Given A = {a, e, i, o, u} and B = {a, l, g, e, b, r}, find A u B

The number of tickets purchased by an individual for Beckham College's holiday music festival is a uniformly distributed random

Zanzabum

1) Mean: 6.5

2) Standard deviation: 3.2

Step-by-step explanation:

1)

A uniform random distribution is the distribution of a variable that can assume n different values, and each of these values is equally likely to occur.

This means that the probability of occurring of each of these values is the same:

$p(x_1)=p(x_2)=...=p(x_n)$

For a uniform random distribution, the mean of the distribution is simply equal to the median value of the distribution, which is exactly at the center of the distribution itself. It can be calculated as

$\bar x = \frac{1}{2}(a+b)$

where

a is the lowest value of the distribution

b is the highest value of the distribution

Here the distribution consists of all values ranging from 1 to 12, so:

a = 1

b = 12

Therefore the mean value is

$\bar x=\frac{1}{2}(1+12)=6.5$

2)

For a uniform random distribution, it can be dimostrated that the variance of the distribution is

$\sigma^2 = \frac{1}{12}(b-a)^2$

For the distribution in this problem, we have:

a = 1

b = 12

Therefore the variance is

$\sigma^2 = \frac{1}{12}(12-1)^2=10.08$

The standard deviation is the square root of the variance, therefore for this distribution it is:

$\sqrt{\sigma^2}=\sqrt{10.08}=3.2$

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3 0

3 years ago

Which equation has a graph that is perpendicular to the graph of -x + 6y = -12?

serious [3.7K]

Answer:

c) 6x + y = -52 is required equation perpendicular to the given equation.

Step-by-step explanation:

If the equation is of the form : y = mx + C.

Here m = slope of the equation.

Two equations are said to be perpendicular if the product of their respective slopes is -1.

Here, equation 1 : -x + 6y = -12

or, 6y = -12 + x

or, y = (x/6) - 2

⇒Slope of line 1 = (1/6)

Now, for equation 2 to be perpendicular:

Check for each equation:

a. x + 6y = -67 ⇒ 6y = -67 - x

or, y = (-x/6) - (67/6) ⇒Slope of line 2 = (-1/6)

but $\frac{1}{6} \times \frac{-1}{6} \neq -1$

b. x - 6y = -52 ⇒ -6y = -52 - x

or, y = (x/6) + (52/6) ⇒Slope of line 2 = (1/6)

but $\frac{1}{6} \times \frac{1}{6} \neq -1$

c. 6x + y = -52

or, y =y = -52 - 6x ⇒Slope of line 2 = (-6)

$\frac{1}{6} \times (-6) = -1$

Hence, 6x + y = -52 is required equation 2.

d. 6x - y = 52 ⇒ -y = 52 - 6x

or, y = 6x - 52 ⇒Slope of line 2 = (6)

but $\frac{1}{6} \times 6 \neq -1$

Hence, 6x + y = -52 is the only required equation .

3 0

3 years ago

Read 2 more answers

Find the product and simplify. (3c-5) ^2

RSB [31]

Answer:

9c² -30c + 25

Step-by-step explanation:

Perfect square trinomial: (a - b)² = a² - 2ab + b²

(3c - 5)²

(3c)² -2(3c * 5) + 5²

9c² -2(15c) + 5²

9c² -30c + 25

Final answer: 9c² -30c + 25

Hope this helps!

7 0

2 years ago

Read 2 more answers

HELP PLEASE ASAP:

VashaNatasha [74]

The average rate of change, of the function, between the intervals, x = 2 to x = 6 is: 180.

<h3>What is the Average Rate of Change of a Function?</h3>

Average rate of change = $\frac{f(b) - f(a)}{b - a}$ .

Given the function, $f(x)= 3^x + 25$ ,

The average rate of change using the intervals of, x = 2 to x = 6 would be solved as shown below:

a = 2

b = 6

f(a) = $f(2)= 3^2 + 25$ = 34

f(b) = $f(6)= 3^6 + 25$ = 754

Average rate of change = $\frac{754 - 34}{6 - 2} = \frac{720}{4}$

Average rate of change = 180

Therefore, the average rate of change, of the function, between the intervals, x = 2 to x = 6 is: 180.

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5 0

2 years ago

The cake store is having a 25\%25%25, percent off sale on all of its cakes.

mina [271]

Answer:

2.25

Step-by-step explanation:

25% is a quarter

therefore a quarter of 9 is

0.25×9

=2.25

7 0

3 years ago