Answer:
tanФ = 2.6363636
Step-by-step explanation:
To find the tangent of the angle in-between the lines we will follow the steps below:
We are going to use the formula;
tanФ = |m₂ - m₁ / 1 + m₁m₂|
We can get the slope m₁ from the first equation
2x+3y–5=0
we will re-arrange it in the form y=mx + c
3y = -2x + 5
Divide through by 3
y = -
x + 
comparing the above equation with y=mx + c
m₁ = -
We will proceed to find the second slope m₂ using the second equation
5x=7y+3
we will re-arrange it in the form y=mx + c
7y = 5x -3
divide through by 7
y = 
x - 
comparing the above with y=mx + x
m₂ =
we can now go ahead and substitute into the formula
tanФ = |m₂ - m₁ / 1 + m₁m₂|
tanФ = | - (- ) / 1 + (-₁)( )|
tanФ = | + / 1 - 
|
tanФ = | 
/ 
|
tanФ = | × 
|
21 will cancel-out 21
tanФ =
tanФ = 2.636363
Answer:
The 90% confidence interval for the mean monthly rent of all 1 bedroom apartments is between $841.67 and $1098.33
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 13 - 1 = 12
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 12 degrees of freedom(y-axis) and a confidence level of 
. So we have T = 1.7823
The margin of error is:
M = T*s = 1.7823*72 = 128.33
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 970 - 128.33 = $841.67
The upper end of the interval is the sample mean added to M. So it is 970 + 128.33 = $1098.33
The 90% confidence interval for the mean monthly rent of all 1 bedroom apartments is between $841.67 and $1098.33
Answer:
-16/6
Step-by-step explanation:
2x-8÷x+10
2(-4)-8÷-4+10
-16÷6
