Answer:
22 2/9
Step-by-step explanation:
When z "varies jointly" with x and y, it can be described by the formula
z = kxy
Here, we have bags of mulch (n) varying jointly with area (a) and depth (d), both in feet. The given information can let us find the value of k.
n = kad
10 = k·(120)(1/4)
10/30 = k = 1/3 . . . . . divide by the coefficient of k
Now, we can fill in the other values of interest.
n = (1/3)·(200)·(1/3) = 200/9
n = 22 2/9
You need 22 2/9 bags of mulch to cover 200 ft² to a depth of 4 inches.
_____
<em>Comment on the problem</em>
This problem requires the formula be written with both area and depth expressed in feet, yet it gives depth in inches. The formula can also be written using depth in inches. In that case, k = 1/36.
we know the x-intercept of the line is 1, recall that an x-intercept is when the graph intercepts or touches the x-axis, and when that happens, y = 0, so the point is really x = 1, y = 0, namely (1,0). We also know another point on the line, is (-2, 9).

9514 1404 393
Answer:
(d) Infinitely Many Solutions
Step-by-step explanation:
Each point of intersection between the lines is a solution. When the lines lie on top of each other, there are infinitely many points of intersection, hence ...
Infinitely Many Solutions
Let X be the national sat score. X follows normal distribution with mean μ =1028, standard deviation σ = 92
The 90th percentile score is nothing but the x value for which area below x is 90%.
To find 90th percentile we will find find z score such that probability below z is 0.9
P(Z <z) = 0.9
Using excel function to find z score corresponding to probability 0.9 is
z = NORM.S.INV(0.9) = 1.28
z =1.28
Now convert z score into x value using the formula
x = z *σ + μ
x = 1.28 * 92 + 1028
x = 1145.76
The 90th percentile score value is 1145.76
The probability that randomly selected score exceeds 1200 is
P(X > 1200)
Z score corresponding to x=1200 is
z = 
z = 
z = 1.8695 ~ 1.87
P(Z > 1.87 ) = 1 - P(Z < 1.87)
Using z-score table to find probability z < 1.87
P(Z < 1.87) = 0.9693
P(Z > 1.87) = 1 - 0.9693
P(Z > 1.87) = 0.0307
The probability that a randomly selected score exceeds 1200 is 0.0307
Remark
Let the pigs = p
Let the chickens = c
Givens
30 heads is another way of saying that there were 30 creatures in the barnyard. In addition each chicken has 2 legs and each pig has 4
c + p = 30
2C + 4P = 100 (2) Divide (2) by 2
C + 2P = 50 (3) Subtract (1) from (3)
<u>C + P = 30</u>
P = 20
So there were 20 pigs.