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1 year ago

Problem: It takes 1200 workers 8 years to build 3 ziggurats. How many years would It take 1600 workers to build 25 ziggurats?

Mathematics

1 answer:

katen-ka-za [31]1 year ago

4 0

17 years

Step-by-step explanation:

1200/3z = 8

400=8/3 year for each building

they take 8

1600 is 2/3 year for each building

2/3 times 25 is 16.666

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The lifetime of a cheap light bulb is an exponential random variable with mean 36 hours. Suppose that 16 light bulbs are tested

photoshop1234 [79]

Answer:

$P(T$

Step-by-step explanation:

Previous concepts

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

$P(X=x)=\lambda e^{-\lambda x}, x>0$

And 0 for other case. Let X the random variable that represent "The number of years a radio functions" and we know that the distribution is given by:

$X \sim Exp(\lambda=\frac{1}{16})$

Or equivalently:

$X \sim Exp(\mu=16)$

Solution to the problem

For this case we are interested in the total T, and we can find the mean and deviation for this like this:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}=\frac{T}{n}$

If we solve for T we got:

$T= n\bar X$

And the expected value is given by:

$E(T) = n E(\bar X)= n \mu= 16*36=576$

And we can find the variance like this:

$Var(T) = Var(n\bar X)=n^2 Var(\bar X)= n^2 *\frac{\sigma^2}{n}=n \sigma^2$

And then the deviation is given by:

$Sd(T)= \sqrt{n} \sigma=\sqrt{16} *36=144$

And the distribution for the total is:

$T\sim N(n\mu, \sqrt{n}\sigma)$

And we want to find this probability:

$P(T< 600)$

And we can use the z score formula given by:

$z=\frac{T- \mu_T}{\sigma_T}$

And replacing we got this:

$P(T$

6 0

2 years ago

A folk band sold CDs at a concert. Each single CD costs $12 and their double CDs cost $17. They sold 14 more single CDs than dou

attashe74 [19]

The band sold 33 single CDs and 19 double CDs.

33 x 12 = 396

19 x 17 = 323

396 + 323 = 719

7 0

1 year ago

Victoria filled up her car with gas before embarking on a road trip across the country. The car uses 1.75 gallons of gas for eve

lozanna [386]

Answer:

G = 14 - 1.75(t)

Where G is the number of gallons of gas remaining;

14 represents the amount of gas in gallons in the full gas tank of the vehicle

t is the number of hours

Step-by-step explanation:

Here, we want to write an equation.

We are told that the car uses 1.75 gallons of gas every hour and after 4 hours 7 gallons were left

In the 4 hours, the amount of fuel used will be 1.75 * 4 = 7 gallons

So therefore since we have 7 gallons left, the amount of gallons in the full tank of the vehicle will be 7 + 7 = 14 gallons

Hence, the equation we want to write will be;

G = 14 - 1.75(t)

6 0

1 year ago

Mr robbins earns a commission on each airfare he books. At the end of the day,he had booked $208.60 worth if airfare and earned

LenKa [72]

Answer:

Mr. Robins commision rate is 15%.

Step-by-step explanation:

Formula

$Percentage = \frac{Part\ value\times 100}{Total\ value}$

As given

Mr robbins earns a commission on each airfare he books.

At the end of the day,he had booked $208.60 worth if airfare and earned $31.29.

Here

Part value = $31.29

Total value = $208.60

Put in the formula

$Percentage = \frac{31.29\times 100}{208.60}$

$Percentage = \frac{312900}{20860}$

Percentage = 15%

Therefore the Mr. Robins commision rate is 15%.

4 0

2 years ago

Consider the vibrating system described by the initial value problem. (A computer algebra system is recommended.) u'' + u = 8 co

krek1111 [17]

Answer:

u(t) = -(3 + w^2 ) cos t /(1- w^2)cos t + 7 sin t + 8 cos wt /(1- w^2)

Step-by-step explanation:

The characteristic equation is k²+1 = 0,⇒k²=−1,⇒ k=±i.

the roots are k = i or -i

the solution has the form u(x)=C₁cosx+C₂sinx.

Using undetermined coefficient method

Uc(t) = Pcos wt + Qsin wt

Uc’(t) = -Pwsin wt + Qwcos wt

Uc’’(t) = -Pw^2cos wt - Qw^2sin wt

U’’ + u = 8cos wt

-Pw^2cos wt - Qw^2sin wt + Pcos wt + Qsin wt = 8cos wt

(-Pw^2 + P) cos wt + (- Qw^2 + Q ) sin wt = 8cos wt

-Pw^2 + P = 8 which implies P= 8 /(1- w^2)

- Qw^2 + Q = 8 which implies Q = 0

Uc(t) = Pcos wt + Qsin wt = 8 cos wt /(1- w^2)

U(t) = uh(t ) + Uc(t)

= C1cos t + c2 sin t + 8 cos wt /(1- w^2)

Initial value problem

U(0) = C1cos(0) + c2 sin (0) + 8 cos (0) /(1- w^2)

C1 + 8 /(1- w^2) = 5

C1 = 5 -8 /(1- w^2) = -(3 + w^2 ) /(1- w^2)

U’(t) = -C1 sin t + c2 cos t - 8 w sin wt /(1- w^2)

U’(0) = -C1 sin (0) + c2 cos (0) - 8 w sin (0) /(1- w^2) = 7

c2 = 7

u(t) = -(3 + w^2 ) cos t /(1- w^2)cos t + 7 sin t + 8 cos wt /(1- w^2)

4 0

2 years ago

Read 2 more answers

Problem: It takes 1200 workers 8 years to build 3 ziggurats. How many years would It take 1600 workers to build 25 ziggurats? ​

Problem: It takes 1200 workers 8 years to build 3 ziggurats. How many years would It take 1600 workers to build 25 ziggurats?