Answer:
- 15 mL of 100% vinegar
- 45 mL of Italian dressing
Step-by-step explanation:
Let v represent the amount of 100% vinegar to be included in the mixture. Then the amount of vinegar in the overall mixture is ...
1.00v + 0.08(60 -v) = 0.31(60)
0.92v = 60(0.23) . . . . . . . collect terms, subtract .08(60)
v = 60(0.23/0.92) = 15 . . . mL of vinegar
60 -v = 45 . . . mL of dressing
15 mL of vinegar and 45 mL of Italian dressing should be used.
Answer:

Step-by-step explanation:
We are given the polynomial:

And we want to determine the value of <em>k</em> such that (<em>x</em> - 2) is a factor of the polynomial.
Recall that the Factor Theorem states that a binomial (<em>x</em> - <em>a</em>) is a factor of a polynomial P(x) if and only if P(a) = 0.
Our binomial factor is (<em>x</em> - 2). Thus, <em>a</em> = 2.
Hence, by the Factor Theorem, P(2) must equal zero.
Find P(2):

This must equal zero. Hence:

In conclusion, <em>k</em> = 34/3.
Answer:
0.45
Step-by-step explanation:
For a uniform distribution,

where a is the minimum and b the maximum\\
cumulatively,
The amount spent as a percentage of the budget can be found from
... (actual amount)/(total budget) × 100%
... = (actual amount)/3600×100%
... = ((actual amount)/36)%
For housing, this is
... (820/36)% = 22.78% . . . . less than budget for housing
For transportation, this is
... (370/36)% = 10.28% . . . . more than budget for transportation