You could also do it with 3, 5, and 9 to get 17, giving you 4 options. Let’s go with 3, 5, and 9 just because then we can use all the numbers in order and don’t have to start with a negative number. That gives us this solution: 1-3-5+7-9+11+13+15=30. This kind mom of 3 obviously learned somehow that her boy wasn't enjoying what her girls were, found somethings TOGETHER that he liked, then posted the helpful hints and finds for ALL. I'm glad you took time with your son to enjoy these activities and took time to post it, if not for anyone else, but me.
- ValueError: operands could not be broadcast together with shapes (97,2) (2,1) When (97,2)x(2,1) is clearly a legal matrix operation and should give me a (97,1) vector EDIT.
- Customers who wish to upgrade to UCS 6.2.0 & plan to use Polycom Better Together over Ethernet Connector (BToE) Application 4.3.0 should follow a mandatory step to first upgrade existing (BToE) Application 3.8.0 onwards (with UCS 5.8 & 5.9 ) to (BToE) Application 4.3.0 followed by UC Software 5.8 & 5.9 upgrade to 6.2.0 to retain successful pairing.
- 5 2/3 = 5.3/3 + 2/3 = 17/3. Changing the mixed fractions to improper fractions is easy if you just remember: multiply the whole number part by the denominator, then add that to the numerator of the fraction part. That will be the new numerator. This allows you to just multiply through like so, 57/8. 17/3 = 57.17/8.3 = 969/24 = 323/8 = 40 3/8.
TOG means Thermal Overall Grade.
The tog is a measure of thermal insulance of a unit area, also known as thermal resistance. It is commonly used in the textile industry and often seen quoted on, for example, duvets and carpet underlay.
The Shirley Institute in Manchester, England developed the tog as an easy-to-follow alternative to the SI unit of m2K/W.[1] The name comes from the informal word togs for 'clothing', which itself was probably derived from the word toga Flyers vs islanders 2019. , a Roman garment.
The basic unit of insulation coefficient is the RSI, (1 m2K/W). 1 tog = 0.1 RSI. There is also a US clothing unit, the clo, equivalent to 0.155 RSI or 1.55 tog, described in ASTM D-1518.
A tog is 0.1 m2K/W. In other words, the thermal resistance in togs is equal to ten times the temperature difference (in °C) between the two surfaces of a material, when the flow of heat is equal to one watt per square metre.[1]
British duvets are sold in steps of 1.5 tog from 4.5 tog (summer) to 16.5 tog (extra-warm). The stated values are minimum, actual values may be up to 3 tog higher. These tog values assume that there is no duvet cover added that can trap air.
Adult comfort ratings against temperature.
Lightweight summer duvet: | 3.0 - 4.5 tog |
Spring/Autumn weight duvet: | 7.5 - 10.5 tog |
Winter weight duvet: | 12.0 - 13.5 tog |
A few manufacturers have marketed combined duvet sets consisting of two duvets; one of approximately 4.5 tog and one of approximately 9.0 tog. These can be used individually as summer (4.5 tog) and spring/autumn (9.0 tog). When joined together using press studs around the edges, or Velcro strips across each of the corners, they become a 13.5 tog winter duvet and as such can be made to suit all seasons.
Testing[edit]
Launched in the 1940s by the Shirley Institute, the Shirley Togmeter[2] is the standard apparatus for rating thermal resistance of textiles, commonly known as the Tog Test. This apparatus, described in BS 4745:2005,[1] measures a sample of textile, either between two metal plates (for underclothing) or between a metal plate and free air (for outer layers).
Each industry has its own specifications and methods for measuring thermal properties. The Shirley Togmeter is claimed to be unsuitable for duvets because the large scale of their quilted construction makes it impractical to obtain a representative sample of suitable size.[disputed] BS5335 describes apparatus for duvet tog testing.[2][self-published source?]This consists of a metal plate at least 1000 mm x 600 mm at skin temperature (33°C) arranged to support the whole duvet, and a mechanism for measuring the air temperature above the quilt. This requires very precise control of the laboratory environment in order to get reliable results.
BS 8510 describes tog testing for baby products, the concern here being to ensure that babies do not overheat, with a maximum tog rating of about 4.[2]BS 8510 has since been withdrawn and replaced by BS EN 16781:2018.
See also[edit]
References[edit]
- ^ abcKennard, Harry (March 7, 2017). 'What's a Tog'.
- ^ abcTim Jackson (19 December 2013). 'Measurement of area thermal resistance'. tim-jackson.co.uk. Retrieved 27 December 2018.
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Tog_(unit)&oldid=977174200'
We have to start somewhere, so let's start with adding fractions. The most important thing about adding fractions is that they need to be 'like' fractions. That means you need to make sure that both addends (numbers being added) have common denominators. 5/6 + 6/7 may look hard, but when they have the common denominator of 42 it is an easy addition problem. Let's get started.
We'll start with easy ones. In class, you will be given addends with the same denominator. All you have to do is add up the numerators (numbers on top) and then simplify your answer. Let's try some.
1/13 + 6/13 = ?
• Create common denominators. They are already the same at 13, so we do nothing.
• Add the numerators from the two addends. 1 + 6 = 7
• Write the sum of the numerators above the common denominator. 7/13.
•Simplify the fraction. 7/13 cannot be simplified. You are done.
Answer: 1/13 + 6/13 = 7/13
5/9 + 1/9 = ?
• Create common denominators: The denominators are the same. Do nothing.
• Add numerators: 5 + 1 = 6
• Write the sum of the numerators above the common denominator: 6/9.
• Simplify: 6 and 9 have a common factor of 3. When you divide the numerator and denominator by 3 you get 2/3.
Answer: 5/9 + 1/9 = 6/9 = 2/3
Let's get more advanced. What about adding unlike fractions? You don't have common denominators. We've looked at creating equivalent fractions in our earlier pages. You will use that process here.
1/7 + 1/3 = ?
•Create common denominators: We have 7 and 3. They have no common factors, so let's just multiply to create two new equivalent fractions. Remember how we multiplied by equivalents of 1? It went like this..
1/7 = 1/7 * 1 = 1/7 * 3/3 = (1*3)/(7*3) = 3/21
1/3 = 1/3 * 1 = 1/3 * 7/7 = (1*7)/(3*7) = 7/21
You now have the common denominator 21. You can now rewrite the problem as 3/21 + 7/21 = ?
• Add numerators: 3 + 7 = 10
• Write the sum of the numerators above the common denominator: 10/21
• Simplify: 10/21 cannot be simplified. You are done.
Answer: 1/7 + 1/3 = 10/21
Together 3 5 90 Degree
You've got common denominators and unlike fractions under control now. Let's look at an example with mixed numbers before we go. Our first example will look at mixed numbers that have common denominators.2 2/9 + 4 3/9 = ?
• Check for common denominators: They are like fractions with a denominator of 9. Do nothing.
• Add the numerators from each fraction: 2 + 3 = 5
• Write the sum of the numerators above the common denominator: 5/9
• Add the whole numbers: 2 + 4 = 6
• Write out the mixed number: 6 5/9
• Simplify: 5/9 can't be simplified. You are done.
Answer: 2 2/9 + 4 3/9 = 6 5/9
What happens if you wind up with an improper fraction in your answer? You need to simplify that improper fraction and then add the whole numbers. We'll use an example like the last one. We just made the first addend a bit bigger.
2 7/9 + 4 3/9 = ?
• Check for common denominators: They are like fractions with a denominator of 9. Do nothing.
• Add the numerators from each fraction: 7 + 3 = 10
• Write the sum of the numerators above the common denominator: 10/9
• Add the whole numbers: 2 + 4 = 6
• Write out the new mixed number: 6 10/9
• Simplify: This example has an improper fraction that you have to simplify. You need to use division to create a new fraction. 10 ÷ 9 = 1r1. The new mixed number will be 1 1/9. You will need to add that new whole number to your original 6. The entire process goes like this..
6 10/9 = 6 + 10/9 = 6 + 1 1/9 = 6 + 1 + 1/9 = 7 1/9
Answer: 2 7/9 + 4 3/9 = 7 1/9
Let's put it all together with an example that has unlike fractions. You're going to need to make common denominators with this one and simplify an improper fraction.
2 5/8 + 5 3/4 = ?
Common denominators: Start with the fractions. We've got 4 and 8. They have a common factor of four so we only need to fix the 3/4 fraction.
3/4 = 3/4 * 1 = 3/4 * 2/2 = (3*2)/(4*2) = 6/8
Add the numerators: 5 + 6 = 11
Rewrite fraction: Sum of the numerators above the common denominator: 11/8
Add whole numbers: 2 + 5 = 7
New mixed number is 7 11/8
Simplify: We've got an improper fraction. Start dividing.. 11 ÷ 8 = 1r3. Your new mixed number is 1 3/8. Add the new mixed number to the original 7.
7 11/8 = 7 + 11/8 = 7 + 1 3/8 = 7 + 1 + 3/8 = 8 3/8
Answer: 2 5/8 + 5 3/4 = 8 3/8
Now it's up to you to practice. If you want to keep going, continue on to subtract fractions. It's very close to addition, so you will do fine.
Together 3 5 90
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