The function y = f(x) is graphed below. What is the average rate of change of the
1 answer:
The average rate of change of the function in the given interval -3 ≤ x ≤-1 is 10.
<h3>What is the average rate of change?</h3>The average Rate of Change of the function f(x) can be calculated as;
Interval -3 ≤ x ≤-1
a = -3, b = -1
f(a) = f(-3) = -20
f(b) = f(-1) = 0
Step 2: Find Average
Therefore, the average rate of change of the function in the given interval -3 ≤ x ≤-1 is 10.
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Answer:
The 95% confidence interval for the difference is (-0.1888, 0.0202).
Step-by-step explanation:
Difference between proportions:
The distribution of the difference between two proportions has mean of the difference between these proportions and standard deviation is the square root of the sum of the variances. So
In a sample of 86 units made with gold wire, 68 met the specification
This means that:
In a sample of 120 units made with aluminum wire, 105 met the specification.
This means that:
Difference:
Confidence interval:
In which z is the zscore that has a pvalue of , with
being 1 subtracted by the confidence level.
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
Lower bound of the interval:
Upper bound of the interval:
The 95% confidence interval for the difference is (-0.1888, 0.0202).
Answer:
(1, 1) is the only one on the graph
Step-by-step explanation:
To determine if an ordered pair lies on the graph, substitute the x-coordinate of the ordered pair into f(x) and evaluate. If the value equals the y-coordinate of the ordered pair then it lies on the graph
f(1) = (2 × 1) - 1 = 2 - 1 = 1 ⇒ (1, 1) lies on graph
f(- 1) = (2 × - 1) - 1 = - 2 - 1 = - 3 ≠ - 4 ⇔ (- 1, - 4 ) not on graph
f(- 2) = (2 × - 2) - 1 = - 4 - 1 = - 5 ≠ - ⇒ (- 2, -
) not on graph
f(0) = (2 × 0) - 1 = 0 - 1 = - 1 ≠ ⇒ not on graph
9514 1404 393
Answer:
(a) 4/3
(b) y -3 = 4/3(x -1)
(c) y -3 = -3/4(x -1)
(d) r = 5
Step-by-step explanation:
a) The slope is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (7 -3)/(4 -1) = 4/3
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b) The radius is normal to the circle. The point-slope form of the equation for a line can be useful here:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
For slope 4/3, the line through point (1, 3) will have the equation ...
y -3 = 4/3(x -1) . . . . point-slope equation of the normal
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c) The tangent is perpendicular to the radius. It will have a slope that is the opposite reciprocal of the slope of the radius: -1/(4/3) = -3/4.
y -3 = -3/4(x -1) . . . . point-slope equation of the tangent
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d) The radius can be found from the distance formula.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((4 -1)² +(7 -3)²) = √(3² +4²) = √25 = 5
The radius of the circle is 5.
