Round 5,403.264 to the nearest hundred?

The set of all polynomials is closed under addition, subtraction, and multiplication, because performing any of these operations on a pair of polynomials will give a polynomial result.

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Comment on the question

The wording is a bit strange, because f(x) and g(x) are elements of a set (of polynomials), so cannot be said to be "closed." "Closed" is a property of a set with respect to some function, it is not a property of an element of the set.

6 0

3 years ago

Sarah is driving. Her distance in km from Tempe after t hours of driving is given by: x = D(t) = 13 + 57t

777dan777 [17]

Answer:

The solutions for your four question problem are:

a) t = D^-1(x) = (1/57)*x -(13/57)

b) t = D^-1(x) = 1 h

c) D^-1(x) represents time.

d) The number of hours of driving needed for Sarah to be x km from Tempe. (option (c))

Step-by-step explanation:

a) Determine a formula in terms of x for: t = D^-1(x)

The distance in km from Tempe after t hours of driving is given by

x = D(t) = 13 + 57t.

We just need to find the value t function of x

x = 13 + 57*t

x -13 = 57*t

57*t = x -13

t = (1/57)*x -(13/57)

We can see the plots of both equation in the picture below.

b) Compute D^-1(70)

Once we find the expression for D^-1(x)

We substitute for x = 70 km

t = D^-1(x) = (1/57)*x -(13/57)

t = D^-1(x) = (1/57)*(70) -(13/57)

t = D^-1(x) = (70/57) -(13/57)

t = D^-1(x) = (1.228) -(0.228)

t = D^-1(x) = 1 h

c) In the expression D^-1(x) : what quantity (distance or time) does the x represent? what quantity (distance or time) does the entire D^-1(x) represent?

x represents Distance in both equations (D(t), and D^-1(x))

t represents Time in both equations (D(t), and D^-1(x))

Since t = D^-1(x),

D^-1(x) represents time.

d) Which of the following statements best describes D^-1(x)?

The number of hours of driving needed for Sarah to be x km from Tempe.

Since, t = D^-1(x), and t represents the amount of time elapsed since Sarah, parted from Tempe, the correct answer is option (c)

The expression for D^-1(x) can be found in the previous answers

t = D^-1(x) = (1/57)*x -(13/57)

The input is x (distance) and the output is t (time)

6 0

3 years ago

When are conclusions said to be statistically significant?

mars1129 [50]

Answer:

If the p-value is less than a given significance level, you reject the null hypothesis and accept the alternative hypothesis.

Step-by-step explanation:

Suppose you have a business in which you'd like to make a change to increase your business. After making the change, you can use a significance test it. To conduct a significance test, you make a null hypothesis which states essentially that no effect happened. You also make an alternative hypothesis that states the change had an effect. You then test the two to see which one stands. In a significance test, using the p-value from your sample you compare it to the null and alternative hypotheses. You make a conclusion when:

If the p-value is less than a given significance level, you reject the null hypothesis and accept the alternative hypothesis since the evidence is in favor of it.

If the p-value is greater than the significance level, then you fail to reject the null hypothesis and cannot conclude. There isn't evidence in favor of the alternative hypothesis.

8 0

3 years ago