Answer: c
Step-by-step explanation:
Answer:
Below.
Step-by-step explanation:
We can write an odd integer as 2x + 1 so consecutive odd digits would be 2x + 1 and 2x + 3, so the equation is:
2x + 1 + 2x + 3 = 156
4x + 4 = 156 can be used to solve for x and find the integers.
4x = 152
Dividing through by 4:
x = 152/4 = 38
So the 2 integers are 2(38) + 1 and 2(38) + 3
= 77 and 79.
Answer:
yes
Step-by-step explanation:
I'm going to give you a slightly different answer, but it's going to make sense :-)
First, let's review what "sin" and "cos" really mean. They are functions that take as an input an angle, which we call theta. They output the base (cos) and height (sin) of a triangle which as a hypotenuse of length 1.
Now, let's pick some examples. If we happen to set theta to 45 degress, you will get a triangle that looks like this:
In this case, both sin(theta) and cos(theta) are the same number, the square root of 1/2. So cos(theta) + cos (theta) is 2 times the square tool of 1/2.
Now imagine that we now want to find cos (theta + theta). Remember that theta was 45 degrees, so this will be cos (45 + 45), or cos (90).
But remember that cos is the base of a triangle where theta is the angle with the base. Well, that's not a triangle at all, is it? It's just a vertical line. In fact, cos(90) will be zero.
Answer:
The mean and standard deviation for the z-scores in this distribution are 0 and 1 respectively.
Step-by-step explanation:
Let the random variable <em>X</em> follow a Normal distribution with mean <em>μ </em>and standard deviation <em>σ.</em>
The <em>z</em>-scores are standardized form of the raw scores <em>X</em>. It is computed by subtracting the mean (<em>μ</em>) from the raw score <em>x</em> and dividing the result by the standard deviation (<em>σ</em>).
These <em>z</em>-scores also follow a normal distribution.
The mean is:
![E(z)=E[\frac{x-\mu}{\sigma} ]=\frac{1}{\sigma}\times [E(x)-\mu] =\frac{1}{\sigma}\times [\mu-\mu]=0](https://tex.z-dn.net/?f=E%28z%29%3DE%5B%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5D%3D%5Cfrac%7B1%7D%7B%5Csigma%7D%5Ctimes%20%5BE%28x%29-%5Cmu%5D%20%3D%5Cfrac%7B1%7D%7B%5Csigma%7D%5Ctimes%20%5B%5Cmu-%5Cmu%5D%3D0)
The standard deviation is:
![Var(z)=Var[\frac{x-\mu}{\sigma} ]=\frac{1}{\sigma^{2}}\times [Var(x)-Var(\mu)] =\frac{\sigma^{2}-0}{\sigma^{2}}=1\\SD(z)=\sqrt{Var(z)}=1](https://tex.z-dn.net/?f=Var%28z%29%3DVar%5B%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5D%3D%5Cfrac%7B1%7D%7B%5Csigma%5E%7B2%7D%7D%5Ctimes%20%5BVar%28x%29-Var%28%5Cmu%29%5D%20%3D%5Cfrac%7B%5Csigma%5E%7B2%7D-0%7D%7B%5Csigma%5E%7B2%7D%7D%3D1%5C%5CSD%28z%29%3D%5Csqrt%7BVar%28z%29%7D%3D1)
Thus, the mean and standard deviation for the z-scores in this distribution are 0 and 1 respectively.
(k + k)(4) =
5x - 6 + 5x - 6 = 10x - 12 =
10(4) - 12 = 40 - 12 = 28
The answer is 28
