Piper is going to invest in an account paying an interest rate of 6.1 % compounded continuously

Answers

Answer 1

Answer:

Answer:

P ≈ 90739.60

Step-by-step explanation:

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The diameter of a particle of contamination (in micrometers) is modeled with the probability density function for . Determine the following (round all of your answers to 3 decimal places): (a) Enter your answer in accordance to the item a) of the question statement .972 (b) Enter your answer in accordance to the item b) of the question statement .0123 (c) Enter your answer in accordance to the item c) of the question statement .028 (d) Enter your answer in accordance to the item d) of the question statement .972 (e) Determine such that . Enter your answer in accordance to the item e) of the question statement

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

a $P(X < 5) = 0.960$

b $P(X > 8) = 0.016$

c $P(6 < x < 10) = 0.018$

d $P(X < 6 or X > 10 ) = 0.982$

e $X = 2$

Step-by-step explanation:

From the question we are told that

The probability density function is $f(x) = (2)/(x^3)$ for x > 1

Considering question a

$P(x < 5) = \int\limits^5_1 {(2)/(x^3) } \, dx$

=> $P(X < 5) = [-(1)/(x^2) ]| \left \ 5} \atop {1}} \right.$

=> $P(X < 5) = - (1)/(25) + (1)/(1^2)$

=> $P(X < 5) = 0.960$

Considering question b

$P(x > 8) =1 - \int\limits^6_1 {(2)/(x^3) } \, dx$

=> $P(X > 8) =1- [-(1)/(x^2) ]| \left \ 8} \atop {1}} \right.$

=> $P(X > 8) = 1 - [- (1)/(64) + (1)/(1^2)]$

=> $P(X > 8) = 0.016$

Considering question c

$P(6 < x < 10) = \int\limits^(10)_(6) {(2)/(x^3) } \, dx$

=> $P(6 < x < 10) = [-(1)/(x^2) ]| \left \ 10} \atop {6}} \right.$

=> $P(6 < x < 10) = [- (1)/(100) + (1)/(36)]$

=> $P(6 < x < 10) = 0.018$

Considering question d

$P(X < 6 or X > 10 ) = 1 - P(6 < x < 10) = 1 - \int\limits^(10)_(6) {(2)/(x^3) } \, dx$

=> $P(X < 6 or X > 10 ) =1- [-(1)/(x^2) ]| \left \ 10} \atop {6}} \right.$

=> $P(X < 6 or X > 10 ) =1- [- (1)/(100) + (1)/(36)]$ [/tex]

=> $P(X < 6 or X > 10 ) = 0.982$

Considering question e

$P(X < x ) = \int\limits^x_1 {(2)/(x^3) } \, dx = 0.75$

$P(X < x ) = [- (1)/(x^2) ]| \left \ x } \atop {1}} \right. = 0.75$

$P(X < x ) = - (1)/(x^2) - [- (1)/(1^2) ]= 0.75$

$P(X < x ) = - (1)/(x^2) + 1 = 0.75$

$- (1)/(x^2) = -0.25$

$X = 2$

Determine if 25110 is divisible by 45

Answers

Answer:

Yes: 558

Step-by-step explanation:

25110 ÷ 45 = 558

Answer:

25110 is divisible by 45

Step-by-step explanation:

25110 : 45 = 558

225

------

=261

225

------

= 360

360

------

= = =

A city council is deciding whether or not to spend additional money to reduce the amount of traffic. The council decides that it will increase the transportation budget if the amount of waiting time for drivers exceeds 18 minutes. A sample of 26 main roads results in a mean waiting time of 21.1 minutes with a sample standard deviation of 5.4 minutes. Conduct a hypothesis test at the 5% significance level.

Answers

Answer:

t = 2.9272 > 1.708 at 25 degrees of freedom

null hypothesis is rejected

The council decides that it will increase the transportation budget if the amount of waiting time for drivers is not exceeds 18 minutes

Step-by-step explanation:

Step (i):-

A sample of 26 main roads results in a mean waiting time of 21.1 minutes with a sample standard deviation of 5.4 minutes.

Given sample size 'n' = 26

The mean of the sample 'x⁻ = 21.1 min

Standard deviation of the sample 'S' = 5.4 min

The Population mean 'μ' = 18min

Step(ii):-

Null hypothesis: H₀ : The council decides that it will increase the transportation budget if the amount of waiting time for drivers exceeds 18 minutes.

'μ' > 18min

Alternative hypothesis :H₁:

'μ' <18min

Level of significance : ∝=0.05

Degrees of freedom γ = n-1 = 26-1 =25

The test statistic

$t = (x^(-)-mean )/((S)/(√(n) ) )$

$t = (21.1-18)/((5.4)/(√(26) ) )$

t = 2.9272

Step(iii):-

The tabulated value t = 1.708 at 25 degrees of freedom

t = 2.9272 > 1.708 at 25 degrees of freedom

Null hypothesis is rejected at 5% significance level of significance

Conclusion:-

The council decides that it will increase the transportation budget if the amount of waiting time for drivers is not exceeds 18 minutes

What is the value of x?

Answers

again, we're assuming that both triangles are similar, and thus using proportions.

$\stackrel{\textit{assuming the triangles are similar}}{\cfrac{x+1}{27}=\cfrac{5}{x-5}\implies x^2+x-5x-5=135}\implies x^2-4x-5=135 \n\n\n x^2-4x-140=0\implies (x-14)(x+10)=0\implies x = \begin{cases} 14~\textit{\large \checkmark}\n -10 \end{cases}$

we do not use the -10, because whatever value "x" may be, can't be negative or even 0.

Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the relative frequency method for computing probability is used, the probability that the next customer will purchase a computer is

Answers

Answer: 0.25

Step-by-step explanation:

The relative frequency of the customers that buy computers is equal to the number of customers that bought a computer divided the total number of customers that entered the shop.

p = 25/100 = 0.25

If we take this as the probability, then the probability that the next customer that enters the shop buys a computer is 0.25 or 25%

Final answer:

The probability that the next customer will purchase a computer, computed using the relative frequency method, is 0.25 or 25%.

Explanation:

The subject at hand relates to the basic concept of probability, specifically the method of computing probability using the relative frequency approach. This is a common topic within high school Mathematics, specifically within statistical studies.

To calculate the relative frequency probability of an event, one divides the number of times the event occurred by the total number of trials. In this case, the event is a customer purchasing a computer from the shop. Given that the event has occurred 25 times out of the last 100 trials (customers entering the shop), the relative frequency probability can be computed as follows:

Probability = (Number of times event occurred) / (Total number of trials) = 25 / 100 = 0.25 (or 25% when expressed as a percentage).

Therefore, using the relative frequency method of computing probability, the probability that the next customer will purchase a computer is 0.25 or 25%.

Learn more about Probability here:

brainly.com/question/22962752

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Select the statements that describe a normal distribution.The density curve is symmetric and bell‑shaped.The normal distribution is a continuous distribution.The normal distribution is a discrete distribution.The density curve is a flat line extending from the minimum value to the maximum value.Approximately 32% of values fall more than one standard deviation from the mean.Two parameters define a normal distribution—the median and the range.

Answers

Answer:

The density curve is symmetric and bell‑shaped.

The normal distribution is a continuous distribution.

Approximately 32% of values fall more than one standard deviation from the mean.

Step-by-step explanation:

Lets take a look at each statement.

The density curve is symmetric and bell‑shaped.

True.

The normal distribution is a continuous distribution.

True, the value of the measure can be a decimal number, like 10.5, for example.

The normal distribution is a discrete distribution.

False. Either the distribution is continuous, or it is discrete. In this case, it is continuous.

The density curve is a flat line extending from the minimum value to the maximum value.

False. This statements describes the uniform probability distribution.

Approximately 32% of values fall more than one standard deviation from the mean.

True. 68% are within 1 standard deviation of the mean and 32% are more than one standard deviation from the mean.

Two parameters define a normal distribution—the median and the range.

False. It is the mean and the standard deviation.

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