Answer:
x ≈ -4.419
Step-by-step explanation:
Separate the constants from the exponentials and write the two exponentials as one. (This puts x in one place.) Then use logarithms.
0 = 2^(x-1) -3^(x+1)
3^(x+1) = 2^(x-1) . . . . . add 3^(x+1)
3×3^x = (1/2)2^x . . . . .factor out the constants
(3/2)^x = (1/2)/3 . . . . . divide by 3×2^x
Take the log:
x·log(3/2) = log(1/6)
x = log(1/6)/log(3/2) . . . . . divide by the coefficient of x
x ≈ -4.419
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A graphing calculator is another tool that can be used to solve this. I find it the quickest and easiest.
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<em>Comment on alternate solution</em>
Once you get the exponential terms on opposite sides of the equal sign, you can take logs at that point, if you like. Then solve the resulting linear equation for x.
(x+1)log(3) = (x-1)log(2)
x=(log(2)+log(3))/(log(2)-log(3))
Answer:
start with what you know
Step-by-step explanation:
makes you smarter
You gave no options but the simplest way to solve this is to set it equal to all of the answers to see if it is correct.
Answer:
6 Nickels
42 Dimes
Step-by-step explanation:
There are 48 coins in total (nickels and dimes). Let the number of nickels be "n" and the number of dimes be "d". So we can write:
n + d = 48
or
n = 48 - d
In dollars, we know nickels are worth 0.05 and dimes are worth 0.10. In total there is $4.50, so we can write:
0.05n + 0.10d = 4.50
Now replacing first equation [n = 48 - d] into 2nd, we get and equation in "d" and solve for d first:
So, there are 42 dimes.
We know from before, n = 48 - d, so
n = 48 - 42 = 6
There are 6 nickels
The fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.
Given that, r= -0.774.
To solve such problems we must know about the fraction of the variability in data values or R-squared.
<h3>What fraction of the variability in fuel economy is accounted for by the engine size?</h3>
The fraction by which the variance of the dependent variable is greater than the variance of the errors is known as R-squared.
It is called so because it is the square of the correlation between the dependent and independent variables, which is commonly denoted by “r” in a simple regression model.
Fraction of the variability in data values = (coefficient of correlation)²= r²
Now, the variability in fuel economy = r²= (-0.774)²
= 0.599076%= 59.91%
Hence, the fraction of the variability in fuel economy accounted for by the engine size is 59.91%.
To learn more about the fraction of the variability visit:
brainly.com/question/2516132.
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