The valid conclusions for the manager based on the considered test is given by: Option
<h3>When do we perform one sample z-test?</h3>
One sample z-test is performed if the sample size is large enough (n  > 30) and we want to know if the sample comes from the specific population.
For this case, we're specified that:
- Population mean =  = $150 = $150
- Population standard deviation =  = $30.20 = $30.20
- Sample mean =  = $160 = $160
- Sample size = n = 40 > 30
- Level of significance =  = 2.5% = 0.025 = 2.5% = 0.025
- We want to determine if the average customer spends more in his store than the national average.
Forming hypotheses:
- Null Hypothesis: Nullifies what we're trying to determine. Assumes that the average customer doesn't spend more in the store than the national average. Symbolically, we get:  
- Alternate hypothesis: Assumes that customer spends more in his store than the national average. Symbolically  
where  is the hypothesized population mean of the money his customer spends in his store.
 is the hypothesized population mean of the money his customer spends in his store.
The z-test statistic we get is:

The test is single tailed, (right tailed).
The critical value of z at level of significance 0.025 is 1.96
Since we've got 2.904 > 1.96, so we reject the null hypothesis.
(as for right tailed test, we reject null hypothesis if the test statistic is > critical value).
Thus, we accept the alternate hypothesis that customer spends more in his store than the national average. 
Learn more about one-sample z-test here:
brainly.com/question/21477856
 
        
                    
             
        
        
        
Dude use the formula of height and distance to find the height of the trangle and then you can find the other side length using Pythagorus theorem
        
             
        
        
        
Answer:
We multiplied by a negative number (-8)
We divided by a negative number (-8)
Step-by-step explanation:
Multiplying or dividing both sides of an equation by a negative number changes the inequality of the equation, because it changes the sign of each side of the equation
 
        
             
        
        
        
Answer:
This means the cost of the item to you is $57.75. You will pay $57.75 for a item with original price of $82.50 when discounted 30%. In this example, if you buy an item at $82.50 with 30% discount, you will pay 82.50 - 24.75 = 57.75 dollars.