Final answer:
The expressions were evaluated after substituting the provided values for x, y, and z, but the correct answers -23/24 and -1.05 do not match any of the given options. Consequently, no answer can be confidently chosen from the options provided for both questions.
Step-by-step explanation:
The question requires us to evaluate expressions given the values for the variables. First, we will evaluate the expression x + 0.3(y - z) given that x = -5/6, y = 1/3, and z = 3/4.
Substituting the values in we get:
-5/6 + 0.3(1/3 - 3/4)
Now, we calculate the parenthesis:
-5/6 + 0.3(1/3 - 3/4) = -5/6 + 0.3(4/12 - 9/12)
-5/6 + 0.3(-5/12) = -5/6 - 0.3(5/12)
Now, to clear the decimal we can write 0.3 as 3/10:
-5/6 - (3/10)(5/12)
We can multiply the fractions:
-5/6 - (3*5)/(10*12)
-5/6 - 15/120
Now, we simplify the second fraction:
-5/6 - 1/8
Now, we find a common denominator and simplify:
-5/6 - 1/8 = (-40/48) - (6/48) = -46/48
Finally, we simplify the fraction:
-46/48 = -23/24
So the first answer is not available in the options provided. Therefore, I cannot confidently choose an answer between a) -0.31 b) -0.54 c) -0.29 d) -0.67.
Now let's calculate the second expression, a + b - d, with the values a = 3/4, b = -1.55, and d = -1/4.
Substituting the values in, we get:
3/4 - 1.55 - (-1/4)
Now, we add 3/4 and -1/4:
3/4 - 1/4 = 2/4 = 1/2
Now, we convert 1/2 to decimal to simplify:
0.5 - 1.55 = -1.05, which again does not match any of the given options a) -0.56 b) -1.25 c) -0.5 d) -1.75.
Both questions presented do not match the provided possible answers. Therefore, I cannot confidently provide a correct selection from the options provided.