Answer:
The first car was traveling 70 mph, while the second was driving 50 mph.
Step-by-step explanation:
Set the cars as a proportion:
X represents the speed of the second car. By cross multiplying, you get the following equation:
You solve by distributing 150 to get 210x = 150x + 3000.
Solving for x gets you 50.
That means the first car was going at 50 mph. Adding 20, you get 70 as the speed for the second car.
Answer:
Step-by-step explanation:
for two lines to be parallel they MUST have the same slope but have different Y intercepts ( Y axis crossing values)
parallel lines will never intersect each other
first I use a graphing calcuator to solve the problem
I like to use y intercept form better, but you don't have use it
I will try to solve it directly without going through the y intercept equation
x + 5y = 10 in y intercept form y = mx + b is
5y = -x + 10 divide both sides by 5
y = -x/5 + 10/5
y = -x/5 + 2
Now I need to find a parallel line that passes through the x =1 and y = 3 point recall this line will have the same slope = m = -1/5
and a different Y axis crossing point 'b' that we don't know
y = -x/5 + b y = 3 when x = 1 so slove for 'b'
3 = -1/5 + b
3 = -0.2 + b add -0.2 to both sides
3.2 = b
y = -x/5 + 3.2 this is answer in y intercept form
if you multiply both sides by 5
5y = -x + 16 add x to both sides
x + 5y = 16 answer in standard form
THE EASIER WAY TO SOLVE THE PROBLEM IS ......
x + 5y = 10 find a line parallel that passes through x = 1, y = 3
x + 5y = Z Z is an unknown value plug in x and y and solve for Z
1 + 5(3) = Z
Z = 16 so the parallel line in standard form is
x + 5y = 16
same as before, my y intercept method was correct, but not worth the effort
There is a missing content in the question.
After the statements and before the the options given; there is an omitted content which says:
Referring to Table 16-5, in testing the coefficient of X in the regression equation (0.117) the results were a t-statistic of 9.08 and an associated p-value of 0.0000. Which of the following is the best interpretation of this result?
Answer:
C. The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05).
Step-by-step explanation:
From the given question:
The resulting regression equation can be represented as:
where;
the estimated number of contracts in a quarter X is the coded quarterly value with X = 0
the first quarter of 2010 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise
Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise
Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise
Our null and alternative hypothesis can be stated as;
Null hypothesis :
The quarterly growth rate in the number of contracts is not significantly different from 0% (? = 0.05)
The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)
The decision rule is to reject the null hypothesis if the p-value is less than 0.05.
From the missing omitted part we added above; we can see that the t-statistics value = 9.08 and the p-value = 0.000 .
Conclusion:
Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e
The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)