Answer:
(Véase la explicación para mayores detalles/See the explanation for further details)
Step-by-step explanation:
a) Tres al cubo (Three to cube):
b) Seis al cubo (Six to cube):
c) Cinco al cuadrado (Five squared):
d) Ocho al cuadrado (Eight squared):
e) Dos a la quinta (Two to five):
f) Diez a la cuarta (Ten to four):
Answer:
Since is a two sided test the p value would be:
And since the p vaue is lower than the significance level we have enough evidence to reject the null hypothesis.
Step-by-step explanation:
Data given
represent the sample mean
represent the sample 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)
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean of interest is different from 2600, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Calculate the statistic
The statistic for this case is given
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a two sided test the p value would be:
And since the p vaue is lower than the significance level we have enough evidence to reject the null hypothesis.
Answer:
the angle between u=(8, -2) and v=(9,3) is 32.5°
Step-by-step explanation:
u=(8,-2)=(u1,u2)→u1=8, u2=-2
v=(9,3)=(v1,v2)→v1=9, v2=3
We can find the angle between two vectors using the formula of dot product:
u . v =║u║║v║cos α (1)
And the dot product is:
u . v = u1 v1 + u2 v2
u . v = (8)(9)+(-2)(3)
u . v = 72-6
u . v = 66
║u║=√(u1²+u2²)
║u║=√((8)²+(-2)²)
║u║=√(64+4)
║u║=√(68)
║u║=√((4)(17))
║u║=√(4)√(17)
║u║=2√(17)
║v║=√(v1²+v2²)
║v║=√((9)²+(3)²)
║v║=√(81+9)
║v║=√(90)
║v║=√((9)(10))
║v║=√(9)√(10)
║v║=3√(10)
Replacing the known values in the formula of dot product (1):
u . v =║u║║v║cos α
66 = 2√(17) 3√(10) cos α
Multiplying:
66 = 6√((17)(10)) cos α
66 = 6√(170) cos α
Solving first for cos α: Dividing both sides of the equation by 6√(170):
Simplifying: Dividing the numerator and denominator on the left side of the equation by 6:
(66/6)/(6√170/6)=cosα→11/√170=cosα→cosα=11/√170
cosα=11/13.03840481→cosα=0.84366149