Answer:
Step-by-step explanation:
![S_{31} = 9 \cdot 31 + [-0.5 \cdot \frac{31(31-1)}{2}] = 46.5](https://tex.z-dn.net/?f=S_%7B31%7D%20%3D%209%20%5Ccdot%2031%20%2B%20%5B-0.5%20%5Ccdot%20%5Cfrac%7B31%2831-1%29%7D%7B2%7D%5D%20%3D%2046.5)
![S_{40} = 40 + [-3 \cdot \frac{40(40-1)}{2}] = -2300](https://tex.z-dn.net/?f=S_%7B40%7D%20%3D%2040%20%2B%20%5B-3%20%5Ccdot%20%5Cfrac%7B40%2840-1%29%7D%7B2%7D%5D%20%3D%20-2300)
Answer:
and 
Step-by-step explanation:
The equation of curve is

We need to find the equation of the tangent line to the curve at the point (-3, 1).
Differentiate with respect to x.
![2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})](https://tex.z-dn.net/?f=2%5B2%28x%5E2%2By%5E2%29%5Cfrac%7Bd%7D%7Bdx%7D%28x%5E2%2By%5E2%29%5D%3D25%282x-2y%5Cfrac%7Bdy%7D%7Bdx%7D%29)

The point of tangency is (-3,1). It means the slope of tangent is
.
Substitute x=-3 and y=1 in the above equation.





Divide both sides by 130.

If a line passes through a points
with slope m, then the point slope form of the line is

The slope of tangent line is
and it passes through the point (-3,1). So, the equation of tangent is


Add 1 on both sides.


Therefore,
and
.
Answer:
<h2>y = -5x - 10</h2>
Step-by-step explanation:


Answer:
The probability is 
Step-by-step explanation:
From the question we are told
The population proportion is 
The sample size is 
The number of graduate who had job is k = 209
Generally given that the sample size is large enough (i.e n > 30) then the mean of this sampling distribution is

Generally the standard deviation of this sampling distribution is

=> 
=> 
Generally the sample proportion is mathematically represented as

=> 
=> 
Generally probability of obtaining a sample proportion as low as or lower than this, if the university’s claim is true, is mathematically represented as


From the z table the area under the normal curve to the left corresponding to -3.022 is

=> 
Answer:b
Step-by-step explanation: