Answer:
y = 1/10x
Step-by-step explanation:
We see that it intersects points (60,6), (120,12), and (0,0)
y = mx + b
m = 6/60 = 1/10
b = 0
y = 1/10x
Answer:
49/8 is the value of k
Step-by-step explanation:
We have the system
x = -2y^2 - 3y + 5
x=k
We want to find k such that the system intersects once.
If we substitute the second into the first giving us k=-2y^2-3y+5 we should see we have a quadratic equation in terms of variable y.
This equation has one solution when it's discriminant is 0.
Let's first rewrite the equation in standard form.
Subtracting k on both sides gives
0=-2y^2-3y+5-k
The discriminant can be found by evaluating
b^2-4ac.
Upon comparing 0=-2y^2-3y+5-k to 0=ax^2+bx+c, we see that
a=-2, b=-3, and c=5-k.
So we want to solve the following equation for k:
(-3)^2-4(-2)(5-k)=0
9+8(5-k)=0
Distribute:
9+40-8k=0
49-8k=0
Add 8k on both sides:
49=8k
Divide both sides by 8"
49/8=k
Answer:
a) 17.09 hours
b) The 95% confidence interval estimate of the population mean flying time for the Pilots is between 31.91 hours and 66.09 hours
Step-by-step explanation:
We have the standard deviation of 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 = 49 - 1 = 48
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 48 degrees of freedom(y-axis) and a confidence level of
. So we have T = 2.0106
The margin of error is:
M = T*s = 2.0106*8.5 = 17.09
s is the standard deviation of the sample. 17.09 hours is the answer for a.
The lower end of the interval is the sample mean subtracted by M. So it is 49 - 17.09 = 31.91 hours
The upper end of the interval is the sample mean added to M. So it is 49 + 17.09 = 66.09 hours
The 95% confidence interval estimate of the population mean flying time for the Pilots is between 31.91 hours and 66.09 hours
Answer:
Yes, these triangles are congruent
∠E≅∠M
Step-by-step explanation:
Yes, these triangles are similar.
<em>Proof:</em>
Each side in LNM is
times longer than the sides in GFE



According CPCTC (corresponding parts of congruent triangles are congruent), angle E is similar to angle M.
Hope this helps :)
Have a good day!
Answer:
The correct answer is option A. r
Step-by-step explanation:
From the figure we can see a circle and a parallelogram.
The circle is divided into a small sectors and these sector then arranged into a parallelogram.
The base of the parallelogram is half the circumference.
The height of parallelogram is equal to the radius of the given circle. Here radius is 'r'.
Therefore the correct answer is option A. r