Answer:
48
Step-by-step explanation:
60 = 5x
x = 12
12x4 = 48
Answer:
The equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:
Step-by-step explanation:
The slope-intercept form of the line equation
where
Given the line
3x - 4y = 7
writing in the slope-intercept form
4y = 3x - 7
dividing both sides by 4
4y/4 = 3/4x - 7/4
y = 3/4x - 7/4
Now, comparing with the slope-intercept form of the line equation
y = 3/4x - 7/4
The slope of the line m = 3/4
We know that parallel lines have the same slopes.
Therefore, the slope of the parallel line is: 3/4
now we have,
The point (-4, -2)
The slope m of parallel line = 3/4
Given the point-slope form of the line equation
where m is the slope of the line and (x₁, y₁) is the point
substituting (-4, -2) and m = 3/4 in the point-slope form of line equation


Thus, the equation in the point-slope form of the line equation is:

Simplifying the equation

Subtract 3 from both sides


Multiplying the equation by 4


Therefore, the equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:
a. Parameterize
by

with
.
b/c. The line integral of
over
is




d. Notice that we can write the line integral as

By Green's theorem, the line integral is equivalent to

where
is the triangle bounded by
, and this integral is simply twice the area of
.
is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.
Answer:
125
Step-by-step explanation:
The total number of marbles is 6+10 = 16
P (black) = black / total
= 10/16 = 5/8
With 200 draws, take the probability of P(black) times 200 since the marble is returned each time
200 * (5/8) = 125
We would expect to get 125 black marbles