28 because 1/4th of 28 is equal to 7
Answer: 70
Step-by-step explanation: The absolute value of a number is its distance from zero on the number line. Since absolute value is a distance, it is always greater than or equal to zero.
.08 cents per ounce, because 2.40 ÷30 =.08
Answer:
The unit vector in component form is
or
.
Step-by-step explanation:
Let be
, its unit vector is determined by following expression:
![\hat {u} = \frac{\vec u}{\|\vec u \|}](https://tex.z-dn.net/?f=%5Chat%20%7Bu%7D%20%3D%20%5Cfrac%7B%5Cvec%20u%7D%7B%5C%7C%5Cvec%20u%20%5C%7C%7D)
Where
is the norm of
, which is found by Pythagorean Theorem:
![\|\vec u\|=\sqrt{2^{2}+(-3)^{2}}](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20u%5C%7C%3D%5Csqrt%7B2%5E%7B2%7D%2B%28-3%29%5E%7B2%7D%7D)
![\|\vec u\| = \sqrt{13}](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20u%5C%7C%20%3D%20%5Csqrt%7B13%7D)
Then, the unit vector is:
![\hat{u} = \frac{1}{\sqrt{13}} \cdot (2,-3)](https://tex.z-dn.net/?f=%5Chat%7Bu%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B13%7D%7D%20%5Ccdot%20%282%2C-3%29)
![\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)](https://tex.z-dn.net/?f=%5Chat%7Bu%7D%20%3D%20%5Cleft%28%5Cfrac%7B2%7D%7B%5Csqrt%7B13%7D%20%7D%2C-%5Cfrac%7B3%7D%7B%5Csqrt%7B13%7D%7D%20%20%5Cright%29)
The unit vector in component form is
or
.
<h3>
Answer: A) 5.4%</h3>
==================================
Explanation:
We use the binomial probability formula here
P(k) = (n C k)*(p)^k*(1-p)^(n-k)
In this case, there are n = 12 trials and p = 0.5 is the probability of getting heads. The value of k = 3 means we want 3 heads.
So,
P(k) = (n C k)*(p)^k*(1-p)^(n-k)
P(3) = (12 C 3)*(0.5)^3*(1-0.5)^(12-3)
P(3) = 220*(0.5)^3*(1-0.5)^(12-3)
P(3) = 0.0537109375
P(3) = 0.054
P(3) = 5.4%
-----------------
Side note: the n C k refers to the nCr combination formula
![_n C _r = \frac{n!}{r!*(n-r)!}](https://tex.z-dn.net/?f=_n%20C%20_r%20%3D%20%5Cfrac%7Bn%21%7D%7Br%21%2A%28n-r%29%21%7D)
where the exclamation marks mean factorials. You could also use Pascal's Triangle as an alternative for this portion.