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3 years ago

If a population gets multiplied by 2 every 5 years, what does it get multiplied by each year?

Mathematics

2 answers:

DerKrebs [107]3 years ago

7 0

Answer:

0.2.5

Step-by-step explanation:

2.5 x 5 = 2

liberstina [14]3 years ago

6 0

Answer: 16.61

Step-by-step explanation:

If we are talking about a 10x the original amount it would be 16.61

You might be interested in

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

4 years ago

How to find cos2theta

SSSSS [86.1K]

You can use the sum and difference identities which for cosine is cos(a+b)= cosacosb-sinasinb

5 0

4 years ago

Read 2 more answers

pleaseeeee hlpppp. i just need the diagraam i can't figure it out.surveyor is measuring the length of a lake. He takes angle mea

kupik [55]

Let the distance from A to the ends of the lake be w and r . From the given it appears that

w / sin 104 = 136 / sin 56 and r / sin 120 = 136 / sin 15....solve for w & r.

then L² = r² + w² - 2 r w cos 65 , where L = length of the lake...

attached a picture

7 0

3 years ago

Based on the Fundamental Theorem of Algebra, how many complex roots does each of the following equations have? Write your answer

mars1129 [50]

Answer:

2, 2, 4, 6, 4

Step-by-step explanation:

Fundamental Theorem of Algebra states that 'An 'n' degree polynomial will have n number of real roots'.

1. The polynomial is given by $x(x^2-4)(x^2+16) = 0$

So, on simplifying we get that, $x(x+2)(x-2)(x^2+16)=0$ .

Since, degree of polynomial is 5, it will have 5 roots.

This gives us that the roots of the equation are x = 0, -2, 2, 4i and -4i

So, the number of complex roots are 2.

2. The polynomial is given by $(x^2+4)(x+5)^2 = 0$

Since, degree of polynomial is 4, it will have 4 roots.

Equating them both by zero, $(x^2+4)= 0$ and $(x+5)^2=0$ gives that the roots of the polynomial are x = 2i, -2i, -5, -5.

So, the number of complex roots are 2.

3. The polynomial is given by $x^6-4x^5-24x^2+10x-3=0$

Since, degree of polynomial is 6, it will have 6 roots.

On simplifying, we get that the real roots of the polynomial are x = -1.75 and x = 4.28.

So, the number of complex roots are 6-2 = 4.

4. The polynomial is given by $x^7+128=0$

Since, degree of polynomial is 7, it will have 7 roots.

On simplifying, we get that the only real root of the polynomial is x = -2.

So, the number of complex roots are 7-1 = 6.

5. The polynomial is given by $(x^3+9)(x^2-4)=0$

Since, degree of polynomial is 5, it will have 5 roots.

Simplifying the equation gives $(x+2)(x-2)(x+\sqrt[3]{9})(x^2-\sqrt[3]{9x}+9^{\frac{2}{3}})=0$

Equating each to 0, we get the real roots of the polynomial is $x=-3^{\frac{2}{3}}$

So, the number of complex roots are 5-1 = 4

6 0

3 years ago

Read 2 more answers

Use the confidence level and sample data to find a confidence interval

stepan [7]

Answer:

The confidence interval at at 99% level of confidence is 93.7 ≤ μ ≤ 96.9.

Step-by-step explanation:

Step 1:

We must first determine the z-value at a confidence level of 99%.

Therefore,

99% = 100%(1 - 0.01)

Thus,

α = 0.01

Therefore, the z-value will be

z_(α/2) = z_(0.01/2) = z_0.005 = 2.58

(The z-value is read-off from the z table from the standard normal probabilities.)

Step 2:

We can now write the confidence interval:

X - z_(α/2) [s/√(n)] ≤ μ ≤ X + z_(α/2) [s/√(n)]

95.3 - 2.58(6.5/√(104)) ≤ μ ≤ 95.3 + 2.58(6.5/√(104))

93.7 ≤ μ ≤ 96.9

Therefore, confidence interval is 93.7 ≤ μ ≤ 96.9 which means that we are 99% confident that the true mean population lies is at least 93.7 and at most 96.9.

4 0

4 years ago