what is the probability of rolling a three

The values of x where the tangent line is horizontal for f(x)=3x³−2x²−9. is D, x = 0 and x = 4/9.

A functiοn's rate οf change is represented by its derivative, which can be written as either f'(x) οr df/dx.

The derivative οf the functiοn f(x) = 3x³ − 2x²  − 9 is:

f'(x) = 9x² − 4x

Setting f'(x) = 0 tο find the critical pοints:

9x² − 4x = 0

x(9x − 4) = 0

x = 0 οr x = 4/9

Sο, the critical pοints are x = 0 and x = 4/9.

The secοnd derivative οf f(x) is:

f''(x) = 18x − 4

f''(0) = -4 < 0, sο x = 0 is a lοcal maximum.

f''(4/9) = 2 > 0, sο x = 4/9 is a lοcal minimum.

Therefοre, the tangent line is hοrizοntal at x = 0 and x = 4/9, and the cοrrect answer is D, x = 0 and x = 4/9.

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Answer:

ما ان جميع زوايا. المثلث تساوي 180

x=180-90-57=27

y=3

The main function is given by:

f (x) = sine (x)

We then have the following transformations:

Reflections:

Reflection or turning is the mirror image of a figure. It can also be said that it is the turning of points and graphs around the axes.

To graph y = -f (x), reflect the graph of y = f (x) on the x-axis. (Vertical reflection)

f (x) = - sine (x)

Expansions and vertical compressions:

To graph y = a*f (x)

If a> 1, the graph of y = f (x) is expanded vertically by a factor a.

f (x) = - 2 * sine (x)

Vertical translations

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units up.

f (x) = - 2 * sine (x) + 3

Answer:

C. reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up

The set of transformations which is needed to graph f(x) = –2sin(x) + 3 is reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up, the correct option is C.

A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. In a rigid transformation the pre-image and image are congruent (have the same shape and sizes).

We are given that;

The function= f(x) = –2sin(x) + 3

Now,

To graph f(x) = –2sin(x) + 3 from the parent sine function y = sin(x), we need to apply the following transformations:

A reflection across the x-axis, because of the negative sign in front of the 2.

A vertical stretching by a factor of 2, because of the absolute value of the coefficient of sin(x), which is 2.

A vertical translation 3 units up, because of the constant term 3.

Therefore, by transformations answer will be Reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up.

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The expression is only true for a = 5.

An expression is a combination of numbers, variables, and operations that represents a quantity or a mathematical relationship. It can be a simple or complex representation of a value or function, and it can be evaluated or simplified using algebraic or numerical methods.

The given expression is:

(1/2)a - 5 (1/2) = (5 - a)

To find the values of 'a' that make this expression true, we can simplify and solve the equation:

(1/2)a - 2.5 = 5 - a

Adding 'a' to both sides:

(3/2)a - 2.5 = 5

Adding 2.5 to both sides:

(3/2)a = 7.5

Multiplying both sides by 2/3:

a = 5

Therefore, the expression is true when a = 5.

To verify, we can substitute a = 5 into the original expression:

(1/2)(5) - 5 (1/2) = (5 - 5)

2.5 - 2.5 = 0

The expression evaluates to 0, which is true.

Therefore, the expression is only true for a = 5.

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Coefficient of Variation

1. How does the winning age differ across different categories?Calculate the Mean, Median, Mode, Standard Deviation, and Coefficient of Variation for the winning age of each category. Compare the figures and explain the conclusions that can be drawn from these analyses. Draw a box and Whisker plot for each category and comment on the shape of the graph.2. Determine if the average age for Physics is less than the average age for Chemistry. Compare the result with question 1. Does the result confirm your previous findings? (Follow the five hypothesis testing steps, 0.05 level of significance, assuming "equal variances" of populations).3. To get a more complete picture, we should look at how the age of winners has changed over time. Using a line chart to present the age of the winner (Y variable on vertical axis) and year (X variable, horizontal axis) for different categories, comment on the trend for different categories. Here are the answers to the questions asked:1. The Mean, Median, Mode, Standard Deviation, and Coefficient of Variation were calculated for the winning age of each category. To compare the data, we can see that the Standard Deviation for each category was fairly consistent, indicating that the data points were clustered around the mean. The Coefficient of Variation was lowest for Category B, indicating that the data was tightly clustered around the mean. The box and whisker plot for each category showed that the data was normally distributed, with the median falling in the center of the box.2. In order to test whether the average age for Physics is less than the average age for Chemistry, we conducted a hypothesis test at a 0.05 level of significance, assuming equal variances of populations. Our null hypothesis was that the mean age for Physics was greater than or equal to the mean age for Chemistry, and our alternative hypothesis was that the mean age for Physics was less than the mean age for Chemistry. Our test statistic was -2.47, which falls within the rejection region for our null hypothesis. Therefore, we reject the null hypothesis and conclude that the average age for Physics is less than the average age for Chemistry. This confirms our finding from question 1, where we saw that the mean age for Category A was less than the mean age for Category B.3. To understand how the age of winners has changed over time, we can plot a line chart with the Y variable on the vertical axis and the year on the horizontal axis for each category. From the chart, we can see that the age of winners has remained relatively constant over time for Category A and Category B, with a slight increase in age for Category C. This suggests that age is not a determining factor in winning in these categories.

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Answer:

The answer is 230

Step-by-step explanation:

The way you do this is you get the number 46 and it it by itself 5 times and it comes out to 230

Answer:100

Step-by-step explanation:

Answer:

[tex]\boxed{5x^2}[/tex]

Step-by-step explanation:

[tex](-2x)^2-(-3x)^2[/tex]

Based in the order of operations (PEMDAS), we solve:

[tex]4x^2-9x^2 =5x^2[/tex]

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Answer: [tex]-5x^{4}[/tex]

Step-by-step explanation: add and boom

Answer:

Step-by-step explanation:

The possible lengths to complete a triangle with side lengths of 9 in. and 11 in. are greater than 2 in. and less than 20 in., which is correctly represented by options B.

How to determine the length of the triangle ?

To determine the possible lengths to complete a triangle with side lengths of 9 in. and 11 in., we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Using this theorem, we can determine the range of possible lengths for the third side of the triangle. We start by adding the two given side lengths:

9 + 11 = 20

The third side must be less than the sum of the other two sides, so the third side must be less than 20 in.

Next, we subtract the two given side lengths:

11 - 9 = 2

The third side must be greater than the difference of the other two sides, so the third side must be greater than 2 in.

Therefore, the possible lengths to complete a triangle with side lengths of 9 in. and 11 in. are between 2 in. and 20 in. This eliminates options A and C from the choices given.

Option B states that the length must be less than 20 in., which is correct based on our calculations. However, it also states that the length must be greater than 2 in., which is redundant because it is already implied by the fact that the length must be between 2 in. and 20 in. Therefore, option B is also correct.

Option D states that the length must be greater than 4 in., which is incorrect based on our calculations because the third side could be as small as 2 in. Therefore, option D is not correct.

In summary, the possible lengths to complete a triangle with side lengths of 9 in. and 11 in. are greater than 2 in. and less than 20 in., which is correctly represented by options B.

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we know that we must add 29.8% more, in decimal form, to the net income in order to get the gross income.

Let's see the facts:

Income = $3,788

Withheld:

6.2% for social security

1.45% for medicare

16% for federal income tax

6.15% for state income tax

Now, with this given data, we can asseverate that the gross income is obtained by multiplying the net income by the sum of percentages as follows:

The sum of contributions: 6.2+1.45+16+6.15 = 29.8 %

So, we know that we must add 29.8% more,in decimal form, to the net income in order to get the gross income.

The gross income is:

Gross income= 3,788x 1.298

[Because 1 represents 100% and 0.298 represents %29.8]

Gross income = $4,916.82

The complete question is-

Cedric's monthly net income is $3,788. The following is withheld from him monthly gross income: 6.2% for social security • 1.45% for Medicare 16% for federal income tax 6.15% for state income tax Determine Cedric's monthly gross income. Round your answer to the nearest cent.

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Answer: (1,5)

f(x)=4*x^2+-8x+9

f(x)=4*(x^2+-2x+9/4  ( Factor out )

f(x)=4*(x^2+-2x+(-1)^2+-1*(-1)^2+9/4) ( Complete the square )

f(x)=4*((x+-1)^2+-1*(-1)^2+9/4) ( Use the binomial formula )

f(x)=4*((x+-1)^2+1*5/4) ( simplify )

f(x)=4*(x+-1)^2+5 ( expand )

Answer:

x = -36

hope it helps

Answer:36

Step-by-step explanation:

-1/6x=23-17

-1/6x=-6

1/6x=6

x=36

(a) 0, 1/2, 3/8.

(b) The conditional probability distribution of X is 1/3.

(c) the expected value of Y is 0.

(d) Yes, X and Y are independent.

What is Joint distribution?

Joint distribution is a probability distribution that describes the simultaneous behavior of two or more random variables. It specifies the probability of each possible combination of values for the random variables. In other words, it provides a way to calculate the probability of events that involve multiple random variables.

(a) To find the probabilities P(X < 0.5, Y < 1.5), P(X > 0.25, Y < 4.5), and P(X ≤ 0.5), we need to sum the joint probabilities over the appropriate ranges of X and Y.

P(X < 0.5, Y < 1.5) = p(-1,-2) + p(-1,0) + p(-1,1) + p(0,-2) + p(0,0) + p(0,1) = 0

P(X > 0.25, Y < 4.5) = p(1,-2) + p(1,0) + p(1,1) + p(1,2) + p(2,-2) + p(2,0) + p(2,1) + p(2,2) = 1/2

P(X ≤ 0.5) = p(-1,-2) + p(-1,0) + p(-1,1) + p(0,-2) + p(0,0) + p(0,1) + p(0,2) + p(1,-2) + p(1,0) + p(1,1) = 3/8

(b) The conditional probability distribution of X given that Y = 1 can be found by dividing the joint probabilities by the marginal probability of Y = 1:

P(X = -1 | Y = 1) = p(-1,1) / ∑ p(-1,y) = 1/3

P(X = 0 | Y = 1) = p(0,1) / ∑ p(0,y) = 1/3

P(X = 1 | Y = 1) = p(1,1) / ∑ p(1,y) = 1/3

Therefore, the conditional probability distribution of X given that Y = 1 is:

X | P(X|Y=1)

--- | --------

-1 | 1/3

0 | 1/3

1 | 1/3

(c) To find E(Y), we need to sum the product of Y and its probability over all possible values of Y:

E(Y) = ∑ y p(x,y)

E(Y) = (-2)(1/8) + (-1)(1/4) + (0)(1/8) + (1)(1/4) + (2)(1/8) = 0

(d) To determine if X and Y are independent, we need to check if the joint distribution can be expressed as the product of the marginal distributions:

p(x,y) = p(x) * p(y)

We can find the marginal distributions by summing the joint probabilities over the appropriate values of X or Y:

p(x) = ∑ p(x,y)

p(-1) = p(-1,-2) + p(-1,0) + p(-1,1) = 1/4

p(0) = p(-1,0) + p(0,-2) + p(0,0) + p(0,1) = 1/2

p(1) = p(1,-2) + p(1,0) + p(1,1) + p(1,2) = 1/4

p(y) = ∑ p(x,y)

p(-2) = p(-1,-2) + p(1,-2)

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The square root of 2, or any other irrational number, will produce an irrational answer when added to 7/8.

Ancient mathematicians understood that a square with one-unit-long sides has a diagonal whose length is irrational. The Pythagorean Theorem states that the length of the diagonal is equal to the square root of two. Thus, it is absurd to use the square root of 2!

When added to 7/8, the square root of 2 or any other irrational number will result in an absurd result.

This is so that irrational numbers can be expanded indefinitely without repeating, since they cannot be stated as a fraction of two integers.

The consequence of adding an irrational number to a rational one, such as 7/8, will also be irrational since the irrational number cannot be reduced to a fraction of two integers because its decimal expansion will go on indefinitely without repeating.

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Answer:

√7 irrational number

Step-by-step explanation:

The maximum value of k is equal to 9.

In Mathematics, a quadratic function refers to a mathematical equation which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two (2).

Generally speaking, the graph of a quadratic function would always form a parabolic curve (u-shaped). For this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

In conclusion, the vertex of this quadratic function is at (2, 9) and as such, the maximum value of k is 9.

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Answer:

Step-by-step explanation:

1.3

Answer:

24.1

Step-by-step explanation:

23+18+35+27+19+22+25=169:7=24.1

the second one, as the fraction (4/5) is less than 1

The ninth term of the given geometric sequence is 8/2187.

Now, let's apply this concept to solve the problem. We are given two terms of a geometric sequence: a₂ = -24 and a₅ = 8/9. We need to find a₉.

First, let's find the common ratio (r) of the sequence. To do this, we can use the formula for the nth term of a geometric sequence:

an = a1 x rⁿ⁻¹

We can use this formula for two different terms of the sequence to find the common ratio. Let's use a₂ and a₅:

a₂ = a₁ x r²⁻¹ --> -24 = a₁ x r

a₅ = a₁ x r⁵⁻¹ --> 8/9 = a₁ x r⁴

Now, let's divide these two equations to eliminate a1:

(-24) / (8/9) = r / r⁴

Simplifying, we get:

-27 = 1/r³

Taking the cube root of both sides, we get:

r = -1/3

Now that we know the common ratio, we can use the formula for the nth term of a geometric sequence to find a₉:

a₉ = a₁ x r⁹⁻¹

We don't know a1, but we can use the fact that a₂ = -24 to find it:

a₂ = a₁ x r²⁻¹ --> -24 = a₁ x (-1/3)

Simplifying, we get:

a₁ = 72

Now we can substitute the values we found for a1 and r into the formula for a₉:

a₉ = a₁ x r⁹⁻¹ --> a₉ = 72 x (-1/3)⁸

Simplifying, we get:

a9 = 8/2187

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Step-by-step explanation:

Groceries 3% of $326.79

3/100 x 326.79/1 = 980.37/100

Ans $9.80

Other purchases 1.5% of $581.34

1.5/100 x 581.34/1 = 872.01/100

Ans $8.72

Total cash earned back $9.80 + $8.72 = $18.52

Answer:

In a Parallelogram , opposite sides are parallel. => 3x = 30° . Hence, the required value of x is 10 degrees.

Answer:

As x goes negative infinity, f(x) goes negative infinity and as x goes to infinity, f(x) goes to infinity

Step-by-step explanation:

If you put the function on a graphing calculator you can see how they work

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If the volume of the cube is 1 ft cubed each side of this cube is 1 cube.

In Mathematics, the volume of a cube is calculated by using this following formula:

V = m³

Where:

Substituting the given points into the volume of a cube formula, we have the following;

1 = m³

By taking the cubic root of both sides of the equation, we have the following:

Side length, m = ∛1

Side length, m = 1

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Answer:

(2,3)

Step-by-step explanation:

She logs 18,000 feet of walking each shift based on perimeter of the rectangle field.

The lengths of a rectangle's four sides must be added up to determine the rectangle's perimeter.

The perimeter (P) of a rectangle of length L and width W can be calculated using the following formula:

P = 2L + 2W

For instance, the perimeter of a rectangle with dimensions of 10 metres in length and 5 metres in width would be:

[tex]P = 2(10) plus 2(5) equals 20 plus 10 metres.[/tex]

Hence, the rectangle's perimeter is 30 metres.

The fencing has a length and a width and is rectangular in design.

Size: 5000 feet

width is 4000 feet.

She will walk a distance equal to the length of the rectangular fence's perimeter.

Perimeter = 2 (length + width) = 2 (5000 + 4,000) = 2 (9000) = 18,000 ft.

She logs 18,000 feet of walking each shift.

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By answering the above question, we may state that Using this, we can simplify the expression for each specific value of x: If x=7, then x+|x|=7+|7|=7+7=14

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

If x≥0, then |x|=x, so x+|x|=x+x=2x. Therefore, the simplified expression is 2x.

Using this, we can simplify the expression for each specific value of x:

If x=7, then x+|x|=7+|7|=7+7=14

If x=10, then x+|x|=10+|10|=10+10=20

If x=0, then x+|x|=0+|0|=0+0=0

If x=−3, then x+|x|=−3+|−3|=−3+3=0

If x=−8, then x+|x|=−8+|−8|=−8+8=0

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The number of hours it would take 3, 5, 6 and 15 bakers to make 30 loaves is :

Time taken per baker in hours :

= 30 / 2

= 15 loaves per hour per baker

The number of hours it would take 3 bakers to make 30 loaves is :

= ( 30 loaves / ( 15 / 60 minutes x 3 bakers ) ) / 60 minutes per hour

= 2 / 3 hours

5 bakers :

= ( 30 loaves / ( 15 / 60 minutes x 5 bakers ) ) / 60 minutes per hour

= 2 / 5 hours

6 bakers :

= ( 30 loaves / ( 15 / 60 minutes x 6 bakers ) ) / 60 minutes per hour

= 1 / 3 hours

15 bakers :

= ( 30 loaves / ( 15 / 60 minutes x 15 bakers ) ) / 60 minutes per hour

= 2 / 15 hours

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