Answer:
3^3×3
81
3^7/3^3
Explanation:
First you should solve the expression you've got there.
(3^6×3^-4)^2
3^6= 3×3×3×3×3×3 the answer is 729
3^-4 A negative exponent means repeated division by the base. So for example 2^-4=1/(2^4)
=1/(2×2×2×2)= 1/16
3^-4= 1/(3^4)
=1/(3×3×3×3)
= 1/81 If you look up the answer in your calculator the answer that will show up will be 0.01234567901
So!
(729×0.01234567901)^2= 9^2
9^2= 81
Now you can look at the following expressions and whichever gives the answer 81 will be correct.
hope it helps!
Answer:
The two given triangles ABC and A'B'C' are congruent by SSS or AA axiom of congruence.
Step-by-step explanation:
Rigid Transformation is a transformation which PRESERVES (keeps it SAME) the LENGTH and the ANGLES in an image and pre- image.
Here, as we can ΔABC goes under Rigid Transformation in to the ΔA'B'C'
⇒Sides AB, BC and AC correspond to the sides A'B',B'C' and A'C' respectively.
Also the ∠A, ∠B and∠C correspond to ∠A', ∠B' and∠C' respectively.
Now, in ΔABC and ΔA'B'C
AB = A'B'
BC = B' C'
AC = A'C'
⇒The two given triangles are congruent by SIDE SIDE SIDE property.
Also, ∠A = ∠A'
∠B = ∠B'
⇒The two given triangles are congruent by ANGLE ANGLE property.
Hence the two given triangles ABC and A'B'C' are congruent by SSS or AA axiom of congruence.
Answer:
The 95% confidence interval obtained with a sample size of 64 will give greater precision.
Step-by-step explanation:
We are given the following in the question:
A 95% confidence interval is calculated with the following sample sizes
The population mean and standard deviation are unknown.
Effect of sample size on confidence interval:
- As the sample size increases the margin of error decreases.
- As the margin of error decreases the width of the confidence level decreases.
- Thus, with increased sample size the width of confidence level decreases.
If we want a confidence interval with greater precision that is smaller width, we have to choose the higher sample size.
Thus, the 95% confidence interval obtained with a sample size of 64 will give greater precision.
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