without using your calculator or computer graphing tool. match each function rule with its graph. In each case, write a sentence explaining the type of variation that relates (x) and (y) for example Y is proportional to ..... with constant of proportionality....?
Answers
For a. the parent function is x^2, so 0.5x^2 should look about the same as x^2, so the answer is VI.
The graphs that match the function given are:
(a) VI, (b) III, (c) I, (d) II, (e) V, (f) IV
Consider the equations of the graphs given :
(a) y = 0.5 x²
This is a quadratic equation and thus will be a parabola.
This matches VI.
y is directly proportional to the square of x.
(b) y = 5/x²
Here negative values of y are not possible since x is squared.
Also, the values of y will be equal to a and -a.
This matches III.
y is inversely proportional to the square of x.
(c) y = x³
Here negative values of x will have the y values also negative.
Also, the value increases when x increases.
This matches I.
y is directly proportional to the cube of x.
(d) y = 1/x³
y value for x = -a is the negative of the y value for x = a.
Also, as x increases y decreases.
The function is not defined at 0.
This matches II.
y is inversely proportional to the cube of x.
(e) y = 3√x
Here since x is inside the cube, not defined for negative values of x.
As x increases, y also increases.
This matches V.
y is directly proportional to the square root of x.
(f) y = (0.5)ˣ
For negative values o x, the value of y will be high and for positive values of x, the value of y will be lower.
This matches IV.
y is exponentially related to x.
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Related Questions
13.What is the circumference of a circle whose area is 16 pi?A. 64 piB. 32 piC. 8 piD. 4 pi
Given the position function, s of t equals t cubed divided by 3 minus 12 times t squared divided by 2 plus 36 times t , between t = 0 and t = 15, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle is moving to the right. (5 points)0 < t < 65 < t < 15t > 15The particle always moves to the right.
Can someone write 3 + x in a words?
The perimeter of a rectangle is 16 inches. The equation that represents the perimeter of the rectangle is 2l + 2w = 16, where l represents the length of the rectangle and w represents the width of the rectangle. Which value is possible for the length of the rectangle?7 in.8 in.9 in.10 in. PLZ HELP
Answers
Answer:
0.0026 = 0.26% probability that the manufacturing line will be shut down unnecessarily
Step-by-step explanation:
We need to understand the normal probability distribution and the central limit theorem to solve this question.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
What is the probability that the manufacturing line will be shut down unnecessarily?
Less than 0.73 or more than 0.77.
Less than 0.73
pvalue of Z when X = 0.73
By the Central Limit Theorem
has a pvalue of 0.0013
More than 0.77
has a pvalue of 0.9987
1 - 0.9987 = 0.0013
2*0.0013 = 0.0026
0.0026 = 0.26% probability that the manufacturing line will be shut down unnecessarily
Answers
-- The function is a sine or cosine that wiggles from 3 below to 3 above its average value. So the amplitude is 3 . That lets out the 1st and 3rd choices.
It has to be the 2nd or 4th choice.
Looking at the graph, the y-intercept is at y=6.
The y-intercept is the point where x=0, so f(0)=6.
Test the 2nd choice: f(x) = 3 cos(x) + 3
f(0) = 3 cos(0) + 3
cos(0) = 1 so f(0) = 3 (1) + 3 = 6
Choice-2 is looking good.
Just to be sure, let's check choice-4:
f(x) = 3 sin(x) + 3
f(0) = 3 sin(0) + 3
sin(0) = 0 so f(0) = 3 (0) + 3 = 3
Beautiful ! Choice-4 flopped. The answer is choice-2 .
Answer: b
Step-by-step explanation:
Answers
Answer:
It is not a solution
Step-by-step explanation:
Plug the point into the equations and check to see if they are true
y=3x - 3
3 = 3(6) -3
3 = 18-3
3 = 15
False
We do not need to check the other equation since this is false
Answers
Subtract 6m from each side:
4 = 2m
Multiply each side by 2 :
8 = 4m
Answers
Final answer:
Cindy's argument is incorrect. 1/3 is a rational number because it can be expressed as the ratio of two integers. The fact that the decimal representation of 1/3 does not terminate does not make it irrational.
Explanation:
Cindy's argument is incorrect. A fraction is considered irrational if it cannot be expressed as the ratio of two integers. In the case of 1/3, it can be expressed as the division of the integer 1 by the integer 3, so it is a rational number. The fact that the decimal representation of 1/3 (0.333...) does not terminate does not make it irrational. Irrational numbers are decimal numbers that do not repeat or terminate, such as π (pi) and √2 (the square root of 2).
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A. n = 10.6 ounces
B. n = 14.4 ounces
C. n = 9.8 ounces
D. n = 15.2 ounces
Answers
so it would be "B"
24 x 5.85 = 140.4
9.75 x n = 9.75n
140.4/9.75 = 14.4
n=14.4