Answer:
The diagonal AB will 7.280 units long
Step-by-step explanation:
A solid with 3-dimensions with all its six faces rectangular is called a rectangular prism. It has the same cross-section along a length, which makes it a prism.
It is also a "cuboid"
Given the edges of th rectangular prism as 1,6, and 4 units, we can find the length of the diagonal by using the formula
where
d is the diagonal AB
l is the length
w is width
h is the height
On Substituting the values
Let's find all the prime numbers.
1,3,5,7,9,11,13,15,17,19
They are not divisible by 2.
Put that into a fraction, where the amount of numbers is the numerator and the total amount of numbers is the denominator.
10/20
That is half of 20.
So, 50% of the 20 first natural numbers are prime.
I hope this helps!
~cupcake
Answer:
P(1, π/4)
P(-1, π/4)
P(4, 5π/6)
P(-4, 5π/6)
Step-by-step explanation:
Knowing the formulas
r = √(x²+y²)
θ = Arctg (y/x)
we have
a) P(1, 1)
i)
r = √(1²+1²) = +1
r = +1
θ = Arctg (1/1) = π/4
P(1, π/4)
ii) r = √(1²+1²) = -1
r = -1
θ = Arctg (1/1) = π/4
P(-1, π/4)
b) P(2√3, -2)
i)
r = √((2√3)²+(-2)²) = +4
r = +4
θ = Arctg (-2/2√3) = 5π/6
P(4, 5π/6)
ii)
r = √((2√3)²+(-2)²) = -4
r = -4
θ = Arctg (-2/2√3) = 5π/6
P(-4, 5π/6)
The formula for a binomial probability function is the one that is attached to the image.
Where:
n = number of trials.
x = number of successes from which you want to know the probability.
p = probability of obtaining success.
In this case, success is defined as obtaining a result of type a.
We look for the probability of obtaining 4 results of type a.
So:
n = 10.
x = 4.
p = 0.70.
In this way:
P (x = 4) = 0.0368. If we now look for the probability of obtaining 5 results of type b.
So:
n = 10.
x = 5.
p = 0.20.
P (x = 5) = 0.0264.
Finally, the probability of obtaining 1 result of type c.
n = 10.
x = 1.
p = 0.1.
P (x = 1) = 0.387. Finally, the probability of obtaining 4 results of type a, 5 of type b and 1 of type c is:
P (4a + 5b + 1c) = 0.0368 * 0.0264 * 0.387.
P = 0.0376%
