Name the value of each 2 in 222,222

The equation is:
f(x) = 2x² - 44x + 185
f(x) = 2(x² - 22x + 121 - 121) + 185 =
= 2(x² - 22x + 121) - 242 + 185 =
= 2(x - 11)² - 57
Conclusion:
The vertex is located at (11, -57) and the vertex form is: f(x) = 2(x - 11)² - 57

The bathtub's depth measures 18 inches

It takes 2 minutes to fill 3 inches of the bathtub

Subsequently

The remaining depth needed for filling with water = (18-3) inches

                                                                        = 15 inches

The time needed to fill the remaining 15 inches of the bathtub = (15*2)/3 minutes

                                                                      = 30/3 minutes

                                                                      = 10 minutes

Therefore, John is right in believing that it will require an additional 10 minutes to fill the tub to the brim at the same rate.

Hope this clarifies things!

We consider all workers as either full-time or part-time. 36 = 24 + 12 If there are 24 or fewer full-time workers, there must be at least 12 part-time workers. (This conclusion is based on the understanding of sums.) You can formulate the inequality in two steps. First, present and resolve an equation for full-time workers in relation to part-time workers. Then, apply the specified limit on full-time workers. This results in an inequality that can be solved for part-time workers. Let f and p represent full-time and part-time positions, respectively. f + p = 36... given f = 36 - p... subtract p to express f in terms of p. f ≤ 24......... given (36 - p) ≤ 24.... substitute for f. This gives your inequality in terms of p. 36 - 24 ≤ p.... rearranging gives p ≥ 12........ this is the solution to the inequality

Answer:

B. y - 2 = 1/3(x - 3)

(a) A child possesses a container filled with colored building blocks. She will select one block without looking. The odds against selecting a blue block are 4/7. What is the probability of selecting a blue block?

Answer:

The likelihood of selecting a blue block is 7/11.

Step-by-step explanation:

To find the probability of selecting a blue block,

Odds:

The odds of a given event is the ratio of the probability of that event occurring to the probability of its absence. This means it compares favorable outcomes to those that are unfavorably likely.

The odds of not selecting a blue block being 4/7 means that out of 11 scenarios, there will be 4 occasions when the block is not blue, and 7 when it is blue.

Thus, the probability of not selecting the blue block is 4/11.

Probability of selecting the blue block is the complement of 4/11 which equals 7/11.

(b) Amanda plays a role-playing game with her friends. She will roll dice to decide if her character accesses a treasure chest. The chance of her character unlocking this chest is 13/20. Determine the odds in favor of her character unlocking the treasure chest.

Answer:

The odds in favor of her character unlocking the treasure chest equal 13/7.

Step-by-step explanation:

The probability of Amanda's character unlocking the treasure chest is given as 13/20.

This indicates that in a total of 20 chances, there will be 13 instances where the character successfully opens the treasure chest, while the remaining 7 times, they will not succeed.

Favorable outcomes: 13

Unfavorable outcomes: 7

Consequently, the odds in favor of her character unlocking the treasure chest are 13/7.