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Dennis_Churaev [7]
2 years ago
6

A rectangular floor measures $a$ feet by $b$ feet, where $a$ and $b$ are positive integers with $b > a$. An artist paints a r

ectangle on the floor with the sides of the rectangle parallel to the sides of the floor. The unpainted part of the floor forms a border of width 1 foot around the painted rectangle and occupies half the area of the entire floor. How many possibilities are there for the ordered pair $(a,b)$?
Business
1 answer:
DENIUS [597]2 years ago
8 0

The number of possibilities that are there for the ordered pair is 2.

<h3>Calculation and Parameters
</h3>

Because the unpainted part of the floor covers 1/2 of the area, then the painted rectangle covers 1/2 of the area as well.

Given that the border width is 1 foot, the dimensions of the rectangle are a-2 by b-2.

Making an equation:

ab= 2((a-2)(b-2))

ab= 2ab-4a-4b+8

ab-4a-4b+8=0

If we apply Simon's Favorite Factoring Trick,

ab-4a-4b+16= 8

(a-4)(b-4)= 8

Since b > a, then we have the possibilities

(a-4) = 1 and (b-4) = 8, or (a-4) = 2 and (b-4) = 4.

(5, 12) or (6,8) which gives us 2 possibilities.

Read more about possibilities here:

brainly.com/question/25870256

#SPJ1

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The operations of Winston Corporation are divided into the Blink Division and the Blur Division. Projections for the next year a
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Answer:

c. $88,700

Explanation:

The computation of operating income for Winston Corporation is shown below:-

Particulars              Dropping before              Dropping after

Sales a                  $469,000                           $383,500

                                                                         ($295,000 × 130%)

Variable cost b     $181,000                              $131,300

($101,000 × 130%)

Contribution margin $288,000                          $252,200

(c = a - b)

Direct fixed cost d  $160,000                          $87,000

Segment margin e $128,000                           $165,200

(e = c - d)

Allocated common cost f $76,500                  $76,500

Operating income(loss) $51,500                      $88,700

(g = d - e)

Therefore to reach the operating income(loss) we simply deduct the allocated common cost from segment margin.

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What are the Holland codes?
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Answer:

A) attractive; timely; durable; and anchored in a product, service, or business that creates or adds value for its buyer or end user

Explanation:

A true business opportunity;

  1. is attractive, must have high profit expectations.
  2. must be durable, should last at least a few years, not only a one time event.
  3. must present itself at the right moment and time. Sometimes great ideas are left behind because they are too disruptive, e.g. the Nash Rambler built in 1950 was the first compact car but wasn't very successful. Japanese compact cars became successful in the 1970s.
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Which conclusion is best supported by the data in the graph?
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Technology is a growing part of the US economy.

The four largest manufacturing industries in America are computers and electronics; chemicals; food, beverages, and tobacco; petroleum and coal—account for about 51 percent of manufacturing GDP. The top nine sectors constitute approximately 79 percent of manufacturing GDP. These sectors accounted for 68 percent of total manufacturing employment in 2010.

From the above graph, we can see clearly that the technology sector had increased from $225billion in 2006 to about $360billion in 2011, which is about a 60% increase in a span of 5 years, thats a massive growth within a short period.

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Lone Wolf Technologies Inc. assembles circuit boards by using a manually operated machine to insert electronic components. The o
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Answer:

Differential analysis for 1 year

                                        Keep old              Change              Differential

                                        machine               machine             amount

sales revenue                  191,000                191,000               0

depreciation expense     -4,840                  -22,760               -17,920

per year

direct materials                -65,200               -65,200               0

direct labor                       -45,300               -15,100                 30,200

power and                        -4,200                 -7,200                  -3,000

maintenance

taxes and                          -1,500                 -5,000                  -3,500

insurance

S&A expenses                  -45,300              -45,300                0

total                                   24,660               30,440                  5,780

If the new machine is purchased, profits will increase by $5,780 every year.

Differential analysis for 5 years

                                        Keep old              Change              Differential

                                        machine               machine             amount

sales revenue                  955,000              955,000             0

depreciation expense     -24,200               -113,800              -89,600

per year

direct materials                -326,000             -326,000            0

direct labor                       -226,500            -75,500               151,000

power and                        -21,000               -36,000               -15,000

maintenance

taxes and                          -7,500                -25,000               -17,500

insurance

S&A expenses                  -226,500           -226,500              0

total                                   123,300             152,200                28,900

If the new machine is purchased, profits will increase by $28,900 for the 5 year period.

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