Alocal weather enthusiast wants to see if the last five summers have been warmer than normal for eloy, arizona. from the national oceanic and atmospheric administration (noaa), he knows the 30-year average for july was 90° with a standard deviation of 2.1°. the last five summers recorded have an average of 92°. if he uses a = 2.5%, which of the following would be valid based on the data he has gathered? a) he can conclude that the summers have been warmer than the 30-year average. b) he can conclude that the summers will continue to be warmer for the next 10 years. c) he does not have enough information to make a decision. d) the average for the last five years fits with the 30-year average.

D) The average for the last five years fits with the 30-year average.

Step-by-step explanation:

Let represent the average temperature for the summers.

According to the given description , we have

Null hypothesis :

Alternative hypothesis :

Since Alternative hypothesis is right-tailed , so the test is a right-tailed test.

Given :  ;  ; n= 5

Test statistic :

From t-distribution table , the critical value for t at and degree of freedom (n-1=4) is 2.776.

Since the observed t-value (2.13) is less than the critical t-value (2.776),  it means we are fail to reject the null hypothesis.

Conclusion: The average for the last five years fits with the 30-year average.

72 is the answer to this problem

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it