let f be the function with derivative given by f'(x)=x^2-2/x. On which of the following intervals is f decreasing ?
A. (- [infinity], -1] only
B. (- [infinity], 0)
C. [- 1,0) only D. (0, ∛2]
E. (∛2, [infinity])

The unit interval [0,1] in the real numbers is a compact set, and we can find a number m such that every open cover of [0,1] contains a finite subcover of m elements.

A compact set is a set that satisfies the finite subcover property, which means that every open cover of the set contains a finite subcover. This means that for any open cover of a compact set, there exists a finite subcover containing a certain number of elements (m) that can cover the entire set.

Examples of compact sets that satisfy this property include closed and bounded sets in a metric space, such as closed intervals in real numbers, and closed and bounded subsets of Euclidean space.

The unit interval [0,1] in the real numbers is a compact set, and we can find a number m such that every open cover of [0,1] contains a finite subcover of m elements.

Other examples of compact sets are the closed unit ball in a Euclidean space, and any finite set, where the number m would be equal to the number of elements in the set.

In summary, compact sets are sets that have the property of finite subcover, and for any open cover of a compact set, there exists a finite subcover containing a certain number of elements (m) that can cover the entire set. Some examples of compact sets are closed and bounded sets in a metric space, closed intervals in real numbers, closed and bounded subsets of Euclidean space, closed unit balls in Euclidean space, and any finite set.

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Answer:

-16

Step-by-step explanation:

A quarter-circle with a radius of 5 has the area: 25π/4, This is where the shaded area in the figure is located.

The area of a circle’s sector is calculated as /360o (r²), where r is the radius of the circle and is the angle of the sector.

The little, subtle distinctions between words are distinguished by shades of meaning. The terms “happy” and “ecstatic,” for example, both express emotion, but one is more powerful than the other. When students study shades of meaning, they learn how to effectively articulate how they feel or think. Shade is any gloomy place where sunshine or other strong light is obstructed. A shadow is a dark form that develops on a surface when an item blocks sunlight or other light.

The shaded area in the illustration is a quarter-circle with a radius equal to 10/2, or 5 units, or half the length of the square's side.

The following formula can be used to determine a circle's area:

A = πr²

If pi is present and r is the radius (approximately equal to 3.14).

A quarter-circle with a radius of 5 has the following area:

A = (π × 5²) / 4 = (π × 25) / 4 = 25π / 4

This is where the shaded area in the figure is located.

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Answer:

1

Step-by-step explanation:

This is an experimental study, as the researcher is manipulating the independent variable (caffeine consumption) to measure the dependent variable (activity level) in a controlled environment.

This is an experimental study, as the researcher is manipulating the independent variable (caffeine consumption) to measure the dependent variable (activity level) in a controlled environment. In an experimental study, the researcher has control over the independent variable and is able to measure the results of the manipulation on the dependent variable. In this study, the researcher is measuring the activity level of the children based on their caffeine consumption, which the researcher can control. The researcher is also measuring the activity level in a controlled environment, the playground, which provides a consistent setting for the experiment. This type of study is designed to test the researcher's hypothesis and determine whether there is a relationship between caffeine consumption and activity level.

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Answer:

96m2

Step-by-step explanation:

First we have to find the perimeter of parallelogram

Now,

Breadth(b)=10m

Height(h)=6m

Perimeter of paralleogram(p)=b×h

=10×6

=60m

Then,

Breadth(b)=12m

Height(h)=6m

Perimeter of triangle(p)=1×b×h

2

= 1 ×6×12

2

=36m2

Now,

Perimeter of above figure= Perimeter of paralleogram+perimeter of triangle

= 60+36

. =96m2

Answer: 8/100 or 2/25

Step-by-step explanation:

8% is automatically out of 100% so it would be

8/100

and the simplified version would be 2/25

Answer: 2/25

Step-by-step explanation:

The functions sin and cosine, sometimes known as sin() and cos(), show how a right triangle is shaped. Answer is 8.212°.

The functions sin and cosine, sometimes known as sin() and cos(), show how a right triangle is shaped.

The ratio of the opposite side to the hypotenuse is called sin(), and the ratio of the adjacent side to the hypotenuse is called cos(), when viewed from a vertex with angle.

So, the Pythagorean identity-based formula for sin is sin²x = 1 - cos²x.

Hypotenuse²=base²+perp²

(8)²=(7)²+(perp)²

64=49+(perp)²

64/49=perp²

1.306=perp²

Now taking square root on both sides

Perp=√1.306

Perp=1.142

Sin C=opposite/hypotenuse

Sin =1.142/8

Sin C=0.14285

C=Sin^-1 0.14285

C=8.212°

Answer is 8.212°.

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B-The two distributions for number of cars in line are both skewed right.

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According to the round off rule, the resulting value of the total distance is  135,000

As we al know that if the rounded number increases then the given number is said to be rounded up on the other hand if the rounded number decreases then it is said to be rounded down.

Here we have given the details about the race is made up of 4 separate stages.

Now, we need to find the total distance, that can be calculated by adding all the given distance, then we get,

=> 30,060 + 21,111 + 33,501 + 49,840

=> 134512.

Now, we have to round off the value to the nearest thousandth term, then it can be written as,

Here we need rounded to the nearest thousands place. The 4 in the thousands place rounds up to 5 because the digit to the right in the hundreds place is 5.

=> 135,000

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The team plots alternatives on a two by two matrix using the 2x2 Matrix decision support technique. The matrix diagram is a straightforward square divided into four equal quadrants, sometimes known as a four blocker or magic quadrant. A decision criterion, such as cost or effort, is represented by each axis.

A diagonal matrix in linear algebra is a matrix with all zero entries outside of the primary diagonal; the word typically applies to square matrices. The major diagonal's components can either have zero or nonzero elements.

The redundant column vectors are all taken out of the kernel when determining the basis of a matrix, leaving only the linearly independent column vectors. A basis is therefore merely the sum of all the linearly independent vectors.

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The trainee's z-score is -1.5.

An illustration of a standardized score is the z-score. A z-score calculates how far a data point deviates from the distribution's mean by standard deviation.

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score, μ is the population mean, and σ is the population standard deviation.

Given:

Mean= 77

standard Deviation = 2

x= 74

Using z score formula

Z score = (x - μ)/ σ

Z score = (74 - 77)/ 2

Z score = -1.5

Now, the P-value from Z-Table:

P(x<74) = 0.066807

P(x>74) = 1 - P(x<74)

            = 0.93319

P(74<x<77) = 0.5 - P(x<74)

                  = 0.43319

Hence, the z- score is -1.5.

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Answer:

   20 miles

Step-by-step explanation:

first, draw a diagram. Then, use the pythagorean theorem to calculate.

The value of x in the simplest radical form is 3.

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given: Let the triangle be ΔABC

The triangle ABC is a right-angled triangle and the angles inside the triangles are 45°, 45° and 90°

tan θ = x / 3

Now , θ = 45°

So, tan 45° = x / 3

The value of x is 3.

Hence, the value of x is 3.

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Solve in equal value Method step by step solution is given below.

Equal value is a concept that states all people, regardless of race, gender, ethnicity, sexual orientation, or any other defining characteristic, are of equal worth and should be treated equally. This concept is fundamental to democracy and is enshrined in the Universal Declaration of Human Rights. Equal value is also a foundation of economic theory, as it states that everyone should be able to access and benefit from economic resources, whatever their background.


Step 1: Isolate the 5y term on one side:
5y = -13-3x

Step 2: Divide both sides by 5:
y = (-13-3x)/5

Step 3: Replace the y with its expression:
x - 7 = (-13-3x)/5

Step 4: Distribute the -7 over the denominator of the right side:
x - 7 = (-13-3x-35)/5

Step 5: Add 7 to both sides:
x = (-13-3x-35+35)/5

Step 6: Simplify the expression:
x = (-13-3x)/5

Step 7: Solve for x:
x = -26/8

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By using a trigonometric relation, we will see that the hypotenuse of the right triangle is:

x = 22

We want to find the value of x on the right triangle.

Notice, it is the hypotenuse of the right triangle.

We know one angle on the triangle, and also the adjacent cathetus, then we can use the trigonometric relation:

cos(a) = (adjacent cathetus)/hypotenuse

We can replace the known values to get:

cos(30°) = 11*√3/x

(√3)/2 = 11*√3/x

Now we can solve this for x.

Dividing both sides by √3 we get:

1/2 = 11/x

x/2 = 11

x = 2*11

x = 22

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The total time taken by the experienced bricklayer to complete the job as per given condition is equal to 13 hours.

As given in the question,

Let the time taken by experienced bricklayer be 't' hours

Then time taken by apprentice bricklayer be '2t' hours

Time to complete 1 complete work is

Experienced bricklayer worked for 4 hours

Apprentice bricklayer worked for ( 4 + 14 ) = 18 hours

Required equation to complete 1 work is :

( 4/x) + ( 18 /2x) = 1

⇒( 8 + 18 )/ 2x = 1

⇒26/2 = x

⇒ x = 13 hours

Therefore, time taken by the experienced bricklayer to complete the job is equal to 13 hours.

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The total monthly payment would be $17.36.

Option (d) is correct.

What is the annuity payment?

An annuity payment is a fixed, regular payment made to an individual or organization over a specific period of time. It is typically used in the context of financial transactions, such as loans, investments, and insurance.

To calculate the monthly payment Bianca will have to make to avoid interest capitalization, we can use the formula for the annuity payment:

PMT = (Loan Amount * Interest Rate / (1 - (1 + Interest Rate)^(-n))) / (Interest Rate / 12)

Where:

PMT is the monthly payment

Loan Amount is the amount of the loan, in this case, $2,600

Interest Rate is the annual interest rate, in this case, 6.2%

n is the total number of payments, in this case, 5 years * 12 months/year = 60 months

Plugging in the values, we get:

PMT = (2600 * 0.062 / (1 - (1 + 0.062)^(-60))) / (0.062 / 12)

PMT = $17.36

Hence, the total monthly payment would be $17.36

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Answer: C

Step-by-step explanation:Bianca took out a $2,600 unsubsidized Stafford loan. She will be attending school for four years, and she wishes to have the loan paid off five years before its normal ten-year duration is finished. The loan has an interest rate of 6.2%, compounded monthly. How much will she have to pay monthly to avoid interest capitalization?

a.

$12.40

b.

$19.29

c.

$13.43

d.

$17.36

Please select the best answer from the choices provided

probability will be 1/2 for obtaining correct number that is ng clues to try to guess a secret number: it is a two-digit integer. the tens digit is odd. the units digit is even. the number is greater than $65$.

How do you calculate probability

Probability is the likelihood that something will happen. Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes

it is a two-digit integer. the tens digit is odd. the units digit is even. the number is greater than $65$.

the numbers are 67,69,83,.....etc

In order to simplify these types of expressions, first of all the external element is distributed into the bracket.

This property is called distributive property where the outer number is distributed into the bracket.

The distributive property is generally stated as:

So applying the property on given expression

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Answer:

[tex]\frac{-1}{2}[/tex]

Step-by-step explanation:

Rate of change = [tex]\frac{Change in Y value}{Change in X value}[/tex]

                    Pick any two sets of 'X' and 'Y' value

I chose (-4, 6) as [tex](X_{1} ,Y_{1} )[/tex]and (12, -2) as [tex](X_{2} ,Y_{2} )[/tex] :

Rate of change = Slope / Gradient of graph = [tex]\frac{Y_{2} -Y_{1} }{X_{2} - X_{1} }[/tex]

                                                                         = [tex]\frac{-2 - (6)}{12 - (-4)}[/tex]

                                                                          = [tex]\frac{-2 - 6}{12 + 4}[/tex]

                                                                           = [tex]\frac{-8}{16}[/tex]

                                                                           =  [tex]\frac{- 1}{2}[/tex]

Answer:

Below in bold.

Step-by-step explanation:

m < DAC  = 360 -15 - 155 - 166

                = 24⁰

The bearing of D from A

                = 180 + 15 + 24

                 =  219⁰

or S 39⁰ W.

The equation for the number of white dots is a(n) = 2n - 1 while the equation for the number of black dots is a(n) = (n - 1)²

The pattern for the number of black and white dots is depicted in the attached picture.

Refer to the the picture, the sequence of the white dots are:

n = 1  number of white dots = 1

n = 2  number of white dots = 3

n = 3  number of white dots = 5

n = 4  number of white dots = 7

Notice that the number of white dots form an arithmetic sequence, with:

first term = a = 1

common difference = d = 3 - 1 = 2

Hence, the equation for the nth term is:

a(n) = a + (n - 1) d

a(n) = 1 + (n - 1) x 2

a(n) = 2n - 1

Now look at the black dots.

n = 1  number of black dots = 0

n = 2  number of black dots = 1

n = 3  number of black dots = 4

n = 4  number of black dots = 9

Notice that the number of black dots is a quadratic sequence starting from 0.

We can write:

n = 1  number of black dots = 0 = (1 - 1)²

n = 2  number of black dots = 1  = (2 - 1)²

n = 3  number of black dots = 4 = (3 - 1)²

and so on. Hence, the equation of the nth term for the number of black dots is:

a(n) = (n - 1)²

The picture in your question was missing, but most likely it was like in the attached picture.

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Answer:

14x - y

Steps:

(9x + 3y) + (5x - 4y)

Determine the sign:

9x + 3y + 5x - 4y

Combine as terms:

14x - y

I hope it helps you :)

Therefore , the solution of the given problem of PMI comes out to be

6 ⁿ -1  is always divisible by 5.

A mathematical method known as mathematical induction is used to demonstrate that a claim, formula, or theorem holds true for every natural number. Step 1 (Base Step) demonstrates the truth of a statement for the starting value.

Here,

Given :  6 ⁿ -1  is divisible by 5

Let,

=> 6 ⁿ -1  

=> 6 ¹ - 1

=>5

P(k) is divisible by 5

P(k+1)=6

k+1−1=6.6k−1

=(5+1).6k−1

=5×6 k+6k−1

=5×6k+5m

=5(6k+m)

P(k+1) is divisible by 5

Therefore , the solution of the given problem of PMI comes out to be

6 ⁿ -1  is always divisible by 5.

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The required system of equation is given as y = 3x + 12 and y=x³+4x²+3x+12.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Given equation,
y=x³+4x²+3x+12

To determine the x-intercept put equation y = 0

0 = x³+4x²+3x+12

Factorize the above equation

0=(x²+3)(x+4)

One of the factors from above is given as

x+4=0  

x = -4

The x-intercept is (-4,0)

For the y-intercepts, x=0 and solve.

y = 12

y = 12

The y-intercept is (0,12)

Now equation of the line passing these points is given as.

m = (y₂ - y₁) /  (x₂ - x₁)
m = 12/3
m = 3

C, we already have C=12

So the equation of the line is
y = mx + c
y=3x+12

Thus, the required system of equation is given as y = 3x + 12 and y=x³+4x²+3x+12.

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The main difference between X1 and x1 is that X1 is a random variable and x1 is a specific numerical value.

In mathematics, variables are often used to represent different values, and the difference between uppercase and lowercase letters is often used to distinguish between different types of variables. X1 is a random variable, which represents a value that can take on different values depending on the outcome of an experiment or a probability distribution. x1, on the other hand, is a specific numerical value, which represents a fixed value that is known or can be determined. In short, X1 refers to a variable whose value is uncertain and x1 refers to a specific value of that variable.

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Answer:

68823600

Step-by-step explanation:

By solving a system of equations and a quadratic equation, we will see that x = 2.

We know that x and y are positive integers, that x < y and:

x*y = 56

We also know that "seven times the reciprocal of the smaller integer plus 14 times the reciprocal of the larger integer equals 4"

Then we can write the equation:

7*(1/x) + 14*(1/y) = 4

So we have a system of equations:

x*y = 56

7*(1/x) + 14*(1/y) = 4

We can rewrite the first equation to get:

x = 56/y

And the second equation as:

14/y = 4 - 7/x

Then the system becomes:

56/y = x

14/y = (4 - 7/x)

Taking the quotient between these, we can remove the variable y:

(56/y)/(14/y) = x/(4 - 7/x)

56/14 = x/(4 - 7/x)

4*(4 - 7/x) = x

4*(4x - 7)/x = x

4*(4x - 7) = x^2

So now we have a quadratic equation:

x^2 - 16x + 28 = 0

Using the quadratic formula, we will get:

[tex]x = \frac{16 \pm \sqrt{(-16)^2 -4*1*28} }{2*1} \\\\x = \frac{16 \pm 12 }{2}[/tex]

So the solutions are:

x = (16 - 12)/2 = 2

x = (16 + 12)/2 = 14

But notice that if x = 14, then:

14 = 56/y

y = 56/14

y = 4

And y is larger than x, then x = 14 can be discarded.

The solution is x = 2.

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Therefore , the solution of the quadratic equation comes out to be x value is 4.

The quadratic solution x = ax2 + foo + c=0 is a regression model for one variable equations. According to the First Theorem of Algebra, this polynomial only has one solution because of its second order. Both straightforward and complex solutions are viable options. The term "quadratic formula" refers to a formula with four variables. According to this, there can only be a single squared word present. Mathematical variables or variables a, b, and c are often used to represent the unknown variable "X" in the formula "ax2 + bx + c = 0," which is frequently used to solve arithmetic problems.

Here,

Given :

=> 4x²+ 6x-2+6 - 4x² - 6x

=>  4x² - 4x² + 6x -6x -2 +6

=> 0 + 0 +4

=> 4

Therefore , the solution of the quadratic equation comes out to be x value is 4.

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