Answer:
0.4077
Step-by-step explanation:
It's important to use parenthesis to avoid confusion.
9^(2x) = 6
Use exponent properties:
(9^2)^x = 6
81^x = 6
Take log of both sides
ln(81^x) = ln(6)
Use log properties:
x ln(81) = ln(6)
Solve for x:
x = ln(6) / ln(81)
x ≈ 0.4077
Answer:
B.
The solution of |2x + 8| > 6 includes all values that are less than –7 or greater than –1.
The solution of |2x + 8| < 6 includes all values that are greater than –7 and less than –1.
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Step-by-step explanation:
You can find the solution by "unfolding" the absolute value, then dividing by 2 and subtracting 4:
-6 > 2x +8 > 6 . . . . . read this as -6 is less than 2x+8 or 2x+8 is greater than 6
-3 > x +4 > 3 . . . . . . .divide by 2
-7 > x > -1 . . . . . . . . . solution to the first inequality: x is less than -7 or greater than -1.
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The solution to the other inequality is identical, except the direction of the comparison is reversed. It is read differently, because the segments overlap, rather than being disjoint.
-7 < x < -1 . . . . . . . . solution to the second inequality: x is greater than -7 and less than -1.
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These descriptions match choice B.
Remember:
a^m * a^n=a^(m+n)
a^-m=1/a^m
8³ x 8⁻⁵=8³⁻⁵=8⁻²=1/8²=1/64<1
Answer: the student is not correct, because 1/64<1, and 8³ x 8⁻⁵=1/64.
Answer:
- 0.9503 ; r is not statistically significant ; 0.9031
Step-by-step explanation:
Given the following :
Age (X) :
37
41
57
65
73
Bone density (Y)
355
345
340
315
310
Using the pearson R value calculator :
The r value of the data % - 0.9503.
This value depicts a very strong negative correlation between age and density of bone.
Using the pearson R calculator to obtain the P- value, the P value obtained is .01332 and hence the r is not significant at P < 0.01.
The Coefficient of determination R^2 can be obtained by getting the square value of R
R^2 = - 0.9503^2
R^2 = 0.90307009
R^2 = 0.9031
