Evaluate the function at the given values of the independent variable and simplify.

f(x)=6x^2-1/x^2


(a) f(5) (b) f(-5) (c) f(-x)

(Type an integer or a fraction. Simplify your answer.)

A) Determine the probability that a disk lasts at least 500 hours.= 0.275

B) Probability that a disk fails before 400 hours=0.685

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

Remind the formula for CDF of Weibull random variable X

[tex]F(x)=1-e^{-(x/\delta)^{\beta}[/tex]

Now apply this formula for the Weibull variable X with the parameters β=0.5 and δ to be deduced from the mean of 600. The formula for the mean is:

[tex]600=\delta\Gamma(1+2)=\delta*2!\\\\\delta=300\\Finally\\\\P(x > 500)=1-F(500)=e^({-5/3})^{0.3}=0.275\\\\p(x < 400)=f(400)=0.685[/tex]

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The total duration of the puberty process can be different for each girl who is about to enter it, as the length of time for the different stages of puberty can vary from person to person.  Hence, if a girl is about to enter puberty, the total process will take a variable length of time for different girls.

The total process of puberty for a girl can take a variable length of time, but typically it takes around 2 to 5 years to complete. The onset of puberty usually occurs between the ages of 8 and 13, with most girls starting around age 11.

The process of puberty includes physical changes such as breast development, the growth of pubic and underarm hair, and the onset of menstruation.

The duration of puberty can also depend on factors such as genetics, nutrition, and overall health. Some girls may experience a shorter or longer duration of puberty than others. However, in general, the process of puberty for a girl usually takes around 2 to 5 years to complete.

Therefore, the correct answer is "a variable length of time for different girls", but typically takes around 2 to 5 years to complete.

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The solution to |x| > |x + 2| is x < -2. This can be determined by looking at the two graphs on the grid, y = |x| and y = |x + 2|.

Inequality is the concept of representing a relationship between two values using a mathematical symbol. This can be used to express various forms of comparison such as greater than, less than, and not equal to. Inequality is an important concept for understanding and applying mathematical principles, such as in algebra and calculus.

The graph of y = |x| is a straight line at y = 0, and increases as x moves further away from 0. The graph of y = |x + 2| has a minimum at x = -2, and increases as x moves further away from -2. Therefore, at all locations where x is less than -2, the value of |x| is greater than the value of |x + 2|. These locations are all solutions to the inequality |x| > |x + 2|.

To visualize this solution, we can look at the graph of the two functions and see that the value of |x| is greater than the value of |x + 2| when x is less than -2. This can also be seen by looking at the numerical values of the two functions; for any x less than -2, the absolute value of x will be greater than the absolute value of x + 2.

In conclusion, the solution to the inequality |x| > |x + 2| is x < -2. This can be seen visually on the graph of the two functions, and can also be determined by looking at the numerical values of the two functions.

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a) We need to find the values of x for which the denominator, cos(x), is equal to zero. b) vertical asymptotes at x = π/2, x = 3π/2, x = -π/2, x = -3π/2, and so on.

The tangent function is periodic, with a period of π radians (or 180 degrees). This means that the tangent function repeats itself every π radians, or every 180 degrees. The tangent function is also an odd function, which means that it is symmetric about the origin.

The graph of the tangent function has a characteristic shape with multiple cycles between consecutive vertical asymptotes. The graph passes through the origin and intersects the x-axis at the vertical asymptotes. The tangent function has a maximum and a minimum value between any two consecutive vertical asymptotes. However, it does not have a maximum or minimum value over its entire domain.

a) To determine the exact location of the asymptotes of the tangent function using the identity tan(x) = sin(x)/cos(x), we need to find the values of x for which the denominator, cos(x), is equal to zero. These values of x correspond to the vertical asymptotes of the tangent function.

Since cos(x) = 0 when x = π/2 + kπ, where k is an integer, the vertical asymptotes of the tangent function occur at these values of x. We can also write this as x = kπ/2, where k is an odd integer.

b) From the graph of the tangent function, we can see that there are vertical asymptotes at x = π/2, x = 3π/2, x = -π/2, x = -3π/2, and so on. These correspond to the values of kπ/2, where k is an odd integer. We can also write the set of vertical asymptotes as:

{x | x = kπ/2, k ∈ Z and k is odd}

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When choosing cereals at Supermarket Eats, it is important to read the nutrition labels and choose cereals that are lower in added sugars and higher in fiber.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants

Based on general nutrition guidelines, it is recommended to choose cereals that are lower in added sugars and higher in fiber.

If the cereals at Supermarket Eats have nutrition labels, it is important to read them carefully to determine the sugar content per serving size. According to the American Heart Association, it is recommended that men limit their intake of added sugars to no more than 9 teaspoons per day, and women limit their intake to no more than 6 teaspoons per day. Choosing cereals that have less than 5 grams of added sugars per serving is a good rule of thumb.

In terms of fiber content, it is recommended to choose cereals that have at least 3 grams of fiber per serving. This will help to keep you feeling full and satisfied, and promote healthy digestion.

Therefore, When choosing cereals at Supermarket Eats, it is important to read the nutrition labels and choose cereals that are lower in added sugars and higher in fiber.

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Answer:

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Area of a rectangle is the product of it width and length:

Given the length and area of a rectangle, find the missing width:

Answer:

Step-by-step explanation:

[tex]f^-1[/tex][tex]\sqrt[3]{1/-1+x | + | 2x/-1+x}[/tex]

Comparing the two simplified ratios, 4:3 and 10:9, we see that they are not equal, so the ratios 60:45 and 10:9 do not form a proportion.

We must examine whether the cross-products are equal in order to determine whether the ratios of 60:45 and 10:9 constitute a proportion.

60 x 9 = 540 is the cross product of 60 and 9.

45 x 10 = 450 is the cross product of 45 and 10.

The cross-products are not equal, hence the ratios of 60:45 and 10:9 do not constitute a proportion (540 is not equal to 450, for example).

Simplifying two ratios to their simplest form is another technique to determine if they constitute a proportion.

By dividing both components by their greatest common factor, which is 15, the ratio 60:45 can be reduced to 4:3.

The 10:9 ratio has already reached its lowest point.

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Therefore , the solution of the given problem of inequality comes out to be   y - 12 = -(3/4)(x - 2)².

Without the equal sign, an association or collection of numbers can be a disparity in mathematics. Equity always comes after equilibrium. When standards are still incompatible, inequality results. Fairness and disparity have different variable characteristics. Because parts aren't always similar or close to one another, we decided to select the most common symbol (). It is also possible to use disparities of any size to assess values.

Here,

We must recast the parabola's equation in this form in order to determine the inequality's standard form. The vertex version of a quadratic equation is as follows:

=> y = a(x - h)² + k

where (h, k) is the parabola's apex. Inputting the numbers provided yields:

=> y = a(x - 2)² + 12

We can use the information that the parabola passes through (-2, 0) and to determine the value of a. (6, 0). When we enter these values into the formula, we obtain:

=> 0 = a(-2 - 2)² + 12

=> 0 = 16a + 12

=>  a = -3/4

The parabola's solution is as follows:

=>  y = -(3/4)(x - 2)²

We need to separate y on one side in order to determine the inequality's standard form:

=> y - 12 = -(3/4)(x - 2)²

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If one student can fill 5 slots with student presentations, then 25 students might be able to fill the slots in 125 different ways.

To calculate the number of ways in which a student can fill a specific slot, the simple arithmetic operation of multiplication is used. In the given question it is already given that there are 25 students in a class and one of the student has filled the slots in 5 different ways. This means that each student will be able to fill the slots in 5 different ways.

Hence total number of ways in which all the students might be able to fill the slots is given as product of total students and number of slots filled.

Total number of ways = 25*5 = 125 ways

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Answer:

22 sq. in.

Step-by-step explanation:

Believe it or not, the area is still length times width in this problem, you just have to subtract 3 sq in from your final answer becasue of the center gap (3in *1in)

5in * 5in =25 sq in -3 sq in= 22 sq in.

The lower confidence level (LCL) and upper confidence level (UCL) are

a. X-Bar = 47; n = 73; 0 = 31; a = 0.05
LCL = 44.35
UCL = 49.65

b. X-Bar = 83; n = 221; 0 = 400; a = 0.01
LCL = 79.91
UCL = 86.09

c. X-Bar = 513; n = 425; 0 = 43; a = 0.10
LCL =  509.27
UCL = 516.73

a. X-Bar = 47, n = 73, σ² = 31, α = 0.05

Using the formula for a confidence interval for the mean of a normal distribution with known variance, we get:

LCL = X-Bar - z(α/2) * √(σ²/n)

= 47 - 1.96 * √(31/73)

= 44.35

UCL = X-Bar + z(α/2) * √(σ²/n)

= 47 + 1.96 * √(31/73)

= 49.65

So, the 95% confidence interval for the population mean is (44.35, 49.65).

b. X-Bar = 83, n = 221, σ^2 = 400, α = 0.01

Using the same formula, we get:

LCL = X-Bar - z(α/2) * √(σ²/n)

= 83 - 2.58 * √(400/221)

= 79.91

UCL = X-Bar + z(α/2) *√(σ²/n)

= 83 + 2.58 * √(400/221)

= 86.09

So, the 99% confidence interval for the population mean is (79.91, 86.09).

c. X-Bar = 513, n = 425, σ² = 43, α = 0.10

Again, using the same formula, we get:

LCL = X-Bar - z(α/2) * √(σ²/n)

= 513 - 1.645 * √(43/425)

= 509.27

UCL = X-Bar + z(α/2) * √(σ²/n)

= 513 + 1.645 * √(43/425)

= 516.73

So, the 90% confidence interval for the population mean is (509.27, 516.73).

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Using trigonometric functions, we can find the area of the triangle to be: 19.68unit². Bob used the wrong dimension in the area of the triangle formula.

There are six basic trigonometric operations in trigonometry. These techniques can be described using trigonometric ratios. The six basic trigonometric functions are the sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function.

Trigonometric identities and functions are based on the ratio of the sides of a right-angled triangle.

The sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle are computed using trigonometric formulas.

Here in the question,

Area of the triangle = 1/2 absinc

= 1/2 × 12 × 16.4 × Sin30°

= 1/2 × 196.8 × 0.2

= 19.68unit².

Bob used the wrong dimension of the triangle. Instead of using the adjacent side of the angle, Bob used the opposite side of the angle.

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If a scooter was brought in April 2005 for rs. 42000 if it's value fall by 10% every year, the value of the scooter in April 2007 would be Rs. 34020.

If the value of the scooter falls by 10% every year, then its value after the first year will be 90% of its original value. Similarly, the value after the second year will be 90% of the value after the first year, or 0.9 * 0.9 = 0.81 times the original value.

To find the value of the scooter in April 2007, we need to apply this formula twice, since there are two years between April 2005 and April 2007.

Starting with the original value of the scooter, we can calculate its value after one year:

Value after 1 year = 0.9 * Rs. 42000 = Rs. 37800

Then, we can use this value to calculate the value of the scooter after two years:

Value after 2 years = 0.9 * Rs. 37800 = Rs. 34020

In this case, the value of the scooter decreases by 10% each year, so its value after two years is 0.9 times its value after one year, which is 0.9 times its original value.

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The expression -3¾ + 1/2 is represented on the number line.

Real numbers are represented by a number line, which is a representation of a graduated straight line, in elementary mathematics.

Every point on a number line is thought to represent a real number, and every real number is thought to represent a point.

Number lines are horizontal lines with uniformly spaced numerical increments.

So, first solves the expressions as follows:

-3¾ + 1/2

-12+3/4 + 1/2

-9/4 + 1/2

-9 + 2/4

-7/4

Now plot -7/4 on the number line as follows:

(Refer to the number line attached below)

Therefore, the expression -3¾ + 1/2 is represented on the number line.

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The P(2nd non-conforming part is obtained in y tests) is given by (n-x) / n * (1-x/n)^(y-1).

The probability that the second nonconforming part is obtained in y tests is given by the formula P(X = k) = (k-1) choose (r-1) * p^r * (1-p)^(k-r).Solution:Given, n = between 15 and 25x = between 11 and 14y = between 3 and 10To find: The probability that the second nonconforming part is obtained in y testsFormula used:P(X = k) = (k-1) choose (r-1) * p^r * (1-p)^(k-r)Where X represents the number of trials, p represents the probability of success, k represents the number of successful outcomes, and r represents the number of trials.Possible values of x:n - xLet the probability of obtaining a non-conforming part be p, then the probability of obtaining a conforming part would be 1-p.Number of non-conforming parts in n: n-xProbability of selecting the non-conforming part p = x/nProbability of selecting the conforming part 1-p = (n-x)/nP(2nd non-conforming part is obtained in y tests) = P(y-th trial is non-conforming) = P(y-1 conforming trials followed by a non-conforming trial)P(2nd non-conforming part is obtained in y tests) = (n-x) / n * (x/n)^(1-1) * (1-x/n)^(y-1)Therefore, P(2nd non-conforming part is obtained in y tests) = (n-x) / n * (x/n)^(0) * (1-x/n)^(y-1)P(2nd non-conforming part is obtained in y tests) = (n-x) / n * (1) * (1-x/n)^(y-1)Hence, P(2nd non-conforming part is obtained in y tests) is given by (n-x) / n * (1-x/n)^(y-1).

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In the following question, among the conditions given, This triangle must be a non-Euclidean triangle, which is not possible to draw on a flat plane without distorting its shape. Therefore, there are no valid angles for this triangle.

To find the angles of a triangle when given the lengths of its sides, we can use the Law of Cosines, which states that:

c^2 = a^2 + b^2 - 2ab*cos(C)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

Using this formula, we can find the cosine of each angle and then use the inverse cosine function (cos^-1) to find the measure of each angle.

Let's use this formula to find the angles of the triangle with sides of 11, 10, and 17:

c^2 = a^2 + b^2 - 2ab*cos(C)

For the side opposite angle C = 17:

17^2 = 10^2 + 11^2 - 2(10)(11)cos(C)

289 = 121 + 100 - 220cos(C)

cos(C) = (121 + 100 - 289)/(21011)

cos(C) = -0.4

We get a negative value for the cosine of angle C. This means that the triangle cannot be a standard triangle in the Euclidean plane, as the Law of Cosines requires that the cosine of an angle be between -1 and 1. This triangle must be a non-Euclidean triangle, which is not possible to draw on a flat plane without distorting its shape.

Therefore, there are no valid angles for this triangle.

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The value of x = 50°

What is the triangle?

A triangle is a 3 line segments with a closed diagram. It has 3 vertices, 3 sides and 3 angles. The sum of all interior angles is 180°.

Given figure y° = 40° and right angle triangle.

So, all interior angles sum is 180°.

90° + y° + x° = 180°

90° + 40° + x° = 180°

x° = 50°

Therefore, the value of x = 50°

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28= (1+2x)(x)

28=x+2x²

2x²+x-28 = 0

2x²+8x-7x-28 =0

2x(x+4) -7(x+4) =0

(x+4)(2x-7) = 0

x = -4 and 7/2

dimensions can't be negative

length=1+2×7/2 =1+7 = 8ft

width= 7/2ft

14x - 2

To find the difference between (−5x+7) and (9x+5), we need to subtract the first expression from the second.

(9x+5) - (-5x+7)

= 9x + 5 + 5x - 7 [Distribute the negative sign to (-5x+7)]

= 14x - 2

Therefore, the difference between (−5x+7) and (9x+5) is 14x - 2.

Answer:

Scale factor is 1/2

Step-by-step explanation:

2.4 x 2 = 4.8

4.8/2 = 2.4

same here

2.1 x 2 = 4.2

4.2/2 = 2.4

3.8/2 =1.9

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The solutions of a system of linear equations are as follows;

1. Their slope is the same but their y-intercept are different

b. y = 3·x + 2 and y = 3·x + 5

c. The equations are the same

d. y = 3·x + 2 and y = 9·x + 15

e. y = 3·x + 2, and y = 8·x + 5

f. x = 0, y = 0

g. Please see the following section

A system of linear equations are equations that have the same variables.

1. a. A system of linear equations have no solution if the equations in the system of equations have the same slope

b. y = 3·x + 2, and y = 3·x + 5

c. A system of two linear equations has more than one solution if the equations in the system are the same

The number of solutions = Infinite number of solutions

d. y = 3·x + 5, 3·y = 9·x + 15

e. y = 3·x + 5, y = 8·x + 5

f. y = 3·x + 5, y = 8·x + 5

Therefore; 3·x + 5 = 8·x + 5

3·x = 8·x

3·x - 8·x = 0

-5·x = 0

x = 0/(-5) = 0

x = 0

y = 3·x + 5

y = 3 × 0 + 5 = 5

y = 5

The solution is therefore;

x = 0, y = 5

g. A customer wants to spend a total of ¢50 to buy drawing pads and pencils. The cost of the pencil the customer intends to buy is ¢2, and the cost of each drawing pad is ¢8. The number of pencils and the number of drawing pads the customer buys are the same.

How many drawing pads and pencils does the customer buy.

Let x represent the number of drawing pad the customer buys and let y represent the number pencils the customer buys, we get;

8·x + 2·y = 50

x = y

Therefore;

8·x + 2·x = 50

10·x = 50

x = 50/10

x = 5

Therefore; y = 5

The number of drawing pads and pencils the customer buys are 5 each.

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Using expression 5⁷ x 9,  there are 59,049,125 ways to answer all 9 tests if you select one option per question and leave nothing blank.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, and exponentiation) that represents a value or a quantity.

Expressions can be simple or complex, and they can contain one or more variables. For example, "2x + 3" is a simple expression that contains the variable x.

Now,

To solve this problem, we can use the multiplication principle of counting, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things.

For each of the 9 tests, there are 5 choices for each of the 7 questions. Therefore, there are 5 x 5 x 5 x 5 x 5 x 5 x 5 possible ways to answer the questions on each test. Using the multiplication principle, we can find the total number of ways to answer all 9 tests by multiplying the number of ways to answer each test together:

5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 5⁷ x 9 = 59,049,125

Therefore,

                 there are 59,049,125 possible ways ways to answer all 9 tests if you select one option per question and leave nothing blank.

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The purchase cost is $40. Question: What is the discount price of shoes if they were originally $80 and are currently on sale for 50% off.  % formula: Sale price equals 50% of $80.

The word puzzle asks you to determine the sale price of shoes that are being offered at a 50% discount. The percent equation, which asserts that the percent of the whole is equal to the part over the entire, or percent = part/whole, may be used to solve this problem. In this instance, the sale price is the component we are interested in, the initial price of $80 is the component as a whole, and 50% is the percentage. With these numbers as inputs, we can calculate the sale price as 50% of $80. When we solve for the sale price, we arrive at $40. Hence, the sneakers are $40 on sale.

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Write a word problem involving percents for which the percent is about one half and the whole is known. Write a percent equation for the problem and then use it to solve the problem. If a store has a sale on shoes for 50% off and the original price is $80, what is the sale price?

The resultant of the expression (((-3/5)+(5/3))-(2-4/3)) will be 2/5.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated to produce a value. Expressions can be as simple as a single number or variable, or they can be more complex, involving multiple numbers, variables, and operations.

For example, 3 + 5 is an expression that represents the sum of two numbers, which evaluates to 8. Another example is 2x - 5, which involves a variable (x) and two operations (multiplication and subtraction).

Now,

Let's start by simplifying (-3/5 + 5/3):

First, we need to find a common denominator between 5 and 3, which is 15

then,

-3/5 + 5/3 = -9/15 + 25/15

Next, we can add the two fractions:

-9/15 + 25/15 = 16/15

So, (-3/5 + 5/3) simplifies to 16/15.

Now, let's simplify (2 - 4/3):

We can rewrite 2 as 6/3, then subtract 4/3:

6/3 - 4/3 = 2/3

So, (2 - 4/3) simplifies to 2/3.

Finally, we can subtract 2/3 from 16/15:

16/15 - 2/3

To subtract fractions, we need a common denominator between 15 and 3, which is 15. then

16/15 - 10/15 = 6/15

So, the resulting constant is 6/15, which can be simplified by dividing both the numerator and denominator by their greatest common factor (which is 3):

6/15 = 2/5

Therefore,

                the resulting constant is 2/5.

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Answer:

This is the answer!!!

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