$\text{Apply Pythagorean theorem,}\\\\~~~~~~~~\text{Hypotenuse}^2=\text{Base}^2 + \text{Perpendicular}^2\\\\\implies 9^2 = \text{Base}^2 + \left(2\sqrt{14} \right)^2\\\\\implies 81 = \text{Base}^2 + 56\\\\\implies \text{Base}^2 = 81-56\\\\\implies \text{Base}^2 = 25\\\\\implies \text{Base} = \sqrt{25}\\\\\implies \text{Base} = 5\\\\\text{The length of the third side is 5 units.}$

4 0

1 year ago

A cuboid has a square base.

padilas [110]

The length of one side of the square base is 8.5 centimeters.

Given the following data:

Volume of cuboid = 867 cm

Height = 12 cm

To find the length of one side of the square base:

Mathematically, the volume of a cuboid is given by the formula:

$Volume = Base \; area$ × $Height$

Substituting the given values, we have:

$867 = Base \; area$ × $12$

$Base\;area = \frac{867}{12}$

Base area = 72.225 $cm^2$

Now, we can find the length by using the formula:

$Area \;of\;a \;square = length^2$

$72.25 = length^2$

$Length = \sqrt{72.25}$

Length = 8.5 centimeters.

Therefore, the length of one side of the square base is 8.5 centimeters.

Find more information: brainly.com/question/11037225

8 0

1 year ago

In June 2005, a CBS News/NY Times poll asked a random sample of 1,111 U.S. adults the following question: "What do you think is

Shtirlitz [24]

Answer:

The appropriate null hypothesis is $H_0: p = 0.25$

The appropriate alternative hypothesis is $H_1: p < 0.25$

Step-by-step explanation:

Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country.

At the null hypothesis, we test if the proportion is still the same, that is, of $\frac{1}{4} = 0.25$ . So

$H_0: p = 0.25$

We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll.

Decreased, so at the alternative hypothesis, it is tested if the proportion is less than 0.25, that is:

$H_1: p < 0.25$

3 0

2 years ago