Jeremy can choose his outfit in following ways:
2 ways to select a shirt
2 ways to select a pant
2 ways to select socks
3 ways to select the footwear.
Total number of ways to select the dress = 2 x 2 x 2 x 3 = 24 ways
Jeremy will select an outfit that includes flip-flops, argyle socks and denim pants. The shirt is not specified, so the shirt can be any.
So there are 2 ways to select a shirt, 1 way to select the pant, socks and footwear. So Jeremy can select the desired outfit in 2 ways.
Thus, the probability that Jeremy will select an outfit that includes flip-flops, argyle socks and denim pants = 2/24 = 1/12
Answer:
The equation is given below as
![\frac{\cos2x}{\cos x}=\cos x-\sin x\tan x](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ccos2x%7D%7B%5Ccos%20x%7D%3D%5Ccos%20x-%5Csin%20x%5Ctan%20x)
Step 1:
We will work on the left-hand side, we will have
![\begin{gathered} \cos x-\sin x\tan x \\ \text{recall that,} \\ Quoitent\text{ identity is} \\ \tan x=\frac{\sin x}{\cos x} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ccos%20x-%5Csin%20x%5Ctan%20x%20%5C%5C%20%5Ctext%7Brecall%20that%2C%7D%20%5C%5C%20Quoitent%5Ctext%7B%20identity%20is%7D%20%5C%5C%20%5Ctan%20x%3D%5Cfrac%7B%5Csin%20x%7D%7B%5Ccos%20x%7D%20%5Cend%7Bgathered%7D)
By substituting the identity above, we will have
![\begin{gathered} \cos x-\sin x\tan x=\cos x-\frac{\sin x.\sin x}{\cos x}=\cos x-\frac{\sin^2x}{\cos x} \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ccos%20x-%5Csin%20x%5Ctan%20x%3D%5Ccos%20x-%5Cfrac%7B%5Csin%20x.%5Csin%20x%7D%7B%5Ccos%20x%7D%3D%5Ccos%20x-%5Cfrac%7B%5Csin%5E2x%7D%7B%5Ccos%20x%7D%20%5C%5C%20%20%5Cend%7Bgathered%7D)
Here, we will make use of the quotient identity
Step 2:
By writings an expression, we will have
![\begin{gathered} \cos x-\sin x\tan x=\cos x-\frac{\sin x.\sin x}{\cos x} \\ \cos x-\sin x\tan x=\frac{\cos^2x-\sin^2x}{\cos x} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ccos%20x-%5Csin%20x%5Ctan%20x%3D%5Ccos%20x-%5Cfrac%7B%5Csin%20x.%5Csin%20x%7D%7B%5Ccos%20x%7D%20%5C%5C%20%5Ccos%20x-%5Csin%20x%5Ctan%20x%3D%5Cfrac%7B%5Ccos%5E2x-%5Csin%5E2x%7D%7B%5Ccos%20x%7D%20%5Cend%7Bgathered%7D)
Here, we will use the definition of subtraction
![\cos x-\frac{\sin^2x}{\cos x}](https://tex.z-dn.net/?f=%5Ccos%20x-%5Cfrac%7B%5Csin%5E2x%7D%7B%5Ccos%20x%7D)
Step 3:
We will apply the double number identity given below
![\begin{gathered} \cos 2\theta=\cos (\theta+\theta)=\cos ^2\theta-\sin ^2\theta \\ \cos 2x=cos(x+x)=\cos ^2x-\sin ^2x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ccos%202%5Ctheta%3D%5Ccos%20%28%5Ctheta%2B%5Ctheta%29%3D%5Ccos%20%5E2%5Ctheta-%5Csin%20%5E2%5Ctheta%20%5C%5C%20%5Ccos%202x%3Dcos%28x%2Bx%29%3D%5Ccos%20%5E2x-%5Csin%20%5E2x%20%5Cend%7Bgathered%7D)
By applying this, we will have
![\frac{\cos^2x-\sin^2x}{\cos x}=\frac{\cos2x}{\cos x}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ccos%5E2x-%5Csin%5E2x%7D%7B%5Ccos%20x%7D%3D%5Cfrac%7B%5Ccos2x%7D%7B%5Ccos%20x%7D)
Here, we will use the double number identity
Answer:
the second girl was. 59 seconds faster than the first girl.
Step-by-step explanation:
14.47-13.88= .59
Answer: 2x + y < 7
Step-by-step explanation:
In the graph we can see that:
The line is a dashed line, and the shaded area is below the dashed line, then we will have something like:
y < a*x + b
We also can see that the slope of the line is negative, and that the y-intercept is +7
Then the inequality will be something like:
y < a*x + 7
Now we can see that the line passes through the points (0, 7) and (3, 1)
Then the slope will be:
a = (1 - 7)/(3 - 0) = -6/3 = -2
that is negative, as we already said.
Then we have:
y < -2*x + 7
we can rewrite this as:
2x + y < 7
This is the first solution shown.