geno3141

If the equation is in the form:  y  =  mx + b  then  m is the slope  and  b is the y-intercept.

Let's take  4x + y  =  -5  and get the y-term alone on the left side by subtracting 4x from both sides:

--->                 y  =  -4x - 5

--->     slope = -4  and  y-intercept is -5

3y + 2  =  -13

Subtract 2 from both sides:

3y  =  -15

Divide both sides by 3:

y  =  -5

Let A be the beginning point. After 85.5 m, it comes to point B. 

Then it makes a 150° angle (180° - 30° = 150°) and procedes 45.0 m to point C.

You wish to find the distance from point A to point C.

Side AB = c, side BC = a, and side AC = b.

Use the Law of Cosines: b²  =  a² + c² - 2a·b·cos(B)

--->   b²  =  45.0² + 85.5² - 2· 45.0 · 85.5 · cos(150)

Can you finish this?

The median is the number in the middle of the data set. Which number is the middle number?

Range is largest minus smallest:  is largest minus smallest equal to 95?

Is the lowest grade 95?

The median is the middle number, when the data is sorted from smallest to largest. (In the case of an even number of numbers, the median is halfway between the two middle numbers.) Is 95 the median score?

The mode is the number found most often in the data set? Is 95 the number found most often?

To create a triangle, the lengths of the two shorter sides, when added together, must be more than the longest side.

In which of the cases is the sum of the two smaller numbers greater than the largest number? 

Must be greater, equal to is not good enough...

Since the order in which these persons are chosen, it is a combinations problem.

To choose 1 instructor from 4:  ₄C₁  =  4

To choose 2 asst profs from 9:  ₉C₂  =  36

To choose 2 assoc profs from 5:  ₅C₂  =  10

To find the final answer, multiply these together:   ₄C₁ · ₉C₂ · ₅C₂  =  4 x 36 x 10 =  ...

3¹ = 3 mod 8 = 3     3³ = 27 mod 8 = 3     3⁵ = 243 mod 8 = 3

3² = 9 mod 8 = 1     3⁴ = 81 mod 8 = 1     3⁶ = 729 mod 8 = 1

So, if the exponent is even, its mod 8 value is 8 ...

and, if the exponent is add, its mode 8 value is 1 ...

Find the mean of the test scores. This will be the answer ...

Go online:     https://stuff.mit.edu/afs/sipb/contrib/pi/