Multiply

21 lb 13 oz x 5 =

12 gal 3 qt 1 pt × 9 =

15 yd 2 ft 8 in x 7 =

• 109 lb 1 oz

• 115 gal 3 qt 1 pt

• 111 yd 8 in

Step-by-step explanation:

The relevant unit relationships are ...

1 lb = 16 oz

1 gal = 4 qt

1 qt = 2 pt

1 yd = 3 ft = 36 in

To convert from one unit to another, multiply by a fraction that has ...

(to unit)/(from unit)

For example, to convert (13 oz)×5 = 65 oz to pounds, multiply by (1 lb)/(16 oz). This will give you ...

(65 oz)·(1 lb)/(16 oz) = 65/16 lb = 4 1/16 lb

Now, if you don't already recognize that 1/16 lb = 1 oz, you can multiply the fraction by the unit conversion from lb to oz: (16 oz)/(1 lb). Doing that gives ...

(1/16 lb)·(16 oz)/(1 lb) = 16/16 oz = 1 oz

When the same units are in the numerator and denominator, they cancel, as do any factors that appear in both numerator and denominator.

___

1. (21 13/16 lb)×5 = 105 65/16 lb = 109 1/16 lb = 109 lb 1 oz

__

2. (12 7/8 gal)×9 = 108 63/8 gal = 115 7/8 gal = 115 gal 3 qt 1 pt

__

3. ((15 2/3 +8/36) yd)×7 = (105 14/3 + 56/36) yd = 109 yd 2 ft + 1 yd 20 in

= 111 yd 8 in

Additional explanation

7/8 gal = 7 pt = 1 pt + 3·2 pt = 1 pt + 3 qt

__

14/3 yd = 4 2/3 yd = 4 yd 2 ft

56/36 yd = 1 20/36 yd = 1 yd + (12 +8)/36 yd = 1 yd + 1 ft + 8 in

Then 14/3 yd + 56/36 yd = (4 yd + 2 ft) + (1 yd + 1 ft + 8 in) = 6 yd + 8 in

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

sinn is the total amount of students now and m were the students before, you subtract them both (n-m) and divide that by m. then, since to get a percentage from a fraction you have to multiply by 100, your answer should look like this: n-m/m*100

step-by-step explanation: