1.10 Systems of measurement  (Page 5/13)

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To make one pan of baklava, Dorothea needs 400 grams of filo pastry. If Dorothea plans to make 6 pans of baklava, how many kilograms of filo pastry will she need?

2.4 kilograms

Convert between the u.s. and the metric systems of measurement

Many measurements in the United States are made in metric units. Our soda may come in 2-liter bottles, our calcium may come in 500-mg capsules, and we may run a 5K race. To work easily in both systems, we need to be able to convert between the two systems.

[link] shows some of the most common conversions.

Conversion Factors Between U.S. and Metric Systems
Length Mass Capacity
$\begin{array}{c}\begin{array}{ccc}\text{1 in.}\hfill & =\hfill & \text{2.54 cm}\hfill \\ \text{1 ft.}\hfill & =\hfill & \text{0.305 m}\hfill \\ \text{1 yd.}\hfill & =\hfill & \text{0.914 m}\hfill \\ \text{1 mi.}\hfill & =\hfill & \text{1.61 km}\hfill \\ \text{1 m}\hfill & =\hfill & \text{3.28 ft.}\hfill \end{array}\hfill \end{array}$ $\begin{array}{c}\begin{array}{ccc}\text{1 lb.}\hfill & =\hfill & \text{0.45 kg}\hfill \\ \text{1 oz.}\hfill & =\hfill & \text{28 g}\hfill \\ \text{1 kg}\hfill & =\hfill & \text{2.2 lb.}\hfill \end{array}\hfill \end{array}$ $\begin{array}{c}\begin{array}{ccc}\text{1 qt.}\hfill & =\hfill & \text{0.95 L}\hfill \\ \text{1 fl. oz.}\hfill & =\hfill & \text{30 mL}\hfill \\ \text{1 L}\hfill & =\hfill & \text{1.06 qt.}\hfill \end{array}\hfill \end{array}$

[link] shows how inches and centimeters are related on a ruler.

[link] shows the ounce and milliliter markings on a measuring cup.

[link] shows how pounds and kilograms marked on a bathroom scale.

We make conversions between the systems just as we do within the systems—by multiplying by unit conversion factors.

Lee’s water bottle holds 500 mL of water. How many ounces are in the bottle? Round to the nearest tenth of an ounce.

Solution

$\begin{array}{cccc}& & & \hfill \text{500 mL}\hfill \\ \begin{array}{c}\text{Multiply by a unit conversion factor relating}\hfill \\ \text{mL and ounces.}\hfill \end{array}\hfill & & & \hfill 500\phantom{\rule{0.2em}{0ex}}\text{milliliters}·\frac{1\phantom{\rule{0.2em}{0ex}}\text{ounce}}{30\phantom{\rule{0.2em}{0ex}}\text{milliliters}}\hfill \\ \text{Simplify.}\hfill & & & \hfill \frac{\text{50 ounce}}{30}\hfill \\ \text{Divide.}\hfill & & & \hfill \text{16.7 ounces.}\hfill \\ & & & \text{The water bottle has 16.7 ounces.}\hfill \end{array}$

How many quarts of soda are in a 2-L bottle?

2.12 quarts

How many liters are in 4 quarts of milk?

3.8 liters

Soleil was on a road trip and saw a sign that said the next rest stop was in 100 kilometers. How many miles until the next rest stop?

Solution

$\begin{array}{cccc}& & & \hfill \text{100 kilometers}\hfill \\ \begin{array}{c}\text{Multiply by a unit conversion factor relating}\hfill \\ \text{km and mi.}\hfill \end{array}\hfill & & & \hfill \text{100 kilometers}·\frac{1\phantom{\rule{0.2em}{0ex}}\text{mile}}{1.61\phantom{\rule{0.2em}{0ex}}\text{kilometer}}\hfill \\ \text{Simplify.}\hfill & & & \hfill \frac{100\phantom{\rule{0.2em}{0ex}}\text{miles}}{1.61}\hfill \\ \text{Divide.}\hfill & & & \hfill \text{62 miles}\hfill \\ & & & \hfill \text{Soleil will travel 62 miles.}\hfill \end{array}$

The height of Mount Kilimanjaro is 5,895 meters. Convert the height to feet.

19,335.6 feet

The flight distance from New York City to London is 5,586 kilometers. Convert the distance to miles.

8,993.46 km

Convert between fahrenheit and celsius temperatures

Have you ever been in a foreign country and heard the weather forecast? If the forecast is for $22\text{°}\text{C},$ what does that mean?

The U.S. and metric systems use different scales to measure temperature. The U.S. system uses degrees Fahrenheit, written $\text{°}\text{F}\text{.}$ The metric system uses degrees Celsius, written $\text{°}\text{C}\text{.}$ [link] shows the relationship between the two systems.

Temperature conversion

To convert from Fahrenheit temperature, F, to Celsius temperature, C, use the formula

$C=\frac{5}{9}\left(F-32\right).$

To convert from Celsius temperature, C, to Fahrenheit temperature, F, use the formula

$F=\frac{9}{5}C+32.$

Convert $50\text{°}$ Fahrenheit into degrees Celsius.

Solution

We will substitute $50\text{°}\text{F}$ into the formula to find C.

 Simplify in parentheses. Multiply. So we found that 50°F is equivalent to 10°C.

Convert the Fahrenheit temperature to degrees Celsius: $59\text{°}$ Fahrenheit.

$15\text{°}\text{C}$

integer greater than 2 and less than 12
2 < x < 12
Felix
I'm guessing you are doing inequalities...
Felix
Actually, translating words into algebraic expressions / equations...
Felix
hi
Darianna
hello
Mister
He charges $125 per job. His monthly expenses are$1,600. How many jobs must he work in order to make a profit of at least $2,400? Alicia Reply at least 20 Ayla what are the steps? Alicia 6.4 jobs Grahame 32 Grahame 1600+2400= total amount with expenses. 4000/125= number of jobs needed to make that min profit of 2400. answer is 32 Orlando He must work 32 jobs to make a profit POP what is algebra Azhar Reply repeated addition and subtraction of the order of operations. i love algebra I'm obsessed. Shemiah hi Krekar One-fourth of the candies in a bag of M&M’s are red. If there are 23 red candies, how many candies are in the bag? Leanna Reply they are 92 candies in the bag POP rectangular field solutions Navin Reply What is this? Donna t muqtaar the proudact of 3x^3-5×^2+3 and 2x^2+5x-4 in z7[x]/ is anas Reply ? Choli a rock is thrown directly upward with an initial velocity of 96feet per second from a cliff 190 feet above a beach. The hight of tha rock above the beach after t second is given by the equation h=_16t^2+96t+190 Usman Stella bought a dinette set on sale for$725. The original price was $1,299. To the nearest tenth of a percent, what was the rate of discount? Manhwa Reply 44.19% Scott 40.22% Terence 44.2% Orlando I don't know Donna if you want the discounted price subtract$725 from $1299. then divide the answer by$1299. you get 0.4419... but as percent you get 44.19... but to the nearest tenth... round .19 to .2 and you get 44.2%
Orlando
you could also just divide $725/$1299 and then subtract it from 1. then you get the same answer.
Orlando
p mulripied-5 and add 30 to it
Tausif
Tausif
how
muqtaar
Can you explain further
p mulripied-5 and add to 30
Tausif
-5p+30?
Corey
p=-5+30
Jacob
How do you find divisible numbers without a calculator?
TAKE OFF THE LAST DIGIT AND MULTIPLY IT 9. SUBTRACT IT THE DIGITS YOU HAVE LEFT. IF THE ANSWER DIVIDES BY 13(OR IS ZERO), THEN YOUR ORIGINAL NUMBER WILL ALSO DIVIDE BY 13!IS DIVISIBLE BY 13
BAINAMA
When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was$1,585. What is the amount of each loan?
Sean took the bus from Seattle to Boise, a distance of 506 miles. If the trip took 7 2/3 hours, what was the speed of the bus?
66miles/hour
snigdha
How did you work it out?
Esther
s=mi/hr 2/3~0.67 s=506mi/7.67hr = ~66 mi/hr
Orlando
No; 65m/hr
albert
hello, I have algebra phobia. Subtracting negative numbers always seem to get me confused.
what do you need help in?
Felix
Heather
look at the numbers if they have different signs, it's like subtracting....but you keep the sign of the largest number...
Felix
for example.... -19 + 7.... different signs...subtract.... 12 keep the sign of the "largest" number 19 is bigger than 7.... 19 has the negative sign... Therefore, -12 is your answer...
Felix
—12
Thanks Felix.l also get confused with signs.
Esther
Thank you for this
Shatey
ty
Graham
think about it like you lost $19 (-19), then found$7(+7). Totally you lost just $12 (-12) Annushka I used to struggle a lot with negative numbers and math in general what I typically do is look at it in terms of money I have -$5 in my account I then take out 5 more dollars how much do I have in my account well-\$10 ... I also for a long time would draw it out on a number line to visualize it
Meg
practicing with smaller numbers to understand then working with larger numbers helps too and the song/rhyme same sign add and keep opposite signs subtract keep the sign of the bigger # then you'll be exact
Meg
hi
albert
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles
168.50=R
Heather
john is 5years older than wanjiru.the sum of their years is27years.what is the age of each
46
mustee
j 17 w 11
Joseph
john is 16. wanjiru is 11.
Felix
27-5=22 22÷2=11 11+5=16
Joyce