-x - 6y - z = -11 3x - 5y - 3z = 23 3x + 5y + 4z = 1

Let the present age of student be x
Present of teacher will be 4x

After 20 years,
Age of student = x + 20
Age of teacher = 4x + 20

According to the given condition after 20 years,
x + 20 = (4x + 20)/2
x + 20 = 2x + 10
2x - x = 20 - 10
x = 10

So student's present age is 10 years while teacher's is 4 x 10 i.e 40 years.

Hope This Helps You!

5 0

3 years ago

A small town has 2000 families. The average number of children per family is mu = 2.5, with a standard deviation sigma = 1.7. A

Nikitich [7]

Answer:

Let X the random variable that represent the number of children per fammili of a population, and for this case we know the following info:

Where $\mu=2.5$ and $\sigma=1.7$

We select a sample of n =64 >30 and we can apply the central limit theorem. From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And for this case the standard error would be:

$\sigma_{\bar X} = \frac{1.7}{\sqrt{64}}= 0.2125$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

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".

Solution to the problem

Let X the random variable that represent the number of children per fammili of a population, and for this case we know the following info:

Where $\mu=2.5$ and $\sigma=1.7$

We select a sample of n =64 >30 and we can apply the central limit theorem. From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And for this case the standard error would be:

$\sigma_{\bar X} = \frac{1.7}{\sqrt{64}}= 0.2125$

6 0

3 years ago

Find the area of a circle whose area equals the half of the sum of the areas of two circles with radil 2 and 3.

OlgaM077 [116]

Step-by-step explanation:

step 1. a circle with r = 2 has area of (pi)r^2 = (pi)(4) = 4pi

step 2. a circle with r = 3 has area of (pi)r^2 = (pi)(9) = 9pi

step 3. the area, A, of a circle is half the sum of the area of the circles with r = 2 and r = 3

step 4. A = (4pi + 9pi)/2 = 13pi/2 = 6.5(pi).

step 5. the answer is not 6.5 but is 6.5(pi) or 6.5 times pi.

8 0

2 years ago