The answer is boxed in. follow the arrows.
Part A
Either Nathan picked 0, or Sonia picked 0, or both.
This is because multiplying nonzero numbers together gets a nonzero result. So one of them must have picked 0.
==============================================================
Part B
It's the same idea as part A. It's not clear what the nonzero values are, but one (or more) person picked 0 as their secret number.
If they picked something like 1, 2 and 3, then the product is 1*2*3 = 6 which is nonzero and the product is larger than the three original values. This is because each value is 1 or larger. If someone picked a small decimal value like 0.1 then 0.1*2*3 = 0.6 is the product. It's closer to 0, but not 0 itself.
==============================================================
Part C
Zero Product Property:
If m*n = 0, then either m = 0 or n = 0 or both.
This idea says that if the product of two numbers is 0, then at least one of the numbers must be 0 itself. It can be extended to three or more numbers.
This idea is useful when it comes to solving factored quadratic equations.
In the case of 2x^2 + 5x - 12, it factors to (2x-3)(x+4)
So using the zero product property, we can solve the quadratic equation like this
2x^2 + 5x - 12 = 0
(2x-3)(x+4) = 0
2x-3 = 0 or x+4 = 0
2x = 3 or x = -4
x = 3/2 = 1.5 or x = -4
The use of the zero product property happens in step 3
Answer:
The null hypothesis μ=4.0 could not be rejected.
Step-by-step explanation:
In this problem we have to perform a hypothesis test of the mean, with s.d. of the population unknown.
The sample is: [3.999, 4.037, 4.116, 4.063, 3.969, 3.955, 4.091]
This sample has a mean of 4.033 and a standard deviation of 0.061.
The null and alternative hypothesis are:
We assume a significance level of 0.05.
The test statistic for this test is:
We have a sample size n=7, so the degrees of freedom are 7-1=6.
For a two-tailed test, t=0.536 and df=6, the P-value can be look up in a t-table.
The P-value is 0.61. Is greater than the significance level, so the effect is not significant and the null hypothesis can't be rejected.
