find the maximum and minimum values of y=1/3x^3 + x^2 -3x

The number of marbles of each color is 2/3.

Tessa puts 50 marbles in a bag. The number of marbles of each color is shown in the table below.

The probability that an event will occur is determined by probability: P(A) = f / N. Probability and odds are connected, but probability determines what the odds are. Probability is required before calculating the likelihood of an occurrence.

P(blue)=10 / 3 = 50 /15, meaning there are 15 blue marbles.

P(yellow)= 2 / 1 = 50 / 25 meaning that there are 25 yellow marbles.

10 black marbles are present.

P(black)=50 /10 = 5 and P(white)= 0

15 / 20 = 2/3.

The number of marbles of each color is 2/3.

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Answer:

x = 23

Step-by-step explanation:

let's square both sides. that eliminates the individual square roots and creates one central term with square roots :

2x + 3 + x + 2 - 2 sqrt(2x + 3)×sqrt(x + 2) = 4

3x + 5 - 2×sqrt((2x + 3)(x + 2)) = 4

3x + 1 - 2×sqrt(2x² + 4x + 3x + 6) = 0

3x + 1 - 2×sqrt(2x² + 7x + 6) = 0

3x + 1 = 2×sqrt(2x² + 7x + 6)

now let's square both sides again

9x² + 6x + 1 = 4(2x² + 7x + 6) = 8x² + 28x + 24

x² - 22x - 23 = 0

a quadratic equation

ax²x+ bx + c = 0

has 2 solutions

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (22 ± sqrt((-22)² - 4×1×-23))/(2×1) =

= (22 ± sqrt(484 + 92))/2 =

= (22 ± sqrt(576))/2 = (22 ± 24)/2 =

= 11 ± 12

x1 = 11 + 12 = 23

x2 = 11 - 12 = -1

since we squared twice in the process, and every solution to a square is a ±sqrt (so, 2 solutions with alternating signs), we need to try both solutions in the original equation to see which ones really fulfill it.

sqrt(2×23 + 3) - sqrt(23 + 2) = 2

sqrt(46 + 3) - sqrt(25) = 2

sqrt(49) - 5 = 2

7 - 5 = 2

correct, x = 23 is a valid solution.

sqrt(2×-1 + 3) - sqrt(-1 + 2) = 2

sqrt(-2 + 3) - sqrt(1) = 2

sqrt(1) - 1 = 2

1 - 1 = 2

wrong. so, x = -1 is not a valid solution to the original equation.

Answer: Option a:   y = 4 + 6x

Step-by-step explanation:

y√y i.e Option (B) is  equivalent to the expression below when y> 0.

Equivalent means that two things have the same value, meaning, or measure. For example, 2 + 2 and 4 + 0 are equivalent equations because both equal 4. Another example is 1/2 and 0.5, which are equivalent because they are both equal to one-half.Equivalent in mathematics refers to two expressions that have the same value or the same outcome when evaluated.

Equivalent means having the same value, measure, or effect as something else. For example, two dollars is equivalent to two euros.

Let's start with the expression:

√[tex]y^{3}[/tex]+√[tex]16y^{3}[/tex]-[tex]4y[/tex]√[tex]y[/tex]

where y > 0. (this allow us to have y inside a square root, so we don't mess with complex numbers).

We want to find the equivalent expression to this one.

Here, we can do the next two simplifications:

√[tex]16y^{3}[/tex] = √[tex]16[/tex] √[tex]y^{3}[/tex] = [tex]4[/tex]√[tex]y^{3}[/tex]

And

[tex]y[/tex]√[tex]y[/tex] = √[tex](y^{2}. y)[/tex]= √[tex]y^{3}[/tex]

If we apply these two to our initial expression, we can rewrite it as:

√[tex]y^{3}[/tex]+√[tex]16y^{3}[/tex]-[tex]4y[/tex]√[tex]y[/tex]

√[tex]y^{3}[/tex] + [tex]4[/tex]√[tex]y^{3}[/tex]-[tex]4[/tex]√[tex]y^{3}[/tex] = √[tex]y^{3}[/tex]=[tex]y[/tex]√[tex]y[/tex]

Therefore, Option (B) is correct.

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The ordered pair that Cam identified is given as follows:

(8,4).

The general format of an ordered pair is given as follows:

(x,y).

For the x-coordinate, we have that:

The point in this problem was 8 units right, hence the x-coordinate is given as follows:

x = 8.

For the y-coordinate, we have that:

The point in this problem is 4 units above the origin, hence the y-coordinate is given as follows:

y = 4.

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The ogive curve for the data has to be obtained by first converting the data into a continuous class one and then plotting the less than cumulative frequency table obtained.

Here we have the data

0-3.9    4.0-7.9    8.0-11.9    12.0-15.9    16.0-19.9    20.0-23.9    24.0-27.9

  63          26          24              37                23               11                  16

Now first we need to convert this to a continuous distribution

We will get

Classes                  Frequency

-0.95-3.95                   63  

3.95-7.95                     26

7.95-11.95                     24

11.95-15.95                    37

15.95-19.95                   23

19.95-23.95                    11

24.0-27.95                     16

Now we need to construct a less than table

Less than                           Cumulative frequency

3.95                                                    63  

7.95                                                    89

11.95                                                   113

15.95                                                 150

19.95                                                 173

23.95                                                 184

27.95                                                200

Now to make an Ogive curve we need to plot the less than column at the x-axis and the frequency on the y-axis. Then draw a free hand line to connect all the points. This will give us our ogive curve

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Complete Question

A sample of 200 high school students was asked how many hours per week they spend watching television. The following frequency distribution presents the results.

0-3.9    4.0-7.9    8.0-11.9    12.0-15.9    16.0-19.9    20.0-23.9    24.0-27.9

  63          26          24              37                23               11                  16

Construct a relative frequency ogive for the frequency distribution.

Answer:

[tex]4\sqrt{6}[/tex]

Step-by-step explanation:

[tex]\sqrt{96}=\sqrt{(6)(16)}\sqrt{6}\sqrt{16}=4\sqrt{6}[/tex]

Answer:

[tex]-i^{2}[/tex] + 25

Step-by-step explanation:

(5-i)(5 + i)

25 + 5i - 5i - [tex]i^{2}[/tex]

25 [tex]-i^{2}[/tex]

The value of x is 5 and the value of y is 6.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two equations are y=2x-4 and y=x+1. The two equations can be solved as below,

y=2x-4 and y=x+1, Equate both the equations and solve for the value of x,

2x-4 =x+1

2x - x = 4 + 1

x =5

y=x+1

y = 5 + 1 = 6

Hence, the value of x is 5 and the value of y is 6.

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Approximating to the nearest degree, θ = arccos(cosθ) ≈ 35°.

The angle between two vectors can be found using the dot product formula:

cosθ = (a⋅b)/(||a|| ||b||)

where ||a|| is the magnitude of vector a, and ||b|| is the magnitude of vector b.

First, let's find the magnitude of the vectors:

||a|| = √(4^2 + (-3)^2 + 1^2) = √(16 + 9 + 1) = √26

||b|| = √(2^2 + 0^2 + (-1)^2) = √5

Next, let's find the dot product of the vectors:

a⋅b = (4i−3j+k)⋅(2i−k) = 8i + 3j - k

Finally, let's substitute into the cosine formula:

cosθ = (a⋅b)/(||a|| ||b||) = (8i + 3j - k)/(√26 * √5)

To approximate the angle to the nearest degree, we can use the inverse cosine function:

θ = arccos(cosθ)

Note: The range of arccos is [0,180], so we need to use the appropriate quadrant to find the correct angle.

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Between every brace of distinct points, there's a positive unique number called t which is the distance.

The positive number between every brace of distinct points is known as the distance and it can be set up as the absolute value of the difference between the corresponding real figures.

The distance represents the space between a brace of distinct points. This is called the distance hypothetical.

In order to find the distance, you would need to break for the absolute value of the difference between the real figures that are at the two points.

The Distance Postulate Given any brace of distinct points, there corresponds a unique positive real number called the distance between the two points.

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I would help, I cant understand it without answers.

I suggest you watch the video for help before answering it, so you can understand the question more, and try and figure it out.

Sorry I couldn't help I was going to, I did not understand I'm so sorry, hope you get the answer right.

I do prefer to watch the video instead.

Thanks for understanding if you do. If u still want to, if u got the answer right from the video, if u want u can give me brainiest?

Anyways I like to help people. pls Make sure to figure it out on ur own sometimes, You can ask for help, if u do get stuck. I'm just telling you so you don't get in trouble ok.

I would like to help you out in the future if you have questions with the answers this time lol .

The 2-category data is nominal. The 3-category data is also nominal. Each number in the set is analyzed as ratio.

The 2 categories- are 0-50 and 50-100, gives nominal data. Because we data has nothing to do with the values itself, it is the frequency.

Now for second scenario here, there are 3 categories, where it is basically low, medium and high, these are the frequencies, not the values itself. This will also be considered as nominal data.

Each number is set, it should be ordered in a set of number, and it is not what it includes denominal and it will be including the 0, which is absolute 0 point. Therefore, this will be considered as ratio.

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Answer:

x√xy²

Step-by-step explanation:

First step is to distribute.

Change ⁴√x⁵y² to ⁴√x · x · x · x · x · y · y

If there are any, (which there are) sets of the same variable greater then or equal to 4, combine them and move them to the left of the radical (the square root sign).  When you are done it should look like this:

x√x · y · y

You will notice there is still an x on the right side.  This is because there were 5 x's and you can only move them (in this case) in sets of 4.  5 - 4 = 1

Combine your like terms and you're done!

x√xy²

The value of [tex]$$45 \sqrt{7930.45}$$[/tex] be 4007.38833.

When multiplied by itself, a square root value equals the original value. There are four ways to calculate the square root: prime factorization, repeated subtraction, long division, and the estimation approach.

Using the square root function, you can convert rational numbers into algebraic numbers (which are a subset of rational numbers). The Euclidean norm (and distance) and generalizations like Hilbert spaces both depend on the square root of a nonnegative number.

Squares are the results of multiplying an integer by itself. Alternatively, the square root of an integer is a value that, when multiplied by itself, returns the original value.

Let the equation be [tex]$$45 \sqrt{7930.45}$$[/tex]

[tex]$$\begin{aligned}& \sqrt{7930.45}=89.05307 \ldots \\& =45 \cdot 89.05307 \ldots\end{aligned}$$[/tex]

= 4007.38833

Therefore, the value of [tex]$$45 \sqrt{7930.45}$$[/tex] be 4007.38833.

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The value of  be 4007.38833.

Let the equation be

= 4007.38833

Therefore, the value of  be  4007.38833.

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Factoring polynomials maze path from start to end is in the attachment.

Factoring polynomials by breaking the polynomial into its factors. We can use the greatest common factor (GCM) to find the factors of two terms.

1. x² + 5x + 6

= x² + 2x + 3x + 6 = x (x + 2) + 3 (x + 2)
= (x + 2) (x + 3)

2. x² + x - 6

= x² + 3x - 2x - 6 = x (x + 3) - 2 (x + 3)
= (x + 3) (x - 2)

3. x² - 4x - 12

= x² - 6x + 2x - 12 = x (x - 6) + 2 (x - 6)
= (x - 6) (x + 2)

4. x² + 7x - 8

= x² - x + 8x - 8 = x (x - 1) + 8 (x - 1)
= (x - 1) (x + 8)

5. x² - 49

= x² - 7x + 7x - 49 = x (x - 7) + 7 (x - 7)
= (x - 7) (x + 7)

6. 2x² + x - 6

= 2x² - 3x + 4x - 6 = x (2x - 3) + 2 ( 2x - 3)
= (2x - 3) (x + 2)

7. 2x² + 7x + 6

= 2x² + 3x + 4x + 6 = x (2x + 3) + 2 (x + 3)
= (2x + 3) (x + 2)

8. 2x² + 6x - 8 = 2 (x² + 3x - 4)

= 2 (x² - x + 4x - 4) = 2 [x (x - 1) + 4 (x - 1)]
= 2 (x - 1) (x + 4)

9. 5x² + 10x + 20 = 5 (x² + 2x + 4)

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The function is negative, and for values of x closer to -2, the function is increasing.

A function is a block of code that performs a specific task. It is a self-contained unit of code that can be reused throughout a program to perform a specific task. Functions accept inputs in the form of parameters, perform a set of operations and then return an output. They allow for a code to be written once and used multiple times, making it easier to read and maintain. Functions also help to organize code into smaller, manageable pieces, making it easier to track down bugs and other errors.

The graph of f(x) is negative and increasing for all real values of x where x < -2, since the graph is a downward-opening parabola with its vertex at x=-2. For values of x less than -2, the function is negative, and for values of x closer to -2, the function is increasing.

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Answer:

52

Step-by-step explanation:

2*(4*3+2*3+4*2) = 52

Answer:

They ordered 432 bottles of water

Step-by-step explanation:

1 multipack = 6 bottles

3 multipacks = 1 box

24 boxes = 24 (3 multipacks)

24 boxes = 72 multipacks

72 multipacks = 72 (6 bottles)

72 multipacks = 432 Bottles

There are no real solutions for this system of equations.

[tex](1)2x - 8y = 11\\ \\(2)x - 4y = 6[/tex]

For this solutions, we're going to solve equation (2) for variable "x".

[tex]x - 4y = 6[/tex]

Add "4y" on both sides of the equation.

[tex]x - 4y+4y = 6+4y \\ \\x=6+4y[/tex]

Calculated value: [tex]x=6+4y[/tex]

Equation to substitute in: [tex](1)2x - 8y = 11[/tex]

Substitution:

[tex]2(x) - 8y = 11\\ \\2(6+4y) - 8y = 11[/tex]

Simplify.

[tex]2(6+4y) - 8y = 11\\ \\(2)(6)+(2)(4y)-8y=11\\ \\12+8y-8y=11\\ \\12=11[/tex]

We obtained a false statement (12=11) which means that there's either no solution, or an infinite amount of solutions.

To see what's the exact case, try to make the coefficients of the equations be the same by multiplying one of the equation by a constant.

In this case, we could multiply all elements of equation (2) by number "2" in order to make the variables have the same coefficients as equation 1:

[tex]2(x - 4y = 6)\\ \\2x-8y=12[/tex]

Comparing the result to the other equation:

[tex]2x - 8y = 11\\ \\2x - 8y = 12[/tex]

There are no real solutions for this equations system, since the variables have the same coefficients and the contant terms are different (11 and 12).

Important note. If after multiplying the equation by a constant we had obtained the exact same equation, then we would've concluded that there where infinite solutions for the equations system.

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The function of the temperature is H = 20cos(2π/12t) + 57

The temperature oscillates between 37°F at 6am and 77°F at 6pm,

So we can use the average of these two temperatures as the "midline" or "average" temperature (C).

The average temperature, C = (37+77)/2 = 57

The amplitude of the oscillation is half the difference between the maximum and minimum temperatures,

Amplitude, K = (77-37)/2 = 20

The period of the oscillation is the time it takes for the temperature to repeat, which is 24 hours.

i.e. T = 24

The angular frequency B is given by:

B= 2π/T

So we have B = 2π/24 = π/12

Finally, we can substitute these values into the formula H = Kcos(Bt) + C

H = 20cos(2π/12t) + 57

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Answer:

- 81, 243

Step-by-step explanation:

to obtain a term in a geometric sequence, multiply the previous term by the common ratio r

here r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-9}{3}[/tex] = - 3

then

27 × - 3 = - 81

- 81 × - 3 = 243

the next two terms are - 81 and 243

An example of a derivative in accounting is a stock option.

The formula is Call Option Value = S * N(d1) - X * e^(-rT) * N(d2)

A derivative in accounting is a financial instrument whose value is derived from the value of one or more underlying assets, such as stocks, bonds, currencies, commodities, or real estate. One common example of a derivative in accounting is a stock option.

A stock option is a contract that gives the holder the right, but not the obligation, to buy or sell a specified number of shares of a stock at a specified price (the strike price) within a specified period of time. The value of a stock option is derived from the value of the underlying stock.

One formula used to calculate the value of a call option is the Black-Scholes model. The formula is as follows:

Call Option Value = S * N(d1) - X * e^(-rT) * N(d2)

Where:

S = the current stock price

X = the strike price

r = the risk-free interest rate

T = the time until expiration (in years)

N(d1) and N(d2) are the cumulative distribution functions of the standard normal distribution

For example, if a stock is currently trading at $50 per share, and the strike price of a call option on that stock is $45, with an expiration date of 1 year and the risk-free interest rate is 2%, the value of the call option can be calculated as follows:

Call Option Value = $50 * N(d1) - $45 * e^(-0.02*1) * N(d2)

N(d1) and N(d2) can be calculated using a financial calculator or software.

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The statement suggests that there is a proportional relationship between the number of selfies Sebastian takes, x, and the amount of storage (in megabytes) he uses taking selfies, y. This means that if we were to graph the number of selfies taken, x, on the x-axis and the amount of storage used, y, on the y-axis, the points would fall on a straight line and the slope of the line would be a constant.

In mathematical terms, we can represent this proportional relationship as y = kx, where k is the proportionality constant, or the constant of proportionality. This equation states that the amount of storage used, y, is directly proportional to the number of selfies taken, x.

Answer: is d

Step-by-step explanation:

Triangle HGI and RPQ are similar triangle. Any options that do not match with the condition of similarity given below would be the required incorrect options.

Similar triangles, are those triangles which have similar properties,i.e. angles and proportionality of sides.

Here,
Triangle HGI and RPQ
GH/RQ = GI /PQ = HI/RP
∠H = ∠R
∠G = ∠Q
∠I = ∠P

Triangle HGI and RPQ are similar triangle

Thus, Triangle HGI and RPQ are similar triangle. Any options that do not match with the condition of similarity given below would be the required incorrect options.

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Answer:

Step-by-step explanation:

10-11 = -1

20x4 = 80

72x12 = 864

124+1234 = 1358

y=3/4x-3 =

y=34x−3

Slope: 3434

y-intercept: (0,−3)

The 98 percent confidence interval for the population of all students using the classroom who write their name on their USB drive is B) 0.4 ± 1.967 (0.4)(0.6) / √300.

The sample proportion (p-hat) of students who write their name on their USB drive is 0.4, based on 180 out of 300 students. The sample size is large enough (n > 30) to use the normal approximation to the binomial distribution to calculate the confidence interval.

The standard error of the sample proportion is (p(1-p)/n)^0.5, where p is the population proportion and n is the sample size.

The confidence interval is calculated by adding and subtracting the critical value (1.967 for a 98 percent confidence level) multiplied by the standard error from the sample proportion. This interval provides an estimate of the true population proportion with 98 percent confidence.

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Graph of the function y = 2x + 1 along with its parent function is attached below.

A function is defined as a relation between a set of inputs having one output each. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input.

Given function,

y = 2x + 1

The parent function is the simplest form of the type of function given

Parent function is y = 2x

Shifting the graph of parent function vertically up 1 unit.

We get the graph of function y = 2x + 1

Hence, following is the graph of function y = 2x + 1 transformed from parent function y = 2x

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