1. simplify the radical expression. sqrt 3 + 4 sqrt 3 A. 5 sqrt 6
B. 5 sqrt 3
C. 3 sqrt 6
D. 3 sqrt 3

2. What is the domain of the function?
y = sqrt 5x - 10

A. x (greater than or equal to) -2
B. x (less than or equal to) -2
C. x (greater than or equal to) 2
D. x (less than or equal to) 2

3. Simplify the radical expression by rationalizing the denominator.
sqrt 8 / sqrt 6x

A. 2 sqrt 3x / 3x
B. 2 sqrt 2x / x
C. x / sqrt 6x / 3x (hopefully I typed this one out right)
D. 4 sqrt 3x / 3x

4. The table shows the number of hours that a group of teammates spent in their first week of training for the swimming finals. In the second week, they each add 4 hours to their training times. What are the mean, median, mode, and range of the times for the second week?

Danielle - 10
Jesse - 8
Julie - 12
Alan - 6
Adam - 5
Bob - 4
Marianne - 10

Please help lol I'm on the test rn and I'm struggling with these 4. I answered everything else but I can't get a bad grade on this ​

its a straight line parallel to the time axis

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt