Answer:
96
Step-by-step explanation:
divide 100 and 64 by 2 than multiply both by 3
Answer:
The shorter leg, which is opposite to the 30- degree angle, is labeled as x. The hypotenuse, which is opposite to the 90-degree angle, is twice the shorter leg length (2x). The longer leg, which is opposite to the 60-degree angle, is equal to the shorter leg's product and the square root of three (x√3).
Step-by-step explanation:
<h2>
Answer with explanation:</h2>
Let p be the population proportion .
Then, ![p=\dfrac{5000}{20000}=0.25](https://tex.z-dn.net/?f=p%3D%5Cdfrac%7B5000%7D%7B20000%7D%3D0.25)
According to the given information, we have
, since alternative hypothesis is two-tailed , so the hypothesis test is a two-tail test.
Since sample size is large (n> 30), we use z-test.
Let us consider 95% confidence i.e.
.
c) Critical value = ![z_{\alpha/2}=\pm1.96](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D%5Cpm1.96)
Sample proportion : ![\hat{p}=\dfrac{96}{300}=0.32](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7B96%7D%7B300%7D%3D0.32)
d) Test statistic : ![z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D)
i.e. ![z=\dfrac{0.32-0.25}{\sqrt{\dfrac{0.25(0.75)}{300}}}=2.8](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B0.32-0.25%7D%7B%5Csqrt%7B%5Cdfrac%7B0.25%280.75%29%7D%7B300%7D%7D%7D%3D2.8)
e) P-value (for two-tail) : ![2(Pz>2.8)=0.0051103](https://tex.z-dn.net/?f=2%28Pz%3E2.8%29%3D0.0051103)
f) P-value is the probability value that we have falsely rejected the null hypothesis.
g) Since observed z-value (2.8) does not lie in critical interval (-1.96, 1.96), it means the null hypothesis is rejected.
Answer:
The larger of the two numbers is the first number which is 14
Step-by-step explanation:
2x+7y=49
x-3y = 5
2x-6y=10
13y=39
y=3
x-9=5
x=14, y=3
The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.
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