The answer would be the choice at the bottom right corner!
I'm positive the answer is correct! :)
Answer:
94.2 cm
Step-by-step explanation:
circumfrence is diameter times pi
Answer:
f(g(x)) = 15x + 2
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Distributive Property
<u>Algebra I</u>
- Functions
- Function Notation
- Composite Functions
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
f(x) = 5x + 7
g(x) = 3x - 1
<u>Step 2: Find</u>
- Substitute in functions: f(g(x)) = 5(3x - 1) + 7
- [Distributive Property] Distribute 5: f(g(x)) = 15x - 5 + 7
- [Addition] Combine like terms: f(g(x)) = 15x + 2
<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.