Answer:
IQ scores of at least 130.81 are identified with the upper 2%.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean 
and standard deviation 
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 100 and a standard deviation of 15.
This means that 
What IQ score is identified with the upper 2%?
IQ scores of at least the 100 - 2 = 98th percentile, which is X when Z has a p-value of 0.98, so X when Z = 2.054.
IQ scores of at least 130.81 are identified with the upper 2%.
Answer:
x = 4
Step-by-step explanation:
Hello!
We can solve for x by expanding the parentheses and isolating x.
<h3>Solve for x</h3>
- 3x - 2(2x - 5) = 2(x + 3)-8
- 3x - 4x + 10 = 2x + 6 - 8
- -x + 10 = 2x - 2
- 10 = 3x - 2
- 12 = 3x
- x = 4
The value of x is 4.
Answer:
what
Step-by-step explanation:
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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:
10 cm³
Step-by-step explanation:
The equation for density is: d = m/v, where d is the density, m is the mass, and v is the volume.
Here, d = 2.5 and m = 25.0, so plug these into the equation to solve for v:
d = m/v
2.5 = 25/v
Multiply both sides by v:
2.5v = 25
Divide by 2.5:
v = 25/2.5 = 10
Thus, the volume is 10 cm³.
