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3 years ago

Using f(x)=2x^2 and g(x)=3x+4. whats (g of f)(5)? whats (f of g)(5)?

Mathematics

1 answer:

3241004551 [841]3 years ago

7 0

Answer:

f(g(x)) = 722, and g(f(x)) = 154

Step-by-step explanation:

f(x) = 2x²

g(x) = 3x + 4

g(f(x)) = 3(2x²) + 4

g(f(5)) = 3(2 × 5²) + 4

g(f(5)) = 3(2 × 25) + 4

g(f(5)) = 3 × 50 + 4

g(f(5)) = 154

f(g(x)) = 2(3x + 4)²

f(g(5)) = 2(3 × 5 + 4)²

f(g(5)) = 2 × 19²

f(g(5)) = 2 × 361

f(g(5)) = 722

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From the given information:

Population mean = 178 cm

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The null hypothesis and the alternative hypothesis can be computed as:

Null hypothesis:

$H_o: \mu = 178$

Alternative hypothesis:

$H_1: \mu \neq 178$

The t-test statistics is determined by using the formula:

$t = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}$

$t = \dfrac{177.5 - 178}{\dfrac{2}{\sqrt{25}}}$

$t = \dfrac{-0.5}{\dfrac{2}{5}}}$

$\mathbf{t= -1.25}$

Degree of freedom df = n- 1

Degree of freedom df = 25 - 1

Degree of freedom df = 24

At the level of significance ∝ = 0.05, the critical value = 2.064

Decision rule: To reject the null hypothesis if the test statistics is greater than the critical value at 0.05 level of significance

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3 years ago

Using f(x)=2x^2 and g(x)=3x+4. whats (g of f)(5)? whats (f of g)(5)?​

Using f(x)=2x^2 and g(x)=3x+4. whats (g of f)(5)? whats (f of g)(5)?