Lorraine computed a confidence interval for μ based on a sample of size 41. since she did not know σ, she used s in her calculations. lorraine used the normal distribution for the confidence interval instead of a student's t distribution. will her interval be longer or shorter than one obtained by using an appropriate student's t distribution? explain.
shorter. for d. f. = 40, zc is greater than tc. shorter. for d. f. = 40, zc is less than tc. longer. for d. f. = 40, zc is less than tc. longer. for d. f. = 40, zc is greater than tc.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

518,400

step-by-step explanation:

the area is multiplying all the given measurements together.

40 * 18 * 30 * 24 = 518,400

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.