A customer placed an order with a bakery for cupcakes. the Baker has completed 37.5% of the order after being 81 cupcakes how ma
1 answer:
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a) 62.855m
We will need to use the Pythagorean Theorem here, as we know a and c, but not b. I have attached an image of a triangle sketch to set up the problem, which should hopefully help us to visualize this problem a bit better.
Pythagorean Theorem: a^2 + b^2 = c^2
(19.8)^2 + b^2 = (65.9)^2
392.04 + b^2 = 4342.81
b^2 = 3950.77
b = 62.855 (rounded to 3 places)
b) m = 0.315
The gradient is also known as the slope. I've shown what the points would be in the image attached. Now that we know the value of b (x in the points in image), we can use points E and C to find the slope.
Point 1: (0,0)
Point 2: (62.855, 19.8)
m = (19.8 - 0) / (62.855 - 0)
m = 19.8 / 62.855
m = 0.315 (rounded to three places)
c) 17.485 degrees
The angle of inclination would be angle C. To find angle C, we will need to use an inverse trigonometry function. Any can be used since we know all of the side lengths, but I will show Sine here, opposite / hypotenuse.
sin(x) = 19.8 / 65.9
x = sin^-1 (19.8/65.9)
x = 17.485 degrees (rounded to 3 places)
Hope this helps!! :)
Answer:
If we compare the p value and a significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the population mean is signficantly higher than 83.2 at 1% of significance.
Step-by-step explanation:
Data given and notation
represent the average life for the sample
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to apply a two tailed test.
What are H0 and Ha for this study?
Null hypothesis:
Alternative hypothesis :
Compute the test statistic
The statistic for this case is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
Give the appropriate conclusion for the test
First we need to calculate the degrees of freedom given by:
Since is a one side right tailed test the p value would be:
Conclusion
If we compare the p value and a significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the population mean is signficantly higher than 83.2 at 1% of significance.