve these equations)

The result of this division is x + 7, and the remainder is 3x - 4. Therefore, we can write: x² + 6x - 4

How to divide given polynomials?

To divide the given polynomials, we will use long division. The first step is to divide the highest degree term of the numerator, which is x², by the highest degree term of the denominator, which is x:

      x

--------------

x - 1 | x² + 6x - 4

     | x² - 1x

     | -------

          7x - 4

The result of this division is x, and we write it above the long division bar. Then, we multiply the divisor x-1 by x, which gives us x² - x. We write this below the numerator, and subtract it from the numerator:

      x

--------------

x - 1 | x² + 6x - 4

     | x² - 1x

     | -------

          7x - 4

          ---------

               7x - 4

Now we bring down the next term of the numerator, which is -4, and repeat the process:

      x + 7

--------------

x - 1 | x² + 6x - 4

     | x² - 1x

     | -------

          7x - 4

          ---------

               3x - 4

The result of this division is x + 7, and the remainder is 3x - 4. Therefore, we can write:

x² + 6x - 4

x - 1 = x + 7 + (3x - 4)/(x - 1)

So, the answer is p(x) = x + 7 and k = 3. Therefore:

x² + 6x - 4

x - 1 = x + 7 + 3/(x - 1)

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Part a:  What quantity order size would minimize the total annual inventory cost? Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying Cost At minimum Total Annual Inventory Cost, the formula for the Economic Order Quantity (EOQ) is used. EOQ formula is given below: EOQ = sqrt((2DS)/H)Where, D = Annual DemandS = Ordering cost

The company should place an order for 168 boxes at a time in order to minimize the total annual inventory cost.Part b: Determine the minimum total annual inventory cost.Using the EOQ, the company can calculate the minimum total annual inventory cost. The Total Annual Inventory Cost formula is:Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying CostAnnual Ordering Cost = (D/EOQ) × S = (16,800/168) × $60 = $6,000Annual Carrying Cost = (EOQ/2) × H = (168/2) × $30 = $2,520Total Annual Inventory Cost = $6,000 + $2,520 = $8,520Therefore, the minimum Total Annual Inventory Cost would be $8,520.Part c: Would you recommend the manager to use your quantity from part (a) rather than 300 boxes? Justify your answer (by determining the total annual inventory cost for 300 boxes)

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The required answers are a) 17.1 km b) 7.1 km, c) 18.6 km away from town A on a bearing of 293°.

To solve this problem, we can use vector addition to find the displacement vector from town A to the cyclist's destination.

a) To find how far east the cyclist's destination is from town A, we need to find the east component of the displacement vector. We can break down the displacement vector into its north and east components using trigonometry:

\($$\text{East displacement} = 5\text{ km} + 10\text{ km}\cos(45^\circ) = 5\text{ km} + 10\text{ km}\frac{\sqrt{2}}{2} = 10\text{ km} + 5\sqrt{2}\text{ km} \approx 17.1\text{ km}$$\)

So the cyclist's destination is approximately 17.1 km east of town A.

b) Similarly, to find how far north the cyclist's destination is from town A, we need to find the north component of the displacement vector:

\($$\text{North displacement} = 10\text{ km}\sin(45^\circ) = 10\text{ km}\frac{\sqrt{2}}{2} = 5\sqrt{2}\text{ km} \approx 7.1\text{ km}$$\)

So the cyclist's destination is approximately 7.1 km north of town A.

c) To find the distance and bearing of the cyclist's destination from town A, we can use the Pythagorean theorem and trigonometry. The displacement vector is the hypotenuse of a right triangle with legs of length 17.1 km and 7.1 km, so its length is:

\($$\text{Displacement} = \sqrt{(17.1\text{ km})^2 + (7.1\text{ km})^2} \approx 18.6\text{ km}$$\)

To find the bearing of the displacement vector, we can use the inverse tangent function:

\($$\text{Bearing} = \tan^{-1}\left(\frac{\text{East displacement}}{\text{North displacement}}\right) \approx 67^\circ$$\)

However, this angle is measured clockwise from north, so we need to subtract it from 360° to get the bearing measured counterclockwise from north:

\($$\text{Bearing} = 360^\circ - 67^\circ = 293^\circ$$\)

So the cyclist's destination is approximately 18.6 km away from town A on a bearing of 293°.

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Answer:

i am pretty sure the answer is a. 6

Step-by-step explanation:

let me know if this is incorrect

Answer:

A. 6

Step-by-step explanation:

Yes, it is likely that a random sample mean could deviate that much from a population mean.

To test whether the sample mean of 112 is significantly different from the population mean of 113.5, we can use a one-sample t-test. With 12 degrees of freedom (n-1), the critical value for a two-tailed test at a 5% significance level is ±2.179.

Using the formula t = (\(\bar{X}\) - μ) / (s / √n), where \(\bar{X}\) is the sample mean, μ is the population mean, s is the standard deviation, and n is the sample size, we get: t = (112 - 113.5) / (15 / √13) = -1.01

Since |-1.01| < 2.179, we fail to reject the null hypothesis that the sample mean is not significantly different from the population mean. Therefore, it is likely that this sample could be a random sample from a population with a mean of 113.5.

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Answer:

6/23

Step-by-step explanation:

The percentage by which the price of the car went up from the original price is 60% (third option)

The first step is to determine the price of the car after the percentage increase. Percentage is the fraction of a number as a value out of 100. The sign that is used to represent percentage is %.

Price of the car after the percentage increase = (1 + percent increase/100) x original cost of the car

Price of the car after the percentage increase = (1 + 20/100) x 20,000

Price of the car after the percentage increase = (1 + 0.2) x 20,000

Price of the car after the percentage increase = 1.2 x 20,000 = $24,000

Price after the $8,000 increase = $24,000 + 8,000 = $32,000

Percentage of the original price = (32,000 / 20,000) - 1 = 0.60 = 60%

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Based on the t-test assuming equal variances a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal."

It is vital to establish whether or not the variances of the two groups being compared are indeed identical before performing a t-test under the assumption of equal variances. This is significant since the t-calculation statistic depends on the assumption that variances are equal.

One can look at the ratio of the variances between the two groups to evaluate the assumption of equal variances. Typically, it is acceptable to infer that the variances are not equal if the ratio of the variances is more than two or lower than half. One can presume that the variances are equal in the absence of such proof. Since the variances are not equal, it is not logical to infer that they are.

Complete and correct Question:

Based on the t-test assuming equal variances on the T-Test Equal worksheet, is it reasonable to assume that the variances are equal?
a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal.
b. Whether the variances are equal or not is not relevant for this situation.
c. Examining the ratio of the variances, it is reasonable to conclude that the variances are equal.
d. It is impossible to determine if the variances are equal given the data we have.

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Answer:

Angle x is 40 degrees

Angle 2x is 80 degrees

Angle x + 20 is 60 degrees

Step-by-step explanation:

First, you should know that all three angles of a triangle add up to 180, so you can set up an equation like so:

x + 2x + x + 20 = 180

Combine like terms:

( x + 2x + x ) + 20 = 180

4x + 20 = 180

Subtract 20 from each side:

4x = 160

Divide each side by 4:

x = 40

Then Substitute in to find each angle:

x

40

-------------------

2x

2 ( 40 ) = 80

-------------------

x + 20

40 + 20 = 60

The equation of g(x) include the following: D. g(x) = 4x² + 2

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) - N

In this context, we can logically deduce that the parent function f(x) = x² was translated 2 units up and vertically stretched by 4 units in order to produce the graph of the image g(x), we have:

g(x) = 4f(x) + 2

g(x) = 4x² + 2

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Answer:

36 inch = 3 feets

72 inch = 6 feets

144 inch = 12 feets

Step-by-step explanation:

Answer:

The length would have to be 9, and the width 1

Step-by-step explanation:

l*W 9*1=9

Answer:

c - (2x)^1/3-7

Step-by-step explanation:

plato

The function  \(y= -x^{1/2}+5\) has a domain of all real numbers.

Thus, option (D) is correct.

As, Domain is the input value of the function.

In the function \(y= -x^{1/2}+5\) .

The square root is defined for all non-negative real numbers (including zero).

When we subtract this square root from 5, the resulting function has a domain of all real numbers.

In options A, B, and C, which involve fractional exponents or roots, option D does not have any restrictions on the values of x.

The function can be evaluated for any real number x, making its domain all real numbers.

Therefore, \(y= -x^{1/2}+5\) , has a domain of all real numbers.

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Answer: 6/25

Step-by-step explanation:

Number of vowels = 8

Number of consonants = 12

Total number of tiles in bag = (number of vowels + number of consonants)

Total = (12 + 8) = 20

Probability = (required outcomes / total possible outcome)

Probability of choosing a consonants = (number of consonants / total number of word tiles)

P( consonants) = 12 / 20 = 3/5

Since it is with replacement, total number of word tiles will still be 20

Probability of choosing a vowel = (number of vowels / total number of word tiles)

P( vowels) = 8 / 20 = 2/5

Therefore,

P(constant then vowel) = 3/5 * 2/5 = 6/25

Given statement solution is:- The function y = √(x + 3) - 2 with at least four integer points on the axes.

To plot points and graph the function y = √(x + 3) - 2, we can utilize technology tools such as graphing calculators or online graphing tools. I'll demonstrate how to use an online graphing tool called Desmos, which is user-friendly and widely accessible.

Please follow these steps to plot the points and graph the function:

Visit the Desmos website or use any other graphing tool of your choice.

Clear any existing equations or plots on the graph.

Enter the function y = sqrt(x + 3) - 2 into the equation field.

The graphing tool will automatically plot the function.

To plot integer points, simply choose four different integer values for x and calculate the corresponding y values.

Let's choose the following integer values for x: -3, -2, 0, and 2.

Calculate the corresponding y values:

For x = -3: y = sqrt(-3 + 3) - 2 = -2

For x = -2: y = sqrt(-2 + 3) - 2 = -1

For x = 0: y = sqrt(0 + 3) - 2 = 1

For x = 2: y = sqrt(2 + 3) - 2 = 0

Plot these points on the graph by clicking on the appropriate locations.

If you accidentally click on a point and want to delete it, simply click on the point again to remove it.

Make sure the graph displays the axes and all the plotted points.

By following these steps, you should be able to plot the points and graph the function y = √(x + 3) - 2 with at least four integer points on the axes.

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Answer:

20,315.00

Step-by-step explanation:

hope this helps not sure if right though

don't put my answer I'm so confused sorry.

The amount that will be in his account after 72 months is $15487.5.

We have given that,

Principal = $15,000

Amount = Principal + Interest

Principal = $15,000

Get the interest

Interest = PRT/100

Interest = 15000*13/4 * 3/100 (72months = 3years)

Interest = 195000/400

Interest = $487.5

Amount = 15000 + 487.5

Amount= $15487.5

Hence he will have $15.

Therefore, The amount will be in his account after 72 months.

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Answer:

f(-12) = -13

Step-by-step explanation:

f(x) = x - 1

Let x = -12

f(-12) = -12-1

       = -13

Answer:

\(f(x) = x - 1 \\ f( - 12) = - 12 - 1 \\ \boxed{ f( - 12) = - 13}\)

It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.

The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.

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The difference between the given values of |-10| and 19 is - 9

What is an algebraic expression ?

Algebraic expression can be defined as the combination of variables , constants and exponents .

Algebraic expressions are the idea of expressing numbers the use of letters or alphabets with out specifying their actual values. The fundamentals of algebra taught us the way to explicit an unknown value the use of letters such as x, y, z, and so on. these letters are called here as variables. An algebraic expression may be a aggregate of both variables and constants. Any cost this is placed before and extended by way of a variable is a coefficient.

Given values ,

|-10| and 19

the difference ,

|-10| - 19 = 10-19

= -9

Hence, The difference between the given values of |-10| and 19 is - 9

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