The caller times at a customer service center has an exponential distribution with an average of 22 seconds. Find the probability that a randomly selected call time will be less than 30 seconds? (Round to 4 decimal places.)

Answer:

a) three eigenvalues, all of them real.

d) one real eigenvalue and two complex eigenvalues.

Step-by-step explanation:

A  3x3 matrix with real entries can have : (a) three eigenvalues, all of them are real and (d) one real eigenvalue and two complex eigenvalues.

Let consider the equation for a  3x3 matrix with real entries :

[tex]\lambda^3+a\lambda^2+b \lambda +c = 0[/tex]

From above ; we will notice that the polynomial is of 3°; as such there will be three eigenvalues in which all of them real.

Also ; complex values shows in pairs, a  3x3 matrix cannot have a three complex eigenvalues but one real eigenvalue and two complex eigenvalues.

Answer:

[tex]\frac{d y}{d x} = \frac{2}{\sqrt{(2 x+1)^{2} -1} } + (\frac{-x}{|x|\sqrt{1-x^2}) }) + (1) Sec h^{-1} (x)[/tex]

Step-by-step explanation:

Step(i):-

Given function

               [tex]y = cosh^{-1} (2 x +1) - x Sec h^{-1} (x)[/tex]   ....(i)

we will use differentiation formulas

i) y = cos h⁻¹ (x)

   Derivative of cos h⁻¹ (x)

           [tex]\frac{d y}{d x} = \frac{1}{\sqrt{x^2-1} }[/tex]

ii)

      y = sec h⁻¹ (x)

   Derivative of sec h⁻¹ (x)

           [tex]\frac{d y}{d x} = \frac{-1}{|x|\sqrt{(x^2-1} }[/tex]

Apply U V formula

[tex]\frac{d UV}{d x} = U V^{l} + V U^{l}[/tex]

Step(ii):-

Differentiating equation (i) with respective to 'x'

[tex]\frac{d y}{d x} = \frac{1}{\sqrt{(2 x+1)^{2} -1} } X \frac{d}{d x} (2 x+1) + x (\frac{-1}{|x|\sqrt{1-x^2}) }) + (1) Sec h^{-1} (x)[/tex]

[tex]\frac{d y}{d x} = \frac{1}{\sqrt{(2 x+1)^{2} -1} } X (2) + (\frac{-x}{|x|\sqrt{1-x^2}) }) + (1) Sec h^{-1} (x)[/tex]

Conclusion:-

[tex]\frac{d y}{d x} = \frac{2}{\sqrt{(2 x+1)^{2} -1} } + (\frac{-x}{|x|\sqrt{1-x^2}) }) + (1) Sec h^{-1} (x)[/tex]

Answer:

25%

I cannot really describe how I did it but I am pretty sure it is correct.

Answer:

x-9

Step-by-step explanation:

Answer:

1 .angle S is 90 degree

2. 12

3. 155 degree

1. x = 3

hope it helps .....

Answer:

D

Step-by-step explanation:

0.2x+5=8

0.2x=3

x=15

Therefore, the correct answer is choice D. Hope this helps!

Answer:

C) To the right.

Step-by-step explanation:

Answer:

[tex] y =y_o e^{kt}[/tex]

Where [tex] y_o = 2[/tex] the relative growth is [tex] k =0.7944[/tex] and t represent the number of days.

For this case we can to find the population after the day 6 so then we need to replace t =6 in our model and we got:

[tex] y(6) =2 e^{0.7944*6} = 234.99 \approx 235[/tex]

And for this case we can conclude that the population of protozoa for the 6 day would be approximately 235

Step-by-step explanation:

We can assume that the following model can be used:

[tex] y =y_o e^{kt}[/tex]

Where [tex] y_o = 2[/tex] the relative growth is [tex] k =0.7944[/tex] and t represent the number of days.

For this case we can to find the population after the day 6 so then we need to replace t =6 in our model and we got:

[tex] y(6) =2 e^{0.7944*6} = 234.99 \approx 235[/tex]

And for this case we can conclude that the population of protozoa for the 6 day would be approximately 235

Answer:

44.93% probability that the person will need to wait at least 7 minutes total

Step-by-step explanation:

To solve this question, we need to understand the exponential distribution and conditional probability.

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]

Conditional probability:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 5 minutes

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

Assume a person has waited for at least 3 minutes to be served. What is the probability that the person will need to wait at least 7 minutes total

Event A: Waits at least 3 minutes.

Event B: Waits at least 7 minutes.

Probability of waiting at least 3 minutes:

[tex]P(A) = P(X > 3) = e^{-0.2*3} = 0.5488[/tex]

Intersection:

The intersection between waiting at least 3 minutes and at least 7 minutes is waiting at least 7 minutes. So

[tex]P(A \cap B) = P(X > 7) = e^{-0.2*7} = 0.2466[/tex]

What is the probability that the person will need to wait at least 7 minutes total

[tex]P(B|A) = \frac{0.2466}{0.5488} = 0.4493[/tex]

44.93% probability that the person will need to wait at least 7 minutes total

Answer:

384cm2

Step-by-step explanation:

surface area

12×12=144

10×12/2=60

60×4=240

240+144=384cm2

Answer:

  [tex]\dfrac{x^2+8x+16}{x-1}[/tex]

Step-by-step explanation:

In general, "over" and "divided by" are used to mean the same thing. Parentheses are helpful when you want to show fractions divided by fractions. Here, we will assume you intend ...

  [tex]\dfrac{\left(\dfrac{x^2+7x+12}{x+3}\right)}{\left(\dfrac{x-1}{x+4}\right)}=\dfrac{(x+3)(x+4)}{x+3}\cdot\dfrac{x+4}{x-1}=\dfrac{(x+4)^2}{x-1}\\\\=\boxed{\dfrac{x^2+8x+16}{x-1}}[/tex]

Answer:

[tex]P(X=6)=(100C6)(0.085)^6 (1-0.085)^{100-6}=0.1063[/tex]

Then the probability that exactly 6 bridges in the sample are structurally deficient is 0.1063 or 10.63%

Step-by-step explanation:

Let X the random variable of interest "number of bridges in the sample are structurally deficient", on this case we now that:

[tex]X \sim Binom(n=100, p=0.085)[/tex]

The probability mass function for the Binomial distribution is given as:

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

Where (nCx) means combinatory and it's given by this formula:

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

And we want to find this probability:

[tex] P(X=6)[/tex]

And if we use the probability mass function and we replace we got:

[tex]P(X=6)=(100C6)(0.085)^6 (1-0.085)^{100-6}=0.1063[/tex]

Then the probability that exactly 6 bridges in the sample are structurally deficient is 0.1063 or 10.63%

Answer:

225º or 3.926991 radians

Step-by-step explanation:

The area of the complete circle would be π×radius²: 3.14×8²=200.96

The fraction of the circle that is still left will be a direct ratio of the angle of the sector of the circle.

[tex]\frac{125.6}{200.96}[/tex]=.625. This is the ratio of the circe that is in the sector. In order to find the measure we must multiply it by either the number of degrees in the circle or by the number of radians in the circle (depending on the form in which you want your answer).

There are 360º in a circle, so .625×360=225 meaning that the measure of the angle of the sector is 225º.

We can do the same thing for radians, if necessary. There are 2π radians in a circle, so .625×2π=3.926991 radians.

Answer:

225º

Step-by-step explanation:

Answer:

Raspberry: 30%

Strawberry: 15%

Apple: 20%

Lemon: 35%

Step-by-step explanation:

18 + 9 + 12 + 21 = 60 (there are 60 gummy worms)

18 out of 60 = 30%

9 out of 60 = 15%

12 out of 60 = 20%

21 out of 60 = 35%

Please mark Brainliest

Hope this helps

Answer:

Raspberry Worms: 30%

Strawberry Worms: 15%

Apple Worms: 20%

Lemon Worms: 35%

Step-by-step explanation:

Raspberry Worms: [tex]\frac{18}{18+9+12+21}=\frac{18}{60}=\frac{30}{100}[/tex] or 30%

Strawberry Worms: [tex]\frac{9}{18+9+12+21}=\frac{9}{60} =\frac{15}{100}[/tex] or 15%

Apple Worms: [tex]\frac{12}{18+9+12+21} =\frac{12}{60} =\frac{20}{100}[/tex] or 20%

Lemon Worms: [tex]\frac{21}{18+9+12+21} =\frac{21}{60} =\frac{35}{100}[/tex] or 35%

Answer:

x+7)^2=x^2+2*7x+7^2= x^2+14x+49

Step-by-step explanation:

Answer:

2x-14

From: iOE your friend :D :)

* Be awesome Be you*

Answer:

Distance = 0.3

Step-by-step explanation:

We have two point in a line (one dimension).

One point is at 2.1 units and 1.8 units.

The distance between two points can be calculated as the absolute value of the difference between the position of each point.

This can be derived from the distance formula for two dimensions:

[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\\\y_1=y_2=0\\\\d=\sqrt{(x_2-x_2)^2}\\\\d=|x_2-x_1|[/tex]

Then, for this case, the distance is:

[tex]d=|1.8-2.1|=|-0.3|=0.3[/tex]

Answer:

y-7=1/2(x-8)

y-4=1/2(x-2)

Step-by-step explanation:

Slope: 3/6, or 1/2

y-7=1/2(x-8)

y-4=1/2(x-2)

Answer:

x = -2

y = -5

Step-by-step explanation:

You can use either substitution or elimination for this problem. I will be using elimination,

Step 1: Add the 2 equations together

-8y = 40

y = -5

Step 2: Plug y into an original equation to find x

-3 (-5) + 10x = -5

15 + 10x = -5

10x = -20

x = -2

And you have your final answers!

Answer:

[tex]6cm^2[/tex]

Step-by-step explanation:

Let x and y be the sides of the rectangle.

Area of the Triangle, A(x,y)=xy

From the diagram, Triangle ABC is similar to Triangle AKL

AK=4-y

Therefore:

[tex]\dfrac{x}{6} =\dfrac{4-y}{4}[/tex]

[tex]4x=6(4-y)\\x=\dfrac{6(4-y)}{4} \\x=1.5(4-y)\\x=6-1.5y[/tex]

We substitute x into A(x,y)

[tex]A=y(6-1.5y)=6y-1.5y^2[/tex]

We are required to find the maximum area. This is done by finding

the derivative of Aand solving for the critical points.

Derivative of A:

[tex]A'(y)=6-3y\\$Set $A'=0\\6-3y=0\\3y=6\\y=2$ cm[/tex]

Recall that: x=6-1.5y

x=6-1.5(2)

x=6-3

x=3cm

Therefore, the maximum rectangle area is:

Area =3 X 2 =[tex]6cm^2[/tex]

Answer:

d) [tex]8.97*10^{-3}[/tex]

Step-by-step explanation:

Move the decimal 3 spaces to the right so that way the decimal can be between the first two numbers. When you move the decimal to the right, it makes the exponent negative, when it moves to the left, it makes it positive

Answer:

4/15 ÷ x + 0.4

When x = 1

4/15 ÷ 1 + 0.4

x = 2/3

When x = 4/9

4/15 ÷ 4/9 +0.4

x = 1

When x = 1 ⅓ = 4/3

4/15 ÷ 4/3 + 0.4

x = 3/5

Hope this helps.

Answer:

Your answer is 3.16227766

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Example:

Consider A vertex. A is connected  with two other vertices  C and B.

Thus 3 line segments are formed. At A, two pair of intersecting lines are formed, AC & AE ;   AE and AB

Each vertex form two pair of intersecting line segments. Totally , there are 8 verteces. So, 8*2 = 16 pair of  intersecting lines

Answer:

Approximately 68% of the customer accounts have payment made between 23 and 37 days.

Step-by-step explanation:

We want to calculate what two values will approximately 68% of the numbers of days be.

For a bell shaped distribution, we can apply the 68-95-99.7 rule, which states that approximately 68% of the data will fall within 1 standard deviation from the mean.

Then, for a mean of 30 and standard deviation of 7, we can calculate the two values as:

[tex]X_1=\mu+z_1\cdot\sigma=30-1\cdot 7=30-7=23 \\\\X_2=\mu+z_2\cdot\sigma=30+1\cdot 7=30+7=37[/tex]

Answer:

   The answer is 16 and 44 days.

Step-by-step explanation:

This is the correct answer for this question.

Answer:

Minimum population of fish in lake = 2400 - 155 = 2245

Maximum population of fish in lake = 2400 + 155 = 2555

Step-by-step explanation:

population of fish in lake = 2400

Variation of fish = 155

it means that while current population of fish is 2400, the number can increase or decrease by maximum upto 155.

For example

for increase

population of fish can 2400 + 2, 2400 + 70, 2400 + 130 etc

but it cannot be beyond 2400 + 155.

It cannot be 2400 + 156

similarly for decrease

population of fish can 2400 - 3, 2400 - 95, 2400 - 144 etc

but it cannot be less that 2400 - 155.

It cannot be 2400 - 156

Hence population can fish in lake can be between 2400 - 155 and 2400 + 155

minimum population of fish in lake = 2400 - 155 = 2245

maximum population of fish in lake = 2400 + 155 = 2555

Answer:

A

Step-by-step explanation:

We can use the trigonometric ratios. Recall that sine is the ratio of the opposite side to the hypotenuse:

[tex]\displaystyle \sin(C)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

The opposite side with respect to ∠C is 24 and the hypotenuse is 26.

Hence:

[tex]\displaystyle \sin(C)=\frac{24}{26}=\frac{12}{13}[/tex]

Our answer is A.

Answer:

x = 3, -7

Step-by-step explanation:

Since you already have the factored form, all you need to do is set the equations equal to zero to find you roots:

x - 3 = 0

x + 7 = 0

x = 3, -7

Answer:

3 or -7

Step-by-step explanation:

For it to equal 0, x must be 3 or -7 because anything multiplied by 0 is 0. So you take each part, x-3 and see how you can make that a 0. x-3=0, therefore x must be 3. Other part x+7=0, x must be -7.

Answer:

b. becomes narrower.

Step-by-step explanation:

Since the 95% confidence interval for a population mean could find out from 100 to 120

And based on this, the coefficient confidence level is declined to 0.90

Therefore the confidence interval for mean should become narrowed

As a 95% confidence interval represents narrower and 99% confidence interval represents wider

Therefore the option B is correct

Using confidence interval concepts, the correct option is:

b. becomes narrower

The margin of error of a confidence interval is given by:

[tex]M = z\frac{s}{\sqrt{n}}[/tex]

In which:

The lower the confidence level, the lower the value of z, hence, the margin of error decreases and the interval becomes narrower, which means that option b is correct.

A similar problem is given at https://brainly.com/question/14377677

Answer:

The 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference between two means is:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

It is provided that:

[tex]\bar x_{1}=45\\\bar x_{2}=33.7\\SE_{\text{diff}} =4.14\\\text{Confidence Level}=90\%[/tex]

The critical value of z for 90% confidence level is,

z = 1.645

*Use a z-table.

Compute the 90% confidence interval for the difference in mean number of days meeting the goal as follows:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

    [tex]=45-33.7\pm 1.645\times 4.14\\\\=11.3\pm 6.8103\\\\=(4.4897, 18.1103)\\\\\approx (4.49, 18.11)[/tex]

Thus, the 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).