Answer:
E) is correct, 2/3
Step-by-step explanation:
The points that are 20 inches apart from P form a circle that contains Q. We can suppose that P is in the position (0,0) and Q in the position (20,0) (we can rotate and move the circle without making any effect on the probability).
A point in the circle at distance 20 of Q has the form (20 cos(Ф), 20 sen(Ф) ) for certain angle Ф between 0 and 2π. Since it is at distance 20 of Q, we have that (20-20cos(Φ))² + (0-20sen(Φ))² = 20²=400, thus
400 - 800 cos(Φ) + 400cos²(Φ) + 400sen²(Φ) = 800-800cos(Φ) = 400, so
400 = 800cos(Φ)
cos(Φ) = 1/2
By looking at a trigonimetric table, you can find that Φ is either π/3 or 2π-π/3 = 5π/3.
As a result, the angles that will give you a point R at distance from Q greater than 20 are between π/3 and 5π/3, hence , the points that are a distance greater than 20 form a chord of length 20*(5π/3-π/3) = 80π/3. Comparing this with the perimeter of the circle (20*2π = 40π), this gives us a probability of 80π/3 / 40π = 2/3 that the point R is closer to P than it is to Q.
Answer:
x=6
Step-by-step explanation:
If each person would get one napkin and one cup then you would need to buy 3 cup packages and 4 napkin packages
Answer:
She can only make 5/6 of her recipe with the amount of milk that she has.
Step-by-step explanation:
Some data of this problem is missing, the data missing is:
Her recipe calls for 3/4 of a pint of milk and she only has 5/8 of a pint of milk.
Now, to know what's the portion she can do with that amount we need to divide the amount of milk she has by the total amount she needs:
÷
When we divide we turn the second fraction upside down (the numerator becomes the denominator and viceversa) and multiply, thus:
÷×
If we simplify this last expression we have:
Thus, she can only make 5/6 of her recipe with the amount of milk that she has.
<em>Note: In case the data missing is different, you can apply this same procedure with the fractions you have. </em>
Start by finding the slope of the line.
m = y2 - y1 / x2 - x1
m = 5 - 2/1 - 0 ⇒ 3/1 ⇒ 3.
So the slope of the line is 3.
This can be used with either one of our two points
to write the equation of the line in point-slope form.
So let's go with the point (0, 2).
Point-slope form is written y - y1 = m(x - x1).
Since we are using the point (0, 2), y - y1 would be y - 2.
"m" would be 3 and x1 would be 0.
So we have y - 2 = 3(x - 0).