We will verify each options
option-A:
we can factor it
so, this is not irrational.........Answer
option-B:
Since, it can not be factored
so, this is irrational.........................Answer
option-C:
we can factor it
so, this is not irrational.........Answer
option-D:
we can factor it
so, this is not irrational.........Answer
Answer:
a)
b) For this case we need to find a critical value that accumulates of the area on each tail, we know that
, so then
, using the normal standard table or excel we see that:
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.
Step-by-step explanation:
Data given and notation
n=420+174=594 represent the random sample taken
X=174 represent the number of yellow peas
estimated proportion of yellow peas
is the value that we want to test
represent the significance level
Confidence=99% or 0.99
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion of yellow peas is 0.23:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statisitc, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis.
b) Critical value
For this case we need to find a critical value that accumulates of the area on each tail, we know that
, so then
, using the normal standard table or excel we see that:
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.
Answer:
The exact work required to pump all the gasoline to the surface of the ground is π × 5.094 × 10⁶ j
Step-by-step explanation:
Here, we note that volume of a slice is given by
Length × Width × Height
Length of slice = Length of cylinder = 15 ft
Since the slice height is Δy ft thick and located y ft above the center of the cylinder, then
Width of slice = 2 × √(r² - y²)
Where:
r = Radius of the cylinder =5 ft
∴ Width of slice = 2 × √(25 - y²)
∴Volume of slice = 15 ×2 × √(25 - y²)×Δy
Mass of slice then = 42 × 15 ×2 × √(25 - y²)×Δy = 1260 × √(25 - y²)×Δy
The force required to lift the slice is the weight of the slice, which is given by
32.2 × 1260 × √(25 - y²)×Δy = 40572 × √(25 - y²)×Δy N (Newtons)
The work done by the force is the product of the force and the distsnce through which the force acts.
Work done = 40752×(10-y) × √(25 - y²)×Δy
Therefore total work done is given by
= 5094000·π J = π × 5.094 × 10⁶ j
The exact work required to pump all the gasoline to the surface of the ground = π × 5.094 × 10⁶ j