$x-\ width\\
y-\ length\\
4x=y\\
(y+4)(x-1)=60\\
(4x+4)(x-1)=60\\
4x^2-4x+4x+4=60\ \ | subtract\ 4\\
4x^2=56\ \ | divide\ by\ 4\\
x^2=14\\
x=\sqrt{14}\\
y=4\sqrt{14}\\\\
Dimensions:\ width=\sqrt{14}in,\ length=4\sqrt{14}in.$

6 0

3 years ago

A die is rolled nine times and the number of times that two shows on the upper face is counted. If this experiment is repeated m

vivado [14]

Answer:

$E(x) = 1.5\\$

Step-by-step explanation:

Given

$n = 9$ -- number of rolls

Required

The mean of 2's

The distribution follows binomial distribution where:

$X \to Binomial(n,p)$

In this case:

$p= \frac{1}{6}$ ---- the theoretical probability of rolling 2

So, the mean of 2's is calculated using:

$E(x) = np$

$E(x) = 9 * \frac{1}{6}$

$E(x) = \frac{9}{6}$

Simplify

$E(x) = \frac{3}{2}$ or

$E(x) = 1.5\\$

5 0

2 years ago