Answer:
Step-by-step explanation:
m∠1 = m∠2 {r ║s , so, corresponding angles are equal}
60 – 2x = 70 – 4x
4x - 2x = 70 -60
2x = 10
x = 10/2
x = 5
Answer:
The function that models this situation is:
![C(n) = \frac{1675}{2^{n} }, 1 \leq n \leq 6](https://tex.z-dn.net/?f=C%28n%29%20%3D%20%5Cfrac%7B1675%7D%7B2%5E%7Bn%7D%20%7D%2C%201%20%5Cleq%20n%20%5Cleq%206)
Step-by-step explanation:
Cost of the bedroom set initially = $1675.00.
Cost of the bedroom set after 1 week = ![\frac{1675}{2^{1} }](https://tex.z-dn.net/?f=%5Cfrac%7B1675%7D%7B2%5E%7B1%7D%20%7D)
Cost of the bedroom set after 2 weeks = ![\frac{(\frac{1675}{2} )}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%28%5Cfrac%7B1675%7D%7B2%7D%20%29%7D%7B2%7D)
![=\frac{1675}{2^{2} }](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1675%7D%7B2%5E%7B2%7D%20%7D)
Cost of the bedroom set after 3 weeks
and so on.
Hence, the function that models this situation is:
.
Answer:
3 packages
Step-by-step explanation:
There are 1000 m in 1 km, so 2500 m is the same as 2.5 km.
1 package = 2.5 km
2 packages = 5.0 km . . . . still too little
3 packages = 7.5 km . . . . more than sufficient
Annabelle needs 3 packages of yarn to satisfy her requirement for 7 km.
Answer:
111 / 190
Step-by-step explanation:
Let us first compute the probability of picking 2 of each sweet. Take liquorice as the first example. There are 12 / 20 liquorice now, but after picking 1 there will be 11 / 19 left. Thus the probability of getting two liquorice is demonstrated below;
![12 / 20 * 11 / 19 = \frac{33}{95},\\Probability of Drawing 2 Liquorice = \frac{33}{95}](https://tex.z-dn.net/?f=12%20%2F%2020%20%2A%2011%20%2F%2019%20%3D%20%5Cfrac%7B33%7D%7B95%7D%2C%5C%5CProbability%20of%20Drawing%202%20Liquorice%20%3D%20%5Cfrac%7B33%7D%7B95%7D)
Apply this same concept to each of the other sweets;
![5 / 20 * 4 / 19 = \frac{1}{19},\\Probability of Drawing 2 Mint Sweets = 1 / 19\\\\3 / 20 * 2 / 19 = \frac{3}{190},\\Probability of Drawing 2 Humbugs = 3 / 190](https://tex.z-dn.net/?f=5%20%2F%2020%20%2A%204%20%2F%2019%20%3D%20%5Cfrac%7B1%7D%7B19%7D%2C%5C%5CProbability%20of%20Drawing%202%20Mint%20Sweets%20%3D%201%20%2F%2019%5C%5C%5C%5C3%20%2F%2020%20%2A%202%20%2F%2019%20%3D%20%5Cfrac%7B3%7D%7B190%7D%2C%5C%5CProbability%20of%20Drawing%202%20Humbugs%20%3D%203%20%2F%20190)
Now add these probabilities together to work out the probability of drawing 2 of the same sweets, and subtract this from 1 to get the probability of not drawing 2 of the same sweets;
![33 / 95 + 1 / 19 + 3 / 190 = \frac{79}{190},\\1 - \frac{79}{190} = \frac{111}{190}\\\\](https://tex.z-dn.net/?f=33%20%2F%2095%20%2B%201%20%2F%2019%20%2B%203%20%2F%20190%20%3D%20%5Cfrac%7B79%7D%7B190%7D%2C%5C%5C1%20-%20%5Cfrac%7B79%7D%7B190%7D%20%3D%20%5Cfrac%7B111%7D%7B190%7D%5C%5C%5C%5C)
The probability that the two sweets will not be the same type of sweet =
111 / 190
Answer:
5/8 * 7/2
Step-by-step explanation:
Whenever you divide fractions, you can use the 'keep change flip' method.
You keep 5/8, change the division sign to multiplication, and then flip the second fraction.
1. 5/8 / 7/2 - Keep 5/8
2. 5/8 * 7/2 - Change division sign
3. 5/8 * 2/7 - Flip the second fraction, 7/2 -> 2/7