Mr. Jamison will stain the deck in his backyard, the deck has an area of 752.4 sqaure feet. If the deck is 33 feet long how wide is it? Justify your procedure.

The width of the deck is 22.8 feet.

Step-by-step explanation:

Since we have given that

Area of the deck = 752.4 square feet

Length of deck = 33 feet

Let width of deck be 'x'.

Since Deck is in the shape of rectangle.

As we know the formula for "Area of rectangle ":

\begin{gathered}Area=Length\times width752.4=33\times xdfrac{752.4}{33}=x22.8=x\end{gathered}

Area=Length×width

752.4=33×x

33

752.4

=x

22.8=x

Hence, the width of the deck is 22.8 feet.

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation:

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