This is deceptively simple: there are only three terms, one is a constant (1) and two are coefficients of q (4q, -2q). To simplify the like terms, just simplify the terms containing q.
a. If any letters and numbers are allowed, there will be
... 26×26×26×10×10×10 = 260³ = 17,576,000 possible plates
b. If the letters and numbers cannot repeat, there will be
... 26×25×24×10×9×8 = 11,232,000 possible plates with no repeats
c. The proabaility that a randomly chosen plate has no repeats is
... 11,232,000/17,576,000 = 108/169 ≈ 0,63905
_____
When no repeats are allowed, the first letter choice can be any of the 26 letters. The second letter choice must exclude the first letter, so there are only 25 different letters to choose from. Likewise, the third letter choice cannot be either of the first two, so there are only 24 letters to choose from. The reasoning applies to numbers in similar fashion.
Step-by-step explanation:
We can set up the ration of the radian angle θ in your problem in terms of degrees given as the ratio: (Θ/2·pi) = (72/360), solving for Θ we get Θ = 1.26 radians. Then for the arc length s = Θ·r using this value gives s = 1.26·4 = 5.04
Given that both triangles are similar and have a scale of 5:2, therefore the true statement about the proportions of the sides is:
B. AC/DF = 5/2
<h3>What are Similar Triangles?</h3>
- Similar triangles have corresponding side lengths that are proportional in length.
- Similar triangles have same shape but are of different sizes.
Thus, given that both triangles are similar and have a scale of 5:2, therefore the true statement about the proportions of the sides is:
B. AC/DF = 5/2
Learn more about similar triangles on:
brainly.com/question/2644832
