4. Heather is putting together a square bulletin board for her new room, and the area of the

Response:

(a) 3, 5, and 6

Detailed explanation:

In this study, 43 participants will be treated with a gel containing tooth-whitening agents, while the remaining 42 will receive a placebo. Consequently, a placebo is in use.

The selection process for the 43 individuals receiving the gel will be random.

Post-experiment, the whiteness levels of both groups will be compared to analyze the gel's effect.

For true randomness in the experiment, options 3, 5, and 6 are applicable.

(b)

In order for the experiment to be double-blind, the evaluators analyzing the whiteness, as well as the participants, must not know which individuals were given the whitening gel versus the placebo.

Answer:

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The relevant equation is: b. 0.75x + 0.15y = 90

An even function can be reflected over the y-axis and still remain unchanged.
Example: y=x^2
On the other hand, an odd function can be reflected around the origin and also remains unchanged.
Example: y=x^3


A straightforward method to determine this is:

if f(x) is even, then f(-x)=f(x)
if f(x) is odd, then f(-x)=-f(x)


Hence, for an even function
substitute -x in for each and check for equivalence
make sure to fully expand the expressions
g(x)=(x-1)^2+1=x^2-2x+1+1=x^2-2x+2 is the original expression
g(x)=(x-1)^2+1
g(-x)=(-x-1)^2+1
g(-x)=(1)(x+1)^2+1
g(-x)=x^2+2x+1+1
g(-x)=x^2+2x+2
Not the same, as the original contains -2x
Therefore, it is not even
g(x)=2x^2+1
g(-x)=2(-x)^2+1
g(-x)=2x^2+1
It matches, hence it is even
g(x)=4x+2
g(-x)=4(-x)+2
g(-x)=-4x+2
Not equivalent, thus not even
g(x)=2x
g(-x)=2(-x)
g(-x)=-2x
Not equal, therefore not even



g(x)=2x²+1 is the confirmed even function.

Answer:

The chance of completing the entire package installation in under 12 minutes is 0.1271.

Step-by-step explanation:

We define X as a normal distribution representing the time taken in seconds to install the software. According to the Central Limit Theorem, X is approximately normal, where the mean is 15 and variance is 15, giving a standard deviation of √15 = 3.873.

To find the probability of the total installation lasting less than 12 minutes, which equals 720 seconds, each installation should average under 720/68 = 10.5882 seconds. Thus, we seek the probability that X is less than 10.5882. To do this, we will apply W, the standard deviation value of X, calculated via the formula provided.

Utilizing , we reference the cumulative distribution function of the standard normal variable W, with values found in the attached file.

Given the symmetry of the standard normal distribution density function, we ascertain .

Consequently, the probability that the installation process for the entire package is completed within 12 minutes is 0.1271.

This problem can be addressed by applying the normal approximation to a binomial distribution.
Calculations:
Mean (μ) = np = 10,000 × 0.5 = 5,000
The standard deviation (σ) is given by:


The probability of obtaining more than 5,100 tails is 0.0228, whereas the probability of fewer than 5,100 tails is 0.9772.
Thus, the odds of having more than 5,100 tails are:
0.0228 : 0.9772 = 1 : 42.86.