Answer: Yes
Step-by-step explanation:
Though x and y can be achieved in a system of equations. The equation
x (t)=0.0411905(t^2)+(-0.164619)t+28.0114
And
y (t)=-0.024127(t^2)+(-0.591143)t+(-87.4403)
Are not system of equations but rather two different models of equations. Nevertheless
To find t in the first equation, x(t) has to be equal to zero.
When the t is substituted in the second equation, t will completely disappear. Given the value of y(t) and vice versa.
Answer:
Since the p value is less than the significance level of 0.1 we have enough evidence to reject the null hypothesis and we can conclude that the true growth rate is significantly less than 3 cm per week
Step-by-step explanation:
Information given
represent the sample mean for the growth
represent the sample standard deviation
sample size
represent the value to check
represent the significance level
t would represent the statistic
represent the p value for the test
System of hypothesis
We want to verify if the true mean for the growth us less than 3cm per week, the system of hypothesis are:
Null hypothesis:
Alternative hypothesis:
We don't know the population deviation so we can use the t statistic:
(1)
Replacing the info given we got:
The degrees of freedom are given by:
The p value for this case would be given by:
Since the p value is less than the significance level of 0.1 we have enough evidence to reject the null hypothesis and we can conclude that the true growth rate is significantly less than 3 cm per week
<span>(2m - n)</span>⁷ can be expanded using the binomial theorem or pascal's triangle, but writing out the work is proving to be really difficult. the application of the theorem is pretty complicated and it isn't easy to format in this textbox.
the expansion of this would be 128m⁷ - 448m⁶n + 672m⁵n² - 560m⁴n³ + 280m³n⁴ - 84m²n⁵ + 14mn⁶ - n⁷. let me know if you're genuinely lost on how to find it and i'll give a written explanation a shot, but i'd really, really encourage you to refer back to your notes if you took any in class (or the lesson, if it's an online class) and see if you can find anything which explains the binomial theorem or pascal's triangle. both of those will help you immensely.
For the surface of rectangle to be minimum the the dimensions must be equal. Let the length=width=height=x cm
thus the volume will be:
x×x×x=28
x³=28
x=∛28
x=2√7 cm
thus the dimensions are such that length=width=height=2√7
