License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is
1 answer:
Answer:
option B is correct
Step-by-step explanation:
We have 5 spaces in the license plate:
_ _ _ _ _
we have 26 available letters, and 10 available numbers.
starting with letters:
- how many choices do i have to place the 1st letter? 26.
26 _ _ _ _
- how many choices do i have to place the 2nd letter? 26 (since we're allowed to repeat letters)
26 26 _ _ _
- how many choices do i have to place the 3rd letter? 26
26 26 26 _ _
we've used all the places for letters, (note: the exact position of the letters doesn't matter here, the first letter could've been placed anywhere in _ _ _ _ _, but the amount of possible choices for letters would always be 26).
let's move on to numbers.
- how many choices do i have to place the 1st number? 10
26 26 26 10 _
- how many choices do i have to place the 2nd number? 10
26 26 26 10 10
we've completed our number plate. Next we'll simply multiply all these numbers to get all the possible arrangements in which numbers and letters can be displayed on a license place.
option B is correct
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Answer:
x = 6
See image.
Step-by-step explanation:
Logarithms are just another way to write exponents. The base on the logarithm that is the small font subscript IS the base (normal font/on the line) of an exponential equation. The "answer" in the logarithmic equation is the exponent (small font/superscript) .It is just a triple shuffle. When the logarithmic equation cant be worked on to solve it, CHANGE IT to exponential form. See image.
Part A
The sequence is geometric because the y values are doubling each time
4*2 = 8
8*2 = 16
16*2 = 32
The common ratio is r = 2.
<h3>Answer: Geometric</h3>=======================================================
Part B
The recursive rule here would be
The first line says that "the first term is 4"
The second line says "the nth term is found by multiplying 2 by the previous (n-1) term". In other words, double any term to get the next term.
The fourth term is 32 which doubles to 64 and that's the fifth term. So the point (5,64) is on this exponential curve.
Answer: She takes <u>64 minutes</u> to complete station 5
========================================================
Part C
We see that a = 4 is the first term and r = 2 is the common ratio.
The explicit nth term formula is a(r)^(n-1) which becomes 4(2)^(n-1)
Plugging in the value n = 8 leads to
4(2)^(n-1)
4(2)^(8-1)
4(2)^7
4(128)
512
You can use the method shown in part B to keep doubling each term until you arrive at the 8th term. This is one way to confirm the answer.
<h3>Answer: 512 minutes</h3>