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sashaice [31]
9 months ago
9

I need help with this practice problem It is from my ACT prep guide It asks to graph the function, if you can, use Desmos to com

plete

Mathematics
1 answer:
Vaselesa [24]9 months ago
6 0

Given the following function:

\text{ f(x) = cot(x + }\frac{\pi}{6})

Use the form a·cot(bx - c) to find the variables used to find the amplitude, period, phase shift and vertical shift.

We get,

a = 1

b = 1

c = -π/6

d = 0

Since the graph of the Cotangent function does not have a maximum or minimum value, there can be no value for the amplitude.

Amplitude: None

For the Period:

\text{ Period = }\frac{\text{ }\pi}{\text{ b}}\text{ = }\frac{\pi}{1}\text{ = }\pi

Therefore, the Period is π.

For the Phase Shift:

\text{ Phase Shift = }\frac{\text{ c}}{\text{ b}}\text{ = }\frac{-\frac{\pi}{6}}{1}\text{ = -}\frac{\pi}{6}

Therefore, Phase Shift is -π/6 → π/6 (To the left).

For the Vertical Shift:

Vertical Shift = 0

Plotting the function will be:

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Answer:

Step-by-step explanation:

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3 0
2 years ago
) One year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million. Suppose a samp
Nutka1998 [239]

Answer:

Probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.

Step-by-step explanation:

We are given that one year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million.

Suppose a sample of 400 major league players was taken.

<em>Let </em>\bar X<em> = sample average salary</em>

The z-score probability distribution for sample mean is given by;

                 Z = \frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} }  ~ N(0,1)

where, \mu = mean salary = $1.5 million

            \sigma = standard deviation = $0.9 million

             n = sample of players = 400

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the average salary of the 400 players exceeded $1.1 million is given by = P(\bar X > $1.1 million)

    P(\bar X > $1.1 million) = P( \frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} } >  \frac{ 1.1-1.5}{{\frac{0.9}{\sqrt{400} } }} } ) = P(Z > -8.89) = P(Z < 8.89)

<em>Now, in the z table the maximum value of which probability area is given is for critical value of x = 4.40 as 0.99999. So, we can assume that the above probability also has an area of 0.99999 or nearly close to 1.</em>

Therefore, probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.

4 0
2 years ago
What is the area of this triangle?
Lana71 [14]

Remember

A=1/2 b x h



4 0
3 years ago
May someone help me out with this please.
Fed [463]
I think The answer is 22.5
5 0
3 years ago
Read 2 more answers
In a statistics​ class, the standard deviation of the heights of all students was 3.8 inches. The standard deviation of the heig
goblinko [34]

Answer:

The reason why standard deviation of the entire class is greater than standard deviation of males and females considered separately, is that mean values for males and females are different from each other.

Step-by-step explanation:

The concept of mean is well represented by the following formula

mean = \frac{(x1 + x2 + x3 + ..... + xn)}{N}, where x1, x2, xn are the observations and N is the number of observations (population).

Standard deviation represents the distance between each observation and the mean of the population (all observations). The formula for this parameter is:

Standard deviation =√[((x1 - x)² + (x2-x)² + ....+ (xn-x)²)/N-1], where x1, x2,..., xn are the observations and x is the mean value.

In this case you have that each height registered is an observation and the number of observations represents the N value. As you can see if the mean for males is different from that of females their standard deviation will be different too. Usually males have heigths greater than that of females (1.77 vs 1.64, in USA for example), and heights inside each group will be more similar than between groups. Then, when you mix all observation there will be an increase in standard deviation, because you are mixing very different heigths

4 0
3 years ago
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