Answer:
c
Step-by-step explanation:
right now 15 is the mode because there are 3 of them
if we made it so that there was another 8 there would also be 3 of them
this would mean that there are two modes
<h3>
Answer: Choice A. P = 1000M</h3>
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Explanation:
Use the log rule
log(A/B) = log(A) - log(B)
this works for any valid log base
So we can say
- log(P/N) = log(P) - log(N)
- log(M/N) = log(M) - log(N)
meaning that
- log(P/N) = 8 turns into log(P) - log(N) = 8
- log(M/N) = 5 turns into log(M) - log(N) = 5
We have this system of equations
Subtract the equations straight down. You'll find the log(N) terms cancel out and we have the new equation log(P) - log(M) = 3 which transforms into log(P/M) = 3
Lastly, convert the log equation into its exponential equivalent form using the idea that log(b,x) = y turns into y = b^x, where b is the base
Throughout this problem, the base wasn't given. Instead its implied we're talking about base 10.
So,
log(P/M) = 3
P/M = 10^3
P/M = 1000
P = 1000M
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Alternatively,
log(P/N) = 8 turns into P/N = 10^8
log(M/N) = 5 turns into M/N = 10^5
meaning that we can divide the two equations to get P/M = (10^8)/(10^5). That simplifies to P/M = 1000 and rearranges to P = 1000M
Answer: There are 33 dimes and 17 quarters in my pocket.
Step-by-step explanation:
Step 1: To assign and label the variables.
Suppose,
The number of dimes= x
The number of quarters= y
Step 2: To write the system of equations.
Equation related to the total coins:
x + y = 50 equation 1
Equation related to the total value of the coins:
0.10x + 0.25y = 9.95 equation 2
Step 3: To solve the system of equations.
Multiply equation 1 by 0.10 and then subtract it from equation 2 to eliminate the variable, x.
0.10x + 0.25y – (0.10x + 0.10y)= 9.95 – 5
0.15y = 4.95
y= 33
So, x=50 - 33= 17
Step 4: Therefore, there are 33 dimes and 17 quarters in my pocket.