If p(a) = 0.25 and p(b) = 0.65, assuming independence of events, then p(a and b.is:

Consider triangle ABC. The legs have a length of 5 units each. What is the length of the hypotenuse of the triangle?

Korvikt [17]

Answer:

$5\sqrt{2}$ units.

Step-by-step explanation:

We have been given that two legs of triangle ABC measures 5 units each. We are asked to find the length of the hypotenuse.

We will use Pythagoras theorem to solve for the hypotenuse of triangle ABC.

$\text{Hypotenuse}^2=\text{Leg}^2+\text{Leg}^2$

Substituting our given values in above equation we will get,

$\text{Hypotenuse}^2=5^2+5^2$

$\text{Hypotenuse}^2=25+25$

$\text{Hypotenuse}^2=50$

Upon taking square root of both sides of our equation we will get,

$\text{Hypotenuse}=\sqrt{50}$

$\text{Hypotenuse}=\sqrt{25*2}$

$\text{Hypotenuse}=5\sqrt{2}$

Therefore, the length of hypotenuse of triangle ABC is $5\sqrt{2}$ units.

6 0

3 years ago

Read 2 more answers

Select the correct answer. Rectangle ABCD is dilated by a scale factor of 2 with the origin as the center of dilation, resulting

Natalija [7]

So I have a illustration

4 0

3 years ago

Read 2 more answers

A filling machine puts an average of four ounces of coffee in jars, with a standard deviation of 0.25 ounces. forty jars filled

Lunna [17]

Let's attack this problem using the z-score concept. The sample std. dev. here is (0.25 oz)/sqrt(40), or 0.040. Thus, the z score representing 3.9 oz. is
3.9 - 4.0
z = -------------- = -2.5
0.040

In one way or another we must find the area under the std. normal curve that lies to the left of z = -2.5. Use a table of z-scores or a calculator with built-in statistics functions. According to my TI-83 Plus calculator, that area is

0.006. One way of interpreting this that with so small a standard deviation, most volumes of coffee put into the jars are very close to the mean, 4 oz.

4 0

4 years ago

Pls help me solve this question, also include step by step calculation ya. Thks

sp2606 [1]

$\displaystyle\\Answer:\ x=\sqrt{2}\ \ \ \ \ x=-\sqrt{2}\ \ \ \ \ x=\frac{ln5}{2}$

Step-by-step explanation:

$5x^2-x^2e^{2x}+2e^{2x}=10$

$Let:\ x^2=t \ \ \ \ \ e^{2x}=v\\Hence,\\5t-tv+2v^2=10\\5t-tv+2v^2-10=10-10\\5t-tv-10+2v^2=0\\t(5-v)-2(5-v)=0\\(5-v)(t-2)=0\\5-v=0\\5-v+v=0+v\\5=v\\5=e^{2x}$