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Answer:

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Step-by-step explanation:

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Answer:

0.6472 = 64.72% probability that a randomly selected page does not need to be retyped.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Poisson distribution with an average of three errors per page

This means that [tex]\mu = 3[/tex]

What is the probability that a randomly selected page does not need to be retyped?

Probability of at most 3 errors, so:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]

[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]

Then

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0498 + 0.1494 + 0.2240 + 0.2240 = 0.6472[/tex]

0.6472 = 64.72% probability that a randomly selected page does not need to be retyped.

Answer: a = 25.67

Step-by-step explanation:

Answer:

260% is the correct answer

Step-by-step explanation:

i hope i helped

D

A

B

C

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Answer:

[tex]x = 3[/tex]

Step-by-step explanation:

Given

[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]

Required

Solve for x

We have:

[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]

Remove log6 from both sides

[tex](4x-5) = (2x+1)[/tex]

Collect like terms

[tex]4x - 2x = 5 + 1[/tex]

[tex]2x = 6[/tex]

Divide by 2

[tex]x = 3[/tex]

Answer:

6

Step-by-step explanation:

First, we can expand the function to get its expanded form and to figure out what degree it is. For a polynomial function with one variable, the degree is the largest exponent value (once fully expanded/simplified) of the entire function that is connected to a variable. For example, x²+1 has a degree of 2, as 2 is the largest exponent value connected to a variable. Similarly, x³+2^5 has a degree of 2 as 5 is not an exponent value connected to a variable.

Expanding, we get

(x³-3x+1)²  = (x³-3x+1)(x³-3x+1)

= x^6 - 3x^4 +x³ - 3x^4 +9x²-3x + x³-3x+1

= x^6 - 6x^4 + 2x³ +9x²-6x + 1

In this function, the largest exponential value connected to the variable, x, is 6. Therefore, this is to the 6th degree. The fundamental theorem of algebra states that a polynomial of degree n has n roots, and as this is of degree 6, this has 6 roots

9514 1404 393

Answer:

  (-13, 10)

Step-by-step explanation:

If M is the midpoint of segment DE, then ...

  D = 2M -E

  D = 2(-3, 4) -(7, -2) = (2(-3)-7, 2(4)+2) = (-13, 10)

The other end point is (-13, 10).

===========================================

Explanation:

There are 3 ways to select the single math book and 4*3/2 = 12/2 = 6 ways to pick the two other books that are either physics or history (order doesn't matter). This is effectively because we have 3+1 = 4 books that are either physics or history, and we're using the nCr combination formula.

Overall, there are 3*6 = 18 ways to select the three books such that one is math, and the other two are either physics or history.

-------------------

There are 3+3+1 = 7 books total. Since we're selecting 3 of them, we use the nCr formula again and you should get 35.

Or you could note how (7*6*5)/(3*2*1) = 210/6 = 35

This says there are 35 ways to select any three books where we can tell the difference between any subject (ie we can tell the difference between the math books for instance).

-------------------

We found there are 18 ways to get what we want out of 35 ways to do the three selections. Therefore, the answer as a fraction is 18/35

Answer:

60

Step-by-step explanation:

10 x 6 = 60

Hope this helped! :)

Answer:

y = 3

Step-by-step explanation:

6sin(30) = 3

y'' - 6y' + 9y = 0

If y = C₁ exp(3x) + C₂ x exp(3x), then

y' = 3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x))

y'' = 9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x))

Substituting these into the DE gives

(9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x)))

… … … - 6 (3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x)))

… … … + 9 (C₁ exp(3x) + C₂ x exp(3x))

= 9C₁ exp(3x) + 6C₂ exp(3x) + 9C₂ x exp(3x))

… … … - 18C₁ exp(3x) - 6C₂ (exp(3x) - 18x exp(3x))

… … … + 9C₁ exp(3x) + 9C₂ x exp(3x)

= 0

so the provided solution does satisfy the DE.

minus sign ironically makes it go to the right

because the function crosses the y axis at -13

It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The equation y = x - 13 represents a transformation of the graph of y = x. To find the type of  transformation, we have to compare the two equations and look for changes.

In the equation y = x - 13, we subtract 13 from the value of x.

This means that the graph of y = x is shifted 13 units downwards,

since every point on the graph has 13 subtracted from its y-coordinate.

Hence,  It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

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Answer:

f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.

Step-by-step explanation:

The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.

* if x>1, then x-1>0.

* Also since the parabola opens up, then y>5.

So let's solve y=(x-1)^2+5 for x.

Subtract 5 on both sides:

y-5=(x-1)^2

Take square root of both sides:

Plus/minus sqrt(y-5)=x-1

We want x-1>0:

Sqrt(y-5)=x-1

Add 1 on both sides:

Sqrt(y-5)+1=x

Swap x and y:

Sqrt(x-5)+1=y

x>5

y>1

Answer:

Given E(t)=1100(100-t)+580(100-t)^2

Put t = 99.5, we get

E(99.5)=1100(100-99.5)+580(100-99.5)^2

E(99.5)=1100(0.5)+580(0.5)^2

E(99.5)=1100(0.5)+580(0.25)

E(99.5)=550+145

E(99.5)=695m

Step-by-step explanation:

It can be concluded that -

E(99.5) = 695

E(100) = 0

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as follows -

E(t) = 1100(100 - t) + 580(100 - t)²

The given function is -

E(t) = 1100(100 - t) + 580(100 - t)²

At → E(99.5)

E(99.5) = 1100(100 - t) + 580(100 - t)²

E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²

E(99.5) = 1100(0.5) + 580(0.5)²

E(99.5) = 550 + 145

E(99.5) = 695

At → E(100)

E(100) = 1100(100 - t) + 580(100 - t)²

E(100) = 1100(100 - 100) + 580(100 - 100)²

E(100) = 0

Therefore, it can be concluded that -

E(99.5) = 695

E(100) = 0

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Answer:

B) All real numbers except 0 and integer multiples of 8π∕5

Step-by-step explanation:

Cotangent function:

The cotangent function is given by:

[tex]y = \cot{ax} = \frac{\cos{ax}}{\sin{ax}}[/tex]

Domain:

All real values except those at which:

[tex]\sin{ax} = 0[/tex]

The sine is 0 for 0 and all integer multiples of [tex]\frac{1}{a}[/tex]

In this question:

[tex]a = \frac{5}{8}[/tex], so the values outside the domain are 0 and the integer multiples of [tex]\frac{8}{5}[/tex]. Then the correct answer is given by option b.

Answer:

[tex]{ \tt{hypotenuse = { \boxed{5}}}} \\ { \tt{opposite = { \boxed{3}}}} \\ { \tt{adjacent = { \boxed{4}}}} \\ \\ { \tt{ \sin \angle R = \frac{{ \boxed{3}}}{{ \boxed{5}}} }} \\ \\ { \tt{ \cos \angle R = \frac{{ \boxed{4}}}{{ \boxed{5}}} }} \\ \\ { \tt{ \tan \angle R = \frac{ \boxed{3}}{{ \boxed{4}}} }}[/tex]

Answer:

jhshejwjabsgsgshshsnsjs

Answer:

Step-by-step explanation:

Put the equation into center-radius form.

x² + y² + 8x - 12y + 24 = 0

x² + y² + 8x - 12y = -24

(x²+8x) + (y²-12y) = -24

(x²+8x+4²) + (y²-12y+6²) = 4²+6²-24

(x+4)² + (y-6)² = 28

Center: (-4,6)

radius: √28

Two workers finished a job in 7.5 days.

How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?

let t = time required by one worker to complete the job alone

then

(t+8) = time required by the other worker (shirker)

let the completed job = 1

A typical shared work equation

7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1

multiply by t(t+8), cancel the denominators, and you have

7.5(t+8) + 7.5t = t(t+8)

7.5t + 60 + 7.5t = t^2 + 8t

15t + 60 = t^2 + 8t

form a quadratic equation on the right

0 = t^2 + 8t - 15t - 60

t^2 - 7t - 60 = 0

Factor easily to

(t-12) (t+5) = 0

the positive solution is all we want here

t = 12 days, the first guy working alone

then

the shirker would struggle thru the job in 20 days.

Answer:7 + 17 = 24÷2 (since there are 2 workers) =12. Also, ½(7) + ½17 = 3.5 + 8.5 = 12. So, we know that the faster worker will take 7 days and the slower worker will take 17 days. Hope this helps! jul15

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

A local minimum is where the curve stops going down and starts going up. It is the bottom of any U-shaped spot. Here, those are identified with dots at the coordinates (-1, -2) and (3, -1).

(a) the x-values at which f has a local minimum are -1 and 3.

(b) the local minimum values of f are -2 and -1 at those x-values.

there are 12 set of months in a year

10% of 360 is 18 more than 5% of 360.

The percentage is defined as ratio expressed as a fraction of 100.

What are Arithmetic operations?

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

Given data as :

10% of 360

5% of 360

Firstly, we have to determine 10% of 360,

⇒ 10% of 360

⇒ (10/100)360

⇒ (0.10)360

So, 10% of 360 is 36.

⇒ 5% of 360

⇒ (5/100)360

⇒ (0.05)360

So, 5% of 360 is 18.

Since 10% of 360 is more than 5% of 360

So, substract 18 from 36, and

⇒ 36 - 18

⇒ 18

Hence, 10% of 360 is 18 more than 5% of 360.

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Answer:

See Below.

Step-by-step explanation:

We are given the equation:

[tex]\displaystyle y^2 = 1 + \sin x[/tex]

And we want to prove that:

[tex]\displaystyle 2y\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right) ^2 + y^2 = 1[/tex]

Find the first derivative by taking the derivative of both sides with respect to x:

[tex]\displaystyle 2y \frac{dy}{dx} = \cos x[/tex]

Divide both sides by 2y:

Find the second derivative using the quotient rule:

[tex]\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{(\cos x)'(2y) - (\cos x)(2y)'}{(2y)^2}\\ \\ &= \frac{-2y\sin x-2\cos x \dfrac{dy}{dx}}{4y^2} \\ \\ &= -\frac{y\sin x + \cos x\left(\dfrac{\cos x}{2y}\right)}{2y^2} \\ \\ &= -\frac{2y^2\sin x+\cos ^2 x}{4y^3}\end{aligned}[/tex]

Substitute:

[tex]\displaystyle 2y\left(-\frac{2y^2\sin x+\cos ^2 x}{4y^3}\right) + 2\left(\frac{\cos x}{2y}\right)^2 +y^2 = 1[/tex]

Simplify:

[tex]\displaystyle \frac{-2y^2\sin x-\cos ^2x}{2y^2} + \frac{\cos ^2 x}{2y^2} + y^2 = 1[/tex]

Combine fractions:

[tex]\displaystyle \frac{\left(-2y^2\sin x -\cos^2 x\right)+\left(\cos ^2 x\right)}{2y^2} + y^2 = 1[/tex]

Simplify:

[tex]\displaystyle \frac{-2y^2\sin x }{2y^2} + y^2 = 1[/tex]

Cancel:

[tex]\displaystyle -\sin x + y^2 = 1[/tex]

Substitute:

[tex]-\sin x + \left( 1 + \sin x\right) =1[/tex]

Simplify. Hence:

[tex]1\stackrel{\checkmark}{=}1[/tex]

Q.E.D.

Answer:

Obtuse Scalene Triangle

Step-by-step explanation:

Sum of the squares of the smaller 2 sides < longest side squared = Obtuse Scalene Triangle

Answer:

[tex]A)\:x<12[/tex]

[tex]5(x+5)<85\\5x+25<85\\5x<85-25\\5x<60\\x<12[/tex]

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Answer:

x < 12.................................

Answer:

[tex]{ \tt{ = ( log_{x}16)( log_{2}x) }}[/tex]

Change base x to base 2:

[tex]{ \tt{ = (\frac{ log_{2}16}{ log_{2}x } )( log_{2}x)}} \\ \\ { \tt{ = log_{2}(16) }} \\ = { \tt{ log_{2}(2) }} {}^{4} \\ = { \tt{4 log_{2}(2) }} \\ = { \tt{4}}[/tex]