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3 years ago

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Mathematics

1 answer:

8_murik_8 [283]3 years ago

3 0

Answer: 7. y = 2 sin (2x) - 3

$\bold{8.\quad y=sin\bigg(8x + \dfrac{8}{\pi}\bigg)}$

<u>Step-by-step explanation:</u>

The general form of a sine equation is: y = A sin (Bx - C) + D where

Amplitude = |A|
Period (P) = $\dfrac{2\pi}{B}$
Phase Shift = $\dfrac{C}{B}$
Vertical Shift = D (positive is up, negative is down)

7. Given:

A = 2
P = π = $\dfrac{2\pi}{B}$ → B = 2
C = 0 (none)
D = -3

--> y = 2 sin (2x) - 3

8. Given:

A = 1
P = $\dfrac{\pi}{4}$ = $\dfrac{2\pi}{B}$ → B = 8

$\text{Phase Shift = }-\pi = \dfrac{C}{8}\implies C = -8\pi$
D = 0 (none)

$\implies y=sin\bigg(8x + \dfrac{8}{\pi}\bigg)$

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The null hypothesis claims that the proportion of community college students who work full-time is 0. 45. The alternative hypoth

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The stronger the evidence is against the null hypothesis, the higher the divergence from it.

What do you mean by null hypothesis ?

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory' veracity. It is sometimes referred to as just "the null," and its symbol is $H_{0}$ . To determine if a theory regarding markets, investing methods, or economies is correct or wrong, quantitative analysts employ the null hypothesis,

The null hypothesis states that the percentage of the population who works full time is 0.45.

As a result, 450 persons who are randomly selected from a population of 1000 work full-time.

A different hypothesis states that the ratio is higher than 0.45.

In the options provided, the proportion for the first option is 300/1000, or 0.3.

In the second choice, 500/1000 equals 0.5

Third alternative: 700/1000 = 0.7

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A 2-column table with 7 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3. The sec

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f(x) ≤ 0 over the interval [0, 2].
f(x) > 0 over the interval (–2, 0).
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<h3>What is the statement about?</h3>

Looking at the values given, the intervals which satisfies the condition are known to be:

f(x)<=0 over the interval [0,2]

f(x)>0 over the interval (-2,0)

f(x)>=0 over the interval [2,∞)

Because:

Since the table with x and f(x) values, we have to examine analyze the table and see the each option that is in line with f(x) or not .

Examine the values of x that is from -3 to 3, the f(x) values are both positive and negative . hence f(x)>0 is false over the interval (-∞,3)

Looking at the the interval from 0 to 2, the f(x) values are 0 and negative. Hence, f(x)<=0 over the interval [0,2]

When you look over the interval (-1,1), the f(x) values are said to be both positive and negative and as such, f(x)<0 is false over the interval (-1,1)

When you look at the interval (-2,0) , the f(x) is positive and as such, f(x)>0 over the interval (-2,0)

Looking at the interval [2,∞), f(x) is positive and as such, f(x)>=0 over the interval [2,∞)

Therefore, Option 2, 4 and 5 are correct.

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