Marisol is being paid $792 to provide nutrition counseling, It took her 8 hours more than she expected, so she earned $4 per hour less than she originally calculated. How long had she anticipated it would take to do
the job?

44 hours.

Step-by-step explanation:

Marisol is being paid $792.

We know that the job took her 8 hours more than she expected, so if we define T as the time she expected, this job took her:

T + 8 hours.

The amount of money per hour that she expected is calculated as:

$792/T = X

And for those 8 extra hours, she won $4 less per hour, then we have:

$792/(T + 8hs) = X - $4

Then we have a system of equations:

$792/T = X

$792/(T + 8hs) = X - $4

To solve this, we can notice that in the first equation X is isolated, then we could replace that in the second equation to get:

$792/(T + 8hs) = $792/T - $4

Now we can solve this for T.

$792 = ($792/T - $4)*(T + 8hs)  = $792 + $792*(8hs/T) - $4*T + $32*hs

0 = $792*(8hs/T) - $4*T + $32*hs

Let´s multiply this both sides by T

0*T = ($792*(8hs/T) - $4*T + $32*hs)*T

0 = $792*8hs - $4*T^2 +$32*T*hs

This is a quadratic equation, where i will write this witout units so it is easier to read and follow:

0 = -4*T^2 + 32*T + 792*8

The solutions cab be found by using the Bhaskara´s formula, these are:

Then the solutions are:

T = (-32 + 320)/-8 = -36 hours (This is a negative time, and it does not really have a meaning in this problem, so we can discard this option)

The other solution is:

T = (-32 - 320)/-8 = 44 hours.

Then we can conclude that she expected the job would take 44 hours in total.

the expected value of the random variable : 0, 1 and 2

step-by-step explanation:

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,