Question

The following questions will provide practice working with simple linear functions. All questions refer to a coordinate graph with the variable X on the horizontal axis and the variable Y on the vertical axis. a. If two points on a straight line are (X = 3, Y = 2) and (X = 12, Y = 5), what is the slope of the line?

b. If point A is at (X = 20, Y = 20) and point B is at (X = 10, Y = 40), what is the slope of the straight-line joining points A and B?

c. What is the slope of the function described by Y = 12000 – 0.5X?

d. What is the slope of a line described by Y = 6.5X?

e. What is the slope of a line described by Y = 27 + 3.2X?

f. What is the Y-intercept of the function Y = 500 + mX?

g. What is the Y-intercept of the function Y = -100 + 10X?

h. What is the X-intercept of the function Y = 10 – 0.1X?

i. What is the X-intercept of the function Y = -1 + 2X?

Answer #1

Find the equation of the tangent line to the function
f(x)=8√(x)−6 at the point (64,58). Provide your answer in
slope–intercept form of a linear equation, y=mx+b, where m is the
slope and b is the y-intercept. Express m and b as exact
numbers.

The graph of
f(x)=−10x+e5sin(x)f(x)=−10x+e5sin(x)
is rotated counterclockwise about the origin through an acute
angle θθ. What is the largest value of θθ for which the rotated
graph is still the graph of a function? What about if the graph is
rotated clockwise?
To answer this question we need to find the maximal slope of
y=f(x)y=f(x), which is , and the minimal slope which
is .
Thus the maximal acute angle through which the graph can be rotated
counterclockwise is θ=θ= degrees.
Thus...

Suppose we have the
following values for the linear function relating X and Y (where Y
is the dependent variable and X is the independent variable:
X Y
0 45
1 25
2 5
What is the value of
the slope for this straight line?
Question 3 options:
25
20
-20
-10

Suppose we have the following values for the linear function
relating X and Y (where Y is the dependent variable and X is the
independent variable:
X Y
0 45
1 25
2 5
What is the value of the slope for this straight line?

QUESTION 21
A linear model is found to be y = 3.5x + 6. At a value of x = 4,
the equation yields y = 20. However, the actual data value for x =4
is found to be y = 22.3. The residual at x = 20 is
a.
3.5
b.
6
c.
20
d.
22.3
e.
2.3
QUESTION 22
A regression equation is found to be y=2x+10. The prediction for
the dependent variable when the independent variable is...

1. Consider the following demand and supply functions for a good
or service: Qd = 400 - 5P and Qs= 3P.
a) Graph the supply and demand functions in the typical manner
with price per unit (P) on the Y-axis and quantity on the X-axis.
Make sure to clearly mark X-intercept and Y-intercept on the
graph.
b) What is the slope of each line? Show your calculations.
c) What is the equilibrium price and quantity? Show your
calculations. Show the...

Following is a simple linear regression model:
The following results were obtained from some statistical
software.
R2 = 0.523
syx (regression standard error) = 3.028
n (total observations) = 41
Significance level = 0.05 = 5%
Variable Parameter Estimate Std. Error of
Parameter Est.
Intercept 0.519 0.132
Slope of X -0.707 0.239
Questions: the correlation coefficient r between the x and y is?
What is the meaning of R2? Show your work.

14. Practice questions
a. Create an anonymous function called func1 for the dummy
argument x that finds the exponential of the negative one-half
times the argument, and multiplies it by the sine of five times the
argument. If given a vector or matrix, the function should perform
element-by-element processing.
b. Using plot(), plot plotr -vs- func1(plotr) as a blue line.
Then plot this same function again over the same range (0, 5) as a
dashed red line using fplot(), keeping...

7. Please answer the following questions
(1)Suppose John is planning to join a sports club. Membership in
the club will allow John to swim at the pool for half price.
Normally swimming for an hour would cost $10. If John has an income
of $1000, the club membership fee is $100, and we plot the number
of visits to the pool on the horizontal axis and a composite "other
goods" which have a price of $1 on the vertical axis,...

Complete the following questions utilizing the concepts
introduced in this unit.
1. A retirement account is opened with an initial deposit of
$8,500 and earns 8.12% interest compounded monthly. What will the
account be worth in 20 years? What if the deposit was calculated
using simple interest? Could you see the situation in a graph? From
what point one is better than the other?
2. Graph the function and its reflection about the
line y=x on the same axis, and give...

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