Susan is interested in determining whether sunflower seedlings treated with compound A resulted in a lower average height of sunflower seedlings than the standard height of 15.7 cm. She treated a random sample of 10 seedlings with compound A and then recorded their heights: 11.5, 15.2, 16.5, 15.1, 12.9, 9.3, 11.8, 15, 8.5 and 9.5. Assuming sunflower seedlings are normally distributed and that Susan must estimate the standard deviation of this distribution, which of the following statements properly analyzes Susan’s hypothesis? a. She needs to conduct a two-tailed t-test; although the average of the sample is below 15.7 she cannot reject the null hypothesis at the 5% level.
b. She needs to conduct a one-sided t-test; the average of the sample is below 15.7 and statistically significant at the 5% level.
c. She needs to conduct a two-tailed z-test; although the average of the sample is below 15.7 she cannot reject the null hypothesis at the 5% level.
d. She needs to conduct a one-sided z-test; the average of the sample is below 15.7 and statistically significant at the 5% level.
e. She needs to conduct a two-tailed t-test; the average of the sample is below 15.7 and statistically significant at the 5% level.

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

x-150=475   x=625

step-by-step explanation:

if the bike after the sale ($150) is $475 then just simply add 150 to 475.