Answer:
1,6,2 and 5
Step-by-step explanation:
(2x/5)² . (1x⁴/4)^-1
=(2²x²/5²) . (4/x⁴)
=4x²/25 × 4/x⁴
= 16/25x²
You use parenthesis first, then brackets. Braces are not always used. They can be used for function notation.
Answer:
see explanation
Step-by-step explanation:
Since lines a and b are parallel, then
∠NMP and ∠MPQ are same side interior angles and are supplementary, thus
a + a - 20 = 180
2a - 20 = 180 ( add 20 to both sides )
2a = 200 ( divide both sides by 2 )
a = 100, hence
∠NMP = a = 100° and
∠MPQ = a - 20 = 100 - 20 = 80°
The required value x in the expression -2/9=8/-3x is 12.
Given that,
-2/9=8/-3x
In the given expression, the value of the x is to be determined by simplification.
<h3>What is simplification?</h3>
The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.
In the given question we have to simplify the given expression as,
-2 / 9 = 8 / - 3x
-2 * -3x = 8 * 9
6x = 72
x = 12
Thus the required value x in the expression -2/9=8/-3x is 12.
Learn more about simplification here: brainly.com/question/12501526
#SPJ1
Answer: 0.0084
Step-by-step explanation:
Let p be the population proportion of the creatures in Wonderland are anthropomorphic animals.
As per given, p = 0.70
Sample size : n=120
Let
be the sample proportion of the creatures are anthropomorphic animals.
Now, required probability :
![P(\hat{p}>0.80)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.80-0.70}{\sqrt{\dfrac{0.70\times (1-0.70)}{120}}})\\\\P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.10}{\sqrt{\dfrac{0.70\times 30}{120}}})\\\\ =P(Z>\dfrac{0.10}{\sqrt{0.00175}})\ \ \ \ \ [Z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]\\\\ =P(Z>\dfrac{0.10}{0.04183})\\\\\=P(Z>2.39)\\\\=1-P(Z\leq2.39)\\\\=1- 0.9916= 0.0084](https://tex.z-dn.net/?f=P%28%5Chat%7Bp%7D%3E0.80%29%3DP%28%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%3E%5Cdfrac%7B0.80-0.70%7D%7B%5Csqrt%7B%5Cdfrac%7B0.70%5Ctimes%20%281-0.70%29%7D%7B120%7D%7D%7D%29%5C%5C%5C%5CP%28%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%3E%5Cdfrac%7B0.10%7D%7B%5Csqrt%7B%5Cdfrac%7B0.70%5Ctimes%2030%7D%7B120%7D%7D%7D%29%5C%5C%5C%5C%20%3DP%28Z%3E%5Cdfrac%7B0.10%7D%7B%5Csqrt%7B0.00175%7D%7D%29%5C%20%5C%20%5C%20%5C%20%5C%20%5BZ%3D%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%5D%5C%5C%5C%5C%20%3DP%28Z%3E%5Cdfrac%7B0.10%7D%7B0.04183%7D%29%5C%5C%5C%5C%5C%3DP%28Z%3E2.39%29%5C%5C%5C%5C%3D1-P%28Z%5Cleq2.39%29%5C%5C%5C%5C%3D1-%200.9916%3D%200.0084)
Hence, the probability that more than 80% of the sampled inhabitants are animals= 0.0084