If f is a function, then f(3x)=3f(x)

Let’s tackle the problem. We know the formula for <span>the height of the ball is as follows:

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Here, x represents </span><span>the horizontal distance in yards that the ball has traveled in the air. Given that distance is always a positive value, we conclude that x must be greater than or equal to 0. Thus:

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The horizontal plane indicates the function's zero point, and since the ball cannot have negative height values, must also remain positive. Ultimately, the graph reveals that the suitable domain is:

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Response:

Option E is the right choice.

A connection seems evident between the app and the reduction of daycare-related illnesses.

Step-by-step breakdown:

Research involved 1200 randomly chosen parents, revealing that the kids of parents who utilized the app had an average of 10 fewer cases of daycare illnesses compared to those whose parents didn’t download it during the study duration.

Reviewing the options individually

a. Since using the app appears to lower child sickness, its effectiveness should extend to decreasing child neglect as well.

The study indicates a reduction in daycare-related illnesses for those using the app but does not address neglect, making this conclusion incorrect.

b. Using the app will ensure daycare employees do not transmit germs.

The research didn't examine how the app functions, nor whether it stops daycare workers from transmitting germs. Thus, this conclusion lacks accuracy.

c. The analysis was performed as an experiment, not an observational study.

In reality, it was primarily observational. Such studies document results without manipulation by the researchers.

d. The sample size of the study was inadequate for drawing conclusions.

A pool of 1200 is sufficiently large to reflect the wider population’s characteristics. Therefore, this assertion is also incorrect.

e. A link seems to exist between the app and reduced transmission of daycare illnesses.

From the provided details, it’s clear that the findings of this study depict a link between using the app and a marked decrease in daycare-related illnesses among children of those who have downloaded it. Hence, the app likely plays a role in lowering the risk of such illnesses in their children.

Hope this is helpful!

H(t) = 15 - 6sin(2.5π(t - 0.5)) Step-by-step explanation: For midline M, amplitude A, period T, and time t0 when the function is decreasing from the midline, the function can be expressed as H(t) = M - Asin(2π/T(t - t0)). Applying the specified values of M=15, A=6, T=0.8, and t0 = 0.5 yields the equation H(t) = 15 - 6sin(2.5π(t - 0.5)).

The function can be expressed as:
f(x) = log(-20x + 12√x)
To ascertain the maximum value, differentiate the equation with respect to x and set the derivative to zero. The procedure unfolds as follows.

The differentiation formula is:
d(log u)/dx = du/u ln(10)
Thus,
d/dx = (-20 + 6/√x)/(-20x + 12√x)(ln 10) = 0
-20 + 6/√x = 0
6/√x = 20
From which we derive x = (6/20)² = 9/100

Therefore,
f(x) = log(-20(9/100)+ 12√(9/100)) = 0.2553

The function's maximum value is 0.2553.

Answer:

This function is continuous.

The situation illustrated corresponds to a linear function because the rate of change remains constant.

For each additional hour, 53 cups of juice are dispensed.

Brainliest please