Working alone, Dan can paint a fence in ten hours. One day his friend Natalie helped him and it only took 4.12 hours. How long would it take Natalie to do it alone?

5.88?

Step-by-step explanation:

Explanation:

Let's say there are 1000 boards to be painted.

Working alone, Dan can paint 1000 boards in 10 hours, so his unit rate is 1000/10 = 100 boards per hour.

In 4.12 hours, he gets 4.12*100 = 412 boards painted. There are 1000-412 = 588 boards left which Natalie takes care of. This is when the two are working together.

Her unit rate is (588 boards)/(4.12 hours) = 142.718447 boards per hour. That value is approximate.

We multiply her unit rate by some unknown amount of time x, and this product will be the 1000 boards we started with. This way she would get the job down by herself.

So the equation we need to solve is

142.718447x = 1000

We divide both sides by 142.718447 to fully isolate x.

142.718447x = 1000

x = 1000/(142.718447)

x = 7.006803

That value is approximate.

If we round to the nearest whole number, then x = 7

So it takes about 7 hours for Natalie to get the job done if she works alone.

Side note:

An alternative pathway is to solve the equation

1/10 + 1/x = 1/(4.12)

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!