Find the indicated limit, if it exists.

See file below.

Answer:

0.0482 = 4.82% probability that at least 6 computers are functioning beyond 6 years

Step-by-step explanation:

For each computer, there are only two possible outcomes. Either it works beyond 6 years, or it does not. The probability of a computer working beyong 6 years is independent of any other computes. This means that the binomial probability distribution is used to solve this question.

As the lifetime of a computer is an exponential variable, the probability of a computer working beyond 6 years is found using the exponential distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Probability of a computer working beyong 6 years:

Mean of 5 years means that [tex]m = 5, \mu = \frac{1}{5} = 0.2[/tex]

The probability is:

[tex]P(X > 6) = e^{-0.2*6} = 0.3012[/tex]

What is the probability that at least 6 computers are functioning beyond 6 years?

10 computers means that [tex]n = 10[/tex]

0.3012 probability of a computer working beyond 6 years means that [tex]p = 0.3012[/tex]

This probability is:

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 6) = C_{10,6}.(0.3012)^{6}.(0.6988)^{4} = 0.0374[/tex]

[tex]P(X = 7) = C_{10,7}.(0.3012)^{7}.(0.6988)^{3} = 0.0092[/tex]

[tex]P(X = 8) = C_{10,8}.(0.3012)^{8}.(0.6988)^{2} = 0.0015[/tex]

[tex]P(X = 9) = C_{10,9}.(0.3012)^{9}.(0.6988)^{1} = 0.0001[/tex]

[tex]P(X = 10) = C_{10,10}.(0.3012)^{10}.(0.6988)^{0} \approx 0[/tex]

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0374 + 0.0092 + 0.0015 + 0.0001 + 0 = 0.0482[/tex]

0.0482 = 4.82% probability that at least 6 computers are functioning beyond 6 years

Answer: x=1.21

Step-by-step explanation:

Given

Function is [tex]f(x)=0.8e^{2x}-9[/tex]

To find the zeroes, equate the function equal to zero

[tex]\Rightarrow 0.8e^{2x}-9=0\\\\\Rightarrow e^{2x}=\dfrac{9}{0.8}\\\Rightarrow e^{2x}=11.25[/tex]

taking natural logarithm both sides

[tex]\Rightarrow \ln (e^{2x})=\ln (11.25)\\\Rightarrow 2x=2.42\\\Rightarrow x=1.21[/tex]

The zero of the equation is 1.21

Answer: B

because its 50/50 chance you'll have heads or tails

Answer:

1/3 x 1/2 x 1/4 = 1/24

Step-by-step explanation:

Answer:

e

Step-by-step explanation:

Answer:

c

exactly 225225225 times

Answer:

The answer is- Close to 225225225 times but probably not exactly 225225225 times

Step-by-step explanation:

according to Khan Academy

Answers

1377

explanation

2:7=9

2=306

9 =?

9×306 = 2754

2 2

=1377 members

Answer:

A: Credit Cards let you spend unlimited amount of money.

Answer:

32

Step-by-step explanation:

Answer:

113.04 yd³

Step-by-step explanation:

The formula of volume of sphere

[tex] = \frac{4}{3} \pi {r}^{3} [/tex]

The volume of the sphere

[tex] = \frac{4}{3} \times 3.14 \times {3}^{3} [/tex]

[tex] = \frac{339.12}{3} [/tex]

= 113.04 yd³

Answer:

can you post the graph so I can answer to the best o my ability

The answer is D. Ask every 20th person listed as a resident of the city

Answer:

hope this help you......

Step-by-step explanation:

Under 18 tickets: 5062-3484=1578

Total money: 3484*18+1578*12=81648$

100%-85%=15% goes to community projects

So, (15/100)*81648=12247.2 $

Answer:

P = 10π + 30 ≈ 61.4

Step-by-step explanation:

Perimeter = s1 + s2 + s3 + s4

= πd/2 + 15 + πd/2 + 15 = 2 (5π + 15) = 10π + 30 ≈ 61.4

Answer:

A

Step-by-step explanation:

[tex] \frac{3\pi}{2} = 270[/tex]

On the unit circle, 270 is located between the third and fourth quadrant.

Sin(-90)=-1

Using the peridoicy formula, sin 270=-1. Whenever Sin is 1 or -1, cos is 0. Sin referred as the y value. Cosine is referred as x value so A is the answer.

The terminal point of the given unit circle is (0.6235, 0.7818).

We have,

To find the terminal point of an angle in a unit circle, we need to use the trigonometric ratios of sine and cosine.

The angle Ф = 3π/7 radians is in standard position,

which means its initial side coincides with the positive x-axis.

The sine of theta is given by the y-coordinate of the terminal point, and the cosine of theta is given by the x-coordinate of the terminal point.

sin(theta) = sin(3π/7) ≈ 0.7818

cos(theta) = cos(3π/7) ≈ 0.6235

The terminal point of the angle theta is (cos(theta), sin(theta)):

Terminal point = (0.6235, 0.7818)

Therefore,

The terminal point of the given unit circle is (0.6235, 0.7818).

Learn more about terminal point of a circle here:

https://brainly.com/question/28973006

#SPJ7

Answer:

x=19.2

Step-by-step explanation:

sin(28)=9/x

x=9/sin(28)

x=19.2

Answer:

3.87

Step-by-step explanation:

? = a

b = 1

c = 4

a² + b² = c²

a² + 1² = 4²

a² + 1 = 16

a² = 15

a = 3.8729

Rounded to hundredths: 3.87

Answer:

y = 1/2x+4

Step-by-step explanation:

First find the slope

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

   = (3 - 5)/(-2 -2)

    = -2/-4

   = 1/2

Using point slope form

y -y1 = m(x-x1)  where m is the slope and (x1,y1) is a point on the line

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

Distribute

y-5 = 1/2x -1

Add 5 to each side

y-5+5 = 1/2x -1+5

y = 1/2x+4

Answer:

X=-4

Step-by-step explanation:

If you are finding x,

set these two functions equal to each other

3/2x+3=-3

3/2x=-6

x=-4

Answer:

c

Step-by-step explanation:

Answer:

(0.2, 3.2)

Step-by-step explanation:

line A, in red, has equation          y=x+3   times 3    3y=3x+9

line B, in blue, has equation 2x+ 3y = 10

                                             -3x + 3y = 9      subtract thes two equations      

                                         (2x - -3x) + (3y -3y) = 10 - 9

                                                  5x + 0y  = 1

                                                         5x  =  1  

                                                           x = 1/5    or  0.2

                                                y = x + 3

                                                y = 0.2 + 3

                                                y = 3.2

Answer:

750 were Farm Mechanics.

Step-by-step explanation:

30% of 2500 is 750.

Hope this helps

Answer:

2794 in³

Step-by-step explanation:

Given

base (a) = 17 in

vertical height (h) = 29 in

Now

Volume of the square pyramid

= 1/3 a²h

= 1/3 * 17² * 29

= 2793.7 in³

= 2794 in³

hope it helps :)

Answer:

2794

Step-by-step explanation:

V=s^2 times height over three

17^2 times 29/3

PEMDAS, exponents first

17^2=289

PEMDAS, next up multiplication

289 times 29/3

8381/3 or 2793.7

round to nearest whole number

2794

Answer:

The amplitude is 1

Step-by-step explanation:

Given

The right function is:

[tex]y = \cos(5x + \frac{2}{5}\pi) +5[/tex]

Required

Determine the amplitude

The general cosine function is:

[tex]y = A\cos(k(x + c)) +d[/tex]

Where

[tex]Amplitude = |A|[/tex]

Compare [tex]y = A\cos(k(x + c)) +d[/tex] and [tex]y = \cos(5x + \frac{2}{5}\pi) +5[/tex]

[tex]A = 1[/tex]

So:

[tex]Amplitude = |1|[/tex]

So, we have:

[tex]Amplitude = 1[/tex]

Answer:

6

Step-by-step explanation:

a=V⅓=216⅓=6

hope this helped

Answer:

the answer is 6 because on each side there is 36 cubic units meaning you need to multiply 6 by what ever number untill you get to 36 and 6*6=36

Step-by-step explanation:

UwU