Are the following statements true or false?

1. if f⃗ is a vector field in 3-dimensional space satisfying div(f⃗ )=1, and s is a closed surface oriented outward, then ∬sf⃗ ⋅da⃗ is equal to the volume enclosed by s.

2. if f⃗ is a vector field in 3-dimensional space, and w is a solid region with boundary surface s, then ∬s f⃗ ⋅da⃗ =∭wdiv(f⃗ )dv.

3. if ∬sf⃗ ⋅da⃗ =12 and s is a flat disk of area 4π, then div(f⃗ )=3/π.

4. if f⃗ is a vector field in 3-dimensional space, then grad(div(f⃗ ))=0⃗ .

5. if f⃗ and g⃗ are vector fields satisfying div(f⃗ )=div(g⃗ ), then f⃗ =g⃗ .

The contents of 3838 cans of coke have a mean of x¯¯¯=12.15x¯=12.15. assume the contents of cans of coke have a normal distribution with standard deviation of σ=0.12.σ=0.12. find the value of the test statistic zz for the claim that the population mean is μ=12.μ=12.

Someone answer asap for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =

Reduce fractions expressing probability to lowest terms. in 3,000 repetitions of an experiment, a random event occurred in 500 cases. the expected probability of this event is?