he radius of a circle is 12 m. Find its circumference in terms of pi

The number of positive and negative real roots of the function

x³ - x² - x - 5 are 1 and 2 respectively.

What is Descartes' Rule?

Descartes' rule of sign is used to determine the number of real zeros of a polynomial function. It tells us that the number of positive real zeros in a polynomial function f(x) is the same or less than by an even numbers as the number of changes in the sign of the coefficients.

Number of positive real roots of f(x) ≤ Number of sign changes f(x)

Number of negative roots of f(x) ≤ Number of sign changes of f(-x)

According to the given questions:

The given polynomial function f(x) = x³ - x² - x - 5

We can observe the number of sign changes in the coefficients

The sign changes only once

hence there is one positive real root

Now, f(-x) = -x³ + x² - x + 5

Clearly sign changes 2 times evenly

Therefore the function has 2 negative real roots

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Answer:

y>2

Step-by-step explanation:

subtract 8 on both sides

Answer:

y > 2

Step-by-step explanation:

y + 8 > 10

Subtract 8 from both sides.

y > 10 - 8

y > 2

The correct answer is The standard deviation for Portfolio P is less than 25

This response is accurate because a portfolio made up of two stocks with a correlation of less than one will always have a standard deviation that is lower than the standard deviation of the stocks added in accordance with their weight in the portfolio. For example, in this scenario, both stocks have a weight of 50% and a standard deviation of 25%, so their sum will be.

The portfolio standard deviation will be smaller than 25% since (0.5*25%) + (0.5*25%) = 25%.

Therefore, the standard deviation for Portfolio P is less than 25

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Answer:

A

Step-by-step explanation:

The others involve more multiplication and addition/subtraction rather than division.

Answer:

- 63

Step-by-step explanation:

Let's translate the sentences into expressions:

1. "product of negative 12 1/2 and 4.8" means:

      (-12 1/2)*(4.8)

    I'll simplify this by stating (-12.5)*(4.8)

2.   "three less than" means subtract 3, or

      -3

Now combine the two expressions:

   (-12.5)*(4.8) - 3

   (-60) - 3

= - 63

In Lorentz transformations we have velocity based factors that is not present in Galilean ones.

The relationship between two distinct coordinate frames that are moving relative to one another at a constant speed is known as a Lorentz transformation. Dutch physicist Hendrik Lorentz is credited with coining the name of the transformation. There are two frames of reference: Inertial Frames, which refer to motion that has a constant speed.

The relationship between two distinct coordinate frames that are moving relative to one another at a constant speed is known as a Lorentz transformation. Dutch scientist Hendrik Lorentz is credited with coining the term transformation. There are two frames of reference: Inertial Frames, which relate to motion that has a constant speed.

Any and all rulers and other self-contained length standards, such as those you might use to set up a measurement frame, can be contracted in length based on velocity. This results in the Lorentz factor at the place in the LT.

Any and all clocks and other physically independent systems, such as those used to record events in a measurement frame, are subject to velocity time dilation. As a result, the LF is temporarily in the LT.

The fact that applying Einstein synchronisation individually for each measurement frame turns out to be natural. Consequently, the position-dependent synchronisation offset between the clocks of one measurement frame and those of the other is represented by the enigmatic second term in the LT for the time.

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Answer:

1. EF ≈ 22.00

2. m∠E ≈ 36.20°

3. m∠F ≈ 53.81°

Step-by-step explanation:

1. Use the trigonometric function sine.

sin(60°) = EF / 25.4

EF = 25.4 sin(60°)

EF ≈ 22.00

2. Use the inverse of the trigonometric function sine (denoted arcsin).

sin(m∠E) = 15/25.4

m∠E = arcsin(15/25.4)

m∠E ≈ 36.20°

3. Use the inverse of the trigonometric function cosine (denoted arccos).

cos(m∠F) = 15/25.4

m∠F = arccos(15/25.4)

m∠F ≈ 53.81°

Answer: 2.5

Step-by-step explanation: 40 divided by 4 = 10  1.4 x 10 = 2.5

Answer:

2.5

Step-by-step explanation:

1/4 is equal to 0.25, So if it's 0.25 for 4 servings, the ratio is 0.25:4. You can the divide 40 by 4 and get 10. You can now take that ten and multiply it by 0.25 to get 2.5 or 2 and 1/2

Answer:

-1/2

Step-by-step explanation:

Slope= [tex]\frac{y_{2}-y_{1} }{x_{2}- x_{1} }[/tex].

(5-2)/(-8+2)

Simplify:

3/-6

-1/2

The mathematical domain of the function is 0<or = 5<or = -0.3

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

the type of behavior that is appropriate for a given person, object, or institution; the reason why something exists; a role. any formal event or gathering that is public or social. a variable connected to or reliant upon another variable: A price depends on both supply and demand.

According to the above statements:-

The mathematical domain of the functions are:-

0<or = 5<or = -0.3

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Check the picture below.

The angle between a clock's minute and hour hands changing at 10 o'clock in the morning is 5.5 degrees/minute.

what is the rate of change in calculus?

The rate of change defines the relationship between two changing variables. Consider a moving object that moves twice as much in the vertical direction (y) as it does in the horizontal direction (x). This can be expressed mathematically as y = 2x.

Let 'θ' represent the angle between the minute and hour hand.

Let θ1 be the angle between the minute hand and 12.

                     [tex]\frac{d\theta_2}{dt}=\frac{1}{60*12}\times2\pi\\\\\frac{d\theta_2}{dt}=\frac{\pi}{360}[/tex](Between hour hand and 12)

                     [tex]\theta=\pm(\theta_1-\theta_2)\\\\\frac{d\theta}{dt}=\pm(\frac{d\theta_1}{dt}-\frac{d\theta_2}{dt})\\\\\frac{d\theta}{dt}=\pm(\frac{\pi}{30}-\frac{\pi}{360})\\\\\frac{d\theta}{dt}=\pm5.5$ degree$[/tex]

Hence the angle between a clock's minute and hour hands changing at 10 o'clock in the morning is 5.5 degrees/minute.

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Since, the average age of 33 fifth-graders is 11. the average age of 55 of their parents is 33. The average age of all of these parents and fifth graders is 24.75.

Average age of the population calculated as the arithmetic mean. Another parameter determining the average age of the population is the median age. High-level terms.

Given In the question:

Average age of 33 fifth graders is 11 years.

Average age of parents is 33 Years.

Therefore,

The sum of the ages of the fifth graders is 33 × 11,

and, the sum of the ages of the parents is 55 × 33.

Therefore, the total sum of all their ages must be 2178,

and given 33 + 55 = 88 people in total, their average age is

                                  = 2178/88

                                  = 99/4

                                  = 24.75    

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The efficiency of slotted aloha by letting n approach infinity is 1/e and the maximum value of probability is 1/n.

Given that:

No. of nodes = (n)

The efficiency of slotted aloha by letting n approach infinity is E (p)= np(1-p)^(n-1).

By derivation,

E' (p) =  n(1-p)^(n-1) - np(n-1)(1-p)^(n-2)

E' (p) =  n(1-p)^(n-2) x [(1- p) - p(n-1)]

E' (p) =  n(1-p)^(n-2) x [1-np]

Let E'(p) =0

i.e. Either,  n(1-p)^(n-2) = 0

=> p = 1 (minima)

Or [1-np] = 0

=> p = 1/n (maxima)

So, for the value of p* = 1/n, we can maximize this expression.

When  p = 1/n, the efficiency of slotted aloha is

E(p*) = n.1/n (1-1/n)^(n-1)

E(p*) = (1-1/n)^(n-1)

E(p*) = (1-1/n)^n/(1-1/n)

Since, [tex]\lim_{n \to \infty} (1-1/n) = 1\\[/tex]

[tex]\lim_{n \to \infty} (1-1/n)^n = 1/e[/tex]

So, when n approaches infinite,

Efficiency =>  [tex]\lim_{n \to \infty} E(p*) = 1/e[/tex]

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Jessica has three dice with 10 sides, 13 sides and 5 sides respectively and she rolls all dice once and if Z is number of ones occur then

The expectation value i.e, E(Z) is 0.376 and variance V[Z] = 0.321..

Indicator method :

This is a powerful way to find expected counts. This follows from the observation that the number of "good" outcomes in a trial can be counted by first coding each "good" outcome as one, coding each other outcome as zero, and then adding 1 and 0.

let X₁ be the outcome of a 10 sided die

X₂ be the outcome of 13 sided die

X₃ be the outcome of 5 sided die

let l₁ ,I₂ ,I₃ be three indicator functions such that

I₁ =1 if X₁ = 1

=0 otherwise

I₂ = 1 if X₂ = 1

=0 otherwise

I₃ = 1 if X₃ = 1

=0 otherwise

so Z denotes the number of ones showing when the three dice are rolled once.

so Z=I₁ +I₂ +I₃

so E[Z]=E[I₁]+E[I₂]+E[I₃]

so E[I₁]=1×P[X₁=1] = 1/10

E[I₂]=1×P[X₂=1] = 1/13

E[I₃]=1×P[X₃=1] = 1/5

so, E[Z]=1/10+1/13+1/5=49/130 = 0.3769

the variance = V[Z] = V[I₁]+V[I₂]+V[I₃] since the outcomes of the 3 different die are independent to each other hence no covariance term.

V[I₁]= 1²P[X₁=1]- E²[I₁]=1/10 -(1/10)²= 0.09

V[I₂]= 1²P[X₂=1]- E²[I₂]=1/13-(1/13)²= 12/169 = 0.071

V[I₃]= 1²P[X₃=1]- E²[I₃]=1/5 -(1/5)²= 4/25 = 0.16

so V[Z]= 0.09 + 0.071 + 0.16 = 0.321

Hence, the expectation value i.e, E(Z) is 0.3769..

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Answer:If Amy is not tardy, then she will not get a detention

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Using law of sine and triangle rule, the value of n will be; 443 inches

The law of sines establishes the relationship between the sides and angles of an oblique triangle(non-right triangle). Law of sines and law of cosines in trigonometry are important rules used for "solving a triangle".

We can apply the sine rule to find the missing angle or side of any triangle using the requisite known data.

The formula is given as;

a / sin A = b / sin B = c / sin C

In this triangle NOP, we can find the value of angle P then;

∠N +  ∠O  +  ∠P = 180

57 + 55 +  ∠P = 180  :

since Sum of angles in a triangle is equal 180 degrees

∠P= 180 - 112

∠P = 68

Using law of sine;

p / sin P = n / sin N

490 / sin68 = n / sin57

n = [(490 x sin 57) / sin 68]

n = 443 inches

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The correct option  b. trial-and-error, is employed in the approach to issue solving that entails testing each potential solution until one is successful.

Trial and error is attempting a way, seeing if it succeeds, and trying a different method if the first one doesn't.

Thus, trial-and-error, is employed in the approach to issue solving that entails testing each potential solution until one is successful.

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The number of movies on which Avery's songs were played is 2 times

From the question, we have the following parameters that can be used in our computation:

Songs played in commercial = $40

Songs played in movie = $140

Total earnings = $480

Number of times played on commercial = 7

The above parameters when represented as an equation is

Total earnings = Songs played in commercial * Number of times played on commercial + Songs played in movie * Number of times played in a movie

Substitute the known values in the above equation, so, we have the following representation

40 * 7 + 140 * Number of times played in a movie = 480

Evaluate the products

280 + 140 * Number of times played in a movie = 480

So, we have

Number of times played in a movie = 200/140

Evaluate

Number of times played in a movie = 2

Hence, the number of times is 2 times

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If the given point is p(x, y) and change the sign of its x coordinates and y coordinates, then the new location will be on third quadrant

The coordinates of the point p = (x, y)

In the graph, there are four quadrants.

In first quadrant the x axis value and y  axis value will be positive. In second quadrant the value of x will be negative and y will be positive. In the third quadrant the value of and y will be negative. In fourth quadrant the value of x will be positive and y will be negative

Here at first both x and y are positive and it will be on first quadrant. The the sign of the x coordinates and y coordinates will change sign. So both of them will be negative.

Therefore, the location of will be on third quadrant

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The graph which represents the equation f ( x ) = [ x + 1 ] is Option 4.

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = [ x + 1 ]

The function f ( x ) can be written as

y = [ x + 1 ] , where the equation f ( x ) = y

Substituting the value for x , we get

a)

when x = 0

The value of equation is

y = [ x + 1 ]

y = [ 0 + 1 ]

y = 1

So , the coordinates are ( 0 , 1 )

b)

when x = 1

The value of equation is

y = [ x + 1 ]

y = [ 1 + 1 ]

y = 2

So , the coordinates are ( 1 , 2 )

c)

when x = 2

The value of equation is

y = [ x + 1 ]

y = [ 2 + 1 ]

y = 3

So , the coordinates are ( 2 , 3 )

d)

when x = -1

The value of equation is

y = [ x + 1 ]

y = [ -1 + 1 ]

y = 0

So , the coordinates are ( -1 , 0 )

Hence ,

On plotting the points in the graph , we get the equation as y = x + 1

And the solution is Option D.

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The equation of the line is [tex]y = -\frac{3}{4}x[/tex].

What is the equation of a line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

We have,

the line passes through the point (4,-3),

the points perpendicular to the line 4x - 3y = 3

The equation of a line in slope-intercept form is y = mx + c ( m is the slope and c is the y-intercept).

rearrange 4x - 3y = 3 into this form

subtract 4x from both sides

- 3y = - 4x + 3 ( divide all terms by - 3 )

[tex]y = \frac{4}{3}x - 1[/tex] ← in slope-intercept form

with slope m = 4/3,

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular} = \frac{1}{-m} = \frac{1}{-\frac{4}{3} } = \frac{3}{-4}[/tex]

[tex]y = -\frac{3}{4}x + c[/tex] ← is the partial equation

To find c substitute (4, -3) into the partial equation,

-3 = -3 + c

c = -3 + 3

c = 0,

[tex]y = -\frac{3}{4}x[/tex]

Hence, the equation of the line is [tex]y = -\frac{3}{4}x[/tex] .

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The critical value of z separates the rejection region from the nonrejection region while observed value of z is the value calculated for a sample statistic such as x.

A critical value of z is used when the sampling distribution is normal, or close to normal. The critical value of z refers to the point that cuts off area under graph for the standard normal distribution separating the rejection and nonrejection region of the data. The Critical value of z can indicate what probability any particular variable will have. These values are typically obtained from a table such as the standard normal distribution table. The observed value of z is a value determined for a sample statistic x. It is a test statistic for Z-tests that measures the difference between an observed statistic and its hypothesized population parameter in units of the standard deviation.

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Answer: 4.857 x 10^4

Step-by-step explanation:

Answer: 212.50

Step-by-step explanation: she has 60% or  127.5

The percent of the probability that a female patient will have type-o blood is 46.7%

To know the percent of female patients who will be having type 0 blood, all you have to do is divide the number of female patients with O-blood type by the total number of patients with O-blood type. Then finally you will have to multiply the quotient by 100 to get the percent as follows:

number of females with o-blood type = 140 Females

total number of patients with o-blood type = 300 patients

Percentage of Females with o-blood type = (140/300) * 100 = 46.7%

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Answer:

Step-by-step explanation:

$28.75